Yang Zhaoqing, Xue Meng, Guo Hanming
School of Optical-Electrical and Computer Engineering, University of Shanghai for Science and Technology, Shanghai 200093, China.
Sensors (Basel). 2025 Apr 12;25(8):2439. doi: 10.3390/s25082439.
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.
研究人员经常使用 Czerny-Turner（C-T）光谱仪的光学初始结构方法（MOIS）进行基于无彗差方程的像差校正研究。虽然这种方法有效，但也存在局限性：狭缝处的数值孔径较小（0.05 - 0.07），阻碍了弱信号检测；艾里斑在不同波长下呈 V 形或 W 形变化；光学分辨率取决于准直透镜的半径，可能与探测器分辨率不匹配；基于光斑图的序列模式在离散采样下无法模拟半高宽（FWHM）。为了解决这些问题，利用光线追迹和成像方程，提出了三个标准：光通量与像差平衡（LFAB）、成像点处艾里斑变化（ADVI）以及光学 - 探测器分辨率匹配（ORDR）。设计了一个波长范围为 500 - 750 nm 且分辨率为 0.4 nm 的验证系统。结果表明，基于这些标准设计光谱仪可将狭缝的数值孔径提高到 0.11，同时控制像差。优化后，切向艾里斑尺寸减小了 28%，变化在 3μm 以内。离散采样表明 FWHM 像素误差保持在理论值的 1/2 像素以内，且 FWHM 至少为 2.5 像素，满足了超出奈奎斯特的更严格采样要求。优化仅涉及将像平面轴向调整 0.017 mm、离轴调整 0.879 mm 和偏心调整 0.48°。本研究强化了光谱仪设计理论并改善了实际应用。
