Effect of aperture and focal ratio on brightness

[rogerg]

Hi all,

Considering the move from 12" to 16", and possibly a fast one (f/3.8).

As aperture increases, we collect more light.

As focal ratio decreases (f/8 to f/3.8) exposures can be shorter for the same image brightness.

But is the change uniform for all objects looked at through a telescope? Eg:
- is a star (single point at infinity) brightness increased the same as the image of a distant galaxy?
- is background light pollution brightness increased the same as the brightness of a star (single point at infinity)?

My logic says all are increased equally as the telescope knows no difference between objects, but I have been caught out by this before in discussions on IIS I think? Where people say point sources operate differently to dispersed light sources?

Thanks,
Roger.

[Wavytone]

Roger,

The real reason people choose fast aperture reflectors is simply size, and the issues associated with the mounting. A short scope is lighter, far more transportable, and more easily mounted.

For visual use you don't use the objective alone, there is also an eyepiece. What matters is the working magnification and the size of the exit pupil, which should be smaller than the entry pupil of your eye. That's the theory.

There are other issues:

- achieving high magnification with a short objective (f/4 or less) implies very short eyepieces that are less than satisfactory; a long focal ratio objective (f/15) coupled with a larger eyepiece will produce far better images.

- achieving very low magnifications with a long focal ratio objective (say f/15) implies using eyepieces that will give an exit pupil too large for your eye.

The optimum turns out to be f/7 where you can achieve a 10:1 range between lowest and highest magnification and still have an exit pupil less around 6mm at low power. But f/7 'scopes aren't small and pose real problems if you want an equatorial mount.

For astrophotography, the focal length and focal ratio are important in different respects:

- the limiting magnitude (faintest stars) that can be recorded is determined by focal length, not aperture or focal ratio;

- increasing the focal length makes the background sky darker, along with extended objects (nebulae etc) whereas the apparent brightness of point sources (stars) remain the same.

- for a given aperture, a shorter focal ratio means a shorter exposure time, brighter nebulae. it also means a brighter background sky, so the longest possible exposure is also limited.

[Satchmo]

Hi Roger

Generally light increases by the ratio of surface areas, or vary simply by the square of the ratio of aperture size. An 8" scope then shows objects 4 times brighter than a 4" . The ratio of sky background brightness to object indeed stays the same - those are properties of the sky not the telescope. The situation with CCD detectors is somewhat more complex and involves pixel size and readout noise .

The f ratio of the telescope is completely irrelevant to the discussion on brightness of objects between different telescopes . Only the aperture and exit pupil used are relevant.

Perceived brightness of point sources may not be as consistent as large apertures will often have their light spread out into a larger disc by the seeing and therefore not show as intense a point source as they are capable of.

If you spread the light of star into a disc twice the size then it becomes somewhat fainter - the star image is usually some kind of Gaussian curve so its not that simple , but its been obvious to me many times that smaller high quality optics can reach a similar magnitude limit visually as poor quality larger ones, although the smaller scope may not have the same ability on extended objects.

[Satchmo]

Nick - Put that old Patrick Moore book back on the shelf , now ! :)

[rogerg]

Thanks for your input, but I realise there's plenty of other factors and reasons which I'm well versed with, I'm keen to keep this conversation to the question at hand :thumbsup:

[Wavytone]

I guess the real issue is whether this concerns visual, or astrophotography ? You didn't indicate...

[rogerg]

Thanks, yes this is what I would expect but I'm pretty sure if I remember my previous discussions here (which I can't find) about such things others might popup and say differently ... :shrug:



Hmm, I'm not knowledgable on exit pupil stuff, but wouldn't the size of the exit pupil change based on focal ratio?



... their light spreads out according to focal length, I would expect, which is related to focal ratio. So while in principal I understand what you're saying aren't you really also saying the light would be spread into a larger disk by a larger aperture only because larger apertures tend to have longer focal lengths?



Agree.

[rogerg]

100% astrophotography. You're right, this is critical to the consideration, worth clarifying.

[Wavytone]

Then what matters is focal length (limiting magnitude) and focal ratio (time to image extended objects).

Focal length matters if image scale is an issue (e.g. trying to resolve planets or close binaries). For "pretty pics" it's irrelevant.

Exit pupil is irrelevant.

[Terry B]

I don't agree with the statement that limiting magnidude of stars is determined by focal length. If this was the case then a tiny refractor with a long focal length would show just as dim stars as a big light bucket of the same focal length. This is not true. The larger aperture collects more light and for point sources like stars it is the light collection that is important and this is determined by the aperture of the scope.

[Wavytone]

Only because taking it to that extreme, you have spread the star over a large area - so its now an extended object, not a point. My initial response was based on stars remaining essentially point sources - as should be the case for most "imagers" (horrible word). If you increase focal length so that the Airy disk is 3 pixels or more this is no longer the case, and they become extended objects.

