Abstract

Spectral resolution is a key parameter of a spectrometer. Typically, the Rayleigh criterion is used to evaluate spectral resolution; however, it is not applicable to a single-lens-based spectrometer, as its principle is different from that using a prism or grating. Therefore, this work proposes that a method resolution is a key parameter to evaluate spectral resolution by exploiting the concept of focus depth. Accordingly, the spectral resolution is determined using three factors, namely, aperture factor ${\rm F}$ of the lens, pixel size $p$ of the charge-coupled device, and the derivative of the rate of change of focal length with respect to wavelength $f^\prime (\lambda)$. The proposed method is verified by simulations with the following lens parameters: a diameter of 50.8 mm, focal length of 200 mm at 587.6 nm, and ${\rm F} = {3.94}$. The calculated and simulated spectral resolution values are, respectively, 1.7 nm and 1.2 nm at 480 nm. Based on an analysis of the influences of ${\rm F}$, $p$, and $f^\prime (\lambda)$ on the spectral resolution, increasing $f^\prime (\lambda)$ or decreasing both ${\rm F}$ and $p$ might improve the spectral resolution. Finally, the proposed method is validated via experiments for lenses with different ${\rm F}$ values as well as materials, and we determine their spectral resolutions; these results are observed to be similar to the calculated values.

© 2021 Optical Society of America

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