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Old 21-06-2015, 05:08 PM
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A way to compare Astrograph sensitivities - long post

Hi.
The question often arises - how sensitive is this imaging system compared to that one. You may wish to compare different setups when deciding what to buy or how to configure what you have. The following provides a way to do this. I am considering asking Mike to put this in the how-to area, but thought it would be useful to run it by the forum beforehand - so would be grateful for comment on the content, the way it's expressed, whether you think it has value and if you have seen this sort of approach published elsewhere. thanks for looking. Regards ray


The question often arises as to which combination of imaging scope and sensor will be the most sensitive. Relative system sensitivity can be found with reasonable accuracy by comparing the S values for systems, where S is:

S = QE * OE * p^2 / FNo^2

Where QE is detector quantum efficiency, OE is optics efficiency, p is pixel size and FNo is F number.
* is multiply, / is divide and ^2 means squared.

To work through an example; say you want to compare:
a 300mm f3.8 Newtonian + 16803 camera (system 1)
with a 200mm f8 RC + 8300 camera (system 2).

The explanatory notes (later on) show how to estimate the parameter values, but for now appropriate numbers are:
For system 1; quantum efficiency QE=0.53, optics efficiency OE=0.65, pixel size p=9, FNo=3.8
For system 2; quantum efficiency QE=0.47, optics efficiency OE=0.75, pixel size p=5.4, FNo=8

from which,

S(system 1) = 0.53 * 0.65 * 9 * 9 / 3.8 / 3.8 = 1.9

S(system 2) =0 .47 * 0.75 * 5.4 * 5.4 / 8 / 8 = 0.16

Since the Newtonian (system 1) S value is ~12 larger than that of the RC (system 2), then the Newtonian system is about 12 times as sensitive. Similar calculations for a range of systems are included in the attached image.

Of course overall sensitivity is not the whole story. Some other equally important issues are resolution, image scale, field of view and required sub length - for the chosen examples, the RC has finer sampling, so it would resolve much finer detail in very good seeing and it would produce much larger scale images of small objects. However, the fact remains that, with the example RC system, you would need to stay out under the stars for ~12 times longer than you would with the Newtonian in order to get to the same SNR (for sky limited imaging). ie, if you got a nice smooth image in a total of 3 hours with the example Newtonian system, you would need ~36 hours to get the same image smoothness with the example RC system.

The other thing that needs to be said is that this should not be read as implying that either large pixel size or low FNo is of prime importance in isolation – neither is inherently better for sensitivity. To show that this is the case, look at the equation – if you increase the FNo by a factor of 2 and also increase the pixel size by a factor of 2, the two increases cancel out and there is no change of sensitivity – ie if you must use a high FNo because that is the characteristic of your chosen scope, just match it with large pixels to retain sensitivity. However, once you have decided on your pixel size and focal length, a faster scope of the same focal length will give you a sensitivity advantage (if such a scope is available with the desired specs). Alternatively, if you decide on a particular focal length and aperture, larger pixels will give you higher sensitivity – but at the price of reduced resolution.

*****************
Explanatory remarks:

The calculated S value is not a standard quantity, but you can use it to say that “system A is 1.4 times as sensitive as system B” by comparing the calculated S values. It was derived from first principles, but could also be extracted from the absolute spectral sensitivity formulae used in professional astronomy.

The S value comparison is only valid for broadband imaging, where shot noise from the sky is the limiting factor. However, it still provides some idea of relative performance with narrow-band imaging. It is based on Signal to Noise Ratios (SNRs), not ADU values – the ADU values you get from different cameras will vary depending on camera gain and they do not tell you much about image quality.

The only parameter with units is p. Use microns for consistency.

