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Author Topic: Sensogren data for D800 seem to be off the mark  (Read 2704 times)
IliasG
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« Reply #20 on: February 22, 2013, 02:56:23 PM »
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Bill,

We have to give a little more thoughts-attention to this method because by subtracting the two shots except from PRNU we subtract the fixed pattern part of the read noise.
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bjanes
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« Reply #21 on: February 22, 2013, 08:59:47 PM »
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Bill,

We have to give a little more thoughts-attention to this method because by subtracting the two shots except from PRNU we subtract the fixed pattern part of the read noise.

Ilias,

The subtraction eliminates PRNU and other fixed pattern noise. Since noise at exposures > 1 sec is almost entirely PRNU, shot noise, and read noise, one can determine RRNU by quadratically subtracting the other components. At higher data numbers, read noise is a negligible proportion and can be ignored. AFAIK read noise is essentially Gaussian--it has a bell shaped histogram. Of course, all of these statistical calculations assume a more or less normal distribution.

Regards,

Bill

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BartvanderWolf
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« Reply #22 on: February 23, 2013, 06:53:31 AM »
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IMHO, perhaps the best method using my approach would be similar to that of Peter Facey, who calculated the number of electrons by squaring the signal-to-noise ratio, and the latter is calculated after quadratically subtracting the read noise from the measured noise. This gives the number of electrons directly without having to plot the data and calculate a slope. This is also the method used by Roger Clark.

Here are my results. For gain, I would use the figures in the mid range of the exposures. What do you think?

Hi Bill,

I agree, basing the calculations on 2 subtracted 'images' will remove all systematic error (including variations in shutterspeed and illumination when taking the image sets), leaving only Random and 'temporal' noise (mostly dark count at long exposures and/or high temperatures). That's why I would also use the higher signal sets of the bracketing series to base the calculations on. The only thing one needs to be careful with, is that there are no ADUs equal to the saturation point for a given channel, which would signal clipping of the upper tail of the noise distribution. I also use Roger Clark's method when the highest quality is required, afterall sensor calibration is part of his job at NASA so we must assume that he knows what he is doing. It's a well known method anyway.

The apparently slightly non-linear response at the high end of your dataset, if we want to be picky, could be addressed by fitting a very slight curve (only based on the samples at the top) instead of a straight line. However, I assume that the sensor engineers attempted to design a relatively linear response package to avoid color conversion issues later on. So an even more elaborate model might have linear and non linear (for the residuals) components. It also depends on the sensor and how reliable the Raw data are, for it to be needed. A possible cause for additional noise may come from the camera heating up while acquiring a large number of bracketed shots, or writing of slightly cooked data instead of pure Raw.

Depending on the type of cooking, a FFT frequency spectrum of a uniform exposure crop may reveal if certain noise reductions were applied.

Cheers,
Bart
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bjanes
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« Reply #23 on: February 23, 2013, 12:43:12 PM »
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Depending on the type of cooking, a FFT frequency spectrum of a uniform exposure crop may reveal if certain noise reductions were applied.

Cheers,
Bart

Bart,

Excellent suggestions, as usual. I selected some raw files at various exposures, split out the green channel in ImagesPlus, and cropped to the central 500x500 pixels and performed FFT with ImageJ. The results are shown. There appears to be some filtering even with short exposures, but it becomes more prominent at 1/3 second and longer. Could you help us interpret these results?

1/100 sec


1/3 sec


30 sec


1 min


5 min


Regards,

Bill

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BartvanderWolf
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« Reply #24 on: February 23, 2013, 07:18:03 PM »
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Bart,

Excellent suggestions, as usual. I selected some raw files at various exposures, split out the green channel in ImagesPlus, and cropped to the central 500x500 pixels and performed FFT with ImageJ. The results are shown. There appears to be some filtering even with short exposures, but it becomes more prominent at 1/3 second and longer. Could you help us interpret these results?

Hi Bill,

The longer exposure times do show signs of noise reduction, which would render the analysis of the Raw data to an exercise in relative futility.

