Apparent intensity of LED

Colleagues,

I’ve put together a simple PIC-based LED dimmer. It has a low-side MOSFET that drives six (6) blue LEDs connected in series. The current through the LEDs is pulse-width modulated. The duty cycle is varied linearly from 0 to 100% in 3 seconds.

An interesting thing happens to the perceived brightness of the LED. It grows much more rapidly in the beginning of the ramp, and slowly towards the end. The curve for measured intensity vs. current is linear for my LED.

On the web, I’ve come across an empirical rule (don’t remember its exact name) that says that often human perception of parameters is a log function.

Could anyone shed some light on this? Are there known good patterns for a “pleasantly gradual” ramping of the LED brightness?

Thanks,
- Nick

You have opened an interesting aspect of our perceptions. Perception of light intensity depends on several factors, including your mood. However, I don't think your mood changes as you increase the duty cycle (i.e., you get depressed).

To explain your observation, I would consider 4 factors:

1) Changing from rod to cone vision as you go from dim to intense light -- I suspect that is relatively unimportant in your example.

2) An optical illusion of perception:

Here is an interesting article on light perception.

This example is taken from that article. The vertical bars are the same intensity.



At low intensity (low duty cycle), you could be perceiving light on a mostly dark background. At higher intensities (higher duty cycle), the light is perceived on a mostly light background (as in the example) and doesn't appear as bright.

3) Flicker response: our eyes are more sensitive to flicker than to steady light, particularly if coming from our peripheral vision. Think of being the hunted in a jungle to see why that would give a survival advantage. Thus, lower duty cycle might excite more flicker response as compared to a higher duty cycle that would be perceived as a steady light.

4) Finally, application of Beer's (Beer-Lambert's) law:

Excluding all perceptive and anatomic factors (e.g., pupillary response, neuro-modulation, and as discussed above) and looking only at the chemistry, the equation for absorption of light is:

O.D. = εcl ;

where ε is a constant (molar absorption, extinction coefficient), c is concentration, and l is the length of the light path. O.D. (optical density) is logarithmic and is defined as:

O.D. = log ( incident intensity/transmitted intensity)

One usually manipulates those equations assuming constant light intensity and variable concentration. But consider it from another aspect. Consider that the light is varying and calculate the proportion of molecules, in this case cones in the eye, that absorb it. Furthermore, assume that each excited cone gives just one unit of response.

Hypothetically, start with a light intensity that excites half of the cones in the eye. Now, double the intensity. Will all of the cones be excited? No, only half of the remaining cones will be. So the light will appear brighter, but the number of excited cones times response per cone will not be twice. It will only be 50% more or 75% of the maximum, if all of the cones were excited. Similarly, if the light is reduced by one-half, one-forth of the cones will be excited. The number of cones times response per cone will be 25% of the max (total). Thus, successive doubling/halving of light intensity would excite 25%, 50% and 75% of the cones. That is, a logarithmic change in intensity gives a linear change in percentage of cones excited. In other words, the relationship would be logarithmic.

I am not at all sure that cones respond/excite so simplistically and that their neuro- response is simply one unit per cone. In fact, I suspect it is much more complicated. Our eyes can see over many orders of magnitude in light intensity. Nevertheless, this over simplification might provide some insight into why it is probably logarithmic (or more complex), not simply linear.

John