“Expose to the Right” & relation to ISO Invariance

[Bart_van_der_Wolf]

Jack and Jim K,

How would these considerations affect my modeling of the Canon sensors using the model proposed by Roger Clark? I don't have matab and am not sufficiently versed in the fine points of probability distributions to carry out this analysis, but perhaps you guys can help. These considerations could well affect the determination of engineering DR, but would be less critical when one is dealing with practical photographic DR.

Hi Bill,

I don't think it will affect the DR assessment like you used much, unless one uses such an extreme under-exposure that we get into those low e- counts that will (occasionally) start showing a larger difference between Poisson and Gaussian distributions. The real issue is that the Poisson statistics at low counts will develop a bias/asymmetry compared to a Gaussian, and they can be quite different from observation to observation. So one would need a large number of observations to make sense of it anyway.

The read-noise is more likely to have a Gaussian distribution, and the exposure a more Poisson distribution particularly when very very low exposures are in play. But for developing a physics model like Jim and Jack did one would need to use the correct distribution model to avoid wrong conclusions over time (multiple observations).

Attached are the Probability Density Functions of the Poisson and the Normal distribution, at a mean of 5, 10 and 20.

Cheers,
Bart

[Jack Hogan]

Hi Bill,

I don't think it will affect the DR assessment like you used much, unless one uses such an extreme under-exposure that we get into those low e- counts that will (occasionally) start showing a larger difference between Poisson and Gaussian distributions. The real issue is that the Poisson statistics at low counts will develop a bias/asymmetry compared to a Gaussian, and they can be quite different from observation to observation. So one would need a large number of observations to make sense of it anyway.

The read-noise is more likely to have a Gaussian distribution, and the exposure a more Poisson distribution particularly when very very low exposures are in play. But for developing a physics model like Jim and Jack did one would need to use the correct distribution model to avoid wrong conclusions over time (multiple observations).

Attached are the Probability Density Functions of the Poisson and the Normal distribution, at a mean of 5, 10 and 20.

Cheers,
Bart

Agreed Bart.  I wish you had shown the histogram for 1 as well  :-)

[Bart_van_der_Wolf]

Agreed Bart.  I wish you had shown the histogram for 1 as well  :-)

Here it is

Means for 1, 5, 10, and 20.

Cheers,
Bart

[bjanes]

So am I

Hi Bill,

If it only were so simple ;-)  Unfortunately the 2006 incarnation of the standard for ISO made things worse than they were originally.

REI is arbitrary and SOS is based on the rendered OOC sRGB jpeg, not raw data.  Thom's article is woefully inaccurate and Kerr's out of date.

If you have any other Nikon camera from an earlier or later generation, test them out.  Both my D90 and D610 put spot metered middle gray below 10% of saturation in the raw data and, with 14 stops of eDR in the D610, I am glad about that.

Jack,

I tested out my D200 and D3 and repeated the tests on the D800e.

Saturations at the metered exposure for the green channels of the D200, D3 and D800e were 10.9%, 10.6%, and 10.3% respectively. Illumination was from a bank of 4800K solux bulbs. My previous test on the D800 was with sunlight. Perhaps the spectral response of the meter accounts for the slightly lower sat with the D800e as compared to my previous result. Adjustments for highlight spot meter adjustments were +3 EV for all the cameras. The indicated meter exposures were 1/25 sec, f/8 @ ISO 100 for the D200 and D800e. The  metered exposure was 1/40 sec, f/8 @ ISO 200 for the D3 (equivalent to 1/20 sec @ f/8 for ISO 100). My Pentax Digital Spotmeter gave a reading of 1/20 sec, f/8 for ISO 100.

Cheers,

Bill

[Jack Hogan]

Jack,

I tested out my D200 and D3 and repeated the tests on the D800e.

Saturations at the metered exposure for the green channels of the D200, D3 and D800e were 10.9%, 10.6%, and 10.3% respectively. Illumination was from a bank of 4800K solux bulbs. My previous test on the D800 was with sunlight. Perhaps the spectral response of the meter accounts for the slightly lower sat with the D800e as compared to my previous result. Adjustments for highlight spot meter adjustments were +3 EV for all the cameras. The indicated meter exposures were 1/25 sec, f/8 @ ISO 100 for the D200 and D800e. The  metered exposure was 1/40 sec, f/8 @ ISO 200 for the D3 (equivalent to 1/20 sec @ f/8 for ISO 100). My Pentax Digital Spotmeter gave a reading of 1/20 sec, f/8 for ISO 100.

Spot on, Bill.

[Jack Hogan]

Here it is

Means for 1, 5, 10, and 20.

Cheers,
Bart

Excellent, thank you Bart!  Note how the 1 gaussian histogram, if shown in its entirety, would show values to,say, -3 while poisson stops at zero.  This acn make quite a difference when measuring signals of the order of magnitude of 1 LSB or below, like when studying quantization effects or determining DR.

Jack