Elliptical trough reflectorfor the collection of light from linear sources

H. Pin Kao and Joseph S. Schoeniger

A trough reflector with a reflective, truncated elliptical surface was designed to efficiently collect freelypropagating light from a linear source. The source was placed at one focus of the reflector, and light wascollected through a rectangular aperture near the second focus. Collection efficiency was much greaterthan that of a spherical integrator and '6.53 greater than that of an objective lens; as much as '55%of the light could be captured from the full aperture. This reflector could be used to efficiently collectsurface fluorescence excited by use of evanescent waves in fluorescence-based fiber optic or capillarywaveguide sensors. © 1998 Optical Society of America

OCIS codes: 000.2170, 120.3890, 170.2520.

1. Introduction

Evanescent fields have been utilized in manyfluorescence-based sensors because of the preferen-tial excitation and collection of fluorescence close toan optical interface.1 This approach is important forchemical sensors based on affinity binding in whichthe analyte causes a change in surface fluorescenceon binding to the optical interface.2 For cylindri-cally shaped sensors ~fiber optic or capillarywaveguide1–5!, fluorescence is typically excited andcollected by use of the trapped or propagating modesof the waveguide. For multimode waveguides theamount of collected fluorescence can be quite low.For example, at the maximum numerical aperture~NA! for a quartz fiber rod immersed in water ~0.6!,only 1–3% of the emitted fluorescence is coupled backinto the waveguide.6 The remainder of the fluores-cence is lost as freely propagating light, forming alinear source.

Several optical geometries have been used to collectthe far-field portion of the light emitted byfluorescence-based fiber optic or other waveguidesensors that may employ evanescent fields for exci-tation. The light can be collected by use of a single

When this research was performed, the authors were with theChemical and Radiation Detection Laboratory, Sandia NationalLaboratories, Livermore, California 94551. H. P. Kao is now withSoane BioSciences, 3906 Trust Way, Hayward, California 94545.

Received 10 October 1997; revised manuscript received 27 Feb-ruary 1998.

0003-6935y98y194194-06$15.00y0© 1998 Optical Society of America

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microscope objective placed at the side of thewaveguide, as in evanescent-wave microscopy.7However, this approach does not permit light collec-tion over .2p s and cannot easily be applied to longlengths of fiber. One can increase the solid angle ofcollection of light emitted from the surface of aevanescent-wave-excited fiber optic by arranging abundle of high-NA fibers around a central fiber.8 Al-ternatively, parabolic reflectors have been used tocollect light from fibers9 and capillaries.10 The twolast-named approaches potentially permit a solid an-gle of collection of .2p sr but, again, do not facilitatecollection over large lengths. One geometry thatwould permit collection over a large solid angle andpotentially large fiber lengths is an elliptical troughreflector ~ETR!. ETR’s have been used in variousapplications to focus light from a cylindrical lightsource into a line. These reflectors utilize the prop-erty of the ellipse that light originating from onefocus will pass through the second focus after a singlereflection at the elliptical surface.11 A common useof ETR’s has been for flash-lamp pumping of dyelasers.12 A single ETR has been used to illuminate asingle line on a photo image by use of a linear fila-ment placed at one focus.13 Opposing trough reflec-tors have been used concentrate light from a tubularultraviolet source to cure coatings onto fiber optics.14

Although ETR’s have been applied primarily in il-lumination applications, their light-collection proper-ties are well suited for the detection of light fromlinear sensors. In this paper a design for a reflectorto collect the freely propagating light from such alinear source is presented. The source is placed atthe focus of an ETR that collects the light propagating

perpendicular to the optical axis into a narrow line.A linear optical detector can then be used to measurethis focused light, or additional optics may focus thelight onto a single photodetector. The light-collection efficiency of the ETR is compared with thatof an integrating sphere and with an objective lens.

2. Design

The ETR has a truncated elliptical cross section per-pendicular to its z axis and a rectangular cross sec-tion parallel to its z axis ~Fig. 1A!. The ellipticalsurface and the side faces are reflective, whereas theexit aperture, which is parallel to the y–z plane, istransparent. The line source is aligned parallel tothe z axis along the elliptical focus farthest from theaperture, and the detector is positioned at the aper-ture. The enhanced efficiency of light collection for alinear light source, such as a fiber optic sensor, be-comes apparent after consideration of the propaga-tion of light rays in the ETR.

