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Old 11-08-2012, 08:22 PM
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RickS (Rick)
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Originally Posted by theodog View Post
Hi All,

My question concerns the effective f.number for the APS-C chips. I know that the effective focal length of a lens will change (usually by 1.5 or 6). So a 10mm on full (35mm) frame is effectively 15mm on a APS-C, but how does this effect the f ratio? And is there a simple way of calculating this?

In astro imaging we don't tend to think in terms of effective focal length. What we care about is field of view and image scale.

FOV (in minutes of arc) is approximately equal to (3439 x d)/F where "d" is the width or height of the sensor and F is the focal length. Both d and F should be in the same units, e.g. millimetres.

There isn't a standard APS-C sensor size which is why the crop factor varies. It is 1.52x for Nikon, 1.6 for Canon, etc. Let's take the Nikon APS-C sensor size which is 23.6 x 15.8mm. If we plug that into the calculation above and assume we have a 530mm focal length (like my FSQ-106ED scope) then we get a FOV of approximately 153x102 arc mins.

If we do the same calculation for a full frame sensor of 36x24mm then we get a FOV of approximately 234x156 arc mins. You'll notice that the FOV varies by the crop factor of 1.52 from the FOV for the APS-C sensor, so maybe this is still a useful idea.

So, FOV tells you how large a piece of the sky is going to be captured by your sensor on a scope with a specific focal length. Image scale tells you about the resolution of the image you might capture.

The angular size of a pixel in arc seconds is approximately (206265 x p)/F where p is the size of a pixel and F is the focal length. Once again, both must be in the same units, e.g. mm.

If have 9 micron pixels (0.009mm) then this calculation gives us an image scale of approximately 3.5 arc seconds/pixel for a 530mm focal length scope. That's the size of the little piece of the sky captured by each individual pixel.

If you're not excited by doing these calculations yourself, here's a Windows application that will do them for you:
It also has samples of some well known astronomical objects and can show you what they look like with different scope and sensor combinations.

You also asked what effect sensor size has on f ratio and the answer is that it has no effect at all. The f ratio depends only on the aperture and focal length of the scope. It is not related to the sensor size.

Hope that helps...

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