Analytical design of an Offner imaging spectrometer

Area of Science:

• Optical Engineering
• Spectroscopy
• Instrument Design

Background:

• Offner configurations are widely used for imaging spectrometers.
• Achieving high optical quality, especially at high speeds, often requires complex aberration-corrected gratings.
• Residual aberrations, particularly astigmatism, limit system performance.

Purpose of the Study:

• To present an analytical design method for three-concentric-mirror (Offner) imaging spectrometers.
• To enable rapid design of high-optical-quality spectrometers.
• To minimize dominant aberrations like astigmatism without specialized gratings.

Main Methods:

• Calculating meridional and sagittal images of off-axis object points.
• Deriving meridional and sagittal curves across the spectral range.
• Making these curves tangent at a specific wavelength to reduce astigmatism.

Main Results:

• Achieved RMS spot radii less than 5 µm.
• Enabled designs for speeds as high as f/2.5.
• Covered a wavelength range of 0.4-1.0 µm.
• Demonstrated the design process with a free interactive optical design tool.

Conclusions:

• The presented analytical design method is effective for Offner imaging spectrometers.
• High optical quality and speed are achievable without aberration-corrected gratings.
• The method significantly reduces astigmatism, a key residual aberration.