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ast scanning method for one-dimensionalurface profile measurement by detecting angulareflection of a laser beam

yo Shinozaki, Osami Sasaki, and Takamasa Suzuki

A fast scanning method for one-dimensional surface profile measurement is proposed. The profile ismeasured by integration of a slope distribution of the surface obtained from angular deflection of ascanning laser beam. A scanning optical system that consists principally of a spherical concave mirrorand a rotating scanner mirror has reasonably low cost and is insensitive to mechanical vibration becauseof its high-speed scanning, of the order of milliseconds. A surface profile of a polygonal mirror along a5-mm width was measured with the scanning method and with an interferometer. The root-mean-square difference between the two measured results is 0.98 nm. © 2004 Optical Society of America

OCIS codes: 120.2830, 120.3940, 120.4640, 120.5800, 120.6650.

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. Introduction

n the development of high-precision technology forurface processing, the control and inspection of sur-ace profiles during manufacturing are important,nd in-process 100% inspection of products should bearried out to prevent the shipment of defective prod-cts. In general, interferometers or instrumentsade by the stylus method have been used for in-

pections. However, these instruments need a spe-ialized measurement room because they areulnerable to mechanical vibration. Therefore in-rocess 100% inspection cannot be expected as longs these measurement instruments are used.We describe a method of one-dimensional surface

rofile measurement by integrating a slope distribu-ion that we obtain by detecting angular deflection ofscanning laser beam. Measurements of slope dis-

ribution have already been made; e.g., Smolka andaudell1 translated a test object for measuring alope distribution. Takacs et al.2 and Weingartnert al.3 translated an optical system and took intoonsideration the influences of a mechanical system.

R. Shinozaki is with Core System Company, Ltd., 2-2 Nakajima, Nagaoka-shi 940-0094, Japan. O. Sasaki �osami@eng.niigata-.ac.jp� and T. Suzuki are with the Faculty of Engineering, Niigataniversity, 8050 Ikarashi 2, Niigata-shi 950-2181, Japan.Received 3 January 2004; revised manuscript received 22 April

004; accepted 27 April 2004.0003-6935�04�214157-07$15.00�0© 2004 Optical Society of America

ince they used a mechanical traverser for the trans-ation of the test object or the translation of the op-ical system, the translating speed was not sufficiento make the measurement insensible to vibration.

In this paper a scanning method with high speed isroposed. This scanning method is insensitive toibration because the high measurement speed is ofhe order of milliseconds. In addition, the opticalystem possesses a measurement accuracy of the or-er of nanometers. Therefore it is possible to applyhe scanning method to an in-process automatic pro-le inspection system for the manufacture of preci-ion products.First, the basic scheme for measuring a one-

imensional profile from a slope distribution of a testurface by detecting angular deflection of a laseream probing the surface is described in Section 2.he concept of the slope measurement is same ashat proposed by Evans.4 Second, it is shown thatn optical system constructed from a spherical con-ave mirror and a rotating scanner mirror can scanprobing beam at high speed. The optical system

s nonaberrational and achromatic. However, someodifications to the arrangement of optical compo-ents are required for a test object to be inserted intohe optical system for measurement of the one-imensional surface profile. After the sequentialodifications, a practical optical system is deter-ined, as described in Section 3. These modifica-

ions cause deviations from the ideal deflection of theaser beam. We analyze the deviations in Section 4o make clear the characteristics of the optical sys-

20 July 2004 � Vol. 43, No. 21 � APPLIED OPTICS 4157

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em. The effects of a positioning error of the testurface are analyzed in Section 5. Third, the quan-itative influence of the errors in the experimentaletup is calculated in Section 6. Finally, in Sectionwe describe a one-dimensional surface profile mea-

urement that is carried out by this scanning methodithout a vibration isolator in the setup. The mea-

ured result is compared with the profile obtained byn interferometer to show the usefulness of the scan-ing method.

