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I'm going to work with a camera, a Photron AX100, which has a non-standard 20.48x20.48 mm sensor, but has an f-mount bayonet for lenses.

I was wondering if it would work with DX lenses without vignetting, because if I did the math right, the Nikon DX sensor has a diagonal of √(24^2+16^2)=28.84 while this sensor's would be √2*20.48=28.96.

Now, I couldn't find figures about the actual diameter of the circle created by average DX lenses, or the minimum diameter guaranteed. If the image circle is very tight it won't fit, but if it's not, well, I can live with a little vignetting but I'd prefer not having the visible edge on the corners.

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    Many DX lenses vignette on DX sensors. I think what you are wondering is about is a hard silhouette. – Michael C May 21 '16 at 16:19
  • That I understand, but having to use the camera for work I'd avoid having the corners totally black – clabacchio May 21 '16 at 17:13
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The only guarantee is that a DX lens will throw an image circle approximately large enough to cover a DX sensor. Some throw them a bit larger, but the only way you'll know if a given lens does that or not will be to try it.

Carrying your math a bit further, the DX diagonal is 0.12mm smaller than that of the AX100. The pixels on that sensor have a diagonal of 0.0283mm, which means a worst-case, very sharp cutoff in the image circle would leave you a 3x3 block of pixels in each corner that show full or partial vignetting.

At 1024x1024, the AX100 isn't going to be challenging the resolving power of anything you screw onto the front. A lot of older, full-frame lenses that would get the job done would be available to you for not much money.

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Most objectives (I have yet to see a counter-example) do not have hard fall-off at the edges because optics make it very rare case - to draw a sharp edge on the sensor an objective should have some inner part of it to be in a specific place. Every objective which you will try will draw a smooth circle on the sensor and you will only have a chance of dark corners if you already see the part of that circle in edges (unless there is a rectangle hood on the rear lens). 0,12 mm is smaller than difference between different APS-C sensors and is not going to hurt you at all.

I can only recall some Sony E objective which has very severe vignetting.

By the way: if you use recent DX objectives on non-Nikon cameras you will need to hold the aperture lever back to have opened aperture.

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