[math-fun] Single pixel cameras
There have been a number of recent articles (from MIT and others) about "single pixel" cameras and "ghost imaging". But IMHO most of these descriptions confuse rather than promote understanding. Here's my take: A classical (1930's-1990's) TV camera *raster scans* an image (which hopefully remains still for the duration of the scan) with a single point spot, so one could -- at least in theory -- dispense with all of the lenses, stage lights, etc., and simply have a single-pixel sensor which receives light that was produced by a laser beam producing a single point scanned over the scene whose image is being captured. The classical TV camera thus converts a 2D image into a "1D" intensity v. time signal. The 2D image can be reconstructed by the same scanning pattern from the same laser, at least in theory, by varying the laser intensity with the original captured intensity values as this laser scans a *blank* screen. Of course, there's nothing special about the raster scanning pattern; indeed, *any* pattern which covers the image will work, so long as the reconstruction laser follows the same pattern. I believe that some of the alternatives to 1920's and 1930's TV systems used other nonraster scanning schemes. But wait -- there's more! There's also nothing special about using a *point* of light! One could illuminate the picture to be scanned with a long sequence of random 2D patterns of light, with the single-pixel sensor converting its *average* taken over the entire scene into a time-varying signal whose next value would be the *average over the entire scene* of the light pattern reflected from the next random pattern, and so on. We can now reconstruct the picture in a manner reminiscent of the laser point scanner by projecting the same sequence of random 2D patterns onto a blank screen and modulating their intensity of the (single) projector bulb with the time-varying signal we just captured. With modern stage lighting coming from large arrays of LED's, whose intensities can be varied at very high frequencies, it should be possible to go through a pattern sequence fast enough to capture a scene in pretty decent resolution relatively quickly. Now we could also choose 2D illuminating light patterns that cycle through various horizontal and vertical wave patterns with various spatial wavelengths and phases. Voila! We have just approximated a 2D Fourier transform of the 2D image.
A precursor of modern television used a mechanical rotating disk, with holes, which scanned the visual field. The playback system used a similar scanning disk, which had to be phase synchronized with the camera. Resolution was low. https://en.wikipedia.org/wiki/Mechanical_television
participants (2)
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Dave Dyer -
Henry Baker