Comparison of Fiber Reference and Zernike Filter Self Referencing Interferometers

1
Comparison of Fiber Reference and Zernike Filter
Self Referencing Interferometers

• Kavita Chand, M.S., M.Tech, and
• Justin Mansell, Ph.D.
• MZA Associates Corporation
• Troy Rhoadarmer
• Air Force Research Laboratory
• Kirtland AFB, Albuquerque, NM

2
Introduction

• Self-referencing interferometers (SRIs) have been
  proposed to provide feedback for adaptive optics
  systems in directed energy applications.
• We performed wave-optics analysis in WaveTrain to
  compare two types of SRI
• Fiber-reference SRIs and
• Zernike filter SRIs.

3
Fiber SRI
0
Aberration
Lens
p/2
Light
p
Splitter
3p/2
4
WaveTrain FiberSRI
5
Zernike SRI
-p/2
Aberration
Light
Lens and Splitter
p/2

• Denominator factor of 6.0 is best for weaker
  aberration.
• Denominator factor of 2.0 is best for stronger
  aberrations.

6
WaveTrain Zernike SRI
7
System-Level Parametric Studies

• Types of Aberrations
• Single Phase Screen Zernike Polynomials
• Multi-Screen Distributed Atmosphere
• Types of Tests
• Intensity Debalancing
• Image Misregistration
• Tilt Rejection
• Camera Signal to Noise Ratio (SNR)
• Metric
• Used measured wrapped wavefront to compensate the
  beam.
• Measured Peak Strehl Ratio (PSR)
• Ratio of peak intensity in the far-field for
  aberrated to that for a perfect beam

8
System-Level Parametric Studies
9
System-Level Parametric Studies
10
System Studies with Zernike Polynomial Phase
Aberration Input
11
Zernike SRI Intensity Debalancing
Used Zernike aberrations with an amplitude factor
of 2?
-p/2
x
(1-x)y
Aberration
Light
(1-x)(1-y)
Lens and Splitter
p/2
Adjusted the splitting ratio of the light into
the three arms using the variables x and y.
DF2.0
12
Fiber SRI Intensity Debalancing
0
Lens
p/2
Light
p
Splitter
Aberration
3p/2
31 splitting ratio
x
Used Zernike aberrations with an amplitude factor
of 0.7?
(1-x)y
(1-x)(1-y)(1-z)
(1-x)(1-y)z
Adjusted the splitting ratio of the input light
into the four arms using the variables x, y, and
z.
13
PSR for 90 Astigmatism for Zernike SRI
14
PSR for 90 Astigmatism for Fiber SRI
15
PSR for Various Zernikes for Zernike SRI
Results for 2nd and 3rd order Zernikes
(astigmatism, focus, coma, and trefoil)
16
PSR for Various Zernikes for Fiber SRI
90 astigmatism
45 astigmatism
y trefoil
focus
x trefoil
y coma
x coma
PSR axis is from 0.5 to 1.0
17
Intensity Debalancing Conclusions

• Zernike SRI is very sensitive to intensity
  debalancing
• PSR varied by about 40 for a 4 change in the
  balancing of the 50/50 beam splitter.
• Fiber SRI is fairly insensitive to intensity
  debalancing
• PSR varied by about 1 for a 10 change in the
  balancing of the 50/50 beam splitter.

18
Zernike SRI Image Misregistration
Used Zernike aberrations with an amplitude factor
of 2?
-p/2
Aberration
Light
Lens and Splitter
p/2
Adjusted the position of the images relative to
the normally centered position to simulate
cameras motion
DF2.0
19
Fiber SRI Image Misregistration
0
Lens
p/2
Light
p
Splitter
Aberration
3p/2
Used Zernike aberrations with an amplitude factor
of 0.7?
Adjusted the position of the images relative to
the normally centered position to simulate
cameras motion
20
PSR for 90 Astigmatism for Zernike SRI
21
PSR for 90 Astigmatism for Fiber SRI
22
PSR for Various Zernikes for Zernike SRI
Results for 2nd and 3rd order Zernikes
(astigmatism, focus, coma, and trefoil)
23
PSR for Various Zernikes for Fiber SRI
90 astigmatism
focus
45 astigmatism
x coma
y trefoil
y coma
PSR axis is from 0.6 to 1.0
x trefoil
24
Image Misregistration Conclusions

• Zernike SRI is sensitive to image misregistration
  of a single image.
• Although some Zernike aberrations seemed to be
  more robust, most of the Zernikes saw a 20
  reduction in Strehl ratio for a motion of 2 of
  the beam diameter
• The Fiber SRI is fairly insensitive to image
  misregistration of a single image for all the
  Zernikes.
• Most of the Zernikes saw a 2 reduction in Strehl
  ratio for a motion of 2 of the beam diameter.
• 2 of the beam diameter corresponds to 160 µm on
  an 8-mm diameter beam

25
Setup with Camera Noise

• Number of Realizations 30
• Input Aberration is 90 degree astigmatism
• Maximum Count Value 10e9
• Eliminates effect of discretization

26
Zernike SRI - Camera SNR Analysis
27
Fiber SRI - Camera SNR Analysis
28
SNR Conclusions

• Zernike SRI seems to be very sensitive to camera
  noise.
• The result might be due to the lack of frames
  over which to average
• Maybe a 4-bin Zernike SRI would have better noise
  performance
• The fiber SRI seems to be very tolerant of noise.
  
