In a recent column (PT May/June 2008) we discussed average scene reflectance. Our analysis of 150 outdoor images led us to conclude an average scene reflects 12.4% of the incident light, about a half-stop darker than Kodak’s 18% gray card, which is popularly assumed to represent average scene reflectance. But we also noted that the instructions accompanying that card sometimes recommend giving a half-stop more exposure than it indicates, making it the functional equivalent of 13% gray. A very closely related topic we will discuss here is what reflected light meters assume average scene reflectance to be.
Surprisingly, they make no explicit assumption whatsoever. The specs for reflected light exposure meters are detailed in ISO 2720-1974 (E), “Photography—General purpose photo- graphic exposure meters (photoelectric type)—Guide to product specification.” The master equation defining such a meter is this: St/A2 = K/L. S is the ISO speed you set on the meter, A (aperture) and t (shutter speed) are the recommended camera settings the meter displays when viewing a scene of luminance L (essentially the brightness of the light being reflected into the meter). And lastly there is the term “K” in the equation, the so-called meter-calibration constant. The ISO standard permits values in the range of 10.6 to 13.4 to be assigned to K. The standard goes on to recommend that a manufacturer select a specific value within this range by having large numbers of observers inspect large numbers of images of large numbers of scenes.
This same standard also details all of the procedural considerations in the design of incident light meters. The equation governing these devices is very similar: St/A2 = C/E. Illuminance, E (incident light), replaces luminance, L (reflected light), and a new calibration constant, C, replaces K. The standard stipulates that C may have values in the range 240–540, depending on details of the meter’s construction. Neither of these equations tells us anything about presumed scene reflectivity. But a combination of the two equations indeed contains an implicit statement about average scene reflectance.
An incident meter will return a single set of shutter speed/aperture settings (value of t /A2), depending on the intensity of the available light. A reflected light meter, on the other hand, can return many different values depending on whether it is pointed at darker or lighter subject matter. But within that spectrum of darker to lighter reflectances, there is a value that will suggest the same camera settings as the incident meter. This is what we take to be a reflected light meter’s intrinsic assumption of average scene reflectance. To learn what value this is, divide the first equation above by the second. Recall we are specifying a situation where both meters display the same value of St/A2, so that term cancels out, leaving L/E = K/C: The ratio of L, light reflected by the average scene, to E, light incident on it, is the same as the ratio of K to C. And any textbook on optics teaches that if L and E are expressed in the units specified in the ISO standard, this ratio of L/E is also equal to R/π – scene reflectance divided by pi. So C/K = R/π, plug in values for C and K, and out spills the magic average scene reflectance, R, assumed by a reflected light meter.
This is where it gets tricky; it’s been just arithmetic to this point. Meter manufacturers appear not to want to publicize the values they assign their meters’ calibration constants. At least we have had little luck unearthing many on the Web. An exception is Sekonic who are quite forthright about their choices for many of their meters. They assign 12.5 to K and either 250 or 340 to C. Why two choices for C? Their incident meters can be used with either the traditional hemispheric dome over the light sensor (C = 340) or a flat diffusing disc (C = 250). The ISO standard recognizes both types, but for the disc type receptor it recommends camera settings be based on the logarithmic average of readings taken with the meter pointed at the camera and at the main light. (Does anybody do this?) Consider instead the popular hemisphere. Take an incident reading with it in place. Then take a reflected light reading from the scene. If both readings suggest the same camera settings, then K/C = 12.5/340 = .0368 = R/π, and R = 11.5%! The 250 value for the disc sensor yields R = 15.7%, but the significance of this figure is less clear given its guidelines for proper use; besides, real subjects are three-dimensional and can receive illumination from all the extreme angles as does the hemispheric dome.
Our conclusion? Reflected meters, at least from Sekonic, make the same camera setting recommendations as their incident meter with the hemispheric dome if looking at a scene averaging 11.5% reflectance. Rounded to the nearest whole number, that 12% assumption is the same as the 12% we actually measured for our 150 scenes. Coincidence? We think not, but if it is,
it’s at least a satisfying one.