Wednesday, June 18, 2008

Calibrated Reflectance

It is commonly stated that reflected-light meters are calibrated to an 18% reflectance, but the calibration has nothing to do with reflectance, as should be evident from the exposure formulas. However, some notion of reflectance is implied by a comparison of incident- and reflected-light meter calibration.

Combining the reflected-light and incident-light exposure equations and rearranging gives

Reflectance ζ is defined as

A uniform perfect diffuser (i.e., one following Lambert's cosine law) of luminance L emits a flux density of πL; reflectance then is

Illuminance is measured with a flat receptor. It is straightforward to compare an incident-light measurement using a flat receptor with a reflected-light measurement of a uniformly illuminated flat surface of constant reflectance. Using values of 12.5 for K and 250 for C gives

With a K of 14, the reflectance would be 17.6%, close to that of a standard 18% neutral test card. In theory, an incident-light measurement should agree with a reflected-light measurement of a test card of suitable reflectance that is perpendicular to the direction to the meter. However, a test card seldom is a uniform diffuser, so incident- and reflected-light measurements might differ slightly.

In a typical scene, many elements are not flat and are at various orientations to the camera, so that for practical photography, a hemispherical receptor usually has proven more effective for determining exposure. Using values of 12.5 for K and 330 for C gives

With a slightly revised definition of reflectance, this result can be taken as indicating that the average scene reflectance is approximately 12%. A typical scene includes shaded areas as well as areas that receive direct illumination, and a wide-angle averaging reflected-light meter responds to these differences in illumination as well as differing reflectances of various scene elements. Average scene reflectance then would be

where “effective scene illuminance” is that measured by a meter with a hemispherical receptor.

ISO 2720:1974 calls for reflected-light calibration to be measured by aiming the receptor at a transilluminated diffuse surface, and for incident-light calibration to be measured by aiming the receptor at a point source in a darkened room.

For a perfectly diffusing test card and perfectly diffusing flat receptor, the comparison between a reflected-light measurement and an incident-light measurement is valid for any position of the light source. However, the response of a hemispherical receptor to an off-axis light source is approximately that of a cardioid rather than a cosine, so the 12% “reflectance” determined for an incident-light meter with a hemispherical receptor is valid only when the light source is on the receptor axis.

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