I'm looking into thermal radiation from hot glass, in particular I'd like to compute the angular and spectral distribution of radiation from borosilicate glass as a function of its temperature.

I am assuming that the "body" of the glass is a uniform, non-crystalline and perfectly isotropic emitter and that the temperature through the "thickness" of this body (that is, as a function of distance from the interface along the interface normal) is constant.

The assumption comes from the fact that I am starting from this work

R. Kitamura, L. Pilon, and M. Jonasz, 2007. Optical Constants of Fused Quartz From Extreme Ultraviolet to Far Infrared at Near Room Temperatures. Applied Optics, Vol. 46, No. 33, pp. 8118-8133.

From which I produced this plot:

enter image description here

(The actual background is that I'm trying to understand better how to interpret how a FLIR i7 thermal imager responds to hot glass).

The plot shows (among other things) that absorption through a skin depth of maybe 100um is effectively complete (maybe except for a 9% peak around 15um?). The glass is approx 750um thich, has air on one side and vacuum on the other, and is heated by thermal radiation from the vacuum side, and I'm observing it from the air side. My expectation is that conduction would make it stabilize to a small temperature gradient along the normal direction in a relatively short time (maybe a few seconds?).

Now, I have from the data in the paper the complex index of refraction of the material, as a function of wavelength (plotted as n and k in the pasted image, referenced to the left axis).

I intend to compute the quantity I'm after (exitant spectral radiance) as follows:

  • assume "the flesh" of the glass is a uniform distribution of small isotropic blackbody radiators,
  • attenuate their contribution using the extinction coefficient and integrate it to derive the incoming radiance field at to the inward facing surface of the interface,
  • use Fresnel and Snell to compute the angular distribution of the exitant radiance field after it has crossed the interface [Edit:] and likely some n^2 compensation will be in order somewhere

It seems this would make sense at visible light wavelengths, the question is whether it continues to hold at these infrared wavelengths (say [6,20um]) as well

Some related literature (that I don't have access to so far):

A Review of Radiant Heat Transfer in Glass Gardon, 1961, Journal of the American Ceramic Society, 44: 305-312

Temperature Measurement of Glass by Radiation Analysis LAETHEM, R. , LEGER, L. , BOFFÉ, M. and PLUMAT, E., 1961, Journal of the American Ceramic Society, 44: 321-332

Radiative transport in hot glass Edward U. Condon, 1968, Journal of Quantitative Spectroscopy and Radiative Transfer Volume 8, Issue 1, January 1968, Pages IN37, 369-385

Many thanks

  • $\begingroup$ Arguably related question: physics.stackexchange.com/questions/61443/… $\endgroup$ Sep 7, 2019 at 6:55
  • $\begingroup$ Are you doing experiments or simulations or both? $\endgroup$
    – boyfarrell
    Sep 7, 2019 at 8:06
  • $\begingroup$ Well. I was trying to measure the temperature of something hot behind glass. Then it occurred to me glass is opaque at IR, and you know, that looked a whole lot like an elegantly dressed white rabbit... But the end of it looks like showing that hot glass is not a lambertian emitter and that it seems to have large spectral distribution variation along theta (angle from the normal). Integrating against the reaponsivity of the instrument should help understanding how big an effect this has $\endgroup$ Sep 7, 2019 at 8:46
  • $\begingroup$ Oh. Certainly I don't have access to a spectrometer with sensitivity in this range $\endgroup$ Sep 7, 2019 at 8:47
  • $\begingroup$ I would attempt a transmission experiment: but it would require a lamp and a spectrometer. From that you could directly measure the absorption coefficient. $\endgroup$
    – boyfarrell
    Sep 7, 2019 at 8:55

1 Answer 1


After gaining access to the literature above and some reading I found this passage:

At the boundary we assume the radiation to be refracted by Snell's law, and the beams to be separated into reflected and transmitted parts as given by the Fresnel formulas. [...] this formulation is rather restrictive in that it does not consider volume or surface scattering properties of the glass. In opal glasses there is a "fog" of tiny crystals, and in articles with matt surfaces rather than optically polished ones there is surface scattering as well, but we do not attempt to take that into account.

From page 377 of Radiative transport in hot glass Edward U. Condon, 1968, Journal of Quantitative Spectroscopy and Radiative Transfer Volume 8, Issue 1, January 1968, Pages IN37, 369-385

So the answer found in Condon 1968 is positive, and he goes on to indicate that further effects to be taken into account, such as surface normal distribution ("roughness") and internal scattering can be modeled with (nowadays, but not back then) common light scattering theory used for the visible spectrum. Condon does acknowledge his awareness of Chandrasekhar's Radiative Transfer 1960 book. (And obviously not Ishimaru, A., 1978. Wave Propagation and Scattering in Random Media. New York: Academic, Vol. I and II.)

In looking through what material I could find online on the subject of volume spectral emissivity, I was unable to find anything more recent that indicates these considerations don't hold. On the contrary this work and Gardon's 1961 and 1956 articles seems to continue to be cited as the current reference (somewhat surprisingly, it seems to be also common to find references to McMahon's 1950 work, which was the starting point of Gardon 1956 article and that misses the n^2 correction term needed upon crossing medium interfaces).

Robert Gardon, “Emissivity of Transparent Materials,” J. Am. Ceram. Soc.. 39 [8] 278-87 (1956).

H. 0. McMahon, “Thermal Radiation from Partially Transparent Reflecting Bodies," J. Opt. Soc. Amer., 40, 376-80 (1950).


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