A New Method for Determining the Optical Constants of Highly Transparent Solids

Highly transparent substrates are of interest for a variety of applications, but it is difficult to measure their optical constants precisely, especially the absorption index in the transparent spectral region. In this paper, a combination technique (DOPTM-EM) using both the double optical pathlength transmission method (DOPTM) and the ellipsometry method (EM) is presented to obtain the optical constants of highly transparent substrates, which overcomes the deficiencies of both the two methods. The EM cannot give accurate result of optical constants when the absorption index is very weak. The DOPTM is suitable to retrieve the weak absorption index; however, two sets of solutions exist for the retrieved refractive index and absorption index, and only one is the true value that needs to be identified. In the DOPTM-EM, the optical constants are measured first by using the EM and set as the initial value in the gradient-based inverse method used in the DOPTM, which ensures only the true optical constants are retrieved. The new method simultaneously obtains the refractive index and the absorption index of highly transparent substrate without relying on the Kramers–Kronig relation. The optical constants of three highly transparent substrates (polycrystalline BaF2, CaF2, and MgF2) were experimentally determined within wavelength range from ultraviolet to infrared regions (0.2–14 µm). The presented method will facilitate the measurement of optical constants for highly transparent materials.

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Infrared Intensities of Liquids XIV: Accurate Optical Constants and Molar Absorption Coefficients between 4800 and 450 cm−1 of Chlorobenzene at 25°C from Spectra Recorded in Several Laboratories

Applied Spectroscopy ◽

10.1366/0003702944027723 ◽

1994 ◽

Vol 48 (1) ◽

pp. 144-159 ◽

Cited By ~ 29

Author(s):

John E. Bertie ◽

R. Norman Jones ◽

Yoram Apelblat

Keyword(s):

Refractive Index ◽

Absorption Coefficient ◽

Optical Constants ◽

Absorption Index ◽

Molar Absorption Coefficient ◽

Refractive Indices ◽

The Real ◽

Infrared Intensities ◽

Refractive Index Spectrum ◽

Liquid Chlorobenzene

Accurate infrared absorption intensities of liquid chlorobenzene at 25°C are presented. Their accuracy was estimated from the agreement between the intensities measured by different spectroscopists using different instruments in different laboratories and by different spectroscopists using the same instrument in the same laboratory. The spectra from different spectroscopists have been averaged, unweighted, to give intensity spectra of chlorobenzene that are presented as the best available. The results are presented as graphs and tables of the molar absorption coefficient, Em (ν˜), and the real and imaginary refractive indices, n(ν˜) and k(ν˜), between 4800 and 450 cm−1. The peak heights and the areas under the bands in the absorption index (imaginary refractive index) spectrum are reported, as are areas under the molar absorption coefficient spectrum. Absorption index, k(ν˜), and molar absorption coefficient, Em (ν˜), values are believed accurate to an average ±2.4% at the peaks of bands with kmax > 0.002 and ±3.3% at the peaks of bands with kmax < 0.002. In the baseline k(ν˜) is accurate to ∼ ±5% above 3000 cm−1 and ∼ ±2.5% below 3000 cm−1. The areas under bands in k(ν˜) and Em (ν˜) spectra for which kmax > 0.002 are accurate to ±1.3% on average. The real refractive index, n(ν˜), values are believed to be accurate to ±0.2%.

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Optical Properties of Strongly Absorbing Media Determined by External Reflection Spectroscopy

Applied Spectroscopy ◽

10.1366/0003702924124295 ◽

1992 ◽

Vol 46 (6) ◽

pp. 1040-1044 ◽

Cited By ~ 5

Author(s):

J. A. Mielczarski ◽

M. Milosevic ◽

S. L. Berets

Keyword(s):

Refractive Index ◽

Optical Properties ◽

Optical Constants ◽

Infrared Region ◽

Absorption Index ◽

Reflection Spectra ◽

Reflection Spectroscopy ◽

Butyl Xanthate ◽

Mid Infrared ◽

Classical Oscillator

Reflection spectra of opaque samples recorded at different angles of incidence and for both polarizations were used to evaluate the optical constants. A subsequent classical oscillator fitting analysis of these spectra provided the dispersion of the refractive index and the absorption index for cuprous ethyl and butyl xanthate complexes across the mid-infrared region. The advantages of recording spectra under certain conditions are discussed.

