Performance Analysis for Mirrors of 30 cm Cryogenic Space Infrared Telescope

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  • ABSTRACT

    We have designed a 30 cm cryogenic space infrared telescope for astronomical observation. The telescope is designed to observe in the wavelength range of 0.5~2.1 μm, when it is cooled down to 77 K. The result of the preliminary design of the support structure and support method of the mirror of a 30 cm cryogenic space infrared telescope is shown in this paper. As a Cassegrain prescription, the optical system of a 30 cm cryogenic space infrared telescope has a focal ratio of f/3.1 with a 300 mm primary mirror (M-1) and 113 mm secondary mirror (M-2). The material of the whole structure including mirrors is aluminum alloy (Al6061-T6). Flexures that can withstand random vibration were designed, and it was validated through opto-mechanical analysis that both primary and secondary mirrors, which are assembled in the support structure, meet the requirement of root mean square wavefront error <λ/8 for all gravity direction. Additionally, when the M-1 and flexures are assembled by bolts, the effect of thermal stress occurring from a stainless steel bolt when cooled and bolt torque on the M-1 was analyzed.


  • KEYWORD

    opto-mechanical analysis , mirror mount , Zernike polynomials , finite element method , mirror support

  • 1. 2012 Technical information (2012.6) [Internet] google
  • 2. Cho MK, Liang M, Neill DR (2009) Performance prediction of the LSST secondary mirror [SPIE] Vol.7424 P.742407 google doi
  • 3. Heo S, Kwak MK (2008) Free vibration analysis of an annular plate by the independent coordinate coupling method [J Korean Soc Noise Vib Eng] Vol.18 P.564-571 google
  • 4. Lin YC, Lee LJ, Chang ST, Cheong YC, Huang TM (2010) An investigation to compare the numerical model between shell and solid for honeycomb light-weighted mirror [AMM] Vol.36 P.80-85 google doi
  • 5. Mandelis A, Li L, Baddour N, Tennyson RC, Morrison WD (2003) Quantitative measurements of sliding friction coefficients of tribological interfaces with a new differential infrared radiometric instrument [RScI] Vol.74 P.407-410 google doi
  • 6. Noll RJ (1976) Zernike polynomials and atmospheric turbulence [JOSA] Vol.66 P.207-211 google
  • 7. Trubert M 1989 Mass acceleration curve for spacecraft structural design google
  • 8. Yoder PR 1993 Opto-mechanical system design google
  • [Fig. 1.] Conceptual design of a 30 cm cryogenic space infrared telescope.
    Conceptual design of a 30 cm cryogenic space infrared telescope.
  • [Table 1.] Design requirements of mirrors of 30 cm cryogenic space infrared telescope.
    Design requirements of mirrors of 30 cm cryogenic space infrared telescope.
  • [Fig. 2.] Configuration dimension of mirrors of 30 cm cryogenic space infrared telescope.
    Configuration dimension of mirrors of 30 cm cryogenic space infrared telescope.
  • [Fig. 3.] A M-1 assy. (a) and M-2 assy. (b) assembled with flexures.
    A M-1 assy. (a) and M-2 assy. (b) assembled with flexures.
  • [Table 2.] Material properties.
    Material properties.
  • [Table 3.] Quasi-static load of a M-1 assy. and M-2 assy. for each gravity.
    Quasi-static load of a M-1 assy. and M-2 assy. for each gravity.
  • [Fig. 4.] First mode configuration of a M-1 assy. (freq = 340 Hz) and M-2 assy. (freq = 1,023 Hz): Translation motion.
    First mode configuration of a M-1 assy. (freq = 340 Hz) and M-2 assy. (freq = 1,023 Hz): Translation motion.
  • [Fig. 5.] Stress distribution of a M-1 assy. for z-gravity: Max. stress = 1.2 MPa.
    Stress distribution of a M-1 assy. for z-gravity: Max. stress = 1.2 MPa.
  • [Fig. 6.] Optical deformation map of a M-1 surface for each gravity. (a) Before aberrations correction: from left, x directional, y directional, and z directional gravity. (b) After aberrations correction: from left, x directional, y directional, and z directional gravity.
    Optical deformation map of a M-1 surface for each gravity. (a) Before aberrations correction: from left, x directional, y directional, and z directional gravity. (b) After aberrations correction: from left, x directional, y directional, and z directional gravity.
  • [Fig. 7.] After aberrations correction, optical deformation map of a M-2 surface for each gravity: from left, x directional, y directional, and z directional gravity.
    After aberrations correction, optical deformation map of a M-2 surface for each gravity: from left, x directional, y directional, and z directional gravity.
  • [Table 4.] RMS WFE of a M-1 and M-2 for each gravity.
    RMS WFE of a M-1 and M-2 for each gravity.
  • [Fig. 8.] The reaction force at bolting points.
    The reaction force at bolting points.
  • [Fig. 9.] Force diagram for bolt pre-load.
    Force diagram for bolt pre-load.
  • [Table 5.] Bolt pre-load calculated through finite element analysis.
    Bolt pre-load calculated through finite element analysis.
  • [Fig. 10.] Performance change of a M-1 according to assembly method of flexures. (a) In case that flexures are directly assembled with a M-1: RMS WFE = λ/2.4. (b) In case that flexures are assembled with a M-1 through the step: RMS WFE = λ/58.6. RMS: root mean square, WFE: wavefront error.
    Performance change of a M-1 according to assembly method of flexures. (a) In case that flexures are directly assembled with a M-1: RMS WFE = λ/2.4. (b) In case that flexures are assembled with a M-1 through the step: RMS WFE = λ/58.6. RMS: root mean square, WFE: wavefront error.
  • [Fig. 11.] Optical surface deformation map of a M-1 for ΔT = -221 K, temperature change. (a) Before correction. (b) After correction.
    Optical surface deformation map of a M-1 for ΔT = -221 K, temperature change. (a) Before correction. (b) After correction.
  • [Table 6.] RMS WFE and Max. stress of a M-1 for bolt torque and thermal stress.
    RMS WFE and Max. stress of a M-1 for bolt torque and thermal stress.
  • [Fig. 12.] Stress distributions for ΔT = -221 K, temperature change. (a) In case of a full mirror model (a side length of a bolt element = 2 mm), stress distribution at a bolt hole. (b) In case of a segment mirror model (a side length of a bolt element = 0.25 mm), stress distribution at a bolt hole. (c) In case of a segment mirror model (a side length of a bolt element = 0.25 mm), stress distribution of a bolt.
    Stress distributions for ΔT = -221 K, temperature change. (a) In case of a full mirror model (a side length of a bolt element = 2 mm), stress distribution at a bolt hole. (b) In case of a segment mirror model (a side length of a bolt element = 0.25 mm), stress distribution at a bolt hole. (c) In case of a segment mirror model (a side length of a bolt element = 0.25 mm), stress distribution of a bolt.