D i v e r g e n c e

[Alaskan]

I was thinking so, I read somewhere that a perfect point source would have no divergence, but being diodes are physical devices, they are not an infinitely small point source.

 

[JoshDeet]

Just some quick input for interests sake:

DISCLAIMER: i am not an expert in the field of optics and rely on my practical experience for this post.

i work in the field of stage lighting for theater and live performances. We differentiate between 3 main kinds of fixtures:
1) Wash (ignored for now)
2) Spot
3) Beam

The spot fixtures typically have beam angles (think of a light shining at a wall at 90 degrees, angle is the angle at the light) of between 8 and 40 degrees. While beam fixtures are designed to shoot almost laser light effects through the air and have beam angles from 6 degrees right down to 0.25 degrees.

What i wanted to highlight here is the way in which adding certain things to the optical train changes the beam profile. in order to project patterns we introduce a "gobo" into the collimated area of light (basically a cut out disk) before it is re-expanded to the desired beam angle.

when this is done with a spot type fixture, using a circle gobo of radius collimated/2 the light output is changed by the same ratio as the area decreases, the beam at exiting the fixture is smaller in diameter, however, the beam angle is still exactly the same.

by contrast, doing the same to a beam fixture, will result in the same power loss, but the beam diameter is the same at leaving the fixture (no matter the focal distance) but smaller (never the same or smaller than the lense though) at the end point.

this fascinates me. i would love to try the same thing with a laser, and see how it compares. now, while a white LED (or discharge lamp or halogen globe) is not a laser diode, i would expect that the "beam angle" of a laser could be reduced in the same way (probably by much smaller margins though.)

maybe an expert would like to help out here?
Regards,
joshua deetlefs

 

[Cyparagon]

they are not an infinitely small point source.

Nothing is an infinitely small point source. But since your eye cannot resolve the difference between a laser dot and an infinitely small point source, it doesn't make any difference.

 

[upaa27]

I was thinking so, I read somewhere that a perfect point source would have no divergence, but being diodes are physical devices, they are not an infinitely small point source.

Can anything correct this? Is there a certain optic that can achieve infinite focus? Is there an equation for lenses required focal length to be focused forever?

 

[Alaskan]

I'm quite the novice when it comes to optics, but my understanding is when you have your laser focused to infinity, it has the smallest linear beam it can produce and only gets bigger at distance due to the divergence of the laser. I still don't quite understand what is happening though, when focused to infinity.

here's a good web page on the subject of beam expanders to reduce divergence but at the cost of increased beam width, if you want to build one too: http://www.edmundoptics.com/technical-resources-center/lasers/beam-expanders

Also, an interesting explanation of coherence: http://amasci.com/miscon/coherenc.html I realllly recommend reading the page at this link, it has some very cool information.

 

[Bionic-Badger]

Here's the math. There will always be some divergence.

 

[KrowBar]

The highest quality single mode beam will still be limited in performance due to diffraction. Thus you will always have divergence in your beam despite any combination of expensive optics you may use. A larger diameter beam can have lower divergence than a small one (all else being equal) so if you were to get a 10m mirror to collimate your beam, then it could produce a spot just over 10m in diameter even at several kilometers, but then you have to worry about keeping that mirror shape perfect - (think billion dollar telescope). Just like a large diameter telescope can produce better "point" images of stars, in reverse the telescope would project a better parallel beam back to the star (Beam expanders and telescopes are the same thing). But atmospheric seeing quickly limits performance way beyond diffraction limitations, and you will have the same class of problem with a huge diameter beam through the atmosphere. There is really no way to win here.

The best possible way to "see" a laser dot at a great distance will be to use a large telescope/ beam expander at the source, and then another large telescope at the observation point. This would best be done using a gas or SS laser with near diffraction limited beam and optics.

In response to the question of using a longer lens to collimate instead of a beam expander - this is indeed a good way to get a large diameter beam with little optical loss, but it is hard (expensive) to get a high quality aspherical, large numerical aperture lens, which gets greatly compounded if your beam has different properties on different axes as seen from many diode lasers. I have spent a significant amount of time trying to find a reasonable cost way to get longer lenses which fit a standard axis module. All of the lenses I have tested so far with FL longer than about 1 cm which cost less than $100 produce undesirable aberrations or losses which more than offset the benefit of a larger beam IMO. I haven't given up yet, but I have not found any new potential lens candidates for a few months now.

 

[Jeffwiz]

the problem of beam divergence is exactly the inverse of astronomical telescope optics ie. resolution. All astronomers want a big diameter and a short focal lenght lens as these make small bright images on their sensor (film or ccd) think of that sensor as your laser diode (it's a bit of a brain twist) wavelenght is irrelevant. Telescope maker figure a 5% loss for each Surface the image passes through (or reflected from)

 

[lazeristasUVISIR]

I read somewhere that a perfect point source would have no divergence, but being diodes are physical devices, they are not an infinitely small point source.

A perfect point source will have a huge divergence assuming it emits a TEM00 Gaussian beam. Check formulas at
Gaussian beam - Wikipedia, the free encyclopedia

wo goes to zero, theta to infinity. At one point the whole Gaussian theory will be ruined as it is based on small angles.

To reduce it the beam must be transformed with lenses. KrowBar answered how.

 

[Alaskan]

Right now, it appears that a good way to reduce divergence is to get a much larger diameter lens with a longer focal point than what are currently used for laser pointers to collimate the beam further away from the diode to produce a much fatter beam with proportionally reduced divergence and only one lens. Yay, nay?

