[Laser] How to measure beam angle?

[Stuart]

Hello again Mike,



I thought I would chip in here. With lasers , divergence depends on the beam divergence of the particular laser. You can improve on this by using an optical beam expander where the the diameter of the output aperture becomes the controlling factor. You can then calculate the spread from diffraction theory. My 6" telescope makes an excellent beam expander. Diffraction angle, Theta, of a circular aperture, diameter D, is 
Theta = 1.22 lambda/D,  where lambda is the wavelength of the light.
For my 6" telescope, D= 0.15m, and lambda = 6.3 x 10-7m for red light which makes the  diffraction about 5 microradians, so at 33km my 6" wide beam would only spread to a patch of light just 1.5m across neglecting the atmospheric "wobbling". You just try finding it at that distance! It is just too difficult to aim without massive mounts and so on.
 
With LEDs, the spread depends on the lens used for focussing the light. I have found that simple magnification theory gives a close result. simply divide the LED diameter by the focal length of the lens to give you the beam angle. for example, my 1mm square Golden Dragon LED in front of the 330mm focal length lens gives a (total) beam angle of sin-1 (1/330) = 0.0030303= about 0.2 degrees. If you relate object  distance (LED to lens), to image distance, (lens to far receiver) you can calculate the ratio of distances, and then the size of the image (equals patch of light you are creating). Again with my rig at 33km the image distance is 100 000 times greater than the object distance and so the image size will be 100 000 times greater at 100m square, and so your aim would have to be good enough to hit your target within this limit. The last time out at 46km I found my error to be of the order of the size of a car using good alignment and powerful optics, so this was practicable.
If you want to hit a retroreflector, I think you would have to calculate from the area of the retroreflector, how much of your beam is going to hit it and then count on the reflected beam travlling back to the transmitter, spreading at the same rate as it travelled out to the reflector. Even a 1m square reflector would only intercept one ten thousandth of my 100m square beam at 33km and then there would be a further loss as the beam returned and would then be a 2m square patch of light ( ie 4m2 area), this would require careful alignment if it could be made to work.


Stuart





,

Hi All,

I should know this but just when I think I have it, puff! So tell me again.

How do you determine/measure the beam angle for a laser or LED?  I know how to 
do the math but I'm looking for beam diameter/spread at any distance. More to 
the point, if a beam 'strikes' a retro-reflector, albeit a long distance away, 
(like a satellite) is the beam spread dependent on the source laser or the 
retro's physics?

Knowing the beam power (laser or LED) what is the signal loss (in db) with 
distance?

Mike C.