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Effective optical constants n and κ and extinction coefficient of silica aerogel

Journal of Materials Research ◽

10.1557/jmr.1996.0083 ◽

1996 ◽

Vol 11 (3) ◽

pp. 687-693 ◽

Cited By ~ 48

Author(s):

J. S. Q. Zeng ◽

R. Greif ◽

P. Stevens ◽

M. Ayers ◽

A. Hunt

Keyword(s):

Extinction Coefficient ◽

Silica Aerogel ◽

Optical Constants ◽

Large Error ◽

Absorption Index ◽

Infrared Spectrometer ◽

Equation Maxwell ◽

Second Procedure ◽

Kronig Relation ◽

Transmission And Reflection

In this work the normal reflectance, R, at a planar silica aerogel interface and the normal transmittance, T, of a silica aerogel slab were measured using a Fourier Transform Infrared Spectrometer. Two procedures were used to obtain the effective optical constants, i.e., the refractive index n and the absorption index κ, of silica aerogel. One procedure determined κ from the measured transmittance T and then determined n from the results for κ and from the measured reflectance R using the Kramers–Kronig relation; the other procedure determined n and κ of silica aerogel from n and κ of fully dense silica glass by using the Clausius–Mossotti equation, Maxwell Garnett formula, and Bruggeman formula. The first procedure has a relatively large error due to the inaccuracy of the transmission and reflection measurements. The second procedure, especially the Clausius–Mossotti equation, yields values of n that are consistent with experiments and may be used for the calculation of the effective optical constants and the extinction coefficient of silica aerogel.

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Direct introduction of elemental sulfur into polystyrene: A new method of preparing polymeric materials with both high refractive index and Abbe number

Polymer ◽

10.1016/j.polymer.2019.121715 ◽

2019 ◽

Vol 180 ◽

pp. 121715 ◽

Cited By ~ 5

Author(s):

Liping Jiang ◽

Ruixia Kong ◽

Yuliang Yi ◽

Siqi Yang ◽

Yu Mei ◽

...

Keyword(s):

Refractive Index ◽

Elemental Sulfur ◽

Polymeric Materials ◽

High Refractive Index ◽

New Method ◽

Direct Introduction

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A new method of measuring lens refractive index

Clinical and Experimental Optometry ◽

10.1111/j.1444-0938.2008.00254.x ◽

2008 ◽

Vol 91 (4) ◽

pp. 364-372 ◽

Cited By ~ 3

Author(s):

John Buckley

Keyword(s):

Refractive Index ◽

New Method

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Long-wavelength lattice vibrations of Ag3In5Se9 and Ag3In5Te9 single crystals — An inversion of LO- and TO-mode frequencies

Modern Physics Letters B ◽

10.1142/s0217984916502298 ◽

2016 ◽

Vol 30 (18) ◽

pp. 1650229 ◽

Cited By ~ 4

Author(s):

Nizami Mamed Gasanly

Keyword(s):

Refractive Index ◽

Single Crystals ◽

Longitudinal Optical ◽

Absorption Index ◽

Energy Losses ◽

Optical Parameters ◽

Lattice Vibrations ◽

Frequency Range ◽

Long Wavelength ◽

Optical Modes

Infrared (IR) reflectivities are registered in the frequency range of 50–2000 cm[Formula: see text] for Ag3In5Se9 and Ag3In5Te9 single crystals grown by Bridgman method. Three infrared-active modes are detected in spectra. The optical parameters, real and imaginary parts of the dielectric function, the function of energy losses, refractive index, absorption index and absorption coefficient were calculated from reflectivity experiments. The frequencies of transverse and longitudinal optical modes (TO and LO modes) and oscillator strength were also determined. The bands detected in infrared spectra were tentatively attributed to various vibration types (valence and valence-deformation). The inversion of LO- and TO-mode frequencies of the sandwiched pair was observed for studied crystals.

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Cross Calibration by FFT Equalization

Journal of Dynamic Systems Measurement and Control ◽

10.1115/1.2801239 ◽

1997 ◽

Vol 119 (2) ◽

pp. 236-242 ◽

Cited By ~ 2

Author(s):

K. Peleg

Keyword(s):

Measurement Method ◽

Functional Relationship ◽

Measurement Methods ◽

New Method ◽

Measurement Systems ◽

True Value ◽

Calibration Problem ◽

Regression Techniques ◽

The Cross ◽

Cross Calibration

The classical calibration problem is primarily concerned with comparing an approximate measurement method with a very precise one. Frequently, both measurement methods are very noisy, so we cannot regard either method as giving the true value of the quantity being measured. Sometimes, it is desired to replace a destructive or slow measurement method, by a noninvasive, faster or less expensive one. The simplest solution is to cross calibrate one measurement method in terms of the other. The common practice is to use regression models, as cross calibration formulas. However, such models do not attempt to discriminate between the clutter and the true functional relationship between the cross calibrated measurement methods. A new approach is proposed, based on minimizing the sum of squares of the differences between the absolute values of the Fast Fourier Transform (FFT) series, derived from the readings of the cross calibrated measurement methods. The line taken is illustrated by cross calibration examples of simulated linear and nonlinear measurement systems, with various levels of additive noise, wherein the new method is compared to the classical regression techniques. It is shown, that the new method can discover better the true functional relationship between two measurement systems, which is occluded by the noise.

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