metrological features of diffractive high-efficiency objectives for laser interferometry
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Metrological features of diffractive high-efficiency objectivesfor laser interferometry
C. pIlISSa, s. Reichelta, H. J. Tiziania, v. P. Korolkovb
atjtt für Technische Optik, Universität Stuttgart, Germany
bjstitute of Automation and ElectrometrySiberian Branch ofRussian Academy of Sciences
1 Acad. Koptyuga Pr., 630090, Novosibirsk, Russia
It has been shown that high precision diffractive objectives are an alternative to their refractive counterparts for applicationin interferometers. A design for an all-diffractive, double-sided objective that fulfills the Abbe sine condition has beenproposed. It allows eliminating aberrations due to a finite field angle. Ray tracing simulations show that field angles up to0. 1 ° cause aberrations less than X/20 PV in single pass.
A single-sided prototype (diameter - 80 mm; NA. - 0.158; designed wavelength - 632.8 nm) has been fabricated bydirect laser writing on photoresist. It was written on a polar coordinate laser system CLWS-300 that is capable of writinghigh precision DOEs up to a diameter of 300 mm. The blazed diffractive structures were written directly into a photoresistlayer that was spinned on a high-precision substrate. Recalibration of the radial coordinate by reading marker positions onthe substrate was used to eliminate machine drifts. The writing parameters were optimized by modelling the writing processin order to maximize the diffraction efficiency. The fabricated objective has a rms wavefront error of less than ?/2O in singlepass. The residual errors are predictable using manufacturing data that is recorded during the writing process for eachelement. This permits to supply calibration data for each element. Measurements of the fabricated DOE show excellentagreement between the predicted and measured wavefront quality.
Keywords: diffractive optical elements, gray scale fabrication, optical testing, circular laser writing system
In laser interferometers objectives for collimation and wavefront adaption are important. They are situated in the test arm ofthe interferometer and expand the collimated probe beam e.g. for testing flat surfaces or form a spherical wavefront whentesting focusing components. Typical setups are depicted in Fig. 1 . However, these objectives have a limited optical qualitythat is usually not better than X/2 for larger diameters. The relatively low quality of large diameter objectives requires a verycareful calibration to eliminate the influence of fabrication errors of the objective.
A way to increase the accuracy of interferometer objectives while dramatically reducing weight and complexity and stillmaintaining a reasonable price is diffractive optics. Diffractive optics have been used for years in optical testing of asphericsurfaces and are on their way to becoming an established technique"2'3'4. In this application, the high accuracy of thegenerated wavefronts is essential and has been analyzed and demonstrated in detail. Problems due to chromatic aberrationsintroduced by the strong dispersion inherent to diffractive optical elements (DOE) do not occur when monochromatic light isused.
Until now mainly binary diffractive optics were used for optical testing because of the relative simplicity of theirfabrication. The drawback of these structures is the relatively low diffraction efficiency of about 40% for binary phasestructures. For objectives, a higher efficiency is required. The development of fabrication technologies in diffractive optics
prussito.uni-stuttgart.de; tel: 0049(0)711/685-6064; fax: 0049(0)711/685-6586; http://www.uni-stuttgart.de/ito/
Seventh International Symposium on Laser Metrology Applied to Science, Industry, and Everyday Life,Yuri V. Chugui, Sergei N. Bagayev, Albert Weckenmann, P. Herbert Osanna, Editors,Proceedings of SPIE Vol. 4900 (2002) © 2002 SPIE · 0277-786X/02/$15.00
permits to manufacture high-efficiency, large aperture DOEs. This allows the realization of diffractive objectives, eitheras a purely diffractive element or as a hybrid combination ofrefractive and diffractive surfaces.
Different techniques have been mentioned in literature to produce high-efficiency DOEs. A common approach is themulti-mask technique that produces elements with 2Nphase levels with N binary masks. The many photoresist steps requiredin this technique are time consuming and sensitive to alignment errors. For the production of high-precision interferometricobjectives, we have chosen to use a single-step, gray scale technique. Gray scale fabrication is a way to avoid many steps. Inprinciple, there are two ways to produce many levels in one step. The first way is to generate a gray scale mask that is usedin a second step to illuminate a photoresist layer. This gray scale mask can be a binary halftone mask or a real gray scalemask on the base of material with variable transmission like HEBS-glass or LDW-glass. The second approach is to write thestructure directly into photoresist. This approach is appropriate for individually manufactured high precision diffractiveelements. The results in this paper are based on elements written directly into photoresist.
