Holographic optical scanning elements with minimumaberrations
Hans Peter Herzig and Rene Dandliker
An analytical method to design holographic optical elements for focusing laser scanners, especially diskscanners, with minimum aberrations and optimum scan line definition is reported. The results reveal thatthe focused spot constraint to a straight line is always astigmatic. However, by accepting small deviationsfrom the straight line, the astigmatism can be eliminated. The second-order analytical solutions areexamined with the help of geometrical ray tracing and compared with experimental results. By extending themethod to higher-order approximations, it was found that the correction of the aberrations is essentiallylimited to the direction perpendicular to the scan line.
I. Introduction
Holographic optical elements (HOEs) can serve asthe deflecting as well as the focusing element in laserscanners. They have been incorporated into super-market point-of-sale systems,1 2 laser beam printers,3
and are expected to be useful in a wide range of futureapplications.4 5
No matter how the hologram is produced, it is possi-ble to represent the hologram structure by a phasefunction 4(x,y). To find the ideal phase function 4 fora special scan configuration is, in general, a complexproblem. Possible solutions involve numerical opti-mum design methods, similar to the ones commonlyused for optimizing lens systems in classical optics. Amerit function has to be defined, which describes thescan quality, and by changing the wavefront parame-ters this merit function is minimized.6 7 Such meth-ods work well to find a local minimum for the specifiedconfiguration but do not yield information about ageneral solution nor about the influence of the differ-ent parameters. An alternative method to determinethe hologram phase function 4' analytically, first intro-duced in 1983 by Winick and Fienup, is based onminimizing the mean-squared wavefront.8 9 Thismethod, however, was never applied to designing holo-graphic scanners.
The authors are with University of Neuchatel, Institute of Micro-technology, 2000 Neuchatel, Switzerland.
Another analytical method, which is differentialrather than integral, was recently presented by theauthors.10 11 There, the phase functions of holograph-ic scanners are found by using second-order approxi-mation for the incident and outgoing beams (astigmat-ic pencil of rays). The extension of the second-ordertheory to higher order leads to overly cumbersomeformulas. This can be avoided if the aberrations,astigmatism, coma, and so on are described by a gener-al error function rather than explicitly. This tech-nique is discussed in the following in order to investi-gate the degree of freedom for the higher-ordercorrections.
In the experimental part, disk scanners with a wave-length shift between recording (514 nm) and recon-struction (633 nm) are described. The measured scanquality (line straightness and spot quality) is com-pared with the theoretical results.
II. Principle of the Error Function
A general scan geometry is assumed as sketched inFig. 1, where a laser beam is deflected and focused by aholographic optical element (HOE). The hologramstructure can be described by a phase function ib(x,y).While displacing the HOE, the incident beam movesalong a line x(s) in the hologram plane and the imagepoint describes another line y(t) in space. A localcoordinate system u,v,w is introduced, so that the waxis is normal to the hologram plane. During the scanmotion, the origin of the system u,v,w, is at the centerof the incident laser beam and on the line x(s) in thehologram plane. The outgoing wave 4 'p(u,v,t) shouldbe ideally focused on the scan line y(t). However,there are in general some aberrations with respect tothe ideal spherical wave bs(u,v,t), which can be ex-pressed by an error function
The difference between the outgoing wave 4'p(u,v,t)and the reconstructing wave 4'r(u,v) in the hologramplane has to be supplied by the holographic scanningelement. This difference T is a function of the posi-tion t of the focus on the scan line y(t) in space, namely,
(uvt) = I'p(uvt) - (uv)
= 's(u,v,t) + F(u,v,t) - ,(u'v), (2)
where 4br(u,v) is the readout beam (plane or sphericalwave), ibs(u,v,t) is the ideally focused (spherical) out-going wave, and F(u,v,t) is the error function.
A. Local Match of the Phase Functions
Now, we describe the scanning of the hologramphase function 4'(x,y) also in the local coordinate sys-tem u,v. The phase function then becomes 4'(u,v,s)and changes with the parameter s, which describes theposition of the readout beam on x(s) in the hologramplane. The relation between the position s on x(s) inthe hologram and the position t of the focus on the scanline y(t) in space is not a priori known. Within thepupil of the laser beam centered at point s, the phasefunction 4'(u,v,s) of the hologram should be identicalto the phase function f(u,v,t) given in Eq. (2). Ingeneral, this condition cannot be fulfilled rigorouslyfor all points of a continuous scan. To get at least alocal match of the two phase functions 4b and 'I, theyare both expanded in Taylor series about the pointx(s), which corresponds to the origin of the u,v-coordi-nate system, namely,
Here and in the following, two notations are used forthe components of the spatial vectors, namely, u =(uvw) = (l,U2,U 3 ) and x = (x,y,z) = (,x 2 ,x3).
