• Journal of Applied Optics
  • Vol. 43, Issue 3, 399 (2022)
Zeyu WANG, Jie CHEN, Lei YANG, and Hongbo XIE
Author Affiliations
  • Key Laboratory of Optoelectronic Information Technology (Ministry of Education), School of Precision Instruments and Optoelectronic Engineering, Tianjin University, Tianjin 300072, China
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    DOI: 10.5768/JAO202243.0301004 Cite this Article
    Zeyu WANG, Jie CHEN, Lei YANG, Hongbo XIE. Wavefront shaping system of tiny optical path difference based on off-axis ellipsoidal surface[J]. Journal of Applied Optics, 2022, 43(3): 399 Copy Citation Text show less

    Abstract

    In order to realize the optical beam transmission with approximately equal optical path for a certain distance in space, a newly-designed wavefront shaping system with off-axis ellipsoidal reflector was proposed. On the basis of the geometric optics and primary aberration theory, the influences of conic coefficients and off-axis amounts of the ellipsoidal reflector on the optical path difference of the image plane were analyzed in optical design software Zemax, the wavefront shaping systems of two kinds of optical structures of planar-ellipsoidal reflector and double ellipsoidal reflector were designed, and the tolerances of the two structures were compared. The analysis results show that both the planar-ellipsoidal reflective system and the double ellipsoidal reflective system realize the optical beam transmission at a distance of 1 m in space, and the optical path difference between each field of view pupil is 0.14 mm and 0.04 mm, respectively, under the condition of 3 mm object height field of view and aperture angle of 6°. Therefore, the shaping effect of the double ellipsoidal reflective structure is better than that of the planar-ellipsoidal reflective system, but the double ellipsoidal reflective structure is more sensitive to the tolerances.
    $ \frac{{{x^2}}}{{{a^2}}} + \frac{{{y^2}}}{{{b^2}}} + \frac{{{{\textit{z}}^2}}}{{{c^2}}} = 1 $(1)

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    $ \left| {AC} \right| + \left| {CB} \right| = \left| {AD} \right| + \left| {DB} \right| $(2)

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    $ {\textit{z}} = \frac{{{c_0}{r^2}}}{{1 + \sqrt {1 - \left( {1 + k} \right){c^2}{r^2}} }} $(3)

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    $ - 1 < k < 0 $(4)

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    $ \frac{1}{{{c_0}}} = {r_0} = \pm \frac{{{b^2}}}{a} $(5)

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    $ k = - {e^2} = - \left( {\frac{{{a^2} - {b^2}}}{{{a^2}}}} \right) $(6)

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    $ \left\{ ΔSI=(nn)e2r03h4=2e2r03h4ΔSII=ΔSIhzhΔSIII=ΔSI(hzh)2ΔSIV=0ΔSV=ΔSI(hzh)3 \right. $(7)

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    $ a - em \leqslant d \leqslant a + em $(8)

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    $ L = 2{a_1} + 2{a_2} $(9)

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    Zeyu WANG, Jie CHEN, Lei YANG, Hongbo XIE. Wavefront shaping system of tiny optical path difference based on off-axis ellipsoidal surface[J]. Journal of Applied Optics, 2022, 43(3): 399
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