Re: Light fall off on dSLRs - an experiment

In article <1142579809.097133.72650@xxxxxxxxxxxxxxxxxxxxxxxxxxxx>, bjw@xxxxxxxxxxxxxxxxx writes


Independent of Lambertianness, think of how it behaves before
getting all the way to the extreme angle. Imagine that the angle
of incidence is 70 degrees off normal - there are cos(70) = 0.34
times as many photons incident per area.

Yes you are correct, it was late last night when I responded - there *should* be a cos(theta) reduction *if* the pixels were flat, without any microlenses at all. The microlenses, however change this characteristic, since they present almost the same collection area independent of the incident angle. Think of a sphere - it has the same diameter from whatever angle you look at it. Obviously being spherical segments rather than full spheres, the lenses will change their effective collection area at extreme angles, but this may be well beyond the angles available from practical camera lenses. So the actual area reduction at each pixel really depends on how completely spherical the microlenses are and also how much they obscure each other at high incidence angles.

These microlenses are actually made by heating etch resist material deposited on the pixel until it melts and reflows into a spherical segment. We make thermal imaging detectors with a similar process to create indium bump bonds at each pixel for connecting each cadmium mercury telluride alloy sensel to its CMOS circuit in the readout matrix. Depending on the thickness of the deposited material, it is possible to create almost perfect spheres with a small flat base of much less than the radius of the sphere itself. So creating almost perfect truncated spheres for microlenses is quite possible, and that would reduce the sensitivity to the incident light compared to a flat surface.

Also, if the microlenses were perfect immersion lenses then there would be no deflection of the light off of the sensitive area at the centre of each hemisphere even at extreme angles of incidence, which is the conventional argument for the angular response. With perfect immersion lenses the only loss in signal would be the obscuration by adjacent microlenses.

Interestingly, if you model the microlenses as spheres with a diameter equal to the pixel pitch, the obscuration of one sphere by its adjacent sphere at an incident angle of 30deg works out at approximately 5.77%. This may be what Paul Furman was talking about when he discussed the Autocad modelling. (Is it, Paul?)

In exact terms, it is 1/3 - sqrt(3)/2pi - I can go into the geometry of this if you like, but it is reasonably simple, just the percentage area intersected by two circles separated by 2r.cos30.

Obviously the lenses will not be complete spheres, but truncated ones, however the result remains the same even if they are only marginally larger than hemispheres, provided the radius is maintained above the surface at the point where the incident ray is tangential to the sphere. This only requires the microlens to be marginally greater than a hemisphere. Finally, to create such a microlens geometry, requires that the lenses themselves be smaller than the actual pixel pitch - reducing the percentage loss significantly for even small reductions in spherical radius.

I think this explains the almost null result - in fact ad *less* than 5.77% it provides a very close match to the actual observed signal reduction of 2.68%!

The other possibility is that due to fluctuations in whatever
(shutter speed? LED output?) the test didn't detect the ~15%
difference that should be there due to a statistical fluke.
I kind of doubt this. But if it were true, it would mean you'd
have to take a number of exposures to figure out what the
noise in each measurement was. (Maybe you did this and
didn't say.)

No, I didn't, but I plan to run a more comprehensive test now, which will use longer separation of the LED from the focal plane, effectively reducing the shutter speed, and hence improving accuracy and repeatability. The LED supply was a stabilised current source, so there should be no variation in its output.
--
Kennedy
Yes, Socrates himself is particularly missed;
A lovely little thinker, but a bugger when he's pissed.
Python Philosophers (replace 'nospam' with 'kennedym' when replying)
.

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