We now require that the two series are equal up tonth order, where the first-order derivatives determinethe direction and the second-order derivatives the cur-vature of the outgoing wave. This yields the followingconditions:
Laserbeam
Fig. 1. General scan configuration. The hologram moves along aline x(s) in the hologram plane and the image point describes anoth-
er line y(t) in space.
pend on the geometry of the particular scan problemand can be formally expressed with the aid of thefunctions fi...j, namely,
04 , = f ( a4 '1 ., Oxi \OUk /
d2 = fi d | 8,> dxiaxj S aUk , OUOUm |s
Introducing Eqs. (5) into Eqs. (6) yields
0x = f[hs(t)] gi(t),
OxI fifh(t), h.(0 _ gij(t).
(6a)
(6b)
(7a)
4[x(s)]= ]T(0,0,t), (5a) The relations of Eqs. (7) have to be fulfilled simulta-neously by one and the same phase function 4(x,y)
04 - O'I' h.(t), i = 1,2, (5b) alongthe lone x(s). Thus, Eqs. (7) determine all possi-aui I., aui t~hi~t >7 1s2 (5bble solutions, for which the outgoing wave has the
desired direction and the desired curvature.024, 2 t( For the solution of a particular scan problem, it isujaujs aujauj necessary to determine first the functions hi ...(t).
They are, following Eqs. (5), equal to the derivatives ofand equivalent for the higher-order terms hi...j(t). the local phase function f(u,v,t) [Eq. (2)] required at
the origin ( = v = 0) to focus the outgoing wave intoB. Local Derivatives of 4'(xy) the point t along the line y(t). In addition, one has to
To find the phase function 4'(x,y), the relations be- establish for the particular scan geometry the relationstween the derivatives in the two coordinate systems x,y (fi..j) between the derivatives in the two coordinateand u,v have to be established. These relations de- systems x,y and u,v [Eqs. (6)] to finally get Eqs. (7) in
Fig. 2. Geometrical relation between the hologram plane (uv) andthe wave vector k of a spherical wave. k' is the projection of k onto
the plane (v,w).
explicit form. The value of the phase function 4(xy)along x(s) [Eq. (5a)] follows by integration of Eq. (7a).
C. Local Derivatives of T(u,vt)
To calculate the derivatives of the local phase func-tion T(u,v,t) at point x(s), it is necessary to determinefirst the phases of the spherical waves 4bs(u,v,t) and4r(u,v). Following Figs. 1 and 2, the spherical wave 4 'sis given by
,s(uvt) = k[(u + sing3/a)2 + (v + sina cosf/a) 2
+ (cosa coso/a)2]112. (8)
Since 4's is assumed to be ideally focused onto the scanline y(t), the directions a(t) and f(t) and the curvaturea(t) are completely determined by the scan geometry.Note that a(t) is negative for a convergent wave. Simi-larly, the readout beam is given by
D,(uVt) = k[(u) 2 + (v + p sin-y)2 + (p cosy)2 1/2, (9)
where y is the inclination with respect to the hologramnormal and p is the radius of curvature.
Now, we get from Eq. (2) for the functions hi. .. j(t)anqf(u,v,t)1/Jui . .. auj:
where Fi ... j(t) =_ nF(uvt)/Oui ... uj.Next, the local derivatives of 4b(u,v,s) have to be
calculated and matched with the above hi. . .j. For thispurpose, we consider a particular geometry, namely, adisk configuration scanner generating a straight line inspace.
