[Aavso-photometry] Cosmic Rays

[Michael Newberry]

Well OK, Ben. But I think you are making too much out of too little. And I
won't say you are wrong. How about E-mailing me 3 such dark frames and
letting me look at them?

Sorry Ben, but you have unearthed the true professor in me and I can't
resist explaining further. I think you need to think more in terms of
probability. Hope you don't mind...  ;^)

It is *well established* that the human brain's pattern recognition system
can detect features at the 1 to 2 sigma level by using the visual memory
system to connect information from one image to the next. This principle was
realized in electronic form during the early '80's as "leaky memory"---Arne
will remember such devices. Using a blinking or animating strategy, one can
indeed pull out low level features that cannot be seen in one image. I agree
with you because I have seen it over and over. But not at the level you
claim.

HOWEVER, looking at isloated points that may appear bright from one image to
the next is unconvincing because of probability arguments. Starting again
with a random draw from the population of pixel values, there is a 16%
chance that a pixel has a value at or brighter than 1-sigma above the mean.
I described how the 1-sigma level in one of your dark frames is not going to
be 6e-. In fact, I would guess it is *AT LEAST* 12e- at the very minimum. So
you are talking about a pixel value being 0.5 sigma's above the mean. If the
noise in one 30 minute dark is really more like 20e-, then you are talking
about 0.3 sigma's above the mean. The probability of a pixel being 0.5 or
0.3 sigma's above the mean is 0.31 or 0.38. Let's assume as usual that any 3
pixels are uncorrelated (that is, one pixel value doesn't influence another
one's value). THis means that the joint probability of 3 of them do
something is the product of the probability of one of them doing it. So the
probability of having 3 pixels be 0.5 or 0.3 sigma's above the mean is
0.31^3 or 0.38^3, which is 0.03 or 0.055. Now, is that the same pixel in 3
consecutive images or 3 pixels in a line in one of the images? The answer is
that it does not matter which 3 pixels we are talking about. They are
uncorrelated and so the probabilities are independent of each other. Let me
say this another way: Any pixel has a 31% chance of being >= +0.5 sigma's or
38% chance of being >= +0.3 sigma's. To get the probability for n such
occurences, you just raise either value to the n-th power. If you invert
these probabilities, then you can get an idea of how many "trials' you need
to perform in order to get a single case in which it happens. The answers
are 33 trials and 18 trials, respectively, for pixel value >= 0.5 sigma's
and pixel value >= 0.3 sigma's. THis means that about 1 out of every 33
trials should have a case in which the same pixel is more than 0.5 sigma's
above the mean, or in a line if you want to talk about lines. A trial can be
interpreted as a rectangular area of pixels. So you don;t need a very large
rectangle to start seeing such low level alignments.

Getting 3 pixels "hot" at the 0.3 to 0.5 sigma level is rather easy, purely
from random chance. I still am not convinced that seeing a chain of 3 pixels
at the 6e- level above the mean is giving you cosmic rays.

Michael Newberry


----- Original Message ----- 
From: "Ben Davies" <ben at davies.net>
To: <aavso-photometry at mira.aavso.org>
Sent: Saturday, January 28, 2006 10:09 AM
Subject: Re: [Aavso-photometry] Cosmic Rays


> Michael,
>
> You are thinking too much.  Did you make the dark frames and look at the
> cosmic ray hits?
>
> As I said previously, I ignore single pixel anomalies.  If you actually
> look at the image you see that cosmic ray hits are very distinctive.  They
> cover many adjacent pixels, fading from brighter to very faint.  In
> addition they are almost never scalars . You should instead be calculating
> the probability of that sort of structure occurring in a stochastic field.
>
> What we are looking for are patterns and the human brain is very, very
> good at picking them out.  In a more limited, but also more precise way,
> software can be designed to do this also.
>
> That was a very good exposition on sources of ccd noise.  Thanks for the
> summary.
>
> Ben
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