Laser energy absorption prediction of silicon substrate surface from a mid- and high-spatial frequency error

Additional laser energy absorption of optical elements limits the further development of high-energy laser systems. In engineering, inexpensive and precise absorption test technology is essential. We attempt to predict energy absorption via surface spatial error value based on the roughness-induced absorption (RIA) theory. However, the absorption coefficients cannot match roughness values measured with an atomic force microscope or white light interferometer. We find three influencing factors and optimize the definition of RIA to spatial error-induced absorption (SEIA). SEIA is proportional to δ² of a mid- and high-spatial frequency error in a certain frequency range. This range depends on laser diameter, wavelength, and coating. Excluding the absorption induced by fabrication defects, the total absorption can be classified into SEIA and background absorption (BGA). BGA is decided by material and process technology, which can be obtained by calculations. The sum of SEIA and BGA is predictable because both can be estimated. The substrate absorption of high-energy optics can be semi-quantificationally predicted. SEIA provides a new angle to research element-absorbed laser energy for high-power laser technologies.