An algorithm of the Monte Carlo method is described which allows evaluation of the effective emissivities of isothermal and nonisothermal specular-diffuse black-body cavities for use in radiometry, photometry and optical pyrometry. The calculation provides estimates of normal spectral effective emissivity for black-body cavities, formed by cone surfaces and a cylinder. It does this for an isothermal cavity and for a cavity having an arbitrary variation of temperature along the cavity length.

https://iopscience.iop.org/article/10.1088/0026-1394/29/1/003/pdf

Calculation of the Effective Emissivities of Specular-Diffuse Cavities by the Monte Carlo Method

Determining the emissivity of pig skin for accurate infrared thermography

A Hybrid Electric and Thermal Solar Receiver

State-of-the-art in the application of the Monte Carlo method (MCM) to the computational problems of optical radiometry is discussed. The MCM offers a universal technique for radiation transfer modelling based on the stochastic approach. Developments of the original MCM algorithms and software for calculation of effective emissivities of black bodies, absorption characteristics of cavity radiometers and photometric properties of integrating spheres are used for designing advanced optical instruments. The capabilities of the developed software are illustrated by several examples. The techniques of convergence improvement and special time-saving algorithms are outlined.

https://iopscience.iop.org/article/10.1088/0026-1394/35/4/44/pdf

Monte Carlo method in optical radiometry

An iterative formula for the directional hemispherical apparent reflectivity of an opaque isothermal cavity with an arbitrary surface is derived on the basis of an integral equation representing the apparent reflectivity. Nested integrals in the formula are computed by the hit-or-miss Monte Carlo method. The formula is applied to right circular cylinders whose surfaces are diffuse and to cylindrical cones whose surfaces are characterized by a uniform specular-diffuse model. For the cylinders, a table is given from which one can easily calculate the apparent emissivities of the center of the bottoms for arbitrary surface reflectivities. An analytical recalculation of I2 of Quinn gives corrected values that agree with those produced by the Monte Carlo method. For the cylindrical cones the directional apparent emissivities of the bottoms are obtained by varying the apex angle and the fraction of specular component. We point out that angles of 120° and 70° have advantages even for cavities with moderate specular components. Results are analyzed by studying numerically the individual terms of the iterative formula. The validity of an approximation for the directional apparent emissivity is discussed in terms of the constant asymptotic distribution of impact points of rays in cavities.

Calculation of the directional emissivities of cavities by the Monte Carlo method

Local, hemispherical, effective emissivities and integrated cavity emissivities have been computed for isothermal and nonisothermal diffuse conical and cylindrical cavities having lids with circular apertures. The local emissivities of the walls increase rapidly with decreasing aperture diameter and are moderately insensitive to the value of the lid emissivity. The integrated emissivity increases or decreases with the distance of the detector from the cavity; the direction of the change depends upon the cavity geometry. For a nonisothermal cavity, the effective spectral emissivity changes substantially with both wavelength and cavity temperature; consequently, it is in general significantly different from the effective total emissivity.

Emissivities of diffuse cavities: Isothermal and nonisothermal cones and cylinders

Local, hemispherical, effective emissivities and integrated cavity emissivities are computed for isothermal and nonisothermal diffuse cylindro-cones (a cylindrical section of radius R2 and length L2 joined to a conical base of length L1 and half-angle θ), with and without lids, and are compared with corresponding values for the limiting cases of right circular cones and cylinders. The local emissivities everywhere along the walls are considerably higher in a cylindro-cone with a lid than in a similar one without, and also increase rapidly with decreasing cone angle. They are considerably higher in a cylindro-cone than in a cone of length L1 or in a cylinder of length L2. On the other hand, for cavities of the same total length, the cylinder has the highest local emissivities except at and near the base, where the emissivity of the cone is highest. There is a regular transition between these two extremes through various intermediary cylindro-cones. The normal integrated cavity emissivities are higher than the hemispherical emissivities for cavities for which (L1 + L2)/2R2 ≳ 0.8. The local and integrated spectral emissivities of nonisothermal cylindro-cones change markedly with wavelength and somewhat with cavity reference temperature. Approximate local emissivities for nonisothermal cylindro-cones can be obtained from corresponding isothermal ones in a simple manner, with useful accuracy.

Emissivities of diffuse cavities, II: Isothermal and nonisothermal cylindro-cones

Local hemispherical effective emissivities and integrated cavity emissivities are computed for isothermal and nonisothermal diffuse double cones (a conical section joined to a conical frustum) with and without lids, and are compared with corresponding values for cylindrocones. The local emissivities increase and become more uniform with increasing taper of the frustum. They are also considerably higher when there is a lid. For cavities with the same conical section, length, and aperture, a lidded double cone is blacker than a lidded cylindrocone when the front half of the frustum is invisible, but less black otherwise. For double cones of the same length, diameter, and aperture, the best choice of cone and frustum angles depends upon the particular viewing conditions. The integrated cavity emissivities vary only slightly with the angles of cone and frustum when the frustum is relatively long, and the normal emissivity (for a small on-axis detector a large distance away) is higher than the hemispherical emissivity (for a detector that fills the cavity aperture). When the frustum is relatively short, all of these vary substantially with angle, and the hemispherical emissivity can be higher than the normal emissivity. There is a marked variation of both local and integrated emissivities with wavelength in nonisothermal double cones; e.g., for the particular cases illustrated, the normal spectral emissivities change by from 4% to 6% and the hemispherical spectral emissivities by from 17% to 20% between 0.3 and 1 μm for a 1% temperature variation at 1300 K. The amount of the change in these spectral emissivities also depends upon the geometry of the cavity.

Emissivities of diffuse cavities. III. Isothermal and nonisothermal double cones

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Emissivities of diffuse cavities: Isothermal and nonisothermal cones and cylinders

Emissivities of diffuse cavities, II: Isothermal and nonisothermal cylindro-cones

Emissivities of diffuse cavities. III. Isothermal and nonisothermal double cones