# Relation between laser frequency and range?

#### cgardhar

Hi,

I am working on building a laser range finder and wanted to know if there is any relation between the frequency/wavelength of laser wave and the maximum distance it can measure.

I read that the maximum distance it can measure depends on the power of the laser.

Any other links, resources etc. are welcome.

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#### berkeman

Mentor
Hi,

I am working on building a laser range finder and wanted to know if there is any relation between the frequency/wavelength of laser wave and the maximum distance it can measure.

I read that the maximum distance it can measure depends on the power of the laser.

Any other links, resources etc. are welcome.
As long as it is travelling through clear air, I don't think it makes much of a difference. Yes, just as with radar, the higher the traansmit power, the greater the range. You will get the biggest range gain if you can put an explicit reflector on the target (like a cube corner reflector). What is your target?

Also, please be aware of laser safety. Especially if you are directing a moderately powerful laser over a distance, you need to be aware of the potential eye safety issues.

#### turin

Homework Helper
Isn't there a relationship between beam spread (θ), wavelength (λ), and aperture (D) such that θ is approximately proportional to λ/D?

Beam spread will result in a lower intensity beam upon reflection, ceteris paribus. So if there is such a relationship, then shorter wavelength will allow larger distances, ceteris paribus.

#### berkeman

Mentor
Interesting, I didn't know that. Thanks.

#### cgardhar

As long as it is travelling through clear air, I don't think it makes much of a difference. Yes, just as with radar, the higher the transmit power, the greater the range. You will get the biggest range gain if you can put an explicit reflector on the target (like a cube corner reflector). What is your target?

Also, please be aware of laser safety. Especially if you are directing a moderately powerful laser over a distance, you need to be aware of the potential eye safety issues.
I am actually building a LIDAR for urban mapping. So its mostly cars and buildings and people.

Isn't there a relationship between beam spread (θ), wavelength (λ), and aperture (D) such that θ is approximately proportional to λ/D?

Beam spread will result in a lower intensity beam upon reflection, ceteris paribus. So if there is such a relationship, then shorter wavelength will allow larger distances, ceteris paribus.
So you mean that a short wavelength laser with high power would be my best bet, as long as it conforms to the safety requirements.
Thanks for the equation. Can divergence be used as a factor to justify the use of laser instead of radar?

#### berkeman

Mentor
I am actually building a LIDAR for urban mapping. So its mostly cars and buildings and people.
So you might consider using an IR laser to be more stealthy (even though it sounds like you will get a little less range compared to visible light). I don't think folks will take too kindly to having a visible laser bounced off of them. You also run a high liability risk (and it may be illegal) bouncing a visible laser off of cars that are in motion...

#### turin

Homework Helper
Well, I put a question mark after my equation for a reason. I think that there is a similar equation that relates theoretical minimum beam waste to theoretical minimum beam divergence, or something like that. And, there is also a similar equation in astronomy, for angular resolution. I just don't know if it is particularly relevant for range finders. For instance, the air itself may introduce some attenuation, and there may be some "windows" for certain wavelengths. This may be much more important consideration than some theoretical beam divergence. I'm not an optics expert.

#### Bob S

The distance to the Moon has been measured to several (10 or 20?) cm by Laser ranging. Astronauts left several corner-cube reflectors on the Moon during one of their visits. The main measurement limitation is primarily due to the laser beam divergence. The laser beam spot on the Moon is roughly 1 km in diameter, so very little laser light gets reflected.
Well, I put a question mark after my equation for a reason. I think that there is a similar equation that relates theoretical minimum beam waste to theoretical minimum beam divergence, or something like that. And, there is also a similar equation in astronomy, for angular resolution. I just don't know if it is particularly relevant for range finders. For instance, the air itself may introduce some attenuation, and there may be some "windows" for certain wavelengths. This may be much more important consideration than some theoretical beam divergence. I'm not an optics expert.
The product of the waist size and the beam divergence represents the beam phase space, which is also a preserved (or should be) constant in charged particle beams. Unfortunately in charged particle beams, Coulomb forces cause the phase space to increase, unless the beam is constrained by strong-focusing magnets.

