Experimental Study on Spatial Filtering Imaging Method of Diffraction Gratings

Fig. 10. Fringe images of multi-beam interferometry holographic grating with spatial frequency of 100 lp/mm before and after filtering imaging processing. (a) Before filtering; (b) after filtering

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Fig. 11. Transmittance functions of multi-beam interferometry holographic grating with spatial frequency of 100 lp/mm before and after filtering imaging processing. (a) Before filtering; (b) after filtering

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Fig. 12. Frequency spectra of multi-beam interferometry holographic grating with spatial frequency of 100 lp/mm before and after filtering imaging processing. (a) Before filtering; (b) after filtering

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$Diffraction light intensity distributions of multi-beam interferometry holographic grating with spatial frequency of 100 lp/mm before and after filtering imaging processing. (a) Before filtering; (b) after filtering$

Fig. 13. Diffraction light intensity distributions of multi-beam interferometry holographic grating with spatial frequency of 100 lp/mm before and after filtering imaging processing. (a) Before filtering; (b) after filtering

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Fig. 14. Frequency spectra of rectangular grating with spatial frequency of 100 lp/mm before and after filtering. (a) Before filtering; (b) after filtering

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$Diffraction light intensity distribution of rectangular grating with spatial frequency of 100 lp/mm$

Fig. 15. Diffraction light intensity distribution of rectangular grating with spatial frequency of 100 lp/mm

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$Diffraction light intensity distributions of rectangular grating with spatial frequency of 100 lp/mm after spatial filtering imaging processing. (a) Light intensity of -1 level and 0 level; (b) light intensity of 0 level and +1 level$

Fig. 16. Diffraction light intensity distributions of rectangular grating with spatial frequency of 100 lp/mm after spatial filtering imaging processing. (a) Light intensity of -1 level and 0 level; (b) light intensity of 0 level and +1 level

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Table 1. Advantages and disadvantages of sine grating fabrication method

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Table 1. Advantages and disadvantages of sine grating fabrication method

Method	Advantage	Disadvantage
Fresnel double sided mirror and biprism	1) Fewer components;2) Symmetrical optical system and the optical path difference is almost zero;3) The range of the grating constant is wide	1) The light spot of interference area is small when using collimating lens;2) Two light beams are non-parallel without collimating lens
Lloyd mirror method	1) Fewer components and no secondary images;2) Simple operation and convenient adjustment	1) Relatively high requirements for the reflectivity of the reflector, collimation property of two light beams and the intensity ratio;2) Only suitable for the fabrication of gratings with larger constant and smaller spatial frequency;3) The interferential light beams are not strictly parallel
Michelson interferometry method	1) Larger size of the grating fabricated;2) Two-dimensional grating fabricated by one exposure	1) More transmissive components, so that the wave surface of the plane wave will be deformed and deviate from the plane wave;2) Only suitable for the fabrication of gratings with larger constant
Mach-Zehnder interferometry method	1) Symmetrical optical system and convenient to set up;2) The optical path difference of two light beams is small and the interference effect is good;3) The adjustment is convenient and the spatial frequency of gratings can be changed with the adjustment of one beam splitter angle	1) More optical components and the fringe is uneven and the symmetry property is decreased;2) The angle between the reflected light and the transmissive light is small and the grating constant is not accurate;3) The angle of two light beams is restricted by the area of beam splitter and this method is not suitable for the fabrication of gratings with small constant

Table 2. Relationship between d0 and f0
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Table 2. Relationship between d0 and f0
$\begin{matrix} {f_{0}}_{} \end{matrix}$ /(lp·mm^-1) 50 100 120 150
$\begin{matrix} {d_{0}}_{} \end{matrix}$ /cm 0.791 1.582 1.898 2.373

Table 3. Relationship between f″0 and p
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Table 3. Relationship between f″0 and p
f″₀ /(lp·mm^-1) 50 100 120 150
p /cm 1.265 2.531 3.037 3.797

Table 4. Relationship among f″0, f″1, and p
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Table 4. Relationship among f″0, f″1, and p
f″ $\begin{matrix} {_{0}}_{} \end{matrix}$ /(lp·mm^-1) 50 100 120 150
p /cm 2.530 5.065 6.075 7.600
f″ $\begin{matrix} {_{1}}_{} \end{matrix}$ /(lp·mm^-1) 100 200 240 300

Table 5. Light intensity ratio of ±2 level to ±1 level of grating with spatial frequency of 100 lp/mm
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Table 5. Light intensity ratio of ±2 level to ±1 level of grating with spatial frequency of 100 lp/mm
$\begin{matrix} y_{100}^{\pm 1} \end{matrix}$ $\begin{matrix} y_{100}^{\pm 2} \end{matrix}$ p₁₀₀ $\begin{matrix} {\bar{p}}_{100} \end{matrix}$
100 5.3850 0.0539
110 5.6617 0.0515
120 6.3600 0.0530
130 6.8419 0.0526
140 7.3262 0.0523
150 7.3800 0.0492 0.0527
160 8.2240 0.0514
170 8.8315 0.0520
180 9.6426 0.0536
190 9.8705 0.0520
200 11.6800 0.0584

Table 6. Light intensity ratio of ±2 level to ±1 level of each grating
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Table 6. Light intensity ratio of ±2 level to ±1 level of each grating
Spatial frequency /(lp·mm^-1) 50 100 120 150
Light intensity ratio /% 8.59 5.27 3.50 2.48

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Xu Gao, Renjie Wang, Jinhuan Li, Yuting Wang, Jipeng Huang. Experimental Study on Spatial Filtering Imaging Method of Diffraction Gratings[J]. Acta Optica Sinica, 2018, 38(2): 0205001

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