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# Determining Refractive Index Function of Amorphous Materials

IP.com Disclosure Number: IPCOM000040570D
Original Publication Date: 1987-Dec-01
Included in the Prior Art Database: 2005-Feb-02
Document File: 2 page(s) / 32K

IBM

## Related People

Gerson, DJ: AUTHOR

## Abstract

An absorbance (infrared) spectrum (As), real or complex, is obtained by using a standard Fourier transform (FT) infrared spectrometer, such as the IR/98 made by IBM, and can be used to determine the refractive index of most materials. If As is real, then the Hilbert transform is applied directly to the spectrum. If As is complex, then the spectrum must be divided into two arrays, one imaginary and one real, prior to applying the Hilbert transform. The complex array is divided into its component real and imaginary arrays and manipulated as follows: 1. The complex absorbance spectrum, As, of the sample material is saved. 2. An inverse Fourier transform is performed on the absorbance spectrum. 3. Real and imaginary points in the resultant digitized array are separated.

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Determining Refractive Index Function of Amorphous Materials

An absorbance (infrared) spectrum (As), real or complex, is obtained by using a standard Fourier transform (FT) infrared spectrometer, such as the IR/98 made by IBM, and can be used to determine the refractive index of most materials. If As is real, then the Hilbert transform is applied directly to the spectrum. If As is complex, then the spectrum must be divided into two arrays, one imaginary and one real, prior to applying the Hilbert transform. The complex array is divided into its component real and imaginary arrays and manipulated as follows: 1. The complex absorbance spectrum, As, of the sample

material is saved.

2. An inverse Fourier transform is performed on the

absorbance spectrum.

3. Real and imaginary points in the resultant

digitized array are separated. (The array is not

shift-inverted or rotated.)

4. An apodization function such as 1/(x+2) is applied

to the array in order to avoid any singularities.

5. A Fourier transform is performed on the real array

resulting from Step 4.

For both real and complex As, the result is saved

and the Hilbert transform is performed on the real

portion of the resulting absorbance spectrum As,

from Step 5. The real portion of the resulting dispersion spectrum (Ds) corresponds to the change in the index of refraction as a function of wavelength (g), i.e., H[As] = Ds[R(g)] The complex array of Ds represents the change in the absorptivity co-efficient as a functio...