Three Criteria of M-Type Spectrometers for Engineering

Researchers frequently utilize the method of optical initial structure (MOIS) of Czerny-Turner (C-T) spectrometers for aberration-correction studies based on the coma-free equation. While effective, this method has limitations: small numerical apertures at slits (0.05-0.07) hinder weak signal detection; V or W-shaped variations in Airy disk across wavelengths; optical resolution depends on the radius of the collimating lens may not match detector resolution; and sequence patterns based on the spot diagrams cannot simulate the full width at half maximum (FWHM) under discrete sampling. To address these issues, using ray tracing and imaging equations, three criteria are proposed: luminous flux and aberration balance (LFAB), Airy disk variation at imaging points (ADVI), and optical-detector resolution matching (ORDR). A verification system with a 500-750 nm wavelength range and 0.4 nm resolution was designed. Results show that designing spectrometers based on these criteria increases the slit's numerical aperture to 0.11 while controlling aberrations. After optimization, the tangential Airy disk size decreased by 28% with variations within 3 μm. Discrete sampling indicates FWHM pixel errors remain within 1/2 pixel of the theoretical value, and FWHM is at least 2.5 pixels, satisfying stricter sampling requirements beyond Nyquist. Optimization only involves adjusting the image plane by 0.017 mm axially, 0.879 mm off-axis, and 0.48° eccentricity. This research strengthens spectrometer design theory and improves practical applications.