So why isn't aperture important for DSO's?

[vlaiv]

7 minutes ago, DrRobin said:

Binning doesn't help that much.  If you use a 2x2 bin (4 times the area), but they way the signal is read it is more like 2x the signal.  To get back to 4x signal you have to use 4x4 bin, roughly speaking.

Smaller pixel sizes often have a lower light sensitive area to total area, due to the need for readout registers.  It's so dfficult to compare different ccds.

If you look at my post from 2013 you will see I differentiated between a DSO (the subject of this thread) and a star.  This is important if you are considering point sources or a light spread out of an area.

No, binning provides you with exact signal improvement as number of pixels would suggest. Add 4 pixels together and you will have x4 signal strength (for uniform signal over those four pixels). It is SNR that doubles in that case - same as when stacking 4 images - SNR improves by factor of SQRT(number of stacked samples).

Sensitive area of pixel is "included" in QE of sensor, so in principle you don't have to worry about that - total area of 2x2 in relation to total sensitive area will be the same as with single pixel, so binning does not change QE over single pixel (neither increases it nor decreases).

All of this is of course for extended sources - surface brightness. With point sources like stars same applies except that you need to factor in PSF of optical system (there also larger aperture has an edge as it will provide tighter PSF for same conditions versus smaller aperture).

We don't need to compare different CCDs. Here is another example:

You have two 6" scopes. One is F/8 and one is F/5. Use the same sensor on both of them.

Only difference being that you bin x2 pixels on F/8 vs no binning on F/5 - which one will be faster? F/8 one will be faster. In this case we have same aperture but different resolution (pixel gathering area). F/8 binned x2 will be of the same speed as F/4 if both scopes have same aperture.

[Jessun]

Things go funny when we include the mystical spot target or the (almost as confusing) baffling choice of sensors and pixel sizes.

In essence F ratio is simply dealing with the theory of optics. It has only a number, and no frills to it. F5 is F5. Not F5 Special because of this or that.

Draw a simple telescope on a paper, one lens, one tube, one focal plane with an image circle. No measurements needed. Imagine it's a small telescope then the image circle is small. And vice versa for a big one. A simple division is all the maths needed. Point what ever sized telescope you envision to the mother of all flat panels and then put a photon counter, the size of a plank length (or half lol) and for any sized version of your design the photons will come in at the same rate at the counter wherever you count, lets say smack in the middle or 10% off centre or anywhere, proportionally.

There is no real mystery to this. Confusion kicks in when there is a large fix sized pixel at the end.

Aperture determines the max theoretical resolution and surely doesn't dictate the faintest object you can detect. A photon is a photon. It won't aim squarely at only large telescopes if they come from afar...

A lower f-ratio is per definition always faster than a higher one.  There is no way around this. One only has to do away with the idea of finite sampling points in the image circle. Imagine an infinite number instead to better understand F ratio.

/Jessun

[vlaiv]

13 minutes ago, Jessun said:

Things go funny when we include the mystical spot target or the (almost as confusing) baffling choice of sensors and pixel sizes.

In essence F ratio is simply dealing with the theory of optics. It has only a number, and no frills to it. F5 is F5. Not F5 Special because of this or that.

Draw a simple telescope on a paper, one lens, one tube, one focal plane with an image circle. No measurements needed. Imagine it's a small telescope then the image circle is small. And vice versa for a big one. A simple division is all the maths needed. Point what ever sized telescope you envision to the mother of all flat panels and then put a photon counter, the size of a plank length (or half lol) and for any sized version of your design the photons will come in at the same rate at the counter wherever you count, lets say smack in the middle or 10% off centre or anywhere, proportionally.

There is no real mystery to this. Confusion kicks in when there is a large fix sized pixel at the end.

Aperture determines the max theoretical resolution and surely doesn't dictate the faintest object you can detect. A photon is a photon. It won't aim squarely at only large telescopes if they come from afar...

A lower f-ratio is per definition always faster than a higher one.  There is no way around this. One only has to do away with the idea of finite sampling points in the image circle. Imagine an infinite number instead to better understand F ratio.

/Jessun

No need to define F/ratio in any other terms than it is defined - as a ratio of focal length to aperture.

If you put a physical constraint on "photon counter" - in terms of its absolute size being always the same and finite, then yes F/ratio of two optical systems will indeed define respective speed in terms of average number of detected photons per unit time.

