I am looking at how to use the thin laser pointer beam

I’m not entirely sure what you mean is that thick and wide are two different things. My view on the product described in her link is a device that uses an IR green laser pointer diode as an illumination source, and uses an adjustable zoom lens type device to spread the light from the laser source to an area that matches the telephoto imaging system on.

I’m looking at the problem of how to use a thin laser beam, it behaves more or less like a line, spreading slowly over a long distance, and then turning it into a wider laser beam, still like a line that travels very slowly, but Now it’s more extensive. If this is the core of the problem, then, yes, of course you can do this, and you do it all the time, mainly to reduce the angular expansion rate of the beam.

For example, the light reflected from a retroreflector on the moon is pre-expanded for this reason-the power density at launch may be lower, but as the angular spread per unit of travel decreases, its power density will Much higher compared to the original beam, the time it takes to reach the moon.

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The simplest is that you only need to pass the laser beam back through the telescope. Under normal circumstances, the telescope will receive a large aperture full of light, and then compress it to the size of the eyepiece for your eyes to receive, so that dim objects appear brighter in the process. Conversely, the laser pointer beam will widen, even if the power density decreases as the light propagates over more cross-sections.

You can make the beam into any shape you want, but the question you need to ask is how long the shape will exist before diffraction causes it to spread to the size you want. You should check the discussion of Gaussian beams in various optics books. In this discussion, you will find a quantity called the Rayleigh range, which is a measure of the collimation distance of the propagating Gaussian wave. The Rayleigh range is a function of the square of the beam width.