中国物理B ›› 2009, Vol. 18 ›› Issue (11): 4881-4886.doi: 10.1088/1674-1056/18/11/044

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Measurement of a discontinuous object based on a dual-frequency grating

乔闹生, 蔡新华, 姚春梅   

  1. School of Physics and Electronics, Hunan University of Arts and Science, Changde 415000, China
  • 收稿日期:2009-02-14 修回日期:2009-04-08 出版日期:2009-11-20 发布日期:2009-11-20
  • 基金资助:
    Project supported by the Science-Technology Program Research Foundation of Hunan Province, China (Grant No 2009FJ3187) and the 11\rm th Five-year Plan for Key Construction Academic Subject (Optics) of Hunan Province, China (Grant No 06GXCD02).

Measurement of a discontinuous object based on a dual-frequency grating

Qiao Nao-Sheng(乔闹生)†,Cai Xin-Hua(蔡新华), and Yao Chun-Mei(姚春梅)   

  1. School of Physics and Electronics, Hunan University of Arts and Science, Changde 415000, China
  • Received:2009-02-14 Revised:2009-04-08 Online:2009-11-20 Published:2009-11-20
  • Supported by:
    Project supported by the Science-Technology Program Research Foundation of Hunan Province, China (Grant No 2009FJ3187) and the 11\rm th Five-year Plan for Key Construction Academic Subject (Optics) of Hunan Province, China (Grant No 06GXCD02).

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摘要： The dual-frequency grating measurement theory is proposed in order to carry out the measurement of a discontinuous object. Firstly, the reason why frequency spectra are produced by low frequency gratings and high frequency gratings in the field of frequency is analysed, and the relationship between the wrapped-phase and the unwrapping-phase is discussed. Secondly, a method to combine the advantages of the two kinds of gratings is proposed: one stripe is produced in the mutation part of the object measured by a suitable low frequency grating designed by MATLAB, then the phase produced by the low frequency grating need not be unfolded. The integer series of stripes is produced by a high frequency grating designed by MATLAB based on the frequency ratio of the two kinds of gratings and the high frequency wrapped-phase, and the high frequency unwrapping-phase is then obtained. In order to verify the correctness of the theoretical analysis, a steep discontinuous object of 600×600 pixels and 10.00~mm in height is simulated and a discontinuous object of ladder shape which is 32.00~mm in height is used in experiment. Both the simulation and the experiment can restore the discontinuous object height accurately by using the dual-frequency grating measurement theory.

Abstract: The dual-frequency grating measurement theory is proposed in order to carry out the measurement of a discontinuous object. Firstly, the reason why frequency spectra are produced by low frequency gratings and high frequency gratings in the field of frequency is analysed, and the relationship between the wrapped-phase and the unwrapping-phase is discussed. Secondly, a method to combine the advantages of the two kinds of gratings is proposed: one stripe is produced in the mutation part of the object measured by a suitable low frequency grating designed by MATLAB, then the phase produced by the low frequency grating need not be unfolded. The integer series of stripes is produced by a high frequency grating designed by MATLAB based on the frequency ratio of the two kinds of gratings and the high frequency wrapped-phase, and the high frequency unwrapping-phase is then obtained. In order to verify the correctness of the theoretical analysis, a steep discontinuous object of 600×600 pixels and 10.00 mm in height is simulated and a discontinuous object of ladder shape which is 32.00 mm in height is used in experiment. Both the simulation and the experiment can restore the discontinuous object height accurately by using the dual-frequency grating measurement theory.

Key words: dual-frequency grating, Fourier transform profilometry, measurement of discontinuous object, phase unwrapping

中图分类号:  (Gratings)

  • 42.79.Dj
42.30.Va (Image forming and processing)