QE (Quantum Efficiency) is the average over the system bandwidth, not the peak. Typical average broadband QE values (400-700nm) for a few popular chips are:
16803 = 0.53
11002 = 0.4
8300 = 0.47
694 = 0.7
OSC/DSLR ~ 0.2 (probably) EDIT: it could be as low as 0.1 - see post 16

The optics efficiency is the nett effect of all optical losses such as reflection loss, transmission loss and central obstruction. For example, my Newtonian telescope has 2 reflective surfaces, each with estimated reflectivity of about 0.87, a central obstruction that reduces the total light to about 0.9 and a coma corrector that has 6 surfaces and 3 bits of glass and probably has something like 0.95 transmission. The total optics efficiency is the product of the individual efficiency factors: 0.87 x 0.87 x 0.9 x 0.95 ~= 0.65. A refractor with a field flattener could possibly be around 0.9. An RC or SCT with large obstruction, high reflectivity coatings and a field flattener may be around 0.75.
In general, geometrical effects are more important than optics efficiency and you probably won’t be too far out if you use:
Refractor = 0.9,
SCT/RC/CDK/premium Newtonian = 0.75,
corrected standard Newtonian = 0.65.

have fun
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Last edited by Shiraz; 22-06-2015 at 08:24 PM.
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Old 22-06-2015, 11:56 AM
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Interesting post Ray. I can see you put a lot of work into it. Is the relationship between pixel size and focal length though a division of their squares though? How did you figure that?

Something must be a little off as it does not match my experience with various scopes.

I doubt using a 200mm RC with a KAF8300 is going to take 12 times longer to get the same signal to noise ratio.

Doesn't it more come down to aperture not focal length? And QE.

I take it when you worked out those average QEs you took the same samples of each of the sensors QE graph? 16803 has peak 60% QE and so does KAF8300. I have noticed a drop in sensitivity with oversampling but its not that dramatic.

From my experience only I would rate a 200mm RC at F8 and KAF8300 taking 4x longer to reach the same signal to noise than a 300 F3.8 an 16803 camera. Perhaps 5X max but unlikely 12X.

For example my RHA is 305/F3.8. If I take an image of something that I have imaged several times with different scopes it sure is faster but not 12X. So perhaps that pixel/focal length formula is not correct.

Camera read noise comes into it as well. What do you think?

Greg.
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Old 22-06-2015, 01:04 PM
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so Ray did I get this correct for my setup?
S = 0.3

newt d300mm, f4
camera pixel size 4.3
QE 40% http://www.sensorgen.info/
?

interesting comparisons

Russ
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Old 22-06-2015, 01:23 PM
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Hi Greg. Thanks for posting. Will try to answer your questions one at a time. Regards Ray

Is the relationship between pixel size and focal length though a division of their squares though? How did you figure that?

Originally from first principles, but this general form seems to be widely used in astronomy - as an example, it is a simplification of equation 4 in http://arxiv.org/pdf/1401.5473v1.pdf Also, it is not focal length, but FNumber

Something must be a little off as it does not match my experience with various scopes.

I doubt using a 200mm RC with a KAF8300 is going to take 12 times longer to get the same signal to noise ratio.

Depends on the camera, but with the chosen examples, that's what happens. If you are looking at ADU signal values from the chip, you might not think that this is the case due to camera gain differences, but the sensitivity difference (based on SNR in the detected charge) will be 12 - but only if the other system has a big pixel 16803.

Doesn't it more come down to aperture not focal length? And QE.

Aperture is included in the FNo and the equation has a QE term. I agree that aperture determines how many photons get in to the system, but the fl and pixel area determine how many end up in a pixel (and hence what the SNR is) - you can't look at any part of the system in isolation.

I take it when you worked out those average QEs you took the same samples of each of the sensors QE graph? 16803 has peak 60% QE and so does KAF8300.

the QE used in the equation is the average over the bandpass, not the peak. These kodak chips do not have a very flat spectral response (maybe I should have included the 3200 in one of the examples - that is pretty good)

I have noticed a drop in sensitivity with oversampling but its not that dramatic.

It is scary how much damage oversampling can do. The simplest way to be convinced of this is to imagine what would happen if you imaged with a 2x Barlow in your scope - I am sure that you would agree that the signal will take a huge hit if you did (try it!) - what you would be doing is simply changing the sampling by 2x (the aperture remains the same), but you would end up with 1/4 the signal in each pixel and need to image for 4x as long to compensate.

From my experience only I would rate a 200mm RC at F8 and KAF8300 taking 4x longer to reach the same signal to noise than a 300 F3.8 an 16803 camera. Perhaps 5X max but unlikely 12X.

would really need measured SNR to check this, but what you may possibly be basing this on is a 4x-5x difference in time to get to the same ADU values. Since an 8300 camera has about 2.5x the gain of a 16803, the time to equal SNR would be 10x-12.5x, which agrees with the equation .

