Using CGH for Testing Aspheric Surfaces

Nasrin GhanbariOPTI 521

IntroductionSpherical 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

CGH

Aspheric Mirror

Design Process

Start with design and optimization of CGH in Zemax:Single pass geometryPhase functionDouble pass geometry

Design of CGH in Zemax

Alignment CGH

Conversion to line pattern

Fabrication

Virtual GlassSnell’s law:

If n1 = 0 then sin θ2 =0

Therefore θ2 =0 and the emerging ray is perpendicular to aspheric surface

Single Pass Geometry

CGH

Beam Footprint Width of the spot

size:

The number of waves of tilt needed to separate diffraction orders:

[1]

A p e r t u r e D i a m e t e r : 4 . 8 8 6 1

Scale: 5.0000 Millimeters

d T _ C G H _ I l l u m i n a t i o n _ I I . Z M XC o n f i g u r a t i o n 1 o f 1

F o o t p r i n t D i a g r a m

1 2 / 1 / 2 0 1 2S u r f a c e 2 0 : R a y X M i n = - 0 . 3 8 7 2 R a y X M a x = 0 . 3 8 7 2R a y Y M i n = - 2 . 4 4 3 1 R a y Y M a x = 1 . 1 9 4 0M a x R a d i u s = 2 . 4 4 3 1 W a v e l e n g t h = 0 . 6 3 2 8

% r a y s t h r o u g h = 1 0 0 . 0 0 %

[1] Dr. Jim Burge, “Computer Generated Holograms for Optical Testing”

Phase Design

ZernikeCoefficient Value

ZernikeCoefficient Value

ZernikeCoefficient Value

A 1 0.00E+00 A 13 3.85E-04 A 25 -9.49E-03A 2 1.10E+02 A 14 6.89E-05 A 26 0.00E+00A 3 0.00E+00 A 15 -2.50E+00 A 27 -7.18E-01A 4 -3.27E+01 A 16 -3.94E-01 A 28 -2.89E-01A 5 7.00E+01 A 17 -3.07E+00 A 29 -4.89E-05A 6 -1.74E-01 A 18 -8.31E-05 A 30 -1.80E-05A 7 -6.57E-02 A 19 -3.30E-05 A 31 7.30E-02A 8 -2.89E+01 A 20 1.60E+00 A 32 6.16E-03A 9 -4.41E+00 A 21 6.22E-01 A 33 2.35E-05A 10 -4.13E-04 A 22 1.06E-04 A 34 2.06E-06A 11 1.24E+01 A 23 -3.56E-06 A 35 -4.81E-03A 12 6.26E+00 A 24 -1.76E-01 A 36 5.94E-04

Zernike Fringe Phase

M is the diffraction order of the CGHN is the number of Zernike terms; Zemax

supports up to 37Zi (ρ,φ) is the ith term in the Zernike polynomial

Ai is the coefficient of that term in units of waves.

Ai Zi (ρ,φ)

A1 1

A2 ρ cos(φ)

A3 ρ sin(φ)

A4 2 ρ2 - 1

A5 ρ2cos (2 φ)

A6 ρ2 sin(2 φ)...

Double Pass Geometry

The double pass geometry models the physical setup.Check the separation of various diffraction ordersFlip the sign of diffraction order for CGH and radius

of curvature for the mirror

Diffraction Orders

A p e r t u r e D i a m e t e r : 1 0 . 0 0 0 0

Scale: 10.2000 Millimeters

g T _ D P _ D i f f r a c t i o n _ O r d e r s . Z M XC o n f i g u r a t i o n : A l l 7

F o o t p r i n t D i a g r a m

1 2 / 2 / 2 0 1 2S u r f a c e 1 1 : B e s t F o c u s V o r w a r dR a y X M i n = - 5 . 4 4 2 8 R a y X M a x = 3 . 5 6 5 0R a y Y M i n = - 3 . 7 5 1 9 R a y Y M a x = 8 . 5 5 7 8M a x R a d i u s = 1 0 . 0 3 6 7 W a v e l e n g t h = 0 . 6 3 2 8

% r a y s t h r o u g h = 7 5 . 7 5 %

( a )

A p e r t u r e D i a m e t e r : 1 0 . 0 0 0 0Scale: 10.2000 Millimeters

g T _ D P _ D i f f r a c t i o n _ O r d e r s . Z M XC o n f i g u r a t i o n : A l l 7

F o o t p r i n t D i a g r a m

1 2 / 2 / 2 0 1 2S u r f a c e 2 1 : B e s t F o c u s R e t u r nR a y X M i n = - 3 . 0 4 9 5 R a y X M a x = 5 . 7 5 1 6R a y Y M i n = - 6 . 7 3 8 4 R a y Y M a x = 5 . 5 1 6 6M a x R a d i u s = 8 . 8 1 0 5 W a v e l e n g t h = 0 . 6 3 2 8

% r a y s t h r o u g h = 7 5 . 7 5 %

( b )

Use multi-configuration editor in Zemax The +1 diffraction order appears in redTo block other orders place an aperture at best

focus.

Sources of ErrorPattern Distortion:

error in the positioning of the fringe linesMisalignment 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

Ph

ase

F

un

ctio

n

Position on Substrate

Wavefront Profile [1]

Chrome Segment

Spacing

[1] Dr. Jim Burge, “Computer Generated Holograms for Optical Testing”

Physical Setup

CGH

*Photos taken at the Mirror Lab

ConclusionPhase function of CGH can be optimized for a

particular testing geometry.The process is carried out in three stepsTilt 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 ZhaoDaewook KimJavier Del HoyoTodd HorneWenrui CaiWon Hyun Park