Computational Optical Sensing and Imaging COSI

1
Computational Optical Sensing and Imaging (COSI)

• Sri Rama Prasanna Pavani

http//moisl.colorado.edu
Grad. student seminar - 2/14/2007
2
Traditional Imaging
Brightfield phase object
Amplitude Object
Phase Object
3D Object
Image
2f
2f
Lens (f)

• Great for 2D objects, not for 3D ones
• Great for amplitude objects, not for phase
  objects
• Resolution is limited by the systems NA
• Detector sampling must obey Nyquist

High NA
Low NA
3
Electronic Imaging
Digital detector
Object
Image
2f
2f
Lens (f)
Final image

• Exploits the cheapness of computing!
• Great for image processing Noise reduction,
  pattern recognition, machine vision, etc.
• Retains the fundamental disadvantages of
  traditional imaging!

4
Computational Optical Sensing Imaging(COSI)
Unconventional Optics Masks! Gratings!
Holograms! sub-apertures! Etc.
Detector
Object
Active illumination
Final image

• Active Illumination and unconventional optics are
  application dependent
• Detected image is only intermediate! Processing
  required to obtain final image
• Captures information thats lost in traditional
  imaging
• Superresolution! Phase imaging! Compressed
  sensing! 3D imaging! Extended depth!

5
COSI examples
S.R.P.Pavani et al, Applied Optics 47 15-24
(2008)
1. Active COSI for phase imaging
Phase Object
S.R.P.Pavani, R. Piestun, Optics Express
(accepted) (2008)
2. Passive COSI for 3D imaging
3D Object
Fourier Plane
6
Phase imaging
Brightfield phase object
Vs

• Amplitude mask in the field diaphragm
• Pattern is imaged on the sample
• Phase object distorts the pattern
• Record the distorted pattern
• Analytical formula calculates phase

0.2 0.1
(mm)
0.4 0.2
0 0.2 0.4
(mm)
(mm)
7
Information retrieval

• Analytically relate deformation to the optical
  path length
• Consider a 1D phase object p(x)
• Ray R from point A, after refraction, appears as
  if it originated from B
• Deformation t(x) is the distance between A and B

Normal
Tangent
n2
p(x)
n1
A
B
t(x)
S. R. P. Pavani et al, Quantitative
structured-illumination phase microscopy,
Applied Optics 47, 15-24, (2008) S. R. P. Pavani
et al, Structured-illumination quantitative
phase microscopy, in COSI CMB4, (OSA, 2007)
8
Information retrieval 2D
1D deformations
After 1D integrations
C1 C2 . . CN
Quantitative Phase
2D deformation
K1 K2 KN
S. R. P. Pavani et al, Quantitative
structured-illumination phase microscopy,
Applied Optics 47, 15-24, (2008) S. R. P. Pavani
et al, Quantitative Phase Estimation with a
Bright Field Microscope, FiO FTuP4, (OSA, 2007)
9
Experimental Results
10
COSI examples
S.R.P.Pavani et al, Applied Optics 47 15-24
(2008)
1. Active COSI for phase imaging
S.R.P.Pavani, R. Piestun, Optics Express
(accepted) (2008)
2. Passive COSI for 3D imaging
11
3D imaging

• Obtain 3D information from 2D image(s)

Parallax
Focus/Defocus
Context
Back
Front

• Defocus is inherently related to depth
• Defocus parameter (y) depends on
• wavelength (l)
• aperture size (r)
• best focus distance (zobj)
• object distance (zobj)

12
Depth from diffracted rotation
Rotating PSF
Standard PSF
f
Slices
Mask
Lens
3 2 1 0

• Use rotating PSF to estimate defocus
• Axial superresolution
• Cramer Rao bound
• One order of magnitude lower than the minima of
  the standard PSF
• Constant through a wide range of defocus

CRB / Estimator variance
-60 -30 0 30
60
(y)
Defocus
13
Experimental Results
US one cent coin
14
Experimental Results
Rotating PSF Image
Standard PSF Image
Optically estimated depth map
80 40 0 -20
A. Greengard, Y. Y. Schechner, and R. Piestun,
Depth from diffracted rotation, Opt. Lett. 31,
181-183 2006 A. Greengard, Y. Y. Schechner, and
R. Piestun, to be published
15
Experimental Results
Rotating PSF Image
Standard PSF Image
Optically estimated depth map
80 40 0 -20
A. Greengard, Y. Y. Schechner, and R. Piestun,
Depth from diffracted rotation, Opt. Lett. 31,
181-183 2006 A. Greengard, Y. Y. Schechner, and
R. Piestun, to be published
16
Experimental Results
Rotating PSF Image
Standard PSF Image
Rotating PSF Image
Standard PSF Image
Optically estimated depth map
Optically estimated depth map
40 20 0 -20
80 40 0 -20
A. Greengard, Y. Y. Schechner, and R. Piestun,
Depth from diffracted rotation, Opt. Lett. 31,
181-183 2006 A. Greengard, Y. Y. Schechner, and
R. Piestun, to be published
17
COSI examples
S.R.P.Pavani et al, Applied Optics 47 15-24
(2008)
1. Active COSI for phase imaging
S.R.P.Pavani, R. Piestun, Optics Express
(accepted) (2008)
2. Passive COSI for 3D imaging
18
More COSI examples
M. G. L. Gustafsson, J. of Microscopy 198 (2),
8287 (2000)
3. Active COSI for transverse super-resolution
Object
E. R.Dowski, W.T. Cathey, Applied Optics 34,
18591866 (1995).
4. Passive COSI for extended depth of field
Detector
3D Object
CDMOptics
19
Conclusion

• COSI is cool!

