Computer Generated Holograms for Optical Testing

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1 Computer Generated Holograms for Optical Testing Dr. Jim Burge Associate Professor Optical Sciences and Astronomy University of Arizona

2 Computer Generated Holograms Introduction to optical testing with CGHs Some particular optical test configurations Design of CGH test for an aspheric surface Error analysis Tips for CGH testing 2

3 Optical testing : measuring aspheric surfaces Interferometers use light to measure to ~1 nm surface errors, for spherical or flat surfaces We need to measure aspheric (non-spherical) surfaces CGH can change spherical wavefronts to aspheric, allowing the use of interferometers for measuring aspheric surfaces Spherical wavefront aspherical wavefront Aspheric surface to be measured Interferometer CGH 3

4 CGHs for optical testing Optical surfaces are nominally spherical + aspheric departure For most optics, this aspheric departure will be in the range of microns This can be accommodated to high accuracy by a CGH For more aspheric departure, use CGH in combination with other optics here alignment becomes difficult For optical testing, we control the shape of the wavefront, determined by phase variations We do not care much about amplitude, as long as we get enough light 4

5 Use of diffraction to define wavefront shape Initial wavefront diffracted wavefront +1 order s θ 0 order -1 order λ Diffraction from CGH alters wavefront, changes slope by sinθ = mλ/s changes wavefront phase by adding mλ per line (m = order of diffraction = 0, ±1, ±2, ) zero order wavefront is same as if there was no pattern 5

$Diffraction at order m adds 2πm phase to$ shapes of the pattern define the shape of

6 CGH description The CGH is a wavy line pattern fabricated onto a substrate Diffraction at order m adds 2πm phase to the wavefront per line on the CGH The shapes of the pattern define the shape of the wavefront CGH phase function CGH pattern CGH pattern with tilt 6

7 Design of CGH pattern 6 Chrome at (x,y) where i+d/2 > W(x,y)/m > i D/2 (D = 0.4, m = 1 in this example) CGH phase phase function (waves) Definition of chrome CGH lines Gaps between lines position on substrate 7

8 Control of diffraction efficiency Unlike other applications, CGHs for optical testing are usually designed to control the phase of the diffracted light, intensity is not important, as long as there is enough light CGH for optical testing is binary, no blaze or multi-tiers Can be amplitude or phase type Amplitude Usually chrome pattern on glass, in transmission 10% diffraction efficiency into -1, +1 order 25% diffraction efficiency into 0 order Pattern defined in a by thin film Cr coating ~0.1 µ thick Phase Usually pattern etched into glass, in transmission 40% diffraction efficiency into -1, +1 order 0% nominal diffraction efficiency into 0 order Pattern etched into glass to give λ/2 phase shift for glass in transmission, the etch depth is λ/2(n-1) ~ 0.6 µm 8

9 CGH fabrication CGHs consist of patterns, made using lithographic techniques: Laser writer Electron beam writer CGH fabrication uses technology that was developed for semiconductor industry The patterns can be transferred using contact printing (at a cost of accuracy + funny diffraction effects) Patterns can be etched into glass using reactive ion or chemical etching 9

10 Orders of diffraction The interferometer uses coherent light. If any light from the wrong order of diffraction sneaks in, it will affect the measurement diffraction efficiency CGH type Amplitude Phase For non-zero m 50% duty cycle η =0.25* sinc 2 (m/2) η = sinc 2 (m/2) sinc(x)=sin(πx)/(πx) order of diffraction 10

11 Some CGH test configurations In general, CGH is used to transform a wellknown spherical wavefront into a wellknown non-spherical wavefront Many different configurations have been used that take advantage of this basic idea 11

12 CGH used as null lens Uses existing interferometer! Most common configuration. Double pass through CGH, must be phase etched for testing bare glass optics Requires highly accurate substrate and phase etching Diffraction International product 12

13 CGH used in common path DIVERGER LENS Original Wyant configuration Typically use +1 order to correct test beam, 0 order for reference Both beams travel through CGH, eliminating sensitivity to substrate Requires custom interferometer 13

14 CGH used to calibrate null corrector NULL LENS Interferometer Null corrector for a big mirror is large and complex For mirrors with rotational symmetry, a CGH can be made of rings that will diffract light to look like reflection from a perfect primary mirror Null lens Most large telescope projects rely on such CGH as the gold standard Typical accuracy is 0.01λ rms (0.003 λ rms achieved in the lab) PRIMARY MIRROR CGH 14

