R-C Telescope Alignment Method Based on Astigmatism Correction of Symmetrical Field of View Misalignment

Hao Wang; Lei Zhang

doi:10.3788/LOP240678

Journals >Laser & Optoelectronics Progress >Volume 62 >Issue 2 >Page 0211003 > Article

Laser & Optoelectronics Progress
Vol. 62, Issue 2, 0211003 (2025)

R-C Telescope Alignment Method Based on Astigmatism Correction of Symmetrical Field of View Misalignment

Hao Wang^* and Lei Zhang

Author Affiliations

School of Optoelectronic Engineering, Changchun University of Science and Technology, Changchun 130012, Jilin , China

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DOI: 10.3788/LOP240678 Cite this Article Set citation alerts

Hao Wang, Lei Zhang. R-C Telescope Alignment Method Based on Astigmatism Correction of Symmetrical Field of View Misalignment[J]. Laser & Optoelectronics Progress, 2025, 62(2): 0211003 Copy Citation Text

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Abstract

This paper proposes a two-mirror telescope alignment method based on the on-axis field of view coma and off-axis symmetrical field of view astigmatism, utilizing vector aberration theory based on the aberration field characteristics of a misaligned Ritchey-Chrétien (R-C) telescope. A simulation alignment experiment is conducted on an R-C telescope, with random misalignments introduced into the secondary mirror. The alignment is successfully completed after three iterations using the proposed method, demonstrating its feasibility. An actual assembly experiment further validates the proposed method, achieving wave aberration values of 0.0730λ for the on-axis field of view and 0.0808λ and 0.0834λ for the two symmetrical off-axis fields of view, respectively. Experimental results indicate that the proposed method effectively aligns the R-C telescope, ensuring high imaging quality across all fields of view.

Keywords

alignment astigmatism symmetrical field of view two-mirror telescope

\begin{array}{l} W = \sum_{j} W_{131 j} [(H - σ_{j}) \cdot ρ] (ρ \cdot ρ) + \\ \sum_{j} W_{222 j} {[(H - σ_{j}) \cdot ρ]}^{2} \end{array}

（1）

W_{C O M A_{3}} = [(W_{131} H - A_{131}) \cdot ρ] (ρ \cdot ρ)

（2）

W_{A S T_{3}} = \frac{1}{2} [W_{222} H^{2} - 2 H A_{222} + B_{222}^{2}] {|ρ|}^{2}

（3）

σ_{P M}^{(s p h)} = [\begin{array}{l} 0 \\ 0 \end{array}]

（4）

σ_{S M}^{s p h} = - \frac{1}{\bar{u_{P M}} (d_{1} + r_{S M})} [\begin{array}{l} X_{D E_{S M}} + B_{D E_{S M}} r_{S M} \\ Y_{D E_{S M}} + A_{D E_{S M}} r_{S M} \end{array}]

（5）

σ_{P M}^{(a s p h)} = [\begin{array}{l} 0 \\ 0 \end{array}]

（6）

σ_{S M}^{a s p h} = - \frac{1}{d_{1} \bar{u_{P M}}} [\begin{array}{l} X_{D E_{S M}} \\ Y_{D E_{S M}} \end{array}]

（7）

W_{C O M A_{3}} = (- A_{131} \cdot ρ) (ρ \cdot ρ)

（8）

Α_{131} = W_{131, S M}^{s p h} σ_{S M}^{s p h} + W_{131, S M}^{a s p h} σ_{S M}^{a s p h}

（9）

δ_{v}^{#} = \frac{[r_{S M} (- W_{131, S M}^{s p h})] / [\bar{u_{P M}} (d_{1} + r_{S M})]}{W_{131, S M}^{s p h} / [\bar{u_{P M}} (d_{1} + r_{S M})] + W_{131, S M}^{a s p h} / \bar{u_{P M}} d_{1}} β^{#}

（10）

[\begin{matrix} - H_{x} & H_{y} & \frac{1}{2} & 0 \\ - H_{y} & - H_{y} & 0 & \frac{1}{2} \end{matrix}] [\begin{array}{l} A_{222, x} \\ A_{222, y} \\ B_{222, x}^{2} \\ B_{222, y}^{2} \end{array}] = [\begin{array}{l} C_{5} - \frac{W_{222}}{2} (H_{x} \cdot H_{x} - H_{y} \cdot H_{y}) \\ C_{6} - W_{222} H_{x} \cdot H_{y} \end{array}]

（11）

[\begin{array}{l} A_{222, x} \\ A_{222, y} \\ B_{222, x}^{2} \\ B_{222, y}^{2} \end{array}] = [\begin{array}{l} σ_{S M, x}^{s p h} σ_{S M, x}^{a s p h} \\ σ_{S M, y}^{(s p h)} σ_{S M, y}^{(a s p h)} \\ σ_{S M, x}^{s p h} \times σ_{S M, x}^{s p h} - σ_{S M, y}^{s p h} \times σ_{S M, y}^{s p h} σ_{S M, x}^{a s p h} \times σ_{S M, x}^{a s p h} - σ_{S M, y}^{a s p h} \times σ_{S M, y}^{a s p h} \\ 2 σ_{S M, x}^{(s p h)} \times σ_{S M, y}^{(s p h)} 2 σ_{S M, x}^{(a s p h)} \times σ_{S M, y}^{(s p h)} \end{array}] [\begin{array}{l} W_{222, S M}^{s p h} \\ W_{222, S M}^{a s p h} \end{array}]

（12）

\{\begin{array}{l} C_{5 x} = C_{5 x}^{'} \\ C_{5 y} = C_{5 y}^{'} \end{array}

（13）

\{\begin{array}{l} H_{x} \cdot A_{222, x} = 0 \\ H_{y} \cdot A_{222, y} = 0 \end{array}

（14）

δ_{v}^{#} = \frac{[r_{S M} (- W_{222, S M}^{s p h})] / [\bar{u_{P M}} (d_{1} + r_{S M})]}{W_{222, S M}^{s p h} / [\bar{u_{P M}} (d_{1} + r_{S M})] + W_{222, S M}^{a s p h} / \bar{u_{P M}} d_{1}} β^{#}

（15）

Δ δ_{v}^{#} = r_{S M} Δ β^{#}

（16）

\begin{array}{l} δ_{v}^{#} - Δ δ_{v}^{#} = \frac{[r_{S M} (- W_{222, S M}^{s p h})] / [\bar{u_{P M}} (d_{1} + r_{S M})]}{W_{222, S M}^{s p h} / [\bar{u_{P M}} (d_{1} + r_{S M})] + W_{222, S M}^{a s p h} / \bar{u_{P M}} d_{1}} \\ (β^{#} - Δ β^{#}) \end{array}

（17）

Hao Wang, Lei Zhang. R-C Telescope Alignment Method Based on Astigmatism Correction of Symmetrical Field of View Misalignment[J]. Laser & Optoelectronics Progress, 2025, 62(2): 0211003

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