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

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

Morphometric parameters and histological study of the filum terminale of adult human cadavers and magnetic resonance images

Background: Morphology and histology of filum terminale (FT) has a role in the pathophysiology of tethered cord syndrome (TCS). This research was implemented to investigate the morphometric parameters and histological structure of normal FT in adult human cadavers and magnetic resonance imaging (MRI) scans to correlate them with the pathophysiology of TCS.   Materials and methods: Twenty five adult human cadavers (15 males, 10 females) and 100 MRI echo scans of lumbosacral region (50 males and 50 females), were used in this study. MRI patients were divided into 21–40 and 41–60 age groups. The cadavers were dissected at the prone position to explore their fila. The length of FT, filum terminale internum (FTI), filum terminale externum (FTE), vertebral level of beginning, dural piercing and termination of FT, and the initial, midpoint, and mid-FTE diameters were determined. Four segments were excised from lower conus, upper, middle, and lower thirds of FT. The specimens were processed for light microscopic examination. Statistical analysis was done for these parameters.   Results: MRI morphometrical parameters of FT, except FTI length, revealed no age effect or sex differences, where length of FTI, FTE, initial diameter, level of conus medullaris termination (CMT) and dural sac termination (DST) were 174.1 ± 16.8, 75.8 ± 9.5, 1.6 ± 0.21, L1-2 and S2U in males and 166.9 ± 18.9, 74.1 ± 9.3, 1.53 ± 0.25, L1-2 and S2M vertebrae in females, respectively. However, non-significant sex difference was observed in morphometric parameters of cadaveric FT, where length of FTI and FTE, initial diameter, CMT and DST levels were 164.2 ± 11.6, 76.7 ± 8.1, 1.7 ± 0.14, L1L and S2U vertebrae in males and 159.2 ± 10.1, 71.02 ± 7.3, 1.6 ± 0.29, L1L and S2U in females, respectively. Moreover, CMT below L2 vertebra was seen in 5% of MRI scans and 8% of cadavers. Also, the initial diameter of FT > 2 mm was recorded in 7% of MRI and 8% of cadaveric cases. Histologically, the structure of FT showed gradual reduction in nervous, glial, and vascular tissues with converse increase in collagen content in FTE compared with those of FTI.   Conclusions: Knowledge of the morphometric parameters and the histological structure of FT are necessary for clinicians who dealing with diagnosis or treatment of tethered cord syndrome

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

Design of film—substrate single-reflection retarders

The design steps for film—substrate single-reflection retarders are briefly stated and applied to the SiO2—Si film—substrate system at wavelength 6328 Å. The criterion of minimum-maximum error of the ellipsometric angle ψ is used to choose angle-of-incidence-tunable designs. Use is made of the (Φ-d) plane (angle of incidence versus thickness) to determine whether a given film—substrate system with known optical properties and film thickness can operate as a reflection retarder and to determine the associated angles of incidence and retardation angles. This leads to the concept of permissible-thickness bands and forbidden gaps for operation of a film—substrate system as a reflection retarder. Experimental measurements on one of the proposed designs proved the validity of the method

Design of film-substrate single-reflection linear partial polarizers

The results of a preceding paper [J. Opt. Soc. Am. 65, 1464,(1975)] are viewed from a different angleas providing the basis for the design of film-substrate single-reflection linear partial polarizers (LPP),which also operate as reflection optical rotators. The important characteristics of a comprehensive set of discrete designs of SiO2-Si LPP’s at λ = 6328 Å are shown graphically