In this paper we present our results on producing a high-accuracy, high-efficiency DOE designed as an interferometerobjective. The fabrication of the element is discussed in detail in the first part. On the basis of a computer model thatincludes all steps of the fabrication the accessible parameters were optimized. The achievable performance of written DOEsis discussed from the standpoint of both accuracy and efficiency. A new method for maintaining the high positioningaccuracy of the writing spot over the whole area during the full writing time is proposed. The second section presentsexperimental results obtained for an objective with a diameter of 80 mm and a focal length of 250 mm. In the third section adouble-sided design is proposed that fulfills the Abbe sine condition. The design was tested with raytracing methods and thegood performance of this design for finite field angles is shown.
Reference:plane mirror- - ---- Reference:
Fresnel Fizeau platezone lens
HeNer / - suace :estE;III:I undertestzone lens
—. — Spatial filter _ — Spatial filter
I I 1
Figure 1 . Interferometer with diffractive objective in the test arm. (a) Twyman-Green setup with a positive diffractive lensfor testing convex spheres (or aspheres) (b) Fizeau setup with a positive diffractive lens
for testing concave spheres (or aspheres).
2. FABRICATION METHOD
In the present work, we report on results of our investigations on diffractive objectives written by means of the circular laserwriting system CLWS-3005 specially modernized for writing of multi-level DOEs. It is a highly universal tool for thefabrication of diffractive optical elements such as computer-generated holograms, zone plates, gratings, optical scales, etc.The substrate for patterning is fixed on the faceplate of a precision air-bearing spindle. A high accuracy rotary encoder ismounted on the spindle axis. The rotary optical encoder delivers the signal for the stabilization of the rotation speed and forsynchronizing the laser recording with the turning of substrate. An argon ion laser is mounted on the granite base with thevibration isolator supports. The laser radiation (50-100 mW at 457 nm wavelength) is modulated by two acousto-opticmodulators (two modulators were needed to get high contrast of beam power modulation) and enters in the focusingobjective through the optical system mounted on a mobile precision air-bearing linear stage. The linear stage is controlledinterferometrically and allows a positioning of the writing head with an accuracy of rim. The objective forms a light spot
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on the substrate surface with a diameter of about 1 tm. An autofocus sub-system maintains a constant spot size. For circularsymmetric elements the system's symmetry (polar coordinate system) is especially advantageous. The substrate rotates at aconstant rotation speed of 600 rpm. The written rings are spaced evenly with a configurable radial step between adjacenttracks.
In our experiments we used the photoresist Shipley 51828. To work in the practically linear part of the characteristiccurve of photoresist we used UV preexposing. A mask aligner provides the necessary uniform intensity distribution. Thepreexposure with energy dose Epre also permits to reduce the influence of laser beam power fluctuations onto the relief depth.The coefficient ofreduction can be estimated by the following equation for the total exposure dose:
Etotai Epre + Eias (1 + ) = (Epre +E1,s)[i
+1a5 Eas las las pre 1
where Eias 5 averaging energy dose from laser exposure , AEias is the fluctuation of energy dose from laser exposure.Therefore the coefficient of reduction Kf of laser exposure fluctuations AEias/Eias 5 defined as follows:
— Eias +Epre1 Elas (2)
For a profile depth of 1 jtm the value Eias 5 approximately equal to Epre. Therefore Kf is equal to 2 for the maximumprofile depth and increases with decreasing profile depth (with decreasing Eias).
Eliminating the influence of drifts
A typical value for the writing time of large diffractive elements is several hours. During this time, the setup must be keptabsolutely stable, since positioning errors directly influence the generated wavefront. A distortion of the written structurecaused by positioning errors results in wavefront aberrations that are proportional to the gradient of the recorded phase
m2WPD(x,y) = -<(x,y)-—-—2-V(x,y), (3)m 2t
where WpD(x,y) is the resulting wavefront change, (x,y) denotes the distortion vector of the DOE, mD and mR are thediffraction orders for design and reconstruction, respectively.
