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Two-dimensional optical Hartley transforms in the presence of errors
Applied Optics
|June 18, 2010
Summary
This study shows how to create an optical Hartley transform using two Fourier transforms. Errors in the process can be identified and corrected to recover the true Hartley transform.
Area of Science:
- Optics
- Image Processing
- Fourier Optics
Background:
- The optical Hartley transform encodes object information in amplitude.
- It is typically constructed by combining two Fourier transforms.
Purpose of the Study:
- To investigate the construction of optical Hartley transforms.
- To determine methods for recovering the Hartley transform when errors occur.
Main Methods:
- Constructing the optical Hartley transform via the addition of two Fourier transforms.
- Analyzing errors in the relative amplitude, phase, and orientation of the Fourier transforms.
Main Results:
- A correctly constructed optical Hartley transform encodes all Fourier amplitude and phase information in amplitude only.
- Deviations from the correct relationship between Fourier transforms result in an incorrect Hartley transform.
Conclusions:
- The optical Hartley transform can be accurately recovered even if errors are present during its construction.
- Knowledge of error type and transform plane measurements are key to Hartley transform recovery.
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