Adaptive-additive algorithm
In the studies of
The algorithm
History
The adaptive-additive algorithm was originally created to reconstruct the
Algorithm
- Define input amplitude and random phase
- Forward Fourier Transform
- Separate 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
- Separate new amplitude and new phase
- Combine new phase with original input amplitude
- Loop back to Forward Fourier Transform
Example
For the problem of reconstructing the spatial frequency phase (k-space) for a desired intensity in the image plane (x-space). Assume the amplitude and the starting phase of the wave in k-space is and respectively. Fourier transform the wave in k-space to x space.
Then compare the transformed intensity with the desired intensity , where
Check against the convergence requirements. If the requirements are not met then mix the transformed amplitude with desired amplitude .
where a is mixing ratio and
- .
Note that a is a percentage, defined on the interval 0 ≤ a ≤ 1.
Combine mixed amplitude with the x-space phase and
Separate and and combine with . Increase loop by one and repeat.
Limits
- If then the AA algorithm becomes the Gerchberg–Saxton algorithm.
- If then .
See also
References
- Dufresne, Eric; Grier, David G; Spalding (December 2000), "Computer-Generated Holographic Optical Tweezer Arrays", Review of Scientific Instruments, 72 (3): 1810, S2CID 14064547.
- Grier, David G (October 10, 2000), Adaptive-Additive Algorithm.
- Röbel, Axel (2006), "Adaptive Additive Modeling With Continuous Parameter Trajectories", IEEE Transactions on Audio, Speech, and Language Processing, 14 (4): 1440–1453, S2CID 73476.
- Röbel, Axel, Adaptive-Additive Synthesis of Sound, ICMC 1999, CiteSeerX 10.1.1.27.7602)
{{citation}}
: CS1 maint: location (link - Soifer, V. Kotlyar; Doskolovich, L. (1997), Iterative Methods for Diffractive Optical Elements Computation, Bristol, PA: Taylor & Francis, ISBN 978-0-7484-0634-0
External links
- David Grier's Lab Presentation on optical tweezers and fabrication of AA algorithm.
- Adaptive Additive Synthesis for Non Stationary Sound Dr. Axel Röbel.
- Hill Labs University of Maryland College Park.]