The geometric optical aberration theory of diffraction gratings

Area of Science:

• Optics
• Spectroscopy
• Geometrical Optics

Background:

• Spectral image formation by gratings is well-studied using geometrical optics.
• Existing models often use fixed pupil coordinate orientations and limited grating surface shapes.

Purpose of the Study:

• To develop a generalized theory for spectral image formation by equally spaced gratings.
• To investigate the impact of variable pupil coordinate orientation and general grating surface shapes.
• To analyze aberrations and derive conditions for optimal grating design.

Main Methods:

• Utilized geometrical optics with a focus on variable pupil coordinate orientation.
• Considered general series expansions for grating surface shapes.
• Analyzed deviations from perfect imaging, including astigmatism, coma, and spherical aberration.
• Included grazing incidence and off-plane mountings.

Main Results:

• Derived expressions for the position, astigmatism, and aberrations of spectral images.
• Quantified the length, radius of curvature, and width of astigmatic spectral lines.
• Identified conditions for optimal slit slant angle and grating surface shape for aberration minimization.

Conclusions:

• The generalized theory provides a comprehensive framework for understanding spectral image formation.
• The findings enable optimized design of diffraction gratings for improved spectral resolution and image quality.
• Ray tracing validation confirms the accuracy of the derived theoretical results.