Using CGH for Testing Aspheric Surfaces Nasrin Ghanbari
![Using CGH for Testing Aspheric Surfaces Nasrin Ghanbari OPTI 521 Using CGH for Testing Aspheric Surfaces Nasrin Ghanbari OPTI 521](https://slidetodoc.com/presentation_image/1a729f9e352741ef47a42966638a5733/image-1.jpg)
Using CGH for Testing Aspheric Surfaces Nasrin Ghanbari OPTI 521
![Introduction �Spherical wavefront from interferometer is incident on CGH �Reflected light will have an Introduction �Spherical wavefront from interferometer is incident on CGH �Reflected light will have an](http://slidetodoc.com/presentation_image/1a729f9e352741ef47a42966638a5733/image-2.jpg)
Introduction �Spherical wavefront from interferometer is incident on CGH �Reflected light will have an aspheric phase function �CGH cancels the aspheric phase �Emerging wavefront will be spherical and it goes back to interferometer Aspheric Mirror CGH
![Design Process Design of CGH in Zemax Conversion to line pattern Fabrication Alignment CGH Design Process Design of CGH in Zemax Conversion to line pattern Fabrication Alignment CGH](http://slidetodoc.com/presentation_image/1a729f9e352741ef47a42966638a5733/image-3.jpg)
Design Process Design of CGH in Zemax Conversion to line pattern Fabrication Alignment CGH �Start with design and optimization of CGH in Zemax: �Single pass geometry �Phase function �Double pass geometry
![Virtual Glass �Snell’s law: �If n 1 = 0 then sin θ 2 =0 Virtual Glass �Snell’s law: �If n 1 = 0 then sin θ 2 =0](http://slidetodoc.com/presentation_image/1a729f9e352741ef47a42966638a5733/image-4.jpg)
Virtual Glass �Snell’s law: �If n 1 = 0 then sin θ 2 =0 �Therefore θ 2 =0 and the emerging ray is perpendicular to aspheric surface
![Single Pass Geometry CGH Single Pass Geometry CGH](http://slidetodoc.com/presentation_image/1a729f9e352741ef47a42966638a5733/image-5.jpg)
Single Pass Geometry CGH
![Beam Footprint �Width of the spot size: �The number of waves of tilt needed Beam Footprint �Width of the spot size: �The number of waves of tilt needed](http://slidetodoc.com/presentation_image/1a729f9e352741ef47a42966638a5733/image-6.jpg)
Beam Footprint �Width of the spot size: �The number of waves of tilt needed to separate diffraction orders: [1] Dr. Jim Burge, “Computer Generated Holograms for Optical Testing”
![Phase Design Zernike Coefficient A 1 A 2 A 3 A 4 A 5 Phase Design Zernike Coefficient A 1 A 2 A 3 A 4 A 5](http://slidetodoc.com/presentation_image/1a729f9e352741ef47a42966638a5733/image-7.jpg)
Phase Design Zernike Coefficient A 1 A 2 A 3 A 4 A 5 A 6 A 7 A 8 A 9 A 10 A 11 A 12 Value 0. 00 E+00 1. 10 E+02 0. 00 E+00 -3. 27 E+01 7. 00 E+01 -1. 74 E-01 -6. 57 E-02 -2. 89 E+01 -4. 41 E+00 -4. 13 E-04 1. 24 E+01 6. 26 E+00 Zernike Coefficient A 13 A 14 A 15 A 16 A 17 A 18 A 19 A 20 A 21 A 22 A 23 A 24 Value 3. 85 E-04 6. 89 E-05 -2. 50 E+00 -3. 94 E-01 -3. 07 E+00 -8. 31 E-05 -3. 30 E-05 1. 60 E+00 6. 22 E-01 1. 06 E-04 -3. 56 E-06 -1. 76 E-01 Zernike Coefficient A 25 A 26 A 27 A 28 A 29 A 30 A 31 A 32 A 33 A 34 A 35 A 36 Value -9. 49 E-03 0. 00 E+00 -7. 18 E-01 -2. 89 E-01 -4. 89 E-05 -1. 80 E-05 7. 30 E-02 6. 16 E-03 2. 35 E-05 2. 06 E-06 -4. 81 E-03 5. 94 E-04
![Zernike Fringe Phase Ai Zi (ρ, φ) A 1 1 A 2 ρ cos(φ) Zernike Fringe Phase Ai Zi (ρ, φ) A 1 1 A 2 ρ cos(φ)](http://slidetodoc.com/presentation_image/1a729f9e352741ef47a42966638a5733/image-8.jpg)
Zernike Fringe Phase Ai Zi (ρ, φ) A 1 1 A 2 ρ cos(φ) A 3 ρ sin(φ) A 4 2 ρ2 - 1 A 5 ρ2 cos (2 φ) A 6 ρ2 sin(2 φ). . . �M is the diffraction order of the CGH �N is the number of Zernike terms; Zemax supports up to 37 �Zi (ρ, φ) is the ith term in the Zernike polynomial �Ai is the coefficient of that term in units of waves.