15 CGH test plate For convex aspheric surfaces Reference surface is spherical concave Hologram consists of ring pattern on curved surface 1.8-m CGHs fabricated at University of Arizona Common path interferometry 15

16 CGH test plate at University of Arizona test plate rotation focused laser 1.8 meter diameter CGH on a curved surface! SECONDARY MIRROR HOLOGRAM TEST PLATE POINT SOURCE APERTURE 2.5-m ILLUMINATOR beamsplitter IMAGER AND CAMERA 16

17 CGH with test plate optical layout REF SURFACE LASER COLLIMATOR PROJECTION LENS 1ST ORDER (TO TEST SURF) 0TH ORDER(TO REF SURF) CGH Object STOP IMAG LENS CCD STOP REF AND TEST BEAMS COINSIDE TEST PLATE ref. beam before Test Plate test beam before Test Plate ref. & test beams after Test Plate ASPHERE SURFACE Optimized for measuring segments of a mirror that must be individually made, then assembled to act as a single optical surface 17

18 Design of CGH test 1. Choose the test configuration 2. Perform first order design Balance cost, accuracy, risk Size of CGH Nominal line spacing Eliminate ghosts 3. Complete specification of CGH phase function 18

19 CGH design CGH will change wavefront according to a phase function Design the CGH by modeling it as a phase function Start by modeling the aspheric wavefront Wavefront fits asphere Rays are normal to asphere w : width of minimum blur CGH Spherical wavefront to interferometer D: Diameter of optic R : radius of curvature (w = 0 for sphere) In optical testing, we define the R-number of the surface R N = R/D Like f-number, but from center of curvature 19

$multiple diffraction orders generated by the binary$

20 Definition of tilt carrier Spot diagram showing multiple diffraction orders generated by the binary hologram. 20

21 Tilt to isolate 1 st order of diffraction Must add enough tilt to isolate order of diffraction Too much tilt will drive cost up, accuracy down dx dx dx Separation of order 1 from order 2 requires dx > w/2 + (2w)/2 or dx > 3w/2 21

22 Maximize spacing to minimize sensitivity to errors calculate wavefront error W from pattern distortion ε Where W W = iε = y ε mλ s mλ θ ε, since s θ ε s θ pattern distortion in direction perpendicular to lines on the hologram center to center spacing of CGH lines diffraction angle wavelength of the light used λ Minimize diffraction angle to minimize sensitivity to errors 22

23 CGH line spacing Incident spherical wavefront CGH Test wavefront l θ 1 st order blur width w Order separation dx CGH with diameter D CGH using light defined by cone with R n = l/d CGH From geometry Grating equation gives line spacing s Total number of lines N, depends on R n = l/d dx 3 2 dx 3w θ = l 2l λ λl 2λl s = θ dx 3w DCGH dx DCGH dx N = = = s λ l λr 3w N For order 2λR separation n w For order separation n 23

24 Choose CGH power, minimizing slope Optimal at minimum blur circle Minimum blur circle allows minimum spacing for order separation CAUSTIC (a) Ray trajectories marginal focus minimum rms wavefront paraxial focus (b) Spot diagrams 24

25 Choose your carrier intelligently 0th order 1st order 2nd order 0th order 1st order 2nd order ε y ε y 3ε y 3ε y 0th order 1st order 2nd order y x y x ε x 2ε x y x 25

$only the selected order Different orders of diffraction come to focus at different positions along the axis This allows the use of CGHs with rotational symmetry concentric rings which are easier to$

26 Power carrier Binary CGH with 1 wave Zernike spherical and 6 waves of power unwanted order (defocused from pinhole) desired order mask with aperture at focus of desired order image of mirror from only the selected order Different orders of diffraction come to focus at different positions along the axis This allows the use of CGHs with rotational symmetry concentric rings which are easier to make and verify 26

27 Design optimization Minimize blur size w with optimal choice of power N, number of tilt fringes is fixed by w, R n, λ Move CGH along beam (change l) to get acceptable Overall size: fabrication limit 150 mm Distortion of mapping from asphere to CGH Line spacing: limits accuracy Set substrate tilt to avoid ghost reflections No more design freedom. There is a unique CGH phase function that can be specified using polynomials or a grid. 27

28 Some rules of thumb Size of CGH Practical CGH tests 50 mm CGH is low cost, low risk 150 mm CGH possible Line spacing 10 µm spacing has good accuracy, low risk 0.1 µm writing errors cause only 0.01λ wavefront error 1 µm spacing is possible, risky, accuracy suffers 28

