Small pixel size sensors for EAA. Pros and Cons?

[Deflavio]

Hi Everyone, 

Sorry for the long post but it's cloudy outside...😅

I have started thinking about different options on how to optimise/improve resolution while still using moderate focal lengths for travel. At the end, it seems that it all comes down to the final arcsec/pixel value and a good sampling of the final FWHM (combining seeing, AIRY disk and tracking errors). A sampling rate between 1.6x to 2x of the FWHM seems “ideal” according recent posts from @vlaiv. Or maybe even less considering the more noisy nature EAA images compared to AP. I guess many high frequency details are probably lost anyway in the noise.

Regardless, it seems then that smaller pixel sensors matched with moderate to short focal lengths would be an interesting combination giving the same sampling resolution of larger sensor matched with longer focal lengths. Pros are obvious: shorter focal length scopes are easier to handle, transport and save weight. Also, the use of smaller pixel sizes can be a way to minimise the intrinsic loss or resolution from the Bayer filter of colour cameras. I.e. a 2.4um sensor colour would have “at least” the same resolution as a 4.8 um mono sensor. Finally, if the FWHM of the night is not good enough a smaller pixel can also allow a wider range of binning combinations to better match the best resolution and possibly boosting SNR, no? 

What are the cons then?

I assume that smaller pixel size also means optics quality and focus issues are more evident when working un-binned under good/excellent seeing. Being this setup for travel then there may be more chances to end up under a good sky… Also I guess tracking errors should be at the same level of setups using bigger sensors and longer focal lengths, right? So lighter equipment yes but still good tracking requirements. To be honest I’m not sure how critical this is for EAA with 5/10 secs subs but I should at least try to quantify how much error is ok. No idea how, though... Any other cons?

Maybe SNR? Not sure but, if I have got this right (again not really sure), this should also not be an issue. With equivalent scope focal ratio, assuming equivalent QE and general sensor specs, given a fixed arcsec/pixel sampling, SNR should be approximatively the same regardless of the specific pixel size, focal length or even aperture, right? I’m referring here to extended object no point sources (where I know aperture always win..).

I guess larger pixel sensor are considered more sensitive or with better SNR than smaller ones when they are directly compared against the same optics but if instead they are arcsec/pixel matched, things should be even out, no? Please correct if I got this wrong... I haven't checked the math for this.

 

So, anyone with practical EAA experience using small sensor like the 178, 183 or similar to confirm or disprove this?  It would be nice to hear your different experiences.

 

 

Just for reference I’m attaching below the equivalent focal length (mm) required to give 1.6x, 2x and 2.5x FWHM sampling given a selected FWHMs (arcsec) and three typical pixel sizes (um). I have highlighted the case for 2/2.5 arcsec FWHM. I used the usual resolution formula as  focal length (mm) = pixel size (um) / resolution (arcsec) * 206.265

The first table show un-binned sensors assuming an ideal “MONO” resolution. I know 533 and 295 sensor are only colour but... The second  table is 2x2 bin to emulate the bayer filter loss of resolution. I don’t think this is fully correct but it would give a sort of worse case scenario for colour cameras. Let me know if any of this make sense...

 

 

Flavio

 

 

Edited September 30, 2020 by Deflavio

[Martin Meredith]

Hi Flavio

Interesting questions. You might find some useful pointers (or not) in the thread below where I implement Raab's algorithm for determing how faint a source you can detect given aperture/focal length/QE/pixel size (admittedly it concerns point sources, but the principle of how many photons falls on a given pixel still applies). The (Python) code is also there in case it helps for simulations of the effect of pixel size while holding the rest constant (or I am happy to run such simulations given a bit of free time).

So this is my understanding of the effect of pixel size: If you hold aperture, focal length and sensor QE constant, then the number of photons that are converted to electrons indeed should be the same regardless of pixel size. But this is across the entire sensor. To be meaningful you need to distinguish between global and local (spatial) SNR. At the level of individual pixels the SNR will vary with pixel size. You can have a huge pixel-wise SNR if you consider the sensor as a single pixel, or a terrible pixel-wise SNR if you have infinitely small pixels.