![Double Pass Geometry �The double pass geometry models the physical setup. �Check the separation Double Pass Geometry �The double pass geometry models the physical setup. �Check the separation](http://slidetodoc.com/presentation_image/1a729f9e352741ef47a42966638a5733/image-9.jpg)
Double Pass Geometry �The double pass geometry models the physical setup. �Check the separation of various diffraction orders �Flip the sign of diffraction order for CGH and radius of curvature for the mirror
![Diffraction Orders �Use multi-configuration editor in Zemax �The +1 diffraction order appears in red Diffraction Orders �Use multi-configuration editor in Zemax �The +1 diffraction order appears in red](http://slidetodoc.com/presentation_image/1a729f9e352741ef47a42966638a5733/image-10.jpg)
Diffraction Orders �Use multi-configuration editor in Zemax �The +1 diffraction order appears in red �To block other orders place an aperture at best focus.
![Sources of Error �Pattern Distortion: error in the positioning of the fringe lines �Misalignment Sources of Error �Pattern Distortion: error in the positioning of the fringe lines �Misalignment](http://slidetodoc.com/presentation_image/1a729f9e352741ef47a42966638a5733/image-11.jpg)
Sources of Error �Pattern Distortion: error in the positioning of the fringe lines �Misalignment of CGH: alignment marks and cross hairs are placed around the main CGH [2] R. Zehnder, J. Burge and C. Zhao, “Use of computer generated holograms for alignment of complex null correctors”
![2 D Line Pattern Phase Function Wavefront Profile [1] Spacing Chrome Segment Position on 2 D Line Pattern Phase Function Wavefront Profile [1] Spacing Chrome Segment Position on](http://slidetodoc.com/presentation_image/1a729f9e352741ef47a42966638a5733/image-12.jpg)
2 D Line Pattern Phase Function Wavefront Profile [1] Spacing Chrome Segment Position on Substrate [1] Dr. Jim Burge, “Computer Generated Holograms for Optical Testing”
![Physical Setup CGH *Photos taken at the Mirror Lab Physical Setup CGH *Photos taken at the Mirror Lab](http://slidetodoc.com/presentation_image/1a729f9e352741ef47a42966638a5733/image-13.jpg)
Physical Setup CGH *Photos taken at the Mirror Lab
![Conclusion �Phase function of CGH can be optimized for a particular testing geometry. �The Conclusion �Phase function of CGH can be optimized for a particular testing geometry. �The](http://slidetodoc.com/presentation_image/1a729f9e352741ef47a42966638a5733/image-14.jpg)
Conclusion �Phase function of CGH can be optimized for a particular testing geometry. �The process is carried out in three steps �Tilt must be added to CGH to separate +1 order from the other diffraction orders. �Diffraction efficiency was not discussed; for an amplitude grating it is about 10% for the +1 order �For accurate placement of CGH in the testing setup, it is necessary to include the alignment CGH.
![Thank You �Chunyu Zhao �Daewook Kim �Javier Del Hoyo �Todd Horne �Wenrui Cai �Won Thank You �Chunyu Zhao �Daewook Kim �Javier Del Hoyo �Todd Horne �Wenrui Cai �Won](http://slidetodoc.com/presentation_image/1a729f9e352741ef47a42966638a5733/image-15.jpg)
Thank You �Chunyu Zhao �Daewook Kim �Javier Del Hoyo �Todd Horne �Wenrui Cai �Won Hyun Park
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