. Basic Scheme for Measurement

basic schematic of one-dimensional surface profileeasurement by detection of angular deflection is

hown in Fig. 1. A beam emitted from light source Ls scanned on sample surface S. Let the x axis be thecanning direction, which is perpendicular to the in-ident beam. The surface profile and the slope of theurface along the x-axis direction are expressed by�x� and ��x�, respectively, as shown in Fig. 1. If �� 1, the differential of f �x� is given by

df � x�

dx� tan �� x� � �� x�. (1)

ow the beam is incident onto point P on the surface.he reflected beam deviates from the incident beamy angle 2�. We find this angle 2� by measuringeam deflection � � 2�l at distance l from point P.arrying out the same measurement of many pointsn the surface, we obtain a distribution of deflection�x�. Integration of distribution ��x� and expres-ion �1� gives the one-dimensional surface profile f �x�s follows:

12l � �� x�dx � � �� x�dx � f � x�. (2)

e make use of a photosensor such as a position-ensing detector �PSD� to make the measurement ofhe deflection ��x�. Because the output of the sensors proportional to the position of the beam spot on theensor, we have to determine proportionality con-tant � by comparing a measured surface profile withknown surface profile.

ig. 1. Basic schematic for measurement of a one-dimensionalurface profile by detection of angular deflection.

158 APPLIED OPTICS � Vol. 43, No. 21 � 20 July 2004

. Optical System

o carry out a high-speed measurement of distribu-ion of deflection ��x� with the basic scheme shown inection 2 we must scan the beam spot along the sur-

ace at a high speed, and the reflected beam musteach a PSD.

For this measurement the optical system shown inig. 2 is considered. The beam emitted from lightource L is incident upon a rotating scanner mirror,M. As scanner mirror SM is placed at focal dis-ance f of lens LN, the beam reflected from the scan-er mirror is incident perpendicularly onto sampleurface S, which is parallel to lens LN. If surface Ss flat plane, the beam reflected from it retraces thencident beam’s path precisely. To make the re-ected beam incident onto position-sensing detectorand measure the distribution of deflection, we in-

ert half-mirror HM between light source L and scan-er mirror SM. If surface S is not flat and has alope �, deflection � � f� appears on the focal plane ofens LN. Deflection � is imaged onto detector D byens DL. To carry out an accurate beam scan and

easurement, we need a lens whose aberration isighly compensated. Because lens LN would be-ome expensive under these conditions, another op-ical system must be considered.

In this paper the optical system shown in Fig. 3,hich makes use of a spherical concave mirror in-

tead of a lens, is proposed. The rotation axis ofcanner mirror SM coincides with the center of cur-

ig. 2. Optical system for scanning a beam by use of lens LN andcanner mirror SM.

ig. 3. Optical system for scanning a beam by use of sphericaloncave mirror CM and scanner mirror SM, where R is the radiusf curvature of the concave mirror.

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ature of spherical concave mirror CM, where R ishe radius of curvature of mirror CM. The beameflected from the scanner mirror is incident perpen-icularly onto concave mirror CM, and the beam re-ected from it retraces the path of the incident beamrecisely. Hence the position of the beam spot onetector D is constant, independently of the rotationngle of the scanner mirror. The optical system iseasonably low cost because it is free of sphericalberration and is achromatic without the need forptical compensation.In this optical system one must consider where

ample surface S should be put to produce deflectionon the detector. Figure 4 shows that plane mir-

or PM and sample surface S are put into the inci-ent path SM–CM and the reflected path CM–SM,espectively. The beam reflected from scannerirror SM is incident onto concave mirror CM

hrough plane mirror PM. The beam reflectedrom concave mirror CM is incident onto scanner

irror SM through surface S. The rotation ofcanner mirror SM makes the beam spot move onurface S. We define Li � �SM–PM–CM� and Lr �CM–S–SM� as the path lengths of the incidenteam and of the reflected beam, respectively. Theondition Li � Lr � R provides a nonaberrationalptical system for the scanning. Moreover, it pro-ides maximization of lateral resolution in the scan-ing because the distance between concave mirrorM and surface S is R�2.However, in practice it is impossible to use the

rrangement shown in Fig. 4. Therefore we mustonsider an arrangement of plane mirror PM, sur-ace S, and concave mirror CM. The arrangementn the z–x plane is shown in Fig. 5, where aartesian-coordinate system is defined. The opti-al axis is the z axis. Concave mirror CM andurface S move away from scanner mirror SM alonghe optical axis, keeping the distance at R�2. Thenlane mirror PM is detached from surface S by �Llong the optical axis. The beam spot on surface Ss scanned parallel to the x axis. Because the con-

ig. 4. Introduction of plane mirror and sample surface S intoig. 3. The PM and the S are put into incident path SM–CM andeflected path CM–SM, respectively.

