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Determining Pixel Saturation for Bin 2 and Bin 3, ASI 294MM/2600MM

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#26 Josch Hambsch

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Posted 20 April 2024 - 03:14 PM

HI, I have a QHY600PH-M COS camera on my remote observatory in Chile since May 2023. Before I had an FLI16803 CCD camera always binned 3x3 also because of file size. I always bin the QHY 4x4 to reduce the file size as I run about 700-1000 images  night. I never go to 50K ADUs as this is not necessary for good photometry. My scope is a 16 inch at f/6.8, hence about 2.7m focal length.

Regards,

Josch



#27 mrm6656

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Posted 21 April 2024 - 11:08 AM

After reading the comments here about problems with photometry having stars of large brightness range, the following train of throught occurred to me, and I'd appreciate any feedback anyone might have.

Photometry of stars having a very wide brightness range could sometimes be improved by defocusing the image a little. Doing that would have two helpful effects on the bright stars. It would spread an image of fixed brightness over more pixels to forestall saturation. Equally important it would smear out a star's Airy disk to reduce the ADU range of the pixels, because the light from different parts of the objective's aperture would no long interfere in the way it must to produce the sharp peak of a focused Airy disk. The same defocusing would, of course, also occur for images of a dimmer star, so what's the effect for it? Many CMOS sensors have negligible thermal noise for rather long exposure times if run below -10C to -15C, so that noise wouldn't have much effect. But read noise would be worse for the dim ones relative to the lower ADU and its Poisson noise. The effects of read noise and Poisson noise could both be mitigated by increasing the exposure time a bit. Increased exposure wouldn't immediately negate the improvement for the bright star, because the defocused Airy disk wouldn't saturate as quickly with increasing exposure because there's no longer a sharp peak in the image. A side benefit of defocusing would be to reduce CMOS telegraph noise somewhat by spreading the image over more pixels and thereby getting a larger sample of its variability.

While this approach makes some sense in principle, I expect that it would be necessary to try it out to see whether it provides substantial improvement in any given practical situation. The optimal amount of defocus would depend on factors that are imponderable, so trying it out would be necessary. In particular, "focused" bright stars are not perfect Airy disks, if the seeing is less than ideal. There may be other problems that have not yet occurred to me. This defocus strategy would have little or no benefit for slit spectroscopy, since defocusing would necessarily occur at the slit and just reduce the signal from bright and dim alike, while grating or grism spectroscopy would suffer a hit on resolution.

 

         --- Mike



#28 GaryShaw

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Posted 21 April 2024 - 11:30 AM

Thanks very much Mike.
Would defocusing differentially impact the SNR of the faint versus the brighter stars? In this case SNR of the Target star is not the problem but avoiding its saturation while allowing the stacked images to yield an SNR >100 on the check star (3+ magnitudes fainter ) has been the challenge. 

rgds

Gary



#29 mrm6656

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Posted 21 April 2024 - 12:03 PM

Gary:

 

Not sure yet what to say about your SNR question. Will require more thought.

 

Meanwhile .. an addition

Less than ideal seeing doesn't seem to negate this defocus strategy, but merely deepens the story a little. In poor seeing the image of in-focus point sources like stars is still due to Airy disks. An overall iin-focus mage consists of the accumulation over the exposure time of multiple, spatially distributed Airy disks, each due to a state of the atmosphere through which the light has passed during a particular short time interval. This must be true, otherwise speckle interferometry of double stars would not work the way it does.

 

So in poor seeing in the image of a bright star, each point (pixel) of the image is the sum of multiple Airy disks and/or partial Airy disks over the exposure time. So if a best-focus pixel gets saturated it's due to multiple Airy disks. Then defocusing will defocus each of those Airy disks to smear the image, just as it does for the Airy disks. Hence the defocus strategy should work about as well in poor seeing as in ideal.

 

         --- Mike



#30 robin_astro

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Posted 21 April 2024 - 01:18 PM

This defocus strategy would have little or no benefit for slit spectroscopy, since defocusing would necessarily occur at the slit and just reduce the signal from bright and dim alike.

 

        

Yes defocusing on the slit will reduce the throughput so has no merit except  perhaps to allow very bright objects to be measured (I heard that some professional observatories have contingency plans in place including defocusing if for example Betelegeuse goes supernova ! )

 

It does make the measurement of bright targets possible without the requirement for accurate guiding though eg as here

http://www.threehill...troscopy_18.htm

 

I am no photometry expert but  have heard that defocussing is common practise to minimise the effects of scintillation on bright targets where exposures would otherwise be too short (though summing many exposures is an alternative) and to avoid the effects of undersampling when using short focal lengths.  Potential downside are blending in crowded fields and an increased sky noise contribution from the larger aperture eg in light polluted skies

 

Cheers

Robin



#31 mrm6656

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Posted 21 April 2024 - 03:48 PM

Gary:

 

Assuming that I've properly understood your question about SNR, I think that the following may respond to it satisfactorily for your present purposes.

