Research On Light Scattering Characteristics Of Random Rough Surfaces Based On BRDF

Light scattering phenomenon from random rough surfaces is one of the important issues in optical applications,which is directly related to the roughness of the material surface.The bidirectional reflectance distribution function(BRDF),as a physical quantity that effectively describes light scattering characteristics,has a wide range of applications in the fields of non-contact metrology,geophysical remote sensing,X-ray imaging,extreme ultraviolet(EUV)photolithography systems,and computer graphics scene rendering,especially in academic research and practical engineering applications related to stray light rejection for weak target detection in bright background.The prediction of light scattering characteristics of random rough surfaces has broad prospects for application,and there are various theories.The main problems currently existing are as follows:(1)Scattering theory is applicable to the scattering of ideal smooth,clean,reflective surfaces,ignoring the scattering effect caused by the actual surface defects and surface particulate contaminants,which leads to poor fit.(2)Scattering theory only considers the scattering effect of the central beam,ignoring the scattering effect of sub-beams around the center beam of the actual light source,which leads to poor fit.(3)There are currently many surface scattering models with complex forms and many parameters.Only a few empirical models are used in the simulation analysis of stray light.Therefore,the application of scattering models for the simulation and analysis of stray light in optomechanical system is an important issue.In addition,the influence of air scattering is also a major challenge in the actual test of optomechanical system stray light and BRDF.In view of the above problems,the main research work and innovation points are summarized as follows:1.Starting from the theoretical basis of random rough surface light scattering,this dissertation introduces the main surface statistical characteristics:height distribution function(HDF),root mean square(RMS)roughnessσ,power spectral density(PSD)function,autocovariance function(ACV),root mean square(RMS)slope m and main surface scattering functions:bidirectional reflectance distribution function(BRDF),angle resolved scattering(ARS)function.The Rayleigh-Rice vector perturbation theory and Harvey-Shack scalar scatter theory are deduced and their applicable ranges are also analyzed.2.Aiming at the problem that the classically generalized Harvey-Shack(GHS)scatter theory is only applicable to the ideal clean surface,neglecting the practical optical surface defects and pollutant scattering,an empirically modified generalized Harvey-Shack(MGHS)scatter model is proposed,which is based on the approximation of the GHS theory under smooth surface,adding an empirical correction factor associated with the practical material.Furthermore,by performing the inverse scattering,we make the scatter prediction at other incident angles from the finite surface metrology data.We use the smooth black mirror BRDF data at incident angles of 15°and 30°as sample,calculate and fit PSD function by superimposing two different K-correlation functions and make the scattering prediction and verification at the incident angles of 5°,15°,30°,and 45°using the MGHS model.The result shows that the MGHS model reduces the RMS error from less than 2%to less than 1%,and the relative peak error from less than 50%to less than 20%compared with the classical theory.3.Aiming at the problem that the classic Harvey-Shack scatter theory only considers the scattering effect of the central beam and as a scalar theory,it can not explain the polarization effect of scattered light,the Gaussian beam Harvey-Shack(GBHS)scatter model is proposed,which is based on the two-dimensional plane-wave decomposition of the three-dimensional converging-diverging Gaussian beam.It linearly superimposes the monochromatic plane-wave components propagating in different directions and can make the scattering prediction for random rough surface at any polarization state,any incident angle and azimuth angle.This scattering model is not only applicable to the fundamental mode Gaussian beam,but also valid for other higher-order modes.Taking the measured BRDF data of s-polarized Gaussian beam incident onto the smooth black mirror as the example,we summarized the effect of Gaussian beam waist radius w on the fitting error of GBHS model.The results show that:for small beam waist radius w(such as w=5μm),the fitting error of the GBHS model to the measured data is much smaller than that of the GHS theory,and with the increase of the incident angle,the gap between the two models becomes bigger.But as the beam waist radius w increases,the fitting error of the two models approaches gradually.At the same time,it is also found that the reflective polarization factor Q plays an important role in the fitting at small incident angles(less than 45°).4.Aiming at the problem that the existing scattering theories and models can not predict the scattering characteristics of all surfaces of unknown or complex materials well,the polynomial fitting model is proposed for surface scatter and internal bulk scatter of non-optical elements,which is based on the law that"the scattered radiance is shift-invariant in direction-cosine space".It can be used for the prediction of the scattering characteristics of commonly used substrate materials(such as the carbon fiber,the titanium alloy,and the aluminum alloy,etc)and after painting treatment.Taking the substrate of the titanium alloy treated with PNC matte black coating and the glass substrate treated with pineblack as examples,the detailed derivation is carried out,separately.The results show that:the RMS error is less than 0.1 when the incident angle is less than 70°and the relative RMS error is less than 0.5 when the incident angle is less than 85°for the first sample.The relative RMS error is less than 0.5 when the incident angle is less than 80°for the second sample.5.Aiming at various sources of scatter on the actual surface and the complex scattering mechanism,empirical scattering models commonly used in stray light simulation software are derived.Three-parameter Harvey model and ABg model are suitable for surface roughness of optical elements.Surface particle pollution model is based on Mie scattering.Surface defect(digs and scratches)model is based on the superposition of geometric refraction and diffraction.Aiming at the difference in the application of the scattering evaluation parameter total integral scattering(TIS)in different fields and the confusion with total scattering(TS),the differences and connections in definition,theoretical calculation and experimental measurement are analyzed,and it is concluded that:total backscattering(TS_b)is calculated in the same way as the TIS in stray radiation,which is the ratio of the surface hemispherical scattering power to the incident power,that is,the diffuse reflectance,while the scattering theory defines the TIS as the ratio of the hemispherical scattering power to the total reflection power.6.Aiming at the problem of testing accuracy is not so good due to air scattering in the point source transmittance(PST)test system for stray light and BRDF scatter system,a continuous spectrum air scattering model is proposed,which is based on the Monte Carlo algorithm,through utilizing the normalized weight of different bands obtained after source radiance calibration and acquisition of spectral response curve of the detector,and the influence of ground air scattering in the stray light test is quantitatively calculated.The model is verified by laboratory test chamber with two air cleanliness levels of ISO 7 and ISO 6,and off-axis angles from 35°to 90°.The results show that:the relative RMS deviation of the full-band simulation from the measurement result is 3.72%in Mie scattering and 24.1%in Rayleigh scattering,showing excellent agreement between measured and predicted values for a 26°full-angle baffle when illuminated by a 550 mm diameter collimated beam.This model is conducive to eliminating the influence of air scattering from the PST or BRDF test results in subsequent research and it is of great significance for the improvement of the test threshold.