Ill. Higher-Order Analysis for Disk ConfigurationScanners
The principle of the error function is now applied toa disk configuration scanner. The geometrical ar-rangement is shown in Fig. 3, where the polar coordi-nates r,0 are the hologram coordinates. The line x(s)is a circle of radius R, i.e., ¢(s) = , r(s) = R. Weassume for the phase function ib(r,O) a fourth-orderapproximation perpendicular to the scan line, namely,
4,(r,o) = k[ao + al(r - R) + 2 a2 (r -R)2
+ 6 a3(r - R)3 + 1 a4 (r - R)4],6 24
(11)
where ak = ak(0)-The incident beam is a spherical wave with a radius
of curvature p and inclined at an angle y. As shown inFig. 3, the generated line y(t) should be a straight linein space. Therefore, the deflection angle $(t) is chosento be equal to the scan parameter t(fl = t), the inclina-tion a(3) is constant (a = ac), and the curvature a(#) isdetermined by the focusing condition a(fl) = -cosfl/f.
To determine the functions ak(0), first the relationsof the hologram coordinates r,0 and the local coordi-nates have to be established [Eqs. (6)]. Then thederivatives of the hologram phase function 4'(r,) [Eq.(11)] and the derivatives of the functions I(u,v,t), i.e.,hi... j(t) in Eqs. (10), have to be matched along x(s)[Eqs. (7)]. This finally yields, arranged by increasingorder of the derivatives of the error function,
F = a0 /R - sino, (12a)
F2 = a, - since cos3 + sin-y, (12b)
F,1 = a;/R2- (a cos 2/ - l/p)
+ (sina cosfl - sin-y)/R + F2/R, (12c)
F12 = a'/R + a since sinf: cosfl - sin#/R - F,/R, (12d)
F222 2 = a4 + 3a 3(1 - 6 sin 2a cos2/ + 5 sin 4 a cos4)
- 3(1 - 6 sin2y + 5 sin4
,y/p3), (12o)
where ak = ak(b) and a(kO) = dak/d, etc. The param-eters a(O) and a(O) of the outgoing spherical wave aregiven by the scan geometry [a = a,a() = -coso/f].The relation f(3G) between the readout position 0 andthe deflection angle fi is still unknown, but it will bedetermined later by the requirements of the scan.The errors become finally also functions of the positionX, namely, Fi ... j = F ... j[#(O)].
B. Minimizing the Error Function
Now, step by step, we try to determine the coeffi-cients a(o) from Eqs. (12), while setting the errorsFi ... j to zero whenever possible. To obtain the func-tions a(0) and al(0), we can setF = O in Eq. (12a) andF2 = 0 in Eq. (12b) without any restrictions and for any0(o). When setting F1 = 0, an additional equation forao(k) is obtained from Eq. (12c), which contains a().Since the relation d(a'0 )/d = a0 has to be fulfilled, wenow obtain the scan equation
which determines the function 0(k).10 At this pointwe have F1 = F 2 = F11 = 0 realized and 0(30),ao(0),ai(0)determined.
Therefore, the error F12 in Eq. (12d) is completelydetermined and cannot be set to zero, unless an addi-tional degree of freedom is introduced. As found in aprevious paper 0 for the astigmatism, it is not possibleto compensate for the error F12 when the scanning isconstrained to a straight line (a = a,). Only by accept-ing a curved scan line a (0) is it possible to set F1 2 = 0.11Equation (12d) then determines the required devi-ation Aa(0) = a(0) - a. It follows [see Ref. 12, Eqs.(3.29) and (3.30), p. 38] that
The structure of the remaining Eqs. (12e)-(12o) showsthat only the errors F22, F2 22, and F22 22 can be set to zeroby choosing the functions a2(0), a3(), and a4(0) ap-propriately, whereas all other F... j are entirely givenby the previously determined ak(k) and their deriva-tives. Note that F22 = 0 determines an optimum solu-tion for a2(0), but it does not necessarily correspond toan optimized astigmatism,10 except for F12 = 0-
C. Discussion of Higher-Order CorrectionsThe analytical method reported in the preceding
sections requires that for all scan positions the outgo-ing beam is focused on the generated scan line y(t) witha minimum of astigmatism. If the geometry of thescan configuration and the scan line y(t) is specified,the solution is already determined up to second orderand with it most of the higher-order aberrations, whichcannot be compensated by higher-order terms in4'(x,y). In particular, the coefficient ao determines thephase function on the line x(s){14[x(s)] = kao} and thescan equation [Eq. (13)] describing the relation (k).Higher-order corrections are essentially limited to thedirection perpendicular to the scan line x(s). But theycannot compensate for the errors on the scan line thatremain from the second-order theory.