ition Li � Lr � R is not satisfied in Fig. 5, the beameflected from surface S does not return to the orig-nal point on scanner mirror SM from which theeam goes out, even if surface S is a flat plane.his displacement of the beam spot can be mini-um on an x–y plane that contains the rotation axis

f scanner mirror SM if a condition for �L given inubsection 4.A below is satisfied. We call the x–ylane the detecting plane, DP. This slight dis-lacement of the beam spot on detecting plane DP ishe spherical aberration of concave mirror CM. Itsnfluence on the measurement is discussed in Sec-ion 4.A below. Deflection � that appears on planeP is imaged onto detector D by lens DL. Because

he distance between the probing beam spot on sur-ace S and plane DP varies with the rotation anglef scanner mirror SM, deflection � is not exactlyqual to 2l�, where l is the distance between surface

and plane DP. This deflection is discussed inubsection 4.B below.Because all beam paths are in the z–x plane in Fig.and concave mirror CM and plane mirror PM in-

ercept the traveling beam, it is still not possible tose the arrangement in practice. A possible ar-angement of optical components is shown in Fig. 6.ectangular concave mirror CM is displaced in the-axis direction such that it does not intercept beamath SM–PM. Beam path PM–CM is inclined to-ard the y-axis direction; it gives a rotation to planeirror PM such that the beam reflected from PM

eaches concave mirror CM. By also giving a rota-ion to the concave mirror, plane mirror PM does notntercept beam path CM–S. Although beam path–SM is detached from beam path SM–PM, the twoaths becomes parallel to each other by giving a ro-ation to surface S. In these arrangements the trackf the beam spot probing surface S is deflected from atraight line, as discussed in Subsection 4.C below.ine tuning of the beam spot radius on surface S iserformed by lens FL.

ig. 5. Separation of sample surface S and plane mirror PM inig. 4. S is detached from the PM by �L, with the distance be-ween CM and S maintained at R�2.

20 July 2004 � Vol. 43, No. 21 � APPLIED OPTICS 4159

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. Characteristics of the Optical System

. Spherical Aberration of the Concave Mirror

enoting beam path lengths Li and Lr on the opticalxis in Fig. 5 by L0i and L0r, respectively, we haveelation

L0r � L0i � 2�L. (3)

or the measurement of deflection �, the conditionhat L0i and L0r are the conjugate distance of concaveirror CM:

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s used. To derive the influence of Eq. �3� on theeasurement, we simplify Fig. 5 and change it to Fig.

. The center of curvature of concave mirror CM is

ig. 6. Optical system modified from Fig. 5. CM is given a dis-lacement and a rotation. PM and S are given different rotations.eam paths PM–CM and CM–S are inclined toward the y direc-

ion.

ig. 7. Displacement of the beam spot on detecting plane DP byhe aberration of spherical concave mirror CM when sample sur-ace S is flat. The center of curvature of CM is at origin O of aartesian-coordinate system. Rotation axis A of scanner mirrorM and DP is placed at conjugate points of CM.

160 APPLIED OPTICS � Vol. 43, No. 21 � 20 July 2004

t origin O of the z–x plane. The radius of curvatureof the concave mirror is 1, so the intersection of

oncave mirror CM and the z axis is B�1, 0�. Theeam emitted from the scanner mirror whose rota-ion axis is at point A�d, 0� is incident onto point C ononcave mirror CM, which corresponds to the beamath SM–PM–CM in Fig. 5, excluding plane mirrorM. An angle formed by the incident beam’s pathnd the z axis is denoted . As the angle varies withhe rotation angle of the scanner mirror, we call acanning angle.The beam reflected from point C is incident onto

oint Q on detecting plane DP, which corresponds toeam path CM–S–DP in Fig. 5, excluding sampleurface S. This situation is equivalent to measuringflat plane. From the relation L0r R L0i, which

s derived from Eqs. �3� and �4�, the z coordinate of theotation axis of scanner mirror SM is 0 � d �� 1, and0i � 1 � d. Assuming that the coordinate of theenter of detecting plane DP is D�zD, 0�, we have0r � 1 � zD and derive

zD � �d��1 � 2d� � 0 (5)

rom Eq. �4�. Beam spot position Q on detectinglane DP varies with scanning angle . The dis-lacement of beam spot Q from point D is obtainedrom the spherical aberration5 of concave mirror CM.he displacement is given by

xabr � �d23, (6)

here �� 1. Incident angle � formed by reflectedeam CQ and the z axis is slightly different fromcanning angle . It is given by

� � �1 � 2d�. (7)

A relation between �L and d is derived from Eq. �3�nd inequality �5�, as follows:

2�L � �zD � d � 2d. (8)

herefore, from Eqs. �6� and �8�, the influence of theberration on the measurement is limited by bothistance �L between plane mirror PM and sampleurface S and a maximum of scanning angle .

