1. Phase amplification in Digital Holographic Microscopes
Sri Rama Prasanna Pavani1, Ethan Schonbrun2, W. T. Cathey1, and Carol Cogswell1
Dept. Of Electrical Engineering
1University of Colorado at Boulder
2Harvard University
Hi!
I am Prasanna Pavani.
My advisor Rafael Piestun and I are from the U of Colorado at Boulder.
MO-ISL Reseach Meeting - 10/4/2007
Pavani et al, CU and Harvard

2. Digital Holographic Microscope
Neuron
Photonic Crystal
P. Marquet, et al, Opt. Lett. 30 (5), (2005)
LynceeTec -
Pavani et al, CU and Harvard

3. MO-ISL’s interferometer
Interferogram
Cubic mask
Reconstruction
Fourier Transform
radians
Pavani et al, CU and Harvard

4. MO-ISL’s Digital Holographic Microscope
Interferogram
Reconstruction
radians
Pavani et al, CU and Harvard

5. Pavani et al, CU and Harvard
Limitations
Vibration sensitive, phase wrapping …. OK! What else??
Amy’s waveguide
Low SNR for weak phase objects makes reconstruction impossible!
Ouch!
Pavani et al, CU and Harvard

6. Pavani et al, CU and Harvard
SNR improvement – How?
Increase signal power?
Cranking up the laser doesn’t change the fringe modulation!
Reduce noise?
At low SNRs, any noise correction might swallow the signal as well!
Pavani et al, CU and Harvard
SNR = infinity
SNR = 10dB
SNR = 0dB

7. Pavani et al, CU and Harvard
Our method
Phase amplifies in higher orders of a hologram!
Interferogram
First order
Analytical proof:
Pavani et al, CU and Harvard

8. Pavani et al, CU and Harvard
Our method
Phase amplifies in higher orders of a hologram!
Higher orders
Interferogram P 2P 3P
Analytical proof:
Pavani et al, CU and Harvard

9. How to get higher orders?DC DC
+1 order
+1 order
Amplitude
binary
Amplitude
grayscale
+3 order
The first attack: Nonlinear amplitude holograms
Pavani et al, CU and Harvard

10. Binary amplitude holograms
Higher
Orders
have
low
diffraction
efficiency
Binarize
Pavani et al, CU and Harvard

11. How to get higher orders?DC DC DC
+1 order
+1 order
+1 order
Amplitude
binary
Phase
Amplitude
grayscale
+3 order
+2 order
The second attack: Phase holograms
Pavani et al, CU and Harvard

12. Pavani et al, CU and Harvard
Phase holograms
Diffraction efficiency of any
arbitrary order can be
maximized by varying k
I – Interferogram recorded with the DHM
k – constant for increasing the diffraction
efficiency of an arbitrary order
Pavani et al, CU and Harvard

13. Pavani et al, CU and Harvard
How about the NOISE?
Phase amplification does not necessarily mean increase in SNR!
What if the noise also amplifies?
Noise model
DHM detected image: I = J + N
Phase hologram
Fourier Transform
Pavani et al, CU and Harvard
Spectrum of Noise convolves with signal spectrum

14. Pavani et al, CU and Harvard
SNR improves!
F-1
1st order:
F-1
2nd order:
Signal amplifies but noise does not!
Pavani et al, CU and Harvard

15. Pavani et al, CU and Harvard
SNR improvement
mP+N
4P+N
3P+N
2P+N
P+N
Order: m
SNR:
SNR increases linearly with the order number!
Pavani et al, CU and Harvard

16. Comparison with existing technique
I = J + N
Fourier Transform
Noise spectrum adds here! For us it convolves!!
Existing
Proposed
Which is better?
Pavani et al, CU and Harvard

17. We WIN! Look at the higher orders!
mP+N
4P+N
White gaussian noise model
3P+N
2P+N
P+N
Order: m
SNR:
Pavani et al, CU and Harvard

18. Pavani et al, CU and Harvard
Conclusion
Discussed phase amplification in amplitude and phase holograms
SNR improves linearly with the order number in phase holograms
For a white gaussian noise model, SNR can be made better than the current state of art!
Pavani et al, CU and Harvard

19. Pavani et al, CU and Harvard
Acknowledgements
Prof. Kelvin Wagner
Prof. Rafael Piestun
Sri Kaushik Pavani
CDMOptics PhD Fellowship
National Science Foundation Grant No
Pavani et al, CU and Harvard