[The analysis of the sampling modulation transfer function and the influence on the Gaussian spectra]

Area of Science:

• Optics and Photonics
• Spectroscopy
• Detector Physics

Context:

• Dispersive spectrometers rely on photoelectric detectors, whose sampling parameters critically influence overall performance.
• Understanding the discrete sampling process of photoelectric detector arrays is essential for optimizing spectrometer accuracy.
• Spatial frequency, pixel width, and initial phase impact sampling results in the frequency domain.

Purpose:

• To establish a sampling model for photoelectric detector arrays in dispersive spectrometers.
• To analyze the influence of spatial frequency, pixel width, and initial phase on sampling outcomes.
• To derive a general expression for the sampling modulation transfer function and propose an average sampling modulation transfer function for practical applications.

Summary:

• A sampling model was developed, and the effects of spatial frequency, pixel width, and initial phase were analyzed in the frequency domain.
• A general expression for the sampling modulation transfer function was derived using an integral function, leading to the concept of an average sampling modulation transfer function.
• The average aliasing error was quantified, and a critical spectrum width value was proposed for precise spectrum restoration, aiding spectrometer design.

Impact:

• The proposed average sampling modulation transfer function simplifies practical applications by eliminating initial phase effects.
• The study provides a functional expression for the modulation transfer function of the entire system for typical Gaussian spectra.
• The identified critical value for spectrum width offers crucial guidance for the design and fabrication of high-performance dispersive spectrometers.