Since there is no way you can avoid all mechanical drifts, the system monitors them and corrects them if necessary andwanted. Basis of the monitoring system is a net of markers that are written on the substrate before direct laser writing on the
Figure 2. Arrangement of high-reflective markers for recalibration of the radial coordinate during the writing process.
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These markers are segments of thin rings. The angular size of the segments is about 1 -2 degrees, the width in radialdirection is about 1 micron. They cover the whole radial range of the fabricated DOE in steps of 1 -2 mm. The markers arewritten on chromium film by thermochemical laser technology .After laser writing on CLWS the substrate with the Crcoating is developed in a selective etchant. As a result, high reflecting markers are formed on the substrate, which is thenused for photoresist spinning. The substrate covered by photoresist is centered on the spindle of CLWS with an accuracy of+-O.25 micron by means of a centering chromium ring written together with the markers. One of the markers is used forsearching  the rotation center of the substrate. At this point the radial coordinate counter is set to zero. Before the writingprocess on the photoresist layer the controlling program measures the positions of these markers by scanning a focusedprobe beam and measuring the power of reflected light. This measurement process is rapidly (< iminute) made, andtherefore no drift happens in the writing system. The obtained list of marker positions is used as reference. During thewriting process, when the radial coordinate of one of the markers is reached, the controlling program measures the positionof this marker a second time. From the difference between the current and beforehand measured values the system calculatesthe effects of the mechanical drift and recalibrates its coordinate system. As result, the small drift cumulative between twomarkers is eliminated. It is evidently that light reflected from Cr markers overexposes photoresist in the area of markers.However, total square of markers is negligible, and the markers have don't influence on total diffraction efficiency.
Optimization of writing strategy
The writing strategy is the most sensitive decision in the fabrication process. It includes the selection of the scanningtrajectory, spot size, scanning increment and exposure data. Two trajectory types are commonly used in circular laser writingsystems: circular and spiral. A spiral trajectory ensures a higher writing rate because of the continuous movement in radialdirection but gives some distortion in the reconstructed phase function of rotationally symmetric DOEs. Thus, it is better touse purely circular scanning for high numerical aperture DOEs. The selection of the other writing parameters is morecomplicated and requires preliminary modelling of the writing process in order to achieve higher diffraction efficiencies.A typical modelling scheme including also the development of photoresist and the transfer of the profile into the opticalsubstrate by plasma etching is shown in Figure 3.
The simulation yielded the following results:
Radial increment: The overlap of neighboring exposure fields when scanning with a finite Gaussian beam is defined by theradial increment. The overlap and spot size determine the obtained backward slope (sidewall) of the diffractive zones andthe profile roughness. A larger track separation results in noticeable profile waves appearing on the photoresist surface.However smaller radial increment results in a less steep backward slope due to the integration over the tails of theoverlapping exposure fields from many Gaussian spots. Figure 4 shows the influence of the described factors on diffractionefficiency. For a Gaussian writing beam, the intensity profile is given by:
Figure 3. Modelling ofthe fabrication process.
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where w is the radius ofthe writing spot at position x0. A distance w from the center of the spot, the intensity has fallen tol/eof the value in the center. We are referring to the diameter of the 1/e -circle as spot size.
Best efficiencies are obtained when the radial increment is about a factor of 0.7 smaller than the spot size. For biggertrack separations noticeable profile waves start appearing on the photoresist surface. Smaller radial increment results in aless steep backwards slope due to the overlap.
Figure 4. Diffraction efficiency as function of the radial increment for a Gaussian writing beamwith spot size (l/e-diameter) of 1 tm. The optimal radial increment is about 0.7 times the spot size
but depends somewhat on the structure size.
