Design of a direct vision spectrometer with a double Amici prism for smile correction

Traditional prism imaging spectrometers suffer from poor direct vision, low spectral linearity, and a large natural smile. Spurred by these limitations, this paper proposes a spectral imaging system based on a double Amici prism, for which the vector refraction law yields expressions for the prism's smile and keystone. Accurate calculations of the smile and keystone for the single and compound prisms are derived using MATLAB. The characteristic curve of a smile is drawn and verified through simulations, with the designed system's waveband ranging from 400 to 1000 nm, spectral resolution across the full waveband exceeding 12 nm, and the maximum smile and keystone values of 3.117 and 3.955 µm, respectively. Notably, the developed system is completely coaxial and meets the requirements of direct vision and smile correction. Furthermore, the new, to our knowledge, method, which combines the vector refraction law with MATLAB programming, is adopted, enabling quick and accurate determination of the smile characteristic of compound prisms. Overall, this paper has general significance for the design of the prism spectral imaging system for smile correction.