The photographic limiting magnitude of a local focal length, small aperture refractor IS indeed the same as the limiting magnitude of a wide aperture light bucket having the same focal length. The limitation however is the exposure time to reach it - which may be horrendously impractical for amateurs using low-cost portable gear.

This is the case even for large professional scopes - there are many examples where large scopes are used at high magnification with imaging sessions running for tens or hundreds of hours in order to reach faint objects at very deep magnitudes.

This is exactly how the Hubble was used to take the "deep field" shots, where the exposures ran for 42.7 hours at each wavelength, using high magnification (and high focal ratio). The wide-field camera working at low focal ratio cannot reach those magnitudes.

[Terry B]

Sorry but that is silly. You are saying that the limiting magnitude is the same for 2 scopes of equal focal length but different aperture as you just take a longer exposure for the smaller scope. Hence the limiting magnitude is infinite for any scope as long as you can take an infinitely long exposure.
You have to be realistic and use a standard length exposure to compare scopes.

[rmuhlack]

This is a very pertinent discussion for me as well, as I have been thinking through these same sorts of ideas.



Question is what do you regard as a "standard" exposure length? If FL determines limiting magnitude, the isn't this where f ratio, QE and image scale now start to come into the equation, if the intention is to compare different setups?

:)

[Terry B]

It doesn't really matter what you define as a "standard"
FL does not determine limiting magnitude.
If you use the example of a scope being used visually then our eyes can only integrate for a short time. This will be constant enough to compare the limiting magnitude for different scopes. The only way to increase the star limiting magnitude visually is to increase the diameter of the scope. Increasing the focal length has no action apart from slightly increasing the size of the airy disc as the optics become less perfect.
f ratio is mostly only important for extended objects not stars.
QE is obviously important to capturing the light more efficiently.
There is a practical limit to how deep a mag can be achieved. It has to do with the number of photons arriving from an object. If 1 photon arrives/m2/min for a very dim object then it is going to take an eternity with any size scope to measure this and get above the background noise. This may seem extreme but for some of the X-ray and gamma ray detections from the respective satelite observatories, only a very few photons are needed to constitute a +ve measurement. The nutrino detectors measured 5 nutrinos for the 1987e SN http://www.sciencedirect.com/science/article/pii/0370269388916516
Optical scopes have more background noise making it more difficult.

[Geoff45]

In regard to imaging, the pixel size of your camera matters. If I have an 10" f10 scope and camera combination imaging at 2" per pixel and then go to a 10" f5 and a new camera with half the pixel size, then I will still be imaging at 2" per pixel, so we get the same number of photons hitting each pixel well for both setups, and there will be no difference in speed between the two combos. (As long as the QE of both cameras is the same, which is unlikely, so this throws in another complication.)
Geoff

[gregbradley]

It all boils down to aperture. CCDs are linear in response meaning it will record at the same rate after 2 minutes as after 10 seconds until the wells are full. Your statement as you decrease F ratio you image with less time. No. You image with less time with larger aperture for the same focal length. Large aperture, short focal length images faster than same aperture and long focal length. Why? As I understand it is merely because when you narrow the field of view there is less light available to collect.

Faster F ratio means a wider field of view and thus more light to collect from the night sky.

I think exit pupil here in imaging should be changed to corrected field. That is the size of the circle of light that is corrected for coma and aberrations. That varies from design to design. That limits how wide a view that scope can image and what size sensor you can use. If you use a small sensor then you have the same situation as if you cropped a terrestial image and discarded the rest. A larger sensor simply gives a larger image with more light collected.

Hence in camera world, APSc sensors collect less light than full frame sensors. Same with telescopes.

So no you can't get say a 2 inch telescope at F1.8 and it will be way brighter than a 10 inch telescope at F8. It will simply be super wider field
but no brighter than the 10 inch. The 10 inch will be brighter because it collects more energy. Scopes merely collect energy not create it so larger aperture is always brighter than smaller.

Longer focal lengths are more susceptible to seeing than shorter focal lengths.

So if you live in an area where the seeing is poor then a longer focal length will not serve you well on most nights.

16 inch at F3.8 is 1546mm focal length and that is medium length focal length and I think in the sweet spot for most Australian imagers given seeing, local cloud, sensors available, difficulty of tracking.

16 inch F3.8 would be good. I use my CDK17 at F4.45 at tims (with its reducer) and that works very to focus more of the collected light onto the sensor giving a lesser imaging time. It works well and makes it less susceptible to seeing conditions.

Greg.

[Shiraz]

That took a lot of thinking about Roger. Many good answers already and here is another try. apologies for such a large post - but here goes.

Optics comments

The aperture of a scope is a fundamental parameter, since it determines the number of photons collected from the external scene. Whatever happens after the aperture cannot increase the number of photons.