Reconstruction order: Another way to increase the diffraction efficiency is to use a higher order for reconstruction. Thisincreases the minimum period but requires a deeper microrelief. To benefit from higher order structures, it is required thatthe backward slope does not change or at least increases slower than the profile depth. As result, the relative area of thebackward slope in a diffractive zone decreases and the diffractive efficiency increases. From the point of the exposureprocess, the backward slope should be the same as for DOE working in 1st order since the light spot is the same.Nevertheless, our experiments show that the low-contrast development used for analog lithography leads to some expandingbackward slope. Besides that, the application of DOE working in higher diffraction orders is limited by their high sensitivityto errors of the profile shape and depth6. Second and third orders are an optimal compromise between fabricationcapabilities, profile tolerances and diffraction efficiency. In addition to an element used in first order we have fabricated anelement that uses the second reconstruction order to reduce the influence of our finite writing spot.
3. EXPERIMENTAL RESULTS
The diameter of the experimental objective was 80 mm. Its numerical aperture is 0. 158. It was designed for 2=632.8 nmwhich leads to a minimal period of the diffractive zones of 4 tm for the first diffractive order. The structure was writtendirectly into photoresist.
Radial increment, tm
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With the help of the three position technique, the error of the interferometer inclusive the diffractive objective can bemeasured absolutely. Three separate interferometric measurements of a spherical test surface are required (test afterJensen)7. The first and the second measurement are made with the test surface positioned so that its center of curvature is atthe focus of the positive diffractive lens (confocal position). After the first measurement, the test surface is rotated by 180°.The third measurement is with the vertex of the test surface at the focus of the positive zone lens, at the so-called cat's eyeposition. Figure 5 shows the three required test setups.
With WR as the aberration of the optics in the reference arm, W0 as the aberration of the optics in the test arm excludingthat of the test surface and W, as the aberration of the test surface, the three measurements can be written as:
Wi = W + W1 + W
w2 = w + w1 + W(
w3 =w1 +!6v +w),2 (5)
where the superscripts 0 and rr indicates a rotation of the test piece by 0° or 1 80° respectively. This set of equations can besolved for the aberrations of the interferometer WINT = W0 + WR , here represented by the expression WPLAN + WFZL , the sumof the plane wave from the interferometer plus the wavefront aberration of the Fresnel zone lens:
WINT WO + WR WPLAN + WFZL
=i44 +w2 - -)+-4 +),4 2 (6)
where the bar indicates a rotation of the wavefront by 180°.
Fresnel zone lens (FZL)
The interferometric test of the zone lens was performed with a Twyman-Green interferometer (Fisba iPhase® DCI2) byusing phase shifting interferometry. The light source was a He-Ne laser operating at a wavelength of 632.8 nm. Firstly, thethree-position test after Jensen was performed with a spherical mirror (Figure 5). As a result of this test, the interferometererror WINT WPLAN + WFZL was estimated absolutely. However, the plane output wave of the interferometer is also notperfect. The error WPLAN was measured separately with a flat calibration mirror whose accuracy is specified better than X/l0.In Figure 6 (a) the residual wavefront aberration WFZL is shown. To eliminate the influence of alignment errors, Zerniketerms tilt, defocus and primary coma were removed from the measured wavefront. The observed PV error of the residualwavefront aberration is 326 nm, the RMSerror is 38 nm. Figure 6 (b) visualizes the result of a 10th order Zernike fit.8
Figure 5. Required measurements for absolute calibration of the systematic interferometer error WINT.
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. o !: . rr1L iC 0 E£ -50 £ )L:> :1) . .
-100 . .
-150 . . .. . ----. - -. --------
40Radial order r Azimuthi r
Figure 6. Residual aberrations of the zone plate WFZL = WNT - WPL. (a) Wavefront error in double passwith PV = 326 nm and RMS = 38 nm. (b) Visualization of a 10th order Zernike fit. Main part of aberrations is astigmatism
with A22 = 74 rim. (c) Synthetic interferogram of the wavefront error in double pass.
Different error types of the Fresnel zone lens can occur from the fabrication process. There are writing errors of thehologram pattern, depth variations and profile shape errors of the diffractive structure. The first and the second error typeresult in phase errors of the reconstructed wavefront, if they do not occur only locally. The latter leads to losses in diffractionefficiency of the desired order. Small local errors, e.g. caused by surface roughness and particles of dust, result in scatteredlight only.
