Multi-Parameter Wavelength Characterization of Array Spectrometers Under Near-Limit Sampling Conditions

Accurate wavelength characterization is essential for high-precision spectral measurements, particularly in applications such as solar-induced chlorophyll fluorescence (SIF) retrieval, where weak spectral signals are highly sensitive to instrument performance. In array spectrometers, characteristic wavelengths can be defined by peak, center, or centroid positions, whereas spectral resolution is commonly represented by full width at half-maximum (FWHM) or equivalent rectangular width (ERW). This study systematically investigates the influence of sampling conditions on wavelength characterization using a crossed Czerny-Turner array spectrometer operating over the 650-800 nm spectral range. The concept of sampling ratio is employed to define near-limit sampling conditions, in which monochromatic spectral peaks are represented by only 2-5 detector pixels. Experimental results show that the spectrometer predominantly operates within this regime. Under these conditions, significant discrepancies arise among different characteristic wavelength definitions owing to the combined effects of discrete sampling and spectral peak shape. Peak-based wavelength estimation is primarily affected by local sampling variations, whereas centroid-based definitions are more sensitive to energy distribution and peak asymmetry. Furthermore, a systematic divergence between ERW and FWHM demonstrates that spectral resolution metrics depend not only on geometric peak width but also on spectral energy distribution, particularly under non-ideal imaging conditions. These results show that wavelength characterization should be regarded as a coupled problem involving sampling conditions, spectral peak representation, and resolution metrics rather than as independent parameters. The proposed multi-parameter characterization approach establishes a practical framework by clarifying the relationships among sampling ratio, characteristic wavelength definitions, and spectral resolution, introducing two deviation metrics to quantify inconsistencies among wavelength definitions, and revealing the complementary physical significance of FWHM and ERW from geometric and energy-distribution perspectives. This approach provides a physically interpretable basis for wavelength calibration, spectral resolution evaluation, and performance assessment of array spectrometers operating under near-limit sampling conditions.