Reciprocity law failure
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Old 07-28-2014   #1
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Default Reciprocity law failure

With film and long exposures, reciprocity law failure had to be taken into consideration. It is not something that ever worried me in particular because for me, any exposure longer than a couple of minutes, always involved lots of guesswork and luck. But I was wondering whether reciprocity law failure also occurs with digital sensors.

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Old 07-28-2014   #2
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Default Re: Reciprocity law failure

The physics (chemistry?) behind reciprocity failure in film is one of those subjects I never really understood and I'm not sure that even the people who formulate film really understood it either. Of course, reciprocity failure is a real effect and it can be compensated for, but my guess is that any pretense at reciprocity failure would be limited to the empirical level, e.g., creating films that perform well with long exposures would be a "black art" guided more by experience than theory.

On the other hand, the physics behind semiconductors is much better-understood. I am not sure that digital sensors suffer from classical reprocity failure at all. However, in long exposures with digital sensors will suffer from "hot" pixels, thanks mainly to leakage of the capacitors where the charge from the exposure in progress is stored. Hot pixels of this kind are primarily the result of defects in the crystalline structure of the silicon. This results in scattered bright pixels in the image, the number and intensity of which depends on the exposure time, the ISO rating at which the exposure was taken, and the temperature of the sensor. Higher temperatures, greater ISO ratings, and longer exposures result in more and brighter "hot" pixels.

Because of their nature, "hot" pixels appear at fixed locations on any one imager, with each imager having a different pattern of defective pixels. If it weren't for the fact that imagers can develop new hot pixels over time, I would call the pattern of hot pixels a digital fingerprint for the imager. Because of the pixels' fixed locations, they are easy to suppress by a method called dark frame cancellation. This can be done manually, but some cameras have the ability to do this automatically. In dark frame cancellation, a second exposure is made at the same exposure time, ISO setting, and temperature as the original, but with the lens covered or the imager otherwise shielded or rendered insensitive to incoming light. The dark frame is then arithmetically subtracted from the original image to render a new image without the hot pixels.

One variation on dark frame subtraction I have seen is similar to mapping out dead or stuck pixels, where the locations of the hot pixels are mapped, the data from the hot pixels thrown out, and the holes filled in by interpolating data from the surrounding pixels. This has the advantage on not requiring a dark frame, but the cancellation is less complete and more prone to artifacts.

Another way to suppress hot pixels is to cool the imager to cryogenic temperatures, say, the temperature of liquid nitrogen (-196 deg C). At that temperature, hot pixels are cut way down. In astronomical applications, they use a more sophisticated version of dark frame subtraction in addition to cryogenic cooling.

I have also heard of what may be a related effect in which a film's sensitivity can be enhanced by and exposure of thirty minutes or so, if I remember right, to light dim enough just barely to increase the background fog level despite the long exposure. Anyone else know more about that?

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