 

[The Lightning Stalker]

That sounds about right. Multiple lenses will
still have better beam profiles, but at the
expense of some light loss.

 

[Bionic-Badger]

Unless you need to communicate with some satellite in orbit or on the Moon or something, I'd just worry more about your parameters satisfying your needs, not whether you are minimizing any one parameters such as divergence.

 

[Alaskan]

Truth is, I do. I wouldn't go to this extent otherwise.

In the past I used to do this with RF, I built a home brew RF power amplifier and antenna system with enough gain to produce 4.5 megawatts of EIRP and used it with the moon as a passive satellite, hearing the echo's come back about two and a half seconds later, my own voice. The antenna system had 16 five wavelength long phased Yagi antennas with several kilowatts of RF power being pumped into them at 144 MHz. For my antenna system, its gain figure is comparable to divergence in lasers, the tighter the divergence the higher the gain, if thought about in the same way. With all sixteen antennas phased together to act as one giant antenna the output power, when aimed toward something, was approximately the same amount of RF strength a single whip antenna being fed with over 4.5 megawatts of RF power would produce, up to 5.5 megawatts EIRP if I pushed my RF amplifier to its maximum output.

I did this in Alaska 20 years ago in the middle of my 4 acre lot, no neighbors and no complaints of RFI.

 

[Alaskan]

Excuse the bump, but not really a bump, no one has posted to this section in days. Here's more info I thought might be interesting to someone looking for a way to reduce the divergence or beam-spread of their laser through the use of a cheap telescope as a beam expander, something I learned about on the forum and finally got around to trying:

I coupled one of my 50mw 532nm laser pointers to a 3 dollar goodwill el-plastic 40X telescope and it works well as a beam expander without the eye piece, with the lens from the laser removed. Expanded the beam to about 18mm, should have many times the throw (to borrow a flashlight term) it had before. I've been wanting to see how well a junk telescope like this might work as a beam expander and it did a fine job.

Removing the lens from the laser so it had an expanding output without the eye piece on the telescope worked much better for this laser than having those lenses in place, for one thing I could then insert the head of the laser into the telescope tube which happened to match very closely to its OD. The eye piece would normally work as an expander lens but wasn't needed with the output collimation lens on the laser removed, as the beam was already expanding from it's own expander lens next to the diode and crystal. In this situation, the lasers own expander lens replaces the eye piece and the variable length tube on the telescope matched the length properly so that I could adjust it for minimum divergence.

Because the lasers expander lens wasn't matched to the length of the tube (also, since it is variable) and collimation lens of the telescope, adjusting the length between them allows you to under or overshoot the spot where minimum divergence occurs, so to get it right, I had to measure the output beam-width near the end of the telescope while spotting on a wall 10 feet away, measuring the output at the telescope and spot on the wall and adjusting until the spots were the same size. I could find the minimum divergence setting easy enough outside at night, adjusting for the brightest spot at a long distance too. I could also adjust it so it would focus a tiny spot on the far wall, I imagine if I had enough power I could burn things at a distance that way.

I don't know the exact amount of expansion, but if it approaches 20X, my 50mw laser now has the same power at a distance of a laser with several hundred milliwatts of output power, perhaps approaching one watt. This due to the reduction of beam spread by the same factor the beam is expanded, making the laser appear far brighter at a far distance. Of course, also more difficult to get the spot on a distant point, if someone were trying to shoot towards a far away observer but the greater the distance, the easier to spot on something because the divergence is still happening, just at a much slower rate for a given amount of travel.

 

[Rifter]

I need to get my hands on a cheap telescope....

 

[Alaskan]

Took me a long time to find one 2nd hand cheap, but I wasn't looking very hard either, just happened to stop in at the Goodwill on a fluke and there it was for $2.95, I didn't want to buy a new one for this. This telescope is probably as cheap as they come, lightweight plastic, no metal in it at all except for a couple of screws and the end lens (objective) looks like it was made out of window glass with edges that weren't even sanded smooth. That lens has a very slight curve to it which produces a long focal point, although the cheapest looking lens I've ever seen, it works well for this.

I later wrapped some tape around the end of the little laser pointer to more closely match the ID of the telescopes eye piece tube. I have a 1 inch concave lens I want to put in front of the telescope and add an extension with another lens a couple of feet further out, that should boost the throw of the visible beam another ten times or more.

This wouldn't have worked out for me if removing the telescopes eye piece except that the laser already had a expander lens deep inside it. The reason I removed the eye piece was because its lens wasn't small enough for the width of the collimated beam coming from the laser (because the curved part of the concave eyepiece glass was so huge compared to the smaller diameter of the collimated beam, it mostly hit the middle or flat part of the lens and little lensing action was taking place), so removing the lasers output or collimation lens was needed too. Together that worked out great, less loss and the beam was able to expand enough as it traveled forward towards the lens on the end of the telescopes tube to match its diameter just right, when adjusting the length of the telescope tube, which is adjustable.

Edit: I took two identical laser pointers, one in the telescope and the other without expansion and aimed them up into the night sky a few minutes ago. On a cloudless night, other than the beam coming out of the telescope being a fat beam, there was very little noticeable difference in the appearance of how far the beam would go, you just can't tell much difference but I did see a few percent more length for the expanded beam verses the pointer without expansion. Since the end of the beam is so far out, that little bit of difference from my view point is probably a hugely greater amount of visible throw, if someone were to view it from the side a half mile away or more.

I'm looking forward to the next cloudy night so I can try this again and see how bright a spot shows on the clouds from one laser to the other