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Aperture, f-ratios, myths, etc.

Q: F-ratio myth - Myth, reality, or what? Does aperture always rule?

A lot has been written and discussed on the web about what f-ratio really means for us as astrophotographers. F-ratio is simply the ratio of the focal length to the size of the aperture. So, if you have a 200 mm telescope that has a focal length of 1000 mm, it is an f/5. This is true for your telescope and for your camera lens. Clearly, the f-ratio can be varied by changing either the aperture or the focal length. If we stick a focal reducer or a barlow on the scope, we’re changing the f-ratio of the system (Note: not of the objective itself, so sticking a barlow on your f/4 Newt to make it f/8 won’t make the coma of an f/4 go away!). Likewise, when the iris inside your camera lens cuts down the light (reduces the aperture) you’re changing the f-ratio.

If we keep the aperture constant and change the f-ratio by somehow scaling the focal length (reducing or extending it), we’re not changing the total number of photons hitting our detector from a given DSO. As Stan Moore and others have pointed out on pages like the one dedicated to the “f-ratio Myth”, it is the aperture alone that determines how many photons we gather from a DSO. If you imagine your scope to be a bucket, catching photons streaming across space, it should be obvious that the bigger a bucket you have, the more photons you get. Period. No ifs, ands, or buts as it were.

I feel Stan does a good job on his page explaining how film differs from CCDs and where the noise comes from. But, in seeing how this is often depicted in online discussions, I feel one key caveat he makes is often lost. Note that at the end of his page, he says that, “There is an actual relationship between S/N and f-ratio, but it is not the simple characterization of the ‘f-ratio myth’.” What is missed by many when they conclude that “f-ratio doesn’t matter” is that this is true ONLY when you are well above the read noise.

Running at a larger f-ratio for a given aperture means that you are spreading the light over more pixels. Thus, each pixel is getting less light and so the signal hitting that pixel is less. Some aspects of the noise (e.g., read noise) will be constant (not scale with the intensity of the signal the way shot noise does). Thus as the signal gets very faint, it gets closer and closer to the read noise. When we hit the read noise, the signal is lost. Doubling the focal length (one f-stop) will have 25% as much light hitting the CCD well, meaning we will be that much closer to the read noise. If the exposure length is long enough such that the edges of our galaxy or nebula are still well above this noise, it matters little if at all. But, if we are pushing this and just barely above the noise (or if our camera has a good bit of noise), this will more rapidly come into play.

Please note, that none of what I am saying here contradicts Stan’s message. He makes this same point and if you look closely at the images on his site, the lower f-ratio shot does appear to have less noise. As noted, it’s not “10x better”, but it’s not the same either.

Here, I’ve taken some data from Mark Keitel’s site. Mark was kind enough to post FITS files of M1 taken through an FRC 300 at f/7.8 and f/5.9. I ran a DDP on the data and used Photoshop to match black and white points and to crop the two frames. Click on the thumbnail for a bigger view and/or just look at the crop.

Here is a crop around the red and yellow circled areas. In each of these, the left image is the one at f/7.8 and the right at f/5.9 (as you might guess from the difference in scale. Now, look carefully at the circled areas. You can see there is more detail recorded at the lower f-ratio. We can see the noise here in the image and that these bits are closer to the noise floor. Again, the point is that it’s incorrect to say that the f-ratio rules all and that a 1” scope at f/5 is equal to a 100” scope at f/5, but it’s also wrong to say that under real-world conditions, it’s entirely irrelevant.

Q: Does aperture always rule?
The most often quoted phrase in our community is that aperture rules and it’s true. It’s true that if all else is equal, bigger scopes will do better. It’s also false to say that big scopes are bad on planets or bad in the city and that smaller is better under these circumstances.

However, there are times when we don’t fully realize what’s not equal. This point was made clearly to me recently when I went out to do some testing on a camera and brought along an 8” f/5 Antares Newtonian (with Paracorr) and a 4” f/4 Borg 101 ED APO. I aimed, among other things, at the Horsehead Nebula and thought I had a good handle on what the images would show me. I thought, as most of you probably would, that the 8” Newt (1000 mm focal length) would spank the 4” APO (400 mm focal length). After all, the Newt gathers 4x as many photons as the APO. I went in thinking less about the caveat to the f-ratio myth than I should have though, and given this, the results were quite surprising.

These are taken right after each other and are both 5 minute frames, with no application of any post-processing other than simple stretching (data from QSI 540). You can click on the image for a 100% version of the shot here.

I don’t know about you, but I’m seeing more detail in the 4” scope than in the 8” scope. The bit of emission nebula by the horse’s mane is one area you can pick this out. Whether you think the 4” is better than the 8” here might be debated (I don’t think so, but some might) but what we can certainly say is that the 4” wasn’t put to shame in this comparison. Despite giving up “4x the number of photons”, it is doing very well.


Is it some “APO magic”? Hardly. The answer, IMHO, comes down to two factors:

1) Much of the signal we’re pulling out here is close to the noise floor and, by having a lower f-ratio (and shorter focal length), the 4” APO is getting more photons onto the CCD wells as a result, getting us into the “caveat” range of the f-ratio myth.