 

A first point is that defocusing stars in photometry is not a novel suggestion (as Robin has already commented). Slight defocusing of star images is a time-honored tradition in stellar photometry. For one example, The "AAVSO_CCDPhotometryGuide" recommends defocusing as one method of correcting undersampling of in-focus images. It notes, as is very important, that defocused images should be calibrated with similarly defocused flat fields. For another example, the documentation of the AAVSO APASS project describes defocusing the telescopes that have been used for all its images: "The pixel scale is 2.57arcsec/pixel, and we purposely defocus the telescopes so that star fwhm is 1.5-2.0 pixels.  In addition, we are using aperture photometry in these early releases, with a circular aperture of 17 arcsecond diameter." The APASS documentation does not discuss stacking.

Analyzing the definition of SNR shows that the SNR of a defocused star will be the same as the SNR for the same star in-focus with minimal effort. Working with the data after calibration, the equation defining SNR is, for example, Equ 10.13 of Berry and Burnell "The Handbook of Astronomical Image Processing".

     SNR = Star / sqrt[ Star + Nap * ( 1 + Nap / Nann) * ( g * Csky + g * Cdrk + sig_ro^2 + g^2 * sig_q^2 ) ]
where
     Nap    = number of pixels in the aperture for the star
     Nann   = number of pixels in the annulus for the sky background
     g      = sensor gain in ADU/electron
     Csky   = ADU of one sky background pixel
     Cdrk   = ADU of one pixel dark current
     sig_ro = sensor readout noise in rms electrons/pixel
     sig_q  = sensor ADU noise associated with quantifying pixel values (approx.=0.29)
with
     Star = g * sqrt[ Cap - Nap * (Cann / Nann) ]
     Cap  = sum of pixel values in aperture
     Cann = sum of pixel values in annulus

 

When a star is defocused, the gain, a sensor property, will not change. The value of Star will be unchanged, so long as the aperture is chosen to collect the same number of star photons and the number of annulus pixels is chosen to make Nap / Nann the same for the defocused and in-focus images. Csky will be unchanged, since the pixel sky brightness will change only by the concomitant change in the telescope's focal length, and that will be negligible for small defocusing. In the method that I have described Cdrk is assumed to be zero for the CMOS sensor at the temperature used, so that the suggested exposure increase will not increase its value. More generally, even if Cdrk is not zero, it would be constant for the defocused but equally exposed images that are more typically involved in stacking. sig_ro, a per pixel quantity will be unchanged, because like the gain it is a sensor property, not an image property, as is sig_q which is a constant. So none of the relevant dependencies changes in the SNR calculation, hence the SNR of the defocused star will be the same as the SNR of the same star in-focus.

 

Nothing more is required to achieve this result in practice besides defocusing a little when making the exposures and then in the analyses, choosing Nap to be sure to include basically all but a negligible number of the star's incident photons and choosing Nann to get a sufficiently large sample for the annulus. Those are tasks that are required for any good stellar photometry.

 

As for stacking: When a number Nstk of images of either in-focus or defocused images are stacked, the net signal-to-noise becomes, as always
     SNRstk = SNR * sqrt( Nstk )
Since SNR will be the same for both focused and unfocused images, SNRstk will be the same, too, because SNR will be the same for each of the stacked images in the two cases.

Applying this result to target star and comp star images, it establishes that defocusing and stacking should not materially change the SNRs from those that would be measured using in-focus and stacked images.

 

In your case of interest with very large differences in magnitude of target and comp star, the only requirement for getting this stacking result with unsaturated input images should be the ability of the stacking software to not "numerically saturate" when performing the necessary calculations. Floating point calculations would obviously be best in this regard. Beginning with 1x1 binned and unsaturated images would free you from worry about what the binning hardware/software was doing to you without your knowledge. And beginning in this way would let you push the exposures up to max linear for the bright star and thereby also maximize the ADU of the dim one whose SNR may need the improvement from stacking.

 

Hope all this is readily understandable and perhaps even helpful.

 

         --- Mike


Edited by mrm6656, 21 April 2024 - 10:37 PM.

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#32 GaryShaw

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Posted 21 April 2024 - 04:31 PM

Thanks again Mike, I'm following most of what you're saying on the first read - a first! I may have mentioned above that I was binning 3x3 to reduce the image size to get past problems I've consistently had uploading the stacked image to VPHOT. If I can find a way to use Bin 1 and also get VPHOT to upload the file size (50-60GB if I recall), then things will be all set.

 

Part of the question I had is how to determine when a Bin 3x3 pixel is saturated versus a Bin 1 saturation. My only approach so far has been to zoom in to the pixels displayed on each image as TSX displays it, and measure the adu value. But even then, I'm not clear on what adu level saturates a Bin 3 'sub-pixel'. Now I need to read again through everyone's great responses above and see where that ended up.

