Concise fractional Fourier transform based on a non-uniform order searching method for estimating physical parameters from Newton’s rings

Author:

Liang Xin12,Xing Ruo-Qi12,Shen De-Ming12,Wei Hong-Tao12,Liu Er-Zhuo12,Ye Fangquan12,Lu Ming-Feng12,Wu Jin-Min3,Zhang Feng12,Tao Ran12

Affiliation:

1. Beijing Institute of Technology

2. Beijing Key Laboratory of Fractional Signals and Systems

3. Beijing Information Science & Technology University

Abstract

Newton’s ring pattern is very common in interferometry. By analyzing it, the physical parameters can be estimated, such as the curvature radius and the rings’ center. However, parameter estimation from large images using fractional Fourier transform (FRFT) consumes considerable time. A concise FRFT based on a non-uniform order searching method is proposed to reduce the computational time without decreasing the accuracy. Experimental results show that the time of the proposed method is about 2.7 s, which is about 1/600 of that of the traditional FRFT-based method and 1/5 of that of the Fast FRFT-based method when processing 960 × 960 pixel images.

Funder

Beijing Municipal Natural Science Foundation

National Natural Science Foundation of China

The Foundation for Basic Research of Beijing Information Science Technology University

Publisher

Optica Publishing Group

Subject

Atomic and Molecular Physics, and Optics,Engineering (miscellaneous),Electrical and Electronic Engineering

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