I'm just saying that special case can't be used as basis of understanding of whole class of phenomena. This comes from day time photography and usage of lens. It works in that domain because two important facts - target shot noise is dominant source of noise (plenty of light bouncing off object being photographed) and when working with single camera and exchanging lens - you are working with fixed size pixels. Daytime AP does not know concept of binning to change pixel size.

When I first started thinking about AP I quickly realized that F/ratio and its use is very limited in determining performance of imaging system. I fiddled around with math and concluded that aperture at resolution is much more "natural" way of thinking of speed of acquisition in AP. I tried to formulate "one number says it all" approach, but while doable - it is too complicated for quick mental comparison (square roots and such).

After all of that, I concluded that aperture at resolution is better approach because it lends itself to more or less "natural" way one would choose scope / camera combination. Instead of thinking of F/ratio - speed of scope, one should go the other way around, and follow similar steps to these:

1. I've got a mount that is capable of X precision in tracking / guiding

2. My average or good seeing (depends on what you base your decision on) is Y

3. From 1 and 2, I can conclude that my average FWHM will be Z and therefore I need to sample at resolution S to capture W% of data available (in terms of resolution)

4. I have choice of cameras .... (and then you think of QE, sensor size, technology, pixel size....) and choice of scopes (regardless of F/ratio) - which combination (including binning) will offer me most aperture at target resolution S and still fit other criteria (mount capacity, budget, preferred optical design, ....)

 

[Jessun]

vlaiv, I really like your thinking and you have the skill to formulate a model that works very well for you.

I gathered that the OP wanted to go down to the logical basics, and for a more logical approach I think it's important to just accept it for what it is. A simple ratio between two measurements. The only other ratio I deal with daily is Mach number. It also has no unit. Mach is not a unit, although Americans often say something like "2 Mach". Don't ask me why this is. It's Mach 2. Ratio 2. Mach 2 is the same for a Lockheed aircraft or a Northrop aircraft. It's an absolute. Just like all F x telescopes are all equal.

F ratio is just the same. It does away with any maths anyone cares to throw at it. 80/10=8. No number is more important than the other. 80 is no more magic than 10 etc. The troubles only begin when we put a finite pixel at the business end and start drawing conclusions, or go down the route that astrophotography is somehow different from normal photography just because we have some very bright, small stars in the mix.

/Jessun

 

 

[vlaiv]

3 minutes ago, Jessun said:

or go down the route that astrophotography is somehow different from normal photography just because we have some very bright, small stars in the mix

O, but it is very different thing

In principle they are the same thing, but normal / daytime photography is operating "subsonic" and AP is operating "supersonic" - two different regimes of the same thing (air drag).

With day time / normal photography you have following "restrictions":

Target shot noise by far most dominant type of noise, or plenty of signal. Dynamic range of target is often quite small. Dealing with relatively short exposures. Capturing image in single exposure (there are of course exceptions - like depth of field stacking, ultra fast exposures and such, but let's not consider those "normal" photography - again special regime).

With AP things are quite different:

Target shot noise is often behind other noise sources (if it's not then one is very lucky to have pristine skies, almost no read and thermal noise and relatively bright target) - minimal signal per exposure (often less than one photon per pixel per exposure). Dynamic range is couple orders of magnitude larger than in normal photography. Dealing with larger number of long exposures.

So you are quite right to say that in principle they are the same thing - sensor / lens / light, but due to different regimes of operation, they are practically very different.

[Jessun]

You are right vlaiv as far as I'm educated. All practical considerations when it comes to taking an actual image are as we all know making it an almost impossible task.

It is just so fundamental to understand F ratio at its core. Noise, pixel size, well depth etc are merely the constraints we have to deal with and don't quite play a part in understanding F ratio. There is for instance no F ratio myth as often proposed. 

As a side note I have attached an pic that I have drawn for most of the pilots I ever flew with. Some 3000 to date.

Riddle:

A man is fishing on a bridge. He is positioned one third in on the bridge. When he detects a train approaching he knows he has to vacate the bridge. He can either go to the left and Juuuuust miss being hit by the train or he can go to the right and Juuuuuust miss being hit.
The man will walk at a pace of 6km per hour as he departs.
Question, what is the speed of the train and how far away is it when he starts walking? You can answer in a unit of your choice if you don't like the metric system.

/Jessun

Edited July 25, 2019 by Jessun

[vlaiv]

I like the hint about choice of units

Train is one bridge distance away from the start of the bridge, and it is moving at 18km/h (x3 speed of that man)

As for F/ratio myth - whether there is in fact myth or truth depends on formulation of that F/ratio myth.