. Deflection of the Beam on the Detecting Plane

igure 8 shows a situation in which sample surface Ss inserted in Fig. 7 at a distance l from detectinglane DP. Point P on surface S is probed now. Ifurface S is a flat plane, the beam reflected fromoncave mirror CM goes straight and reaches point Qn detecting plane DP, as indicated by the longestashed line PQ in the figure. If the slope at point Ps �, the reflected beam is given a change of 2� in theraveling direction and reaches point Q on plane DP.hen the angle formed by the reflected beam and theaxis is 2� � �. From Fig. 8, the x coordinate of

eam spot Q on plane DP is given by

x � l tan � � l tan�2� � �� � x , (9)

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here xabr is the aberration given by Eq. �6�. Wexpand Eq. �9� in the lowest order of , d, and �; usingq. �7�, we obtain

x� � �2l� � 2l�2 � xabr, (10)

here � �� 1, �� 1, and d �� 1. The first term ofq. �10� is what we need to measure the slope distri-ution of the sample surface. The second term isaused by the fact that the distance between point Pnd detecting plane DP varies with scanning angle .ts influence on the measurement is ignored if max-mum scanning angle max is limited, as shown inubsection 6.B below.

. Track of the Beam Spot Probing the Sample Surface

he incident beam’s path and the reflected beam’sath are not on the same plane in the optical systemhown in Fig. 6, so the beam spot’s track probing theample surface is deflected from a straight line. Be-ause deriving an equation for the deflection in therack of the beam spot is rather complicated and isot so important here, only the resultant equation ishown below.It is assumed that an angle formed by beam paths

M–CM and CM–S in Fig. 6 is 2�. Then the deflec-ion from a straight line in the track of the beam spots given by 2R�. If the deflection is less than beampot diameter w on the sample surface, the beampot’s track on the surface is regarded as a straightine. This condition is given by

2R� � w. (11)

. Effect of the Positioning Error of the Sample

he influence on the measurement of the positioningrror of the sample’s surface is discussed in this sec-ion.

It is assumed that sample surface S shifts by �l inhe direction of the z axis in Fig. 5. Then Fig. 8hanges to Fig. 9, where the distance between surface

and detecting plane DP is l � �l. The beam re-ected from concave mirror CM reaches point P onurface S, which shifts by �l from its original position.he beam reflected at point P is incident onto detect-

ng plane DP, which shifts by 2� from its original

ig. 8. Deflection of the beam spot on detecting plane DP. Sam-le surface S is inserted into beam path CM–DP. The travelingirection of the reflected beam is changed at point P owing to thelope � of surface S.

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osition. Replacing l with l � �l in Eq. �9�, we derivehe x coordinate x� of point Q as

x� � �l � �l�tan � � �l � �l�tan�2� � �� � xabr. (12)

isplacement xobs of the beam spot on the shiftedetecting plane DP is equal to x� � 2�l tan�2� � ��.herefore, if �l �� 1 and we expand displacement xobs

n the lowest order, we obtain

xobs � �2�l � �l�� � 2�l � �l��2 � d23 � 2�l,(13)

sing Eq. �7�. Coefficient �l � �l� of the first andecond terms of Eq. �13� is found from the distanceetween a detecting plane DP and surface S. Theourth term, 2�l, contains an error caused by a po-itioning error of sample surface S. Because thiserm is a linear function of scanning angle that isroportional to the x coordinate of the probing posi-ion, the influence of the error on the profile measure-ent appears as a quadratic function of the x

oordinate. If it is necessary to eliminate the error,he quadratic functional component should be sub-racted from integral of xobs by the least-squaresethod.

