How many dark frames?

[dld]

In references like the university course Modern Observational Techniques or the Lowell Observatory Exposure Time Calculator (at the bottom of the page there is a short documentation as a PDF file) some of the noise terms are weighted by an aperture term. In this discussion, every noise term has the same weight, implying a single-pixel aperture. If this happens here for simplification reasons, I have to express my worries:

What is the purpose of dithering? Besides better outlier rejection, it tries to "break the correlation" of noise sources which have spatial correlations. These noise sources live in the spatial domain and have a typical correlation length l. Such a length term (or an estimate of it) must be present somewhere in the formulas. Remember, in practice we have good dithering if we pick a random direction angle and a random length d with d>l.

In other words, with dithering we benefit from randomization in the spatial domain because we live in the imperfect world of Bayer matrices and confined between the bars of CCD columns. A single-pixel approach forgets about any such spatial correlations. Somewhere a term with units of length should be present, and (in my opinion) even if we don't account for dithering.

I'll end my math/theoretical mumble with the notes of another course. Lecture 5 may be of interest! My experimentalist part of self agrees with Charles, it takes less time doing it than think about it

[dld]

Remember, in practice we have good dithering if we pick a random direction angle and a random length d with d>l.

Light pollution contribution to sky glow has such a large correlation length and that's why it is difficult to get rid of it with dithering. This also means it is smooth enough ("predictable" within our field of view) and we can use this observation for our benefit. With many light frames we can use an interpolation method and build a good DBE map to subtract from our data and make do even under light-polluted skies.

[STEVE333]

Always entertaining watching math guys spend more time debating a concept than actually just taking care of the issue. You can take 50, 180 second, darks in 2.5 hours + download time. I shoot three exposure times, 1800 secs, 600 secs, and 300 secs. I put my camera in a dark room in my house for a little less than two days and banged out 50 darks each plus about 100 bias. No one have two cloudy days to do that?

My wife had a good laugh when I read your response!

You'll be glad to know that I captured three days of darks (all at 540 secs) while debating this concept.  Having a Physics background is a curse. There is just something about "knowing" how something works. The pleasure when it's done is kind of like how good it feels when you quit hitting yourself in the head.

Steve

[STEVE333]

In references like the university course Modern Observational Techniques or the Lowell Observatory Exposure Time Calculator (at the bottom of the page there is a short documentation as a PDF file) some of the noise terms are weighted by an aperture term. In this discussion, every noise term has the same weight, implying a single-pixel aperture. If this happens here for simplification reasons, I have to express my worries:

What is the purpose of dithering? Besides better outlier rejection, it tries to "break the correlation" of noise sources which have spatial correlations. These noise sources live in the spatial domain and have a typical correlation length l. Such a length term (or an estimate of it) must be present somewhere in the formulas. Remember, in practice we have good dithering if we pick a random direction angle and a random length d with d>l.

In other words, with dithering we benefit from randomization in the spatial domain because we live in the imperfect world of Bayer matrices and confined between the bars of CCD columns. A single-pixel approach forgets about any such spatial correlations. Somewhere a term with units of length should be present, and (in my opinion) even if we don't account for dithering.

I'll end my math/theoretical mumble with the notes of another course. Lecture 5 may be of interest! My experimentalist part of self agrees with Charles, it takes less time doing it than think about it

Hi did -

1)

• I looked at the articles you referenced (thanks for sharing those). All of those articles are related to the specific task of measuring the brightness of a single star. I believe you will find that the "aperture" they refer to is related to the size of the star image they are trying to measure. The "aperture" (actually a software aperture to eliminate signal outside of the star) is only used to determine how many pixels will be summed up to yield the brightness of the star. Thus the noise they are interested in is the noise of the summed pixels, not the noise in one pixel.
• In other words, they have the same noise analysis we were discussing, but, they add the mathematics to determine how many pixels they will have to sum to accurately measure the star brightness, and, determine the noise when those pixels are summed.
• I don't believe this "aperture" is relevant to my analysis of the noise in each individual pixel.

2) I'm not aware of any spatial coherence of the noise. As far as I am aware, the noise in each pixel is independent of the noise in any other pixel no matter how close or far apart the pixels are. I've never seen any "spatial coherence" term included in any of the other noise analyses. However, if I'm wrong I would be interested in learning about such a phenomenon.

Thanks for taking the time to respond.

Steve

[dld]

Hello Steve, and thank you for the reply,

For (2) consider the bias frames of a DSLR. If we blink (with PI) some bias frames we will notice an underlying fixed pattern and (at least for my Canon cameras) horizontal bands which significantly differ from frame to frame. This is correlated noise, meaning that while random, it has structure, with a large correlation length across the horizontal direction. That's the reason we see horizontal bands: while random, in each instance (realization) it is more likely to see similar values across the horizontal axis than the vertical axis.

For (1) I will have to think about it 

I'll be glad to hear what others think about the subject (preferably with references)! Thanks again!