For example my RHA is 305/F3.8. If I take an image of something that I have imaged several times with different scopes it sure is faster but not 12X. So perhaps that pixel/focal length formula is not correct.

The formula uses FNo and pixel area. It seems to be widely used in other guises - I am pretty sure that it is OK.

Camera read noise comes into it as well. What do you think?

Read noise only determines how long the subs should be - this approach assumes that they are long enough that shot noise from the sky is dominant, so read noise does not come into it. It is also assumed that dark current is under control (but that is a given with modern cameras and broadband imaging)

Last edited by Shiraz; 22-06-2015 at 05:24 PM.
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Old 22-06-2015, 02:08 PM
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Quote:
Originally Posted by rustigsmed View Post
so Ray did I get this correct for my setup?
S = 0.3

newt d300mm, f4
camera pixel size 4.3
QE 40% http://www.sensorgen.info/
?

interesting comparisons

Russ
Hi Russ.

Yes, but I wouldn't rely on the Sensorgen info at all - its full of obvious contradictions. eg, they quote QE for one camera as 87% whereas the Bayer filter restricts the maximum possible average QE to less than 40% (so who knows what they mean by QE). they also have a Powershot with 0.9 electron read noise ???? If you could find a science camera with 0.9 electron read noise, you would be paying $50k or more - and it won't be a Powershot. Assuming that the technology of DSLR sensors is roughly on par with modern mono chips, it would probably be reasonable to expect about 20% average QE for a DSLR, but that is still a guess.

Hence your system possibly works out at around S=0.15. ie you have a system that is slanted towards high resolution sampling and large image scale rather than sensitivity.

Last edited by Shiraz; 22-06-2015 at 08:32 PM.
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Old 22-06-2015, 02:12 PM
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Good stuff Ray. Bookmarked!
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Old 22-06-2015, 04:01 PM
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Thanks for answering my questions Ray. As always you provide some interesting insights and makes even happier with the F3.8 system.

By the way I think some DSLRs are probably up around 65% QE. CMOS sensors in digital cameras are getting all the research. Take a look at the about to hit the market Sony A7r - backside illuminated full frame 42.4 mp sensor with copper wiring rather than aluminium and 3.5X throughput as a result. So higher QE than A7r which is currently rated around 60% QE. I believe it as a 30 second ISO6400 image at F2.8 lights up everything.

Greg.
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Old 22-06-2015, 04:10 PM
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Quote:
Originally Posted by gregbradley View Post
Thanks for answering my questions Ray. As always you provide some interesting insights and makes even happier with the F3.8 system.

By the way I think some DSLRs are probably up around 65% QE. CMOS sensors in digital cameras are getting all the research. Take a look at the about to hit the market Sony A7r - backside illuminated full frame 42.4 mp sensor with copper wiring rather than aluminium and 3.5X throughput as a result. So higher QE than A7r which is currently rated around 60% QE. I believe it as a 30 second ISO6400 image at F2.8 lights up everything.

Greg.
Hi again. Modern sensors could have a peak QE of 65%, but the sensitivity calculation outlined above is based on average QE - the Bayer filter absorbs about 2/3 of the photons that hit it (just doing it's job), so it is not possible for a Bayer chip to have anything much more than about 30% average QE. It suits camera makers to quote peak QE, because it looks better, but Bayer chips actually take a huge hit in average (true) QE.
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Old 22-06-2015, 04:10 PM
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Good stuff Ray. Bookmarked!
Thanks Marc - hope it is useful
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Old 22-06-2015, 04:11 PM
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The equation that I have been using for a while (takes 20 seconds on my phone) doesn't go into much depth with average sensitivity or even different telescope efficiencies BUT.

P= Pixel in micron
Fl= Focal Length
A= Aperture
QE= Quantum Efficiency

((((P*206.265)/Fl)^2)*A^2)*QE

What this calculation does is give a correlation between the amount of light entering the system (the aperture) compared to the amount of sky that each pixel covers. With a very slight modification to the above equation, adding:
TE= Telescope Efficiency

This gives the difference between different optical qualities and telescope designs if you so desire.

