Characteristic analysis of aspheric quasi-opticallens antenna in millimeter-wave

radiometer imaging system

Won-Gyum Kim1 Nam-Won Moon1 Manoj Kumar Singh2

Hwang-Kyeom Kim3 and Yong-Hoon Kim11School of Information and Mechatronics Gwangju Institute of Science and Technology

No 123 Cheomdan-gawiro Buk-Gu Gwangju 500-712 South Korea2DST-Centre for Interdisciplinary Mathematical Sciences (DST-CIMS) Banaras Hindu University (BHU)

Varanasi 221 005 India3Defense Acquisition Program Administration No 23 Yongsango-Gil Yongsan-Dong

Yongsan-Gu Seoul 140-841 South Korea

Corresponding author yhkimgistackr

Received 22 October 2012 revised 4 January 2013 accepted 6 January 2013posted 7 January 2013 (Doc ID 178435) published 11 February 2013

Quasi-optical imaging systems require low blurring effect and large depth of focus (DOF) to get an ac-ceptable sharpness of the image To reduce aberration-limited blurring the aspheric convex plano lenseswith an aperture diameter of 350 mm are designed in W-band We analyzed theoretically and experi-mentally the millimeter-wave band lens characteristics such as beam spot size spatial resolution(SR) and DOF via f -number It is first used to verify the DOF through f -number in the system-leveltest with the developedW-band radiometer imaging systemWe have confirmed that the larger f -numberof quasi-optical lens leads to a larger DOF but a lower SR copy 2013 Optical Society of AmericaOCIS codes 0401240 0804225 1100110 2203630 2804991 3504010

1 Introduction

Imaging systems have been developed in the milli-meter-wave (MMW) region because of in contrast toa visible imager and infrared their ability to seethrough bad weather for surveillance and to pene-trate opaque objects such as clothing polymers andsome building materials for security applications[1ndash4] There are two optimum frequency bands forthe use in MMW imaging Q-band (35 GHz band)and W-band (94 GHz band) This is because trans-mission through the atmosphere is significantlybetter in these atmospheric windows compared tothe other frequencies in MMW region W-band offersbetter image quality and spatial resolution (SR) as

governed by the diffraction limit compared to theQ-band The range of MMW imaging system is gen-erally from meters to kilometers between targetsand the sensors However there are fewer researchresults for short-range MMW imaging applicationsespecially less than hundreds of centimeters Pre-vious works have demonstrated capacities for obtain-ing high resolution images at close range [5ndash8] Thefocal plane array (FPA) technology is useful due tothe high frame rate of the MMW imaging systemat the expense of the cost of large area arrays [9ndash12]The image acquisition methods are introduced inmany papers using mechanically scanned 1D and2D FPA A dielectric lens antenna is a good candidateas quasi-optics for the MMW imaging radiometersystem due to its advantages of size weight andefficiency compared with a metal reflector antenna[13ndash17] The SR the field of view (FOV) and the

1559-128X13061122-10$15000copy 2013 Optical Society of America

1122 APPLIED OPTICS Vol 52 No 6 20 February 2013

depth of focus (DOF) are the major parameters for aFPA imaging system The SR based on Rayleigh cri-teria depends on f -number (f∕) of a lens in a givenfrequency FOV is limited by the SR and the numberof receivers but it is also limited by the optical cou-pling efficiency of a close placed receiverrsquos antennasThe DOF is the variable image distance from a lensto a receiver and it depends on f∕ of a lens In thispaper we present theoretically and experimentallythe relationship between lens characteristics andf ∕ forW-band quasi-optical radiometer imaging sys-tem at the short range For verification we have de-signed two lenses with the different f ∕ and the sameaperture size at 94 GHz

The rest of this paper is organized as followsSection 2 theoretically describes the characteristicsof a quasi-optical lens in a MMW focal plane imagingsystem The design of an aspheric quasi-optical lensantenna is presented in Section 3 The characteris-tics of aspheric quasi-optical lenses are experimen-tally analyzed in Section 4 The conclusion followsin Section 5

2 Characteristics of Aspheric Quasi-Optical Lens inMMW Imaging System

The schematic of a quasi-optical lens is shown inFig 1 The main characteristics of a lens are beamspot size dblur the SR rsp and the DOF To explainthe lens characteristics it is suitable to understandthe relationship between the characteristics and f∕of a lens in accordance with Gaussian beam propaga-tion It is necessary to consider the conjugation ratiodepending onmagnification of a lens in analyzing therelationship The Gaussian lens equation is given asfollows [18ndash20]

1Si

1So

1F (1)

where Si So and F are the distance between imageplane and lens distance of object plane from lens

and the focal length of the lens The expression forthe magnification M of the lens is given as

M Si

So (2)

Combining Eqs (1) and (2) we get the relation be-tween image distance focal length andmagnification

Si M 1F (3)

If the magnification M is relatively low the lens isused at the infinite conjugate ratio correspondingto Si F

The incoming beam is focused by a lens to obtain asmall beam spot as shown in Fig 1 The focusedbeam spot spreads on the image plane because ofaberration and diffraction of the lens And theseintroduce blurring in the image

In general the aberration is caused by the spheri-cal geometry of lens surfaces The aberration-limitedspot size dab is determined by multiplying theaberration-limited angle angular blur ΔΘab by theimage distance Si The aberration-limited angularblur based on third-order aberration theory andaberration-limited spot is given as [1821]

ΔΘab D∕F3n2minus 2n 1q

n 2q2∕n∕32n minus 12 (4)

dab ΔΘab middot Si (5)

where D F n and q are the diameter focal lengthmaterial refractive index and shape factor of thelens respectively The shape factor q of a lens is givenby [21]

q R2∕R2 minus R1 (6)

Fig 1 (Color online) Schematic of quasi-optical lens

20 February 2013 Vol 52 No 6 APPLIED OPTICS 1123

where R1 and R2 are the radius of curvature forleft and right side surface of the lens as shown inFig 1 The variation of the aberration-limited angularblur with shape factor shown in Fig 2 for the lensmade of high-density polyethylene (HDPE) whichhas a refractive index (n) of 15187 at 94 GHz [1720]and it is being operated at the infinite conjugate ratioAn asymmetric shape that corresponds to a q-valueof about 087 is the best singlet shape It is importantto note that the best-form shape of lens is dependenton the refractive index In case of a typical dielectricsinglet the convex plano shape (q 1) with convexside toward the infinite conjugate performs nearlyaswell as the best-form lens Equation (5) is simplified

to Eq (7) for a spherical convex plano lens in the caseof HDPE and the finite conjugate ratio

dab HDPE 0068M 12

F

f∕3 (7)

where f∕ F∕D denotes the f -number of the lensThe diffraction accounts for the spreading of the

radiation as it passes through an aperture Thus apoint object is never imaged on a point in the imageplane as shown in Fig 3(a) The irradiance distribu-tion in the image plane and its cross section is shownin Figs 3(b) and 3(c) The diffraction is a naturalproperty and it always present on any quasi-opticallens Its effects may be masked if the lens has signif-icant aberration In the case of aspheric convex planolenses the diffraction is dominant over aberrationThe diffraction-limited half-angle angular blur andcorresponding circular ring of the diffraction patterncontaining 86 of irradiance distribution Fig 3(b) isgiven as follows [22]

ΔΘdiff 164λ

D (8)

where λ is the wavelength of MMW beam Thediffraction-limited blur spot size for finite conjugateratio is given as [22]

-05 00 05 10 15 20 2500

01

02

03

04

05

Abe

rrat

ion-

limite

d an

gula

r bl

ur

[(D

F)3

]

Shape factor q

Fig 2 Aberration-limited angular blur via shape factor

Point Source Focal

PlanefD

84

86

(a) (b)

(c)

Fig 3 (a) Image of a point object (b) Airy pattern 2-D plot of the diffracted irradiance distribution (c) Cross-section of (b) ρ is normalizedradial distance from the center [22]

1124 APPLIED OPTICS Vol 52 No 6 20 February 2013

ddiff ΔΘdiff middot Si 164λM 1f∕ (9)

The diffraction-limited blur spot size given by Eq (9)is the radius of the circular ring of the diffraction pat-tern in the focal plane having 86 irradiance distri-bution [22]

Comparing the aberration-limited spot size to thediffraction-limited spot size suggests a criterion of asingle lens If the spot size dab is larger than ddiff then dblur is limited by aberration If the spot sizedab is smaller than ddiff the spot size is essentiallydiffraction limited Figure 4 depicts the spot sizeas a function of f∕ in the case of the convex-planelens with the infinite conjugate ratio using Eqs (7)and (9) Figure 4(a) shows that the spot size causedby spherical aberration is inversely dependent on thecube of f∕ and the diffraction-limited spot size in-creases linearly with f ∕ The resultant spot sizeby the dominant fact decreases for small f ∕ andthen increases with f∕ as shown in Fig 4(b) Itmeans that there is some optimum point (P) for aminimum of both aberration and diffraction The op-timum spot size is about 87 mm at the f∕ of 165 forthe convex plano lens The diffraction a naturalproperty is always present on any quasi-optical lensalthough its effects may be masked if the lens has asignificant aberration However the spherical aber-ration can be reduced by aspherical lens or multiplelenses Accordingly an aspheric convex plano lens ismainly dominated by the diffraction and its focusedbeam spot diameter can be represented by the twicethe diffraction-limited spot size given by Eq (9)

In imaging applications the SR is ultimatelylimited by diffraction Calculating the maximumpossible SR of a lens requires an arbitrary definitionof what is meant by resolving two features In theRayleigh criterion it is assumed that two separatepoint source can be resolved when the center of theAiry disc from one overlaps the first dark ring inthe diffraction pattern of the second In this casethe smallest resolvable distance is [22]

rsp ddiff o

2 122λM 1f ∕ (10)

where ddiff o is the spot diameter at which theintensity distribution of the Airy disc is the first 0

intensity point of its maximum value on the axis forthe finite conjugated lens The SR is linearly propor-tional to f ∕ as shown in Eq (10) It is also related tothe physically minimum space between the adjacentreceivers for a FPA imaging system

The Gaussian beam focuses from a lens down to awaist and then expands proportionally to x as shownin Fig 5 The wavefront radius of curvature whichwas infinite at x 0 will become finite and initiallydecrease with x At some point it will reach a mini-mum value and then it increases with larger x even-tually becoming proportional to x The equationsdescribing the Gaussian beam radius wx and thewavefront radius of curvature Rx are [1920]

wx wo

1

λx

πw2o

05

(11)

Rx x1

πw2

o

λx

2 (12)

where x is the distance propagated from the planewhere the wavefront is flat and wo 05ddiff o is theradius of the 1∕e2 irradiance contour at x 0 TheRayleigh range XR defined as the distance overthe beam radius by a factor of

2

p is given by [1920]

XR πw2o

λ (13)

DOF is the range of the image distance over whichthe focused spot diameter remains below an arbi-trary limit Normally it is defined as the distance

Fig 4 (a) Aberration- and diffraction-limited and (b) dominant spot size of convex plano lens

Fig 5 Focusing of Gaussian beam

20 February 2013 Vol 52 No 6 APPLIED OPTICS 1125

between2

pwo spot size points or 2 times Rayleigh

range [1920] For the finite conjugated lens it canbe written as [1920]

DOF 2timesXR 2timesπw2

o

λ 297πλM1f ∕2 (14)

It is clear from Eq (14) that the DOF is proportionalto the square of f∕

For the aspheric convex plano lens with two differ-ent f∕ the main lens characteristics are calculatedby using Eqs (9) (10) and (14) and their values aresummarized in Table 1 The quasi-optical lenseshave the spot diameter of 84 and 40 mm the SRof 62 and 30 mm and DOF of 766 and 173 mmfor high f∕ and low f ∕ respectively Howeverthe real beam pattern of the low f ∕ lens may be re-latively broad compared with the ideal pattern be-cause the SR cannot be less than a wavelength32 mm The theoretical results show that largerDOF requires larger f∕ lens even though it leadsto lower SR because of the larger focused beam

3 Design of W-band Quasi-Optical Lens Antenna

The quasi-optics configuration shown in Fig 6 consi-sts of a dielectric lens and a feed antenna An asphericconvex plano lens type is selected for a quasi-opticallens in the W-band imaging system because of itsadvantages of low manufacturing cost and loweraberration-limited blurring than the sphericalnonequiconvex and convex plano lens We designedtwo aspheric convex plano lenses with aperture size

of 350 mm in the region band using the optics designtool CODE V [23] Equation (15) shows the design for-mula for the aspheric convex surface and it is basedon the conic equation as follows

y x2

R1

11 kx2∕R2

p

ax4 bx6 cx8 dx10 (15)

where x and y are the design coordinates of the lenssurface The high-order coefficients of the conic equa-tion are a b c and d R is the radius of the asphericsurface and k is the conic constant The constant va-lues of the aspheric surface described in Table 2 areoptimized to achieve low spherical aberration Thedesigned two lenses have the different focal lengthwith the same diameter to analyze the quasi-opticalcharacteristics with respect to f -number which is theratio of the focal length over the diameter of the lensf ∕ F∕D The focal lengths of the designed asphericlenses with the lens diameter of 350 mm are 524 and326 mm corresponding to high f∕ of 150 and lowf ∕ of 093 The fabricated aspheric dielectric lensesare shown in Fig 7 For low weight and low dissipa-tion loss the lenses are made of HDPE material withthe refractive index of 15187 at 94 GHz [1720]

As a feed antenna of quasi-optics in Fig 6 the di-electric rod antenna (DRA) is adapted due to compactsize and high gain compared with a standard wave-guide type antenna in the MMW band We designedDRA which consists of a tapered dielectric rod and aWR-10 waveguide for good quasi-optical transforma-tion efficiency between a lens and a feed antennausing computer simulation technology microwavestudio simulator [24] The sharp dielectric rod ofDRA is made of acrylonitrile butadiene styrene ma-terial with refractive index of 16105 at 94 GHz [17]because this material is harder than HDPE used forDRA in [25] The fabricated DRA shown in Fig 8 isthe total length of about 30 mm The return loss andradiation pattern of DRA as shown in Figs 9(a) and9(b) are measured by HP 8510 vector network ana-lyzer and near-field measurement equipment Thereturn loss is below minus15 dB over the full W-bandand the H-plane radiation pattern has a gain of about153 dB the first side lobe level of below minus20 dB and10 dB beam widths of about 511deg at 94 GHz

