Silly question about flashing...

February 6, 2008 7:44 AM

I have a question about persistence of vision and flashing lights... There will be maths and biology involved.

Imagine you have two LEDs. They each produce one hypthetical unit of light (1 HUL if you will). If they're both turned on, they produce a combined 2HUL.

Now imagine that they flash at a rate greater than 25fps in a way that when one is on the other is off.

Ideally they are producing 1HUL. In reality the light up time probably means it's a little less than this. But here is my question:

What does the human eye *think* they are producing? Do you see the equivalent of 1HUL, 2HUL or somewhere in between? Does it matter if you are looking directly at the LEDs or at a surface being illuminated by them?

I've used 25 fps here since with cartoons a frame rate above 25 fps creates a moving image... it may be a red herring.

posted by twine42 to science & nature (3 answers total)

AFAIK, 1HUL - but you might want to find out if human perception to light is linear. I don't know off the top of my head, but many human senses are logarithmic (hearing for sure).
posted by plinth at 8:46 AM on February 6, 2008

Unfortunately the answer is not simple and depends on the luminance of the lights, the wavelength, ambient conditions, and what part of the retina the lights fall on. So the short answer is you have to do the experiment.

I'll try to explain why. This website is an excellent resource for understanding how vision works and includes some nice charts of the psychophysics that I'll try to explain.

Boch's law says that luminance is interchangeable with duration. So if you have half the luminance but it goes on for twice the duration then the apparent luminance is the same. In equation form it would be L x t = k, where L = luminance, t = time and k = a constant. The period over which this relationship holds is called the integration time. For cones it is ~20 ms and for rods, ~100 ms. A signal of 25 Hertz has a period of 40 ms, which is above the integration time of the cones but less than that of the rods. This leads me to think that the rods will see 2 HUL and the cones, 1 HUL, but that isn't the whole story.

The critical flicker frequency (CFF) is the frequency at which the eye shifts from perceiving individual flashes to a continuous light source. As you may imagine it's actually a function of luminance. The critical frequency increases with brightness so brighter lights need to flash at higher frequencies to appear constant.

Unfortunately it's even more complicated because the CFF depends on the wavelength of light. Short wavelengths (blue) of light have a lower CFF than higher wavelengths. This is a result of the separate system of S (blue) cones in the retina. The S cones are more widely spaced and wired separately from the M (green) and L (red) cones.

Also, because rods and cones have different response times, the CFF depends on where on the retina you shine the light because the fovea is cone dominated and the periphery is rod dominated. It also depends on the apparent size of the light for the same reason.

The light will most likely be stimulating rods and cones simultaneously so my guess is somewhere between 1 and 2 HUL but the exact value is dependent on too many factors to know.
posted by euphorb at 9:34 AM on February 6, 2008 [2 favorites]

euphorb - thank you! I had assumed that the question was either unanswerable or depended on too many things. Thanks for taking the time for that. I have lots to read...

And to everyone who may read this at some point or other - I did indeed mean Hertz not fps. That's what happens when you rearrange the question and don't proof read. :)
posted by twine42 at 1:22 PM on February 6, 2008