((((P*206.265)/Fl)^2)*(A*TE)^2)*QE

Quote:
To work through an example; say you want to compare:
a 300mm f3.8 Newtonian + 16803 camera (system 1)
with a 200mm f8 RC + 8300 camera (system 2).
S1= 126,487
S2= 9110

This is a difference of 13.89 times. Of course, this is the difference between S1 having a sample size of 1.63 arcsec/pixel and S2 having 0.696 arcsec/pixel. This is to be expected when you have a smaller telescope with smaller pixels imaging with a longer focal length.
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Old 22-06-2015, 04:17 PM
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thanks Colin.

It's basically the same equation, but I don't think that the telescope efficiency term should be squared. I have also assumed that a constant is meaningless for comparisons. apart from that, thanks for confirming the validity of the original idea

Do you by any chance have a source reference?

regards Ray

Last edited by Shiraz; 22-06-2015 at 05:25 PM.
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Old 22-06-2015, 06:49 PM
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Yep, you're correct about squaring the telescope efficiency, should be EF(A^2).

I usually put the "206.265" in there mostly because I am curious about sample size, interested in doing photometric studies. As you say, it isn't needed outside of that.

No source, came up with it on the drive home from work a month or two ago when I was trying to decide on a camera :-)
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Old 22-06-2015, 07:52 PM
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Quote:
Originally Posted by Atmos View Post
Yep, you're correct about squaring the telescope efficiency, should be EF(A^2).

I usually put the "206.265" in there mostly because I am curious about sample size, interested in doing photometric studies. As you say, it isn't needed outside of that.

No source, came up with it on the drive home from work a month or two ago when I was trying to decide on a camera :-)
thanks for that. It seems surprising that such a basic idea does not appear to be very widely quoted - I also derived from first principles, but then could find only one reference to anything similar on the web (and that by happenstance). Maybe it is just so obvious that nobody bothers to formalise it, or maybe I wasn't looking in the right places.

Last edited by Shiraz; 22-06-2015 at 09:17 PM.
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Old 22-06-2015, 08:02 PM
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an analogous equation is given at 17:16 of the Dragonfly youtube video linked to in this thread: http://www.iceinspace.com.au/forum/s...d.php?t=135928
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Old 22-06-2015, 08:07 PM
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an analogous equation is given at 17:16 of the Dragonfly youtube video linked to in this thread: http://www.iceinspace.com.au/forum/s...d.php?t=135928
Thanks very much Richard - yes, I followed that up and their paper is my reference in post 4 - Eden's thread was nice happenstance, since I hadn't been able to find anything else that confirmed the simplified relationship. The video implied that this type of relationship is commonly known ("astronomy 101" from memory), which is what I expected, but couldn't confirm. In any event, hopefully it is useful to bring it to the forum's attention, since it is dead easy to use in this form and clears up all those "what difference does Fnumber make" type issues.

you have just moved from OSC to mono - do you have any feel for the relative sensitivities of OSC and mono? - ie do you think that it is reasonable to assume that the QE of an OSC is about 1/3 that of an equivalent mono chip?

Last edited by Shiraz; 23-06-2015 at 10:56 AM.
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Old 22-06-2015, 08:16 PM
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Thanks very much Richard - yes, I followed that up and their paper is my reference in post 4 - Eden's thread was nice happenstance, since I hadn't been able to find anything else.

you have just moved from OSC to mono - do you have any feel for the relative sensitivities of OSC and mono? - ie do you think that it is reasonable to assign a QE to OSC of about 1/3 that of a mono chip?
using your formula to compare my own equipment, i think a DSLR QE of 0.2 seems too generous (at least for my 1000D) when comparing its relative sensitivity with that of the ST10. After playing with the numbers in my spreadsheet here i'm inclined to think that a DSLR QE of 0.1 to 0.15 is a better match to my own anecdotal observations.
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Old 22-06-2015, 08:26 PM
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Originally Posted by rmuhlack View Post
using your formula to compare my own equipment, i think a DSLR QE of 0.2 seems too generous (at least for my 1000D) when comparing its relative sensitivity with that of the ST10. After playing with the numbers in my spreadsheet here i'm inclined to think that a DSLR QE of 0.1 to 0.15 is a better match to my own anecdotal observations.
thanks very much - that's really useful. have edited the original post to incorporate your advice, but will leave the spreadsheet as is for now.