Fig 6 (Color online) Configuration of quasi-optical lens antenna

Table 1 Theoretical Characteristics of Aspheric Lenses

CharacteristicsHigh f ∕

Lens(f ∕ 150)Low f ∕

Lens(f∕ 093)

D [mm] 350 350Si [mm] 561 265So [mm] 2500 2500F 458 240M 022 011f -number 13 07dblur [mm] 84 40rsp [mm] 62 30DOF [mm] 766 173

Table 2 Designed Constants of Aspheric Lenses

ConstantHigh f∕

Lens (f ∕ 150)Low f∕

Lens (f∕ 093)

R 271847 168998k minus0184 minus5761a minus2056eminus9 minus1123eminus7b minus5852eminus14 4229eminus12c 1458eminus18 minus1123eminus16d minus2625eminus23 1189eminus21

1126 APPLIED OPTICS Vol 52 No 6 20 February 2013

4 Measurement and Optical Performance Analysis ofQuasi-Optical Lens Antenna

The validation of the quasi-optical characteristics viaf -number of a lens is implemented in component-level and system-level test The test is mainlyfocused on measuring the main characteristics suchas focal length DOF beam spot size and SR of twomanufactured lenses

The component-level test is used to verify all oflens characteristics by measuring Gaussian beam

pattern of a lens Figure 10 shows the experimen-tal setup for component-level test of a lens [17]A W-band source and a DRA are applied as a trans-mitter AW-band power meter was attached to a DRAas a receiver antenna to measure the received powerTo test the focal length and DOF of the designedquasi-optical lenses the receiver was scanned on theoptical axis by scan step size of 1 mm to measure thereceived power through the image distance Si at thefixed object distance So 2500 mm In this test set-up the optimum image distance is the space from thelens to the receiver when themaximum output powerof the receiver was observed The experimental focallength and DOF of the lenses can be calculated byusing Eq (1) and by computing minus3 dB level rangeswhere the received power is 3 dB lower than themax-imum power at the optimum image distance Fortest of the beam spot size and SR of the lensesthe receiver was horizontally scanned on the originof the optimum image distance by scan step size of05 mm to measure the focused beam pattern onH-plane at So 2500 mm We can get the experi-mental beam spot diameter and SR of the lenses byusing minus86 dB level ranges and first inflection pointfrom the maximum power point of the measuredbeam pattern

Fig 7 (Color online) Photo of fabricated aspheric lenses with (a) high f∕ and (b) low f ∕ (Courtesy Millisys Inc)

Fig 8 (Color online) Fabricated DRA (Courtesy Millisys Inc)

Fig 9 Measurement results of DRA (a) return loss and (b) H-plane radiation pattern

20 February 2013 Vol 52 No 6 APPLIED OPTICS 1127

As for the results of component-level test theGaussian propagation beam pattern at 94 GHz viaimage distance is depicted in Fig 11 for two differentf ∕ lenses As shown in Fig 11(a) the image distanceSi 561 mm of the high f ∕ lens is measured atSo 2500 mm According to the distance informa-tion the focal length F of about 458 mm can becalculated by using Gaussian lens formula TheDOF of minus3 dB ranges is around 65 mm As shownin Fig 11(b) the measured image distance of the

low f ∕ lens is Si 265 mm at So 2500 mm Thisleads to a focal length of approximately 240 mm andDOF of about 23 mm Further the object distance isset by 2500 mm and then the measurement of thefocused H-plane beam patterns of the quasi-opticallenses on the image plane are performed at threedifferent frequencies of 90 94 and 100 GHz As de-picted in Fig 12 the focused H-plane beam patternsfor each high f∕ and low f ∕ lens are very similar atall frequencies The beam diameters at minus86 dBpoint are about 94 and 75 mm at 94 GHz for two

Fig 10 (Color online) Experimental setup of aspheric lens incomponent-level

Fig 11 Received power via image distance for (a) high f∕ and (b) low f ∕ lens at 94 GHz

Fig 12 (Color online) H-plane focused beam pattern of (a) high f∕ and (b) low f ∕ at So 2500 mm

Fig 13 (Color online) (a) Configuration and (b) signal flow of94 GHz radiometer imaging system

1128 APPLIED OPTICS Vol 52 No 6 20 February 2013

quasi-optical lenses The results of the component-level test demonstrate that larger f ∕ of a lens leadsto larger DOF although it induces larger beam spotsize and lower SR

The DOF can be also measured through system-level test using aW-band radiometer imaging systemwhose configuration and signal flow are shown inFig 13 The fabricated 94 GHz system consists ofquasi-optical lens antenna with a reflector mirrorradiometer receiver scanner and PC with a DAQThe performance of the imaging system are tempera-ture sensitivity of below 1 K [17] SR of about 064degand FOV of above 10deg times 10deg in W-band Figure 14shows the experimental setup for the system-leveltest of a quasi-optical lens The manufactured radio-meter imaging system is used to measure DOF oftwo designed quasi-optical lenses by getting W-bandradiometer images depending on the image distance

Fig 14 (Color online) Experimental setup of aspheric lens insystem-level test

Fig 15 Measured images and relative IC via image distance for (a) high and (b) low f ∕ lens

20 February 2013 Vol 52 No 6 APPLIED OPTICS 1129

at the fixed object distance So 2500 mm The DOFis the image distance ranges where the acceptablesharpness image is achieved It can be representedby image contrast (IC) which is given by

IC Voltage amplitudeVoltage average

Vmax minus Vmin

Vmax VminV∕V (16)

where Vmax and Vmin are the maximum and mini-mum output voltage of the receiver within a radio-meter image frame The DOF is the range between0707 points of IC via the image distance The circle-shaped Teflon plastic positioned at 25 m from thelens is used as a target and it is surrounded byabsorber sheets to reduce the effects of environmen-tal clutters on the image The measured images andIC for each image are shown in Fig 15 The IC via therelative image distance are first normalized by themaximum value and then interpolated due to widestep size compared with that of the component-leveltest The experimental DOF in the system-level testare 68 and 25 mm for high f ∕ and low f∕ lens asshown in Fig 16 The results are very similar to thatof the component-level test

All measurement data of the two lenses are sum-marized in Table 3 The measurement results showthat if the lens has higher f ∕ the lens will be largerSR and depth of field The experimental results andtrends are very well-matched with the theoreticaloutcomes However the difference between two datacan be caused by the difficulty to know exactly the

electrical characteristics of HDPE material used at94 GHz and the manufacturing error of the largeaperture aspheric lens In addition the experimentallimitations such as alignment and step size betweentest points causes the difference especially morecritical for low f∕ lens because of the relationshipbetween the lens characteristic and f∕

5 Conclusion

The quasi-optical characteristics via f∕ are theore-tically and experimentally analyzed in a MMW ima-ging system Two low aberration aspheric convexplano lenses are designed at 94 GHz and the lenseshave a diameter of 350 mm and different f ∕ of 13and 07 The experimental results show that theaveraged DOF is 66 and 24 mm and the SR is 67and 50 mm for high f∕ and low f ∕ lens It is con-formed that the large f ∕ lens gives large DOF to thequasi-optical imaging system The proper f ∕ of alens should be selected to complete sharpness imagefor a FPA imaging system because there is a tradeoffbetween the DOFand the SR This result can be usedas an important design guideline of the quasi-opticallens antenna for the MMW imaging system withlower SR compared to IR cameras

The work was supported by the basic research pro-gram from the Agency for Defense Development(ADD) and by the BK21 program at Gwangju Insti-tute of Science and Technology in the Republic ofKorea All radiometer hardware was manufacturedand supported by Millisys Inc (httpwwwmillisyscom)

References1 J P Samluk C A Schuetz T Dillon E L Stein A Robbins

D G Mackrides R D Martin J Wilson C Chen and D WPrather ldquoQ-band millimeter wave imaging in the far-fieldenabled by optical upconversion methodologyrdquo J InfraredMillimeter Terahertz Waves 33 54ndash66 (2012)

2 S Yeom D S Lee J Y Son M K Jung Y Jang S W Jungand S J Lee ldquoReal-time outdoor concealed-object detectionwith passive millimeter wave imagingrdquo Opt Express 192530ndash2536 (2011)

3 J J Lynch P A Macdonald H P Moyer and R G NageleldquoPassive millimeter wave imaging sensors for commercialmarketsrdquo Appl Opt 49 E7ndashE12 (2010)

Fig 16 Normalized IC via relative image distance for (a) high f∕ lens and (b) low f ∕ lens

Table 3 Experimental Results of Aspheric Lenses at 94 GHz

CharacteristicsHigh f∕ Lens(f ∕ 150)

Low f∕ Lens(f∕ 093)

D [mm] 350 350Si [mm] 561 265So [mm] 2500 2500F 458 240M 022 011f ∕ 13 07dblur [mm] 94 63rsp [mm] 67 50DOF [mm](componentsystem)

65∕68 23∕25

1130 APPLIED OPTICS Vol 52 No 6 20 February 2013

depth of focus (DOF) are the major parameters for aFPA imaging system The SR based on Rayleigh cri-teria depends on f -number (f∕) of a lens in a givenfrequency FOV is limited by the SR and the numberof receivers but it is also limited by the optical cou-pling efficiency of a close placed receiverrsquos antennasThe DOF is the variable image distance from a lensto a receiver and it depends on f∕ of a lens In thispaper we present theoretically and experimentallythe relationship between lens characteristics andf ∕ forW-band quasi-optical radiometer imaging sys-tem at the short range For verification we have de-signed two lenses with the different f ∕ and the sameaperture size at 94 GHz

The rest of this paper is organized as followsSection 2 theoretically describes the characteristicsof a quasi-optical lens in a MMW focal plane imagingsystem The design of an aspheric quasi-optical lensantenna is presented in Section 3 The characteris-tics of aspheric quasi-optical lenses are experimen-tally analyzed in Section 4 The conclusion followsin Section 5

2 Characteristics of Aspheric Quasi-Optical Lens inMMW Imaging System

The schematic of a quasi-optical lens is shown inFig 1 The main characteristics of a lens are beamspot size dblur the SR rsp and the DOF To explainthe lens characteristics it is suitable to understandthe relationship between the characteristics and f∕of a lens in accordance with Gaussian beam propaga-tion It is necessary to consider the conjugation ratiodepending onmagnification of a lens in analyzing therelationship The Gaussian lens equation is given asfollows [18ndash20]

1Si

1So

1F (1)

where Si So and F are the distance between imageplane and lens distance of object plane from lens

and the focal length of the lens The expression forthe magnification M of the lens is given as

M Si

So (2)

Combining Eqs (1) and (2) we get the relation be-tween image distance focal length andmagnification

Si M 1F (3)

If the magnification M is relatively low the lens isused at the infinite conjugate ratio correspondingto Si F

The incoming beam is focused by a lens to obtain asmall beam spot as shown in Fig 1 The focusedbeam spot spreads on the image plane because ofaberration and diffraction of the lens And theseintroduce blurring in the image

In general the aberration is caused by the spheri-cal geometry of lens surfaces The aberration-limitedspot size dab is determined by multiplying theaberration-limited angle angular blur ΔΘab by theimage distance Si The aberration-limited angularblur based on third-order aberration theory andaberration-limited spot is given as [1821]

ΔΘab D∕F3n2minus 2n 1q

n 2q2∕n∕32n minus 12 (4)

dab ΔΘab middot Si (5)

where D F n and q are the diameter focal lengthmaterial refractive index and shape factor of thelens respectively The shape factor q of a lens is givenby [21]

q R2∕R2 minus R1 (6)

Fig 1 (Color online) Schematic of quasi-optical lens

20 February 2013 Vol 52 No 6 APPLIED OPTICS 1123

where R1 and R2 are the radius of curvature forleft and right side surface of the lens as shown inFig 1 The variation of the aberration-limited angularblur with shape factor shown in Fig 2 for the lensmade of high-density polyethylene (HDPE) whichhas a refractive index (n) of 15187 at 94 GHz [1720]and it is being operated at the infinite conjugate ratioAn asymmetric shape that corresponds to a q-valueof about 087 is the best singlet shape It is importantto note that the best-form shape of lens is dependenton the refractive index In case of a typical dielectricsinglet the convex plano shape (q 1) with convexside toward the infinite conjugate performs nearlyaswell as the best-form lens Equation (5) is simplified

to Eq (7) for a spherical convex plano lens in the caseof HDPE and the finite conjugate ratio

dab HDPE 0068M 12

F

f∕3 (7)

where f∕ F∕D denotes the f -number of the lensThe diffraction accounts for the spreading of the

radiation as it passes through an aperture Thus apoint object is never imaged on a point in the imageplane as shown in Fig 3(a) The irradiance distribu-tion in the image plane and its cross section is shownin Figs 3(b) and 3(c) The diffraction is a naturalproperty and it always present on any quasi-opticallens Its effects may be masked if the lens has signif-icant aberration In the case of aspheric convex planolenses the diffraction is dominant over aberrationThe diffraction-limited half-angle angular blur andcorresponding circular ring of the diffraction patterncontaining 86 of irradiance distribution Fig 3(b) isgiven as follows [22]

ΔΘdiff 164λ

D (8)

where λ is the wavelength of MMW beam Thediffraction-limited blur spot size for finite conjugateratio is given as [22]

-05 00 05 10 15 20 2500

01

02

03

04

05

Abe

rrat

ion-

limite

d an

gula

r bl

ur

[(D

F)3

]

Shape factor q

Fig 2 Aberration-limited angular blur via shape factor

Point Source Focal

PlanefD

84

86

(a) (b)

(c)

Fig 3 (a) Image of a point object (b) Airy pattern 2-D plot of the diffracted irradiance distribution (c) Cross-section of (b) ρ is normalizedradial distance from the center [22]

1124 APPLIED OPTICS Vol 52 No 6 20 February 2013

ddiff ΔΘdiff middot Si 164λM 1f∕ (9)

The diffraction-limited blur spot size given by Eq (9)is the radius of the circular ring of the diffraction pat-tern in the focal plane having 86 irradiance distri-bution [22]