Perpendicular to the z axis, most of the light ema-nating from the source, F, will be refocused at F9 ~Fig.1B!. Any light ray originating at F and reflectingwithin the arc AOB will pass through F9 and exitthrough the aperture A9B9. Light rays originatingat F and reflecting within arc AA9 or BB9 will passthrough F9 and reconverge at F. These rays will nowstrike the elliptical surface within arc AOB, passthrough the F9 again ~assuming no change in thedirection of propagation as the rays pass through thesource! and exit the ETR through A9B9. Thus themajority of the source rays ~those within A9OB9! willexit the ETR after one or three reflections and appearas if they had originated from the focus F9. The

Fig. 1. Elliptical tube reflector: A, structure of the reflector; B,ray paths of light from a linear source as viewed through a per-pendicular cross section of the reflector.

remaining rays escape the ellipse without being re-focused. Note that the exiting rays will not form aLambertian source; rather, the intensity of the fo-cused light will be greatest at low divergence anglesand decrease monotonically as the angle is increased.Hence the effect of the ETR will be to concentrate thelight emitted from the source into a lower NA fordetection. Note that as the aperture size is de-creased, the NA of the emergent rays will also de-crease. The efficiency of collection perpendicular tothe reflector axis, E', defined as those rays that passthrough F9 before exiting the reflector, can be calcu-lated ~assuming a uniformly fluorescing source! as

E' 5 ~fraction of light emitted into AOB9!R

1 ~fraction of light emitted into AA9 and BB9!R3,(1)

where R is the reflectivity of the reflector surface.This efficiency does not take into account the effect oftotal internal reflections or the NA of the collectionoptics ~see below!; rather, it represents an upper limitto the maximum collection efficiency of the collector.Note that the percentage of light undergoing threereflections is determined by the elliptical ratio; as theelliptical ratio increases, the percentage of light un-dergoing three reflections increases and hence E'

will increase.It is important to note the NA over which light rays

emanating from the second focal point can be de-tected. This range is determined by one of threefactors. First, if the aperture width is small and thecross section has a large elliptical ratio, the NA of thelight rays emerging from the reflector is low. Hencethe emergent NA is determined by the aperturewidth and the collection efficiency is as described byEq. ~1!. Second, if the reflector is solid ~i.e., con-structed from glass or quartz!, then at a sufficientlylarge aperture width some rays could totally inter-nally reflect at the exit aperture. For this case therefractive index of the reflector limits the emergentNA. Note that for cross sections of large ellipticalratio, only rays reflecting once in the ellipse can un-dergo total internal reflection. For hollow reflectors,total internal reflection cannot occur. Third andmost important, only rays within the NA of the de-tection optics will be collected. Increasing the aper-ture width beyond this angle will not result inincreased collection efficiency. Thus, if either therefractive index of the reflector or the NA of the de-tection optics is improperly chosen, the diminishedfraction of light rays that undergo one or three reflec-tions in the ellipse will reduce the collection efficiencydescribed in Eq. ~1!.

Parallel to the z axis there is no focusing of light.The maximum light collectable from the source perunit length will be the same as for a bare fiber. Alinear detector, such as a linear CCD array, could beplaced at the exit aperture for maximum light collec-tion. Alternatively, the light at the exit aperturecould be further focused by a high-NA lens onto a

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smaller area for detection by a photomultiplier orphotodiode.

3. Experiment

Two ETR’s were custom manufactured from fusedsilica ~Team Technologies, Auburn, Calif.!. Each re-flector had a 25-mm major axis, a 12.5-mm minoraxis, and a 96-mm longitudinal axis length. Alumi-num ~reflectivity through fused silica, '0.85 from 400to 700 nm! was vacuum deposited onto the ellipticalsurface and the side faces. The exit aperture of bothETR’s were polished flat to a surface quality of 80y50,but one reflector had an '1.1-mm-wide aperture~Team Technologies!, whereas the other had an'3.4-mm-wide aperture ~Cutting Edge Technology,Santa Rosa, Calif.!. Each reflector had a 2.1-mm-diameter polished hole bored at the center of its focalline, into which a 110-mm quartz tube ~2-mm O.D.y405-mm I.D.; Model PQNN405y2000, PolymicroTechnology, Phoenix, Ariz.! was inserted. The lin-ear source was inserted into the lumen of this quartztube for measurement ~Fig. 2!. Index-matching oil~Type FF, refractive index 1.48; R. P. Cargille Labo-ratories, Inc., Cedar Grove, N.J.! optically coupled thetube to the reflector and the capillary to the tube.Care was taken to ensure that no air bubbles weretrapped in the oil within reflector. The light-collection efficiency of the ETR was compared withthat of a capillary measured through a 1-mm-thickquartz slide and immersed in the index-matching oil.

