Reciprocity Failure

I did a search for this but I could only find comments on fairly ancient threads so I'm asking the question again, in the light of more modern sensors.

I seem to notice that (with my k10D) the noise in dark areas of scenes in poor light seems much worse than the equivalent in bright scenes, despite both having the 'correct' exposure (i.e. longer exposure time for lower lighting). If reciprocity applied, then this should, surely, not be the case. What is going on? It just doesn't seem possible to compensate by using extended exposure times in low light.

This is because the signal produced by the sensor in dull light is weaker, has to be amplified more and this results in increased levels of electronic noise.

On film, if you keep on sending more photons of light (long exposure) more silver halide crystals will be activated and be able to be developed. These crystals either activate or not and the total that do affect the density of the silver image produced.

The sensor does not behave in the same way, rather producing an analogue signal from each pixel that needs to be digitised in the A/D converter.

OK but the problem with that explanation is that it implies that Exposure Time would not be relevant. Reciprocity applies over a huge range of light levels and, when it fails, it must be because each sensor needs a certain rate of photons arriving in addition to the specified number during the exposure time for it to produce a given voltage (which would correspond to the brightness of the scene in that direction.
I guess it implies that the sensor is, effectively, discharging at some, albeit slow, rate which corresponds to long exposure times, whereas the film crystals remain permanently changed, once the light has activated them.

Fixed pattern noise includes what are called "hot pixels," which are defined as such when a pixel's intensity far surpasses that of the ambient random noise fluctuations. Fixed pattern noise generally appears in very long exposures and is exacerbated by higher temperatures. Fixed pattern noise is unique in that it will show almost the same distribution of hot pixels if taken under the same conditions (temperature, length of exposure, ISO speed).

from here link

Might that explain it?

I did write about it in some topic here, can't find it now though .
Problem you are seeing is related to noise-signal ratio.
Simply in dark conditions the number of photons hitting sensor produces lower number of eletrons (that in bright conditions) which is nearer to noise level, hence noise is more pronounced.
Simple example could be, imagine you are listening to quiet music (like: poor light), so lower level of energy (like: photons) hits your ears (like: sensor), at the same time you have some background noise (like: noise produced by sensor and electronics) which is only a bit quiter than music, obviously background music would be a bit distracting.
Turning volume up (like: good light) "covers" backgroud noise and it is no longer distracting (like: less noisy image).

There is no reciprocity in the way you describe it above, as properly exposed dark scene is darker than a scene in good light anyway, so it delivers (to the sensor) less light anyway than properly exposed bright scene. To get similar level of light on the sensor in poor conditions, you would have to boost exposure much more than dictated by "proper" exposure (what would produce other problems, related to veryyyy long exposure).

You can try something, on relatively low ISO (100, 200) take 3 pictures (raw) of the same scene, first underexposed by some 2 stops, second with correct exposure, third overexposed by 2 stops. Then develop all pictures, add 2 stops in your raw converter to the first picture, don't change exposure of the second image, lower exposure of the third image by 2 stops. So all pictures at the end should be exposed more-less at the same level, now compare noise on all pictures, diference should be clearly visible.

I hear what you say about 'correct' exposure but there is another issue which the simple audio example doesn't address. That's the issue of what would be called receiver bandwidth, in communications terms. Increasing the exposure time is, effectively, decreasing receiver bandwidth. This improves signal (carrier) to noise ratio pro-rata in signalling applications. However, we aren't dealing with the same sort of signal (i.e. it's a non coherent source of random photons rather than a coherent, weak radio or audio signal) and this will make some difference. I think it is that difference which explains the phenomenon.
However, the same thing applies to film - you get single crystals affected by a stream of individual non-coherent photons and there will be similar statistics involved. The thing about film is that you can't just 'screw up the gain'. You have to use different emulsions. Compensating / exposing for longer in the printing is the equivalent and that will give odd results.
I guess that, in a practical way, you are right and that the ISO number applies to higher light levels and that, indeed, reciprocity does fail at low light levels but the subjective appearance is different. One just has to allow for this.

Do you mean at the same ISO?

One thing with CCD (as in the K10D) is they get pretty warm, so longer exposures heat up the CCD and increase the level of noise.
A cooled CCD (or indeed a lower current CMOS sensor as in the K20D & K7) is less susceptible to this phenomenon.

Additionally, battery noise has to be factored in - though this is less of an issue with the K10D, K20D, K7 that have Lithium Ion cells. In the *ist-D, using poor batteries for longer exposures dramatically increased the level of noise - the batteries get warm and can generate their own noise.

So, I don't think it can be compared film... but there are additional factors in the circuit design as a whole that need to be considered

HTH!
Matt

"Do you mean at the same ISO?"
Yes - selected manually. Left to its own devices, the camera would upset the 'fairness' of any test.

I imagine that, as the effect of low light get noticed more, there will be a plethora of opinions and folklore about how to get the best out of low light shots. I must say, the effect of noise in darker areas can be quite aesthetically pleasing., although it is sometimes a bit of a surprise.

It's not necessarily amplified more. If it was you'd lose dynamic range and dark parts would be as light as light parts. In the audio world this is known as compression.

In darker areas of the picture then the light exposed to the sensor ( or film ) is of less energy and thus closer to the noise of the sensor ) or noise of the film ) and therefore you can see the noise more easily. i.e less signal to noise ratio.

The amplification of the signal from the sensor should remain equal across each pixel, otherwise you're getting into the realms of dynamic range manipulation which is a post processing function.

The principle of expose to the right ( ETTR ) is about maximising the dynamic range of the sensor by exposing the shot soi that the brightest parts are captured just below clipping of the Analogue to digital converter of the sensor.