Comparing the aberration-limited spot size to thediffraction-limited spot size suggests a criterion of asingle lens If the spot size dab is larger than ddiff then dblur is limited by aberration If the spot sizedab is smaller than ddiff the spot size is essentiallydiffraction limited Figure 4 depicts the spot sizeas a function of f∕ in the case of the convex-planelens with the infinite conjugate ratio using Eqs (7)and (9) Figure 4(a) shows that the spot size causedby spherical aberration is inversely dependent on thecube of f∕ and the diffraction-limited spot size in-creases linearly with f ∕ The resultant spot sizeby the dominant fact decreases for small f ∕ andthen increases with f∕ as shown in Fig 4(b) Itmeans that there is some optimum point (P) for aminimum of both aberration and diffraction The op-timum spot size is about 87 mm at the f∕ of 165 forthe convex plano lens The diffraction a naturalproperty is always present on any quasi-optical lensalthough its effects may be masked if the lens has asignificant aberration However the spherical aber-ration can be reduced by aspherical lens or multiplelenses Accordingly an aspheric convex plano lens ismainly dominated by the diffraction and its focusedbeam spot diameter can be represented by the twicethe diffraction-limited spot size given by Eq (9)

In imaging applications the SR is ultimatelylimited by diffraction Calculating the maximumpossible SR of a lens requires an arbitrary definitionof what is meant by resolving two features In theRayleigh criterion it is assumed that two separatepoint source can be resolved when the center of theAiry disc from one overlaps the first dark ring inthe diffraction pattern of the second In this casethe smallest resolvable distance is [22]

rsp ddiff o

2 122λM 1f ∕ (10)

where ddiff o is the spot diameter at which theintensity distribution of the Airy disc is the first 0

intensity point of its maximum value on the axis forthe finite conjugated lens The SR is linearly propor-tional to f ∕ as shown in Eq (10) It is also related tothe physically minimum space between the adjacentreceivers for a FPA imaging system

The Gaussian beam focuses from a lens down to awaist and then expands proportionally to x as shownin Fig 5 The wavefront radius of curvature whichwas infinite at x 0 will become finite and initiallydecrease with x At some point it will reach a mini-mum value and then it increases with larger x even-tually becoming proportional to x The equationsdescribing the Gaussian beam radius wx and thewavefront radius of curvature Rx are [1920]

wx wo

1

λx

πw2o

05

(11)

Rx x1

πw2

o

λx

2 (12)

where x is the distance propagated from the planewhere the wavefront is flat and wo 05ddiff o is theradius of the 1∕e2 irradiance contour at x 0 TheRayleigh range XR defined as the distance overthe beam radius by a factor of

2

p is given by [1920]

XR πw2o

λ (13)

DOF is the range of the image distance over whichthe focused spot diameter remains below an arbi-trary limit Normally it is defined as the distance

Fig 4 (a) Aberration- and diffraction-limited and (b) dominant spot size of convex plano lens

Fig 5 Focusing of Gaussian beam

20 February 2013 Vol 52 No 6 APPLIED OPTICS 1125

between2

pwo spot size points or 2 times Rayleigh

range [1920] For the finite conjugated lens it canbe written as [1920]

DOF 2timesXR 2timesπw2

o

λ 297πλM1f ∕2 (14)

It is clear from Eq (14) that the DOF is proportionalto the square of f∕

For the aspheric convex plano lens with two differ-ent f∕ the main lens characteristics are calculatedby using Eqs (9) (10) and (14) and their values aresummarized in Table 1 The quasi-optical lenseshave the spot diameter of 84 and 40 mm the SRof 62 and 30 mm and DOF of 766 and 173 mmfor high f∕ and low f ∕ respectively Howeverthe real beam pattern of the low f ∕ lens may be re-latively broad compared with the ideal pattern be-cause the SR cannot be less than a wavelength32 mm The theoretical results show that largerDOF requires larger f∕ lens even though it leadsto lower SR because of the larger focused beam

3 Design of W-band Quasi-Optical Lens Antenna

The quasi-optics configuration shown in Fig 6 consi-sts of a dielectric lens and a feed antenna An asphericconvex plano lens type is selected for a quasi-opticallens in the W-band imaging system because of itsadvantages of low manufacturing cost and loweraberration-limited blurring than the sphericalnonequiconvex and convex plano lens We designedtwo aspheric convex plano lenses with aperture size

of 350 mm in the region band using the optics designtool CODE V [23] Equation (15) shows the design for-mula for the aspheric convex surface and it is basedon the conic equation as follows

y x2

R1

11 kx2∕R2

p

ax4 bx6 cx8 dx10 (15)

where x and y are the design coordinates of the lenssurface The high-order coefficients of the conic equa-tion are a b c and d R is the radius of the asphericsurface and k is the conic constant The constant va-lues of the aspheric surface described in Table 2 areoptimized to achieve low spherical aberration Thedesigned two lenses have the different focal lengthwith the same diameter to analyze the quasi-opticalcharacteristics with respect to f -number which is theratio of the focal length over the diameter of the lensf ∕ F∕D The focal lengths of the designed asphericlenses with the lens diameter of 350 mm are 524 and326 mm corresponding to high f∕ of 150 and lowf ∕ of 093 The fabricated aspheric dielectric lensesare shown in Fig 7 For low weight and low dissipa-tion loss the lenses are made of HDPE material withthe refractive index of 15187 at 94 GHz [1720]

As a feed antenna of quasi-optics in Fig 6 the di-electric rod antenna (DRA) is adapted due to compactsize and high gain compared with a standard wave-guide type antenna in the MMW band We designedDRA which consists of a tapered dielectric rod and aWR-10 waveguide for good quasi-optical transforma-tion efficiency between a lens and a feed antennausing computer simulation technology microwavestudio simulator [24] The sharp dielectric rod ofDRA is made of acrylonitrile butadiene styrene ma-terial with refractive index of 16105 at 94 GHz [17]because this material is harder than HDPE used forDRA in [25] The fabricated DRA shown in Fig 8 isthe total length of about 30 mm The return loss andradiation pattern of DRA as shown in Figs 9(a) and9(b) are measured by HP 8510 vector network ana-lyzer and near-field measurement equipment Thereturn loss is below minus15 dB over the full W-bandand the H-plane radiation pattern has a gain of about153 dB the first side lobe level of below minus20 dB and10 dB beam widths of about 511deg at 94 GHz

Fig 6 (Color online) Configuration of quasi-optical lens antenna

Table 1 Theoretical Characteristics of Aspheric Lenses

CharacteristicsHigh f ∕

Lens(f ∕ 150)Low f ∕

Lens(f∕ 093)

D [mm] 350 350Si [mm] 561 265So [mm] 2500 2500F 458 240M 022 011f -number 13 07dblur [mm] 84 40rsp [mm] 62 30DOF [mm] 766 173

Table 2 Designed Constants of Aspheric Lenses

ConstantHigh f∕

Lens (f ∕ 150)Low f∕

Lens (f∕ 093)

R 271847 168998k minus0184 minus5761a minus2056eminus9 minus1123eminus7b minus5852eminus14 4229eminus12c 1458eminus18 minus1123eminus16d minus2625eminus23 1189eminus21

1126 APPLIED OPTICS Vol 52 No 6 20 February 2013

4 Measurement and Optical Performance Analysis ofQuasi-Optical Lens Antenna

The validation of the quasi-optical characteristics viaf -number of a lens is implemented in component-level and system-level test The test is mainlyfocused on measuring the main characteristics suchas focal length DOF beam spot size and SR of twomanufactured lenses

The component-level test is used to verify all oflens characteristics by measuring Gaussian beam

pattern of a lens Figure 10 shows the experimen-tal setup for component-level test of a lens [17]A W-band source and a DRA are applied as a trans-mitter AW-band power meter was attached to a DRAas a receiver antenna to measure the received powerTo test the focal length and DOF of the designedquasi-optical lenses the receiver was scanned on theoptical axis by scan step size of 1 mm to measure thereceived power through the image distance Si at thefixed object distance So 2500 mm In this test set-up the optimum image distance is the space from thelens to the receiver when themaximum output powerof the receiver was observed The experimental focallength and DOF of the lenses can be calculated byusing Eq (1) and by computing minus3 dB level rangeswhere the received power is 3 dB lower than themax-imum power at the optimum image distance Fortest of the beam spot size and SR of the lensesthe receiver was horizontally scanned on the originof the optimum image distance by scan step size of05 mm to measure the focused beam pattern onH-plane at So 2500 mm We can get the experi-mental beam spot diameter and SR of the lenses byusing minus86 dB level ranges and first inflection pointfrom the maximum power point of the measuredbeam pattern

Fig 7 (Color online) Photo of fabricated aspheric lenses with (a) high f∕ and (b) low f ∕ (Courtesy Millisys Inc)

Fig 8 (Color online) Fabricated DRA (Courtesy Millisys Inc)

Fig 9 Measurement results of DRA (a) return loss and (b) H-plane radiation pattern

20 February 2013 Vol 52 No 6 APPLIED OPTICS 1127

As for the results of component-level test theGaussian propagation beam pattern at 94 GHz viaimage distance is depicted in Fig 11 for two differentf ∕ lenses As shown in Fig 11(a) the image distanceSi 561 mm of the high f ∕ lens is measured atSo 2500 mm According to the distance informa-tion the focal length F of about 458 mm can becalculated by using Gaussian lens formula TheDOF of minus3 dB ranges is around 65 mm As shownin Fig 11(b) the measured image distance of the

low f ∕ lens is Si 265 mm at So 2500 mm Thisleads to a focal length of approximately 240 mm andDOF of about 23 mm Further the object distance isset by 2500 mm and then the measurement of thefocused H-plane beam patterns of the quasi-opticallenses on the image plane are performed at threedifferent frequencies of 90 94 and 100 GHz As de-picted in Fig 12 the focused H-plane beam patternsfor each high f∕ and low f ∕ lens are very similar atall frequencies The beam diameters at minus86 dBpoint are about 94 and 75 mm at 94 GHz for two

Fig 10 (Color online) Experimental setup of aspheric lens incomponent-level

Fig 11 Received power via image distance for (a) high f∕ and (b) low f ∕ lens at 94 GHz

Fig 12 (Color online) H-plane focused beam pattern of (a) high f∕ and (b) low f ∕ at So 2500 mm

Fig 13 (Color online) (a) Configuration and (b) signal flow of94 GHz radiometer imaging system

1128 APPLIED OPTICS Vol 52 No 6 20 February 2013

quasi-optical lenses The results of the component-level test demonstrate that larger f ∕ of a lens leadsto larger DOF although it induces larger beam spotsize and lower SR

The DOF can be also measured through system-level test using aW-band radiometer imaging systemwhose configuration and signal flow are shown inFig 13 The fabricated 94 GHz system consists ofquasi-optical lens antenna with a reflector mirrorradiometer receiver scanner and PC with a DAQThe performance of the imaging system are tempera-ture sensitivity of below 1 K [17] SR of about 064degand FOV of above 10deg times 10deg in W-band Figure 14shows the experimental setup for the system-leveltest of a quasi-optical lens The manufactured radio-meter imaging system is used to measure DOF oftwo designed quasi-optical lenses by getting W-bandradiometer images depending on the image distance

Fig 14 (Color online) Experimental setup of aspheric lens insystem-level test

Fig 15 Measured images and relative IC via image distance for (a) high and (b) low f ∕ lens

20 February 2013 Vol 52 No 6 APPLIED OPTICS 1129

at the fixed object distance So 2500 mm The DOFis the image distance ranges where the acceptablesharpness image is achieved It can be representedby image contrast (IC) which is given by

IC Voltage amplitudeVoltage average

Vmax minus Vmin

Vmax VminV∕V (16)

where Vmax and Vmin are the maximum and mini-mum output voltage of the receiver within a radio-meter image frame The DOF is the range between0707 points of IC via the image distance The circle-shaped Teflon plastic positioned at 25 m from thelens is used as a target and it is surrounded byabsorber sheets to reduce the effects of environmen-tal clutters on the image The measured images andIC for each image are shown in Fig 15 The IC via therelative image distance are first normalized by themaximum value and then interpolated due to widestep size compared with that of the component-leveltest The experimental DOF in the system-level testare 68 and 25 mm for high f ∕ and low f∕ lens asshown in Fig 16 The results are very similar to thatof the component-level test

All measurement data of the two lenses are sum-marized in Table 3 The measurement results showthat if the lens has higher f ∕ the lens will be largerSR and depth of field The experimental results andtrends are very well-matched with the theoreticaloutcomes However the difference between two datacan be caused by the difficulty to know exactly the

electrical characteristics of HDPE material used at94 GHz and the manufacturing error of the largeaperture aspheric lens In addition the experimentallimitations such as alignment and step size betweentest points causes the difference especially morecritical for low f∕ lens because of the relationshipbetween the lens characteristic and f∕

5 Conclusion

The quasi-optical characteristics via f∕ are theore-tically and experimentally analyzed in a MMW ima-ging system Two low aberration aspheric convexplano lenses are designed at 94 GHz and the lenseshave a diameter of 350 mm and different f ∕ of 13and 07 The experimental results show that theaveraged DOF is 66 and 24 mm and the SR is 67and 50 mm for high f∕ and low f ∕ lens It is con-formed that the large f ∕ lens gives large DOF to thequasi-optical imaging system The proper f ∕ of alens should be selected to complete sharpness imagefor a FPA imaging system because there is a tradeoffbetween the DOFand the SR This result can be usedas an important design guideline of the quasi-opticallens antenna for the MMW imaging system withlower SR compared to IR cameras

The work was supported by the basic research pro-gram from the Agency for Defense Development(ADD) and by the BK21 program at Gwangju Insti-tute of Science and Technology in the Republic ofKorea All radiometer hardware was manufacturedand supported by Millisys Inc (httpwwwmillisyscom)

References1 J P Samluk C A Schuetz T Dillon E L Stein A Robbins

D G Mackrides R D Martin J Wilson C Chen and D WPrather ldquoQ-band millimeter wave imaging in the far-fieldenabled by optical upconversion methodologyrdquo J InfraredMillimeter Terahertz Waves 33 54ndash66 (2012)

2 S Yeom D S Lee J Y Son M K Jung Y Jang S W Jungand S J Lee ldquoReal-time outdoor concealed-object detectionwith passive millimeter wave imagingrdquo Opt Express 192530ndash2536 (2011)

3 J J Lynch P A Macdonald H P Moyer and R G NageleldquoPassive millimeter wave imaging sensors for commercialmarketsrdquo Appl Opt 49 E7ndashE12 (2010)

Fig 16 Normalized IC via relative image distance for (a) high f∕ lens and (b) low f ∕ lens

Table 3 Experimental Results of Aspheric Lenses at 94 GHz

CharacteristicsHigh f∕ Lens(f ∕ 150)