Bob S

The present laser-ranging limit to the Moon is about 1 mm, using a 532-nm Nd:YAG laser.

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#### Claude Bile

Typically the spot-size of the laser does not affect the overall dynamic range of the measurement. That is, a large, low intensity spot is just as easy to detect as a small, high-intensity spot.

Spot-size typically affects the resolution of your measurement. A small spot-size will be able to pick out smaller features than a large spot-size.

Typically with LIDAR you are constrained by the laser sources and detectors you have available. High-powered solid-state lasers are best, and of these, Nd:YAG lasers are king. Short-pulsed lasers also have found some use, as their high intensity induces filamentation, which prevents the beam from spreading as it propagates.

In short, power is your primary consideration, wavelength will be determined by available sources (and also other considerations such as atmospheric transmission windows, eye-safety etc.).

Claude.

#### Redbelly98

Staff Emeritus
Homework Helper
Isn't there a relationship between beam spread (θ), wavelength (λ), and aperture (D) such that θ is approximately proportional to λ/D?
Yes.

For a Gaussian-shaped intensity profile, we have

θ = (λ/wo) / π
where
θ is the 1/e2 half-angle, or approximately the FWHM angle of spread,
wo is the 1/e2 intensity radius, or approximately the FWHM beam diameter, at the beam focus.

.

Note: Θ = 2θ
Figure from http://en.wikipedia.org/wiki/Gaussian_beam

You can google: gaussian laser beam -- for more details.

#### Andy Resnick

Hi,

I am working on building a laser range finder and wanted to know if there is any relation between the frequency/wavelength of laser wave and the maximum distance it can measure.

I read that the maximum distance it can measure depends on the power of the laser.

Any other links, resources etc. are welcome.
Other than the good discussion regarding beam divergence, nobody has really mentioned atmospheric absorption, nor safety regulations regarding beam power- both constraints limit the range. LIDAR systems generally use pulsed sources as well, Nd:YAG and CO2 are very common.

ERIM's IR/EO handbook (I believe available online) has a lot of good information about LIDAR systems. A simplified version of the laser range equation they present is:

SNR = $$\frac{\int I d\omega}{NEI} f \frac{exp[-2(kR+\alpha L)]}{R^{2}}$$

where
SNR = signal to noise ratio
I = radiant intensity of laser, the integral is performed over the solid angle of the target as seen by the receiver
NEI = noise of rceiver
f = reflectance of target
k = atmospheric attenuation
R = range to target
$\alpha$ = absorption coefficient of particulates in atmosphere
L = effective thickness of particulates

#### yutian.tan

loss of laser transmission through air

Hi,

Is there a way to calculate the loss of laser transmission through air?

Appreciate that you can help.. Thanks...

#### berkeman

Mentor
Re: loss of laser transmission through air

Hi,

Is there a way to calculate the loss of laser transmission through air?

Appreciate that you can help.. Thanks...
The post right above yours would seem to answer your question, no?

#### yutian.tan

Difference between Specular Reflection on the Sea

Hi,

Need help on the calculation of Specular Reflection on the sea, what formula can i use to calculate?

Thank You..

#### berkeman

Mentor
Re: Difference between Specular Reflection on the Sea

Hi,

Need help on the calculation of Specular Reflection on the sea, what formula can i use to calculate?

Thank You..
That would appear to be an entirely different question from what was asked originally in thie thread. What is your application?

#### phythpr

Hi,

I am working on building a laser range finder and wanted to know if there is any relation between the frequency/wavelength of laser wave and the maximum distance it can measure.

I read that the maximum distance it can measure depends on the power of the laser.

Any other links, resources etc. are welcome.

Well, the range depends on 3 factors, if it's a pulsed laser :
1) Power o/p of the laser
2) Beam divergence
3) pulse frequency

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