As I see it, when doing EEVA we are explictly or implictly trading off 3 variables: pixel size (i.e. spatial resolution when focal ratio is fixed), SNR and total exposure time.

• SNR, at least for EEVA purposes, needs to be 'good enough' to see the faint details in DSOs, faint quasars, etc (this is probably the main thing distinguishing EEVA and AP)
• Exposure time is the thing we have most control over, but total exposure tends to be relatively short in EEVA (~10-15 mins max, often shorter) 
• Pixel size needs to be small enough to achieve the spatial resolution we are seeking, at least up to the limit imposed by seeing (unless we are using lucky imaging)

What you really want is a good SNR all the way down to the seeing limit on any one night. But the only guaranteed way to achieve this at the chosen resolution is to increase exposure time (everything else being equal ie aperture/focal ratio/sensor QE).

Looked at like this, small pixel sizes (at least down to the best seeing we expect) are advantageous IMO mainly because they give us a second way to increase SNR (via binning) instead of having to use longer total exposure i.e. more flexibility. I say this as the owner of a camera with huge pixels!

Martin

 

 

 

 

Edited September 30, 2020 by Martin Meredith

[Mike JW]

Hi Flavio,

As Martin knows my technical knowledge is poor. I am a "point and shoot" person. However having said that here are a few thoughts from someone who has observed visually  in rural GB for 20 yrs, under mag 5.0 (poor night) to mag 5.7 skies (good night), using a variety of quality scopes, anywhere between 150 to 200 hrs in a year.

Nights of excellent seeing are so rare that they are truly memorable - count them on the fingers of one hand in any given year.  Short periods of excellent seeing sometimes happen on what is otherwise a good - ish night. Nights when I have been able to push the magnification to close to the Rayleigh limit with a scope have been rare (whether I was using a 5" Apo, 7"MN, 8"OMC, C9 or a top of the range 15" Dob.) Splitting doubles below 1" second has been rare. 

Nights of good seeing are more common but not exactly guaranteed.

The point I am driving towards is as you ponder the best combination then work on the basis that most nights in GB are pretty average to good.

Martin uses the Lodestar with large pixels (8.2 um pixels) and if I remember rightly rarely uses binning.

I use the Ultrastar with smaller pixels (6.45 um pixels) and use 2x2 binning pretty well all the time on the 15" or the C11. Sometimes I try 1x1 and find it gives tighter stars but not any obvious difference in resolution. However in 1x1 mode the time to getting a decent image is much longer and for me doing EEVA is about being as "live" as possible and preferably no post image processing. It seems to me that for DSOs then large pixels are fine. I t would be interesting to compare the Lodestar and Ultrastar on the same object/same scope.....

I have a friend who uses a Watec (8um pixels) on a large Dob and compared it to the Ultrastar ( no stacking but same time for the single sub). He found the Watec went "deeper" - large pixels better for a given time?

SNR - casual observation on my part - after 20 to 30 stacks the detail does not improve but the background noise does get less - I like a "clean" image. (reminds what I use to see when when using big Dobs).

I also remember reading that it is best to work on the practical 2-4 arc second Airy Disk - not that I really know what that means, other than that is likely to be seeing conditions in GB.

I will be very interested in your conclusions.

All the best

Mike

Edited September 30, 2020 by Mike JW

[Martin Meredith]

That's interesting practical experience Mike. Excellent seeing is rare for me too. And I can confirm that I never use binning. A paltry 752 x 580 pixels is already few enough, thank you...

Having said that, from an aesthetic viewpoint it would be good to have rounder stars on occasion.

Martin

Edited September 30, 2020 by Martin Meredith

[Deflavio]

6 hours ago, Martin Meredith said:

Interesting questions. You might find some useful pointers (or not) in the thread below where I implement Raab's algorithm for determing how faint a source you can detect given aperture/focal length/QE/pixel size (admittedly it concerns point sources, but the principle of how many photons falls on a given pixel still applies). The (Python) code is also there in case it helps for simulations of the effect of pixel size while holding the rest constant (or I am happy to run such simulations given a bit of free time).

