Single-order diffraction gratings with quasi-random structures are effective optical elements in suppressing harmonics contamination. However, background intensity fluctuations introduced by quasi-random structures may affect the measurement of the spectra and the fluctuations lack quantitative description. A unified theoretical method is provided to describe quasi-random diffraction structures with arbitrary distribution functions and an arbitrary number of microstructures. The effect of the number of microstructures and distribution functions on the level of background fluctuations is evaluated. This work provides important guidance for the design and optimization of single-order diffraction gratings, which are attractive for spectral analysis and monochromator applications in synchrotron beam lines.
