Consider a pinhole camera shown in the below figure. Assume that the object is incoherent and nearly monochromatic, the distance \(R\), from the object is so large that it can be treated as infinite, and the pinhole is circular with diameter \(2 d\).

(a) Under the assumption that the pinhole is large enough to allow a purely geometrical optics estimation of the point-spread function, find the optical transfer function of this camera. If we define the "cutoff frequency" of the camera to be the frequency where the first zero of the OTF occurs, what is the cutoff frequency under the above geometrical-optics approximation? (Hint: First find the intensity point-spread function, then Fourier transform it. Remember the second approximation above.)

(b) Again calculate the cutoff frequency, but this time assuming that the pinhole is so small that Fraunhofer diffraction by the pinhole governs the shape of the point-spread function.

(c) Considering the two expressions for the cutoff frequency that you have found, can you estimate the "optimum" size of the pinhole in terms of the various parameters of the system? Optimum in this case means the size that produces the highest possible cutoff frequency.

Transcribed Image Text:

Object Zo Pinhole Z Film