Hi Martin, 

Very interesting paper, it covers quite lot. Interesting that max SNR is achieved at 0.83x FWHM assuming a centred voxel...and accepting bad under-sampling and aliasing of course, but at least, no need to go further than that for more SNR. It also confirms that to preserve details and still have good SNR, sampling should be between 1.5 to 2.0x FWHM which is in line with what has been said before on this and other forums. Unfortunately, the formula and the script are as you said for point sources. At fix angular resolution (pixel value in your python script) SNR goes up with aperture. That is what I would expect for detecting fainter stars or how to reach deeper magnitudes... we need bigger apertures. This is probably the right definition for pixel-SNR, I should use.

Probably "SNR for extended object" is not the right term for what I have in mind.  I found quite a few "heated" discussion around on this issue, about SNR and the f-ratio myth and I may be confused... In short, if I keep the f-ratio constant, by increasing both aperture and focal length at the same time, I would get the same surface brightness on my image simply because the increased photons for the large aperture are spread on an equivalent a larger surface on the focal plane by the longer focal length. It makes sense. What I'm not sure is if I have the same surface brightness, do I have also same contrast or ability to see minute features within extended objects? Also, to have this same brightness do I need to fix to same pixel size or the same angular resolution? I'm bit stuck on this 🤔.

I guess my main point of the post is, if I use a smaller pixel AND a shorter focal length how close I can get to results obtained to larger pixels on longer focal length? It seems I can match resolution, not SNR but same surface brightness...and details? 

Regarding to the other points, I agree, I would say time of all parameters is the one I can be more relaxed with. If an object is interesting I don't time how long to stay on it. I'll be happy to trade a bit more averaging if I can just pull out more features. 

 

F

Edited September 30, 2020 by Deflavio

[Deflavio]

6 hours ago, Mike JW said:

using a variety of quality scopes, anywhere between 150 to 200 hrs in a year.

wow that's a lot of hours in a year. I like to do the "theory" but I definitely do less practice 😅

I completely agree regarding bigger pixels and seeing condition. Given a fixed focal length (and aperture) the larger sensor would go always deeper. However, what about details and object features/contrast? 

As you say, average or bad sky conditions would actually push to use binning but the same angular sampling can be achieved using a shorter focal length. Even more if I also consider a smaller pixel size. I'm curious to know if someone has tried this.

Clearly the C11 or 15’’ will go deeper but what about objects with moderate brightness? Will be details there comparable if sampling resolution is the same? SNR will be lower but as I said I can wait a bit more if more features are emerging...

 

F

 

Edited October 1, 2020 by Deflavio

[Mike JW]

Hi Flavio,

Noting that I am not really following the interesting discussions above - as stated I lack the technical knowledge. You ask if details will be comparable if sampling resolution is the same. The C11 at f6.3 (which is the f ratio I use for EEVA) and the 15" at f4.5 have similar focal length and as stated I tend to use the Ultrastar in 2x2 mode for both telescopes. The 15 gets an image so much quicker than the C11 and my gut reaction is I see more detail with the 15 on moderate brightness objects. Given a choice I would always go for the 15. Often when using the 15 I will reduce the time for each sub down to as little as 5 seconds (knowing that with all that light gathering power I will still quickly get a decent shot). I then get sharper stars and I suspect sharper details in the DSOs (I could of course be imagining this as the physics involved in cameras might be saying otherwise?).

As a casual observation when it comes to choosing a scope for EEVA and DSOs, my feeling is get a bigger scope as is reasonable for one's circumstance. If I had to travel to do my observing then it would be at least an 8" scope on a suitable alt/az mount. (I use to mount a C9 on the iOptron Minitower - very portable set up and the mount was good enough for EEVA style work even when loaded up with the C9). Sometimes I use my current 7" Mak Cas for EEVA - nice results but disappointing compared to the C11 or 15.

Can I ask what do you mean by terms such as 1.5 x FWHM.

Have fun,

PS - I no longer do the hours observing that I use to - age has caught up and over the last 10-15 years cloud levels have increased noticeably (climate change and aircraft con-trails).

