Computer-Generated Holography (CGH)

Joel E. Tohline
tohline@physics.lsu.edu

According to my derivation in class, the amplitude A_tot that is produced at any point "y₁" along the image screen is

What we have found empirically (by experimentation) is that the 1-D FFT from Numerical Recipes creates a 1-D array of "N" A_tot values as given by equation (1), but for each element "i" within the output array,

where w^* = N - w.

With this information in hand, we can now understand what physical location on the image screen y₁ should be identified with each array element "i" in the output file of the 1-D FFT routine. Specifically,