# Formula for blurring out a grid of holes

Place a camera lens with focal length f_l mm and camera sensor size w mm and h mm behind an rectangular array of small holes with diameter d0 mm being d1 mm apart at a distance d mm between the holes and the outer curvature of the lens.

How do you have to change d for the small holes to blur for them to disappear on the photo?

I am asking for a formula. Basically a d = f(f_l,d,d0,d1) respectively d = f(f_l,d,d0,d1,w,h).

From f and the distance between the lens and the detector, you can calculate the distance to where things will be sharply focused onto the detector. Things a little in front or behind that place will be a little out of focus, perhaps so little that you can't tell the difference. The depth of the region where things are acceptably in focus is called depth of field.

You want the thing you are photographing to be in the center of that region, and the holes to be as far from it as possible.

You can make the depth of field small by using a wide aperture. This is also called a small f-stop.

You can also move the camera so the lens is right up against the holes, making them maximally out of focus. This works best with a large diameter lens, like in old cameras. The tiny lens on a phone might be between holes and not see anything.

• I am asking for a formula.
– Alex
Commented Aug 4, 2019 at 7:16
• Melles Griot is a manufacturer of lenses. They publish a very good introduction to optics and optical design. This is a good reference to get you started. google.com/… Commented Aug 4, 2019 at 8:23
• This is a special application, they are describing fundamental approaches.
– Alex
Commented Aug 4, 2019 at 8:27