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Learning about aperture, and depth of field. I have understood it as such

Larger the aperture, the more shallow the depth of field,
while Smaller the aperture, the further the depth of field. 

But in astrophotography, you want to use large aperture. What I don't understand is, how are the stars in "focus" when we have such large of an aperture? My logic is, since stars are so far, you would need a small aperture.

I understand with Larger apertures, more light is able to get in, but what about the depth of field?

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    \$\begingroup\$ Focus is always at a set distance. No matter what aperture you use, some (configurable) distance will be in focus. That distance can be "infinity" (which is where stars are, for photographic purposes). You don't need deep depth-of-field for something just because it's far away; you just need to focus on it. A large aperture lets in more light in a dark environment. \$\endgroup\$
    – osullic
    Apr 16, 2023 at 22:14
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    \$\begingroup\$ Don't talk about "higher" or "lower" apertures. Call them "larger" and "smaller". It's clearer. \$\endgroup\$
    – osullic
    Apr 16, 2023 at 22:15

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The question...

What I don't understand is, how are the stars in "focus" when we have such large of an aperture?

confuses the difference between "aperture" and "focal ratio".

Aperture vs. Focal Ratio

The focal ratio is found by dividing the focal length of the lens (or telescope or other optical instrument) by the aperture of the objective lens.

A few examples... if I have a 100mm camera lens and the objective lens is 25mm wide (that's the entrance pupil) then that is an f/4 because 100 ÷ 25 = 4. The aperture is 25mm but the focal ratio is f/4.

An 8" Schmidt-Cassegrain Telescope (that's an optical design, not a specific brand/model) will usually be an f/10 telescope. That means an 8" scope would have a focal length of about 2000mm and an aperture of 200mm. And since 2000 ÷ 200 = 10, that's an f/10 instrument. The aperture is 200mm but the focal ratio is f/10.

Focal Ratios and Depth of Field

In typical photography ... where your subject is probably not very distant ... as you focus the lens you are adjusting the distance where focus is optimal. But it turns out you get a bit of wiggle room ... some range of distances will appear to be reasonably well focused even though they are not precisely at the optimal focus distance. This range of distances is referred to as the "depth of field".

For example, if I use a 50mm lens on a full-frame camera and I focus on a subject located 10 feet away f/4 ... then everything from roughly 9' away to 12' away will be acceptable focus. If we switch to a higher focal ratio ... say f/16 ... then the depth of field increases and everything from about 6' to nearly 30' will be in acceptable focus.

But astrophotography is different because the objects are so very far away that the instrument is focused to "infinity". The Moon is probably the closest object an astrophotographer might select as a subject and, in rough round numbers, it is about 240,000 miles away.

It turns out (and as Alan has pointed out in his answer), that once you've focused on one object at such a large distance then every object in the sky is also in focus.

Why do astronomers prefer larger aperture telescopes?

There is another aspect of photography that isn't related to depth-of-field ... and this has to do with resolving power.

There are limits on the ability to resolve details in an image and, it turns out, that limit is related to the aperture of the telescope's entrance pupil (I'd say "objective lens" but some telescopes use mirrors and don't have a lens.)

That discovery was credited to Will Rutter Dawes and is referred to as Dawes' Limit. https://en.wikipedia.org/wiki/Dawes%27_limit I should mention that the discovery is also credit to Lord Rayleigh and referred to as the Rayleigh criterion. https://en.wikipedia.org/wiki/Angular_resolution#The_Rayleigh_criterion

It is a relatively simple formula that says the finest detail you can resolve (in arcseconds) can be found by dividing 4.56 by the diameter of the aperture (in inches) or ... dividing 11.6 by the diameter (in centimeters).

Examples:

If I have a 4" telescope then 4.56 ÷ 4 = 1.14 arcseconds.
If I have a 12" telescope then 4.56 ÷ 12 = 0.38 arcseconds.

Suppose we would like to capture an image of Mars. Mars is currently about 1.6 AU from Earth (1 AU is the mean distance between Sun and Earth and is about 93,000,000 miles.) So that puts Mars at nearly 150 million miles away (at the time I am writing this).

At that distance, Mars has an angular diameter of just 5.8 arcseconds. This means that if we use a telescope with a smaller aperture, we wont see as much detail. But we can improve the amount of detail by using a larger telescope ... and the larger we go, the more detail we can resolve.

If we test the opposite direction... say we use a tiny telescope with a 1" aperture, Mars would appear as a completely featureless dot.

You can see how having a larger telescope means you can resolve finer amounts of detail.

Can you see one of the flags on the Moon?

You didn't ask this, but I'll add it because it really helps make the point. This is a common question that members of the public will ask when asking astronomers what can be seen when looking at the Moon.

NASA says they did not source a special flag for use on the Moon. It was made out of ordinary materials -- much like what you could buy going to a local hardware store (meaning these flags are likely all sun-bleached and UV damaged so horribly that they are likely in tatters if anything remains of them at all). The flag measured roughly 5' x 3'. When you run the trig and do the math ... that works out to roughly 0.002 arcseconds. That means if you had a telescope large enough to resolve 0.002 arcseconds, the flag would appear as just a single dot (you wouldn't see any details). The telescope would need a diameter of about 200 feet (about 60 meters).

To see detail (e.g. to make out the fact that the flag has "stripes") ... you'd need something that could resolve an order of magnitude finer -- or a telescope with an aperture of around 2000 feet.

This problem ignores issues such as distortions caused by the atmosphere (which limits and interferes with how much detail can be seen regardless of the optics). In reality if you wanted to see (what is left of) the flag on the Moon ... it would probably be easier to just fly to the Moon to get the photo rather than figure out how to build a telescope big enough and deal with the problems created by Earth's atmosphere.

But ... hopefully that explains why astronomers are always trying to get bigger telescopes.

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  • \$\begingroup\$ (And to some extent why astronomers want to put telescopes in space - or at the top of big mountains - so there's as little atmosphere as possible between the telescope and the big glowing things in the sky) \$\endgroup\$
    – Philip Kendall
    Apr 17, 2023 at 20:21
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Depth of field is that zone fore and aft of the distance focused upon that will be perceived as acceptable as to focus. The zone of depth of field can be contracted or expanded based on the aperture setting. No matter, if the subject had no depth (flat object) depth of field is moot.

Now objects that are at a far distance from the camera behave exactly like a flat object. In other words, the stars, moon, sun, and planets are distant objects. We say they are at an infinite distance (infinity). The light rays coming from objects at infinity arrive at the camera as parallel rays. This distance is about 3000 x the focal length of the camera lens or further. Once the camera is set to infinity focus, all object 3000 x the focal length and further will reproduce as “in-focus”. Further, all astronomical imaging is done with the camera set to infinity focus.

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Background blur is limited in size to a spot with the diameter of the entrance pupil (very rarely larger than 100mm) when placed in the focusing plane (if you try focusing accurately, light years for typical stars and rather sizable even for lunar photography). The relation for foreground blur is a bit larger, taking that entrance-pupil size spot in the focusing plane and moving it tp where you want to estimate the foreground blur. Since the size of astronomical objects is miniscule compared to their distance, this does not make a difference either way.

That 100mm spot will be indiscernably small at astronomical distances either way. Instead, the sharpness will be determined by lens aberrations and diffraction. Diffraction gets better at larger apertures, lens aberrations will typically have more of an effect at larger apertures, however. But light yield is also important, and longer exposures will give you motion blur, primarily due to Earth rotation. So all in all, with reasonably good lenses, your results will tend to be best for large apertures.

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