If we examine the statement:

"Having two scopes of different F/ratio, there is a relationship in corresponding times for attaining given SNR which depends solely on F/ratio of said scopes", then I have to say - it is a myth.

[lukebl]

Reading this thread reminds me that this subject crops up rather frequently, and always, i mean ALWAYS, ends up in a lengthy, conflciting and complicated dabate. At the end of which I am none the wiser. And I'm still none the wiser!

I have a personal issue related to this. I like to measure asteroid occulations, and use a RunCam Night Eagle camera which operates at a fixed frame rate of 25 per second. It's very sensitive, and with my 200mm RC with a 0.5x focal reducer making it effectively f/4 (I think) it will easily capture stars to about 13th magnitude even with such a short exposures. Most occultations don't pass over my obs, so I've decided to have a mobile lightweight rig, using either my ST80 f/5 scope, or my 90mm f/13.9  Cass with focal reducer (making it f/7?).

Anyway, my tests have shown that neither scope can capture stars fainter than about mag 10, and the 'slower' Cass perfoms better than the ST80, so I will have to stuck to brighter occultations when operating away from home.

The point being is that this says to me that the aperture really is everything. I dont understand the F-ratio myth, and probably never will. It's all above my pay grade!

[DrRobin]

A focal reducer doesn't change the F ratio of the scope, it changes the size of the sensing element. Your 200mm RC is still F/8, but the pixel size has effectively doubled in size (4 x the area) and this makes it more sensitive at the cost of resolution.

[vlaiv]

1 hour ago, DrRobin said:

A focal reducer doesn't change the F ratio of the scope, it changes the size of the sensing element. Your 200mm RC is still F/8, but the pixel size has effectively doubled in size (4 x the area) and this makes it more sensitive at the cost of resolution.

Not sure if there is a simple way to say it and still be 100% correct.

You can say that it alters F/ratio as it creates the light beam that has properties of altered F/ratio - system behaves as if it has shorter focal length with the same aperture. Light beam converges as if it came from shorter focal length and same size aperture - in that sense it "changes F/ratio" - whatever you put after focal reducer "experiences" different F/ratio. On the other hand saying that F/ratio of the scope changed is not correct either - scope still has certain focal length and certain aperture.

Similarly you don't change size of sensing element - it is still the same size of pixel in physical terms. We might say that "mapping" between angular size and physical size of pixel changed. Similar thing happens with binning - physical pixel size stays the same, but "logical" or perhaps better termed "effective" pixel size is increased. In similar way reducer alters "effective" focal length and "effective" F/ratio of the system.

1 hour ago, lukebl said:

Reading this thread reminds me that this subject crops up rather frequently, and always, i mean ALWAYS, ends up in a lengthy, conflciting and complicated dabate. At the end of which I am none the wiser. And I'm still none the wiser!

I have a personal issue related to this. I like to measure asteroid occulations, and use a RunCam Night Eagle camera which operates at a fixed frame rate of 25 per second. It's very sensitive, and with my 200mm RC with a 0.5x focal reducer making it effectively f/4 (I think) it will easily capture stars to about 13th magnitude even with such a short exposures. Most occultations don't pass over my obs, so I've decided to have a mobile lightweight rig, using either my ST80 f/5 scope, or my 90mm f/13.9  Cass with focal reducer (making it f/7?).

Anyway, my tests have shown that neither scope can capture stars fainter than about mag 10, and the 'slower' Cass perfoms better than the ST80, so I will have to stuck to brighter occultations when operating away from home.

The point being is that this says to me that the aperture really is everything. I dont understand the F-ratio myth, and probably never will. It's all above my pay grade!

Best thing to do when having this requirement of capturing single star and doing measurements is to make sure star is covered by single pixel. Star profile in focal plane plays important role here, and in principle best results are when you have single read noise "dose" per star intensity readout - that would mean placing it on a single pixel. Second important thing is of course aperture - you want as many photons in given time coming from star to be captured.

[Jessun]

I agree vlaiv. It's just optics and the 'sensor' should be though of as a white postage stamp rather than something that is segmented.

Well done on the train question. It's just one of those riddles that only has a ratio at heart. 4 people ever solved it during the day I flew with them. One guy put in the speed of sound in a series of equations and came up with a number of miles. The simple ratio never clicked.

