Numerical Modeling and Spectral Balancing of an LED-Based Reflectance Spectrophotometer (360–760 nm)

Mikhail E. Parfyonov orcid (Login required)
Samara National Research University, Russian Federation

Dmitry N. Artemyev
Samara National Research University, Russian Federation


Paper #9513 received 15 Feb 2026; revised manuscript received 6 Apr 2026; accepted for publication 6 Apr 2026; published online 29 Jun 2026.

DOI: 10.18287/JBPE26.12.020311

Abstract

This study presents numerical modeling and constrained spectral balancing of a compact LED-based reflectance spectrophotometer operating in the 360–760 nm range. The detected spectral response was modeled as a weighted superposition of individual LED emission spectra explicitly multiplied by the wavelength-dependent detector quantum efficiency QE(λ). In the baseline configuration with unit weights, the detected spectrum exhibited strong modulation, characterized by a coefficient of variation CV of 41.5%, peak-to-peak deviation of 131%, and maximum-to-minimum ratio of 4.24. Spectral balancing was formulated as a constrained minimization of the normalized variance over a 0.5 nm wavelength grid using a differential evolution algorithm with bounded non-negative weights. The optimized configuration reduced CV to 8.36%, peak-to-peak deviation to 32.2%, and max/min ratio to 1.39, corresponding to an approximately 80% reduction in global spectral non-uniformity as quantified by variance-based metrics. The proposed approach provides a quantitative methodology for spectral equalization in multi-LED reflectance spectrophotometers.

Keywords

reflectance spectrophotometry; diffuse reflection; optical design; CCD detector; constrained optimization

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