How does aFresnellens work

The triangles (large and small) are similar, that is angles are the same. So Angle of view will be the same as top angle (at the lens) of the smaller triangle. From that, since you know what sensor size and angle of view is, you can calculate focal length in pixels, as @remco calculated for you.

In fact, units of the sensor size should be exactly the same as units of the focal length to make sense of F=A/tan(a). What you can get from that is, if you have bigger pixels (in cm), you will need larger focal length (in cm) for same field of view and number of pixels.

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It's basic geometry: you have a right angle triangle, with half the FOV as one of the angles (a), and half your image size as the opposite side (A). To calculate the focal length F, use tan(a) = A/F, which gives F = A/tan(a).

FresnelLens Sheet

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As your sensor size is given in pixels (assumed square pixels!), your focal length will also be in pixels. To get it in a more usual unit (m), you need to know the pixel size.

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It is what Hermann said, focal length is NOT measured in pixels. I strongly doubt the engineering journal said focal length was pixels.

What you need to know for field of view is the camera sensor size (or film size) measured in mm. You must compute with sensor dimensions in mm.

What are fresnel lensescalled

The article specifies that the horizontal FOV is 47°, so we have to use A = 640/2 = 320, a = 47°/2 = 23.5°, which give F = 736 pixels.

There is a calculator that will do this at https://www.scantips.com/lights/fieldofview.html (Option 6). The geometry is shown at bottom of that page, however, you must use Trig for angles.