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Journals >Chinese Optics Letters >Volume 13 >Issue 6 >Page 060702 > Article

Chinese Optics Letters
Vol. 13, Issue 6, 060702 (2015)

Filtering characteristics of spatial filter for spatial filtering velocimeter

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

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Abstract

In order to select a suitable spatial filter for the spatial filtering velocimeter, the filtering characteristics of the spatial filters with a rectangular window and rectangular transmittance are investigated by the power spectrum of transmittance function method. The filtering characteristics of differential filters are investigated and compared with that of common ones. The influences of the number of spatial periods on the spectral bandwidth, deviation to central frequency, and peak transmittance are deeply analyzed. The results show that the influence is due to the form of superposition of the signal components and other components, the pedestal and higher-order components, and the superposition results from the finite size of the spatial filter. According to the results, a method is proposed to compensate for the deviation to central frequency.

v = p f / M,

(1)

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h (x, y) = {\begin{matrix} 1, & (l p - \frac{ω}{2}) \leq x \leq (l p + \frac{ω}{2}), - \frac{X}{2} \leq x \leq \frac{X}{2}, - \frac{Y}{2} \leq y \leq \frac{Y}{2}, \\ 0, & otherwise . \end{matrix}

(2)

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H_{p} (f_{x}, f_{y}) = \frac{X^{2} Y^{2}}{4} {| H_{Y} (f_{y}) |}^{2} {[H_{X} (f_{x}) + H_{X m} (f_{x})]}^{2},

(3)

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H_{Y} (f_{y}) = \sin c (f_{y} Y),

(4)

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H_{X} (f_{x}) = \sin c (f_{x} X),

(5)

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H_{X m} (f_{x}) = \sum_{m = 1}^{\infty} {(- 1)}^{m - 1} \frac{2}{(2 m - 1) π} [H_{X m}^{-} (f_{x}) + H_{X m}^{+} (f_{x})],

(6)

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H_{X m}^{-} (f_{x}) = \sin c (f_{x} X - \frac{2 m - 1}{p} X),

(7)

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H_{X m}^{+} (f_{x}) = \sin c (f_{x} X + \frac{2 m - 1}{p} X),

(8)

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H_{X m}^{-} (f_{x}) = \sin c {[f_{x} p - (2 m - 1)] n},

(9)

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H_{X m}^{+} (f_{x}) = \sin c {[f_{x} p + (2 m - 1)] n},

(10)

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h (x, y) = {\begin{cases} 1, & (l p - \frac{ω}{2}) \leq x \leq (l p + \frac{ω}{2}), - \frac{X}{2} \leq x \leq \frac{X}{2}, - \frac{Y}{2} \leq y \leq \frac{Y}{2}, \\ - 1, & (l p + \frac{ω}{2}) \leq x \leq (l p + \frac{3 ω}{2}), - \frac{X}{2} \leq x \leq \frac{X}{2}, - \frac{Y}{2} \leq y \leq \frac{Y}{2}, \\ 0, & otherwise . \end{cases}

(11)

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H_{p} (f_{x}, f_{y}) = \frac{X^{2} Y^{2}}{4} {| H_{Y} (f_{y}) |}^{2} {[H_{X m} (f_{x})]}^{2},

(12)

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H_{X m} (f_{x}) = \sum_{m = 1}^{\infty} {(- 1)}^{m - 1} \frac{4}{(2 m - 1) π} [H_{X m}^{-} (f_{x}) + H_{X m}^{+} (f_{x})] .

(13)

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D = \frac{0.8924}{n} .

(14)

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ε = Δ (f_{x} p) .

(15)

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v = \frac{1}{(1 + ε)} p f / M,

(16)

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References (12)

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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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