 

Thanks very much for sharing your expertise and the time it takes to do so.   That goes for everyone above !

regards,

Gary



#33 mrm6656

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Posted 21 April 2024 - 05:42 PM

Gary:

The suggested strategy is to not only defocus the images but to also increase the exposure time. So far my  description has not shown the effect of this aspect of the strategy. Doing so will show that the SNR of a defocused star that has an increased exposure will have an increased/better/higher SNR compared to the SNR of the in-focus star. Quite simply that's because it will have a longer exposure, of course.

 

An easy way to see this is to begin with the following version of for the SNR equation

SNR = Star / sqrt( Star + terms )

in which all the other terms inside the square root of Equ 10.13 are denoted as "terms"

 

Now increase the Star's the exposure by the amount dStar. The equation for SNR now becomes

SNR+ = (Star + dStar) / sqrt( Star + dStar + terms)

 

Then factor out Star from the numerator and sqrt(Star+terms) from the denominator to get

SNR+ = Star / sqrt(Star+terms) * [ (1 + dStar/Star) / sqrt( 1 + dStar/(Star+terms) ) ]

 

The shows that the new SNR+ is just the old one times the quantity in  [ ]. Now in [ ] the denominator will always be less than the numerator. Thus the factor in [ ] is bigger than 1, and that establishes that SNR+ will always be greater than SNR. That is as an inequality

SNR+ > SNR

 

If, for example the exposure is increased by 50%, then dStar/Star = 1.5 and SNR+ would be approximately 1.22 * SNR; if by 100%, then SNR+ would be approximately 1.414 * SNR. The increased SNR would occur for all stars in the image.

 

I apologize for putting this all out piecemeal. I hope now that I've maybe come to the end of the story.

 

 

Regarding the necessity of binning for convenient uploading to VPHOT: 50 MByte or more is no longer an uncommon file size for 1x1 sensors. If it's a problem for VPHOT, that problem needs to get quickly fixed by AAVSO. Until then an alternative would be to use AIJ instead of VPHOT. I use AIJ on my 50 MByte images after running astrometry with ASTAP all the time with no problems to date. And there is an AIJ macro that will prepare AAVSO reports from the AIJ results. I've not used VPHOT so I can't compare it to AIJ, but I do know that AIJ is an incredibly versatile application for photometry. As far as I know, the only thing that it lacks is the ability to do transformations.

 

         --- Mike


Edited by mrm6656, 21 April 2024 - 07:13 PM.


#34 robin_astro

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Posted 22 April 2024 - 06:45 AM

Doing so will show that the SNR of a defocused star that has an increased exposure will have an increased/better/higher SNR compared to the SNR of the in-focus star.

Only provided you are not sky or camera noise limited. These will increase compared with the in focus case because you have to increase the aperture. 

 

In the absence of systematic effects, the best tactic for highest SNR in a given exposure time would be to concentrate the star image on the minimum number of pixels, run as close to saturation as possible and combine multiple exposures, thus minimising sky and camera noise. The difference with bright targets at high SNR though is probably insignificant. Spreading the light over more pixels does potentially help with systematics and non-stochastic effects like  cosmetics, pixel/pixel non uniformity and telegraph noise though.

 

Cheers

Robin



#35 mrm6656

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Posted 22 April 2024 - 09:59 AM

Robin's correct that sky-noise-limited and/or camera-noise-limited images are not going to gain SNR from defocusing and increasing exposure. I deliberately dropped those "terms" from the last math I posted, because Gary's situation is probably not limited in that way, and I'm not surprised that someone has pointed out that I dropped them. Gary states that he's working with a magnitude range of 4 which means that when the bright star peaks at 55,000 ADU, the dim star at 4 magnitudes dimmer will be at about 1400 ADU and should not be sky noise limited. Gary's sky count should be pretty low, if his observatory is in Wyoming, as I believe it is. If the magnitude range dropped below 5, any improvement from defocus+exposure would begin to be iffy.

 

If the "terms" that I dropped are included in the math, one could calculate an estimate of just how big Cksy or Cdrk  could get before they would start cutting into the SNR improvement. (Cdrk is often not much of a problem, because it is near 0 in fairly long exposures for many CMOS when run at at low temperature.)

 

It would be possible to do a lot more math to put flesh on the bones that I've included here. One could calculate by how much different amounts of defocus each reduce the peak of the Airy disk. That would then show how much exposure increase is possible for each amount of defocus before the brightest pixel(s) of the defocused image would return to the infocus value. And finally the results could be compared to Csky to determine the limits of the defocus+exposure strategy before it runs out of utility. I've not carried out those calculations and probably won't at this time. I would guess that useful exposure increases might top out at 3 or 4 times the infocus limits, but that's purely a guess.

 

         --- Mike




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