. Experimental Setup

he configuration of the experimental setup is de-cribed and the error estimation for measuring a sur-ace profile of a polygonal mirror along a 5-mm widths shown in this section.

. Configuration

he optical system of the setup was the same ashown in Fig. 6. Light source L was a He–Ne laser,nd the laser beam emitted from it was collimated 5m in half-width by focusing lens FL. Spherical

oncave mirror CM had an 80-mm diameter, a radiusf curvature of R � 400 mm, and surface flatness ��4.t was cut into a 15 mm � 80 mm strip. The dis-ance between concave mirror CM and surface S was� 200 mm, which was the focal distance of concaveirror CM. In this condition, the half-width of the

eam spot diameter on surface S was w � 30 �m.irrors PM, SM, and HM had ��10 surface flatness.

ig. 9. Effect of positioning error of sample surface S. The po-ition of S is shifted by �l.

20 July 2004 � Vol. 43, No. 21 � APPLIED OPTICS 4161

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ens DL with 100-mm focal distance was achromatic.istance �L, almost equal to d between plane mirrorM and sample surface S, was 7 mm.The PSD was a Hamamatsu Photonics K.K. model

1880 detector. The output current of the PSD isroportional to both the beam spot’s position on itsurface and the beam’s intensity. After the outputurrent of the PSD was converted into a voltage by anperational amplifier, it was divided by a voltage pro-ortional to the beam’s intensity to eliminate the de-endence of the output current on the beam’sntensity. A Burr Brown MPY634 analog divideras used for the division. The output signal of therocessing circuit described above was fed to a com-uter through a 12-bit analog-to-digital converter.Scanner mirror SM was mounted upon a motorith a 250-rpm rotating speed. The distance be-

ween scanner mirror SM and sample surface S waspproximately 200 mm, so the scan speed of the beampot on surface S was 5 mm�ms. Because the mea-urement time was 1 ms, the setup was insensitive toibrations lower than 1 kHz. Therefore the experi-ent could be performed with no vibration isolator.

. Error Estimation

ecause positioning error �l of the sample surfaceould be less than 0.4 mm, the ratio of �l to l was 10�3.herefore we can regard the term l � �l as l in Eq.

13�, and a one-dimensional surface profile is ob-ained from the integral of the first term of Eq. �13�.

The second term of Eq. �13� is the error that de-ends on scanning angle . The ratio of the seconderm to the first term is 2. As a surface profile waseasured along a 5-mm width, the maximum scan-

ing angle was max � 2.5�200 � 10�2. The value ofmax

2 � 10�4 was less than the resolution of the2-bit analog-to-digital converter. Therefore theecond term of Eq. �13� could be ignored.The third term of Eq. �13� indicates the spherical

berration of the spherical concave mirror. The ra-io of the third term to the first term is �d23��2l����R.t was found from measurement with a Veeco Instru-ents Wyko NT3300 interferometer that the rootean square of the slope distribution of the polygonalirror was �rms � 10�4. Because d2max

3��2l�rms��� 10�6, the spherical aberration of the concave

irror could also be ignored.The fourth term of Eq. �13� caused by the position-

ng error of the sample is the linear function of .he ratio of the fourth term to the first term waslmax��2l�rms� � 10�1. As mentioned in Section 5,he influence of the positioning error appears in thentegration of Eq. �13� as the quadratic functionalomponent. This error component was derived by aeast-squares method and was subtracted from thentegration of the output signal of the processing cir-uit. Moreover, in the condition that sample surface

was not parallel to the x axis, the signal had aonstant current that appeared as a linear compo-ent in the integration of the signal. This compo-ent was eliminated in the same manner as theuadratic component.

162 APPLIED OPTICS � Vol. 43, No. 21 � 20 July 2004

We had � � 5�200 and max2�R� � 0.001 mm for

nequality �11�. As w � 0.03 mm, inequality �11�as satisfied.The angular speed of the scanner mirror is con-

tant, but the motion of the beam spot on the sampleurface is not constant, as shown by Eq. �7� and Fig.. The data were not sampled at a constant intervalith respect to the x coordinate. The variation of

his spatial sampling interval is estimated here. Ifhe aberration and the slope � in Fig. 8 are ignored,he x coordinate of the beam spot on surface S is giveny x � l tan � � l tan��1 � 2d��. By differentiatingwith , we have

� x�

� l�1 � 2d� � l2, (14)

here d �� 1 and �� 1. As the relative magnitudef the variation in the spatial sampling intervals wasmax

2��1 � 2d� � 10�4 at most, it was considered thathe slope data were sampled at a constant spatialnterval.

