Gerchberg–Saxton algorithm: Difference between revisions

Revision as of 21:44, 23 May 2006

Revision as of 13:40, 24 May 2006

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It is often necessary to know only the phase distribution from one of the planes, since the phase distribution on the other plane can be obtained by performing a Fourier transform on the plane whose phase is known.

( Although often used for two dimensional signals the GS algorithm is also valid for 1-d signals).

The Pseudo-code below performs the GS algorithm to obtain a phase distribution for the plane, Source, such that its Fourier transform would have the amplitude distrribution of the plane, Target.

===Pseudo-code algorithm===

Let:

Target and Source be the Target and Source Amplitude planes respectively

A, B, C & D be complex planes with the same dimension as Target and Source

Amplitude - Amplitde extracting function: eg. for complex z = x + iy, Amplitude(z) = x*x + y*y

Phase - Phase extracting function: eg. Phase(z) = arctan(y/x)

FT - Forward Fourier Transform

IFT - Inverse Fourier Transform

end of Let:

Gercberg Saxton Algorithm(Source, Tareget)

A = IFT(Target)

while error criterion is not satified

B = Amplitude(Source) * exp(Phase(A))

C = FT(B)

D = Amplitude(Target) * exp(Phase(C))

A = IFT(D)

end while

Retrieved Phase = Phase(A)

end of Gerchberg Saxton Algorithm

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