Diffraction and holography from a signal processing perspective

The fact that plane waves are solutions of the Helmholtz equation in free space allows us to write the exact solution to the diffraction problem as a superposition of plane waves. The solution of other related problems can also be expressed in similar forms. These forms are very well suited for directly importing various signal processing tools to diffraction related problems. Another signal processing-diffraction link is the application of novel sampling theorems and procedures in signal processing to diffraction for the purpose of more convenient and efficient discrete representation and the use of associated computational algorithms. Another noteworthy link between optics and signal processing is the fractional Fourier transform. Revisiting diffraction from a modern signal processing perspectiv is likely to yield both interesting viewpoints and improved techniques.