Setting the errors Fi ... j to zero whenever possible is astraightforward analytical method. Such a procedurewould yield phase functions 4'(x,y) for which the holo-graphic scanners have low aberrations and distortions.However, the optimum solution may correspond to amore balanced distribution of the errors Fi ...j. Thiscan be done, for example, by using numerical methodswhich are beyond the scope of this paper.
IV. Experimental InvestigationsThis section reports the experimental investigations
of our calculated holographic disk scanners, whichwere recorded with the aid of computer-generated hol-ograms (CGHs). First the setups for recording andreconstruction are described. Then the experimentalresults for three different disk scanners are presented.
A. Realization of the Holographic Scanners
For given readout geometry and wavelength Xr theholographic scanner phase function 4'(xy) can be cal-
Fig. 5. Experimental setup for measuring the performances of theholographic scanners. The holographic disk rotates around its axisand generates a line perpendicular to the drawing plane. The obser-vation system is translated along the generated line to determine the
image point for different scan positions.
Fig. 4. Recording setup to realize a holographic scanning elementwith the aid of a computer-generated hologram (CGH).
culated according to Eq. (11). Phase 'b is formed byrecording the interference of a spherical object wave4'o and an aspherical reference wave R at the record-ing wavelength XR(F, Xr). The relation between thephases in the hologram plane is then given by
(15)
The spherical wave o is chosen so that the Braggcondition is fulfilled and the spatial bandwidth of theaspherical wave 4 R is low.12 The aspherical wave isgenerated with the aid of a CGH.
The experimental setup for recording is shown inFig. 4. The laser beam is split into a plane wavebranch for the reference wave and a spherical branchfor the object wave. The CGH is inserted into theplane wave branch of the recording setup. A telescop-ic lens system creates a 1:1 image of the CGH at theholographic scanner, which is inclined with respect tothe CGH image plane. The phase function CGH nec-essary to generate ?R in the hologram plane can becalculated with the aid of the ray tracing method,taking into account the optical path length betweenthe CGH image plane and the hologram plane. Thecarrier frequency v of the CGH, which is a binaryhologram, separates the higher-order wavefronts fromthe zero order, so that by using a spatial filter only thefirst order is allowed to pass, thereby forming thedesired aspherical wave.
The CGH also includes a correction for the change inwavelength between recording and readout of thescanning element.12 The wavelength shift is imposedbecause the spectral sensitivity of the high efficiencyphotosensitive materials is typically <520 nm, whereasthe wavelength of the readout sources, used for thelaser scanners, are >630 nm (e.g., He-Ne, AlGaAs).
B. Experimental Setup for Measuring the Performance ofthe Scanners
In the following we shall describe the experimentalsetup for measuring the image spot quality and itsposition with respect to a straight scan line.
Fig. 6. Holographic optical element corresponding to one segmentof a disk scanner.
We determined the spot quality of the holographicscanning elements at different scan positions. Figure5 shows the experimental setup for measuring the im-age spot quality and its position with respect to astraight line. An incident laser beam is deflected bythe holographic disk scanner and focused on a scatterplate at the image plane. The holographic disk rotatesaround its axis and generates a scan line y(t) in theimage plane; the scan line is perpendicular to the draw-ing plane. The observation system magnifies the im-age point and detects the spot quality with a CCDcamera. To avoid the disturbing laser speckles, thescattering plate was rotated. During scanning, theobservation system, including the scatter plate, wastranslated parallel to the generated scan line. Thescan line deviation Ay of the spot as a function of thescan length L was measured with the aid of a micro-meter mounted on the observation system.
In our experiments, the scanning elements were seg-ments of a disk, as shown in Fig. 6. A complete holo-graphic scanner would, of course, be a disk with severalholograms, each generating its own line.
Fig. 7. Calculated and measured deviation Ay of the scan from astraight line as a function of the scan length L for the straight-linescanner. The maximum scan length was L = ±105 mm. Calculated(solid line) is based on the center of gravity of the spots. Experi-
mental (+).
C. Specific Scanner Configurations and Results
Two disk configuration scanners were recorded,namely, (1) straight-line scanner and (2) astigmatism-free scanner. Both scanners were calculated accord-ing to the second-order theory. Certain geometricalproperties were identical for the two scanners: (a)symmetrical arrangement for the incident and outgo-ing beams (a = -- y); (b) total deflection (Ial + I-yI) of-90°; (c) scan length L = +105 mm; (d) distance fromthe hologram to the scan line f = 300 mm; and (d) diskradius R = 40 mm. Also, the readout beam was a planewave at wavelength Xr = 633 nm. The recording wave-length was different, namely, XR = 514 nm.
