Abstract

In a Fourier transform system, an object f(x) is interrelated to its Fourier spectrum F(u) by Fourier transform. Our goal is to recover the phase factor of the object from the measured intensity data. By means of the discrete Fourier transform, assuming the sampling number is N, it is shown that the intensity at one point in the Fourier plane directly connects with both the phase term and the amplitude term of N points in the object plane. Because of the large number N, the relationship as usual is somewhat complex. To simplify it, we may allow fewer sampling points into the system. A particularly successful approach to solving this problem is to let only two neighboring points, n and n+ 1, pass the system. Therefore, the corresponding formula tells us that, if three intensity measurements at three points in the Fourier plane are taken, the phase difference of the object between the two sampling points will then be mastered. Letting n change from 1 to N — 1, we now can reconstruct the phase distribution of the object function.

© 1989 Optical Society of America