Algebraic ray trace analysis of spatial heterodyne spectrometers

Area of Science:

• Optics and Spectroscopy
• Instrument Design
• Computational Physics

Background:

• Spatial heterodyne spectrometers (SHS) are powerful tools for high-resolution spectral measurements.
• Accurate prediction of SHS performance is crucial for instrument design and optimization.
• Existing analytical models may not cover all SHS configurations comprehensively.

Purpose of the Study:

• To derive general, approximate algebraic formulas for key performance parameters of various SHS configurations.
• To provide a simplified analytical framework for understanding SHS behavior.
• To establish a basis for rapid design and analysis of SHS instruments.

Main Methods:

• Development of algebraic ray tracing techniques for different SHS configurations.
• Analysis of Michelson, all-reflective, and field-widened SHS designs.
• Validation of derived formulas against exact numerical ray tracing using optical design software.

Main Results:

• General, approximate formulas were derived for resolving power, fringe localization plane, and admissible off-axis angle.
• Formulas were developed for Michelson, all-reflective, and field-widened SHS configurations.
• The derived algebraic formulas showed good agreement with numerical ray tracing results.

Conclusions:

• The developed algebraic ray tracing approach provides accurate approximations for SHS performance.
• These formulas offer a valuable tool for the preliminary design and analysis of various SHS configurations.
• The findings facilitate more efficient development of advanced spectroscopic instruments.