• Chinese Optics Letters
  • Vol. 13, Issue 6, 060702 (2015)
Xin He, Jian Zhou, Xiaoming Nie, and Xingwu Long*
Author Affiliations
  • College of Optoelectronic Science and Engineering, National University of Defense Technology, Changsha, 410073, China
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    DOI: 10.3788/COL201513.060702 Cite this Article Set citation alerts
    Xin He, Jian Zhou, Xiaoming Nie, Xingwu Long. Filtering characteristics of spatial filter for spatial filtering velocimeter[J]. Chinese Optics Letters, 2015, 13(6): 060702 Copy Citation Text show less
    Basic setup of a spatial filtering velocimeter.
    Fig. 1. Basic setup of a spatial filtering velocimeter.
    Schematic diagram of (a) a rectangular-type spatial filter with rectangular transmittance and (b) its transmittance function.
    Fig. 2. Schematic diagram of (a) a rectangular-type spatial filter with rectangular transmittance and (b) its transmittance function.
    Power spectrum of a rectangular-type spatial filter with rectangular transmittance for n=10.
    Fig. 3. Power spectrum of a rectangular-type spatial filter with rectangular transmittance for n=10.
    Schematic diagram of (a) a rectangular-type differential spatial filter with rectangular transmittance and (b) its transmittance function.
    Fig. 4. Schematic diagram of (a) a rectangular-type differential spatial filter with rectangular transmittance and (b) its transmittance function.
    Power spectrum of a rectangular-type differential spatial filter with rectangular transmittance for n=10.
    Fig. 5. Power spectrum of a rectangular-type differential spatial filter with rectangular transmittance for n=10.
    Power spectra Hp(fx,0) for a rectangular-type rectangular-transmission spatial filter with n=2, 4, 8, and 16.
    Fig. 6. Power spectra Hp(fx,0) for a rectangular-type rectangular-transmission spatial filter with n=2, 4, 8, and 16.
    Power spectra Hp(fx,0) for a differential rectangular-type rectangular-transmission spatial filter with n=2, 4, 8, and 16.
    Fig. 7. Power spectra Hp(fx,0) for a differential rectangular-type rectangular-transmission spatial filter with n=2, 4, 8, and 16.
    Dependence of the specific bandwidth on the number of spatial periods n for both common and differential filters.
    Fig. 8. Dependence of the specific bandwidth on the number of spatial periods n for both common and differential filters.
    Influence of pedestal components fxp=0 on the deviation of the central frequency fx=1/p. The signal (red curve) and pedestal components (green curve) are separately calculated and plotted. The two of them are plotted together by the blue curve.
    Fig. 9. Influence of pedestal components fxp=0 on the deviation of the central frequency fx=1/p. The signal (red curve) and pedestal components (green curve) are separately calculated and plotted. The two of them are plotted together by the blue curve.
    Influence of higher spatial frequencies on the deviation of the central frequency fx=1/p. The signal fxp=1 (red curve) and higher spatial frequencies (green curve) are separately calculated and plotted. The two of them are plotted together by the blue curve.
    Fig. 10. Influence of higher spatial frequencies on the deviation of the central frequency fx=1/p. The signal fxp=1 (red curve) and higher spatial frequencies (green curve) are separately calculated and plotted. The two of them are plotted together by the blue curve.
    Interaction of fxp=1 and fxp=−1 on the deviation of central frequency fx=1/p. fxp=1 (red curve) and fxp=−1 (green curve) are separately calculated and plotted. The two of them are plotted together by the blue curve.
    Fig. 11. Interaction of fxp=1 and fxp=1 on the deviation of central frequency fx=1/p. fxp=1 (red curve) and fxp=1 (green curve) are separately calculated and plotted. The two of them are plotted together by the blue curve.
    Dependence of the peak value of transmittance on the number of spatial periods n for (a) common and (b) differential filters.
    Fig. 12. Dependence of the peak value of transmittance on the number of spatial periods n for (a) common and (b) differential filters.
     Deviation of central frequency 
    nCommon filter/ε1Differential filter/ε2ε1/ε2
    20.11000.04102.68
    3−0.03580.0190−1.88
    40.03540.01103.22
    5−0.01250.0070−1.79
    60.01700.00543.15
    7−0.00630.0030−2.10
    80.01000.00273.70
    9−0.00370.0021−1.76
    100.00600.00173.53
    11−0.00250.0014−1.79
    120.00400.00123.33
    13−0.00170.0010−1.70
    140.00300.00093.33
    15−0.00120.0008−1.50
    160.00200.00072.86
    Table 1. Dependence and Quantization of the Deviation ε on the Number of Spatial Periods n for Both Common and Differential Filters
    Xin He, Jian Zhou, Xiaoming Nie, Xingwu Long. Filtering characteristics of spatial filter for spatial filtering velocimeter[J]. Chinese Optics Letters, 2015, 13(6): 060702
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