Understanding the Gerchberg-Saxton Algorithm through Convex Optimization

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In summary, the Gerchberg–Saxton algorithm is a computational method used to find the phase of a wave produced in the diffraction plane when the dimensions of the object are unknown. It works by iteratively improving the phase calculation to get a closer result, and more information can be found in the paper linked above.
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Please help me understand the Gerchberg–Saxton algorithm

what I comprehended so far

1) A source is shone on an object and produces a diffraction pattern in the diffraction plane. We do not know the dimensions of the object.

2) We are unable to calculate the phase of the of the wave, due to the "phase problem"

Now we want to computationally find the phase of the wave that is produced in the diffraction plane


I do not understand how the Gerchberg–Saxton algorithm works. i.e. how we improve to get a closer phase through the iterative method

Thanks
 
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If you have checked Wikipedia and your doubts are still not clear, trying reading this paper available freely at ResearchGate:

https://www.researchgate.net/publication/11281090_Phase_retrieval_Gerchberg-Saxton_algorithm_and_Fienup_variants_A_view_from_convex_optimization
 

FAQ: Understanding the Gerchberg-Saxton Algorithm through Convex Optimization

What is the Gerchberg-Saxton algorithm?

The Gerchberg-Saxton algorithm is an iterative method used to reconstruct an image or signal from its Fourier transform. It is commonly used in optics and signal processing applications.

How does the Gerchberg-Saxton algorithm work?

The algorithm works by alternating between the Fourier domain and the image domain, using constraints on the desired image and its Fourier transform to iteratively improve the reconstruction. This process continues until the desired accuracy is achieved.

What are the applications of the Gerchberg-Saxton algorithm?

The Gerchberg-Saxton algorithm has a wide range of applications in fields such as optics, signal processing, and image reconstruction. It is commonly used in holography, optical microscopy, and image processing techniques.

What are the advantages of using the Gerchberg-Saxton algorithm?

One of the main advantages of this algorithm is its ability to reconstruct images with high accuracy, even in the presence of noise. It is also a relatively simple and efficient method compared to other image reconstruction techniques.

Are there any limitations to the Gerchberg-Saxton algorithm?

One limitation of this algorithm is that it can only be used for deterministic signals, meaning that the input image must have a unique Fourier transform. It also requires a good initial estimate of the image, which can be difficult to obtain in some cases.

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