/Jessun

[DrRobin]

It's a simultaneous equation, x is the distance of the train from the bridge, y is the length in the bridge (in terms of time)

x = y/3 and x+y = 2*(y/3)

x therefore equals y and therefore the speed of the train is 3x.

We did these in school.

[vlaiv]

18 minutes ago, Jessun said:

It's just optics and the 'sensor' should be though of as a white postage stamp rather than something that is segmented.

This is the one I'm not comfortable with. Both due to nature of light (that it comes in photons) and due to fact that there is no continuous measuring device that will give exact x/y position of a photon hit (nor could there be - uncertainty principle).

For me it is much easier to consider finite pixel size (as one more variable) and it also leads to correct results in terms of calculated / obtained SNR in given time.

[Jessun]

Very neat. 

The risk is of course to over complicate matters sometimes.

lukebl is right as we are all painfully aware that discussions on this subject never reached consensus. It's odd in a way that this is.

/Jessun

[Jessun]

My response above is to DrRobin

Edited July 26, 2019 by Jessun

[Jessun]

vlaiv, I think it's easy to do away with numbers and pixels to grasp the basic concept of F ratio. The number is a fraction with no end to the decimal places, and it has no unit. 

Then we put something tricky to observe in front of the lens and something even trickier (a sensor) at the focal plane and practical matters kick in in abundance.

I enjoy these discussions but I don't want to be the broken record on the subject...

It's often the case that your OTA slips, the sensor ices over, the laptop crashes or clouds gathering above etc, way before you really have to lose sleep over the F ratio of the rig...

/Jessun

[dph1nm]

23 hours ago, DrRobin said:

How faint you can see depends on how many arc-seconds per pixel and the signal to noise ratio of the chip.

No - within reason, it is not dependent on the pixel size unless you have a significant contribution from read-noise. If your exposures are dominated by sky noise then all that matters is the ratio of the number photons you receive from an object to the noise in the area on the sky the object covers. These will be the same for the same aperture, irrespective of f-ratio.

NigelM

[dph1nm]

1 hour ago, vlaiv said:

Best thing to do when having this requirement of capturing single star and doing measurements is to make sure star is covered by single pixel.

Strictly not quite true as if you did this you would get more sky than necessary. There is an optimum sampling area for best S/N which is some fixed fraction of the FWHM of the star, but I can never remember exactly what it is.

NIgelM

[vlaiv]

1 hour ago, dph1nm said:

Strictly not quite true as if you did this you would get more sky than necessary. There is an optimum sampling area for best S/N which is some fixed fraction of the FWHM of the star, but I can never remember exactly what it is.

NIgelM

Would it depend on difference between stellar magnitude and sky surface brightness? (something tells me that it should, but I did not give it much thought).

[lukebl]

20 hours ago, Jessun said:

.....Question, what is the speed of the train and how far away is it when he starts walking? You can answer in a unit of your choice if you don't like the metric system.

I thought this was a trick question. My immediate thought was to simply jump off the bridge.

[dph1nm]

On 26/07/2019 at 15:22, vlaiv said:

Would it depend on difference between stellar magnitude and sky surface brightness? (something tells me that it should, but I did not give it much thought).

Yes - obviously if there was no background noise at all then you would do best with an infinite aperture (i.e. collecting all possible photons).  If background noise is the dominant source of noise then it comes out at about 0.67*FWHM (for a Gaussian PSF)

http://wise2.ipac.caltech.edu/staff/fmasci/GaussApRadius.pdf

NIgelM

[MarsG76]

On 7/26/2019 at 3:22 AM, Jessun said:

You are right vlaiv as far as I'm educated. All practical considerations when it comes to taking an actual image are as we all know making it an almost impossible task.

It is just so fundamental to understand F ratio at its core. Noise, pixel size, well depth etc are merely the constraints we have to deal with and don't quite play a part in understanding F ratio. There is for instance no F ratio myth as often proposed. 

As a side note I have attached an pic that I have drawn for most of the pilots I ever flew with. Some 3000 to date.

Riddle:

A man is fishing on a bridge. He is positioned one third in on the bridge. When he detects a train approaching he knows he has to vacate the bridge. He can either go to the left and Juuuuust miss being hit by the train or he can go to the right and Juuuuuust miss being hit.
The man will walk at a pace of 6km per hour as he departs.
Question, what is the speed of the train and how far away is it when he starts walking? You can answer in a unit of your choice if you don't like the metric system.

/Jessun

Cool riddle.. I'm going to use it at work tomorrow.