Advanced Optical System Design Through CGH Technology
Explore the innovative design process and principles behind Computer-Generated Holograms (CGH) in optical system development. Learn about the intricate phases, Zernike coefficients, and fringe patterns that are key to optimizing performance and accuracy in optical systems.
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Presentation Transcript
Nasrin Ghanbari OPTI 521
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 Start with design and optimization of CGH in Zemax: Single pass geometry Phase function Double pass geometry
Virtual Glass Snell s law: If n1= 0 then sin 2 =0 Therefore 2 =0 and the emerging ray is perpendicular to aspheric surface
Beam Footprint Width of the spot size: s e r e t i m l l M i 0 The number of waves of tilt needed to separate diffraction orders: 0 0 . 0 5 e : a l S c A p e r t u r e D i a m e t e r : 4 . 8 8 6 1 % r a y s t h r o u g h = 1 0 0 . 0 0 % F o o t p r i n t D i a g r a m [1] 1 S R R M 2 u a a a / r y y x 1 f / a X Y R 2 c a 0 e M M d 1 i i i 2 2 n n u 0 s : = = = - - 0 2 2 . . . 3 4 4 8 4 4 7 3 3 2 1 1 R R W a a a y y v e X Y l e M M n a a g x x t h = = = 0 1 0 . . . 3 1 6 8 9 3 7 4 2 2 0 8 d C T o _ n C G f H i _ g I u l l r u a m t i n i a o t n i o n 1 _ I I o . f Z M 1 X [1] Dr. Jim Burge, Computer Generated Holograms for Optical Testing
Phase Design Zernike Coefficient Zernike Coefficient Zernike Coefficient Value Value Value A 1 A 2 A 3 A 4 A 5 A 6 A 7 A 8 A 9 A 10 A 11 A 12 0.00E+00 1.10E+02 0.00E+00 -3.27E+01 7.00E+01 -1.74E-01 -6.57E-02 -2.89E+01 -4.41E+00 -4.13E-04 1.24E+01 6.26E+00 A 13 A 14 A 15 A 16 A 17 A 18 A 19 A 20 A 21 A 22 A 23 A 24 3.85E-04 6.89E-05 -2.50E+00 -3.94E-01 -3.07E+00 -8.31E-05 -3.30E-05 1.60E+00 6.22E-01 1.06E-04 -3.56E-06 -1.76E-01 A 25 A 26 A 27 A 28 A 29 A 30 A 31 A 32 A 33 A 34 A 35 A 36 -9.49E-03 0.00E+00 -7.18E-01 -2.89E-01 -4.89E-05 -1.80E-05 7.30E-02 6.16E-03 2.35E-05 2.06E-06 -4.81E-03 5.94E-04
Zernike Fringe Phase M is the diffraction order of the CGH N is the number of Zernike terms; Zemax supports up to 37 Zi ( , ) is the ith term in the Zernike polynomial Ai is the coefficient of that term in units of waves. Ai A1 A2 A3 A4 A5 A6 Zi ( , ) 1 cos( ) sin( ) 2 2 - 1 2cos (2 ) 2sin(2 ) . . .
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 r s r s t e t e m e m e l i l i i l i l M M 0 0 0 0 2 0 2 0 0 . 0 . 1 1 e : e : a l a l S c S c A p e r t u r e D i a m e t e r : 1 0 . 0 0 0 0 % r a y s t h r o u g h = 7 5 . 7 5 % A p e r t u r e D i a m e t e r : 1 0 . 0 0 0 0 % r a y s t h r o u g h = 7 5 . 7 5 % F o o t p r i n t D i a g r a m F o o t p r i n t D i a g r a m 1 S R R M 2 u a a a / r y y x 2 f / a X Y R 2 c a 0 e M M d 1 i i i 2 1 n n u 1 S R R M 2 u a a a / r y y x 2 f / a X Y R 2 c a 0 e M M d 1 i i i 2 2 n n u ( a ) ( b ) 1 s : = = = B e s - - 1 t 5 3 0 . . . F 4 7 0 o 4 5 3 c 2 1 6 u 8 9 7 s R R W V a a a o y y v r e w X Y l a e r M M n d a a g 1 s : = = = B e s - - t 3 6 8 . . . F 0 7 8 o 4 3 1 c 9 8 0 u 5 4 5 s R R W R a a a e y y v t e u X Y l r e n M M n x x t h = = = 3 8 0 . . . 5 5 6 6 5 3 5 7 2 0 8 8 a a g x x t h = = = 5 5 0 . . . 7 5 6 5 1 3 1 6 2 6 6 8 g C T o _ n D P f _ i D i g f u f r r a a c t t i i o o n n _ O : r d e A r l s l . Z M 7 X g C T o _ n D P f _ i D i g f u f r r a a c t t i i o o n n _ O : r d e A r l s l . Z M 7 X 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 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
2D Line Pattern Wavefront Profile [1] Phase Function 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
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 Hyun Park