Wavefront aberrations introduced by the zone plate must be calibrated. The wavefront errors of the FZL can be separatedinto figure errors of the CGH substrate, errors of the hologram pattern and depth variations of the diffractive structure. Fromall error sources, the most important is due to writer distortion. The wavefront error WPD introduced by an incorrecthologram pattern is given by eq. (3).
A detailed discussion of the pattern distortion error and their sources for a circular laser writing system is given in thereferences.9 The pattern distortion errors for a circular writing system can be separated in rotationally symmetric and non-rotationally symmetric parts. There is an unique characteristic of a circular writing system, which can be used for estimationand/or characterization of the pattern errors: rotationally symmetric cRS and non-rotationally symmetric error parts NRS areindependent from each other, caused by different error sources. While a rotationally symmetric writing error is introduced byradial drifts of the writing head relating to the rotation center of the CGH substrate, whereas a non-rotationally symmetricerror is caused by runout of the air-bearing spindle. So, the radial drift error is constant over the whole azimuth(cRs() = const.) and the spindle runout error is identical at a certain angle over the entire radial range (cNRs(r) = const.).
-..J-40 -20 0 20
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This allows estimating both error types by a one-dimensional measurement (e.g. radial drift monitoring during writingprocess or photo-electrical scanning measurement of rotation trajectory on one central circular marker to detect the spindleerror). The results are combined, and a two-dimensional error estimate is calculated. Methods to specify the writing errorand to define the wavefront error function WPD from fabrication data of a specific CGH are described in the
Here we used an adapted fit procedure to eliminate the non-rotationally symmetric wavefront error (spokes error)numerically. This typical error is clearly visible in Figure 6 (a). The wavefront was weighted by the gradient of the phasefunction and then fitted by an appropriate polynomial. The result of the numerical elimination procedure is shownin Figure 7.
The rotationally symmetric wavefront error was monitored during the writing process of the CGH. We used a newdescribed above monitoring algorithm that measures and saves the position of the markers relative to their known position inthe original coordinate system. Then, during the hologram writing the system measures the radial position of the knownmarkers. When the permitted tolerance is locally exceeded the controlling program recalibrates the current radial coordinate.To specify the wavefront quality reconstructed by the CGH we used the result of this marker search. The error of the radialcoordinate gives the rotationally symmetric pattern distortion error cR5. Thus, all quantities from the right side of Eq. (1) areknown and therefore, the expected wavefront error due to an incorrect hologram pattern can be evaluated.
Figure 7. Numerical elimination ofthe non-rotationally symmetric wavefront error (spokes error).( a) Measured wavefront error WFZL.
(b) Frequency analysis of the pattern distortion error cPD NRS(B)(c) Approximation of the non-rotationally symmetric wavefront error.
( d) Residual wavefront aberrations after numerical elimination procedure (Figures (a) -(c)).
In Figure 8 the expected rotationally symmetric wavefront error is compared with the rotationally symmetric part of themeasured wavefront. The rotationally symmetric part of the wavefront was determined by means of the average radial profile
-20 0 20 40
0 2 4 6
4020 0 20 40
-4C-40 -20 0 20 40
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of the measured data' ' . Due to this averaging a low-pass filtering occurs and strong phase jumps are smeared. Nevertheless,we found a good agreement between measurement and error prediction.
E -20C-40: -60
Radius h [mm]
Figure 8. Comparison between the measured wavefront errors (average radial profile of Figure 7 (a)) and the wavefront errorprediction which was evaluated from the marker search data monitored during the fabrication process and
from the design data of the CGH. A good agreement between error prediction and measured error was found,especially for the phase jumps at h 22 mm and about h 35 mm.
The diffraction efficiency was measured with a small probe beam that probes different areas of prototype diffractiveobjectives. We measured the efficiency of the diffractive structure only, i.e. the efficiency is the ratio of the intensity in thedesired order and the transmitted intensity of an unstructured area of the element. Figure 9 shows diffraction efficiencies inmain diffraction order for DOEs working in 1st order (curve 1) and 2nd order (curve 2) as function of relative radiusnormalized to maximum radius Rmax of DOE. Zone width at Rmax was 4 micron for 1 Storder and 8 micron for 2nd order.This figure proves evident advantage of the operation in second order. However, it is also evident that calibration of writingprocess was not ideal and errors in profile depth decreased efficiency even for wide central zones.
