Averaging integration doesn't...uh, average

[Stonius]

Take 4 dark frames.

12 bit mean values as follows;

51.47
51.47
51.47
51.46

Average them and you get 51.4675, right?

But, if you take those frames and integrate them using averaging, no noise evaluation, no weighting and no pixel rejection, you get;

Average 51.4682 (and Median gives you 51.4353).

Which is 0.007 higher than a straight up mathematical averaging.

I wonder what's going on?

Is the 'statistics' proccess limited in it's reporting, or is something funky happening during integration?

Anyone know?

Cheers

Markus

[dld]

I assume that you have set Weights = 1 and No normalization since you're integrating darks. Do you use Pixel Rejection? If most of your darks have cold pixels, these will pull some of your dark means at a lower value. After Pixel Rejection, with these cold pixels removed, your master dark mean may be higher, and with only four darks the difference may be noticeable.

[Niall Saunders]

Hi Markus,

I was also wondering if you were seeing a 'rounding error' - after all, those original four values are based on the 'average' ADU of all the pixels on an image-by-image basis.

However, plain ImageIntegration returns the 'average' ADU value of the four pixel values at every location in the image. Only then do you look at the statistics, and expect that the two processes should reurn the same values for you.

Further, you are inspecting the ADU data using rational numbers - it might be interesting to see what the values look like if you view the data as 16-bit integers. For example, how much of a change in value do you actually get when viewing as integers? Is this change still enough to give you concern?

Bear in mind that your observed error is only of the order of 0.001%, or just under 1 ADU count in 65,535 (the full range of a 16-bit, unsigned, integer). So, should you really be concerned?

Hope this helps.

[Geoff]

You cannot expect to get 3 decimal point accuracy from what are presumably rounded two decimal point numbers. The 51.47 means that the true figure is somewhere between 51.465 and 51.475.

[Stonius]

I'm looking into the noise characteristics of my camera.

Some of those measurements differ by quite small amounts.

I guess I'm after the most accurate data I can get, but in terms of practical day-to-day use it doesn't matter too much, no.

So if I read this right, the integration will be more accurate (and to more decimal places) than the statistics panel?

Cheers

Markus

[Niall Saunders]

Hi Markus,

the integration will be more accurate (and to more decimal places) than the statistics panel?

No, I don't think that I would want to make that statement. The information from the Statistics panel is for the single image that you happen to have selected - that's all. It will five you the average ADU value for all the pixels in the image, added together and divided by the number of pixels that were counted.

Just keep in mind that (plain, i.e. 'sverage') ImageIntegration considers each pixrl site on its own, and averages the ADU data for the number of images in the ImageIntegration data set - and builds a new image based on these average values. Of course, you can then examine this new image using the process described in the preceding paragraph.

So, neither process gives a more 'accurate' result - they just give differing results due to the method used to obtain the answer.

Personally, neither of these two tests are processes that I ever need to be interested in. I just want to integrate a suitably large number of images, and would be relying on ImageIntegration to perform far more than simple averaging - so the whole question has little or no 'validity' for normal pre-processing.

[Stonius]

Thanks Niel, that makes sense. IOW, my manual process was averaging entire frames first, whereas integration averages each pixel location first, hence the difference.

Cheers Mate