Einstein and digital cameras

Started Jan 19, 2005 | Discussions thread
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Grenville
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Einstein and digital cameras
Jan 19, 2005

It is just one hundred years since Einstein published his three remarkable papers on the theory of special relativity, the explanation of Brownian motion and the explanation of the photoelectric effect. The last of these, for which he was awarded the Nobel prize, introduced the idea that light is ‘quantized’, consisting of discrete bundles of energy now referred to as photons. Spurred by the ever-increasing pixel count in digital cameras and the familiar problem of noise I wondered what are the fundamental limits on ISO and pixel size determined by the detection of individual photons. It’s a simple enough calculation but the results are interesting for anyone trying to see what the future could or could not hold for digital photography. Apologies if this has already been covered on the forum

A useful starting point is the definition of ISO for film. According to this Kodak web site: http://www.kodak.com/global/plugins/acrobat/en/digital/ccd/papersArticles/PhotographyWithAn11-megapixel35mmFormatCCD.pdf

ISO is equal to 10 divided by the exposure in lux.seconds at the film plane, for what is judged to be a correctly exposed 18% grey card. In order to calculate the corresponding photon noise of a digital camera we need to convert the photometric units into numbers of photons. Lux is defined in terms of the sensitivity of the eye to different wavelengths and corresponds to 1/680 of a watt per square metre at a wavelength of 555 nm. Using Einstein’s formula for the photoelectric effect (energy equals Planck’s constant times frequency) it is a simple matter to show that 1 lux corresponds to 4,100 photons per second per square micron.

From the definition of ISO the detector illumination for a ‘correctly exposed’ 18% grey card is therefore (41,000 / ISO) photons per square micron and the corresponding number of photons per pixel is 41,000 A / (ISO x M), where A is the total detector area in mm squared, and M the megapixel count.

This formula indicates the trade off between pixel count and ISO setting and the advantage of large detector size. What does it say, for example, about the Canon EOS 20D and the 1Ds Mk II at the 3,200 ISO setting? The maximum numbers of photons available per pixel are, respectively, 530 and 660 (the similarity reflects the similar pixel sizes for the two cameras). Signal/noise ratio equals the square root of number of counts, i.e. 23 and 26 in these examples. A hypothetical 20D with 16.7 megapixels would have 257 photons per pixel (signal/noise = 16). Dividing photons between the three RGB colours will reduce the count per detector by a factor of (at least) three. For the shadow areas of an actual photograph the photon count and the signal to noise would of course be correspondingly much lower, too low in fact for high quality images.

These calculations ignore the negative effects of electrical noise generated in the detector, typically a few counts per pixel, and photon detection efficiencies of no more than 50% in the best current examples. On the other hand they also ignore the beneficial use of clever signal processing and signal averaging in the camera software to reduce the visible effects of noise in individual pixels. Nevertheless the calculations suggest that the current breed of digital cameras is not far away from the fundamental limits set by nature and Einstein, and that the scope for increasing both pixel count and ISO beyond current values is rather limited.

So Canon, you must have done these calculations, please produce an affordable full format 16.7 megapixel digital SLR for serious amateurs in a body the size of the 20D. When that happens, in the not too distant future (?), I will trade in my 10D.

Plots of signal/noise ratio against exposure for some actual detectors are given in the Kodak web reference above.

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