How Many Lumens Are Needed to See a Flashing LED at 500 Meters?

[Shnuk]

Hey,

I want to know how many luminous (of lamp/led) do I need to see well a flashing lamp/led in the night in a distance of 500 meters.
I would like also to know how to calculate it.

Thanks ahead

 

[arunma]

Here's one way you could do it. If you know the luminosity (i.e. wattage) of the lamp, you could calculate the intensity like this:

$$I = \dfrac{L}{4\pi r^2}$$

This of course assumes that the radiation is distributed isotropically, which means you're not enclosing the lamp in a mirror or anything. Next, you can multiply the intensity by the surface area of a human pupil to find the total power of the light entering the eye:

$$P = IA$$

$$P = \dfrac{LA}{4\pi r^2}$$

Now, you can impose light quantization ($E = nhc/\lambda$), and write:

$$P = \dfrac{hc}{\lambda}\dfrac{dn}{dt}$$

$$\dfrac{LA}{4\pi r^2} = \dfrac{hc}{\lambda}\dfrac{dn}{dt}$$

$$\dfrac{dn}{dt} = \dfrac{\lambda}{hc}\dfrac{LA}{4\pi r^2}$$

Now we talk to the physiologists, who tell us that the human eye can see as little as ten photons per second (if the source is flashing). So you go and measure the area of the human pupil, plug in the 500 meters and the luminosity of the bulb as well as the wavelength (i.e. color) of the light, and see if you've got at least ten photons per second.

Of course my calculation didn't really take into account certain wave effects, like diffraction through the pupil, so this is really only a first approximation.

 

[Shnuk]

Hey,

Thanks you very much, that was a really good explanation.
I have one more question. If I want to calculate it for the white light, as I understand I need to integral
$$\int{\dfrac{dn}{dt}}{d{\lambda}} = \int{\dfrac{\lambda}{hc}\dfrac{LA}{4\pi r^2}{d{\lambda}}$$
where lambda runs from 0.4um to 0.7um

Am I right?
if I am not, so how should I do?

Thanks ahead.

 

[Danger]

Math aside (and those were some great equations), remember that the eye is a biological structure that isn't governed entirely by such things. My eyesight isn't great by any means, but I can see a firefly flash at a hundred metres on a dead-dark night. With moonlight, or in daylight, I couldn't see the damned thing if it were sitting on the end of my nose. Ambient light plays a huge role in how things are perceived.

 

[Shnuk]

Maby my initial quiestion was wrong.
What I want is to see a flashing light diode (power diode) at a clear night from a distance of 500 meters when 3-4Km from me there are lights of a city.
I want to know what led should I choose (how many luminous does the led have) to see the flashing light clearly.

Thanks ahead

 

[Doug Huffman]

Now we talk to the physiologists, who tell us that the human eye can see as little as ten photons per second (if the source is flashing).

Single photons of sufficiently high energy have been reported as visible by astronauts.

The OP may be seeking conspicuity, that is a very specialized subject important to bicyclists.

 

[Andy Resnick]

Hey,

I want to know how many luminous (of lamp/led) do I need to see well a flashing lamp/led in the night in a distance of 500 meters.
I would like also to know how to calculate it.

Thanks ahead

You need a lot of specifications. First, a specification for the radiance or alternatively, a function of emittance with angle. That tells you how much light is going in a particular direction. Then you need to know the spectrum of emittance, because that tells you how well your eyes can see it (standard eyes, color blindness will affect this). Then you also need to know the contrast between the light and background. Finally, you need to know the rate of flashing- your vision has different acuity for flashing/moving lights than for static sources.

Some points of reference: for unresolved (point-like) sources, the visual threshold is about 1 milliLambert for 100% contrast, and 100 milliLambert for 20% contrast.