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n-Hindle-sphere arrangement with an exact ray trace for testing hyperboloid convex mirrors
M E Percino-Zacarias1, A Cordero-Dávila
1Instituto Nacional de Astrofisica, Optica y Electrónica, Apdo. Postal 216, CP 72000 Puebla, Pue. México. ferliz2696@aol.com
Applied Optics
|March 8, 2008
Summary
This study presents exact ray tracing calculations for Hindle sphere dimensions, crucial for small f-number convex hyperboloid mirrors where paraxial theory fails. The generalized equations and experimental results aid in designing advanced telescope optics.
Area of Science:
- Optics and Astronomy
- Telescope Design
Background:
- Paraxial theory is insufficient for convex hyperboloid mirrors with small f-numbers.
- Hindle spheres offer a solution for specific optical designs.
Purpose of the Study:
- To determine dimensions for one or two Hindle spheres using exact ray tracing.
- To generalize equations for 'n' Hindle spheres for further dimension reduction.
- To validate calculations with experimental results.
Main Methods:
- Exact ray tracing calculations.
- Generalization of equations for multiple Hindle spheres.
- Experimental validation for the Large Milimetric Telescope.
Main Results:
- Precise dimensions for Hindle spheres were calculated.
- The generalized 'n' Hindle sphere equations allow for greater dimension reduction.
- Experimental results confirmed the accuracy of the calculations.
Conclusions:
- Exact ray tracing is essential for accurate Hindle sphere design with small f-numbers.
- The generalized equations provide a scalable method for optical mirror design.
- The study validates a novel approach for advanced telescope mirror fabrication.
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