Alignment Method of R-C Telescope Based on Astigmatism Correction

Reflecting telescopes are widely used in various fields due to their advantages such as no chromatic aberration and easy lightweighting. Among them, double-reflecting telescopes are the most commonly used. The R-C telescope is an important type of double-reflecting telescope. Its alignment process is crucial to the imaging quality, but currently, it mostly relies on experience in engineering, resulting in high costs.

1. Aberration Field of Double-Reflecting Telescope

i. Coordinate System and Symbol Definition: When an optical surface deviates from its theoretical position, there are six forms of decentration and tilt.

schematic diagram of introducing decenter and tilt in system

ii. Coma and Astigmatism: Based on the vector wave aberration theory, the wave aberration of a double - reflecting telescope includes coma and astigmatism components. The third - order coma and third - order astigmatism of a misaligned system are related to the decentration and tilt of the secondary mirror.

2. Analysis of the Alignment Method of R-C Telescope: The traditional alignment method that takes the coma in the on - axis field of view as a reference cannot ensure that both the on - axis and off - axis fields of view achieve the best imaging quality simultaneously. If the coma in the on - axis field of view is first adjusted to 0, the relationship between the decentration and tilt of the secondary mirror can be determined at this time. Then, adjust the astigmatism in the off - axis symmetric field of view. By selecting off - axis fields of view in the xoz plane and yoz plane to observe and adjust the astigmatism, simultaneous correction can be achieved through multiple iterations.

flow chart of alignment process for RC telescope

3. Simulation Alignment Experiment: Taking an R - C telescope with specific parameters as an example, randomly introduce the misalignment amount of the secondary mirror. First, adjust the decentration of the secondary mirror to make the coma in the on - axis field of view 0. Then, adjust the decentration and tilt of the secondary mirror in the yoz plane and xoz plane to make the astigmatism in the off - axis field of view symmetric. After 3 iterations, the secondary mirror is adjusted to the theoretically designed position, verifying the feasibility of the alignment method.

system wave aberration of different fields

4. Alignment Experiment and Results: Apply the alignment method verified by simulation to the actual alignment of the R - C telescope. Take the primary mirror as a reference, fix the secondary mirror on a six - dimensional adjustment frame, and use a 4D interferometer for inspection. After alignment, the wave aberration of the on - axis field of view of the system is 0.0730λ, and the wave aberration of the off - axis symmetric field of view is approximately 0.08λ, meeting the usage requirements.

5. Conclusion: The alignment method proposed based on the vector wave aberration theory has been verified by simulation and actual alignment experiments. For a misaligned R - C telescope, the alignment can be completed through 3 iterations. After alignment, the wave aberration of both the on - axis and off - axis fields of view of the system meets the usage requirements.