telescope speed ... F4.0 vs F5.6 ..twice as fast for double the price ?

Having spent a long time researching this, there's a lot of bad information out there based on how camera lenses work.  You can't blindly apply the same logic as a camera lens because adjusting the f stop means adjusting aperture.  The focal length of the lens is unchanged, and the native focal ratio is unchanged, therefore the field of view is unchanged.  Telescopes do not work this way unless you're using an aperture mask.  

Focal ratio is a bad means of comparison between scopes, so don't use it.  In fact, there's not really any one parameter that's a useful means of comparison.  You have to think about it as a system, including your camera and any focal reducer you might use.  The best means of comparison I've come up with is aperture per pixel.

First and foremost, aperture wins.  More aperture means finer details.  More aperture means more light enters the scope, meaning more light can reach the sensor.  Focal reducers factor into this by shrinking the image circle to fit smaller sensors or sacrificing resolution and expanding the FOV for larger sensors.  Using the FRA500 as an example, natively it has a 55mm image circle, comfortably illuminating a full frame sensor.  With the 0.7x reducer, mathematically the image circle shrinks to 38.5mm (55*0.7).  Based on the spot diagrams, the scope still accommodates a full frame sensor, though there may be some vignetting, or the native illuminated circle is wider than 55mm (wider than the corrected image circle) to avoid this.  Assuming a constant pixel size, the 0.7x reducer increases the amount of light hitting each pixel by 1.43x, meaning you would be able to image considerably faster with the reducer.  The cost is a loss of resolution, the logical tradeoff of a larger FOV.  More importantly, the reducer can't change the physics of the scope its attached to.  The FRA500 still has a 90mm aperture and is f/5.6.  When considering a reducer in a comparison, I find it more useful to divide the sensor diagonal by the reduction factor (effective sensor size) instead of changing focal length. 

An interesting thought experiment along these lines is considering the ZWO ASI2400MC Pro (Full Frame) and ASI2600MC Pro (APS-C).  If you put the ASI2600MC Pro behind a 0.65x reducer, it has a similar FOV and resolution as the ASI2400MC Pro on the same scope natively.  Therefore, despite the significantly faster effective focal ratio of the scope with the 0.65x reducer, both cameras will capture roughly the same image in the same amount of time.

Ultimately, it's a question of what are you hoping to image.  If it fits in the FOV, there's no point in going faster because you're already capturing all the light it's emitting.  Telescopius and the Field of View Calculator are your friends.  Beyond that, I recommend that you buy the largest scope you are willing to deal with that meets your requirements.

If you match the sensor to the telescope for equal sampling in object space, the only thing a reducer does for you is to increase the field of view.  If you hold the pixel size constant (as you do in a standard camera), increasing the optical speed (by decreasing the focal ratio) increases the signal by the square of the ratio of the focal ratios.  Here's a formula that I posted a number of years on CN that explains it (F1 and F2 are the focal ratios of the two telescopes).  I believe that this is what the Compare-Telescopes site is computing.




John

John Hayes:
If you match the sensor to the telescope for equal sampling in object space, the only thing a reducer does for you is to increase the field of view.  If you hold the pixel size constant (as you do in a standard camera), increasing the optical speed (by decreasing the focal ratio) increases the signal by the square of the ratio of the focal ratios.  Here's a formula that I posted a number of years on CN that explains it (F1 and F2 are the focal ratios of the two telescopes).  I believe that this is what the Compare-Telescopes site is computing.




John

Yes, the Compare-Telescopes site does a similar thing. Going off an old thread where you used your equation, I plugged in those same variables to the Compare-Telescopes site and it spat out the same solutions.


To the other folks posting in this thread, its important to understand what aperture helps you with in long exposure, deep space astrophotography. More aperture means a longer focal length at a respectable focal ratio, which allows you to use cameras with bigger pixels while still maintaining a good image resolution. If you used the same camera on a small telescope at F/4 and a much larger telescope at F/8, the F/4 telescope wins in building signal but not in resolution. However, if your telescope is big enough, you can beat the F/4 telescope both in building signal AND resolution if you use larger pixels in your camera.

Just saying "go and buy the biggest telescope you can afford" is not super helpful advice in my opinion. There are a lot of factors at play, some of which cannot be helped by a huge mirror or lens.

We are in the signal-to-noise ratio business here, and one of the more useful calculators that I have found for comparing systems is this website: https://lambermont.dyndns.org/astro/code/compare-telescopes.html



With the same camera, 124 seconds on the slower system is about 62.7 seconds on the faster system.

Interesting tool. I’m a little confused by “object signal.”  What’s the difference between this and etendue?

Filter economics may also be a consideration.  The faster f/ratio will result in a steeper light cone & shifting of the band pass, whether the result of native focal length or a focal reducer.  That may mean purchase of f3 shifted narrow band filters.  The steeper light cone may also make a larger filter diameter desirable to reduce vignetting.

