The measurements are carried out on each sample over the mid-infrared spectral region of interest, using the NPL Hemispherical Reflectometer/Transmissometer as adapted for direct absolute reflectance measurements.

The techniques and equipment used are variants of those for the more usual relative method, which have been described in Ref. 1. That technique requires the equipment to be calibrated separately for the diffuse and regular components of reflection, due to the existence of significant interreflection effects that are appreciably larger for the regular component than for the diffuse component. It also requires that the sample has spatial reflection characteristics that can be validly analysed into a sum of a diffuse and of a regular component of reflection.

However, a direct absolute technique is described below. The basic principle and the initial method used for the implementation of this absolute method are described in Ref. 2, but an improved technique and design of reflectometer has now been produced, see below, although it has not yet been described fully in the open literature.

This direct absolute technique makes no distinction between any regular or diffuse component of reflection that might exist for a particular sample, as it incorporates a valid compensating correction for the actual interreflection effects that occur with each sample, irrespective of the angular distribution of reflection involved. This technique can therefore be used for samples that have reflection and scattering characteristics that cannot be analysed into a simple additive combination of regular and diffuse components. These samples include various constructions of energy-efficient building materials that have an aluminium foil layer bonded onto the surfaces of some kind of insulating layer. For such a sample the foil is not flat like a true mirror, and its shape causes its local regular reflections to be deflected in a range of directions. The concept of there being a regular and a diffuse component of reflection is not valid for this kind of sample.

Technique for calibrating the samples

A custom-built hemispherical focusing absolute reflectometer is aligned and clamped in the large sample compartment of a Perkin-Elmer 580B ratio-recording spectrophotometer, which is continually purged of water vapour and carbon dioxide by means of a recirculating air purifier. In order to prevent local over-heating of the sample, the source is markedly under run and the sample is backed by a water-cooled copper block. The sample temperature is maintained at 30 °C ± 3 °C. The infrared source is stabilised using a unique constant-load-resistance power supply which negates the effect of the purging draught and the heating effect of interreflection between source and sample, Ref. 1.

A complication in this work is that the amount of irradiance on the sample is still influenced directly by its own reflectance, due to the inter-reflections between the sample and the source, even when the source temperature is held constant. This interreflection effect depends on the angular distribution of reflectance from the sample, varies with wavenumber and varies non-linearly with the spectral reflectance. However, it can be measured using two extra types of spectral scan that record source radiances, and a correction ratio term can then be applied to the reflectometer ratio (the apparent reflectance).

A specially modified hemisphere mirror is used with the NPL Reflectometer, which has one small aperture only slightly larger than the measuring beam cross section there and located centrally in Hemisphere the hemispherical mirror. A precision slide for the mounting bars of the reflectometer allows it to be moved sideways to reproducible positions that are adjustable with locked stop-screws. One position is the normal position, with the bars centrally aligned with the sample beam optical axis, so that the sample beam axis passes through the centre of the sample aperture. This allows the usual types of spectral scan to record hemisphere mirror radiance (Figure 1, top diagram) and sample radiance (Figure 1, middle diagram). The other position is displaced 20 mm, adjusted so that the sample beam axis passes through the centre of the source. This allows the two extra types of scan to be made, of the source radiance, with and without the sample present, (see Figure 1, bottom diagram).

Figure 1: The three orientations and two positions of the NPL hemisphere reflectometer
as modified and used for absolute measurement. No sample is present in the top diagram,
but its position is shown unshaded.

In the middle section of the diagram showing the Sample Scan setup, the focusing of the source onto the sample involves rays that can contribute to any regular component of reflectance (full line) and rays that can contribute to any diffuse component of reflectance (dotted lines).

Nine scans are made in the following sequence : Rf 1, S 1, Cs 1, Ce 1, D 1, Ce 2, Cs 2, S 2, Rf 2 where

1. Rf are Reference Scans (hemisphere radiance) (reflectometer on axis).
2. S are Sample Scans (sample radiance) (reflectometer on axis).
3. Cs are Correction Scans of source, with sample (reflectometer displaced).
4. Ce are Correction Scans of source, no sample (reflectometer displaced).
5. D1 is a Dark Sample Scan for zero offset (beam blocked with black card).

This sequence of scans is symmetrical with respect to time, and hence is likely to nullify most of the effects of instrumental drift.

The absolute reflectance is given by :

where the first ratio expression is the usual reflectometer value (the apparent reflectance) while the second ratio expression is the correction factor for the interreflection effect, and provided that the sample receives a complete and uniform hemispherical irradiation.

In practice, when strongly diffusing samples are measured small geometrical corrections have to be applied for the missing flux-weighted solid angle of the small central aperture and for the missing flux-weighted solid angle beyond 85°. For samples that are mirror-like or which spread reflected flux over a small solid angle, no such corrections are appropriate.

Emittance

For samples where there is no transmittance in the spectral range of interest the spectral absorptance may be calculated as the complement of the spectral hemispherical reflectance and then by Kirchhoff's Law the spectral absorptance is equal to the spectral emittance.

Where values of total emittance are provided, the spectral emittance multiplied by Planck's Radiation Function is integrated over the full range of measurement for each of the temperatures of interest to give the corresponding total emittances. The full wavenumber-dependent version of Planck's Radiation Function is used, and the result normalised by dividing by the integral of the Planck spectral power over the same wavenumber range. This spectral range for integration is sufficient to prevent significant errors arising from the absence of contributions to the integrals from beyond either end of the spectral range covered. Total emittances are given as absolute decimal fractions to conform to usual practice in heat-flow work.

The above procedure assumes that the spectral absorptances are unaffected by modest temperature changes. This will be substantially true for surfaces that undergo no chemical or physical change over the temperature range from ambient to that used for a calculation of total emittance.

References

1. F J J Clarke and J A Larkin, High Temperatures - High Pressures, 17, 89 - 96 (1985).
2. F J J Clarke and J A Larkin, Procs. Soc. Photo-Opt. Instrum. Engs., 917, 7 - 14, (1988).