Low f∕ Lens(f∕ 093)

D [mm] 350 350Si [mm] 561 265So [mm] 2500 2500F 458 240M 022 011f ∕ 13 07dblur [mm] 94 63rsp [mm] 67 50DOF [mm](componentsystem)

65∕68 23∕25

1130 APPLIED OPTICS Vol 52 No 6 20 February 2013

where R1 and R2 are the radius of curvature forleft and right side surface of the lens as shown inFig 1 The variation of the aberration-limited angularblur with shape factor shown in Fig 2 for the lensmade of high-density polyethylene (HDPE) whichhas a refractive index (n) of 15187 at 94 GHz [1720]and it is being operated at the infinite conjugate ratioAn asymmetric shape that corresponds to a q-valueof about 087 is the best singlet shape It is importantto note that the best-form shape of lens is dependenton the refractive index In case of a typical dielectricsinglet the convex plano shape (q 1) with convexside toward the infinite conjugate performs nearlyaswell as the best-form lens Equation (5) is simplified

to Eq (7) for a spherical convex plano lens in the caseof HDPE and the finite conjugate ratio

dab HDPE 0068M 12

F

f∕3 (7)

where f∕ F∕D denotes the f -number of the lensThe diffraction accounts for the spreading of the

radiation as it passes through an aperture Thus apoint object is never imaged on a point in the imageplane as shown in Fig 3(a) The irradiance distribu-tion in the image plane and its cross section is shownin Figs 3(b) and 3(c) The diffraction is a naturalproperty and it always present on any quasi-opticallens Its effects may be masked if the lens has signif-icant aberration In the case of aspheric convex planolenses the diffraction is dominant over aberrationThe diffraction-limited half-angle angular blur andcorresponding circular ring of the diffraction patterncontaining 86 of irradiance distribution Fig 3(b) isgiven as follows [22]

ΔΘdiff 164λ

D (8)

where λ is the wavelength of MMW beam Thediffraction-limited blur spot size for finite conjugateratio is given as [22]

-05 00 05 10 15 20 2500

01

02

03

04

05

Abe

rrat

ion-

limite

d an

gula

r bl

ur

[(D

F)3

]

Shape factor q

Fig 2 Aberration-limited angular blur via shape factor

Point Source Focal

PlanefD

84

86

(a) (b)

(c)

Fig 3 (a) Image of a point object (b) Airy pattern 2-D plot of the diffracted irradiance distribution (c) Cross-section of (b) ρ is normalizedradial distance from the center [22]

1124 APPLIED OPTICS Vol 52 No 6 20 February 2013

ddiff ΔΘdiff middot Si 164λM 1f∕ (9)

The diffraction-limited blur spot size given by Eq (9)is the radius of the circular ring of the diffraction pat-tern in the focal plane having 86 irradiance distri-bution [22]

Comparing the aberration-limited spot size to thediffraction-limited spot size suggests a criterion of asingle lens If the spot size dab is larger than ddiff then dblur is limited by aberration If the spot sizedab is smaller than ddiff the spot size is essentiallydiffraction limited Figure 4 depicts the spot sizeas a function of f∕ in the case of the convex-planelens with the infinite conjugate ratio using Eqs (7)and (9) Figure 4(a) shows that the spot size causedby spherical aberration is inversely dependent on thecube of f∕ and the diffraction-limited spot size in-creases linearly with f ∕ The resultant spot sizeby the dominant fact decreases for small f ∕ andthen increases with f∕ as shown in Fig 4(b) Itmeans that there is some optimum point (P) for aminimum of both aberration and diffraction The op-timum spot size is about 87 mm at the f∕ of 165 forthe convex plano lens The diffraction a naturalproperty is always present on any quasi-optical lensalthough its effects may be masked if the lens has asignificant aberration However the spherical aber-ration can be reduced by aspherical lens or multiplelenses Accordingly an aspheric convex plano lens ismainly dominated by the diffraction and its focusedbeam spot diameter can be represented by the twicethe diffraction-limited spot size given by Eq (9)

In imaging applications the SR is ultimatelylimited by diffraction Calculating the maximumpossible SR of a lens requires an arbitrary definitionof what is meant by resolving two features In theRayleigh criterion it is assumed that two separatepoint source can be resolved when the center of theAiry disc from one overlaps the first dark ring inthe diffraction pattern of the second In this casethe smallest resolvable distance is [22]

rsp ddiff o

2 122λM 1f ∕ (10)

where ddiff o is the spot diameter at which theintensity distribution of the Airy disc is the first 0

intensity point of its maximum value on the axis forthe finite conjugated lens The SR is linearly propor-tional to f ∕ as shown in Eq (10) It is also related tothe physically minimum space between the adjacentreceivers for a FPA imaging system

The Gaussian beam focuses from a lens down to awaist and then expands proportionally to x as shownin Fig 5 The wavefront radius of curvature whichwas infinite at x 0 will become finite and initiallydecrease with x At some point it will reach a mini-mum value and then it increases with larger x even-tually becoming proportional to x The equationsdescribing the Gaussian beam radius wx and thewavefront radius of curvature Rx are [1920]

wx wo

1

λx

πw2o

05

(11)

Rx x1

πw2

o

λx

2 (12)

where x is the distance propagated from the planewhere the wavefront is flat and wo 05ddiff o is theradius of the 1∕e2 irradiance contour at x 0 TheRayleigh range XR defined as the distance overthe beam radius by a factor of

2

p is given by [1920]

XR πw2o

λ (13)

DOF is the range of the image distance over whichthe focused spot diameter remains below an arbi-trary limit Normally it is defined as the distance

Fig 4 (a) Aberration- and diffraction-limited and (b) dominant spot size of convex plano lens

Fig 5 Focusing of Gaussian beam

20 February 2013 Vol 52 No 6 APPLIED OPTICS 1125

between2

pwo spot size points or 2 times Rayleigh

range [1920] For the finite conjugated lens it canbe written as [1920]

DOF 2timesXR 2timesπw2

o

λ 297πλM1f ∕2 (14)

It is clear from Eq (14) that the DOF is proportionalto the square of f∕

For the aspheric convex plano lens with two differ-ent f∕ the main lens characteristics are calculatedby using Eqs (9) (10) and (14) and their values aresummarized in Table 1 The quasi-optical lenseshave the spot diameter of 84 and 40 mm the SRof 62 and 30 mm and DOF of 766 and 173 mmfor high f∕ and low f ∕ respectively Howeverthe real beam pattern of the low f ∕ lens may be re-latively broad compared with the ideal pattern be-cause the SR cannot be less than a wavelength32 mm The theoretical results show that largerDOF requires larger f∕ lens even though it leadsto lower SR because of the larger focused beam

3 Design of W-band Quasi-Optical Lens Antenna

The quasi-optics configuration shown in Fig 6 consi-sts of a dielectric lens and a feed antenna An asphericconvex plano lens type is selected for a quasi-opticallens in the W-band imaging system because of itsadvantages of low manufacturing cost and loweraberration-limited blurring than the sphericalnonequiconvex and convex plano lens We designedtwo aspheric convex plano lenses with aperture size

of 350 mm in the region band using the optics designtool CODE V [23] Equation (15) shows the design for-mula for the aspheric convex surface and it is basedon the conic equation as follows

y x2

R1

11 kx2∕R2

p

ax4 bx6 cx8 dx10 (15)

where x and y are the design coordinates of the lenssurface The high-order coefficients of the conic equa-tion are a b c and d R is the radius of the asphericsurface and k is the conic constant The constant va-lues of the aspheric surface described in Table 2 areoptimized to achieve low spherical aberration Thedesigned two lenses have the different focal lengthwith the same diameter to analyze the quasi-opticalcharacteristics with respect to f -number which is theratio of the focal length over the diameter of the lensf ∕ F∕D The focal lengths of the designed asphericlenses with the lens diameter of 350 mm are 524 and326 mm corresponding to high f∕ of 150 and lowf ∕ of 093 The fabricated aspheric dielectric lensesare shown in Fig 7 For low weight and low dissipa-tion loss the lenses are made of HDPE material withthe refractive index of 15187 at 94 GHz [1720]

As a feed antenna of quasi-optics in Fig 6 the di-electric rod antenna (DRA) is adapted due to compactsize and high gain compared with a standard wave-guide type antenna in the MMW band We designedDRA which consists of a tapered dielectric rod and aWR-10 waveguide for good quasi-optical transforma-tion efficiency between a lens and a feed antennausing computer simulation technology microwavestudio simulator [24] The sharp dielectric rod ofDRA is made of acrylonitrile butadiene styrene ma-terial with refractive index of 16105 at 94 GHz [17]because this material is harder than HDPE used forDRA in [25] The fabricated DRA shown in Fig 8 isthe total length of about 30 mm The return loss andradiation pattern of DRA as shown in Figs 9(a) and9(b) are measured by HP 8510 vector network ana-lyzer and near-field measurement equipment Thereturn loss is below minus15 dB over the full W-bandand the H-plane radiation pattern has a gain of about153 dB the first side lobe level of below minus20 dB and10 dB beam widths of about 511deg at 94 GHz

Fig 6 (Color online) Configuration of quasi-optical lens antenna

Table 1 Theoretical Characteristics of Aspheric Lenses

CharacteristicsHigh f ∕

Lens(f ∕ 150)Low f ∕

Lens(f∕ 093)

D [mm] 350 350Si [mm] 561 265So [mm] 2500 2500F 458 240M 022 011f -number 13 07dblur [mm] 84 40rsp [mm] 62 30DOF [mm] 766 173

Table 2 Designed Constants of Aspheric Lenses

ConstantHigh f∕

Lens (f ∕ 150)Low f∕

Lens (f∕ 093)

R 271847 168998k minus0184 minus5761a minus2056eminus9 minus1123eminus7b minus5852eminus14 4229eminus12c 1458eminus18 minus1123eminus16d minus2625eminus23 1189eminus21

1126 APPLIED OPTICS Vol 52 No 6 20 February 2013

4 Measurement and Optical Performance Analysis ofQuasi-Optical Lens Antenna

The validation of the quasi-optical characteristics viaf -number of a lens is implemented in component-level and system-level test The test is mainlyfocused on measuring the main characteristics suchas focal length DOF beam spot size and SR of twomanufactured lenses

The component-level test is used to verify all oflens characteristics by measuring Gaussian beam

pattern of a lens Figure 10 shows the experimen-tal setup for component-level test of a lens [17]A W-band source and a DRA are applied as a trans-mitter AW-band power meter was attached to a DRAas a receiver antenna to measure the received powerTo test the focal length and DOF of the designedquasi-optical lenses the receiver was scanned on theoptical axis by scan step size of 1 mm to measure thereceived power through the image distance Si at thefixed object distance So 2500 mm In this test set-up the optimum image distance is the space from thelens to the receiver when themaximum output powerof the receiver was observed The experimental focallength and DOF of the lenses can be calculated byusing Eq (1) and by computing minus3 dB level rangeswhere the received power is 3 dB lower than themax-imum power at the optimum image distance Fortest of the beam spot size and SR of the lensesthe receiver was horizontally scanned on the originof the optimum image distance by scan step size of05 mm to measure the focused beam pattern onH-plane at So 2500 mm We can get the experi-mental beam spot diameter and SR of the lenses byusing minus86 dB level ranges and first inflection pointfrom the maximum power point of the measuredbeam pattern

Fig 7 (Color online) Photo of fabricated aspheric lenses with (a) high f∕ and (b) low f ∕ (Courtesy Millisys Inc)

Fig 8 (Color online) Fabricated DRA (Courtesy Millisys Inc)

Fig 9 Measurement results of DRA (a) return loss and (b) H-plane radiation pattern

20 February 2013 Vol 52 No 6 APPLIED OPTICS 1127

As for the results of component-level test theGaussian propagation beam pattern at 94 GHz viaimage distance is depicted in Fig 11 for two differentf ∕ lenses As shown in Fig 11(a) the image distanceSi 561 mm of the high f ∕ lens is measured atSo 2500 mm According to the distance informa-tion the focal length F of about 458 mm can becalculated by using Gaussian lens formula TheDOF of minus3 dB ranges is around 65 mm As shownin Fig 11(b) the measured image distance of the

low f ∕ lens is Si 265 mm at So 2500 mm Thisleads to a focal length of approximately 240 mm andDOF of about 23 mm Further the object distance isset by 2500 mm and then the measurement of thefocused H-plane beam patterns of the quasi-opticallenses on the image plane are performed at threedifferent frequencies of 90 94 and 100 GHz As de-picted in Fig 12 the focused H-plane beam patternsfor each high f∕ and low f ∕ lens are very similar atall frequencies The beam diameters at minus86 dBpoint are about 94 and 75 mm at 94 GHz for two

Fig 10 (Color online) Experimental setup of aspheric lens incomponent-level

Fig 11 Received power via image distance for (a) high f∕ and (b) low f ∕ lens at 94 GHz

Fig 12 (Color online) H-plane focused beam pattern of (a) high f∕ and (b) low f ∕ at So 2500 mm

Fig 13 (Color online) (a) Configuration and (b) signal flow of94 GHz radiometer imaging system

1128 APPLIED OPTICS Vol 52 No 6 20 February 2013

quasi-optical lenses The results of the component-level test demonstrate that larger f ∕ of a lens leadsto larger DOF although it induces larger beam spotsize and lower SR

The DOF can be also measured through system-level test using aW-band radiometer imaging systemwhose configuration and signal flow are shown inFig 13 The fabricated 94 GHz system consists ofquasi-optical lens antenna with a reflector mirrorradiometer receiver scanner and PC with a DAQThe performance of the imaging system are tempera-ture sensitivity of below 1 K [17] SR of about 064degand FOV of above 10deg times 10deg in W-band Figure 14shows the experimental setup for the system-leveltest of a quasi-optical lens The manufactured radio-meter imaging system is used to measure DOF oftwo designed quasi-optical lenses by getting W-bandradiometer images depending on the image distance

Fig 14 (Color online) Experimental setup of aspheric lens insystem-level test

Fig 15 Measured images and relative IC via image distance for (a) high and (b) low f ∕ lens

20 February 2013 Vol 52 No 6 APPLIED OPTICS 1129

at the fixed object distance So 2500 mm The DOFis the image distance ranges where the acceptablesharpness image is achieved It can be representedby image contrast (IC) which is given by

