Question

An aperture in the object plane of a Fourier Transform system is a rectangle.

a) Design a filter for the Fourier plane that passes just the horizontal edges. Sketch what it would look like and explain your reasoning. Indicate which parts are transmitting and which parts are opaque.

b) If your filter had good fidelity, could the result in the image plane, in principle, anyway, be used to measure the dimensions of the rectangle?

c) Could one determine, from the image plane, whether the initial aperture was an opaque rectangle on a clear background or a clear rectangle on an opaque background?

Answer 1

(c) It is solved using the concept of Babinet's principle. If the intensity in the fourier plane varies in the form of square of sinc funcion, then the object is aclear rectangle on an opaque background. If there is a central bright spot and next bright spot is sufficiently large distance, then the object is a opaque rectangle on a clear background.

The explanation is that the summation of fourier transfor pattern from both the cases will have to be uniform.