Speckle spectrometers based on disordered media have shown great prospects and attracted more and more attention. To obtain a larger bandwidth and higher light-energy utilization ratio, a novel speckle spectrometer scheme is proposed based on a random pixelated grating. The speckle generation mechanism of the random pixelated grating is derived by using the diffraction and Fourier transform theory, and the speckle–spectral correlation properties are analyzed through numerical simulation. The influences of system parameters, such as variation ranges of grating periods and orientations, lens focal length, grating pixel size, and pixel number, are investigated. According to the simulation results, the speckle spectrometer system is optimized, and a spectral resolution of up to 0.01 nm can be achieved.
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