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Combining the mathematical relationships between the grating wavefront and surfaces with the spatial relationships between the two grating wavefront, a mathematical model of the mosaicking errors is established to mosaic gratings. The five-dimensional mosaicking errors will respectively be calculated and then removed by the adjustment mechanisms. Mosaicking experiments are performed by using two gratings. First, by using zeroth order, the longitudinal offset is calculated and removed. Second, by using the diffraction order, the in-plane angle and grating spacing are calculated and removed, while the tip and tilt angles are calculated and removed. And then a mosaic grating is obtained.

Spatial heterodyne Raman spectroscopy is a spectroscopic detection technique that is particularly suitable for Raman measurements. The spectral range of traditional spatial heterodyne Raman spectrometer (SHRS) is limited by its spectral resolution and the number of detector elements. We propose an SHRS with an echelle-mirror structure that employs multiple diffraction orders to achieve a broad spectral coverage and high spectral resolution simultaneously. This SHRS is used to obtain the Raman spectra of organic liquids, inorganic solid targets, and mixed targets. Observations of aqueous solutions, and minerals are presented. In addition, anti-Stokes Raman shifts are also presented. The proposed SHRS technique shows good performance for broadband, high-resolution Raman measurements.