n
According to
Bloch’s Law of vision
, a photoreceptor will fire whenever the summed luminous energy over a critical time period reaches the photoreceptor’s threshold. That is, a photoreceptor can sum luminous energy over time. Thus, the total luminous energy reaching a photoreceptor within a critical period is considered to be a constant k , which is also the firing threshold of a photoreceptor.
The threshold of the photoreceptor is reached whenever the product of the luminosity of the light source (L) and the duration of that light course (t) equals that constant (k). The exponent (n) on t describes whether temporal summation is complete (n = 1), partially complete (0<n<1), or when light has not been presented (n = 0).
For example, say we have a light that is equal to 100 cd/m 2 (candelas per meter-squared: a measure of luminance), and it presented for 10 ms. Here, we have a total luminous energy (k) equal to 1000, which can stimulate photoreceptors with thresholds (k) equal to 1000.
Interestingly, and based on Bloch’s Law, luminance (L) and time (t) are reciprocal: if you change one you can do the opposite to the other and achieve the same total luminous energy. Thus, if you double the luminance (200 cd/m
2
) you would need to halve the time that the light is presented (5 ms) to achieve k = 1000 units of energy.
Below is a table displaying how lights presented at different durations (10 ms, 20 ms and 40 ms) can have the same perceived brightness by varying the luminance of the light. In this table, “Brightness Level” is simply the subjective brightness of the light, and “Total Energy” is simple the duration of the light multiplied by the luminance level of the light.
Brightness Level 10 ms duration 20 ms duration 40 ms Duration Total Luminous Energy (k)
1 10 ms x 20 cd/m
2
20 ms x 10 cd/m
2
40 ms x 5.0 cd/m
2
200
2
3
4
10 ms x 30 cd/m 2 20 ms x 15 cd/m 2 40 ms x 7.5 cd/m 2
10 ms x 40 cd/m
2
20 ms x 20 cd/m
2
40 ms x 10.0 cd/m
2
10 ms x 50 cd/m
2
20 ms x 25 cd/m
2
40 ms x 12.5 cd/m
2
300
400
500
Try the following:
1) Light A is flashed for 50 ms with a luminance of 3 cd/m
2
. Light B is flashed for 75 ms. To have equal brightness, at what luminance must Light B be presented?
2) Light C has luminance of 5 cd/m
2
and a Total Luminous Energy (k) of 5000. For how long was Light C presented?
[Answer #1: 2 cd/m 2 , because 50 ms x 3 cd/m 2 = 150, and we know that the total luminous energy of the Light
B must also be 150 for both lights to be equally bright. By rearranging Bloch’s Law to solve for L, which is what we need for Light B, we have: L = k/t. Thus, 150/75 = 2 cd/m
2
.]
[Answer #2: 1000 ms, because we can rearrange Bloch’s Law to solve for t, which is what we need to determine for Light C. Thus, we have: t = k/L = 5000/5 = 1000 ms.]