Problem of ambiguity in the determination of optical constants of thin absorbing films from spectroscopic reflectance and transmittance measurements

We propose a new and simple procedure to overcome the ambiguity in the determination of optical constants of thin absorbing films from spectroscopic reflectance and transmittance measurements. The basis for the proposed method is an error analysis with the help of an error simulation technique and an error variation technique. We show that in practice (owing to experimental errors) it is not possible to overcome the problem of ambiguity by normal-incidence spectroscopic measurements alone. At least one oblique-incidence measurement is necessary for unambiguously determining the optical constants of the film. We discuss the consequences of experimental errors of the measured transmittance and reflectance values for the determination of the optical constants.     

Single-scale spectroscopy of structurally colored butterflies: measurements of quantified reflectance and transmittance

Butterfly scales generally have very elaborate structures in submicrometer size, and some of them show distinctive optical effects through interaction with light. We describe two methods to quantitatively characterize the optical properties of the individual scales in those structurally colored butterflies. Owing to the small dimensions of the scale and to the fact that the reflection and transmission are very diffuse, it is generally difficult to accurately measure the reflectance and transmittance. To overcome these difficulties, we have carefully constructed an optical system including an integrating sphere and investigated variously colored nine kinds of scale. It is shown that the obtained spectra clearly characterize the optical differences among those structurally colored scales and also the differences between structural and pigmentary colors. Further, we have performed the angle-resolved measurement of the reflected light to characterize the spatial pattern of reflection, which is closely related to the mechanism of reflection.     

Photomodulated reflectance and transmittance: optical characterisation of novel semiconductor materials and device structures

Photomodulation spectroscopy, in reflection and transmission modes, is presented here as a powerful non-destructive optical technique for the investigation of fundamental physical properties of new semiconductor materials and complex micro- and nano-structures. The abilities of photoreflectance and phototransmittance in application to many kinds of semiconductor structures are demonstrated. The following aspects are discussed: (1) separation of the optical response and built-in electric field determination in different depths of the sample by a selection of the pump beam wavelength; (2) electric field in δ-doped structures by an application of a fast Fourier transformation; (3) electron concentration dependence of the band gap related transitions in wurtzite GaN epitaxial layers; (4) comparison of different spectroscopic techniques used for investigations of InGaSb/GaSb quantum wells within 1.5-2 μm spectral region; (5) quantum well intermixing effects in InGaAsP/InP 1.55-μm laser structures; (6) photomodulation spectroscopy of self-assembled quantum dots.     

Real-time method for fitting time-resolved reflectance and transmittance measurements with a monte carlo model

An efficient method is proposed for the evaluation of theabsorption and the transport scattering coefficients from atime-resolved reflectance or transmittance distribution. Theprocedure is based on a library of Monte Carlo simulations and is fastenough to be used in a nonlinear fitting algorithm. Tests performedagainst both Monte Carlo simulations and experimental measurements ontissue phantoms show that the results are significantly better thanthose obtained by fitting the data with the diffusion approximation, especially for low values of the scattering coefficient. The methodrequires an a priori assumption on the value of theanisotropy factor g. Nonetheless, the transportscattering coefficient is rather independent of the exact knowledge ofthe g value within the range 0.7 < g < 0.9.     

Diffuse reflectance and transmittance spectra of an interference layer: 1. Model formulation and properties

A model for the calculation of the diffuse reflectance and transmittance of a single interference layer with rough interfaces on a transparent substrate is presented. The model is based on electric field calculations and scalar scattering theory, and it assumes that the interfaces of the layer are totally uncorrelated. Examples are given of calculated spectra in which the parameters of the model are varied systematically to show the influence from different interface roughness and refractive index combinations as well as absorption in the film. A wavelength-dependent effective root-mean-square roughness is introduced. This depends on the nature of the roughness, and the bandwidth limits are given by the experimental conditions. Finally, total integrated scattering spectra are calculated and the importance of taking multiple reflections in the substrate into account is shown.     

Determination of optical constants of thin films and multilayer stacks by use of concurrent reflectance, transmittance, and ellipsometric measurements

Using measurements of reflectance, transmittance, and the ellipsometric parameter D, we have determined the thickness, refractive index, and the absorption coefficient of various thin films and thin-film stacks. (D, the relative phase between the p- and s-polarized components, is measured for both reflected and transmitted light.) These optical measurements are performed with a specially designed system at the fixed wavelength of lambda = 633 nm over the 10 degrees -75 degrees range of angles of incidence. The examined samples, prepared by means of sputtering on fused-silica substrates, consist of monolayers and trilayers of various materials of differing thickness and optical constants. These samples, which are representative of the media of rewritable phase-change optical disks, include a dielectric mixture of ZnS and SiO(2), an amorphous film of the Ge(2)Sb(2.3)Te(5) alloy, and an aluminum chromium alloy film. To avoid complications arising from reflection and transmission losses at the air-substrate interface, the samples are immersed in an index-matching fluid that eliminates the contributions of the substrate to reflected and transmitted light. A computer program estimates the unknown parameters of the film(s) by matching the experimental data to theoretically calculated values. Although our system can be used for measurements over a broad range of wavelengths, we describe only the results obtained at lambda = 633 nm.     