2) There is more light loss in the Newt than we might expect.

Let’s put some quick and dirty numbers onto these images and pretend we’re imaging a flat field (e.g., the emission nebula around the Horesehead). What do we have here? Well, if the aperture were the same and we’re running one at 1000 mm and one at 400 mm of focal length, we can figure the difference in photon number hitting the well by (1000 / 400) ^ 2. This is a factor of 6.25. So, if we took a 1000 mm scope and reduced the focal length to 400 mm, each CCD well would be hit with 6.25x as much light. Again, this won’t matter a lot for brighter areas, but when you’re right near the noise, this will certainly come into play.

The aperture isn’t the same, of course, and the 4” scope is collecting 25% as many photons as the 8” scope, owing to the difference in aperture. So, if we’re counting the number of photons from a diffuse source hitting the CCD, that 6.25 factor goes down to 1.56x. But, that is still in favor of the 4” APO. Note, if this were a 3” APO, the light loss due to aperture would be down to 14% of the 8” scope, which would put the photon count hitting each well at a factor of 0.88, now tipped to the Newt’s favor.

All this is still pretty close and I don’t think enough to account for the images. Here’s something we’ve not considered yet, however. The Newt uses two Al-coated mirrors and several lenses in the Paracorr. The APO here is a doublet with several more lenses in its reducer / corrector. If we suppose that the two correctors loose similar amounts of light, we’re left with two mirrors vs. a doublet. That doublet is passing on the order of 97% of the light, but each surface of the Newt is only passing about 86% of the light. With two mirrors, we’re down to about 76% of the light. We’re also not at an effective 8” of aperture in terms of photon gathering owing to the central obstruction (about 2.5” here). The central obstruction alone puts us down to a 7.6” scope and if we factor in the mirrors’ light loss it’s down to a 6.6” scope. So, rather than an 8” vs. 4” scope with a 4x total photon boost for the 8”, it’s more like a 6.6” scope which is only a 2.75x total photon boost.

Now, if the total photon boost is only 2.75x instead of 4x (aka, the light throughput on the 4” scope is 36% of the bigger scope instead of 25%), we can update the numbers from above. Ignoring the aperture (keeping it constant), the focal length had 6.25x as many photons hitting the CCD well and getting us above the noise. With perfect optics, the light cut was 1.56x (6.25 * 0.25), but it’s now at 2.27x with more real-world numbers. That means that each pixel recording the nebula is getting 2.27x as many photons hitting it when the 4” scope is attached as when the 8” scope is attached.

Math, math, math... does this really happen? My camera’s bias signal is about 209 in this area. I measured the mean intensity in a 10x10 region using Nebulosity’s Pixel Info tool for three areas right around and in the Horsehead. On the Borg, they measured 425, 302, and 400. On the Newt, they measured 287, 254, and 278. Now, if we pull out the 209 for the bias signal we have 216, 93, and 191 vs. 78, 45, and 69. If we calculate the ratios, we have 2.76x, 2.07x, and 2.77x. Average these and we’re at 2.5x.

The back-of-envelope math said I should have 2.27x as much light hitting each CCD well with the 4” scope all things considered and the practical measurement came up with 2.5x. In my book, that’s close enough for jazz and a clear verification of the basic idea. Aperture did not win here. When all else is equal, it wins, but all else is not always equal. To my eye, the image with the 4” looks better and we find that despite seeming to be a bit light in the photon department when all one considers is aperture, it’s actually pulling in more photons onto each CCD well. While it has fewer photons on the whole target still (36% of the 8” scope’s amount), per CCD well it’s doing better. If aperture were all that mattered and that focal length didn’t matter at all, the 8” would have soundly trounced the 4”.

Must this be the case? Will a 4” APO always beat out an 8” Newt? Hardly. If we run them both at the same focal length, the APO won’t have a chance. Only 36% of the photons are now spread out to the same image scale and so each CCD well has only 36% as many photons hitting it. The Newt will clearly win here. Now, keep in mind, that if aperture were all that mattered, the 4” would have handily lost the competition above. It didn’t. Put them on par on image scale and it will.

This last bit is really the key for people to understand. What aperture buys you are more photons. You can trade these photons off in various ways. If you keep the image scale the same, your SNR will go up relative to a scope with a smaller aperture. If you like, you can trade things off here and buy magnification (aka resolution) for that aperture and keep the same SNR. By varying the focal length (and therefore image scale and f-ratio) we control this trade-off.

And yes, it is true, that once we’re well above the read noise, the effects I’ve mentioned here become weaker. But, a lot of the things we amateurs try to do aren’t always well above the read noise. I know I’m often plumbing the depths to see just what I can pull out. Just as we shouldn’t look only at the f-ratio when making our decisions and think that we can shoot for a quarter as long given a 2-stop difference (e.g., f/8 to f/4) we shouldn’t entirely ignore this. In addition to easing guide constraints and getting a wider FOV, running that f/10 SCT at f/6.3 or so will let you get above that read noise faster.