Radiative heat transfer is an inherently spectrally broadband phenomenon, with room temperature matter emitting energy in the wavelength range of approximately 3 to 100 micrometers. For many common materials, important quantities in the engineering analysis of radiative heat transfer, such as reflectance, transmittance, and emittance, may be computed from first principles using only geometric dimensions and the wavelength-dependent complex refractive index (CRI) of the emitting material. That makes the CRI a crucial material property in the design of any technology depending on radiative heat transfer.

Despite its ubiquity in radiative heat transfer calculations, the CRI is not well known for many common materials. Even in cases where it is known at some wavelengths, it is often not known over a sufficiently broad spectral range to be useful in radiative heat transfer calculations. This is due, in part, to the relative difficulty in measuring it. In most cases, one cannot measure CRI directly from an experiment and instead relies on measuring a material’s reflectance and/or transmittance and using Fresnel’s equations to link the measurands to the CRI. Many past attempts of extracting the CRI from Fresnel’s equations using direct inversions of the equations have suffered from massive uncertainty amplification. Similarly, indirect methods tend to suffer from non-unique solutions. Another class of methods, known as phase retrieval methods, attempt to reconstruct the phase angle of the complex Fresnel reflection coefficient from its measured amplitude. The most common approach employs the Kramers-Kronig relations and a set of reflectance extrapolation techniques to extend the measured spectral range to include all wavelengths.

In this work, I report a novel algorithm which can directly determine the CRI of a material using only routine spectrophotometric measurements (such as those taken using a Fourier-transform infrared spectrometer) and no extrapolation techniques. The algorithm is a synthesis of a direct inversion method and the Kramers-Kronig relations, which have complementary strengths and weaknesses. The algorithm is applicable to a wide class of solid materials, with the only requirement being that the material transmits in two portions of the electromagnetic spectrum enclosing the region of interest. This assumption is satisfied by a wide class of materials common in engineering design, such as glasses, polymers, and semiconductors. I demonstrate the validity of the algorithm by measuring the CRI of a common industrial polymer over a broad spectral range and comparing my results with published literature values. Further, I present an uncertainty analysis of the algorithm which provides both the value and uncertainty of the extracted CRI. This work has implications for the speed and ease at which researchers can characterize scientifically relevant materials using common laboratory instruments.


Novel Algorithm for Extracting Complex Refractive Index From Infrared Spectrophotometric Measurements

Division / Sponsors: 
Heat Transfer Division (HTD), Fluids Engineering Division (FED)

Heat Transfer Summer Conference
Paper Proceedings: https://asmedigitalcollection.asme.org/HT/HT2020/volume/83709

18th International Conference on Nanochannels, Microchannels, and Minichannels
Paper Proceedings: https://asmedigitalcollection.asme.org/ICNMM/ICNMM2020/volume/83693

Fluids Engineering Division Summer Meeting
Paper Proceedings: https://asmedigitalcollection.asme.org/FEDSM/FEDSM2020/volume/83716

HT-ICNMM2020 - Virtual Conference, SHTC - Virtual Conference, FEDSM2020 - Virtual Conference

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