Power and Divergence calculations?

[grw110]

Hi,

I'm a self-confessed newb, and am hoping to get some guidance from the much-more-experienced folks in the forum, so that a science project I'm looking to perform ends up being a) viable, and b) as safe as possible. Thanks in advance for any guidance or suggestions.

There are 2 calculations I'm trying to work through. First, on safety: the project involves shooting a (ideally, low-powered) laser across a 2- to 4-mile distance, to a retroreflector / cat's eye, in a nearly-uninhabited rural area (eastern Washington state - effectively middle-of-nowhere.) My question is: how do I think about delivered power, for the retroreflector target approx 2 4 miles away? Will, say, a 100mW laser dissipate to a something more like 5mW laser, at that distance? (Is there a simple equation to use that shows landed power - and that I can trust enough, if eye safety is involved?) What should i think about for factors-of-safety?

It may seem strange, but it's possible that at that distance, there could be wildlife that a laser could land on before it tracks to the target. I want to know how much I should sight my target with something low-power, before increasing (as little as possible) the power in order to get something visible reflected back. I know that laser power should fall off with the square of the distance - I'm looking for something that formalizes that a bit more in a calculation so that I know the potential consequences of the power landing at the target (and reflecting back).

2nd question - i'm looking for similar calculations that can help with choosing a beam expander. Over that distance, I (obviously) need to expand the beam in order to minimize divergence. When buying a beam expander, how should I think about trading off between beam diameter and divergence? Does anyone know of example calculations that would be helpful to follow?

Incidentally, this science project (for kids) is a bit of a poor-man's take on the link follows) re-discovering the Lunokhod soviet lunar rover - great story if you haven't read it. I'm essentially trying to replicate the same technique, using inexpensive gear and over a few-mile (horizontal) distance, instead of bouncing a laser all the way to the moon and back .

thanks!

 

[Alaskan]

Here's a link to a online calculator where you can determine how big your spot will be at a given distance, of course if the beam is oval or rectangular, there will be the same exaggeration, just larger. To use this, you need to know how wide the laser beam is within a specific distance of leaving the laser, i.e. 2mm @ 1 foot, as well as the lasers divergence. These specifications can sometimes be obtained from the manufacturer, if they don't give them, there are methods of determining them yourself too:

pseudonomen137's JScript Diameter Calculator

After you have determined the at a distance beam diameter, you can calculate the amount of power from the spot which can enter the eye by knowing what the percentage of its total area is compared to the diameter of a open pupil, if the diameter of an open pupil (adjusted to low light conditions) is 1% of the spot size, that's an easy conversion, just one percent of the total power in the spot. However, most 532nm lasers aren't purely TEM00 or may have some of the power higher or lower within a portion of the beam, so your figures could only be approximations. Here's a online power density calculator:

Laser Power Density Calculator | Calculator.swiftutors.com

You can search "laser power density" either here or on google and get the formula. If the amount of power entering the pupil is far below 5 mw I suspect there is little to worry about, but some animals have very large pupils and further research is needed to know how they may be affected. As far as atmospheric loss over that distance, that can vary, but if you assume no loss, you can't go wrong there. What do you plan on using, 532nm, 520nm, 445nm+ ?

Go to this web site too, they have some graphs showing some power levels at distance and the eye hazards they can produce from common pointer lasers:

Laser Pointer Safety Info: http://www.laserpointersafety.com/safetyinfo/styled-10/index.html

Here's a another one of their pages, perhaps is exactly what you are seeking: http://www.laserpointersafety.com/safetyinfo/safetycalcs/index.html

Regarding beam expanders, if your laser produces a divergence of 1.5 mRad, and you expand the beam by 10X, the divergence will be about 1/10th, or .15 mRad. You can pretty much figure anything out from there, using the above online spot size calculator, just input the lasers divergence after the expander into the calcuator.

There are some members here who can be very concise and perhaps just throw some numbers out for you, let's see what other kinds of responses we get in the thread. I'm fairly new to lasers as a hobby, don't work in this area professionally, some members do.

 

[lazeristasUVISIR]

First, on safety:

Very good. :beer:

Will, say, a 100mW laser dissipate to a something more like 5mW laser, at that distance?

The laser power will not dissipate a lot if there is no fog/dust/smog/haze. Do you see well trees/bushes over 2 miles distance?
However, (in general) the beam power intensity (Power/BeamArea) will decrease if your optics are not optimized - the beam is sent with a large divergence.

It may seem strange, but it's possible that at that distance, there could be wildlife that a laser could land on before it tracks to the target.

Shoot little higher than your highest animal. Don't shoot too high as a helicopter might be around. Check your local rules about lasers shows, even if you are not doing it. Even a call to police might prevent you from a jail time later.

I'm looking for something that formalizes that a bit more in a calculation so that I know the potential consequences of the power landing at the target (and reflecting back).

A range (lidar) equation is your friend. Just google it. It is complicated but as for a project it is great to learn about it.

2nd question - i'm looking for similar calculations that can help with choosing a beam expander. Over that distance, I (obviously) need to expand the beam in order to minimize divergence. When buying a beam expander, how should I think about trading off between beam diameter and divergence? Does anyone know of example calculations that would be helpful to follow?

imho, the 532-nm laser has a great circular beam and math is quite simple with it. Gaussian beams are your friends again. Gaussian beam - Wikipedia, the free encyclopedia

Good luck. And keep posting updates