To distinguish the geometrical parametersPR,fR,aR,'YR,XR for recording, from the parametersPrefrsarYrXr for reconstruction, we write them with anindex. Note that fr is the distance from the hologramto the scan line, which is equal to the radius of thereconstructed wave in the scan center (deflection angle
= 0).
1. Straight-Line ScannerAccording to our analytical design method, the
straight-line scanner, discussed in a previous paper,10
should generate a straight line with minimized astig-matism of the focal spot. To test this prediction, werecorded and tested a straight-line scanner. For re-cording, the reference wave was an aspherical wavegenerated by a CGH, the object wave was a sphericalwave with radius fR = 428 mm and the angles were aR =-YR = 34.5°. The recording wavelength XR = 514 nmis chosen to be different from the reconstructing wave-length Xr = 633 nm. The geometrical parameters forreconstruction were Pr (i.e., incident plane wave)and ar = -Yr = 44.15°.
The calculated and experimental results are shownin Figs. 7 and 8. Figure 7 shows the deviation Ay froma straight line as a function of the scan length L.Although our design predicts a strictly straight line,there is some curvature. After closure scrutiny, wedetermined that indeed the principal ray of the cor-
U
v'
200 gm
u'
U
U
L<m
.. * . 105 mm
90 mm
60 mm
30 mm
0 mm
Fig. 8. Spot quality for the straight-line scanner with D = 5 mm(diffraction-limited spot sizeDs = 38,umat half-intensity). Experi-mental results and geometrical ray tracing for nine scan positionscorresponding to scan lengths of L = 0, +30, +60, +90, and +105 mm.The scan line y(t) is parallel to the u' axis and the configuration is
symmetrical with respect to the v' axis.
rected scan moves strictly on a straight line; however,the center of gravity of the focal spot does not. Thetheoretical calculation for the center of gravity (solidline) were performed using the ray tracing method.The maximum deviation was found to be +88,4m for atotal scan length of L = +105 mm, both for the experi-mental and theoretical results.
Next we determined the spot quality at various scanpositions L = 0, +30, +60, +90,+105 mm in the imageplane. The experimental as well as the calculatedresults are shown in Fig. 8 for D = 5 mm. The maxi-mum diameter of the spot size is 110 Am at half-inten-sity. We can see that for a beam diameter of D = 5 mma uniform scan is still not possible. The nearly diffrac-tion-limited spot in the center (L = 0 mm) is muchbetter than the spot at the end of the scan (L = +105mm). The decreasing quality can also be observed inthe spot diagrams. The aberrations are much largerthan the diffraction from the aperture. A smalleraperture increases the diffraction effect but decreasesthe aberrations. For a diameter D = 3 mm, thestraight-line scanner generates a scan line with a gooduniformity of the focal spot. The experimental spotsize (diameter at half-intensity) was found to be small-er than 85 m for any position within the maximumscan length of L = ±105 mm.
Fig. 9. Calculated and measured deviation Ay of the scan from astraight line as a function of the scan length L for the astigmatism-free scanner. The maximum scan length wasL = +105 mm. Calcu-lated (solid line) is based on the center of gravity of the spots.
Experimental (+).
2. Astigmatism-Free ScannerStill better performance for the spot quality can be
realized by a scanner which accepts a slightly curvedscan line to compensate for the astigmatism of theoutgoing wave [seeRef.12, da/d #d 0 inEq. (14)]. Werecorded such a scanner according to our design meth-od and determined its behavior.1 For recording, thereference wave was an aspherical wave, generated by aCGH, the object wave was spherical with a radius fR =430 mm and the angles were aR = -YR = 34.81°. Therecording wavelength XR = 514 nm was again chosendifferent from the reconstruction wavelength Xr = 633nm. For reconstruction, the incident beam was aplane wave Pr = and the angles ar = -Yr = 44.6°.