[pre]
 [/pre]Telescope 1 f/ 3.90 fl= 350mm D= 90mm O= 0% res=2.24"/p FOV=37.3'x37.3'=34.31x eoi= 6.57x poi= 1.26x e= 6.57x pe= 6.57x ps= 6.57x os= 0.19x #

Telescope 2 f/10.00 fl=2050mm D=205mm O= 0% res=0.38"/p FOV= 6.4'x 6.4'= 0.03x eoi= 0.15x poi= 0.79x e= 0.15x pe= 0.15x ps= 0.15x os= 5.22x
and for example, a c8 at native f10 images an object 5x as fast as a 350mm f4

Pixel signal will always favor a wider fov. I don’t think it’s a metric that can be used to compare two different fov’s. it’s the same as comparing focal ratio and ignoring aperture.

We are in the signal-to-noise ratio business here, and one of the more useful calculators that I have found for comparing systems is this website: https://lambermont.dyndns.org/astro/code/compare-telescopes.html



With the same camera, 124 seconds on the slower system is about 62.7 seconds on the faster system.

Interesting tool. I’m a little confused by “object signal.”  What’s the difference between this and etendue?

From the website:
"Object Signal is based on the Etendue of an extended object that fits in the FOV of both scopes, corrected for the sensor Quantum Efficiency and total optical system Transmittance losses."

Formula: object_signal = aperture_area [m^2] * QE-factor * Transmittance_factor

So it makes sense that the bigger telescope would win in this case.

I think I'm still confused.  Isn't this just comparing FOV?  A given object will generally fit in the FOV of two systems of comparable focal lengths.  Exceptions would be for very large objects, but this doesn't really seem to have anything to do with exposure.  The faster, smaller aperture system just captures the target faster because the slower, larger aperture system would need multiple nights mosaicing to get the full field. 

In the below comparison, I've put in the values for my Rokinon 135 lens and Takahashi Epsilon 130D.  The Epsilon blows the lens out of the water in "object signal."  For the others the Rokinon is generally ahead.  This leads me to think I'm much worse off going after most extended objects with the Rokinon than with the Epsilon, despite the Rokinon being f/2.  The Rokinon is really just for those huge objects that I don't want to sit around mosaicing.  Am I missing something?

We are in the signal-to-noise ratio business here, and one of the more useful calculators that I have found for comparing systems is this website: https://lambermont.dyndns.org/astro/code/compare-telescopes.html



With the same camera, 124 seconds on the slower system is about 62.7 seconds on the faster system.

thanks @SemiPro for the advice and details...
while this thread was evolving, in another place I found a simplified formula, similar with what was put above by @John Hayes : (F2*F2) / (F1*F1).
how did you compute the 62.7s for the faster scope ? .. maybe I interpret the numbers wrongly, but I get 60.7s

I must admit, I understood maybe less than half of what has been discussed in this tread. topic is more complex than I originally thought

to give a better idea of why I'm looking at the speed:
I'm going to image in light polluted city with Bortle 9 skies.. and without an opportunity to drive to the country side to better skies. Singapore is a small country/city.
even so .. I will still need to drive out to a park or area where I'm not blocked by city building.. but I'll still be with a lot of light pollution.
because of the light pollution, I will need significant more imaging time to get decent imaging. this I've learned and got my inspiration after reading Lee Pullen blog on https://urbanastrophotography.com/. 
I will need to be mobile and make the most of my nights out sessions with the constraints of the place I'm in.

in a nutshell:
- a faster setup/system that will reduce the imaging time, is appealing. .. and why I started to study the topic.
- setup/system can not be big either.. so it's easy to transport and setUp.
- price is also a constraint,.. as budget is NOT unlimited.

400-500mm focal length is more than enough for a portable setUp.

I'm still unsure what "object signal" means but the other indicators make sense.

A simple way I look at this is the following.

The light entering your scope does not know (or care) what size pixels, sensor etc. you have. In object space, meaning for a given square arc second of object in the sky, the SNR is therefore determined purely by aperture and integration time (ignoring things like light pollution). Games we play, like the use of reducers, pixel size of cameras, size of sensors, etc., simple serve to change how that light is concentrated or the field of view actually captured

If you take two systems, of different f ratios but which both capture the FOV of interest, the system with the larger aperture will always provide the better SNR regardless of focal ratio when the images are presented at the same viewing scale. The most important question to ask is "will what I want to image fit in the FOV of X system"? Within this constraint, a larger aperture will always give you the better result.

Arun H:

I'm still unsure what "object signal" means but the other indicators make sense.

A simple way I look at this is the following.

The light entering your scope does not know (or care) what size pixels, sensor etc. you have. In object space, meaning for a given square arc second of object in the sky, the SNR is therefore determined purely by aperture and integration time (ignoring things like light pollution). Games we play, like the use of reducers, pixel size of cameras, size of sensors, etc., simple serve to change how that light is concentrated or the field of view actually captured

If you take two systems, of different f ratios but which both capture the FOV of interest, the system with the larger aperture will always provide the better SNR regardless of focal ratio when the images are presented at the same viewing scale. The most important question to ask is "will what I want to image fit in the FOV of X system"? Within this constraint, a larger aperture will always give you the better result.

This makes sense.  So perhaps it should say "fill the FOV" rather than "fit in the FOV."  But where does "signal" come in?  Say I'm going to a dark site and want to capture a given object in one night and I don't care much about the amount of detail in it.  For argument's sake, let's also say I don't care about the FOV.  Do I take the instrument with the lower f-ratio?  Or is "signal" just referring to the amount of detail in the image and not the amount of time it takes for the object itself to show up in the image?