Scattering and absorption cross sections of light diffusing materials retrieved from reflectance and transmittance spectra of collimated radiation

Four-flux radiative transfer models have been extensively used to describe reflectance and transmittance (R&T) spectra of light scattering and absorbing (S&A) media. Solutions to the differential equations corresponding to the collimated fluxes are obtained by subsequent application of boundary conditions. Explicit expressions for the collimated R&T of light are reported, when considering a light S&A medium contained between two glass slides, an experimental arrangement which is appropriate for liquid suspensions and viscous matrices containing solid particles. A spectral simulated annealing method is applied to retrieve, from measured R&T spectra of collimated light under normal incident radiation, the scattering and absorption coefficients of the composite medium. First, the accuracy of the method is established by applying it to synthetic collimated R&T data. Secondly, we apply the method to experimental data and use it to determine the S&A coefficients of a layer of TiO₂ particles dispersed in a PVP/water matrix.     

Straightness measurements with a reflection confocal optical system-an experimental study

Straightness measurement is an important technique in the field of mechanical engineering. We previously proposed a novel optical method for measuring straightness of motion using reflection confocal optics. The advantage of this method in comparison with the transmission optical systems of others [Opt. Laser Technol. 6, 166 (1974)] is that the lateral displacements in the two axes perpendicular to the optical axis and the rotation angles around all three axes can be measured simultaneously. We demonstrate straightness measurements using reflection confocal optics and show these measurements to be in good agreement with the theory.     

Symmetry X system and method for absolute measurements of reflectance and transmittance of specular samples

A symmetry X system that has been constructed for the absolute measurements of reflectance and transmittance of specular samples in the infrared region is described. The system has been designed so that it can be incorporated into commercial Fourier-transform infrared spectrometers. Although ten mirrors were used in this system, it is disclosed that the geometric mean of two reflectance values is independent of the reflectance difference of the individual mirrors and the optical loss at each mirror. This system achieves spectral measurements with high accuracy and within a short period of time. In particular, the system affords us the self-diagnostic ability for measured spectra, and the simultaneous measurements of reflectance and transmittance under the same geometry enable us to evaluate measurement uncertainties. Although the symmetry X system is used for infrared spectral measurements, the measurement method, design principles, and features are generally applicable to other wavelengths as well.     

Correlation between optical path modulations and transmittance spectra of a-Si:H thin films

The optical constants of plasma-enhanced chemical-vapor-deposited amorphous silicon (a-Si:H) thin film upon a transparent substrate are determined within the UV-visible region by measurement of the transmittance spectrum. Apart from thickness irregularities, the effects of vertical film inhomogeneities (refractive-index distribution) on the spectrum are discussed. In this respect, although consideration of any possible variation in thickness of the film within the area illuminated by the probe beam is sufficient for correcting the modulation of the extrema of interference fringes, including in the model the thin transitional regions at substrate-film and film-air interfaces might be an alternative method for understanding the overall optical behavior of the spectrum.     

Characterization of thin films based on reflectance and transmittance measurements at oblique angles of incidence

The optical parameters of a SiO2 thin-film coating determined from the spectral reflectance and transmittance measurements at various incidence angles, including the normal incidence and the Brewster's angle, are compared in this paper. The high-accuracy measurements were carried out through visible-near-infrared spectral regions by using our purpose-built instruments. The optical parameters obtained from the reflectance and the transmittance data are consistent over the angles of incidence and agree within 0.2%. The effect of important systematic factors in the oblique-incidence spectrophotometric measurements is also discussed.     

Far-ultraviolet reflectance measurements and optical constants of unoxidized aluminum films

The far-UV reflectance of thin unoxidized aluminum films prepared and maintained in ultra-highvacuum conditions was measured versus the angle of incidence, and the complex refractive index was obtained from those measurements on several wavelengths from 82.6 to 113.5 nm. Measurements were made on two perpendicular planes of incidence to deal with the unknown of the polarization state of the radiation beam. The surface roughness was characterized by atomic force microscopy. The refractive index is obtained for the first time, to our knowledge, from direct optical measurements in this spectral range. Current results match well the former values in the literature that were calculated through the Kramers-Kronig analysis by using in the above interval reflectances estimated from electron-energy-loss spectra and from optical measurements on surfaces of unstated roughness.     

Sequential estimation of optical properties of a two-layered epithelial tissue model from depth-resolved ultraviolet-visible diffuse reflectance spectra

A method for estimating the optical properties of two-layered media (such as squamous epithelial tissue) over a range of wavelengths in the ultraviolet-visible spectrum is proposed and tested with Monte Carlo modeling. The method first used a fiber-optic probe with angled illumination and the collection fibers placed at a small separation (or=1000 microm) was used to detect diffuse reflectance preferentially from the bottom layer. A second Monte Carlo-based inverse model for a two-layered medium was applied to estimate the bottom layer optical properties, as well as the top layer thickness, given that the top layer optical properties have been estimated. The results of Monte Carlo validation show that this method works well for an epithelial tissue model with a top layer thickness ranging from 200 to 500 microm. For most thicknesses within this range, the absorption coefficients were estimated to within 15% of the true values, the reduced scattering coefficients were estimated to within 20% and the top layer thicknesses were estimated to within 20%. The application of a variance reduction technique to the Monte Carlo modeling proved to be effective in improving the accuracy with which the optical properties are estimated.