Adaptive-additive algorithm
The Adaptive-Additive Algorithm (or AA algorithm) is an iterative numerical technique that utilizes the Fast Fourier Transform to find the phase of a propagating wave in the input plane, given the amplitudes of the input and output planes. The algorithm was first created to the reconstruct the phase of light intensity in the spatial frequency plane. Implimentations of the algorithm can be found in Fourier optics, sound synthesis, stellar interferometry, and optical tweezers.
A variation of the AA algorithm is the Gerchberg–Saxton algorithm.
Pseudo-code algorithm
- Define input amplitude and random phase
- Forward Fourier Transform
- Seperate transformed amplitude and phase
- Compare transformed amplitude/intensity to desired output amplitude/intensity
- Check convergence conditions
- Mix transformed amplitude with desired output amplitude and combine with transformed phase
- Inverse Fourier Transform
- Seperate new amplitude and new phase
- Combine new phase with orginal input amplitude
- Loop back to Forward Fourier Transform
References
- Dufresne, Eric; Grier, David G; and Spalding. “Computer-Generated Holographic Optical Tweezer Arrays.” Review of Scientific Instruments, vol 72-3, December 2000.
- Grier, David G. Adaptive-Additive Algorithm. October 10, 2000. [1].
- Robel, Axel. Adaptive Additive Modeling With Continuous Parameter Trajectories [2].
- Robel, Axel. Adaptive-Additive Synthesis of Sound. Technical University of Berlin Germany, Einsteinufer 17, 10587 Berlin, Germany. [3]
- Soifer, V. Kotlyar, and L. Doskolovich, Iterative Methods for Diffractive Optical Elements Computation (Taylor & Francis, Bristol, PA, 1997).