The light-collection efficiency of the ETR was alsocompared with that of a 100-mm I.D. spherical inte-grator ~Model FM-040-SF, Labsphere, Inc., NorthSutton, N.H.! that had a reflective coating of Spec-traflect ~;0.98 reflectivity from 400 to 700 nm!. Thelinear source ~a dry, Teflon-coated capillary! was

Fig. 2. Schematic of the optical setup for measurement of thereflector efficiency and the preparation of a capillary waveguide asa Lambertian linear source.

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mounted through the integrator by use of two fiberoptic chucks. Aluminum foil was placed at themounting aperture of the chucks and the exit aper-ture to reduce absorption losses. The light-collection efficiency of the integrator was comparedwith that for the dry capillary suspended in air.

A Teflon-coated quartz capillary ~100y360-mm I.D.yO.D.; Model TSU100360, Polymicro Technology!filled with deionized water was used as a linearsource. The Teflon cladding ~refractive index, 1.31!of the capillary acted as the optical cladding for thecapillary waveguide and limited the sensor NA to0.60 for aqueous samples. A fraction of the lightlaunched into one end of the capillary scattered ra-dially, creating a linear, Lambertian source. Theuniformity of the scattered light increased, but itsintensity decreased when the capillary was immersedin index-matching fluid; hence the control measure-ments were conducted under conditions that matchedthose in either the reflectors or the spherical integra-tor ~i.e., dry versus immersion fluid!. Each capillarywas 1 m in length and contained four sections of fluid~Fig. 2!. At a distance of 2 cm from either end of thecapillary, plugs approximately 1–2 cm long of blackpaint ~Versatex textile paint; Siphon Art, San Rafael,Calif., diluted 3:1 with water, solution n 5 1.339!were placed to block excitation light from propagat-ing through the lumen of the capillary; 30 cm of thecentral portion of the capillary was filled with eitherdeionized water or a fluorescent solution ~fluoresceinisothiacyanate; Molecular Probes, Eugene, Ore.! formeasurement of the fluorescence collection efficiencyof the reflectors. Finally, a small plug of optical ce-ment ~Adhesive 73; Norland Adhesives, North Bruns-wick, N.J.! was cured at the distal end of the capillaryto prevent any movement of the fluid sections. Theaqueous section of the prepared capillary wasmounted into either the ETR or the integratingsphere, with the distal end immersed in index-matching oil ~Type FF, refractive index 1.48; CargilleLaboratories!.

Light from a 50-W tungsten lamp was launchedinto the proximal end of the capillary through a 203objective ~Fig. 2!. Care was taken to prevent straylight from the lamp from entering either the reflectoror the spherical integrator. Light was collected fromthe sides of the capillary by an inverted epifluores-cence microscope ~Model IX70, Olympus Precision In-struments, Ithaca, N.Y.! with four differentobjectives ~poweryNA 5 43y0.13, 103y0.40, 203y0.40; Fig. 2!. The light intensity was measured by aphotomultiplier ~Model R3896, Hamamatsu, Mid-dlesex, N.J.! operating at 2625 V; the photomulti-plier current was amplified with a current-to-voltageamplifier ~Model SR570 Stanford Research Systems,Sunnyvale, Calif.! and measured with an analog-to-digital board ~Model 1600CX, National Instruments,Houston, Tex.! in a 486DX133 computer. For meas-urements of fluorescent capillaries, filtered excitationlight ~Model 480DF20 filter, Olympus Precision In-struments! was launched into the capillary. The col-lected fluorescence was filtered through a Model

500DRLP dichroic mirror and a 515-long wave-passemission filter ~Olympus Precision Instruments! anddetected by the photomultiplier.

