Primary mirror segmentation for large optical telescopes: an inverse map projection approach.

Area of Science:

• Astronomy and Optical Engineering
• Large segmented-mirror telescope design

Background:

• Primary mirror segmentation is crucial for large telescope construction, impacting support, fabrication, and cost.
• Hexagonal tiling is effective for segmenting curved surfaces with specific solid angles.

Purpose of the Study:

• To present and unify three map projection-based approaches for primary mirror segmentation.
• To numerically verify the performance of these segmentation methods.

Main Methods:

• Conformal map projection for optimal local angle preservation and regularity.
• Equal-area map projection for zero area variation.
• Equidistant map projection to minimize segment circumscribed diameter.
• A novel compromise approach unifying the above methods.

Main Results:

• The conformal method offers superior regularity.
• The equal-area method ensures consistent segment area.
• The equidistant method optimizes segment size.
• The compromise approach allows for adjustable segmentation based on specific needs.

Conclusions:

• The presented map projection methods effectively segment large telescope primary mirrors.
• The study validates a scaling rule and provides insights into mirror segmentation mechanisms.
• These findings aid in the design and fabrication of advanced astronomical instruments.