Method for evaluating spectral resolution based on a single-lens spectrometer

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 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^'(λ). 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 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 F, p, and f^'(λ) on the spectral resolution, increasing f^'(λ) or decreasing both F and p might improve the spectral resolution. Finally, the proposed method is validated via experiments for lenses with different F values as well as materials, and we determine their spectral resolutions; these results are observed to be similar to the calculated values.