A good method to help detecting noise reduction is by using an ImageJ plugin called Radial Profile Plot on the FFT result. One just selects the centered FFT output with a square selection box, and invokes the plugin. It will turn the square selection into a circular one, and calculates the radial profile for radii from 0 in the 'center' to Nyquist (2 pixels per cycle) at the edge of the circle. A perfectly uniform (white noise) power spectral density will have a horizontal profile plot with little fluctuation (especially at the larger radii where more pixels are sampled at the radius perifery than in the center).

A declining slope, or a drop at certain spatial frequencies, indicates noise reduction, as can be verified by doing the same on a known uniform noise image.

I find the ImageJ RandomJ plugin, very useful for such base-line reference simulations, since it can be used on all sorts of image bit depths. It also allows to first create a reference image e.g. an absolute value average 14-bit uniform gray image (create single layer 16-bit image, select all, and Process|Math|Set pixels to desired value) in a 16-bit image file, with modulatory Poisson noise replacing the original average (to simulate photon shot noise with a given average e-) for subsequent FFT and Radial profile analysis. The width of the Profile Plot window, and the thus the granularity of the sampling along the radii, can be influenced by the Edit|Options|Profile Plot Options width settings (for copying the Radial Profile values to e.g. an Excel spreadsheet to allow combined plotting of multiple XY (+trend) charts).
 
Cheers,
Bart
« Last Edit: February 23, 2013, 07:33:36 PM by BartvanderWolf » Logged
bjanes
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« Reply #25 on: February 25, 2013, 09:48:14 AM »
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Hi Bill,

The longer exposure times do show signs of noise reduction, which would render the analysis of the Raw data to an exercise in relative futility.

A good method to help detecting noise reduction is by using an ImageJ plugin called Radial Profile Plot on the FFT result. One just selects the centered FFT output with a square selection box, and invokes the plugin. It will turn the square selection into a circular one, and calculates the radial profile for radii from 0 in the 'center' to Nyquist (2 pixels per cycle) at the edge of the circle. A perfectly uniform (white noise) power spectral density will have a horizontal profile plot with little fluctuation (especially at the larger radii where more pixels are sampled at the radius perifery than in the center).

A declining slope, or a drop at certain spatial frequencies, indicates noise reduction, as can be verified by doing the same on a known uniform noise image.

I find the ImageJ RandomJ plugin, very useful for such base-line reference simulations, since it can be used on all sorts of image bit depths. It also allows to first create a reference image e.g. an absolute value average 14-bit uniform gray image (create single layer 16-bit image, select all, and Process|Math|Set pixels to desired value) in a 16-bit image file, with modulatory Poisson noise replacing the original average (to simulate photon shot noise with a given average e-) for subsequent FFT and Radial profile analysis. The width of the Profile Plot window, and the thus the granularity of the sampling along the radii, can be influenced by the Edit|Options|Profile Plot Options width settings (for copying the Radial Profile values to e.g. an Excel spreadsheet to allow combined plotting of multiple XY (+trend) charts).
 
Cheers,
Bart

Bart,

I have implemented your suggestions and am returning for more advice. The longest exposure I used for my analysis was for 1 second. The FFT of the individual duplicate files does demonstrate a non-Gaussian component as shown below. The noise at this exposure level consists of shot noise and PRNU. However, when one subtracts the pair to eliminate fixed pattern noise, the FFT is essentially that of Poisson noise as demonstrated by the radial plot shown below in comparison to a Poisson generated file generated with ImageJ using a mean of 13085 which is the mean raw level of the files at that exposure level. The normalized integrated intensity is higher, since the SD of the subtracted images is for two images and was not divided by sqrt(2).

I conclude that the raw files were filtered for PRNU and after this was removed, the files were suitable for analysis. Is this correct in your estimation?

Thanks,

Bill
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BartvanderWolf
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« Reply #26 on: February 25, 2013, 11:28:36 AM »
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Bart,

I have implemented your suggestions and am returning for more advice. The longest exposure I used for my analysis was for 1 second. The FFT of the individual duplicate files does demonstrate a non-Gaussian component as shown below. The noise at this exposure level consists of shot noise and PRNU.

Hi Bill,

Indeed, the plot shows that there was a significant amount of low frequency signal (already visble in the FFT result).

Quote
However, when one subtracts the pair to eliminate fixed pattern noise, the FFT is essentially that of Poisson noise ...

