1 electron = 1 photon?

Started Apr 12, 2013 | Discussions thread
alanr0
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Re: Photon rate vs Optical Power: photometric or radiometric values
In reply to Jack Hogan, Apr 14, 2013

Jack Hogan wrote:

Marianne Oelund wrote:  Photons near 400nm do occasionally produce more than 1 electron in silicon, but the rate is low enough that it isn't a significant factor in the operation of our camera sensors.

Ok, thanks Marianne.  So if one were to try to calculate from an estimate of the sensor's electron output (calculated through shot noise SNR) the number of Exposure related photons reaching the area of the relative photosite, one could simply divide the number of electrons by a wavelength dependent conversion factor (what is sometimes referred to at various levels as QE).  Which brings us to the question of estimating this conversion factor.

1) I assume that for practical purposes one should use an average value across the sensor's spectrum for the conversion factor, a sort of effective QE, it being determined keeping in mind the spectral power distribution of the illuminating light and the wavelength dependent attenuating properties of the various filters/lenses/coatings above silicon, CFA and charge collection efficiency being two main contributors, right?

QE and irradiance both vary with wavelength.  To calculate the average QE, sum the product of QE and spectral irradiance over the wavelength range of interest, and divide by the sum of spectral irradiance over the same wavelength range.

In general, if the irradiance spectrum changes, then so does the average QE.  You will need to re-calculate the number of photons incident, and the number of electrons released.

How do you decide what constitutes an 'exposure related photon'.  Does a 750 nm photon count? The human eye can (just) detect such wavelengths, but is around 8000 times more sensitive to green light.  The sensor's QE will vary strongly in this region too, especially if an IR blocking filter is installed.  If you specify a sharp spectral cut-off, the number of 'related photons' you calculate will depend on the cut-off wavelength selected.  For black body illumination, increasing the upper wavelength of the summation from 700 to 800 nm would increase the number of photons counted, without changing the number of electrons generated.

2) Intuitively I would use floating point math for this operation.  Is there a good reason why one should use integer math instead?

I can't think of a good reason.  The transmission and conversion probabilities are all fractional.

For instance if I do this for a D4 and D50 or so light off of DxO SNR curves, I get an effective QE of 15.9%, which for 7.01 e-/ADU at ISO 100 mean 44.11 photons/ADU.  electron Unity Gain is around ISO 700 and photon unity gain is around ISO 4400 - whatever the value of these gains is.

I assume these values are averaged over all types of sensel (R, G, B).  Are these 'green equivalent' spectrally weighted photons, or are you simply counting photons over the full visual spectrum?

Are you looking for precise photon numbers for some specific purpose, or just interested in the relative efficiency of D4/D50 and other sensors?

The DxO curves are linked to ISO speed, so presumably use ISO 7589 D55 (daylight) illumination.  ISO speed is based on photometrically weighted illuminance (lux) values, rather than radiometric irradiance (W/m^2) values.  If you want pure unweighted photon numbers then you need to acount for photometric weighting as well as the illumination spectrum and the wavelength dependence of QE.

Cheers

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Alan Robinson

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