CS: Discussion with Ashwin Wagadarikar on Duke's Coded Aperture Snapshot Spectral Imagers

In light of the small conversation with Ramesh Raskar where he does a beautiful work in computationa photography, I wanted to also give the proper light on the hardware development at Duke that uses coded aperture. This is a short e-mail discussion I had with Ashwin Wagadarikar, a Ph.D. student, about a year ago. It was mostly about a discussion about the reasoning that went into the single and dual disperser system in the Coded Aperture Snapshot Spectral Imagers.

Me:

I have read both articles and here is the thing I cannot seem to fully understand: Why do you need two dispersive elements ? to provide another layer of mixing ?

Ashwin:

The two dispersive elements in the dual disperser architecture are arranged in opposition, so that the two dispersions cancel each other out. However, given that there is an aperture code placed after the first disperser, what the detector essentially measures is a well registered spatial scene with the code modulation on top of each object in the scene corresponding to the localized spectrum of the object.

The well registered spatial scene means that it is very easy to focus the camera on the objects.

As you will see with our single disperser papers, it is not necessary to have both dispersers to have a snapshot spectral imager. There are differences between the two instruments, which can influence the choice of which instrument to use for what spectral imaging application. These differences are discussed in greater detail in the paper that is under review with Applied Optics, but not so much in the SPIE paper.

Me:

So I am taking out of this that the main reason for the second disperser has more to do with convenience than with a compressed sensing mixing requirement. Hence there is no imperative need for a second disperser.

Ashwin:

I suppose you can look at it from both perspectives. The way the dispersers and the coded aperture are arranged in the dual disperser results in a purely spectral mixing at each spatial location. Having just one disperser will result in both spatial AND spectral mixing, which is more 'aggressive' coding. The dual disperser arrangement luckily gives us that convenient result of having a spatially well registered image on the detector.

Ultimately, using either design, we're going to have to recover a 3 dimensional dataset of information from just one 2 dimensional array of measurements. In the case of the dual disperser, we are able to recover an (x, y, lambda) datacube from just (x, y) measurements.

To give some perspective as tow why this design is interesting. The average cost of a hyperspectral imager is $100,000.