The calculated and experimental results are shownin Figs. 9 and 10. For this scanner a slightly curvedscan line is expected. Figure 9 shows the deviation Ayfrom a straight line as a function of the scan length Lfor the experimental (+) and theoretical results (solidline). The calculations were performed using the raytracing method, where the position of the focal spot inthe image plane was assumed to be the center of gravityof the spot diagrams. We found that the scan line isslightly curved, within +30,m around a center line, fora total scan length of L = +105 mm, as predicted by thetheoretical calculations.
Next, we determined the spot quality at various scanpositions L = 0, +30, +60, +90, +105 mm in the imageplane. The experimental as well as the calculatedresults are shown in Fig. 10 for a beam diameter of D =5 mm. From the ray tracing results, the spot quality isexpected to be still better than in the case of a straight-line scanner. This is in fact so, comparing the resultsshown in Fig. 10 (astigmatism-free scanner) with Fig. 8(straight-line scanner). Already for a diameter of D =5 mm the spot has a good uniformity during scanning.The experimental spot size (diameter at half-intensi-ty) was found to be smaller than 60 gm for any positionwithin the maximum scan length of L = +i105 mm.
L<0 L<0
- - 105 mm
E U E X90mm
U,- 60 mm
4 1|1 0. g 30 mm
V
0 gm 0 mm
Fig. 10. Spot quality for the astigmatism-free scanner with D = 5mm (diffraction-limited spot size Ds = 38 Axm at half-intensity).Experimental results and geometrical ray tracing for nine scan posi-tions corresponding to scan lengths of L = 0, +30, ±60, +90, and±105 mm. The scan line y(t) is parallel to the ' axis and the
configuration is symmetrical with respect to the v' axis.
3. Improvement by Higher-Order DesignThe higher-order analysis of the two special scanner
configurations mentioned above tells us that the maxi-mum spot diameter during scanning cannot be re-duced further. Using ray tracing, it follows that theaberrations are mainly caused by rays emerging frompoints on the scan line x(s) in the hologram plane [Fig.3]. On this line, the solution for the phase functionb(x,y) [Eq. (11)] is entirely determined by the coeffi-cients ao and a, and cannot be changed by higher-orderterms. These coefficients are determined by the firstand the second derivatives of the phase function c1i,describing the direction and the curvature of the out-going beam. However, although a reduction of themaximum diameter is impossible, higher-order designcan improve the uniformity of the spot during scan-ning.
For other scanner configurations, the results may bedifferent.12 Especially if the aberrations due to thecoefficients a and a are low compared with the otherremaining aberrations, higher-order corrections per-pendicular to the scan line x(s) become effective. Thishas to be analyzed individually for each configuration.
An analytical method for the design of holographicoptical elements (HOE) for focusing laser scannerswith minimum aberrations and optimum scan line def-inition is reported. We were especially interested indisk scanners that generate straight lines in space. Wefound that a circular motion cannot generate a straightline without astigmatism in the focal spot. By accept-ing a slightly curved scan line, the astigmatism can beeliminated and the spot quality improved.
The second-order analytical solutions were exam-ined with the help of geometrical ray tracing and com-pared with experimental results. We measured spotdiameters (at half-intensity) of <60MAm for a maximumscan line deviation of +30 Am and <85 um for a maxi-mum scan line deviation of +8 im, for any positionwithin the scan length of +105 mm at an image planedistance of 300 mm. The experimental results and thetheoretical predictions are in a good agreement.
Extending the method to higher-order approxima-tions, we found that aberrations perpendicular to thescan line can be minimized with appropriate correc-tions of the hologram phase function. However, astig-matism and other higher-order aberrations, especiallyin the scan direction, cannot be removed completely.It is possible that numerical optimum design methodscould be used to further improve the solutions foundby our analytical approach.
Our design method need not be restricted to holo-graphic optical scanning elements. For example, oth-er HOEs which have to transform a continuous set ofinput wavefronts into a continous set of output wave-fronts can also be designed with our method.
This research was performed in close collaborationwith the Optical Systems Department of the Centre
suisse d'6lectronique et de microtechnique S.A., Neu-chatel, where the CGHs were produced. In particular,we wish to thank H. Buczek, head of this department,for his helpful advice and A. A. Friesem from theWeizmann Institute of Science, Rehovot, Israel, formany fruitful discussions.
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W. Southwell, Rockwell Science Center, photographed by W. J.Tomlinson, Bellcore, at the Annual Meeting of the Optical Society of