Yes, there is no clear sign of boosted or suppressed frequencies (the horizontal spectrum is uniform with some random statistical sample fluctuations), the noise is pretty random as we can expect from purely Poisson/Gauss and White noise.

Quote
as demonstrated by the radial plot shown below in comparison to a Poisson generated file generated with ImageJ using a mean of 13085 which is the mean raw level of the files at that exposure level. The normalized integrated intensity is higher, since the SD of the subtracted images is for two images and was not divided by sqrt(2).

Yes, the benefit of comparing with the spectrum of a known (Poisson only) noise spectrum is that significant differences with the empirical spectrum of the subtracted images should be apparent. One improvement, but it won't change the outcome much, is that you can use the Modulatory Poisson noise option of RandomJ, since it will keep the average intensity of the original and add a proportional amount (sqrt(signal level)) of Poisson distributed noise (regardless of the mean value setting, it's based on image content levels).

Quote
I conclude that the raw files were filtered for PRNU and after this was removed, the files were suitable for analysis. Is this correct in your estimation?

It's hard to tell what caused it exactly, but there was a 'significant' amount of low frequency information still present in the individual Raw file(s). This is not necessarily different with other cameras, it's just there (maybe from the camera electronic circuits). That may be caused by periodic pattern noise, as evidenced in the FFT conversion mostly horizonal and vertical. It was not removed yet, because that would have lowered the spectral component in the radial profile plot.

Most of the signal is in the most central (approx. 25 pixel) radius of the FFT representation, and ImageJ allows to readout the spatial frequency (less than 20 pixels/cycle) when you hover the mouse over the FFT image. Maybe the readout circuits use 8 or 16 parallel rows or columns? Other than that, there does not seem to be any active frequency based noise reduction (no gradual or abrupt decline towards higher frequencies) that can be detected. I'm not sure if Hot Pixel Suppression can be spotted this way, because that is also pretty random across the image. Selecting a larger crop than 512x512 pixels will give more samples (and even lower frequencies) to analyse, but vignetting may start to influence the average signal level of single Raws, and gain can be evaluated at these levels.

After subtraction, the image data was purely random, as demonstrated by a uniform radial spectrum plot, and suitable for random (read+Poisson) noise analysis. That means that there should be no pattern noise influence in the images close to the clipping level.

Cheers,
Bart
« Last Edit: February 25, 2013, 11:31:53 AM by BartvanderWolf » Logged
bjanes
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« Reply #27 on: February 25, 2013, 01:08:28 PM »
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It's hard to tell what caused it exactly, but there was a 'significant' amount of low frequency information still present in the individual Raw file(s). This is not necessarily different with other cameras, it's just there (maybe from the camera electronic circuits). That may be caused by periodic pattern noise, as evidenced in the FFT conversion mostly horizonal and vertical. It was not removed yet, because that would have lowered the spectral component in the radial profile plot.

Most of the signal is in the most central (approx. 25 pixel) radius of the FFT representation, and ImageJ allows to readout the spatial frequency (less than 20 pixels/cycle) when you hover the mouse over the FFT image. Maybe the readout circuits use 8 or 16 parallel rows or columns? Other than that, there does not seem to be any active frequency based noise reduction (no gradual or abrupt decline towards higher frequencies) that can be detected. I'm not sure if Hot Pixel Suppression can be spotted this way, because that is also pretty random across the image. Selecting a larger crop than 512x512 pixels will give more samples (and even lower frequencies) to analyse, but vignetting may start to influence the average signal level of single Raws, and gain can be evaluated at these levels.

After subtraction, the image data was purely random, as demonstrated by a uniform radial spectrum plot, and suitable for random (read+Poisson) noise analysis. That means that there should be no pattern noise influence in the images close to the clipping level.

Bart,

Thank you very much for your analysis. I understand that the D800e does use parallel readout with 12 channels, and this may contribute to some pattern noise if the channels are not well balanced. Hot pixel suppression (HPS) occurs with exposures 1/4 sec and upwards, so ideally one would not expose in this range, if possible. I did increase the crop to 500x500, from the 200x200 used for the bulk of the analysis.

Regards,

Bill
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