Mike

[Deflavio]

Hi Mike,

For 1.5x FWHM I mean a sampling rate that is 1.5 times higher than the actual Full Width Half Maximum of your final "star disk". This star disk would be the combined effects of seeing (main factor), Airy disk and tracking errors. In practice, this means that you need to cover the central part (or most luminous portion) of your star with at least 1.5 pixels.

In the tables I posted above, I just took 8 different FWHMs to represent different sky conditions or star sizes and tried to see what would be the ideal focal length given 3 different pixel sizes.

If I look at your set up, a C11 at f6.3 on a 6.45um pixel and 2x2 binning gives a sampling resolution of 1.51 arcsec/pixel. The 15'' at f4.5 gives a similar 1.55 arcsec/pixel and they seem really good sampling. If we consider as "typical" sky condition or star shapes FWHM of 2 to 3 arcsec you are nicely going from 1.3x to 2x sampling rate in most of the cases.

Interesting that you see a difference between your two setups. Could it be just the better SNR helping revealing more details faster or maybe the different obstruction in the scopes reducing slightly contrast on C11? 

F

 

[Martin Meredith]

Hi Flavio

When talking about things like surface brightness, contrast and detail, we are still fundamentally talking about per-pixel SNR and resolution. So all the SNR machinery that applies to point sources essentially applies to diffuse sources too. I would go further, and say that for all but the fainter point sources, we typically have way too much SNR on bright sources (in the same way as when listening to speech in noise, beyond a certain level of noise it has no effect on intelligibility of the speech), so it is exactly in the diffuse regions where achieving an adequate SNR is critical. This concurs with my experience of e.g. awful colour noise in short exposures of anything nebulous that is anything but quite bright! 

For the sake of argument, if we were to remove all external sources of noise (e.g. read noise, thermal noise, sky noise) that can be handled in various ways, and just talk about the intrinsic noise due to uncertainty in arrival times of photons, then the only thing that matters is to collect as many photons as possible. In other words, getting as much target signal S per pixel  in the timescales of a typical EEVA observation. Let's assume also that we want to keep resolution constant. How can we achieve this?

There are at least 6 ways I can think of increasing S, but not all are permitted if we want to keep resolution constant, assuming all other factors are fixed.

1. Increase sensor quantum efficiency. This is a 'free' lunch (except that it costs), in the sense that we increase S without losing resolution. Most sensors have a highish QE these days so there is not much to gain here.

2. Use a sensor with larger pixels. This results in a loss of resolution.

3. Use binning. Same as 2.

4. Use focal reduction. This results in a loss of resolution too.

5. Increase exposure time. This increases S with no loss of resolution.

6. Increase aperture (all else being fixed). Now we get an increase in resolution but SNR-per-pixel stays the same. However, we don't want this increased resolution, so we combine this increase in aperture with focal reduction to get back to our original desired resolution. Then S (and hence SNR) increases. 

So it seems to me that in this idealised (but close to realistic scenario) where the only noise source is the uncertainty in photon arrival time, the only variables that can be traded to reach our target resolution at an adequate SNR are QE, exposure duration and aperture (as one would a priori expect, I guess!).

Of course, I might have forgotten something! Happy to hear other opinions as always.

Martin

 

[Edit: one factor I didn't mention is field of view and how this affects the target; I've a horrible feeling this also need to be taken into account...]

Edited October 1, 2020 by Martin Meredith

[Deflavio]

Thanks Martin!

I think your last message finally cleared my doubts.  SNR is aperture, exposure and QE, yep I fully agree with this.

What got me confused was the story of the "equivalent" time required by equivalent f-ratio systems I read around. I see now, this works IF I don't change pixel size. Like a photographer changing lenses but keeping the same camera body. Longer focal lengths give bigger pictures on the focal plane spreading more the photons on a larger surface but density will stay the same for constant focal-ratio. So yes, by using the same pixel size, you can get same SNR with smaller apertures but you have to trade your resolution by using shorter focal lengths...As you said in your point 4.

