• Infrared and Laser Engineering
  • Vol. 50, Issue 9, 20200528 (2021)
Jianxiang Du, Xiaoying Zong, Shikui Luo, and Chao Gao
Author Affiliations
  • Beijing Institute of Space Mechanics & Electricity, Beijing 100190, China
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    DOI: 10.3788/IRLA20200528 Cite this Article
    Jianxiang Du, Xiaoying Zong, Shikui Luo, Chao Gao. Plane wave transmitted wavefront simulation and measurement of filter with multi-spectrum[J]. Infrared and Laser Engineering, 2021, 50(9): 20200528 Copy Citation Text show less

    Abstract

    Optical filter is widely used in multi-spectrum imaging of space remote sensor. Usually the base of the filter is optical glass. And optical coating on the glass is used to filter the specific spectrum. Plane wave transmitted wavefront testing is the main technique used to evaluate the wavefront distortion of the filter. The wavelength of the light interferometer uses is fixed. It can not cover the filter’s spectrum. And it is impossible to test every spectrum transmitted wavefront of the filter. In order to solve this problem, one solution was provided in this article. The interferometer with one fixed light wavelength was used. The front and back surface sag data, transmitted wavefront data of the filter before coating, and the front and back surface sag data after coating were used in a special algorithm together, the plane wave transmitted wavefront of the filter after coating can be obtained. The theoretical derivation of the algorithm was fully discussed in this article. And the experiments show the error of the transmitted wavefront RMS can be less than 0.004λ (λ=632.8 nm). The technique can be applied on the testing of infrared filter, experiments show the error is about 0.002λ (λ=3.39 μm), The accuracy requirement is satisfied and the cost is reduced.
    $ {OPL } = {PL } \times { n} $(1)

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    $ \begin{split} OP{L_{DMQ}} =& (d_0 + \varDelta dF) + (d - \varDelta dF + \varDelta dR){n_m} + (d_0 - \varDelta dR) =\\ &2d_0 + d{n_m} + ({n_m} - 1)(\varDelta dR - \varDelta dF) \end{split} $(2)

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    $OP{L_{coating}} = \sum\limits_{i = 1}^k {{t_i}{n_i}} $(3)

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    $OP{L_{coating}} = \sum\limits_{i = 1}^k {{t_i}{n_i}} = \sum\limits_{i = 1}^k {{t_i}} \times \frac{{\displaystyle\sum\limits_{i = 1}^k {{t_i}{n_i}} }}{{\displaystyle\sum\limits_{i = 1}^k {{t_i}} }} = \sum\limits_{i = 1}^k {{t_i}} \times {n_{ca}}$(4)

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    ${n_{ca}} = \frac{{\displaystyle\sum\limits_{i = 1}^k {{t_i}{n_i}} }}{{\displaystyle\sum\limits_{i = 1}^k {{t_i}} }}$(5)

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    $\begin{split} OP{L_{DMH}} =& {d_0 + \varDelta tF + ({T_c} - \varDelta tF + \varDelta dF'){n_{ca}} + (d - \varDelta dF' + dR'){n_m} +}\\ &({T_c} + \varDelta tR - \varDelta dR'){n_{ca}} + d_0 - \varDelta tR \end{split}$(6)

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    $\begin{split} OP{L_{DMH}} =& (2{T_c}{n_{ca}} + 2d_0) + d{n_m} + ({n_{ca}} - 1)(\varDelta tR - \varDelta tF) -\\ &({n_m} - {n_{ca}})(\varDelta dR' - \varDelta dF') \end{split}$(7)

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    $\varDelta dR' - \varDelta dF' = \varDelta dR - \varDelta dF$(8)

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    $\begin{split} OP{L_{DMH}} =& (2{T_C}{n_{ca}} + O{P_{DMQ}}) - ({n_{ca}} - 1)(\varDelta tR - \varDelta tF) +\\ &(2{n_m} - {n_{ca}} - 1)(\varDelta dR - \varDelta dF) \end{split}$(9)

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    $RM{S_{TW}} = \sqrt {\frac{{\displaystyle\sum\limits_{i = 1\atop j = 1}^{i = m\atop j = n} {OP{L_{DMH}}^2(i,j)} }}{{m \times n}}} $(10)

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    ${\varepsilon _1}{\rm{ = }}0.003\;3\lambda $()

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    ${\varepsilon _2}{\rm{ = }}0.000\;35\lambda $()

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    ${\varepsilon _3}{\rm{ = }}0.002\lambda $()

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    ${\varepsilon _4}{\rm{ = 4\cdot0}}{\rm{.000\;1}}\cdot0.004\lambda {\rm{ = }}1.6 \times {10^{ - 6}}\lambda $()

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    $\varepsilon {\rm{ = }}\sqrt {\varepsilon _1^2 + \varepsilon _2^2 + \varepsilon _3^2 + \varepsilon _4^2} {\rm{ = }}0.003\;9\lambda $()

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    Jianxiang Du, Xiaoying Zong, Shikui Luo, Chao Gao. Plane wave transmitted wavefront simulation and measurement of filter with multi-spectrum[J]. Infrared and Laser Engineering, 2021, 50(9): 20200528
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