Spectrophotometer for measuring spectral reflectance and transmittance

The development of a computer-controlled spectrophotometer that enables measurement of spectral transmittance, reflectance, and optical loss of thin-film specimens is discussed. We also describe the design and testing procedure of the spectrophotometer, incorporating test sample performance data. In the visible region the overall photometric accuracy is verified to be 0.1% and 0.2% for transmittance and reflectance, respectively. The wavelength scale is accurate to within 0.5 nm with a reproducibility of 0.1 nm.     

Dedicated spectrophotometer for localized transmittance and reflectance measurements

A dedicated spectrophotometer is built to achieve localized transmittance and reflectance measurements. The spatial resolution can be chosen from 100 microm to 2 mm, the spectral resolution from 0.5 to 5 nm, and the spectral range from 400 to 1700 nm. This apparatus can be used to study the index and thickness uniformity on single layers to determine and optimize the characteristics of the deposition chamber. It can also be used to measure the spatial variations of optical properties of intended nonuniform coatings such as linear variable filters.     

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.     

Generalized matrix method for analysis of coherent and incoherent reflectance and transmittance of multilayer structures with rough surfaces, interfaces, and finite substrates

A generalized matrix method is presented for calculating the optical reflectance and transmittance of an arbitrary thin-solid-film multilayer structure on very thick substrates with rough surfaces and interfaces. We show that the effect of roughness and the influence of incoherently reflected light on the back side of a thick layer can be accounted for with a more general transfer matrix that enables the inclusion of modified complex Fresnel coefficients. Coherent, partially coherent, and incoherent multiply reflected light inside the multilayer structure is treated in the same way. We demonstrate the method by applying it to simulated and experimental reflectance spectra of thin epitaxial Si overlayers on very thick SiO(2) substrates and on a separation by ion implantation of oxygen structure with a SiO(2) buried layer exhibiting substantial roughness on both of its interfaces (Si/SiO(2) and SiO(2)/Si).     

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.     

Sample holder and methodology for measuring the reflectance and transmittance of narrow-leaf samples

Measuring the reflectance and transmittance of narrow samples can be difficult, as the width of the illuminating beam may be greater than the width of the sample. The small sample area can also compound the already time-consuming process of reconfiguring the instrument between reflectance and transmittance measurements by introducing additional alignment problems. A method of measuring the reflectance and transmittance properties of narrow-leaf samples using reflectance configurations only is developed and tested. The method uses a mask and mask correction and relationships between reflectance measurements against contrasting backgrounds to determine sample reflectance and transmittance. The design of the accompanying sample-holding apparatus is also described. In testing, the mean error was less than 1% reflectance/transmittance, and standard deviation of the error was approximately 1% reflectance and 2% transmittance as compared to samples measured using conventional measurement configurations.     

Fast transmittance model for satellite sounding

Through the use of new line-by-line spectral calculations in both the infrared and microwave regions, coefficients have been generated for the transmittance stage of the fast radiative transfer model used by the United Kingdom Meteorological Office. These permit the fast model to calculate the transmittance for the high-resolution infrared sounder and the microwave sounding unit instruments aboard the National Oceanic and Atmospheric Administration polar-orbiting satellite for a given atmospheric profile, simply by taking these coefficients in linear combination with a set of predictors. These are expressed in terms of the deviation of the profile from a reference. However, the method can be applied to any instrument within the range of the spectral calculations, thereby permitting new coefficients to be calculated as soon as the spectral response details for the instrument become available. It also permits effective consideration to be given in the longer term to new line data or improvements in line-shape theory. The process by which these coefficients have been obtained is described, along with a discussion of some of the tests carried out on their installation into the fast model; these tests show that they are suitable for operational use. The predictors employed by the fast model are discussed, and changes are proposed for those that relate to the water-vapor transmittance. In this respect it was found that the inclusion of predictors that depend primarily on the zenith angle of the radiation path leads to improvements in the transmittance calculation.     

On calculating the reflectance and transmittance of light for a simple thick grating structure

Abstract

This paper presents a formulation for calculating the reflectance and transmittance of classical light for a simple structure that contains a rectangularly shaped line grating layer that lies atop a thick transparent or weakly absorbing substrate layer. It is assumed that the substrate thickness is sufficiently large and non-uniform that when the light traverses it is averaged over a large surface area, the averaged field is considered as losing phase coherence and intensities can be added. It is assumed that the optical properties of the media in the various homogeneous regions of the structure are complex, local, linear, isotropic, and non-magnetic. This kind of structure has important applications in the metrology of linewidths for the semiconductor integrated circuit industry.     