IC Voltage amplitudeVoltage average

Vmax minus Vmin

Vmax VminV∕V (16)

where Vmax and Vmin are the maximum and mini-mum output voltage of the receiver within a radio-meter image frame The DOF is the range between0707 points of IC via the image distance The circle-shaped Teflon plastic positioned at 25 m from thelens is used as a target and it is surrounded byabsorber sheets to reduce the effects of environmen-tal clutters on the image The measured images andIC for each image are shown in Fig 15 The IC via therelative image distance are first normalized by themaximum value and then interpolated due to widestep size compared with that of the component-leveltest The experimental DOF in the system-level testare 68 and 25 mm for high f ∕ and low f∕ lens asshown in Fig 16 The results are very similar to thatof the component-level test

All measurement data of the two lenses are sum-marized in Table 3 The measurement results showthat if the lens has higher f ∕ the lens will be largerSR and depth of field The experimental results andtrends are very well-matched with the theoreticaloutcomes However the difference between two datacan be caused by the difficulty to know exactly the

electrical characteristics of HDPE material used at94 GHz and the manufacturing error of the largeaperture aspheric lens In addition the experimentallimitations such as alignment and step size betweentest points causes the difference especially morecritical for low f∕ lens because of the relationshipbetween the lens characteristic and f∕

5 Conclusion

The quasi-optical characteristics via f∕ are theore-tically and experimentally analyzed in a MMW ima-ging system Two low aberration aspheric convexplano lenses are designed at 94 GHz and the lenseshave a diameter of 350 mm and different f ∕ of 13and 07 The experimental results show that theaveraged DOF is 66 and 24 mm and the SR is 67and 50 mm for high f∕ and low f ∕ lens It is con-formed that the large f ∕ lens gives large DOF to thequasi-optical imaging system The proper f ∕ of alens should be selected to complete sharpness imagefor a FPA imaging system because there is a tradeoffbetween the DOFand the SR This result can be usedas an important design guideline of the quasi-opticallens antenna for the MMW imaging system withlower SR compared to IR cameras

The work was supported by the basic research pro-gram from the Agency for Defense Development(ADD) and by the BK21 program at Gwangju Insti-tute of Science and Technology in the Republic ofKorea All radiometer hardware was manufacturedand supported by Millisys Inc (httpwwwmillisyscom)

References1 J P Samluk C A Schuetz T Dillon E L Stein A Robbins

D G Mackrides R D Martin J Wilson C Chen and D WPrather ldquoQ-band millimeter wave imaging in the far-fieldenabled by optical upconversion methodologyrdquo J InfraredMillimeter Terahertz Waves 33 54ndash66 (2012)

2 S Yeom D S Lee J Y Son M K Jung Y Jang S W Jungand S J Lee ldquoReal-time outdoor concealed-object detectionwith passive millimeter wave imagingrdquo Opt Express 192530ndash2536 (2011)

3 J J Lynch P A Macdonald H P Moyer and R G NageleldquoPassive millimeter wave imaging sensors for commercialmarketsrdquo Appl Opt 49 E7ndashE12 (2010)

Fig 16 Normalized IC via relative image distance for (a) high f∕ lens and (b) low f ∕ lens

Table 3 Experimental Results of Aspheric Lenses at 94 GHz

CharacteristicsHigh f∕ Lens(f ∕ 150)

Low f∕ Lens(f∕ 093)

D [mm] 350 350Si [mm] 561 265So [mm] 2500 2500F 458 240M 022 011f ∕ 13 07dblur [mm] 94 63rsp [mm] 67 50DOF [mm](componentsystem)

65∕68 23∕25

1130 APPLIED OPTICS Vol 52 No 6 20 February 2013

ddiff ΔΘdiff middot Si 164λM 1f∕ (9)

The diffraction-limited blur spot size given by Eq (9)is the radius of the circular ring of the diffraction pat-tern in the focal plane having 86 irradiance distri-bution [22]

Comparing the aberration-limited spot size to thediffraction-limited spot size suggests a criterion of asingle lens If the spot size dab is larger than ddiff then dblur is limited by aberration If the spot sizedab is smaller than ddiff the spot size is essentiallydiffraction limited Figure 4 depicts the spot sizeas a function of f∕ in the case of the convex-planelens with the infinite conjugate ratio using Eqs (7)and (9) Figure 4(a) shows that the spot size causedby spherical aberration is inversely dependent on thecube of f∕ and the diffraction-limited spot size in-creases linearly with f ∕ The resultant spot sizeby the dominant fact decreases for small f ∕ andthen increases with f∕ as shown in Fig 4(b) Itmeans that there is some optimum point (P) for aminimum of both aberration and diffraction The op-timum spot size is about 87 mm at the f∕ of 165 forthe convex plano lens The diffraction a naturalproperty is always present on any quasi-optical lensalthough its effects may be masked if the lens has asignificant aberration However the spherical aber-ration can be reduced by aspherical lens or multiplelenses Accordingly an aspheric convex plano lens ismainly dominated by the diffraction and its focusedbeam spot diameter can be represented by the twicethe diffraction-limited spot size given by Eq (9)

In imaging applications the SR is ultimatelylimited by diffraction Calculating the maximumpossible SR of a lens requires an arbitrary definitionof what is meant by resolving two features In theRayleigh criterion it is assumed that two separatepoint source can be resolved when the center of theAiry disc from one overlaps the first dark ring inthe diffraction pattern of the second In this casethe smallest resolvable distance is [22]

rsp ddiff o

2 122λM 1f ∕ (10)

where ddiff o is the spot diameter at which theintensity distribution of the Airy disc is the first 0

intensity point of its maximum value on the axis forthe finite conjugated lens The SR is linearly propor-tional to f ∕ as shown in Eq (10) It is also related tothe physically minimum space between the adjacentreceivers for a FPA imaging system

The Gaussian beam focuses from a lens down to awaist and then expands proportionally to x as shownin Fig 5 The wavefront radius of curvature whichwas infinite at x 0 will become finite and initiallydecrease with x At some point it will reach a mini-mum value and then it increases with larger x even-tually becoming proportional to x The equationsdescribing the Gaussian beam radius wx and thewavefront radius of curvature Rx are [1920]

wx wo

1

λx

πw2o

05

(11)

Rx x1

πw2

o

λx

2 (12)

where x is the distance propagated from the planewhere the wavefront is flat and wo 05ddiff o is theradius of the 1∕e2 irradiance contour at x 0 TheRayleigh range XR defined as the distance overthe beam radius by a factor of

2

p is given by [1920]

XR πw2o

λ (13)

DOF is the range of the image distance over whichthe focused spot diameter remains below an arbi-trary limit Normally it is defined as the distance

Fig 4 (a) Aberration- and diffraction-limited and (b) dominant spot size of convex plano lens

Fig 5 Focusing of Gaussian beam

20 February 2013 Vol 52 No 6 APPLIED OPTICS 1125

between2

pwo spot size points or 2 times Rayleigh

range [1920] For the finite conjugated lens it canbe written as [1920]

DOF 2timesXR 2timesπw2

o

λ 297πλM1f ∕2 (14)

It is clear from Eq (14) that the DOF is proportionalto the square of f∕

For the aspheric convex plano lens with two differ-ent f∕ the main lens characteristics are calculatedby using Eqs (9) (10) and (14) and their values aresummarized in Table 1 The quasi-optical lenseshave the spot diameter of 84 and 40 mm the SRof 62 and 30 mm and DOF of 766 and 173 mmfor high f∕ and low f ∕ respectively Howeverthe real beam pattern of the low f ∕ lens may be re-latively broad compared with the ideal pattern be-cause the SR cannot be less than a wavelength32 mm The theoretical results show that largerDOF requires larger f∕ lens even though it leadsto lower SR because of the larger focused beam

3 Design of W-band Quasi-Optical Lens Antenna

The quasi-optics configuration shown in Fig 6 consi-sts of a dielectric lens and a feed antenna An asphericconvex plano lens type is selected for a quasi-opticallens in the W-band imaging system because of itsadvantages of low manufacturing cost and loweraberration-limited blurring than the sphericalnonequiconvex and convex plano lens We designedtwo aspheric convex plano lenses with aperture size

of 350 mm in the region band using the optics designtool CODE V [23] Equation (15) shows the design for-mula for the aspheric convex surface and it is basedon the conic equation as follows

y x2

R1

11 kx2∕R2

p

ax4 bx6 cx8 dx10 (15)

where x and y are the design coordinates of the lenssurface The high-order coefficients of the conic equa-tion are a b c and d R is the radius of the asphericsurface and k is the conic constant The constant va-lues of the aspheric surface described in Table 2 areoptimized to achieve low spherical aberration Thedesigned two lenses have the different focal lengthwith the same diameter to analyze the quasi-opticalcharacteristics with respect to f -number which is theratio of the focal length over the diameter of the lensf ∕ F∕D The focal lengths of the designed asphericlenses with the lens diameter of 350 mm are 524 and326 mm corresponding to high f∕ of 150 and lowf ∕ of 093 The fabricated aspheric dielectric lensesare shown in Fig 7 For low weight and low dissipa-tion loss the lenses are made of HDPE material withthe refractive index of 15187 at 94 GHz [1720]

As a feed antenna of quasi-optics in Fig 6 the di-electric rod antenna (DRA) is adapted due to compactsize and high gain compared with a standard wave-guide type antenna in the MMW band We designedDRA which consists of a tapered dielectric rod and aWR-10 waveguide for good quasi-optical transforma-tion efficiency between a lens and a feed antennausing computer simulation technology microwavestudio simulator [24] The sharp dielectric rod ofDRA is made of acrylonitrile butadiene styrene ma-terial with refractive index of 16105 at 94 GHz [17]because this material is harder than HDPE used forDRA in [25] The fabricated DRA shown in Fig 8 isthe total length of about 30 mm The return loss andradiation pattern of DRA as shown in Figs 9(a) and9(b) are measured by HP 8510 vector network ana-lyzer and near-field measurement equipment Thereturn loss is below minus15 dB over the full W-bandand the H-plane radiation pattern has a gain of about153 dB the first side lobe level of below minus20 dB and10 dB beam widths of about 511deg at 94 GHz

Fig 6 (Color online) Configuration of quasi-optical lens antenna

Table 1 Theoretical Characteristics of Aspheric Lenses

CharacteristicsHigh f ∕

Lens(f ∕ 150)Low f ∕

Lens(f∕ 093)

D [mm] 350 350Si [mm] 561 265So [mm] 2500 2500F 458 240M 022 011f -number 13 07dblur [mm] 84 40rsp [mm] 62 30DOF [mm] 766 173

Table 2 Designed Constants of Aspheric Lenses

ConstantHigh f∕

Lens (f ∕ 150)Low f∕

Lens (f∕ 093)

R 271847 168998k minus0184 minus5761a minus2056eminus9 minus1123eminus7b minus5852eminus14 4229eminus12c 1458eminus18 minus1123eminus16d minus2625eminus23 1189eminus21

1126 APPLIED OPTICS Vol 52 No 6 20 February 2013

4 Measurement and Optical Performance Analysis ofQuasi-Optical Lens Antenna

The validation of the quasi-optical characteristics viaf -number of a lens is implemented in component-level and system-level test The test is mainlyfocused on measuring the main characteristics suchas focal length DOF beam spot size and SR of twomanufactured lenses

The component-level test is used to verify all oflens characteristics by measuring Gaussian beam

pattern of a lens Figure 10 shows the experimen-tal setup for component-level test of a lens [17]A W-band source and a DRA are applied as a trans-mitter AW-band power meter was attached to a DRAas a receiver antenna to measure the received powerTo test the focal length and DOF of the designedquasi-optical lenses the receiver was scanned on theoptical axis by scan step size of 1 mm to measure thereceived power through the image distance Si at thefixed object distance So 2500 mm In this test set-up the optimum image distance is the space from thelens to the receiver when themaximum output powerof the receiver was observed The experimental focallength and DOF of the lenses can be calculated byusing Eq (1) and by computing minus3 dB level rangeswhere the received power is 3 dB lower than themax-imum power at the optimum image distance Fortest of the beam spot size and SR of the lensesthe receiver was horizontally scanned on the originof the optimum image distance by scan step size of05 mm to measure the focused beam pattern onH-plane at So 2500 mm We can get the experi-mental beam spot diameter and SR of the lenses byusing minus86 dB level ranges and first inflection pointfrom the maximum power point of the measuredbeam pattern

Fig 7 (Color online) Photo of fabricated aspheric lenses with (a) high f∕ and (b) low f ∕ (Courtesy Millisys Inc)

Fig 8 (Color online) Fabricated DRA (Courtesy Millisys Inc)

Fig 9 Measurement results of DRA (a) return loss and (b) H-plane radiation pattern

20 February 2013 Vol 52 No 6 APPLIED OPTICS 1127

As for the results of component-level test theGaussian propagation beam pattern at 94 GHz viaimage distance is depicted in Fig 11 for two differentf ∕ lenses As shown in Fig 11(a) the image distanceSi 561 mm of the high f ∕ lens is measured atSo 2500 mm According to the distance informa-tion the focal length F of about 458 mm can becalculated by using Gaussian lens formula TheDOF of minus3 dB ranges is around 65 mm As shownin Fig 11(b) the measured image distance of the

low f ∕ lens is Si 265 mm at So 2500 mm Thisleads to a focal length of approximately 240 mm andDOF of about 23 mm Further the object distance isset by 2500 mm and then the measurement of thefocused H-plane beam patterns of the quasi-opticallenses on the image plane are performed at threedifferent frequencies of 90 94 and 100 GHz As de-picted in Fig 12 the focused H-plane beam patternsfor each high f∕ and low f ∕ lens are very similar atall frequencies The beam diameters at minus86 dBpoint are about 94 and 75 mm at 94 GHz for two

Fig 10 (Color online) Experimental setup of aspheric lens incomponent-level

Fig 11 Received power via image distance for (a) high f∕ and (b) low f ∕ lens at 94 GHz

Fig 12 (Color online) H-plane focused beam pattern of (a) high f∕ and (b) low f ∕ at So 2500 mm

Fig 13 (Color online) (a) Configuration and (b) signal flow of94 GHz radiometer imaging system

1128 APPLIED OPTICS Vol 52 No 6 20 February 2013

quasi-optical lenses The results of the component-level test demonstrate that larger f ∕ of a lens leadsto larger DOF although it induces larger beam spotsize and lower SR

