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Arcsec/pix

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#1 hherzy

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Posted 14 October 2021 - 01:22 AM

I think i have a clear understanding of how to calculate angular resolution in arcsec/pix.

 

 

I have attached an image of my calculation for my T3i camera and AT72ED refractor. 

pixel size - 4.29 microns, FL = 430mm

 

What I dont undertsand is that the final output is simply arcsec. The units seem to cancel out that way. Given that the solid angle is a measure of angular size, shouldn't the units be squared? arcsec^2?

 

I want to ultimately solve for the entire area in arc-sec^2 visible in my camera's FOV. Should I simply square my calculation for arc-sec/pix and then apply it over the 18,000,000 pixels? Im not sure if im missing something. My math could be completely wrong. If anyone has any knowledge about this, please chime in - im at a sort of a crossroads.

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#2 Aleksandr Naumov

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Posted 14 October 2021 - 01:55 AM

The formula above calculates the square per pixel, not sure why. Dimensions marked are wrong.

 

The angular size of a pixel is equal to

2 * arctg(pixel_size / focal_length),

where pixel_size and focal_length are expressed in same units.

Result will be expressed in radians (as usually arctg function does) and, if you need arcseconds, multiply that with 206265 (number of arcseconds per radian).



#3 hherzy

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Posted 14 October 2021 - 02:26 AM

I factored in the unit conversion between microns and millimeters for the focal length and pixel size. Thats why the solid angle equation factor is 206.265 instead of 206265. I divided by 1000 to account for the dimmensions. I still dont understand why it is in arcsec rather than arcsec^2, however.

 

Here is the equation I was going off of:

 

Screenshot.png

 



#4 james7ca

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Posted 14 October 2021 - 02:47 AM

The reason why the units don't match in your final equation is that you are multiplying your arc seconds per pixel by a pixel count (18 million) which will be the number of arc seconds (NOT squared) in a single row of 18 million pixels. So, the units are correct but you haven't calculated what you really want (the number of square arc seconds on the sensor).

 

So, you need to calculate the width and height of the sensor in arc seconds and then multiple those two number to get arc seconds squared. So, if a sensor was 6k x 4k in pixel size (24,000,000 pixels) and it had a pixel scale of 4.235 arc seconds per pixel you'd do the following calculation:

 

(6k pixels x 4.235 arc seconds per pixel) x (4k pixels x 4.235 arc seconds per pixel) ≈ 430.4 million arc seconds squared (the correct units)


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#5 Alex McConahay

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Posted 14 October 2021 - 08:30 AM

Interesting, and I should not butt in.....but, if I am told that my pixels are 9 microns (for example), and my sensor is 3000x4000 pixels, does it necessarily follow that the overall sensor is 27000 x 36000 microns? I mean, does the edge of one pixel end where the edge of the next begins, or is there some kind of spacing between them?

 

Alex



#6 bobharmony

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Posted 14 October 2021 - 08:50 AM

Interesting, and I should not butt in.....but, if I am told that my pixels are 9 microns (for example), and my sensor is 3000x4000 pixels, does it necessarily follow that the overall sensor is 27000 x 36000 microns? I mean, does the edge of one pixel end where the edge of the next begins, or is there some kind of spacing between them?

 

Alex

I think you have this just right, Alex.  The quantity to put into the formula is the pixel pitch, not the pixel diameter.  As an example my Nikon D5300 has a pixel diameter of 3.87 microns and the pixel pitch is 3.92 microns.  The pitch value will give the area of the sensor when doing calculations which is about 2.6% larger than what using the pixel diameter would calculate out to.

 

Bob


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#7 kathyastro

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Posted 14 October 2021 - 08:58 AM

When you say that your sensor has 18,000,000 pixels, you have removed the concept of area.  Expressing it as a raw number has collapsed the two dimensions to one.

 

To keep it as an area, which is what you are looking for, it is 5184 pixels x 3456 pixels = 17,915,904 pixels^2.  So the units on your 18,000,000 should be pixels squared, not pixels.

 

You can multiply linear arcseconds per pixel by linear pixel counts, as James did (post #4), or you can square the image scale and multiply 17.935 square arcseconds per square pixel by the 17.916 square pixels.  (Note that the ~17.9 in both terms is just a coincidence.)


Edited by kathyastro, 14 October 2021 - 09:07 AM.

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#8 hherzy

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Posted 15 October 2021 - 09:48 PM

Thank you I understand now. I was multiplying over number of pixels rather than pixel area. Im working on fixing the equation now. Thanks for the clarification!




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