基于三角形收缩法改进的分数傅里叶变换估计牛顿环参数

武进敏; 姜盛; 鲁溟峰; 沈德明; 范军芳; 李亚峰; 张峰; 陶然

doi:10.3969/j.issn.1000-1158.2023.12.01

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计量学报 ›› 2023, Vol. 44 ›› Issue (12) : 1783-1790. DOI: 10.3969/j.issn.1000-1158.2023.12.01

光学计量

基于三角形收缩法改进的分数傅里叶变换估计牛顿环参数

武进敏¹,姜盛¹,鲁溟峰²,沈德明²,范军芳¹,李亚峰¹,张峰²,陶然²

作者信息 +

Parameters Estimation of Newton Rings Based on Fractional Fourier Transform Modified by Triangle Shrinkage Method

WU Jin-min¹,JIANG Sheng¹,LU Ming-feng²,SHEN De-ming²,FAN Jun-fang¹,LI Ya-feng¹,ZHANG Feng²,TAO Ran²

Author information +

文章历史 +

摘要

针对分数傅里叶变换用于牛顿环参数估计时速度较慢的问题,通过分析牛顿环条纹图分数傅里叶域幅值最大值与相应旋转角的分布规律,提出基于三角形收缩法改进的分数傅里叶变换进行牛顿环参数估计的方法。实验结果表明:该方法具有可行性,对于图像尺寸小于640×640pixels的条纹图,处理所需时间＜1s,随着图像尺寸增加,条纹图中包含的条纹数目增加,曲率半径估计值相对误差降低,而处理时间仍可满足工程实际需求。以处理1080×1080pixels的图像为例,估计值相对误差为0.001%,处理时间为3.31s。该方法估计720×720pixels高斯噪声污损的牛顿环干涉条纹图像平均用时1.28s,约为传统分数傅里叶变换用时的1/700。

Abstract

Aiming at a slower rate when the fractional Fourier transform is used for the estimation of Newton rings parameters, the method based on the triangle shrinkage of the improved fractional Fourier transform is proposed by analyzing the distribution law of the maximum value of the amplitude in the fractional domain of the Newton rings fringe images and the corresponding angle of rotation. The experimental results show that the method is feasible, and the processing time is less than 1s for the fringe images with an image size less than 640×640pixels. With the increase of the image size, the number of fringes contained in the fringe image increases, and the relative error of the estimated value of the radius of curvature decreases. The processing time is still able to meet the practical needs of engineering. When processing the image of 1080×1080pixels, the relative error of the estimated value is 0.001%, and the processing time is 3.31s. The method estimates the 720×720pixels Gaussian noise-damaged Newton ring interferometric fringe image in an average time of 1.28s, which is about 1/700 of the traditional fractional Fourier transform time.

导出引用

武进敏,姜盛,鲁溟峰,沈德明,范军芳,李亚峰,张峰,陶然. 基于三角形收缩法改进的分数傅里叶变换估计牛顿环参数[J]. 计量学报. 2023, 44(12): 1783-1790 https://doi.org/10.3969/j.issn.1000-1158.2023.12.01

WU Jin-min,JIANG Sheng,LU Ming-feng,SHEN De-ming,FAN Jun-fang,LI Ya-feng,ZHANG Feng,TAO Ran. Parameters Estimation of Newton Rings Based on Fractional Fourier Transform Modified by Triangle Shrinkage Method[J]. Acta Metrologica Sinica. 2023, 44(12): 1783-1790 https://doi.org/10.3969/j.issn.1000-1158.2023.12.01

中图分类号： TB96

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