F ratio and exposure time.

[ollypenrice]

Following a discussion on another thread I've revised the bit of graphics I use to explain this in imaging tutorials. I'd welcome any comments. We are only addressing, here, the capture of targets which will fit on the chip at the baseline focal length (the middle example.)

The idea of the page is to show that there are two ways to reduce F ratio. You can add aperture* (the left hand example) or reduce focal length (the right hand example.) The idea that exposure time reduces as the square of the F ratio is only applicable to the addition of aperture. This is what happens with camera lenses whose FL remains fixed and whose aperture is varied by means of opening up or stopping down the diaphragm. 

There are also effects arising from the reduced number of pixels onto which the captured photons are placed in the focal reducer example but that is not within the remit of this page. Here we ae simply looking into the idea that the exposure time goes as the square of the F ratio and why that is not necessariy the case in telescopic imaging.

Olly

*££££££££££££££££££££££££££££££ 

[zicklurky]

Thanks for this great explanation Olly. It took me a while to understand this when starting out.

[ngwillym]

Only one other thing - as far as my understanding goes -  f/ratio only affects extended objects - nebula, galaxies etc, not point sources - so f/ratio has no effect on stars - so the situation is a little different for open clusters

[ollypenrice]

1 hour ago, ngwillym said:

Only one other thing - as far as my understanding goes -  f/ratio only affects extended objects - nebula, galaxies etc, not point sources - so f/ratio has no effect on stars - so the situation is a little different for open clusters

You're right, though I often wonder whether stars in small amateur astrographic systems really do operate as point sources. A star, for us, covers many pixels.

Olly

[ngwillym]

Ollie - I must admit that I'm of the same opinion - never sure if they are truly point sources - especially given that pixel sizes are dropping all the time. and of course - if they are the only factor that is important is aperture - the bigger the light bucket - the better.

 

And of course - there is the effect of seeing - just slightly blurring all images - even point sources - so is it a good assumption that one should use an image scale to match the seeing as opposed to the actual resolution of the scope?

[ollypenrice]

24 minutes ago, ngwillym said:

 

And of course - there is the effect of seeing - just slightly blurring all images - even point sources - so is it a good assumption that one should use an image scale to match the seeing as opposed to the actual resolution of the scope?

I'd have thought so, yes. 'Lucky imaging' (fast frame solar system) can beat the seeing by exlpoiting rare moments of best seeing but in DS I think your pixel scale shouldn't be below what the guiding and seeing allow. In a perfect world, anyway.

Olly

[andrew s]

Hi Olly, I am afraid I don't agree with your diagram and conclusion in regard to reducing focal length. The reason is that I think what counts in exposure time is not just the number of photons per second (I agree a function of aperture) but the number of photons per pixel per second. This is a function of both aperture and focal length.  As you reduce the focal length the image scale reduces and for a given aperture and pixel size the number of photons per pixel per second goes up.

Now I know the area of sky imaged increases as the image scale reduces but for a correctly designed system (no vignetting)  the entrance pupil will admit a wider angle of sky increasing the number of photon, that reach the CCD, to compensate for the increased field of view.

Regards Andrew

PS If this were not true binning would not work

[zicklurky]

Question - for the reduced focal length (but same aperture), there's no new photons coming from M33, but will the pixels over M33 not expose quicker as the light of M33 is split over fewer pixels?

[ollypenrice]

1 hour ago, andrew s said:

Hi Olly, I am afraid I don't agree with your diagram and conclusion in regard to reducing focal length. The reason is that I think what counts in exposure time is not just the number of photons per second (I agree a function of aperture) but the number of photons per pixel per second. This is a function of both aperture and focal length.  As you reduce the focal length the image scale reduces and for a given aperture and pixel size the number of photons per pixel per second goes up.

Now I know the area of sky imaged increases as the image scale reduces but for a correctly designed system (no vignetting)  the entrance pupil will admit a wider angle of sky increasing the number of photon, that reach the CCD, to compensate for the increased field of view.

Regards Andrew

PS If this were not true binning would not work

Sure, but this is why I put in my caveat stating that the diagrams address only such targets as already fit on the image without reducer. The wider entrance pupil collects sky photons, not object photons, so these make no contribution to the object in the image. (If you want all the FOV brought in by the reducer then you reach an acceptable S/N ratio in accordance with the F ratio-exposure equation.) I think I cover this in a different diagram, which says what you are saying unless I'm mistaken.

1 hour ago, zicklurky said:

Question - for the reduced focal length (but same aperture), there's no new photons coming from M33, but will the pixels over M33 not expose quicker as the light of M33 is split over fewer pixels?

Yes they will. Again I covered this, I think, 

6 hours ago, ollypenrice said:

There are also effects arising from the reduced number of pixels onto which the captured photons are placed in the focal reducer example but that is not within the remit of this page. Here we are simply looking into the idea that the exposure time goes as the square of the F ratio and why that is not necessariy the case in telescopic imaging.