For most measurements the objective field of viewwas simply centered and focused on the capillary, theexit aperture of the ETR, or the aperture of the spher-ical integrator. For the second ETR, however, thefields of view of the 103 and the 203 objectives ~'2.1and '1.1 mm-diameter, respectively! were less thanthe 3.4-mm aperture. To compare the collectionfrom this reflector accurately with that from a barecapillary ~per unit length of capillary! we measuredthe integrated signal over the full width of the aper-ture for the reflector. We measured this signal insections by sequentially moving the reflector in 0.5-or 1.0-mm increments from one end of the aperture tothe other with respect to a slit ~0.5- or 1.0-mm-wideslit for the 203 or the 103 objective, respectively!placed in front of the reflector aperture.

4. Results and Discussion

The fluorescence collected by the ETR is as much as6.53 greater than that from an objective lens aloneand more than 103 greater than that from a spher-ical integrator ~Fig. 3!, depending on the exit aper-ture size and the objective. As the apertureincreased from the 1.1 to 3.4 mm, gain increased bymore than 23 for each of the objectives. This in-crease is contrary to what is predicted by Eq. ~1!because the smaller aperture should result in agreater percentage of the light’s escaping through theaperture. Most likely, the increase reflects factorsthat degrade the ability of the reflector to concentratethe source light onto the second focus, such as thenonzero diameter of the light source, the accuracy ofthe elliptical cross section, and the effect of the cap-illary and the quartz tube on light rays passingthrough them. Such factors distribute the light col-lection over a wider range of divergence angles pass-

Fig. 3. Comparison of the light collection of the elliptical reflec-tors and of the spherical integrator relative to the capillary alone.Data are the mean 6 sample standard deviation of measurementsfrom three distinct positions on a single length of capillary. Mea-surements obtained from the 100-mm-length of capillary withinthe spherical integrator were normalized to the field of view of theobjective. The data point for the 203 objective and the sphericalintegrator is smaller than can be shown in the figure.

ing through the second focus, thus resulting in agreater number of reflections within the ellipse andconsequently in higher losses. Hence, because the1.1-mm aperture permits a smaller percentage ofthese light rays to exit the aperture, light collectionwith the larger, 3.4-mm aperture was greater. Asthe objective power increased, gain decreased for bothaperture sizes, which demonstrates the concentra-tion of light into lower divergence angles. However,for the 103 and the 203 objectives, gains are approx-imately the same for the 1.1-mm aperture becauseboth objectives have a NA of 0.40 and the exit aper-ture was smaller than the field of view for theselenses. For the 3.4-mm aperture the gains are sig-nificantly different because both fields of view aresmaller than the aperture width, and a truncationeffect was observed. When the integrated signalover the full aperture of the 3.4-mm reflector wasmeasured, all three objectives achieved their highestgain of approximately 6.5. For the spherical inte-grator a relatively poor collection efficiency was mea-sured, and this probably resulted from the less thanperfect diffusive reflectivity of the coating and thesphere diameter.

When a high-NA objective ~0.40! was used, a largepercentage of the light per unit length of capillary~'55% for both the 103 and the 203 objectives! wascollected over the full aperture of the 3.4-mm ETR~Fig. 4!. By comparison, E' ' 81% was calculatedfrom Eq. ~1!, assuming that R ' 0.85. More than90% of the light from the capillary should exit thereflector after only one reflection, and thus the effectof multiple reflections is not responsible for the dis-crepancy between the theoretical and the measuredvalues. However, if the objective NA ~0.40! is takeninto account, the range of angles collected ~'16° inquartz! will limit the total collection efficiency ~again,assuming that R ' 0.85!, to '60%, in good agreementwith the experimental value. To improve collection,the detector may be placed at the exit aperture, theaperture could be slightly smaller to take advantage

Fig. 4. Comparison of the total percentage of the collected powerby the elliptical reflector under different conditions. We calcu-lated by dividing the percentages the gains shown in Fig. 3 by themaximum possible gain. The maximum possible gain was calcu-lated as uyp, where u 5 sin21 ~objective NAynquartz!, and nquartz 51 46.

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of multiple reflections, or the reflector could be hol-lowed or constructed from a material of lower refrac-tive index than quartz.

