Time efficient Chinese remainder theorem algorithm for full-field fringe phase analysis in multi-wavelength interferometry

Phase and fringe order determination in wavelength scanning interferometry.

A method to obtain unambiguous surface height measurements using wavelength scanning interferometry with an improved repeatability, comparable to that obtainable using phase shifting interferometry, is reported. Rather than determining the conventional fringe frequency-derived z height directly, the method uses the frequency to resolve the fringe order ambiguity, and combine this information wi...

The Chinese Remainder Theorem

Fast Parallel Garner Algorithm for Chinese Remainder Theorem

This paper presents a fast parallel garner algorithm for Chinese remainder theorem. The variables in garner algorithm are divided into public parameters that are constants for fixed module and private parameters that represent random input integers. We design the parallel garner algorithm by analyzing the data dependencies of these arithmetic operations for computing public variables and privat...

Robustness in Chinese Remainder Theorem

Chinese Remainder Theorem (CRT) has been widely studied with its applications in frequency estimation, phase unwrapping, coding theory and distributed data storage. Since traditional CRT is greatly sensitive to the errors in residues due to noises, the problem of robustly reconstructing integers via the erroneous residues has been intensively studied in the literature. In order to robustly reco...

A Multivariable Chinese Remainder Theorem

Using an adaptation of Qin Jiushao’s method from the 13th century, it is possible to prove that a system of linear modular equations ai1xi + · · · + ainxn = ~bi mod ~ mi, i = 1, . . . , n has integer solutions if mi > 1 are pairwise relatively prime and in each row, at least one matrix element aij is relatively prime to mi. The Chinese remainder theorem is the special case, where A has only one...