Principal Mueller matrix of reflection and scattering measured for a one-dimensional rough surface

Reflectance R, ellipsometric parameters (c, D), depolariza- tions D, and cross-polarized depolarization Dv of specular reflection, and scattering by a rough stainless steel surface are measured using a null ellipsometer. The three polarization elements (Px ,Py ,Pz) of a principal Mueller matrix are obtained from D, c, and D. The measured c and D of specular reflection for incident angle u.70 deg are fit to the Fresnel equations to obtain n and k. The measured specular R(u) is fit to Beck- mann's scattering theory to obtain the root mean square (rms) rough- ness s. The fits (5 392 nm) is of the same order as the stylus measured s (5 484 nm). The D of specular reflection is small ( , 0.07). Scattering measurements are made with variable sample orientation at a detection direction 40 deg backward from the incident direction. The Dv of scatter- ing is very small (, 0.002). The values of c, D, Px , Pz , and Dv of scattering are about constant for an off-specular angle (OSA) within 660 deg and can be explained by the facet model with single scattering. The measured bidirectional reflectance distribution function (BRDF) in this region can be converted to slope angle distribution with OSA52 slope angle. The values of c, D, Px , Pz , and Dv of scattering deviate signifi- cantly and symmetrically from a constant level for uOSAu.60 deg, for which the simple facet model with single scattering does not apply.

[1]  P. Beckmann,et al.  The scattering of electromagnetic waves from rough surfaces , 1963 .

[2]  H. E. Bennett,et al.  Relation between Surface Roughness and Specular Reflectance at Normal Incidence , 1961 .

[3]  G. Videen,et al.  Polarized light scattered from rough surfaces , 1992 .

[4]  Soe-Mie F. Nee Birefringence characterization using transmission ellipsometry , 1992, Optics & Photonics.

[5]  H. Davies The reflection of electromagnetic waves from a rough surface , 1954 .

[6]  W. Bickel,et al.  Polarized light-scattering matrix elements for select perfect and perturbed optical surfaces. , 1987, Applied optics.

[7]  Soe-Mie F. Nee,et al.  Effects of near-specular scattering on polarimetry , 1994, Optics & Photonics.

[8]  John G. Webster,et al.  The Measurement, Instrumentation and Sensors Handbook , 1998 .

[9]  J. Bennett,et al.  Introduction to Surface Roughness and Scattering , 1999 .

[10]  E Marx,et al.  Autocorrelation functions from optical scattering for one-dimensionally rough surfaces. , 1993, Applied optics.

[11]  S. Nee,et al.  Depolarization and principal mueller matrix measured by null ellipsometry. , 2001, Applied optics.

[12]  H. E. Bennett,et al.  Scattering from Infrared Missile Domes , 1978 .

[13]  K. O'Donnell,et al.  Measurements of light scattering by a series of conducting surfaces with one-dimensional roughness , 1994 .

[14]  Eugenio R. Mendez,et al.  Experimental study of scattering from characterized random surfaces , 1987 .

[15]  Thomas Rinder,et al.  Polarized light-scattering measurements of polished and etched steel surfaces , 2000, SPIE Optics + Photonics.

[16]  A. Kostinski Depolarization criterion for incoherent scattering. , 1992, Applied optics.

[17]  J. Stover Optical Scattering: Measurement and Analysis , 1990 .

[18]  R. Azzam,et al.  Ellipsometry and polarized light , 1977 .

[19]  L F Johnson,et al.  Slope distribution of a rough surface measured by transmission scattering and polarization. , 2000, Applied optics.

[20]  Soe-Mie F. Nee Polarization characterization for target surfaces , 1995, Defense, Security, and Sensing.

[21]  Soe-Mie F. Nee,et al.  Effects of incoherent scattering on ellipsometry , 1992, Optics & Photonics.

[22]  E Marx,et al.  Direct and inverse problems for light scattered by rough surfaces. , 1990, Applied optics.

[23]  S. Nee,et al.  Ellipsometric view on reflection and scattering from optical blacks. , 1992, Applied optics.

[24]  S M Nee Error analysis of null ellipsometry with depolarization. , 1999, Applied optics.

[25]  Soe-Mie F. Nee,et al.  Error reductions for a serious compensator imperfection for null ellipsometry , 1991 .

[26]  Tsu-Wei Nee,et al.  Polarization of scattering by rough surfaces , 1998, Optics & Photonics.

[27]  Soe-Mie F. Nee,et al.  Polarization of specular reflection and near-specular scattering by a rough surface. , 1996 .

[28]  A. G. Navarrete,et al.  Statistics of the polarization properties of one-dimensional randomly rough surfaces , 1995 .

[29]  S. Nee,et al.  Depolarization and retardation of a birefringent slab. , 2000, Journal of the Optical Society of America. A, Optics, image science, and vision.

[30]  Michael E. Knotts,et al.  Stokes matrix of a one-dimensional perfectly conducting rough surface , 1992 .

[31]  Marion L. Scott,et al.  Design and construction of three infrared ellipsometers for thin film research , 1982 .

[32]  Soe-Mie F. Nee,et al.  Effects of depolarization of polarimetric components on null ellipsometry , 1998 .

[33]  Soe-Mie F. Nee,et al.  Characterization of optical blacks by infrared ellipsometry and reflectometry , 1990, Optics & Photonics.

[34]  L. Tanner,et al.  The use of laser ligth in the study of metal surfaces , 1976 .

[35]  H. E. Bennett Scattering Characteristics Of Optical Materials , 1978 .

[36]  G. Kattawar,et al.  Relationships between elements of the Stokes matrix. , 1981, Applied optics.

[37]  T V Vorburger,et al.  Light-scattering measurement of the rms slopes of rough surfaces. , 1991, Applied optics.

[38]  S. Nee,et al.  Characterization for imperfect polarizers under imperfect conditions. , 1998, Applied optics.