Let us calculate LR_GIA, WLR_GIA, LR_MSU, and the brilliance BR, for this new object. Since the angular size of the original mirror is small, LR_GIA will remain almost the same, slightly fluctuating around LR_GIA0. (Since GIA weighs the light return using COS*COS function, a weighted coefficient, WLRGIA may slightly change with respect to WLR_GIA0 and fluctuate, depending on the distribution of the tilt angles of the mirror portions.

Probably, one of the main purposes of introducing the weighing procedure was the necessity of some non-negligible variations of LR_GIA. In fact, the coefficient WLR_GIA is a measure of the spatial distribution of the reflected light. As for the observer, he will see a certain number of lamp reflections. The minimum possible number is 0. The maximum equal to 100 is achieved in the case when each mirror portion reflects light towards the observer's eye. All the lamp reflections will be as bright as the single reflection visible before the mirror was split. The actual number of these reflections depends on the tilt angles of the mirror portions and the positions of the lamp and the eye.

(If the observer views the mirror with two eyes, the number of visible reflections fluctuates within the same limits, but the average number will be two times as large as that in the case of single-eye viewing. This is because each reflection could be detected by either the right or the left eye, which are spatially separated. When your eyes see the two spots on the flat mirror your brain merges them into one spot. But when you look at two mirrors and each eye sees one reflection in each mirror the brain will perceive two reflections).

You will probably agree that the brilliance (BR) substantially depends on the number of simultaneously viewed reflections. The larger this number, the more brilliant the mirror looks.

To a first approximation, we can assume that the BR coefficient is proportional to the number of visible reflections. (Here we use the fact that all the reflections have the same brightness). Accordingly, BR will randomly oscillate in the range from 0 to 100 BR₀ (the expectancy of this function depends on many parameters, in particular, on the distribution function of the tilt angles of the mirror portions). This is easier to comprehend if you again imagine a mirrored disco ball. In any specific case, you would see a few lamps, the brightness of each lamp coinciding with that of the single reflection visible before the mirror was split.

The software calculates the coefficients LR_GIA, WLR_GIA, and LR_MSU, the left column containing their current values. As for the right column, it contains the mean values of the coefficients, averaged over the time passed since the software was started or the Refresh button was pressed. You may vary the maximum tilt angle of the portions and change the random orientations of all the portions at once. How many highlights do you see on average?

Run Brill software - Mirror example #3

By comparing his/her own impression of the highlights with the values of the coefficients, a careful reader may notice that the visual impression suggests that there are a few highlights, while the coefficients hardly exceed unity.

This is due to "inertia" of human vision: visual stimuli do not abruptly decay after the object causing them disappears from the computer screen. If this decay time exceeds the mean interval between successive highlights, we see more highlights than that the screen instantly contains. This feature of human vision is very important when observing scintillation of a diamond.

The authors suppose that if there was no such feature (temporal contrast), the observer would not distinguish scintillation from the general impression of the diamond.

The software operates exactly as before, but the mirror swings slower than in the previous case. How many highlights do you see on average now?

Run Brill software - Mirror example #4