29 Design of CGH phase function Start with wavefront that matches the aspheric mirror Propagate using ray trace to CGH Choose CGH location to give appropriate CGH size Too large : cost too much Too small: line pattern will be too tight, image will be distorted Model CGH as phase function: Phase out = incident phase + CGH phase Make this into a spherical wavefront, coming to an ideal point focus Axial position optimize amount of power in CGH Lateral position set by the amount of tilt needed for order separation Incorporate tilt into phase function Use polynomials or grid to specify phase function 29

30 Source of error in the phase Pattern distortion Substrate surface figure Etching variations Duty cycle variations 30

31 Pattern Distortion The hologram used at m th order adds m waves per line; CGH pattern distortions produce wavefront phase error: ε ( xy, ) W( x, y) = mλ s ( xy, ) ε(x,y) = grating position error in direction perpendicular to the fringes; s(x,y) = localized fringe spacing; For m = 1, phase error in waves = distortion/spacing 0.1 µm distortion / 20 µm spacing -> λ/200 wavefront 31

32 Effect of surface irregularity INCIDENT WAVEFRONT CGH SUBSTRATE (n = INDEX OF REFRACTION) REFLECTED WAVEFRONT TRANSMITTED WAVEFRONT 2δs δs (n-1)δs 32

33 Substrate distortion is a fundamental difficulty E-beam written patterns must be fabricated onto standard reticle substrates: thin and flat to only about 1 micron. These can be printed onto precision substrates, with some (unknown) loss in accuracy. For phase etched holograms, it is difficult to measure the substrate and back it out. Some solutions: Use direct laser writing onto custom substrates Use amplitude holograms, measure and back out substrate 33

34 Duty cycle and phase etch errors limit the substrate measurement For phase holograms, Zero order (direct measurement) has different sensitivity to variations in duty cycle and etch depth than does non-zero order of diffraction Around 50% duty cycle D, 0.5 wave phase etch φ, the zero order is acutely sensitive to tiny variations in D and φ Zero-order st order (insensitive to duty cycle) Sensitive to phase depth from etch phase [waves] phase depth [waves] 34

35 CGH accuracy Line spacing of 10 µm is standard Pattern distortion ε of 0.1 µm is readily achievable. This gives wavefront errors of ~0.01 λ Etch depth variations are good to 2%, causing wavefront errors of <0.01 λ Duty cycle: the diffracted light is insensitive If you try to measure the substrate at 0 order, then both duty cycle and etch depth couple strongly watch out! Substrate : custom substrates are good to ~0.01 λ Overall wavefront can be controlled to ~0.02 λ for each pass through the CGH 35

36 CGH testing tips Use CGH patterns for alignment Complex CGHs solve complex problems Tricks of the trade 36

Using multiple patterns outside the clear aperture, many

37 Use of CGH for alignment Commonly CGH s have patterns that are used for aligning the CGH to the incident wavefront. Using multiple patterns outside the clear aperture, many degrees of freedom can be constrained using the CGH reference. 37

38 Multiple holograms, co-aligned on the same substrate 1 5 give different wavefronts for correction across field 6 gives return to align CGH to interferometer 38

39 CGH projection of alignment marks The basic idea multiplex numerous holograms on a single substrate to provide both wavefront and alignment information. For alignment, the CGH projects bright crosshair patterns 39

40 CGH alignment for null test of a 24-in off axis parabola λ/20 rms measured surface interferogram CGH null lens incorporates alignment marks Easily align axis to by eye Phase map 40

41 Tricks of the trade Design using single-pass model, but analyze full system Verify isolation of orders of diffraction Avoid ghost reflections Incorporate alignment into CGH CGHs are accurate and flexible. A new CGH configuration could solve your impossible problem For anything new, test it out using a spherical CGH. You can measure the wavefront directly to assess accuracy. Double check your specifications using some end-to-end verification. It is easy to get signs backwards for aspheric terms, or other embarrassing things. (BTDT). 41

USE OF COMPUTER- GENERATED HOLOGRAMS IN OPTICAL TESTING

14 USE OF COMPUTER- GENERATED HOLOGRAMS IN OPTICAL TESTING Katherine Creath College of Optical Sciences University of Arizona Tucson, Arizona Optineering Tucson, Arizona James C. Wyant College of Optical