The focal length determines how big the physical image is. If the FL is long, the image will be large and the photons will be spread out, so the brightness will be low (where brightness is the number of photons passing through a fixed area of the image) - if the FL is short, the image will be small and bright. FL can be readily varied (eg with a Barlow or FR), so it is not a fundamental measure.

You don’t really need to use focal ratio, although it is useful for comparing optical systems. It is not a fundamental parameter.

If you have a good mount, the long integration resolution will be determined almost exclusively by the seeing blur due to atmospheric turbulence (except for very small apertures and discounting lucky imaging). Halfway decent optics above about 100mm aperture will have better resolution than the atmosphere in most Australian conditions - where the seeing limits you to a resolution of typically 1.5-2 arc sec FWHM at best. Even the 3.9m AAT will have about the same long integration resolution as the average on-axis Skywatcher 8 inch Newt under 2 arcsec seeing – the AAT will take a picture in a flash, but the image detail will not be better.

Extended objects in a physical image will not vary in brightness if the seeing-limited resolution changes, but the level of detail will change. However, star images get larger and dimmer as their energy is spread out by bad seeing.

Sampling

This is where it all happens in CCD imaging. What ends up in the digital image is determined primarily by how you sample the physical image when you place a CCD in the focal plane - and that is a function of the angular pixel size relative to the angular resolution of the atmosphere/optics (the sampling).

There are four basic approaches to choosing the angular pixel size:
1. Undersample. If the pixels are larger than the FWHM of the star blobs then dim stars fit within a single pixel – they are rarely lined up exactly on a pixel centre, so they put photons into ~4 pixels. Thus, most stars end up about the same size, but with varying brightness – only the brighter ones extend beyond ~4 pixels. Detail is lost in extended objects because small features in the physical image fit within a single pixel and are averaged out.
The two big advantages of undersampling are high sensitivity and wide field of view. For example, in 2 arc sec seeing, an undersampled system at 4 arcsec per pixel will have ~16 times the signal per pixel (4x the SNR) of a system that samples at the Nyquist optimum of ~1 arc sec per pixel (all else being equal). It will have 16 times the field of view as well. This sort of system is used by many who post on IIS and is ideal for imaging large faint nebulae, but it is not suitable for resolving the finest detail in galaxies or planetaries. Undersampling is the wide-field realm of the FSQ106/NP101 guys with 9 micron chips. Their huge images look very sharp because the available detail is determined entirely by the CCD pixel size and neither the scope resolution nor typical atmospheric seeing has much effect on apparent sharpness.
Example: 500mm fl system with 9 micron pixels.

2. Nyquist optimum. When you have 2-3 pixels across each FWHM of the image, you are able to record all of the detail present in the physical image and you get the best possible signal to noise ratio for that maximum detail. This is the optimum sampling for galaxy or planetary nebula imaging. In typical/good 2 arc sec seeing, this will require a little less than 1arcsec/pixel sampling.
Images taken in this realm have the most detail possible, but can often look less sharp than undersampled images because the finest detail, although present, has low contrast due to the rolloff of the atmospheric MTF at high spatial frequencies. Resolution is entirely determined by the atmospheric seeing and that can vary a lot. Stars will vary in size - determined by seeing PSF rather than CCD pixel size.
Sensitivity is much lower than for undersampled systems.
Examples: 2m fl system with 9 micron pixels or 1m fl system with 4.5micron pixels in 2 arcsec seeing.

3. Oversample. If the angular size of your pixels is much smaller than the Nyquist optimum, you will have decreased signal in each pixel, but no more detail in the image – you are looking with a fine grid for detail that has already been blurred out. There is no advantage in oversampling, except that such a system will be great on that night of exceptionally good seeing, where it can operate nearer Nyquist.
Eg, in 2 arcsec seeing, a system that has 0.5 arc sec resolution will have 1/4 the signal levels (1/2 the SNR) of a near-Nyquist sampled one (at 1 arcsec/pixel), but it will not record any additional information. The field of view will be small, stars will look bloated and the best processing strategy would be software binning to restore some of the SNR lost in the extra read noise. Images will look less sharp under almost all conditions, since even fine detail looks fatter when spread out over more pixels.
Example: 2m fl system with 4.5 micron pixels in 2 arcsec seeing.

4. Compromise. Many successful imagers operate in the no man’s land between about 1 and 2 arc sec per pixel, where they get better sensitivity than Nyquist, wider field of view, but still don’t lose too much detail in good seeing. Stars and extended object detail will look nice and tight with moderate undersampling, so aesthetics will be OK in average seeing. If you are more interested in aesthetics than in ultimate resolution and want images that look pleasingly sharp most of the time, this looks like a good approach.

In summary, for a given aperture, sampling determines how sensitive your system will be, how well it resolves detail, what your field of view will be and what your image aesthetics will be like.