The ETR design is well suited for the constructionof field portable sensors based on capillary waveguideconfiguration.3–5 For such sensors, the wall of thecapillary acts as a waveguide carrying the excitationlight and the evanescent field created at the innerwall of the capillary excites the fluorescence. In pre-vious studies this surface fluorescence was measuredthrough either epifluorescence or an etched grating,both of which require careful optical alignment foroptimal fluorescence collection.3–5 If an ETR wereused, capillaries could easily be inserted into andremoved from the measurement apparatus withoutthe need for precise optical alignment. Moreover,because the excitation light is introduced into thewaveguide along a path separate from the collectionof fluorescence, a high percentage of the excitationlight is rejected from the measurement path. Thiseffect was demonstrated with a fluorescein-filled cap-illary. For this capillary, the gain with the 3.4-mmETR and a 103 objective measured separately for thefluorescence and for the scattered light ~which com-prised both fluorescence and scattered excitationlight! was '3.5. As expected, this value was thesame as that measured for scattered light from awater-filled capillary. However, the scattered lightsignal from the fluorescein-filled capillary was only4.53 greater than the fluorescence, demonstrating arejection of the excitation light by several orders ofmagnitude.

The signal-to-background ratio for the collection offluorescence from a capillary waveguide sensor wasgreater when the ETR was used than for the epifluo-rescence approach. As noted above, the epifluores-cence approach measures only 1–3% of the totalfluorescence signal6 ~that which is captured into thepropagating modes of the waveguide!, whereas theETR can measure a large percentage of the remaining~approximately 55%! freely propagating fluorescence.However, the background signal measured by thesetechniques does not scale in proportion to the meas-ured fluorescence. Background, such as autofluores-cence and Raman scattering, increases in proportion tothe length of the waveguide through which excitationlight travels. For the epifluorescence approach, fluo-rescence is obtained from a relatively small region ofthe fiber and transmitted over a length of thewaveguide before reaching the detector, thereby re-sulting in a higher background signal. Moreover,these signals are generated within the waveguide, andsubsequently a much higher percentage of this back-ground relative to fluorescence is trapped in the prop-agating modes of the waveguide. Thus the ETR has ahigher signal-to-background ratio because it measuresmore fluorescence and less background per unit lengthof waveguide than the epifluorescence approach.

In addition to the factors discussed above that limitthe collection efficiency of the reflector, the geometryand optics of the detector are highly important.Higher efficiencies are achieved with a high-NA and

4198 APPLIED OPTICS y Vol. 37, No. 19 y 1 July 1998

low-magnification objective, but light is collected onlyfrom a single spot on the ETR aperture. In practice,it would be desirable to collect light from the completelength of capillary within the reflector. An efficientapproach to achieve this result would use a detectorthat has the same active dimension as the exit aper-ture and is positioned at the aperture. Alterna-tively, the light leaving the aperture can be focusedonto a smaller detector, such as a photomultiplier, byuse of a high-NA Fresnel or cylindrical lens.

A disadvantage of the ETR would be the inclusionof fluorescence that has traversed the capillary andthe potential measurement variability introduced byabsorbers in the sample. If the maximum accept-able loss for a ray crossing the capillary is taken as10%, then the greatest absorption coefficient, a, thatthe sample may have in the fluorescence emissionwavelengths is 0.105y~capillary diameter in centime-ters!. For example, the maximum a for a 100-mmcapillary would be '1.05. Although the maximum awill in general be relatively high, such variabilitymay be reduced through the use of smaller capillarydiameters.

5. Conclusions

An elliptical trough reflector greatly increases theefficiency of collecting the freely propagating fluores-cence from a fiber optic or capillary waveguide sensorcompared with that of a simple objective or a spher-ical integrator. The reflector is small in size andsimple to use and could be manufactured at poten-tially low cost. Such a design would collect fluores-cence from fiber optic sensors at a much higherefficiency ~as much as 553 greater! than by use oftrapped guided-wave fluorescence.

The authors acknowledge technical assistance pro-vided for this project by Gary Hux. The researchdescribed in this paper was performed as part of aSandia Laboratory Directed Research and Develop-ment program sponsored by the U.S. Department ofEnergy under contract DE-AC04-94AL85000.

Address correspondence to J. S. Schoeniger, Chem-ical and Radiation Detection Laboratory, Sandia Na-tional Laboratories, Mail Stop 9671, P.O. Box 969,Livermore, California 94551-0969.

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