Evaluation of data for one-dimensional gratings by improved fast Fourier transform method

LI Tong-bao; WENG Jun-jing; LEI Li-hua; LI Yuan; Cai Xiao-yu; MA Yan

doi:10.3788/OPE.20152301.0230

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Evaluation of data for one-dimensional gratings by improved fast Fourier transform method

更新时间：2020-08-13

- Evaluation of data for one-dimensional gratings by improved fast Fourier transform method
- Optics and Precision Engineering Vol. 23, Issue 1, Pages: 230-236(2015)
- 作者机构：
  
  1. 同济大学物理科学与工程学院上海,200092
  2. 上海市计量测试技术研究院上海,201203
- 作者简介：
- 基金信息：
- DOI：10.3788/OPE.20152301.0230
  CLC： TB92;O438.2
- Received：02 April 2014，
  
  Revised：28 May 2014，
  
  Published：25 January 2015
- 稿件说明：
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李同保, 翁浚婧, 雷李华等. 用改进的快速傅里叶变换法评估一维标准样板线节距数据[J]. 光学精密工程, 2015,23(1): 230-236

LI Tong-bao, WENG Jun-jing, LEI Li-hua etc. Evaluation of data for one-dimensional gratings by improved fast Fourier transform method[J]. Editorial Office of Optics and Precision Engineering, 2015,23(1): 230-236
李同保, 翁浚婧, 雷李华等. 用改进的快速傅里叶变换法评估一维标准样板线节距数据[J]. 光学精密工程, 2015,23(1): 230-236 DOI： 10.3788/OPE.20152301.0230.

LI Tong-bao, WENG Jun-jing, LEI Li-hua etc. Evaluation of data for one-dimensional gratings by improved fast Fourier transform method[J]. Editorial Office of Optics and Precision Engineering, 2015,23(1): 230-236 DOI： 10.3788/OPE.20152301.0230.

摘要

由于利用快速傅里叶变换(FFT)法定量测量标准样板的平均节距时会因为频谱分辨率Δ

有限而在数据分析过程中丢失信息

故本文对常用的FFT法进行了改进.首先在FFT的频谱中得到最大振幅值对应的频率分量

max

使用二分法缩小

max

附近的频率范围;然后利用连续傅里叶变换法寻找更大的振幅值与更精确的

max

以求得更接近真实值的线节距.为了验证该方法的可行性

利用Matlab软件仿真被测标准样板(TGD1)的轮廓图

比较了FFT与改进后的FFT对不同扫描长度下数据的评估结果

并展示了改进FFT法评估时部分数据的运算过程.同时

通过计量型原子力显微镜实测20 μm×2 μm内的TGD1形貌.两种评估法下的数据比对结果显示:改进FFT评估后的线节距为(277.84±0.39) nm

符合标称值(278±1) nm

验证了改进后FFT方法对线节距求解的准确性与合理性.

Abstract

An improved Fast Fourier Transform(FFT) method was proposed to solve the lack of information resulted from frequency resolution limitation of the FFT. Firstly

a frequency component

max

which is corresponding to the maximum value of amplitude

(

max

) was searched with FFT method

and the frequency scope around

max

was reduced by the dichotomy. Then

the inverse Fourier transform was used to seek a larger value of amplitude in the extent scope including the

max

as the center. The frequency scope will be bisected every iteration until smaller than the target uncertainty. To prove the validity of the improved FFT method

a measured object (TGD01)was simulated with software Matlab. The data from the different acquisition ranges were evaluated by FFT and improved FFT respectively

meanwhile the evaluating progress was illustrated. Moreover

the topography of grating within 20 μm×2 μm was scanned with a metrological atomic force microscope. The results of two kinds of data evaluation were compared with each other. It shows that the pitch of the grating under the improved FFT is (277.84±0.39)nm

which is consistent to the nominal value (278±1)nm very well. The simulation and experiment both prove the validity of improved FFT method in analyzing pitches of gratings.

关键词

Keywords

references

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