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Thread: Virtual Point Source of Laser Beam?

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    Default Virtual Point Source of Laser Beam?

    I need to design some beam shaping optics to control the divergences of R, G, and B laser beams to make three color holograms. For that I need to know the virtual point source of where the beams originate to do the geometric ray-tracing.

    Beam diameter as given in manufacturers spec’s is measured at the output aperture, correct? And if the beam has a given divergence, then it should be simple enough trigonometrically to find the tip of the triangle, no? Here are some examples of my homework.

    For example, my Coherent Compass 315M has a divergence of < 2.2 mrad, and diameter of .32 mm. Constructing an isosceles triangle with a base of .32 mm and apex angle of 2.2 mrad gives a height of 145 mm, which should mean that the virtual point source I am looking for is 145 mm behind the output end of the laser. (Breaking the isosceles into two right triangles, each with a base of .16 mm and an angle opposite that of 1.1 mrad yields the 145 mm distance.)

    My Lasos RLK 40200 TS has a divergence of 1.4 mrad, and diameter of .7 mm. Following the same reasoning I get the virtual point source 1 meter behind the laser.

    And my Melles Griot BLD 605 with its funky elliptical beam has two divergences and dimensions, but I need to only get the narrow side to coincide with the other two’s dimensions, so its .15 mm wide beam and < 5 mrad divergence places its virtual source 60 mm behind the output window.

    This is probably way too simplistic, as diffraction plays into forming a beam waist, but at least it could be a starting point in doing the geometric ray tracing to make some beam shaping telescopes. Anybody see any flaws in my reasoning? Is this how you guys cipher (to use a Jethro-ism) for same sized beams in laser light shows?
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    I can make this a bit easier for you, while also making it a bit of physical research. Almost all lasers (there is always an exception somewhere!) are in fact a Gaussian near point source radiating a diverging wavefront. The point source is the "beam waist" location. So, Looking around the house, I have Hene's with the beam waist a few cm behind the rear mirror, I have an ion laser (nearly confocal cavity) with the "virtual" waist at the middle of the cavity, and a DPSS and a Hene with the waist just off the OC.
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    If you you know the radius and spacing of the cavity mirrors this is calculable. Or if you know waist location and size, and exit location and size, some place in Wiki land is a plug and chug equation. That equation works when your "X" distance away from the waist. In other words a few cm away..
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    If you have some time, and can open up the laser safety, you generally can find the primary waist of the beam..
    +
    Beware of vicious stray beams and pump diode reflections when "waist hunting".
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    The Good news is most western laser makers can give you the physical location and diameter of the beam waist. Once you have that, calculations get easier, because you should know the diameter and divergence off the exit.
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    If you have a two mirror cavity, or in some cases a folded three mirror cavity, you can easily calculate it using the PSST! laser resonator simulator.
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    https://www.st-andrews.ac.uk/~psst/
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    I'd play with PSST! to find out the basic behavior of the cavity. Start with a 5 meter radius OC optic, and a flat as a high reflector spaced a meter apart. Then decrease the radius of the optic till you loose stability of the cavity on the stability graph... You can try flat flat, flat to radius, and confocal till you get the hang of whats going on with the waist location.
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    If you caculating it using published equations, if I remember right, you set the waist diameter (Z0) to zero to find its location using the other known beam parameters.
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    About half way down the page linked is the simplified waist angle equation from Newport:
    http://www.newport.com/Gaussian-Beam...3/content.aspx
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    Angle Theta = four Lambda divided by 2 Pi Omega (Omega = radius of waist)
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    I don't think there are more then 3-4 PLers in the past ten years who have tried your line of approach...
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    I've attached a copy of Self's paper on the math under education use clause. I'll delete it in a day or two.
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    Cheers,

    Steve
    Attached Thumbnails Attached Thumbnails Self_1983_focusing_gaussian_beams_AWC.pdf  

    Last edited by mixedgas; 12-03-2015 at 13:18.
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    Steve's information is spot on and reminds me that this forum is about both the art and the physics. Nice, Steve!

