Optical distortions and focus losses calculation

Question

I'm working with a megapixel camera and lens that needs to be focused for an OCR application. In order to measure the focus quality during the set-up, I've built a tool that gives the contrast value between two pixels. In very simply words, more the contrast is high more the focus is good... Due to optical distortions, the focus value in the sides of my field of view, is not the same as in the center. My question is how could I calculate the distortion between center and sides, in %. For examples fcenter = 62 ; fleftside = 42. Is that correct to say Leftdistortion = 1-(42/62)*100 ??

Thanks,

Raphael

Answer 1

You cannot figure that via pure math. It 100% depend of specific lens design you have - you could have 0 difference, you could have sphere-like focal plane, you could have anything.

So your best bet is to measure focal plane differences across the frame, and interpolate.

Answer 2

If you don't know the specifications of your objective you can't calculate this. I describe a method you could try to measure the optical transfer function.

Print out gratings 10 (or so) gratings with different periods. Capture images of these gratings. Make sure that the central part of the camera is as sharp as possible for the finest grating and make sure that the gratings are oriented in the same way.

If your lens has an aperture try opening it as far as possible. This decreases your depth of field and allows you to find the focus more precisely. Conversely for your application of capturing OCR images you should close the aperture as far as possible (use a bright lamp) this improves the point spread function of the system.

If your lens doesn't have an aperture you can try to build one with black paper and a hole punch.

For a raytracer you have to evaluate this equation on every surface: $${\bf t}=\eta{\bf i}-\left(\eta{\bf i n}+\sqrt{1-\eta^2(1-({\bf i n})^2)}\right){\bf n}$$ with $\eta=n_1/n_2$, $n_1$ the index on the left (downstream) side of the surface, ${\bf n}$ the normal of the surface at the intersection with the ray.

Its possible to write a write a ray surface intersector for conic surfaces as a 10 line function that you can use among the other things for plane and spherical surfaces.

Another thing you might need to look into is the Sellmeier coefficients of the glasses in your system.

You can find the image position by tracing rays from the object into the image plane and look where beams starting from one point intersect. In a good system the focus spot will be smaller.

You can also draw a Gaussian sphere around each image point and sum up the optical distances along the ray. That way you'll obtain the wave aberrations.