The pixels in the reducer scenario will 'fill' faster. However, if you software bin or downsize the native FL image of the object  to that of the object in the reduced image I don't believe the reducer advantage will be anything like equivalent to a doubling of exposure time. I'm not persuaded that there will be any significant advantage but, here, it would be good to have some experimental data. I no longer have any system with focal reducer so I can't explore this at present.

Olly

[andrew s]

30 minutes ago, ollypenrice said:

Sure, but this is why I put in my caveat stating that the diagrams address only such targets as already fit on the image without reducer. The wider entrance pupil collects sky photons, not object photons, so these make no contribution to the object in the image. (If you want all the FOV brought in by the reducer then you reach an acceptable S/N ratio in accordance with the F ratio-exposure equation.) I think I cover this in a different diagram, which says what you are saying unless I'm mistaken.

Yes they will. Again I covered this, I think, 

The pixels in the reducer scenario will 'fill' faster. However, if you software bin or downsize the native FL image of the object  to that of the object in the reduced image I don't believe the reducer advantage will be anything like equivalent to a doubling of exposure time. I'm not persuaded that there will be any significant advantage but, here, it would be good to have some experimental data. I no longer have any system with focal reducer so I can't explore this at present.

Olly

Sorry I confused my point be adding the bit about the field of view changing - I was trying to avoid an objection. When you say the "The pixels in the reducer scenario will 'fill' faster" this is exactly a reduction in exposure. If you reduce the FL by one half you will also reduce the image scale by half so if you object covered exactly 4 pixels initially then in the reduced case it will cover 1 pixel and will fill 4 times as fast as predicted by the normal focal ratio formula.

I agree an experiment would be good. I will try in the next few days with a conventional zoom lens on a DSLR in manual with a fast F/ set to avoid vignetting.

Regards Andrew

[wimvb]

Where's a pudding when you need one? In lieu of a pudding, here are som pics.

Olly, in your original post the middle galaxy should be dimmer than the left one: larger aperture and smaller f-number (unless the exposure time was longer, of course)

As for the enclosed pics:

First setup: 24 mm, 50 mm and 135 mm lens at f/4

To quote Ansel Adams: "all lenses set at f/8 (or any other aperture) transmit the same intensity of light to the film." (The Camera, p 46)

Second setup: 24 mm and 135 mm lens at aperture = 6 mm (f/4 resp. f/22)

But what would happen with the first case, if we were to optically shrink the image from the 135 mm lens such that it would be as large as that from the 24 mm lens?

[ollypenrice]

1 hour ago, wimvb said:

 

To quote Ansel Adams: "all lenses set at f/8 (or any other aperture) transmit the same intensity of light to the film." (The Camera, p 46)

 

To be strict, F8 is not an aperture, it is a focal ratio. Daytime photographers take no notice of their real aperture, per se, and don't even know what it is unless they work it out. The camera doesn't give it to them because, for their purposes, F ratio is what contains all the useful information about exposure time and depth of field. This is why they use aperture to mean focal ratio when it isn't!  My argument is that we are different and that what interests us are object photons, not sky photons. Object photons are collected by 'real' aperture. How many pixels they land on is controlled by focal length.

You can find a lengthy exposition of this debate in the first chapter of Rob Gendler's Lessons from the Masters.

Olly

 

[andrew s]

1 hour ago, ollypenrice said:

To be strict, F8 is not an aperture, it is a focal ratio. Daytime photographers take no notice of their real aperture, per se, and don't even know what it is unless they work it out. The camera doesn't give it to them because, for their purposes, F ratio is what contains all the useful information about exposure time and depth of field. This is why they use aperture to mean focal ratio when it isn't!  My argument is that we are different and that what interests us are object photons, not sky photons. Object photons are collected by 'real' aperture. How many pixels they land on is controlled by focal length.

You can find a lengthy exposition of this debate in the first chapter of Rob Gendler's Lessons from the Masters.

Olly

 

Nonetheless, when imaging the same object, and assuming it is resolved by both systems for simplicity, then, the Hale telescope at F/3.3 exposed for 10secs will produce an image of the same surface density profile as a 1000mm fl telephoto lens set at F/3.3 exposed for 10secss its just one will be much larger than the other.

However, I agree that "Object photons are collected by 'real' aperture. How many pixels they land on is controlled by focal length" leading to the Object photons per pixel depending on focal ratio. It is just that in a normal photographic lens you can vary the real aperture and this is not normally done, or desirable, with an astronomical telescope. 

Regards Andrew.

 

[wimvb]

Rob Gendler's book added to my wish list; I have to read up on this.

[ollypenrice]

12 hours ago, andrew s said:

Nonetheless, when imaging the same object, and assuming it is resolved by both systems for simplicity, then, the Hale telescope at F/3.3 exposed for 10secs will produce an image of the same surface density profile as a 1000mm fl telephoto lens set at F/3.3 exposed for 10secss its just one will be much larger than the other.

However, I agree that "Object photons are collected by 'real' aperture. How many pixels they land on is controlled by focal length" leading to the Object photons per pixel depending on focal ratio. It is just that in a normal photographic lens you can vary the real aperture and this is not normally done, or desirable, with an astronomical telescope. 