• The PSR dropped to 80 when the SNR was around 1.0

29
System Studies with Distributed Atmosphere
30
Zernike SRI Image Misregistration for Atmospheric
Aberrations Setup

• We are using tilt-removed model of the
  atmosphere.
• D / r0 1,2,3,4,5
• Range 2.0 m
• Fresnel Number 5
• Denominator Factor
• 6 for D / r0 1, 2, and 3 .
• 2 for D / r0 4, and 5 .
• Number of screens 3
• Number of Realizations 9

31
Zernike SRI Image Misregistration
1
0.9
Average Peak Strehl Ratio
0.8
D / r0 5 DF 2
0.7
0.6
0.5
0.4
0.3
0.2
0.01
0.05
0.06
0.07
-0.01
0
0.04
0.03
0.02
dy/Dbeam
Error bars are standard deviation
32
Fiber SRI Image Misregistration
1
0.9
0.8
Average Peak Strehl Ratio
0.7
0.6
0.5
0.4
0.3
0.2
DoverR0 5
0.1
0
0.02
0.04
0.06
0.08
0.1
-0.02
0
0.12
dy/Dbeam
Error bars are standard deviation
33
Zernike SRI Image Misregistration
PSR is averaged over 9 realizations
D/r0 4
34
Fiber SRI Image Misregistration
35
Image Misregistration Conclusions

• For Zernike SRI, image misregistration effect
  increases with increasing turbulence.
• Again, the fiber SRI seems to be very insensitive
  to the misalignment of a single detector.

36
Zernike SRI Setup with Camera Noise

• Number of Realizations 30
• D/r0 5
• Range 2 m
• Fresnel number 5
• Maximum Count Value 10e9
• Eliminates the effect of discretization

37
Zernike SRI - Camera Noise
D / r0 5
38
Fiber SRI - Camera Noise
D / r0 5
39
Atm. Camera Noise Conclusions

• The Zernike SRI is sensitive to noise, but not as
  bad as with the astigmatism term tested earlier.
• Again the noise performance seems to be better
  for the fiber SRI than for the Zernike SRI.

40
System-Level Parametric Studies
41
SRI Comparison Overview

• In almost every comparison between the 3-bin
  Zernike SRI and the 4-bin fiber SRI, the fiber
  SRI had better performance.
• Future Work
• Compare a 4-bin fiber SRI to a 4-bin Zernike SRI.
• Complete rigorous AO study with both devices.

42
Questions?

• [phone] x137

43
Backup Slides
44
Peak Strehl Ratio
45
Intensity Debalancing
DoverR0 3
46
Mesh Parameters for FiberSRI
Effective Focal Length 37.4 mm Fiber Waist
5.2 µm Wavelength 1.55 µm Aperture diameter 8
mm
NOTE Determined using Steve Coys theory of mesh
parameters.
47
Mesh Parameters for Zernike SRI
Effective Focal Length 1 m Turbulence Strength
2.6 Wavelength 1.55e-06 m Aperture diameter
8mm
NOTE Determined using Steve Coys theory of mesh
parameters.
48
New Test System Components

• Ideal Compensator
• Used to apply the conjugate of the measured phase
  to the beam.
• Operates like an ideal deformable mirror.
• Peak Strehl Ratio Meter
• Used to calculate the ratio of the peak intensity
  of the far-field spot with the residual
  aberration remaining after ideal compensation to
  that without any aberration.
• We also used on-axis Strehl ratio which was
  calculated using the discrete version of the
  integral form.

49
Fiber SRI Intensity Debalancing for Atmospheric
Aberrations Setup

• We are using tilt-removed model of atmosphere
• Range 3.45 m
• Frenel number 3
• Number of Screens 3
• Number of Realizations 8
• Data is recorded for low ,medium and high
  turbulence.
• - D/r0 1,2,3,4,5

50
Fiber SRI Intensity Debalancing Conclusions

• Often saw increase in performance by adjusting
  splitting ratios.
• Saw a similar result with Zernike SRI
• More investigation needs to be done here to
  determine the reason for this effect.

51
Image Misregistration Setup

• We are using tilt-removed model of the
  atmosphere.
• D / r0 1,2,3,4,5
• Denominator Factor
• 6 for D / r0 1, 2, and 3 .
• 2 for D / r0 4, and 5 .
• Moving Image at 4 bin processing from 0 to 0.6
  times input beam diameter.
• Number of Screens 3