Reflectance and transmittance model for recto-verso halftone prints

We propose a spectral prediction model for predicting the reflectance and transmittance of recto-verso halftone prints. A recto-verso halftone print is modeled as a diffusing substrate surrounded by two inked interfaces in contact with air (or with another medium). The interaction of light with the print comprises three components: (a) the attenuation of the incident light penetrating the print across the inked interface, (b) the internal reflectance and internal transmittance that accounts for the substrate's intrinsic reflectance and transmittance and for the multiple Fresnel internal reflections at the inked interfaces, and (c) the attenuation of light exiting the print across the inked interfaces. Both the classical Williams-Clapper and Clapper-Yule spectral prediction models are special cases of the proposed recto-verso reflectance and transmittance model. We also extend the Kubelka-Munk model to predict the reflectance and transmittance of recto-verso halftone prints. The extended Kubelka-Munk model is compatible with the proposed recto-verso reflectance and transmittance model. In the case of a homogeneous substrate, the recto-verso model's internal reflectance and transmittance can be expressed as a function Kubelka-Munk's scattering and absorption parameters, or the Kubelka-Munk's scattering and absorption parameters can be inferred from the recto-verso model's internal reflectance and transmittance, deduced from spectral measurements. The proposed model offers new perspectives both for spectral transmission and reflection predictions and for characterizing the properties of printed diffuse substrates.     

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.     

Polychromatic reflectance and transmittance of a slab with a randomly rough boundary

We investigated four different approximation models for describing the polychromatic reflectance and transmittance of a slab with a randomly rough boundary while taking into account the coherent and the incoherent scattering of the rough boundary. Comparisons with experiments (an etched-silicon wafer) show that approximation models that apply a two-scale roughness to the randomly rough boundary and that take into account the coherent and the incoherent scattering yield better agreement and extend the range of validity of the approximation to shorter wavelengths.     

Directional statistics-based reflectance model for isotropic bidirectional reflectance distribution functions

We introduce a novel parametric bidirectional reflectance distribution function (BRDF) model that can accurately encode a wide variety of real-world isotropic BRDFs with a small number of parameters. The key observation we make is that a BRDF may be viewed as a statistical distribution on a unit hemisphere. We derive a novel directional statistics distribution, which we refer to as the hemispherical exponential power distribution, and model real-world isotropic BRDFs as mixtures of it. We derive a canonical probabilistic method for estimating the parameters, including the number of components, of this novel directional statistics BRDF model. We show that the model captures the full spectrum of real-world isotropic BRDFs with high accuracy, but a small footprint. We also demonstrate the advantages of the novel BRDF model by showing its use for reflection component separation and for exploring the space of isotropic BRDFs.     

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.     

Rapid simulation of steady-state spatially resolved reflectance and transmittance profiles of multilayered turbid materials

We present a technique for efficiently computing the reflection and transmission of light by arbitrary systems of turbid layers. To approximate the steady-state reflectance and transmittance without the need to solve difficult boundary conditions, we convolve the reflectance and transmittance profiles of individual layers. We extend single-slab boundary conditions to handle index-of-refraction mismatches between turbid slabs and account for interlayer scattering by applying methods similar to Kubelka-Munk theory in frequency space. We demonstrate good agreement between the reflectance and the transmittance predicted by our model and numerical Monte Carlo methods and show that the far-source reflectance and transmittance of multilayered turbid materials are dominated by interlayer scattering.     

Sub-quarter-wave multilayer coatings with high reflectance in the extreme ultraviolet

Multilayer coatings with a small number of layers were designed and prepared to provide an increase in normal-incidence reflectance in the extreme ultraviolet compared with the reflectance of available single-layer coatings, namely, SiC, B4C, and Ir. Multilayers were designed to produce coatings with the highest possible reflectance at 91.2 and at 58.4 nm. At these wavelengths all the materials absorb radiation strongly, but still a reflectance enhancement can be obtained by means of sub-quarter-wave multilayer coatings with two or more different materials. Sub-quarter-wave multilayer coatings based on Al, MgF2, diamondlike carbon, B4C, SiC, and Ir showed higher reflectance than single-layer coatings of SiC and B4C not only at the target wavelength but in a wide band ranging from 50 nm to the 121.6-nm H Lyman-alpha line. Multilayer coatings suffered some reflectance degradation over time. However, after approximately 80-100 days of aging in a desiccator, the reflectance for the multilayer coatings was greater than for the single-layer coatings.