Reflectometers have been constructed with a variety of light sources. Pulsed sources, such as a pulsed xenon source, have the following advantages: (a) high ratio of usable light to power and heat generated; and (b) a use of power that is limited to the time when a test element is to be read. A pulsed xenon source is particularly useful in illuminating at wavelengths between 300 and 400 nm, such wavelengths being of particular interest for certain test elements. However, such pulsed light sources have the disadvantage of being structured rather than diffuse. That is, the arc itself rather than a general light is imaged. The structure and position of the arc generating the light varies from pulse to pulse as does the color temperature. Therefore, it has been well recognized that reflectometers using such a source require integrating means to convert the structured light into diffuse light. Examples are shown in FIG. 1 of U.S. Pat. No. 4,076,421 and in U.S. Pat. No. 4,022,534 wherein a mirrored surface is used in conjunction with a diffusely transmitting surface. One problem with such prior reflectometers has been that light that is not initially diffusely sent direct to the sample, tends to be lost. For example, the device of the '421 patent states such light is either absorbed by the wells of the cavity or reflected out through the detecting aperture, without ever striking the sample (col. 2, lines 36-38). The device of the '534 patent directs such light to baffles that absorb the light. Such lost light drastically reduces the efficiency of the reflectometer, necessitating a more powerful light source to make up for the reduction in efficiency. Such increased power requirements in turn have made the use of pulsed light sources less attractive, prior to this invention.