The DOF can be also measured through system-level test using aW-band radiometer imaging systemwhose configuration and signal flow are shown inFig 13 The fabricated 94 GHz system consists ofquasi-optical lens antenna with a reflector mirrorradiometer receiver scanner and PC with a DAQThe performance of the imaging system are tempera-ture sensitivity of below 1 K [17] SR of about 064degand FOV of above 10deg times 10deg in W-band Figure 14shows the experimental setup for the system-leveltest of a quasi-optical lens The manufactured radio-meter imaging system is used to measure DOF oftwo designed quasi-optical lenses by getting W-bandradiometer images depending on the image distance

Fig 14 (Color online) Experimental setup of aspheric lens insystem-level test

Fig 15 Measured images and relative IC via image distance for (a) high and (b) low f ∕ lens

20 February 2013 Vol 52 No 6 APPLIED OPTICS 1129

at the fixed object distance So 2500 mm The DOFis the image distance ranges where the acceptablesharpness image is achieved It can be representedby image contrast (IC) which is given by

IC Voltage amplitudeVoltage average

Vmax minus Vmin

Vmax VminV∕V (16)

where Vmax and Vmin are the maximum and mini-mum output voltage of the receiver within a radio-meter image frame The DOF is the range between0707 points of IC via the image distance The circle-shaped Teflon plastic positioned at 25 m from thelens is used as a target and it is surrounded byabsorber sheets to reduce the effects of environmen-tal clutters on the image The measured images andIC for each image are shown in Fig 15 The IC via therelative image distance are first normalized by themaximum value and then interpolated due to widestep size compared with that of the component-leveltest The experimental DOF in the system-level testare 68 and 25 mm for high f ∕ and low f∕ lens asshown in Fig 16 The results are very similar to thatof the component-level test

All measurement data of the two lenses are sum-marized in Table 3 The measurement results showthat if the lens has higher f ∕ the lens will be largerSR and depth of field The experimental results andtrends are very well-matched with the theoreticaloutcomes However the difference between two datacan be caused by the difficulty to know exactly the

electrical characteristics of HDPE material used at94 GHz and the manufacturing error of the largeaperture aspheric lens In addition the experimentallimitations such as alignment and step size betweentest points causes the difference especially morecritical for low f∕ lens because of the relationshipbetween the lens characteristic and f∕

5 Conclusion

The quasi-optical characteristics via f∕ are theore-tically and experimentally analyzed in a MMW ima-ging system Two low aberration aspheric convexplano lenses are designed at 94 GHz and the lenseshave a diameter of 350 mm and different f ∕ of 13and 07 The experimental results show that theaveraged DOF is 66 and 24 mm and the SR is 67and 50 mm for high f∕ and low f ∕ lens It is con-formed that the large f ∕ lens gives large DOF to thequasi-optical imaging system The proper f ∕ of alens should be selected to complete sharpness imagefor a FPA imaging system because there is a tradeoffbetween the DOFand the SR This result can be usedas an important design guideline of the quasi-opticallens antenna for the MMW imaging system withlower SR compared to IR cameras

The work was supported by the basic research pro-gram from the Agency for Defense Development(ADD) and by the BK21 program at Gwangju Insti-tute of Science and Technology in the Republic ofKorea All radiometer hardware was manufacturedand supported by Millisys Inc (httpwwwmillisyscom)

References1 J P Samluk C A Schuetz T Dillon E L Stein A Robbins

D G Mackrides R D Martin J Wilson C Chen and D WPrather ldquoQ-band millimeter wave imaging in the far-fieldenabled by optical upconversion methodologyrdquo J InfraredMillimeter Terahertz Waves 33 54ndash66 (2012)

2 S Yeom D S Lee J Y Son M K Jung Y Jang S W Jungand S J Lee ldquoReal-time outdoor concealed-object detectionwith passive millimeter wave imagingrdquo Opt Express 192530ndash2536 (2011)

3 J J Lynch P A Macdonald H P Moyer and R G NageleldquoPassive millimeter wave imaging sensors for commercialmarketsrdquo Appl Opt 49 E7ndashE12 (2010)

Fig 16 Normalized IC via relative image distance for (a) high f∕ lens and (b) low f ∕ lens

Table 3 Experimental Results of Aspheric Lenses at 94 GHz

CharacteristicsHigh f∕ Lens(f ∕ 150)

Low f∕ Lens(f∕ 093)

D [mm] 350 350Si [mm] 561 265So [mm] 2500 2500F 458 240M 022 011f ∕ 13 07dblur [mm] 94 63rsp [mm] 67 50DOF [mm](componentsystem)

65∕68 23∕25

1130 APPLIED OPTICS Vol 52 No 6 20 February 2013

between2

pwo spot size points or 2 times Rayleigh

range [1920] For the finite conjugated lens it canbe written as [1920]

DOF 2timesXR 2timesπw2

o

λ 297πλM1f ∕2 (14)

It is clear from Eq (14) that the DOF is proportionalto the square of f∕

For the aspheric convex plano lens with two differ-ent f∕ the main lens characteristics are calculatedby using Eqs (9) (10) and (14) and their values aresummarized in Table 1 The quasi-optical lenseshave the spot diameter of 84 and 40 mm the SRof 62 and 30 mm and DOF of 766 and 173 mmfor high f∕ and low f ∕ respectively Howeverthe real beam pattern of the low f ∕ lens may be re-latively broad compared with the ideal pattern be-cause the SR cannot be less than a wavelength32 mm The theoretical results show that largerDOF requires larger f∕ lens even though it leadsto lower SR because of the larger focused beam

3 Design of W-band Quasi-Optical Lens Antenna

The quasi-optics configuration shown in Fig 6 consi-sts of a dielectric lens and a feed antenna An asphericconvex plano lens type is selected for a quasi-opticallens in the W-band imaging system because of itsadvantages of low manufacturing cost and loweraberration-limited blurring than the sphericalnonequiconvex and convex plano lens We designedtwo aspheric convex plano lenses with aperture size

of 350 mm in the region band using the optics designtool CODE V [23] Equation (15) shows the design for-mula for the aspheric convex surface and it is basedon the conic equation as follows

y x2

R1

11 kx2∕R2

p

ax4 bx6 cx8 dx10 (15)

where x and y are the design coordinates of the lenssurface The high-order coefficients of the conic equa-tion are a b c and d R is the radius of the asphericsurface and k is the conic constant The constant va-lues of the aspheric surface described in Table 2 areoptimized to achieve low spherical aberration Thedesigned two lenses have the different focal lengthwith the same diameter to analyze the quasi-opticalcharacteristics with respect to f -number which is theratio of the focal length over the diameter of the lensf ∕ F∕D The focal lengths of the designed asphericlenses with the lens diameter of 350 mm are 524 and326 mm corresponding to high f∕ of 150 and lowf ∕ of 093 The fabricated aspheric dielectric lensesare shown in Fig 7 For low weight and low dissipa-tion loss the lenses are made of HDPE material withthe refractive index of 15187 at 94 GHz [1720]

As a feed antenna of quasi-optics in Fig 6 the di-electric rod antenna (DRA) is adapted due to compactsize and high gain compared with a standard wave-guide type antenna in the MMW band We designedDRA which consists of a tapered dielectric rod and aWR-10 waveguide for good quasi-optical transforma-tion efficiency between a lens and a feed antennausing computer simulation technology microwavestudio simulator [24] The sharp dielectric rod ofDRA is made of acrylonitrile butadiene styrene ma-terial with refractive index of 16105 at 94 GHz [17]because this material is harder than HDPE used forDRA in [25] The fabricated DRA shown in Fig 8 isthe total length of about 30 mm The return loss andradiation pattern of DRA as shown in Figs 9(a) and9(b) are measured by HP 8510 vector network ana-lyzer and near-field measurement equipment Thereturn loss is below minus15 dB over the full W-bandand the H-plane radiation pattern has a gain of about153 dB the first side lobe level of below minus20 dB and10 dB beam widths of about 511deg at 94 GHz

Fig 6 (Color online) Configuration of quasi-optical lens antenna

Table 1 Theoretical Characteristics of Aspheric Lenses

CharacteristicsHigh f ∕

Lens(f ∕ 150)Low f ∕

Lens(f∕ 093)

D [mm] 350 350Si [mm] 561 265So [mm] 2500 2500F 458 240M 022 011f -number 13 07dblur [mm] 84 40rsp [mm] 62 30DOF [mm] 766 173

Table 2 Designed Constants of Aspheric Lenses

ConstantHigh f∕

Lens (f ∕ 150)Low f∕

Lens (f∕ 093)

R 271847 168998k minus0184 minus5761a minus2056eminus9 minus1123eminus7b minus5852eminus14 4229eminus12c 1458eminus18 minus1123eminus16d minus2625eminus23 1189eminus21

1126 APPLIED OPTICS Vol 52 No 6 20 February 2013

4 Measurement and Optical Performance Analysis ofQuasi-Optical Lens Antenna

The validation of the quasi-optical characteristics viaf -number of a lens is implemented in component-level and system-level test The test is mainlyfocused on measuring the main characteristics suchas focal length DOF beam spot size and SR of twomanufactured lenses

The component-level test is used to verify all oflens characteristics by measuring Gaussian beam

pattern of a lens Figure 10 shows the experimen-tal setup for component-level test of a lens [17]A W-band source and a DRA are applied as a trans-mitter AW-band power meter was attached to a DRAas a receiver antenna to measure the received powerTo test the focal length and DOF of the designedquasi-optical lenses the receiver was scanned on theoptical axis by scan step size of 1 mm to measure thereceived power through the image distance Si at thefixed object distance So 2500 mm In this test set-up the optimum image distance is the space from thelens to the receiver when themaximum output powerof the receiver was observed The experimental focallength and DOF of the lenses can be calculated byusing Eq (1) and by computing minus3 dB level rangeswhere the received power is 3 dB lower than themax-imum power at the optimum image distance Fortest of the beam spot size and SR of the lensesthe receiver was horizontally scanned on the originof the optimum image distance by scan step size of05 mm to measure the focused beam pattern onH-plane at So 2500 mm We can get the experi-mental beam spot diameter and SR of the lenses byusing minus86 dB level ranges and first inflection pointfrom the maximum power point of the measuredbeam pattern

Fig 7 (Color online) Photo of fabricated aspheric lenses with (a) high f∕ and (b) low f ∕ (Courtesy Millisys Inc)

Fig 8 (Color online) Fabricated DRA (Courtesy Millisys Inc)

Fig 9 Measurement results of DRA (a) return loss and (b) H-plane radiation pattern

20 February 2013 Vol 52 No 6 APPLIED OPTICS 1127

As for the results of component-level test theGaussian propagation beam pattern at 94 GHz viaimage distance is depicted in Fig 11 for two differentf ∕ lenses As shown in Fig 11(a) the image distanceSi 561 mm of the high f ∕ lens is measured atSo 2500 mm According to the distance informa-tion the focal length F of about 458 mm can becalculated by using Gaussian lens formula TheDOF of minus3 dB ranges is around 65 mm As shownin Fig 11(b) the measured image distance of the

low f ∕ lens is Si 265 mm at So 2500 mm Thisleads to a focal length of approximately 240 mm andDOF of about 23 mm Further the object distance isset by 2500 mm and then the measurement of thefocused H-plane beam patterns of the quasi-opticallenses on the image plane are performed at threedifferent frequencies of 90 94 and 100 GHz As de-picted in Fig 12 the focused H-plane beam patternsfor each high f∕ and low f ∕ lens are very similar atall frequencies The beam diameters at minus86 dBpoint are about 94 and 75 mm at 94 GHz for two

Fig 10 (Color online) Experimental setup of aspheric lens incomponent-level

Fig 11 Received power via image distance for (a) high f∕ and (b) low f ∕ lens at 94 GHz

Fig 12 (Color online) H-plane focused beam pattern of (a) high f∕ and (b) low f ∕ at So 2500 mm

Fig 13 (Color online) (a) Configuration and (b) signal flow of94 GHz radiometer imaging system

1128 APPLIED OPTICS Vol 52 No 6 20 February 2013

quasi-optical lenses The results of the component-level test demonstrate that larger f ∕ of a lens leadsto larger DOF although it induces larger beam spotsize and lower SR

The DOF can be also measured through system-level test using aW-band radiometer imaging systemwhose configuration and signal flow are shown inFig 13 The fabricated 94 GHz system consists ofquasi-optical lens antenna with a reflector mirrorradiometer receiver scanner and PC with a DAQThe performance of the imaging system are tempera-ture sensitivity of below 1 K [17] SR of about 064degand FOV of above 10deg times 10deg in W-band Figure 14shows the experimental setup for the system-leveltest of a quasi-optical lens The manufactured radio-meter imaging system is used to measure DOF oftwo designed quasi-optical lenses by getting W-bandradiometer images depending on the image distance

Fig 14 (Color online) Experimental setup of aspheric lens insystem-level test

Fig 15 Measured images and relative IC via image distance for (a) high and (b) low f ∕ lens

20 February 2013 Vol 52 No 6 APPLIED OPTICS 1129

at the fixed object distance So 2500 mm The DOFis the image distance ranges where the acceptablesharpness image is achieved It can be representedby image contrast (IC) which is given by

IC Voltage amplitudeVoltage average

Vmax minus Vmin

Vmax VminV∕V (16)

where Vmax and Vmin are the maximum and mini-mum output voltage of the receiver within a radio-meter image frame The DOF is the range between0707 points of IC via the image distance The circle-shaped Teflon plastic positioned at 25 m from thelens is used as a target and it is surrounded byabsorber sheets to reduce the effects of environmen-tal clutters on the image The measured images andIC for each image are shown in Fig 15 The IC via therelative image distance are first normalized by themaximum value and then interpolated due to widestep size compared with that of the component-leveltest The experimental DOF in the system-level testare 68 and 25 mm for high f ∕ and low f∕ lens asshown in Fig 16 The results are very similar to thatof the component-level test

All measurement data of the two lenses are sum-marized in Table 3 The measurement results showthat if the lens has higher f ∕ the lens will be largerSR and depth of field The experimental results andtrends are very well-matched with the theoreticaloutcomes However the difference between two datacan be caused by the difficulty to know exactly the

electrical characteristics of HDPE material used at94 GHz and the manufacturing error of the largeaperture aspheric lens In addition the experimentallimitations such as alignment and step size betweentest points causes the difference especially morecritical for low f∕ lens because of the relationshipbetween the lens characteristic and f∕