Regards Andrew.

 

It will indeed and I have agreed with this from the outset. But when the Hale image of the object is reduced to the size of the image of the object produced by the 1000mm telephoto lens it will be a considerably better image.  This is at the heart of the F ratio myth debate. (To put it another way, the Hale collected more object photons than the lens. Where did they go? Their contribution does not vanish when the image size is reduced.)

On a practical note I often collect data from the TEC140/F7 to enhance key parts of widefield images taken at half that focal length in the Taks (106/F5). If I want the TEC image to be a standalone picture in its own right I need to capture a serious amount of data. If, however, I only want to use it to enhance part of a widefield then it's quite amazing how little data I need to collect in order to do so. Once downsized to the scale of the widefield a very noisy TEC image becomes a very clean one. I did this once with a Sagittarius Triplet image taken at 328mm. 'Serious' TEC data was added to the Trifid and Lagoon but clouds stopped play when it came to NGC 6559. I collected only a trivial dataset and could only make a dreadful image from it. However, downsized to fit the widefield it proved to be little different in effectiveness from the good sets for the other two objects. Here's the image.

It should click for full size.

Olly

 

[wimvb]

Thanks to that semi-legitimate effort that is Google Books, I've been able to read up on this.

Olly, thanks for bringing the breakdown of the F-rule to my attention. Also thanks for pointing me to Gendler's book. I believe Moore's writing also puts a sizeable nail into the coffin of modern small-chip CMOS cameras.

[ollypenrice]

2 hours ago, wimvb said:

Thanks to that semi-legitimate effort that is Google Books, I've been able to read up on this.

Olly, thanks for bringing the breakdown of the F-rule to my attention. Also thanks for pointing me to Gendler's book. I believe Moore's writing also puts a sizeable nail into the coffin of modern small-chip CMOS cameras.

So, Wim, are you persuaded that the F ratio rule does break down in the case of focal reducers?

Olly

[pete_l]

Yes, this illustrates concisely that when you opt for shorter FL (on DSOs) in order to get smaller exposure times, you are sacrificing image size - or "magnification" in layman's terms.

Small and bright and quick or large and slow. Your choice of DSO image.

[andrew s]

I think we are in heated agreement of the physics of the situation.  I just don't think there is a "F ratio myth" the equations are correct they work.

Regards Andrew

PS Having "googled" this it seems there is a lot of discussion about the F ratio myth but I am none the wiser on what it is actually is. 

Is it that all scopes with the same focal ratio produce identical images? If not what is it?

[andrew s]

2 hours ago, ollypenrice said:

It will indeed and I have agreed with this from the outset. But when the Hale image of the object is reduced to the size of the image of the object produced by the 1000mm telephoto lens it will be a considerably better image.

I agree it will have a better signal to noise ratio and all else being equal higher resolution (both proportional to aperture).

So the Myth is equal focal ratio produce equal quality images when viewed at the same scale? Which begs the question on what quality means but....

A mystified Andrew 

[ollypenrice]

19 minutes ago, andrew s said:

I think we are in heated agreement of the physics of the situation.  I just don't think there is a "F ratio myth" the equations are correct they work.

Regards Andrew

PS Having "googled" this it seems there is a lot of discussion about the F ratio myth but I am none the wiser on what it is actually is. 

Is it that all scopes with the same focal ratio produce identical images? If not what is it?

The 'F ratio myth' is encapsulated my right hand example at the top of the thread. The 'myth' (if there is one, and I believe there is) states that you will capture (in this case) M33 faster by using a focal reducer than without one. I believe this is a myth because the number of object photons will not be increased by using the reducer and there are other ways of putting them onto fewer display pixels at the end if you work at native FL.

Olly

[wimvb]

2 hours ago, ollypenrice said:

So, Wim, are you persuaded that the F ratio rule does break down in the case of focal reducers?

Olly

Absolutely. The F-rule is based on image brightness, whereas what we are dealing with in AP is object S/N. An increase in aperture allows a decrease in exposure time with no S/N loss, whereas a decrease in FL and subsequent decrease in exposure time will lead to a loss in S/N.

[ollypenrice]

Yes, I think the same.

Olly

[andrew s]

1 hour ago, wimvb said:

Absolutely. The F-rule is based on image brightness, whereas what we are dealing with in AP is object S/N. An increase in aperture allows a decrease in exposure time with no S/N loss, whereas a decrease in FL and subsequent decrease in exposure time will lead to a loss in S/N.

I agree. Somewhat perversely it shows why small quality refactors do so well at AP. Given that S/N ratio scales with aperture (i.e. square root of the number of photons) you need to double the aperture to double the S/N ratio. Normally it is more cost effective to quadruple the exposure time.

Regards Andrew

[ollypenrice]

...and then there are the practicalities of making ultra fast reflecting systems (since they have to be reflecting in order to be ultra fast.) You don't have to quadruple the exp time, though, if you go about it the right way...

lly