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 http://moisl.colorado.edu 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

Digital Holographic Microscope Neuron Photonic Crystal P. Marquet, et al, Opt. Lett. 30 (5), 468-470 (2005) LynceeTec - http://www.lynceetec.com Pavani et al, CU and Harvard

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

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

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

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

Pavani et al, CU and Harvard Our method Phase amplifies in higher orders of a hologram! Interferogram First order Analytical proof: http://moisl.colorado.edu/phaseamp/phaseamp.html Pavani et al, CU and Harvard

Pavani et al, CU and Harvard Our method Phase amplifies in higher orders of a hologram! Higher orders Interferogram P 2P 3P Analytical proof: http://moisl.colorado.edu/phaseamp/phaseamp.html Pavani et al, CU and Harvard

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

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

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

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

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

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

Pavani et al, CU and Harvard SNR improvement mP+N 4P+N 3P+N 2P+N P+N Order: 1 2 3 4 m SNR: SNR increases linearly with the order number! Pavani et al, CU and Harvard

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

We WIN! Look at the higher orders! mP+N 4P+N White gaussian noise model 3P+N 2P+N P+N Order: 1 2 3 4 m SNR: Pavani et al, CU and Harvard

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

Pavani et al, CU and Harvard Acknowledgements Prof. Kelvin Wagner Prof. Rafael Piestun Sri Kaushik Pavani CDMOptics PhD Fellowship National Science Foundation Grant No. 0455408 Pavani et al, CU and Harvard