I have a 5 mm (diameter) solid ball lens that I intend to place in front of a 36mm X 24mm camera sensor (I have already made preparations for the image to be focused and for the sensor to not be flooded with light). I want to calculate the resulting horizontal and vertical field of view from the ball lens when I take a picture.

Please see the link for a diagram of the setup if the image does not work.


I have already calculated the back focal length of the ball lens to be 1.479 mm.

  • $\begingroup$ I didn't do the calculations so I don't know the answer, but if the sensor is at the effective focus of the ball lens, you can't even define an object space FOV, you really only can give an object space NA. Are you imaging something a finite distance away (not objects at $\infty$)? $\endgroup$ – daaxix Aug 12 '14 at 5:28

A ball lens will introduce spherical aberration to your image. Spherical abberation enlarges the focus point to a small focus area.

Spherical abberation enlarges the focus point to a small focus area. The sharp part of the focus point is refracted by the center of the ball lens. The outer rays will introduce more an more spherical aberration an blur your image. Find the optimal compromise between sharpness an image brightness.

Adressing your field of view (FOV) in terms of photography is easy: $$\text{FOV} = 2\cdot \arctan\left(\frac{\vec x_{sensor}}{2\cdot f}\right)$$ $$ = 2\cdot \arctan\left(\frac{ \begin{bmatrix}36 mm \\24 mm\end{bmatrix} }{2\cdot 1.479 mm}\right)$$ $$ = \begin{bmatrix}171 mm \\165 mm\end{bmatrix} $$ Your field of view will be smaller, if you redefine it to be a spharp image. To adress this problem you will have to look up the pitch and width of the individual pixels of your sensor. Than calculate the size of the focus region and compare it to the size of the Airy disc of your focus.

  • $\begingroup$ Wouldn't a bigger problem be that the focal plane is curved? $\endgroup$ – Dr Chuck Jul 11 '14 at 11:57
  • $\begingroup$ Yes, this is an additional problem. $\endgroup$ – Stefan Bischof Jul 15 '14 at 9:24

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