Wednesday at FiO – More computational imaging, phase-space anlaysis, and phase-retrieval

I know this post is late, but I hope it is worth the wait (if anyone was waiting ). My energy levels were just not sufficient for me to write anything coherent at the end of the fourth day of conference, but I am feeling better now that the conference has ended. So let’s begin with events of Wednesday.

Wednesday’s program convinced me that parallel universes do exist. I was shuttling between ground floor and first floor (aka banquet floor) trying to pop-in and pop-out of talks at right times. Keeping with theme of last post, I will point out one talk each from above three areas. As a bonus, I also point out how my talk went.

Computational imaging:

The first session of the day that I went to was the joint interdisciplinary session of AO/COSI/SRS. The talk that I remember clearly is Marc Levoy’s on light-field photography and microscopy (JWA3). Marc has visited Singapore earlier and given a similar talk. So he had advised me against attending his talk and spend time gathering something new. But it was good to see how he is planning to apply these methods to decoding of neuronal wiring in zebra fish (or another?) embryos. The idea is to stimulate neurons located at arbitrary 3D locations using light-field illumination architecture. This ’stimulate firing’ of neuron should be followed by fast 3D imaging of activation of neighboring neurons. Yes, the neurons have to be labelled correctly – you need to label neuronal ion channels (rhodopsin) in such a way that when the label is excited the channel opens. Plus, all neurons have to be labelled with calcium indicator dye which indicates when certain neuron becomes active. The enabling technology in labeling is genetic modification of the zebra fish to express these proteins in live animals.

Phase retrieval:

The next noteworthy talk I attended was Greg Gbur’s (SWA1) on intensity diffraction tomography. The idea is rather neat – you measure the phase of the specimen by tomography but without explicitly measuring phase (e.g. by interferometry or otherwise). The idea relies on the fact that phase information of the specimen does affect intensity of diffracted light and hence one ought to be able to retrieve the phase distribution from intensity measurements alone. I should note that similar goal is achieved in a different way by transport of intensity formulation.

In the same session was my talk about registration of gradient information (SWA4). We know that traditional methods of image registration are meant to register measurements of the same function. Therefore, when we want to register gradients of some function along X and Y directions, these methods don’t work. I figured that registration of gradients requires that you reformulate the registration problem and devise a new procedure for computing the registration information. This registration has allowed me to accurately reconstruct phase information from phase-gradients that I measure with differential interference contrast (DIC) and differential phase contrast (DPC). I did better at this talk than the one on Monday and had some useful discussion after it. I was helped by the fact that the speaker after me had withdrawn, giving me more time to delve onto details.

Phase-space analysis:

It was pointed out by Prof. William Rhodes that Wigner distribution computed from discrete samples of a signal may contain erroneous structures (FWW1). This happens because when a temporal signal is sampled, it becomes periodic in frequency with the period equal to the sampling frequency. These periodic components of frequency produce cross-terms. These cross-terms cancel out if one projects the signal along frequency (to obtain signal intensity) but do not if one projects the signal along space (to obtain spectrum density). These errors are exacerbated when one operates on this distribution (e.g. propogate by shearing) and then again tries to compute intensity or spectral density by projection.

Phase-space optics 1: Introduction

As noted in the last post about Frontiers in Optics (FiO), one of the interesting things that will happen at the conference is the special symposium on phase-space optics. I have been intrigued by these ideas since sometime now. In upcoming posts, I will recount some basics of the phase-space optics. I hope those who are getting started in this area will find these posts informative or at least interesting, and those (particularly FiO attendees) who already have some insights will share them via comments.

I have found books by Leon Cohen [1] and a compilation of selected papers as part of SPIE milestone series [2] useful. Cohen has contributed greatly to the basic ideas of phase-space representations and showed that all phase-space distributions are special cases of a particular distribution – which has come to be known as the Cohen class. The phase-space representations have been used in optics (and signal processing in general) for analysis and representation of signals and systems in a way that matches our intuition more closely. However, once someone has been used to the Fourier tools for few years , the phase-space representations may not seem that intuitive, as happened in my case:-).

Joint distributions were first invented in quantum mechanics. They were used by Eugene Wigner [2, pp. 30] to represent probability of a particle possessing given position and given momentum. The distribution represented how particle may be `distributed’ as a function of position and momentum. Gabor [2, pp. 120] and Ville [2, pp. 149] introduced joint distributions to signal analysis to represent temporal signals in a way that matches human intuition. Until the works by Gabor and Ville, signal analysis was performed either in time-domain or in frequency-domain. However, when a human analyzes signal, he/she is usually interested in how signal’s frequency changes over time, e.g., how pitch of some one’s voice changes over time. The last sentence of the abstract of Ville’s paper reads “These notions of instantaneous frequency and of the instantaneous spectrum are introduced to furnish a firm theoretical basis for studies of frequency modulation, …, and in a general way,of all problems for which classical harmonic analysis furnishes a description which departs too far from physical reality.”