Fig. 1. Angular resolved scattering distribution under gaussian statistical distribution. (a) Different incident angles; (b) Different autocorrelation lengths; (c) Different surface roughness

Fig. 2. Angular resolved scattering distribution under fractal statistical distribution. (a) Different incident angles; (b) Different slopes; (c) Different surface roughness

Fig. 3. Angular resolved scattering distribution under Cauchy-Lorentz statistical distribution. (a) Different incident angles; (b) Different cutoff frequencies; (c) Different surface roughness

Fig. 4. Schematic of prediction method for surface characteristics parameters of ultra-smooth optical components. (a) Flowchart of prediction method; (b) Flowchart of graphical solution for the equation system

Fig. 5. The graphical method process for solving the system of equations in three iterations. (a) Surface scattering rate distribution for the first iteration (θ₁=5°); (b) Surface scattering rate distribution for the first iteration (θ₂=40°); (c) Result of the first iteration; (d) Surface scattering rate distribution for the second iteration (θ₁=5°); (e) Surface scattering rate distribution for the second iteration (θ₂=40°); (f) Result of the second iteration; (g) Surface scattering rate distribution for the third iteration (θ₁=5°); (h) Surface scattering rate distribution for the third iteration (θ₂=40°); (i) Result of the third iteration

Fig. 6. The relative error curves of predicted values for surface roughness and autocorrelation length of the elements under different surface characteristic parameters. (a) Relative error curves of predicted values for different surface roughness; (b) Relative error curves of predicted values for different autocorrelation lengths