Characterization of power spectral density of optical surface

Using the Si substrate and the HfO2 single layer as the examples, the power spectral density (PSD) of the optical surface was calculated and characterized. First, the method that calculates the 1D power spectral density(PSD1D), 2D power spectral density(PSD2D) and isotropic power spectral density (PSDISO) was introduced. Then, the surface morphologies of the Si substrate and the HfO2 single layer were measured using atomic force microscopy with four scan areas, for example, 1 m1 m, 5 m5 m, 10 m10 m, 20 m20 m. Using a MATLAB program, the PSDISOs of the different scan area were calculated. And the PSDISO-Combined over a larger spatial frequency range was given using the geometric mean of these PSDISOs. The result shows that the PSDISO-Combined of Si substrate before and after HfO2 coating were similar for the low spatial frequency region but quite different for the middle and high frequency region. The poly-crystallized microstructure of the HfO2 coating is the main reason for the observed PSD difference between the Si substrate and the HfO2 coating. The ISO and STD were calculated and compared. The results are quite similar, which proves the correctness of the proposed method for the PSD calculation.