Optics and Precision Engineering, Volume. 33, Issue 12, 1864(2025)

Desensitization design methods for reflective telescopes with freeform surfaces

Yang WANG1, Shengbo PENG1, and Zhiyuan GU2、*
Author Affiliations
  • 1College of Optoelectronic Engineering, Changchun University of Science and Technology, Changchun30022, China
  • 2Changchun Institute of Optics,Fine Mechanics and Physics,Chinese Academy of Sciences, Changchun130031,China
  • show less
    Figures & Tables(21)
    Schmidt system layout
    Ray trace diagram for a coaxial system with a freeform surface on a non-aperture stop surface
    Ray trace diagram for a decentered elements with a freeform surface on the aperture stop surface
    Ray trace diagram for a decentered elements with a freeform surface on a non-aperture stop surface
    Ray tracing diagram with tilted elements
    Field sampling points of an off-axis two-mirror telescope
    Optical layout of the off-axis two-mirror telescope
    Histogram and yield curve of Monte Carlo simulation results for an off-axis two-mirror telescope
    Field Sampling points of an off-axis three-mirror telescope
    Optical layout of the off-axis three-mirror telescope
    Histogram and yield curve of Monte Carlo simulation results for an off-axis three-mirror system
    • Table 1. Aberration equations for a freeform surface located at the aperture stop in a coaxial system.

      View table
      View in Article

      Table 1. Aberration equations for a freeform surface located at the aperture stop in a coaxial system.

      表面类型奇数像面偶数像面
      反射面像差WH=-2nλCZρWH=-2nλCZ-ρ
      透射面像差WH=n2-n1λCZρWH=n2-n1λCZ-ρ
    • Table 2. Aberrations generated by different freeform surface terms

      View table
      View in Article

      Table 2. Aberrations generated by different freeform surface terms

      像差类型像差系数
      Z5

      B20.5s2+0.5Q5

      3B2Q80.5s2-1.5hy +uy

      12B2Q91.5s2-0.5hx +ux2+0.5s2-1.5hy +uy2

      3B2Q110.5s2+0.5hy +uy

      12B2Q12s2hx +ux2+hy +uy2

      6B2Q170.5s2+0.5hx +ux2-hy +uy2

      -3B2Q9s2-1-3B2Q120.5s2+0.5

      Z6

      3B2Q8shx +ux 

      3B2Q9shx +ux hy +uy 

      3B2Q11shx +ux 

      -12B2Q17shx +ux hy +uy 

      Z7

      8B3Q90.75s3+0.25shx +ux 

      4B3Q12s3hx +ux 

      4B3Q17s3-shx +ux 

      Z8

      B3Q80.25s2+0.75

      8B3Q90.75s3+0.25shy +uy 

      B3Q110.25s2-0.25

      B3Q12-4hy -4dy 

      4B3Q171-s3hy +uy 

    • Table 3. Lens data of an off-axis two-mirror telescope optimized with the traditional optimization methods

      View table
      View in Article

      Table 3. Lens data of an off-axis two-mirror telescope optimized with the traditional optimization methods

      表面半径/mm厚度/mm圆锥系数YDE/mmC5(λC8(λC11(λC12(λ
      PM-1741.71-646.94-0.95-240.5081.2193.0100
      SM-631.00769.98-2.46-240.50-90.29-136.85-7.800.36
    • Table 4. Lens data of an off-axis two-mirror telescope optimized with the as-built performance model

      View table
      View in Article

      Table 4. Lens data of an off-axis two-mirror telescope optimized with the as-built performance model

      表面半径/mm厚度/mm圆锥系数YDE/mmC5(λC6(λC7(λC8(λ
      PM-1 770.19-650.83-0.60-171.97-33.26137.570.000.00
      SM-664.62799.33-0.52-171.97-70.29-160.77-25.17-11.47
    • Table 5. Lens data of an off-axis two-mirror telescope optimized with the TOLR method

      View table
      View in Article

      Table 5. Lens data of an off-axis two-mirror telescope optimized with the TOLR method

      表面半径/mm厚度/mm圆锥系数YDE/mmC5(λC6(λC7(λC8(λ
      PM-1 742.55-647.37-0.81-171.17-59.9474.350.000.00
      SM-631.10769.24-1.39-171.17-103.42-108.6011.22-5.34
    • Table 6. Monte Carlo simulation statistics for the off-axis two-mirror telescopes

      View table
      View in Article

      Table 6. Monte Carlo simulation statistics for the off-axis two-mirror telescopes

      传统优化法竣工性能模型优化法TOLR优化法
      名义值(λ0.072 70.083 00.075 1
      最佳(λ0.076 10.083 60.077 2
      最差(λ0.884 70.620 30.636 0
      平均值(λ0.426 70.313 10.321 5
      标准差0.160 80.113 20.115 5
    • Table 7. Lens data of an off-axis three-mirror telescope optimized with the traditional optimization methods

      View table
      View in Article

      Table 7. Lens data of an off-axis three-mirror telescope optimized with the traditional optimization methods

      表面曲率半径/mm厚度/mm二次系数YDE/mmC5(λC8(λC9(λC11(λC12(λC17(λ
      主镜-623.91-279.76-0.78-100.03000000
      次镜-217.94315.81-7.49-100.03-39.67-71.78-97.3214.19-19.730.42
      三镜-286.53-306.26-0.11-100.0338.570.4010.503.802.080.19
    • Table 8. Lens data of an off-axis three-mirror telescope optimized with the as-built performance model

      View table
      View in Article

      Table 8. Lens data of an off-axis three-mirror telescope optimized with the as-built performance model

      表面曲率半径/mm厚度/mm二次系数YDE/mmC5(λC8(λC9(λC11(λC12(λC17(λ
      主镜-651.57-299.89-0.78-94.81000000
      次镜-216.66292.22-11.6-94.81-46.47-48.55-113.3424.90-22.182.46
      三镜-278.20-302.23-0.09-94.81-27.334.1017.671.411.330.13
    • Table 9. Lens data of an off-axis three-mirror telescope optimized with the tolr method

      View table
      View in Article

      Table 9. Lens data of an off-axis three-mirror telescope optimized with the tolr method

      表面曲率半径/mm厚度/mm二次系数YDE/mmC5(λC8(λC9(λC11(λC12(λC17(λ
      主镜-658.86-299.84-0.74-96.34000000
      次镜-224.20332.11-5.84-96.34-205.70-8.26-72.2426.35-21.721.34
      三镜-308.07-326.62-0.09-96.34-77.41-11.4116.790.781.810.76
    • Table 10. Monte Carlo simulation statistics for the off-axis three-mirror telescopes

      View table
      View in Article

      Table 10. Monte Carlo simulation statistics for the off-axis three-mirror telescopes

      传统优化法竣工性能模型优化法TOLR优化法
      名义值(λ0.045 00.050 70.049 5
      最佳(λ0.058 80.062 60.051 4
      最差(λ0.575 20.492 50.524 0
      平均值(λ0.261 10.226 60.225 6
      标准差0.088 10.070 40.070 1
    Tools

    Get Citation

    Copy Citation Text

    Yang WANG, Shengbo PENG, Zhiyuan GU. Desensitization design methods for reflective telescopes with freeform surfaces[J]. Optics and Precision Engineering, 2025, 33(12): 1864

    Download Citation

    EndNote(RIS)BibTexPlain Text
    Save article for my favorites
    Paper Information

    Category:

    Received: Mar. 10, 2025

    Accepted: --

    Published Online: Aug. 15, 2025

    The Author Email:

    DOI:10.37188/OPE.20253312.1864

    Topics