    I'm curious as to how you plan to source the actual optics that the analysis dictates. Do you have an idea of the coherence length of each of these lasers?

    The problem you will face with distinct laser sources as opposed to say, a white-light argon laser is similar to the problem a laser projector manufacturer faces. If the beams have different exit beam diameters and different divergences then no matter what output optics you choose, there will be only one point in the far-field where they will have the same diameter. If the holography set up has some significant beam path through it then these beams cannot be the same at multiple points.

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    Steve, a brain the size of a small planet.
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    Even Whitelight Ions are not exactly con-focal on the colors, SP ion laser data sheets have the correction factor. N/2 wavelengths have to fit in the cavity for each line, where N is a big integer... So 514.5 has a bit different spacing then 488.2 etc...

    The attached paper is helpful for those who wish to try spatial filtering for RGB Projection as well.

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    In practice, I think the only way to get common diameter and divergence that holds up over long beam paths is to focus and up-collimate to a slightly larger diameter than desired (putting all beam waists at infinity), and pass them through apertures of the same diameter before combination.

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    I believe Eidetic is correct. By utilizing the added degree of freedom that comes with the willingness to sacrifice power you can achieve similar divergence and diameter.

    Now, back to one of my earlier questions. The divergence of two of your lasers is pretty high. Are all of these lasers single mode and what are the coherence lengths? Most diode lasers have coherence lengths that are very short and will not be suitable for interference work at say 1/2M from the laser.

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    Thanks for all the info. The attachments are all the specifications that I have from the manufacturers, beam waist location is not provided, just the divergence and diameter. As far as opening these things up, it would be next to impossible for me to do so. The 315M is soldered together, the BLD 605 is probably not going to come apart without some resistance, and I fear Mr. Butterfingers here not be able to get it back together properly. The Lasos has not yet arrived.

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    “If you calculate it using published equations, if I remember right, you set the waist diameter (Z0) to zero to find its location using the other known beam parameters.” Isn’t this the same as the question I asked above?

    “I'm curious as to how you plan to source the actual optics that the analysis dictates.” My grand plan was to a.) find the “virtual point source” of each laser, b.) intercept the blue and green beams (they are aligned to the red laser by way of mirrors and dichroic beam combiners) with a negative-positive lens set at the appropriate distance from the laser to get the proper beam size, and controlling the spacing of the two lenses to vary the focal length so that the real image of these “virtual point sources” are coincident with the “virtual point source” of the red laser.

    I have been using a pair of 150 mm focal length lenses on the BLD as described by Laser Sam Goldwasser in his FAQ site, and I have been successful in matching the width of the BLD’s beam to the He-Ne hidden in the back of the picture. By moving this telescope back and forth to capture the size, then moving the second lens on a translating stage, I could focus the blue beam to go through a spatial filter’s pinhole that was already tuned to the He-Ne’s. I could do the same with the 315M green, but wasn’t getting its diameter to match the other two. That’s when I decided to get out the calculator and graph paper again.

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    “Do you have an idea of the coherence length of each of these lasers?” Check out this link: http://edweslystudio.com/Research/Co...rence2013.html

    I recently ordered the Lasos 200 mW SLM DPSS 640 laser, as I was having some less than satisfactory results using the 1145P as my red beam on an HOE project on account of the low power and not so great coherence. Since I will be revamping the whole laser breadboard I thought I should dig a bit deeper into the beam shaping optics to perfectly align all 3 for the next project. So I will let you know how it goes in a month or so.
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    your rig is a thing of beauty. i wish i still lived in chicago. i'd love to see it in action.
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    The usual trick is to call the laser manufacturer and ask for the waist location. When I was a FSE for a pulsed laser company, this was a common question. It may not be on the common data sheet, but the engineers WILL know it. If not, they can get it. For an application like holography, most sales engineers will get you the data, even on a used laser.


    Steve
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