. Experimental Tests

. Measurement of a Standard Plane

hereas the root mean square of the profile of theolygonal mirror was 3.5 nm, the spherical concaveirror had a surface flatness of ��4 � 160 nm, and

ther mirrors had ��10 � 63 nm. Therefore weould not ignore the influence of surface distortion ofhe optical components. We estimated this influ-nce by measuring a flat plane as a standard planehat was a square plane mirror with surface flatness�20 � 32 nm.A profile FST, which indicates the influence of sur-

ace distortion of the optical components, was ob-ained in the following way: �1� The slope data wereollected by a computer, and we obtained an inte-rated value Vs by numerical integration. �2� Theuadratic functional component Vq of the integratedalue Vs was derived by a least-squares method. �3�e obtained a profile fs � Vs � Vq. �4� As fine com-

onents of fs were not required, profile fs wasmoothed to a width of 0.24 mm, so FST was obtained.Profile FST is shown in Fig. 10. Profile FST shows

istortion of both plane mirror PM and concave mir-or CM. To perform the profile measurement withompensation for this distortion, one should subtractrofile FST from a surface profile obtained from steps1�–�3� of the procedure above for a sample surface.

. Calibration and Surface Profile Measurement

surface profile of the polygonal mirror was mea-ured in steps �1�–�3� of the procedure describedbove. The measured profile is denoted fCi

. It is ex-ected that profile fCi

will be proportional to the trueurface profile of the polygonal mirror. Toetermine this proportionality constant �, we alsoeasured the profile with a Wyko NT3300 inter-

erometer, and we eliminated the quadratic func-ional component contained in the measured profile

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and fi are shown in Fig. 11.

ig. 10. Profile FST obtained from measurement of the standardlane with ��20. Profile FST shows the influence of the surfaceistortion of optical components used in the setup.

5Fig. 11. Measured surface profiles of a polygonal mirror.

he root-mean-square difference between profilesfCi

and fi was 0.98 nm.To investigate the stability of the measurement by

his scan method, we repeated this measurement 20imes. The root-mean-square measurement repeat-bility was 0.31 nm.

. Conclusions

e have described one-dimensional surface profileeasurement by detection of the angular deflection offast-scanning laser beam. Because the scanning

ptical system consists principally of a spherical con-ave mirror and a rotating scanner mirror, it has aeasonably low cost and is insensitive to vibrationecause of its high-speed measurement, of the orderf milliseconds.Although the use of the concave mirror ideally of-

ers a nonaberrational and achromatic optical sys-em, the practical optical system finally decided onnvolved deviations from the ideal deflection of theaser beam. A theoretical analysis of the optical sys-em has made it clear that the influence of the devi-tions on the surface profile measurement can begnored in the experimental setup.

A surface profile of a polygonal mirror along a-mm width was measured with the setup. Theeasurement time was 1 ms, and no vibration isola-

or was needed. Compared with the surface profileeasured with a Wyko NT3300 interferometer, the

oot-mean-square difference between the two mea-ured surface profiles was 0.98 nm.

eferences. F. M. Smolka and T. P. Caudell, “Surface profile measurement

and angular deflection monitoring using a scanning laser beam:a noncontact method,” Appl. Opt. 17, 3284–3289 �1978�.

. P. Z. Takacs, S. K. Feng, E. L. Church, S. Qian, and W. Liu,“Long trace profile measurements on cylindrical aspheres,” inAdvances in Fabrication and Metrology for Optics and LargeOptics, J. B. Arnold and R. E. Parks, eds., Proc. SPIE 966,354–364 �1988�.

. I. Weingartner, M. Schulz, and C. Elster, “Novel scanning tech-nique for ultraprecise measurement of topography,” in OpticalManufacturing and Testing III, H. P. Stahl, ed., Proc. SPIE3782, 306–317 �1999�.

. J. D. Evans, “Method for approximating the radius of curvatureof small concave spherical mirrors using a He–Ne laser,” Appl.Opt. 10, 995–996 �1971�.

. M. V. Klein, Optics �Wiley, New York, 1970�.

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