5 Conclusion

The quasi-optical characteristics via f∕ are theore-tically and experimentally analyzed in a MMW ima-ging system Two low aberration aspheric convexplano lenses are designed at 94 GHz and the lenseshave a diameter of 350 mm and different f ∕ of 13and 07 The experimental results show that theaveraged DOF is 66 and 24 mm and the SR is 67and 50 mm for high f∕ and low f ∕ lens It is con-formed that the large f ∕ lens gives large DOF to thequasi-optical imaging system The proper f ∕ of alens should be selected to complete sharpness imagefor a FPA imaging system because there is a tradeoffbetween the DOFand the SR This result can be usedas an important design guideline of the quasi-opticallens antenna for the MMW imaging system withlower SR compared to IR cameras

The work was supported by the basic research pro-gram from the Agency for Defense Development(ADD) and by the BK21 program at Gwangju Insti-tute of Science and Technology in the Republic ofKorea All radiometer hardware was manufacturedand supported by Millisys Inc (httpwwwmillisyscom)

References1 J P Samluk C A Schuetz T Dillon E L Stein A Robbins

D G Mackrides R D Martin J Wilson C Chen and D WPrather ldquoQ-band millimeter wave imaging in the far-fieldenabled by optical upconversion methodologyrdquo J InfraredMillimeter Terahertz Waves 33 54ndash66 (2012)

2 S Yeom D S Lee J Y Son M K Jung Y Jang S W Jungand S J Lee ldquoReal-time outdoor concealed-object detectionwith passive millimeter wave imagingrdquo Opt Express 192530ndash2536 (2011)

3 J J Lynch P A Macdonald H P Moyer and R G NageleldquoPassive millimeter wave imaging sensors for commercialmarketsrdquo Appl Opt 49 E7ndashE12 (2010)

Fig 16 Normalized IC via relative image distance for (a) high f∕ lens and (b) low f ∕ lens

Table 3 Experimental Results of Aspheric Lenses at 94 GHz

CharacteristicsHigh f∕ Lens(f ∕ 150)

Low f∕ Lens(f∕ 093)

D [mm] 350 350Si [mm] 561 265So [mm] 2500 2500F 458 240M 022 011f ∕ 13 07dblur [mm] 94 63rsp [mm] 67 50DOF [mm](componentsystem)

65∕68 23∕25

1130 APPLIED OPTICS Vol 52 No 6 20 February 2013

4 Measurement and Optical Performance Analysis ofQuasi-Optical Lens Antenna

The validation of the quasi-optical characteristics viaf -number of a lens is implemented in component-level and system-level test The test is mainlyfocused on measuring the main characteristics suchas focal length DOF beam spot size and SR of twomanufactured lenses

The component-level test is used to verify all oflens characteristics by measuring Gaussian beam

pattern of a lens Figure 10 shows the experimen-tal setup for component-level test of a lens [17]A W-band source and a DRA are applied as a trans-mitter AW-band power meter was attached to a DRAas a receiver antenna to measure the received powerTo test the focal length and DOF of the designedquasi-optical lenses the receiver was scanned on theoptical axis by scan step size of 1 mm to measure thereceived power through the image distance Si at thefixed object distance So 2500 mm In this test set-up the optimum image distance is the space from thelens to the receiver when themaximum output powerof the receiver was observed The experimental focallength and DOF of the lenses can be calculated byusing Eq (1) and by computing minus3 dB level rangeswhere the received power is 3 dB lower than themax-imum power at the optimum image distance Fortest of the beam spot size and SR of the lensesthe receiver was horizontally scanned on the originof the optimum image distance by scan step size of05 mm to measure the focused beam pattern onH-plane at So 2500 mm We can get the experi-mental beam spot diameter and SR of the lenses byusing minus86 dB level ranges and first inflection pointfrom the maximum power point of the measuredbeam pattern

Fig 7 (Color online) Photo of fabricated aspheric lenses with (a) high f∕ and (b) low f ∕ (Courtesy Millisys Inc)

Fig 8 (Color online) Fabricated DRA (Courtesy Millisys Inc)

Fig 9 Measurement results of DRA (a) return loss and (b) H-plane radiation pattern

20 February 2013 Vol 52 No 6 APPLIED OPTICS 1127

As for the results of component-level test theGaussian propagation beam pattern at 94 GHz viaimage distance is depicted in Fig 11 for two differentf ∕ lenses As shown in Fig 11(a) the image distanceSi 561 mm of the high f ∕ lens is measured atSo 2500 mm According to the distance informa-tion the focal length F of about 458 mm can becalculated by using Gaussian lens formula TheDOF of minus3 dB ranges is around 65 mm As shownin Fig 11(b) the measured image distance of the

low f ∕ lens is Si 265 mm at So 2500 mm Thisleads to a focal length of approximately 240 mm andDOF of about 23 mm Further the object distance isset by 2500 mm and then the measurement of thefocused H-plane beam patterns of the quasi-opticallenses on the image plane are performed at threedifferent frequencies of 90 94 and 100 GHz As de-picted in Fig 12 the focused H-plane beam patternsfor each high f∕ and low f ∕ lens are very similar atall frequencies The beam diameters at minus86 dBpoint are about 94 and 75 mm at 94 GHz for two

Fig 10 (Color online) Experimental setup of aspheric lens incomponent-level

Fig 11 Received power via image distance for (a) high f∕ and (b) low f ∕ lens at 94 GHz

Fig 12 (Color online) H-plane focused beam pattern of (a) high f∕ and (b) low f ∕ at So 2500 mm

Fig 13 (Color online) (a) Configuration and (b) signal flow of94 GHz radiometer imaging system

1128 APPLIED OPTICS Vol 52 No 6 20 February 2013

quasi-optical lenses The results of the component-level test demonstrate that larger f ∕ of a lens leadsto larger DOF although it induces larger beam spotsize and lower SR

The DOF can be also measured through system-level test using aW-band radiometer imaging systemwhose configuration and signal flow are shown inFig 13 The fabricated 94 GHz system consists ofquasi-optical lens antenna with a reflector mirrorradiometer receiver scanner and PC with a DAQThe performance of the imaging system are tempera-ture sensitivity of below 1 K [17] SR of about 064degand FOV of above 10deg times 10deg in W-band Figure 14shows the experimental setup for the system-leveltest of a quasi-optical lens The manufactured radio-meter imaging system is used to measure DOF oftwo designed quasi-optical lenses by getting W-bandradiometer images depending on the image distance

Fig 14 (Color online) Experimental setup of aspheric lens insystem-level test

Fig 15 Measured images and relative IC via image distance for (a) high and (b) low f ∕ lens

20 February 2013 Vol 52 No 6 APPLIED OPTICS 1129

at the fixed object distance So 2500 mm The DOFis the image distance ranges where the acceptablesharpness image is achieved It can be representedby image contrast (IC) which is given by

IC Voltage amplitudeVoltage average

Vmax minus Vmin

Vmax VminV∕V (16)

where Vmax and Vmin are the maximum and mini-mum output voltage of the receiver within a radio-meter image frame The DOF is the range between0707 points of IC via the image distance The circle-shaped Teflon plastic positioned at 25 m from thelens is used as a target and it is surrounded byabsorber sheets to reduce the effects of environmen-tal clutters on the image The measured images andIC for each image are shown in Fig 15 The IC via therelative image distance are first normalized by themaximum value and then interpolated due to widestep size compared with that of the component-leveltest The experimental DOF in the system-level testare 68 and 25 mm for high f ∕ and low f∕ lens asshown in Fig 16 The results are very similar to thatof the component-level test

All measurement data of the two lenses are sum-marized in Table 3 The measurement results showthat if the lens has higher f ∕ the lens will be largerSR and depth of field The experimental results andtrends are very well-matched with the theoreticaloutcomes However the difference between two datacan be caused by the difficulty to know exactly the

electrical characteristics of HDPE material used at94 GHz and the manufacturing error of the largeaperture aspheric lens In addition the experimentallimitations such as alignment and step size betweentest points causes the difference especially morecritical for low f∕ lens because of the relationshipbetween the lens characteristic and f∕

5 Conclusion

The quasi-optical characteristics via f∕ are theore-tically and experimentally analyzed in a MMW ima-ging system Two low aberration aspheric convexplano lenses are designed at 94 GHz and the lenseshave a diameter of 350 mm and different f ∕ of 13and 07 The experimental results show that theaveraged DOF is 66 and 24 mm and the SR is 67and 50 mm for high f∕ and low f ∕ lens It is con-formed that the large f ∕ lens gives large DOF to thequasi-optical imaging system The proper f ∕ of alens should be selected to complete sharpness imagefor a FPA imaging system because there is a tradeoffbetween the DOFand the SR This result can be usedas an important design guideline of the quasi-opticallens antenna for the MMW imaging system withlower SR compared to IR cameras

The work was supported by the basic research pro-gram from the Agency for Defense Development(ADD) and by the BK21 program at Gwangju Insti-tute of Science and Technology in the Republic ofKorea All radiometer hardware was manufacturedand supported by Millisys Inc (httpwwwmillisyscom)

References1 J P Samluk C A Schuetz T Dillon E L Stein A Robbins

D G Mackrides R D Martin J Wilson C Chen and D WPrather ldquoQ-band millimeter wave imaging in the far-fieldenabled by optical upconversion methodologyrdquo J InfraredMillimeter Terahertz Waves 33 54ndash66 (2012)

2 S Yeom D S Lee J Y Son M K Jung Y Jang S W Jungand S J Lee ldquoReal-time outdoor concealed-object detectionwith passive millimeter wave imagingrdquo Opt Express 192530ndash2536 (2011)

3 J J Lynch P A Macdonald H P Moyer and R G NageleldquoPassive millimeter wave imaging sensors for commercialmarketsrdquo Appl Opt 49 E7ndashE12 (2010)

Fig 16 Normalized IC via relative image distance for (a) high f∕ lens and (b) low f ∕ lens

Table 3 Experimental Results of Aspheric Lenses at 94 GHz

CharacteristicsHigh f∕ Lens(f ∕ 150)

Low f∕ Lens(f∕ 093)

D [mm] 350 350Si [mm] 561 265So [mm] 2500 2500F 458 240M 022 011f ∕ 13 07dblur [mm] 94 63rsp [mm] 67 50DOF [mm](componentsystem)

65∕68 23∕25

1130 APPLIED OPTICS Vol 52 No 6 20 February 2013

As for the results of component-level test theGaussian propagation beam pattern at 94 GHz viaimage distance is depicted in Fig 11 for two differentf ∕ lenses As shown in Fig 11(a) the image distanceSi 561 mm of the high f ∕ lens is measured atSo 2500 mm According to the distance informa-tion the focal length F of about 458 mm can becalculated by using Gaussian lens formula TheDOF of minus3 dB ranges is around 65 mm As shownin Fig 11(b) the measured image distance of the

low f ∕ lens is Si 265 mm at So 2500 mm Thisleads to a focal length of approximately 240 mm andDOF of about 23 mm Further the object distance isset by 2500 mm and then the measurement of thefocused H-plane beam patterns of the quasi-opticallenses on the image plane are performed at threedifferent frequencies of 90 94 and 100 GHz As de-picted in Fig 12 the focused H-plane beam patternsfor each high f∕ and low f ∕ lens are very similar atall frequencies The beam diameters at minus86 dBpoint are about 94 and 75 mm at 94 GHz for two

Fig 10 (Color online) Experimental setup of aspheric lens incomponent-level

Fig 11 Received power via image distance for (a) high f∕ and (b) low f ∕ lens at 94 GHz

Fig 12 (Color online) H-plane focused beam pattern of (a) high f∕ and (b) low f ∕ at So 2500 mm

Fig 13 (Color online) (a) Configuration and (b) signal flow of94 GHz radiometer imaging system

1128 APPLIED OPTICS Vol 52 No 6 20 February 2013

quasi-optical lenses The results of the component-level test demonstrate that larger f ∕ of a lens leadsto larger DOF although it induces larger beam spotsize and lower SR

The DOF can be also measured through system-level test using aW-band radiometer imaging systemwhose configuration and signal flow are shown inFig 13 The fabricated 94 GHz system consists ofquasi-optical lens antenna with a reflector mirrorradiometer receiver scanner and PC with a DAQThe performance of the imaging system are tempera-ture sensitivity of below 1 K [17] SR of about 064degand FOV of above 10deg times 10deg in W-band Figure 14shows the experimental setup for the system-leveltest of a quasi-optical lens The manufactured radio-meter imaging system is used to measure DOF oftwo designed quasi-optical lenses by getting W-bandradiometer images depending on the image distance

Fig 14 (Color online) Experimental setup of aspheric lens insystem-level test

Fig 15 Measured images and relative IC via image distance for (a) high and (b) low f ∕ lens

20 February 2013 Vol 52 No 6 APPLIED OPTICS 1129

at the fixed object distance So 2500 mm The DOFis the image distance ranges where the acceptablesharpness image is achieved It can be representedby image contrast (IC) which is given by

IC Voltage amplitudeVoltage average

Vmax minus Vmin

Vmax VminV∕V (16)

where Vmax and Vmin are the maximum and mini-mum output voltage of the receiver within a radio-meter image frame The DOF is the range between0707 points of IC via the image distance The circle-shaped Teflon plastic positioned at 25 m from thelens is used as a target and it is surrounded byabsorber sheets to reduce the effects of environmen-tal clutters on the image The measured images andIC for each image are shown in Fig 15 The IC via therelative image distance are first normalized by themaximum value and then interpolated due to widestep size compared with that of the component-leveltest The experimental DOF in the system-level testare 68 and 25 mm for high f ∕ and low f∕ lens asshown in Fig 16 The results are very similar to thatof the component-level test

All measurement data of the two lenses are sum-marized in Table 3 The measurement results showthat if the lens has higher f ∕ the lens will be largerSR and depth of field The experimental results andtrends are very well-matched with the theoreticaloutcomes However the difference between two datacan be caused by the difficulty to know exactly the

electrical characteristics of HDPE material used at94 GHz and the manufacturing error of the largeaperture aspheric lens In addition the experimentallimitations such as alignment and step size betweentest points causes the difference especially morecritical for low f∕ lens because of the relationshipbetween the lens characteristic and f∕

