Imaging Without Lenses

February 3, 2018

Imaging Without Lenses Computational #photography w. compressive sensing (reconstruction from arbitrary image bases) & diffractive imaging (forming an image via scattering from gratings) via @AmSciMag


Computational Imaging

As its name suggests, the key advance in this new paradigm is the essential role played by computation in the formation of the final digital image. …
When the orbiting Hubble Space Telescope first sent its photos to Earth in the late 1980s, the images were far blurrier than expected; it quickly became apparent that something was wrong with the telescope optics. NASA scientists diagnosed the optical problems and, in the years before the unmanned telescope could be repaired, designed sophisticated digital processing algorithms to correct the images by compensating for many of the effects of flawed optics.

In the mid-1990s, W. Thomas Cathey and Edward R. Dowski, Jr., realized that one could go further still: One could intentionally design optics to produce blurry, “degraded” optical images, but degraded in such a way that special digital processing would produce a final digital image as good as, or even better than, those captured using
traditional optics

Diffraction for Imaging

One class of lensless devices for imaging macroscopic objects relies on miniature gratings consisting of steps in thickness in a
transparent material (glass or silicate) that delay one portion of the incident light wave with respect to another portion. The pattern of steps expresses special mathematical properties that uniquely ensure that the pattern of light in the material does not depend much on the wavelength of the light and thus upon the unintended variations in thickness arising during the manufacture of the glass. …The light from the scene
diffracts through the grating, yielding a pattern of light on the array that does not appear like a traditional image—it does not “look good” but instead more like a diffuse blob, unintelligible to the human eye. Nevertheless, the blob contains enough visual information (albeit in an unusual distribution) such that the desired image can be reconstructed through a computational process called image

Compressive Sensing

….An optical image on a sensor is just a
complicated signal that can be represented as a list of numbers and processed digitally. Just as a complicated sound can be built up from a large number of simpler sounds, each added in a proportion that depends on the sound in question, so too can an image be built up from lots of simpler images. …

Enter compressive sensing. Theoretical results from statisticians have shown that, as long as the information from the scene is redundant (and the image is thus compressible), one does not need to measure such mathematically elegant bases, but can use measurements from a suitably random one. If such “coded measurements” are available then one can still exploit the idea that the signal can be well represented in the elegant basis elements (such as cosines or wavelets) and recover the image through compressive sensing.