Just a suggestion, but you are in a unique situation to comment with authority on the relative sensitivities of OSC and mono - would you possibly be in a position to get up a new thread on that topic? I am sure it would be of interest to a lot of people.

Last edited by Shiraz; 22-06-2015 at 10:20 PM.
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Old 23-06-2015, 06:47 AM
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There are already sites that post measured QEs of various digital cameras. With all due respect none are as low as 10%. 10% would mean they would not be able to take a photo in any sort of dim light and we know that is not true. This is getting a bit subjective and opinion rather than fact.

Greg.
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Old 23-06-2015, 09:11 AM
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There are already sites that post measured QEs of various digital cameras. With all due respect none are as low as 10%. 10% would mean they would not be able to take a photo in any sort of dim light and we know that is not true. This is getting a bit subjective and opinion rather than fact.

Greg.
different measures of QE Greg - we are comparing apples and oranges.

With DSLRs, the widely used QE measures gloss over the fact that about 2/3 of white light photons never actually get to the sensor (they are absorbed in the Bayer filter). That is fine for comparing DSLRs, where you can assume that all Bayer filters are similar and the performance of the underlying array is what distinguishes between cameras. However the use of the term "QE" without any qualifications causes confusion when comparing DSLRs with mono chips.

A mono chip has no Bayer filter so it sees about 3x more white light photons than an OSC (regardless of how many photons either underlying array detects). Thus, broadband QE for a mono chip starts out about 3x better than that of an equivalent DSLR - something that is completely hidden by the methods used to measure DSLR QE.

Results from the two different ways of measuring QE are well illustrated in http://www.astrosurf.com/buil/50d/test.htm (figures from that below) The first figure shows QE measured the DSLR way (pixel QE in the left hand panel) and the broadband way (geometric QE in the right hand panel). The second figure shows the QE of some DSLRs when compared with a 3200 and when accounting for broadband illumination - the broadband QE is the sum of the 3 colour curves and this figure clearly shows the "chasm" between DSLR and mono when QE apples are compared with QE apples. .

This thread is about broadband QE and Buil's results match Richard's observation that a good DSLR may have an average broadband QE of around 10-15%. Of course 10% is still very sensitive - it is about an order of magnitude better than a fully dark adapted human visual system. In any event, it is not physically possible for the broadband QE of a Bayer DSLR to get much above 30% using any detector technology, so 10% is not bad.
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Last edited by Shiraz; 23-06-2015 at 01:50 PM.
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Old 23-06-2015, 04:30 PM
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Here is another link:

http://www.dpreview.com/forums/post/53054826

Per his measurements the QE is much higher.

There is no way most DSLRs QE is under 10%. Use a Nikon D800e or a Sony A7r in pitch dark at ISO6400 and you'll se plenty of image.

Also the DSLRs images here posted. For example those nice images from the Pentax K5 that's been modded. If it were only 8% QE then he'd no way get that much of the Helix nebula in that amount of exposure time.

Also the Bayer array definitely absorbs light, for sure, but not that much. Also some sensors are coming out with higher transmission colour filter arrays. There are a few models with that already.

Plus Bayer matrix is interpolated so that adds some sensitivity with nearby neighbour pixels being interpolated its kind of similar to binning (its not but it must add to the QE).

I have also imaged with an STL11 which was one shot color so this was much the same as a DSLR CMOS sensor. It was definitely less QE than the mono but not 1/4 more like half or 60%. Kodak lists the QE of their one shot colour CCDs. These mostly have Bayers, some have Trusense which is an PRGB matrix. Normal Bayers are around 20-30% with the larger pixel size generally higher in the range.

The latest Sony A7rii sensor for example is backside illuminated with the pixels close to the surface. The QE on that will be particularly high. It also uses thicker copper wiring for 3.5X faster readout. That camera is likely to be the highest QE of any except perhaps the Aony A7s which must be right up there as ISO102K shots are workable.

Greg.

Last edited by gregbradley; 23-06-2015 at 04:42 PM.
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