Pre-shuttle lidar system research

Included are the results of the initial phase of a simulation study in connection with photomultiplier tubes (PMT) and associated networks and an analytical study of atmospheric physics (including multiscattering) leading to modeling studies in connection with differential absorption lidar (DIAL) observations. This effort was in support of the ER-2 aircraft DIAL projects

Single-element rotating-polarizer ellipsometer for film-substrate systems

A novel and very simple ellipsometer for the characterization of film-substrate systems that employs one rotating optical element (a polarizer) is proposed. The ellipsometer is based on detecting the angles of incidence at which a film-substrate system has equal amplitude attenuations for light polarized parallel (p) and perpendicular (s) to the plane of incidence. At a certain wavelength, the film thickness of the filmsubstrate system has to lie within permissible-thickness bands (PTB) for the technique to apply

Brewster and pseudo-Brewster angles of uniaxial crystal surfaces and their use for determination of optical properties

Brewster and pseudo-Brewster angles are defined for surfaces of transparent and absorbing uniaxial crystals parallel and perpendicular to the optic axis. Two Brewster angles of a transparent uniaxial crystal surface parallel to the optic axis, measured when the optic axis is oriented perpendicular and parallel to the plane of incidence, readily determine the ordinary and extraordinary indices No and Ne. No and Ne can also be obtained from two Brewster angles measured on a surface perpendicular to the optic axis in contact with two media of different refractive indices. Conditions for the existence of two Brewster angles are discussed. The complex No and Ne of an absorbing uniaxial crystal can be derived from pseudo-Brewster-angle and minimum-reflectance data obtained in two symmetrical orientations of a surface parallel to the optic axis. An approximate, but accurate, explicit inversion procedure is presented for this purpose

Constant-psi constant-delta contour maps: applications to ellipsometry and to reflection-type optical devices

Constant-psi constant-delta contour maps in the reduced angle-of-incidence-film-thickness plane that are useful in ellipsometry and in design of reflection-type optical devices are discussed. As a specific example, a contour map is given for the SiO2-Si film-substrate system at the 6328-Å He-Ne laser wavelength

Constant-psi constant-delta contour maps: applications to ellipsometry and to reflection-type optical devices

Constant-psi constant-delta contour maps in the reduced angle-of-incidence-film-thickness plane that are useful in ellipsometry and in design of reflection-type optical devices are discussed. As a specific example, a contour map is given for the SiO2-Si film-substrate system at the 6328-Å He-Ne laser wavelength

Principal angle, principal azimuth, and principal-angle ellipsometry of film-substrate systems

When the film thickness is considered as a parameter, a system composed of a transparent film on an absorbing substrate (in a transparent ambient) is characterized by a range of principal angle ø¯min ≤ ø¯ ≤ ø¯max over which the associated principal azimuth ψ¯ varies between 0° and 90° (i.e., 0° ≤ ψ¯ ≤ 90°) and the reflection phase difference Δ assumes either one of the two values: +π/2 or −π/2. We determine the principal angle ø¯(d) and principal azimuth ψ¯(d) as functions of film thickness d for the vacuum-SiO2-Si system at several wavelengths as a concrete example. When the film thickness exceeds a certain minimum value, more than one principal angle becomes possible, as can be predicted by a simple graphical construction. We apply the results to principal-angle ellipsometry. (PAE) of film-substrate systems; the relationship between ø¯ and ψ¯ during film growth is particularly interesting

Inversion of the nonlinear equations of reflection ellipsometry for uniaxial crystals in symmetrical orientations

The complex ordinary (No) and extraordinary (Ne) refractive indices of an absorbing uniaxial crystal can be determined using reflection ellipsometry. The measurements are taken with the optic axis parallel and perpendicular to the crystal’s surface. The equations obtained are solved without resort to iterative methods; No and Ne are determined separately. Sixteen solution sets (No, Ne) are obtained and the correct solution can be easily identified. We present an optimum angle of incidence that minimizes the relative errors in No and Ne

Ellipsometric function of a film-substrate system: Applications to the design of reflection-type optical devices and to ellipsometry

The ratio ρ = Rp/Rs of the complex amplitude-reflection coefficients Rp and Rs for light polarized parallel (p) and perpendicular (s) to the plane of incidence, reflected from an optically isotropic film-substrate system, is investigated as a function of the angle of incidence ϕ and the film thickness d. Both constant-angle-of-incidence contours (CAIC) and constant-thickness contours (CTC) of the ellipsometric function ρ(ϕ,d) in the complex ρ plane are examined. For transparent films, ρ(ϕ,d) is a periodic function of d with period Dϕ that is a function of ϕ. For a given angle of incidence ϕ and film thickness d (0 ≤ ϕ ≤ 90, 0 ≤ d ≤ Dϕ), the equispaced linear array of points (ϕ,d + mDϕ) (m = 0, 1, 2,…) in the real (ϕ,d) plane is mapped by the periodic function ρ(ϕ,d) into one distinct point in the complex ρ plane. Conversely, for a given film-substrate system, any value of the ellipsometric function ρ can be realized at one particular angle of incidence ϕ and an associated infinite series of film thicknesses d, d + Dϕ, d + 2Dϕ,.... This analysis leads to (1) a unified scheme for the design of all reflection-type optical devices, such as polarizers and retarders, (2) a novel null ellipsometer without a compensator, for the measurement of films whose thicknesses are within certain permissible ranges, and (3) an inversion procedure for the nonlinear equations of reflection ellipsometry that separates the determination of the optical constants (refractive indices and extinction coefficients) of the film and substrate from the film thickness. Extension of the work to absorbing films is discussed

Polarizer-surface-analyzer null ellipsometry for film-substrate systems

Single-pass polarizer-surface-analyzer null ellipsometry (PSA-NE) can be used to characterize film-substrate systems, provided that the film thickness lies within one of a set of permissible-thickness bands (PTB). For a transparent film on a transparent or absorbing substrate, the PTB structure consists of a small number of finite-bandwidth bands followed by a continuum band that extends from a film thickness of about half the wavelength of light to infinity. We show that this band structure is a direct consequence of the periodicity of the ellipsometric function ρ (the ratio Rp/Rs, of the complex amplitude-reflection coefficients for the p and s polarizations) with film thickness. The PTB for the SiO2-Si film-substrate system at He-Ne laser and mercury spectral lines are calculated. The angles of incidence for PSA-NE ona film-substrate system with known film thickness are easily predicted with the help of a graphical construction in the angle of incidence-vs-thickness φdplane. PSA-NE is generally applicable to the determination of both film thickness and optical properties of a film-substrate system. The procedure for its application to the special, but important, case of film-thickness measurement alone, when the optical properties are known, is given and is checked experimentally by the determination of the oxide-film thickness on Si wafers. In an automated form, PSA-NE can be a serious competitor for interferometric reflectance methods