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Spatial incoherence in phase retrieval based on focus variation
A V Martin1, F-R Chen, W-K Hsieh
1School of Physics, University of Melbourne, Victoria 3010, Australia.
Ultramicroscopy
|June 9, 2006
Summary
Spatial incoherence limits phase retrieval methods like transport of intensity equation and iterative wave function reconstruction by defining defocus step size bounds. Insufficient resolution prevents phase information retrieval, impacting applicability.
Area of Science:
- Optics and Photonics
- Image Reconstruction
- Phase Retrieval
Background:
- Phase retrieval techniques are crucial for reconstructing object wavefronts from intensity measurements.
- Focus variation methods, including the transport of intensity equation (TIE) and iterative wave function reconstruction (IWFR), are widely used.
- The impact of spatial incoherence on the performance and limitations of these phase retrieval methods requires detailed investigation.
Purpose of the Study:
- To investigate the effect of spatial incoherence on TIE and IWFR phase retrieval methods.
- To determine the upper and lower bounds for defocus step size based on spatial incoherence and image variation.
- To identify the conditions under which phase information cannot be retrieved by these techniques.
Main Methods:
- Analysis of spatial incoherence effects on defocus step size in TIE and IWFR.
- Establishing upper bounds for defocus step size based on spatial incoherence.
- Establishing lower bounds for defocus step size based on phase information variation in defocused images.
Main Results:
- Spatial incoherence imposes an upper bound on the defocus step size for both TIE and IWFR.
- Sufficient variation in defocused images imposes a lower bound on the defocus step size.
- The scaling of these bounds with object size and imaging resolution differs, leading to limitations at low resolutions where phase retrieval fails.
Conclusions:
- Neither TIE nor IWFR can retrieve phase information at sufficiently low resolutions, given specific spatial incoherence properties.
- The study defines the operational limits and regions of applicability for these phase retrieval techniques under spatial incoherence.
- Understanding these bounds is critical for successful phase retrieval in various imaging applications.
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