5 Conclusion

The quasi-optical characteristics via f∕ are theore-tically and experimentally analyzed in a MMW ima-ging system Two low aberration aspheric convexplano lenses are designed at 94 GHz and the lenseshave a diameter of 350 mm and different f ∕ of 13and 07 The experimental results show that theaveraged DOF is 66 and 24 mm and the SR is 67and 50 mm for high f∕ and low f ∕ lens It is con-formed that the large f ∕ lens gives large DOF to thequasi-optical imaging system The proper f ∕ of alens should be selected to complete sharpness imagefor a FPA imaging system because there is a tradeoffbetween the DOFand the SR This result can be usedas an important design guideline of the quasi-opticallens antenna for the MMW imaging system withlower SR compared to IR cameras

The work was supported by the basic research pro-gram from the Agency for Defense Development(ADD) and by the BK21 program at Gwangju Insti-tute of Science and Technology in the Republic ofKorea All radiometer hardware was manufacturedand supported by Millisys Inc (httpwwwmillisyscom)

References1 J P Samluk C A Schuetz T Dillon E L Stein A Robbins

D G Mackrides R D Martin J Wilson C Chen and D WPrather ldquoQ-band millimeter wave imaging in the far-fieldenabled by optical upconversion methodologyrdquo J InfraredMillimeter Terahertz Waves 33 54ndash66 (2012)

2 S Yeom D S Lee J Y Son M K Jung Y Jang S W Jungand S J Lee ldquoReal-time outdoor concealed-object detectionwith passive millimeter wave imagingrdquo Opt Express 192530ndash2536 (2011)

3 J J Lynch P A Macdonald H P Moyer and R G NageleldquoPassive millimeter wave imaging sensors for commercialmarketsrdquo Appl Opt 49 E7ndashE12 (2010)

Fig 16 Normalized IC via relative image distance for (a) high f∕ lens and (b) low f ∕ lens

Table 3 Experimental Results of Aspheric Lenses at 94 GHz

CharacteristicsHigh f∕ Lens(f ∕ 150)

Low f∕ Lens(f∕ 093)

D [mm] 350 350Si [mm] 561 265So [mm] 2500 2500F 458 240M 022 011f ∕ 13 07dblur [mm] 94 63rsp [mm] 67 50DOF [mm](componentsystem)

65∕68 23∕25

1130 APPLIED OPTICS Vol 52 No 6 20 February 2013

quasi-optical lenses The results of the component-level test demonstrate that larger f ∕ of a lens leadsto larger DOF although it induces larger beam spotsize and lower SR

The DOF can be also measured through system-level test using aW-band radiometer imaging systemwhose configuration and signal flow are shown inFig 13 The fabricated 94 GHz system consists ofquasi-optical lens antenna with a reflector mirrorradiometer receiver scanner and PC with a DAQThe performance of the imaging system are tempera-ture sensitivity of below 1 K [17] SR of about 064degand FOV of above 10deg times 10deg in W-band Figure 14shows the experimental setup for the system-leveltest of a quasi-optical lens The manufactured radio-meter imaging system is used to measure DOF oftwo designed quasi-optical lenses by getting W-bandradiometer images depending on the image distance

Fig 14 (Color online) Experimental setup of aspheric lens insystem-level test

Fig 15 Measured images and relative IC via image distance for (a) high and (b) low f ∕ lens

20 February 2013 Vol 52 No 6 APPLIED OPTICS 1129

at the fixed object distance So 2500 mm The DOFis the image distance ranges where the acceptablesharpness image is achieved It can be representedby image contrast (IC) which is given by

IC Voltage amplitudeVoltage average

Vmax minus Vmin

Vmax VminV∕V (16)

where Vmax and Vmin are the maximum and mini-mum output voltage of the receiver within a radio-meter image frame The DOF is the range between0707 points of IC via the image distance The circle-shaped Teflon plastic positioned at 25 m from thelens is used as a target and it is surrounded byabsorber sheets to reduce the effects of environmen-tal clutters on the image The measured images andIC for each image are shown in Fig 15 The IC via therelative image distance are first normalized by themaximum value and then interpolated due to widestep size compared with that of the component-leveltest The experimental DOF in the system-level testare 68 and 25 mm for high f ∕ and low f∕ lens asshown in Fig 16 The results are very similar to thatof the component-level test

All measurement data of the two lenses are sum-marized in Table 3 The measurement results showthat if the lens has higher f ∕ the lens will be largerSR and depth of field The experimental results andtrends are very well-matched with the theoreticaloutcomes However the difference between two datacan be caused by the difficulty to know exactly the

electrical characteristics of HDPE material used at94 GHz and the manufacturing error of the largeaperture aspheric lens In addition the experimentallimitations such as alignment and step size betweentest points causes the difference especially morecritical for low f∕ lens because of the relationshipbetween the lens characteristic and f∕

5 Conclusion

The quasi-optical characteristics via f∕ are theore-tically and experimentally analyzed in a MMW ima-ging system Two low aberration aspheric convexplano lenses are designed at 94 GHz and the lenseshave a diameter of 350 mm and different f ∕ of 13and 07 The experimental results show that theaveraged DOF is 66 and 24 mm and the SR is 67and 50 mm for high f∕ and low f ∕ lens It is con-formed that the large f ∕ lens gives large DOF to thequasi-optical imaging system The proper f ∕ of alens should be selected to complete sharpness imagefor a FPA imaging system because there is a tradeoffbetween the DOFand the SR This result can be usedas an important design guideline of the quasi-opticallens antenna for the MMW imaging system withlower SR compared to IR cameras

The work was supported by the basic research pro-gram from the Agency for Defense Development(ADD) and by the BK21 program at Gwangju Insti-tute of Science and Technology in the Republic ofKorea All radiometer hardware was manufacturedand supported by Millisys Inc (httpwwwmillisyscom)

References1 J P Samluk C A Schuetz T Dillon E L Stein A Robbins

D G Mackrides R D Martin J Wilson C Chen and D WPrather ldquoQ-band millimeter wave imaging in the far-fieldenabled by optical upconversion methodologyrdquo J InfraredMillimeter Terahertz Waves 33 54ndash66 (2012)

2 S Yeom D S Lee J Y Son M K Jung Y Jang S W Jungand S J Lee ldquoReal-time outdoor concealed-object detectionwith passive millimeter wave imagingrdquo Opt Express 192530ndash2536 (2011)

3 J J Lynch P A Macdonald H P Moyer and R G NageleldquoPassive millimeter wave imaging sensors for commercialmarketsrdquo Appl Opt 49 E7ndashE12 (2010)

Fig 16 Normalized IC via relative image distance for (a) high f∕ lens and (b) low f ∕ lens

Table 3 Experimental Results of Aspheric Lenses at 94 GHz

CharacteristicsHigh f∕ Lens(f ∕ 150)

Low f∕ Lens(f∕ 093)

D [mm] 350 350Si [mm] 561 265So [mm] 2500 2500F 458 240M 022 011f ∕ 13 07dblur [mm] 94 63rsp [mm] 67 50DOF [mm](componentsystem)

65∕68 23∕25

1130 APPLIED OPTICS Vol 52 No 6 20 February 2013

at the fixed object distance So 2500 mm The DOFis the image distance ranges where the acceptablesharpness image is achieved It can be representedby image contrast (IC) which is given by

IC Voltage amplitudeVoltage average

Vmax minus Vmin

Vmax VminV∕V (16)

where Vmax and Vmin are the maximum and mini-mum output voltage of the receiver within a radio-meter image frame The DOF is the range between0707 points of IC via the image distance The circle-shaped Teflon plastic positioned at 25 m from thelens is used as a target and it is surrounded byabsorber sheets to reduce the effects of environmen-tal clutters on the image The measured images andIC for each image are shown in Fig 15 The IC via therelative image distance are first normalized by themaximum value and then interpolated due to widestep size compared with that of the component-leveltest The experimental DOF in the system-level testare 68 and 25 mm for high f ∕ and low f∕ lens asshown in Fig 16 The results are very similar to thatof the component-level test

All measurement data of the two lenses are sum-marized in Table 3 The measurement results showthat if the lens has higher f ∕ the lens will be largerSR and depth of field The experimental results andtrends are very well-matched with the theoreticaloutcomes However the difference between two datacan be caused by the difficulty to know exactly the

electrical characteristics of HDPE material used at94 GHz and the manufacturing error of the largeaperture aspheric lens In addition the experimentallimitations such as alignment and step size betweentest points causes the difference especially morecritical for low f∕ lens because of the relationshipbetween the lens characteristic and f∕

5 Conclusion

The quasi-optical characteristics via f∕ are theore-tically and experimentally analyzed in a MMW ima-ging system Two low aberration aspheric convexplano lenses are designed at 94 GHz and the lenseshave a diameter of 350 mm and different f ∕ of 13and 07 The experimental results show that theaveraged DOF is 66 and 24 mm and the SR is 67and 50 mm for high f∕ and low f ∕ lens It is con-formed that the large f ∕ lens gives large DOF to thequasi-optical imaging system The proper f ∕ of alens should be selected to complete sharpness imagefor a FPA imaging system because there is a tradeoffbetween the DOFand the SR This result can be usedas an important design guideline of the quasi-opticallens antenna for the MMW imaging system withlower SR compared to IR cameras

The work was supported by the basic research pro-gram from the Agency for Defense Development(ADD) and by the BK21 program at Gwangju Insti-tute of Science and Technology in the Republic ofKorea All radiometer hardware was manufacturedand supported by Millisys Inc (httpwwwmillisyscom)

References1 J P Samluk C A Schuetz T Dillon E L Stein A Robbins

D G Mackrides R D Martin J Wilson C Chen and D WPrather ldquoQ-band millimeter wave imaging in the far-fieldenabled by optical upconversion methodologyrdquo J InfraredMillimeter Terahertz Waves 33 54ndash66 (2012)

2 S Yeom D S Lee J Y Son M K Jung Y Jang S W Jungand S J Lee ldquoReal-time outdoor concealed-object detectionwith passive millimeter wave imagingrdquo Opt Express 192530ndash2536 (2011)

3 J J Lynch P A Macdonald H P Moyer and R G NageleldquoPassive millimeter wave imaging sensors for commercialmarketsrdquo Appl Opt 49 E7ndashE12 (2010)

Fig 16 Normalized IC via relative image distance for (a) high f∕ lens and (b) low f ∕ lens

Table 3 Experimental Results of Aspheric Lenses at 94 GHz

CharacteristicsHigh f∕ Lens(f ∕ 150)

Low f∕ Lens(f∕ 093)

D [mm] 350 350Si [mm] 561 265So [mm] 2500 2500F 458 240M 022 011f ∕ 13 07dblur [mm] 94 63rsp [mm] 67 50DOF [mm](componentsystem)

65∕68 23∕25

1130 APPLIED OPTICS Vol 52 No 6 20 February 2013

4 C F Cull D A Wikner J N Mait M Mattheiss and D JBrady ldquoMillimeter-wave compressive holographyrdquo ApplOpt 49 E67ndashE82 (2010)

5 S Y Li B L Ren H J Sun W D Hu and X Lv ldquoModifiedwavenumber domain algorithm for three-dimensional milli-meter-wave imagingrdquo Prog Electromagn Res 124 35ndash53(2012)

6 F Gumbmann and L P Schmidt ldquoMillimeter-wave imagingwith optimized sparse periodic array for short-range applica-tionsrdquo IEEE Trans Geosci Remote Sens 49 3629ndash3638(2011)

7 K Haddadi D Glay and T Lasri ldquoA 60 Ghz scanningnear-field microscope with high spatial resolution sub-surfaceimagingrdquo IEEE Microw Wireless Compon Lett 21 625ndash627(2011)

8 F Qi V Tavakol I Ocket P Xu D Schreurs J K Wang andB Nauwelaers ldquoMillimeter wave imaging system modelingspatial frequency domain calculation versus spatial domaincalculationrdquo J Opt Soc Am A 27 131ndash140 (2010)

9 N N Wang J H Qiu P Y Zhang and W B Deng ldquoPassivemillimeter wave focal plane array imaging technologyrdquoJ Infrared Millimeter Waves 30 419ndash424 (2011)

10 E L Jacobs and O Furxhi ldquoTarget identification and naviga-tion performance modeling of a passive millimeter waveimagerrdquo Appl Opt 49 E94ndashE105 (2010)

11 F Qi V Tavakol D Schreurs and B Nauwelaers ldquoLimita-tions of approximations towards Fourier optics for indooractive millimeter wave imaging systemsrdquo Prog ElectromagnRes 109 245ndash262 (2010)

12 F Hu and Y Feng ldquoPassive millimeter wave focal planeimaging method combined with interferometryrdquo J InfraredMillimeter Waves 28 382ndash385 (2009)

13 A Rolland M Ettorre A V Boriskin L Le Coq andR Sauleau ldquoAxisymmetric resonant lens antenna withimproved directivity in Ka- bandrdquo IEEE Antennas WirelessPropag Lett 10 37ndash40 (2011)

14 Z X Wang and W B Dou ldquoFull-wave analysis of monopulsedielectric lens antennas at W-bandrdquo J Infrared MillimeterTerahertz Waves 31 151ndash161 (2010)

15 B Fuchs R Golubovic A K Skrivervik and J R MosigldquoSpherical lens antenna designs with particle swarm optimi-zationrdquo Microw Opt Technol Lett 52 1655ndash1659 (2010)

16 A H Lettington D Dunn M Attia and I M Blankson ldquoPas-sive millimetre-wave imaging architecturesrdquo J Opt A 5S103ndashS110 (2003)

17 W G Kim N W Moon J M Kang and Y H Kim ldquoLoss mea-suring of large aperture quasi-optics for W-band imaging radio-meter systemrdquo Prog Electromagn Res 125 295ndash309 (2012)

18 C D Meinhart and S T Wereley ldquoThe theory of diffraction-limited resolution in microparticle image velocimetryrdquo MeasSci Technol 14 1047ndash1053 (2003)

19 Technical guide on fundamental optics httpwwwcvimellesgriotcom

20 P F Goldsmith Quasi-optical Systems Gaussian Beam Quasi-optical Propagation and Applications 4th ed (IEEE 1998)

21 Technical document about lens theory from httpwwwlasercomponentscomde

22 G D Boreman Modulation Transfer Function in Optical andElectro-Optical Systems (SPIE 2001)

23 httpwwwopticalrescom24 httpwwwcstcom25 K W Gyum J P Thakur and Y H Kim ldquoEfficient DRW

antenna for quasi-optics feed in W-band imaging radiometersystemrdquo Microw Opt Technol Lett 52 1221ndash1223 (2010)

20 February 2013 Vol 52 No 6 APPLIED OPTICS 1131