Skip to main content

Emissivity of Triangular Surfaces Determined by Differential Method

From Homogenization to Validity Limit of Geometrical Optics
Author: Taoufik Ghabara, Faouzi Ghmari and M. Salah Sifaoui

Geometric optics approximation for emissivity from triangular surfaces was compared with exact scattering predictions from electromagnetic theory. Rigorous electromagnetic scattering theory was numerically formulated based on the differential method. We have used a numerical simulation of the emissivity of gold and tungsten for a wavelength equal 0.55 micron to explore the validity of the geometric optics.

Surface parameter domains for the regions of accuracy of the geometric optics approximation are quantified and presented as functions of surface slope and roughness. Influence on the validity of the approximate method of multiple scattering, the shadowing effect and the cavity effect of metallic surface have been investigated.

For the latter, our interest was focused on the mechanism that enhances the emissivity of an interface when ruling a grating. It has been seen that the mechanism responsible for the enhancement of the emissivity depends very much on the period of the grating.

For gratings with a period much smaller than the wavelength, the roughness essentially behaves as a transition layer with a gradient of the optical index. For different period / wavelength ratio, we have found a good agreement between the differential method and the homogenization regime when the period was smaller.

Journal: American Journal of Applied Sciences
Issn: 15469239
EIssn: 15543641
Year: 2007
Volume: 4
Issue: 3
pages/rec.No: 146-154

DOAJ – Directory of Open Access Journals, 2008, Lund University Libraries, Head Office

ASTM E423 – 71(2008): Standard Test Method for Normal Spectral Emittance

Standard Test Method for Normal Spectral Emittance at Elevated Temperatures of Nonconducting Specimens ASTM E423 – 71(2008) –

1. Scope

1.1 This test method describes an accurate technique for measuring the normal spectral emittance of electrically nonconducting materials in the temperature range from 1000 to 1800 K, and at wavelengths from 1 to 35 ?m. It is particularly suitable for measuring the normal spectral emittance of materials such as ceramic oxides, which have relatively low thermal conductivity and are translucent to appreciable depths (several millimetres) below the surface, but which become essentially opaque at thicknesses of 10 mm or less.

1.2 This test method requires expensive equipment and rather elaborate precautions, but produces data that are accurate to within a few percent. It is particularly suitable for research laboratories, where the highest precision and accuracy are desired, and is not recommended for routine production or acceptance testing. Because of its high accuracy, this test method may be used as a reference method to be applied to production and acceptance testing in case of dispute.

1.3 This test method requires the use of a specific specimen size and configuration, and a specific heating and viewing technique. The design details of the critical specimen furnace are presented in Ref (1), and the use of a furnace of this design is necessary to comply with this test method. The transfer optics and spectrophotometer are discussed in general terms.

1.4 The values stated in SI units are to be regarded as standard. No other units of measurement are included in this standard.

1.5 This standard does not purport to address all of the safety concerns, if any, associated with its use. It is the responsibility of the user of this standard to establish appropriate safety and health practices and determine the applicability of regulatory limitations prior to use.

2. Referenced Documents

E349 Terminology Relating to Space Simulation –

Full document current and on sale at the ASTM web store.

A Temperature and Emissivity Separation Algorithm…

A Temperature and Emissivity Separation Algorithm for Advanced Spaceborne Thermal Emission and Reflection Radiometer (ASTER) Images

by: Alan Gillespie, Shuichi Rokugawa, Tsuneo Matsunaga, J. Steven Cothern, Simon Hook, and Anne Kahle
Click Here to view or save

Manuscript received October 31, 1997. This work was a collaborative effort of the U.S. and Japanese EOS/ASTER instrument teams, sponsored by the NASA EOS Project and ERSDAC.

A. Gillespie and J.S. Cothern are with the Department of Geological Sciences, University of Washington, Seattle, Washington 98195-1310, USA.

S. Rokugawa is with The University of Tokyo, Faculty of Engineering, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113, JAPAN.

T. Matsunaga is with the Geological Survey of Japan, 1-1-3 Higashi, Tsukuba, Ibaraki 305, JAPAN.

S. Hook and A. Kahle are with the Jet Propulsion Laboratory 183-501, Pasadena, California 91109, USA


The ASTER scanner on NASA’s EOS-AM1 satellite (launch: June, 1998) will collect five channels of TIR data with an NE DT of <0.3 K to estimate surface temperatures and emissivity spectra, especially over land, where emissivities are not known in advance. Temperature/emissivity separation (TES) is difficult because there are five measurements but six unknowns. Various approaches have been used to constrain the extra degree of freedom. ASTER’s TES algorithm hybridizes three established algorithms, first estimating the normalized emissivities, and then calculating emissivity band ratios. An empirical relationship predicts the minimum emissivity from the spectral contrast of the ratioed values, permitting recovery of the emissivity spectrum. TES uses an iterative approach to remove reflected sky irradiance. Based on numerical simulation, TES should be able to recover temperatures within about 1.5K, and emissivities within about 0.015. Validation using airborne simulator images taken over playas and ponds in central Nevada demonstrates that, with proper atmospheric compensation, it is possible to meet the theoretical expectations. The main sources of uncertainty in the output temperature and emissivity images are the empirical relationship between emissivity values and spectral contrast, compensation for reflected sky irradiance, and ASTER’s precision, calibration, and atmospheric correction.


NORMAL SPECTRAL EMITTANCE, 800-1400 K, Authors: Harrison, W.N. ; Richmond, J.C. ; Skramstad, H.K.

From the Energy Citations Database, OSTI IdentifierOSTI ID: 4830164

Technical Report, WADC-TR-59-510(Pt.III), National Bureau of Standards, Washington, D.C.,1961 Sep 01


The equipment for direct measurement of normal spectral emittance was extensively modified by incorporation of a new external optical system that increased the amount of radiant energy available for measurement by a factor of about 10, and other associated changes. The test procedure was modified by incorporation of a zero line” correction. The equipment was calibrated by means of sector-disk attenuators which passed known fractions of the radiant flux from a blackbody furnace. Working standards of normal spectral emittance were prepared, calibrated, and shipped. An equation relating the normal spectral emissivity of a metal to five other parameters of the metal, each of which makes a non-linear contribution to the emissivity, was solved for one set of data by long hand” methods. Some progress was made in setting up a program for solution of the equation by use of an electronic computer. Equipment for the automatic recording of spectral emittance data in a form suitable for direct entry into an electronic computer, and on-line computation from spectral emittance data of total emittance or solar absorptance, was designed. Specifications for the equipment were prepared and bids received preparatory to placing an order for its procurement. (auth)

Spectral emissivity & brightness temperatures of platinum

Spectral emissivity and the relation of true temperatures and brightness temperatures of platinum
Robert E. Stephens
JOSA, Vol. 29, Issue 4, pp. 158-161 (1939)

R. E. Stephens, “Spectral emissivity and the relation of true temperatures and brightness temperatures of platinum,” J. Opt. Soc. Am. 29, 158-161 (1939)