Background: There is a method in optics for determining the electric field of light (both intensity and phase) via a three step process:
- Add a known phase shift to the light (called the "diversity phase").
- Perform a Fourier transform (via a lens) and measure the intensity.
- Repeat this for several different diversity phases (at least two), and use certain algorithms to infer the light field.
The inference process is typically done numerically. However, I've found an analytical method for solving the problem, but it only works in 1D (whereas optics is 2D). This has me wondering: Are there situations in signal processing where one would like to identify e.g. a time-domain signal from only it's power spectrum? If so, do there already exist good algorithms or analytic solutions for this problem?
I am a physicist by training, so I have little background in signal processing, but I would appreciate any references or context that seasoned signal analysts can provide.