20
Acknowledgments
Tom Cathey
Sharon King
Adam Greengard
Ariel Libertun
CDMOptics PhD Fellowship
21
References

• J. W. Goodman, Introduction to Fourier Optics,
  (Roberts Company, 2005)
• M Pluta, Advanced Light Microscopy, vol 2
  Specialised Methods, (Elsevier, 1989)
• M. R. Arnison, K. G. Larkin, C. J. R. Sheppard,
  N. I. Smith, C. J. Cogswell, Linear phase
  imaging using differential interference contrast
  microscopy Journal of Microscopy 214 (1), 712
  (2004)
• C. Preza, "Rotational-diversity phase estimation
  from differential-interference-contrast
  microscopy images," J. Opt. Soc. Am. A 17,
  415-424 (2000)
• Sharon V. King, Ariel R. Libertun, Chrysanthe
  Preza, and Carol J. Cogswell, Calibration of a
  phase-shifting DIC microscope for quantitative
  phase imaging, Proc. SPIE 6443, 64430M (2007)
• E. Cuche, F. Bevilacqua, and C. Depeursinge,
  Digital holography for quantitative
  phase-contrast imaging, Opt. Lett. 24, 291-293
  (1999)
• P. Marquet, B. Rappaz, P. J. Magistretti, E.
  Cuche, Y. Emery, T. Colomb, and C. Depeursinge,
  Digital holographic microscopy a noninvasive
  contrast imaging technique allowing quantitative
  visualization of living cells with subwavelength
  axial accuracy, Opt. Lett. 30, 468-470 (2005)
• M. Born and E. Wolf, Principles of Optics, ed. 7,
  (Cambridge University Press, Cambridge, U.K.,
  1999).
• A. C. Kak, M. Slaney, Principles of Computerized
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• A. C. Sullivan, Department of Physics, University
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• Huang D, Swanson EA, Lin CP, Schuman JS, Stinson
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  tomography, Science1991 Nov 22254(5035)1178-81.
  
• A. F. Fercher, C. K. Hitzenberger, Optical
  coherence tomography, Chapter 4 in Progress in
  Optics 44, Elsevier Science B.V. (2002)
• A. F. Fercher, W. Drexler, C. K. Hitzenberger and
  T. Lasser, Optical coherence tomography -
  principles and applications, Rep. Prog. Phys. 66
  239303 (2003)
• M. R. Ayres and R. R. McLeod, "Scanning
  transmission microscopy using a
  position-sensitive detector," Appl. Opt. 45,
  8410-8418 (2006)
• Barone-Nugent, E., Barty, A. Nugent, K.
  Quantitative phase-amplitude microscopy I
  optical microscopy, J. Microsc. 206, 194203
  (2002).
• J. Hartmann, "Bemerkungen uber den Bau und die
  Justirung von Spektrographen," Z. Instrumentenkd.
  20, 47 (1900).
• I. Ghozeil, Hartmann and other screen tests, in
  Optical Shop Testing, D. Malacara, second edition
  Wiley, New York, 1992, pp. 367396.
• R. V. Shack and B. C. Platt, Production and use
  of a lenticular Hartmann screen, J. Opt. Soc.
  Am. 61, 656 (1971).
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22
Metrology - Cubic phase mask
120 80 40 0
360 180
480 240 0
Deformation
Quantitative OPL profile
140 70 0
Cubic phase mask
360 180
480 240 0
Deformation
Quantitative OPL profile
23
Our method How?
1 Dimensional analysis
(from geometry)
(Snells law,
)
(Taylor expansion)
C 2 (C2 C1)
24
Our method How?
M
2 Dimensional analysis
N
Apply 1D solution along x and y to obtain
and
P2
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3D imaging simulation
f
f
f
f

• Parabola focussed a little farther from the
  apex
• Efficient rotating transfer function in the
  Fourier plane

Detector
Textured Parabolic surface
Lens (f)
Lens (f)
Mask
Reconstructed depth map
Traditional system
Rotating PSF system
0.2 0 -0.2
1 0.5
0 0.5 1
(cm)
(cm)
Z Depth Z0 Rayleigh range
26
Experimental analysis of Wavefront coding

• Acquired psfs of a Cubic, CF, and CC over a 30cm
  range.
• Built LS filters and saw EDF in real time.
• Compared different masks

Traditional
EDF with cubic mask
27
Low efficiency problems

• 1. Transfer function is absorbing

Transfer function intensity
Transfer function phase
1.09

• 2. Low diffraction efficiency of DOE
  implementation

4 2 0
Continuous amplitude CGH
Binary phase CGH
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Comparison
Quasi-rotating PSFs
Exact rotating PSF
Optimal quasi-rotating PSFs
1.84
42.07
57.01
CRB / Estimator variance
Phase only super-resolving mask
Defocus
Pavani and Piestun, Quasi-rotating point spread
functions, Optics Letters (in preparation)