5 10 15 20 25 30 35 40
0.25 0.5 0.75 Rmax
Figure 9. Measured diffraction efficiency as a function of diffractive zone period for the second order element.
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The diffraction efficiency decreases towards the outer regions of the diffractive element. This is caused by the roundedprofile shape near the zone boundaries (Figure 10), defined by the finite writing spot and its imperfectness. For higher radii,the structure size decreases and thus the fraction of the imperfect sidewalls relative to the whole structure increases. Thediffraction efficiency can be increased by two methods: reduction of writing spot size or optimization of exposure data withpurpose to get sharper sidewalls12.
Figure 10. Microinterferogram of a 60 tm diffractive zone in DOE working in Vtorder.
4. DESIGN CONSIDERATIONS
Although the designed objective forms a perfect spot on axis, it does not perform well for a finite field. The Abbe sinecondition is not fulfilled for this element. This shows e.g. in high first order aberrations like coma when the diffractiveobjective is tilted. For null tests, this issue is of lesser importance, since the objective can be oriented precisely in theinterferometer with the help of the flat, unstructured regions surrounding the actual DOE. For non-null tests a correction ofthe off-axis errors is desirable. It has been shown that this is possible with holographic elements on curved substrates13. Mostfabrication methods for computer-generated holograms, however, require flat substrates.
We therefore suggest a double-sided DOE design that fulfills the Abbe sine condition and only uses flat surfaces.
,.L t.:CGH2 CGHI
Figure 1 1 . Aplanatic, double-sided DOEs. A and B are the on axis object and image points, c and 3 are arbitrary angles ofthe input and output beams. The first computer generated hologram, CGH 1, directs the incoming beam to the correct heighton CGH 2, according to the Abbe condition. CGH 2 corrects the phase in order to form a perfect spherical wave centered at
B. Left: Setup for finite object and image distances. Right: Special case for infinite object distance.
According to the considerations of Figure 11 we designed a double-sided element on a 10 mm fused silica substrate,focal length 250 mm, clear aperture 80 mm. The first surface has a minimum feature size of 4 tm, the second surface 22 rim.
i— dCGH 1
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The element was tested with raytracing simulations. Figure 12 shows the performance of the element for different fieldangles. The introduced wavefront aberrations are kept below X/20 PV in single pass for field angles less than 0.10.
Figure 12. Aberrations introduced for increasing field angles. The graph shows raytracing resultsfor an aplanatic diffractive objective (NA=0. 158) in comparison to a Fresnel zone plate with the same NA.
We have shown that high precision diffractive interferometer objectives are an alternative to their refractive counterparts.A design for an all-diffractive, double-sided objective that fulfills the well-known Abbe sine condition has been proposed.It allows to eliminate aberrations due to a finite field angle. Ray tracing simulations show that field angles up to 0. 1° causeaberrations less than X/20 PV in single pass.
A single-sided prototypes have been fabricated by direct laser writing in photoresist. It is well suited for null tests. It canbe aligned easily and precisely in the collimated beam of the interferometric setup with the help of the unstructured regionssurrounding the actual element.
The elements were written on a polar coordinate laser direct writing system that is capable of writing DOEs up to adiameter of 300 mm. The blazed diffractive structures were fabricated directly into a photoresist layer that was spinned on ahigh-precision substrate. Recalibration ofradial coordinate by reading marker position on the substrate was used to eliminatemachine drifts. The writing parameters were optimized with the help of a modelling the fabrication process in order tomaximize the diffraction efficiency.
The fabricated objective has a rms wavefront error of less than X/20 in single pass. The residual errors are predictable onthe basis of manufacturing data that is recorded for each element. This allows to supply calibration data for each element.Measurements of the fabricated DOE show excellent agreement between the predicted and measured wavefront quality.
The authors would like to thank Michael Kremer, Thomas Schoder and Johann Westhauser, all from the InstitutfUr Technische Optik, for photoresist processing, control of CLWS-300 and the inspection of the manufacturedmicrostructures.
0 0.05 0.1 0.15 0.2 0.25 0.3
Field angle 
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