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.