Okay, how much water do we *want* in the bucket? The size of the bucket is analogous to the sensitivity of the sensor (including the photodiode and amplifier) - the ISO, if you will. A small bucket will fill quickly - a high ISO. A large bucket will fill slowly - a low ISO.
Jim,
I like the bucket analogy but I think you've confused matters by equating the bucket size to the sensitivity of the sensor. This is perhaps a hangover from the film era when we could choose the sensitivity of the film.
With a digital camera, the sensors have a fixed sensitivity. Correct exposure for optimum, noise-free results is at one ISO only. Increase the ISO and you are basically sending the camera a forewarning, "I'm about to send you an underexposed image. Make the best of it." At which point, all the electronic wizadry the camera can muster whirs into action to often produce a surprisingly good result.
In fact, the result is often so good it's difficult to believe the sensitivity of the individual photosites has not been increased. However, I think part of this success is due to 'early' processing. I know from my own experience when scanning a seriously underexposed slide, if I scan at default settings, I know I'm never going to be able to compensate for that underexposure adequately in Photoshop. However, if I make the right adjustments at the scanning stage, which will include moving the middle slider on the histogram from a value of 1.00 to maybe 3.00, as well as increasing the analogue gain, I can get quite remarkable results. And after applying the noise reduction program 'Neat Image', I've got what I consider to be a remarkable transformation of a 'write-off' slide.
To get back to the bucket analogy, I would say the size of the bucket equates to the size of the photodetectors, the # of photons to the quantity of water, the diameter of the hose to the diameter of the aperture, the ISO to the inverse of the water pressure and the shutter speed to the time the water is flowing.
As far as I can see, these analogies will work across all digicam formats. For example, a really tiny digicam like the Minolta DiMage xt, will have tiny photosites or buckets (about 2.5 microns). It doesn't take much to fill them, therefore the diameter of the hose has to be small in proportion to the diameter of the lens aperture. The 3x zoom of the xt has apertures ranging from f2.8 to f3.6, but the format is so small (about 1/36th of the area of 35mm cropped to the 4/3 format), the aperture diameters are proportionally small. A fully exposed image on the Dimage xt, all buckets full (say a white wall) will be equivalent to an underexposed image on the Canon G2 with buckets only half full as a result of double the ISO. The noise levels will be similar, ie. xt at 100 ISO = G2 at 200 ISO, exposure compensated.
Of course, these figures are not in any way precise and different levels of technology in different cameras will appear to change these relationships. I'm rather amazed at how good the 3MP Dimage xt is, considering how tiny the camera and its pixels are. I'm thinking of getting one as a second camera