On the contrary, if we want keep the same resolution (using smaller pixels) we have to sacrifice SNR or increase exposure. Great now all fits.

 

So, going back at the original post, small pixel sensors can help to achieve higher resolutions with shorter focal lenses but at the price of SNR or exposure time. For an ideal travel EAA setup, I guess it all comes down how much longer I'm ok to integrate.

Any quick way to calculate how longer exposure would be compared to a reference scope?

 

Ps.

Why FOV? I'm thinking about still relative small objects like galaxies and planetary nebulas...

Edited October 1, 2020 by Deflavio

[Martin Meredith]

For what its worth, I applied the point source code to a range of scope/camera combinations and plotted SNR versus exposure for a single sub, for detecting a mag18 point source in a mag18 brightness sky and got this result:

The Lodestar has 8.2um pixels while the ASI 178 has 2.4um pixels. The Borg has a focal length of 331mm versus 800mm for the Quattro 8" (I threw in the Quattro 10" to see what a near-doubling of mirror surface area would deliver). I applied a read noise of 7e for the Lodestar and 1e for the ASI 178 and appropriate central obstructions for the reflector and refractor.

I'm a bit surprised by the Borg + Lodestar result but it looks like it is related to the FWHM. Here are results for FWHM=3, 4 and 5

Edited October 2, 2020 by Martin Meredith
added new plots and reordered

[Deflavio]

Hi Martin, 

I think the reason Borg+Lodestart results are strange for FWHM 2 and 3 is because you are well past the 0.83xFWHM threshold (i.e. when you are under-sampled but SNR is maximum according to Raab's paper) and your pixel is now bigger than the whole star so you don't have benefit by going bigger than that.

Specifically with FWHM=2,3,4 you are sampling at 0.44x, 0.66x and 0.89x FWHM. These results replicate pretty well what said in the paper.[Just checking, FWHM =2 and 3 seem the same plot but I can follow the pattern on the rest].

Also it is interesting that by using larger FWHMs (e.g. 4,5) overall SNR decrease across all configurations because we are losing more photons from the central pixel (which is what this algorithm is only taking into account) but more or less the Borg still seems to maintain the same SNR (~8/6 at t=300sec) or with only just a slightly decrease. This is because is still able to mostly swallow the whole star.

I think these results are really useful to calculate pixel-SNR or the limit magnitude but now I'm more convinced they don't tell the whole story for extended objects. In the examples above the calculation of the central pixel is ignoring what is happening to the surrounding pixels. When we have a single point source and increasingly larger FWHM we spread photons more and lose them outside the central pixel and SNR is going down. That's fine.

In the presence of extended objects with increasingly larger FWHM, photons are spread/blurred from all voxels but now if I consider a pixel within this extended object it will both spread photons but also receive for surrounding voxels. SNR behaviour of extended objects is different than a point source. In a way, I see now, this is a very convoluted way to explain blurring. 😅

 

F

 

Edited October 1, 2020 by Deflavio

[Martin Meredith]

Hi Flavio

Thanks for spotting the equivalence of 2 and 3! I've now included the correct versions and reordered from 2 to 5 so the progression is clearer. 

I fully agree that these plots don't tell us the whole story about extended objects for the reasons you give. They're useful for detecting limiting magnitude, and for predicting the effects of seeing.

I've often wondered whether it would be possible/feasible to simulate the kinds of effects we're discussing by taking a very high resolution Hubble image and treating it as an emitter of photons ie mapping each pixel intensity to the mean of a Poisson noise generator. I've too little time at the moment to pursue this unfortunately...

cheers

Martin 

[Deflavio]

Eh, that would be really nice. This could be the base for a full EAA/AP simulator  ..including noise, optics and sky, etc. Ok, I'm dreaming now but I saw some time ago Aberrator software. It was nice to simulate the effect of optics on planets and doubles, no noise though.

Regarding SNR, I think it should be possible to adapt the point source algorithm to extended object by changing how the number of photon are computed for the pixel, the rest hopefully should be similar. I'll try to get more reading on it. 

 

Flavio