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Generalized emissivity inverse problem.

DengMing Ming¹, Tao Wen, XianXi Dai

¹Group of Quantum Statistics and Methods of Theoretical Physics and Surface Physics Laboratory, Department of Physics, Fudan University, Shanghai 200433, People's Republic of China.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics

|May 15, 2002

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This study introduces a generalized inverse problem for emissivity and transmissivity, allowing for temperature and frequency-dependent emissivity. An exact solution is derived, offering a practical method for realistic calculations.

Area of Science:

Physics
Thermodynamics
Applied Mathematics

Background:

Inverse problems are crucial in physics with broad applications.
Previous work focused on temperature-independent emissivity.
Determining emissivity g(nu) from radiated power J(T) is a known inverse problem.

Purpose of the Study:

To propose a new generalized emissivity and transmissivity inverse (GETI) problem.
To allow the unknown emissivity function g(nu) to be both temperature and frequency dependent.
To develop an exact solution for this generalized inverse problem.

Main Methods:

Development of an exact solution formula for the GETI problem.
Utilizing published experimental information.
Suggesting a universal function set for numerical calculations.

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Main Results:

An exact solution formula for the generalized emissivity and transmissivity inverse problem has been derived.
The proposed universal function set demonstrates robustness for numerical calculations.
The GETI problem allows for temperature and frequency-dependent emissivity.

Conclusions:

The developed GETI problem and its exact solution offer a practical and convenient inversion method.
The method is suitable for realistic calculations involving temperature and frequency-dependent emissivity.
This advancement extends previous inverse problem methodologies in physics.