Optics and Precision Engineering, Volume. 23, Issue 1, 230(2015)
Evaluation of data for one-dimensional gratings by improved fast Fourier transform method
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 fmax which is corresponding to the maximum value of amplitude F(fmax) was searched with FFT method, and the frequency scope around fmax 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 f′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.
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LI Tong-bao, WENG Jun-jing, LEI Li-hua, LI Yuan, Cai Xiao-yu, MA Yan. Evaluation of data for one-dimensional gratings by improved fast Fourier transform method[J]. Optics and Precision Engineering, 2015, 23(1): 230
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Received: Apr. 2, 2014
Accepted: --
Published Online: Feb. 15, 2015
The Author Email: Tong-bao LI (tbli@tongji.edu.cn)