Physics of laser pointer attachments: stars, butterflies, etc.

[iLIKEstuff]

http://nerdapproved.com/misc-gadgets/dolphin-laser-pointer-keychain/"

So in the above image they have little attachments for laser pointers that can make different designs. I've played around with similar types of attachments for laser pointers and have never thought about the physics behind it. They are small attachments and if you look through it, you can't really see any discernable shapes or patterns with the naked eye. The images of the patterns above do show a little bit of fuzziness around the main image, but the shapes are well defined.

From what I know about lasers, diffraction, and focusing of light, this can't simply be a small "cut-out" can it? (like a "shadow" kind of thing?) If you have a cut-out in the shape of a star that's on the order of tens to hundreds of microns, wouldn't diffraction kick in and give you a blurry image? I mean the shapes and patterns projected from these attachments are crystal clear at any distance from the output. Sure the size of the shape gets a little bit bigger as you go further away, but it's still a pretty clear image. Can a microlens do that?

I know there are some attachments that just give arrays of dots or something. I'm pretty sure that's just a diffraction pattern which would be pretty simple. However, I have seen attachments that give like arrays of stars patterns or other complex geometries that are in a periodic arrangement. How does that work?

What are the physics behind this attachment such that at any distance from the output of the laser, you get a clear image of a butterfly, star, octopus, etc.? Could it some kind of Fourier-space thing that shows up like that? or is it just a simple microlens? What is it? It can't be something too crazy since they got to be pumping these things out for a few pennies a piece.

 

[ZapperZ]

My guess is that this is a "numerical hologram".

What happens here is that, you take the image you want to display, you then make a 2D digitization of it, i.e. where there is an image, you put a step function. Then you perform a 2D FFT. The result will be a 2D "plot" of dark and light pattern, depending on how you calibrate the result. If you cut out on that paper, say, the dark pattern and then use a monochromatic light source behind it, you get back the original pattern.

Zz.

 

[Andy Resnick]

What are the physics behind this attachment such that at any distance from the output of the laser, you get a clear image of a butterfly, star, octopus, etc.? Could it some kind of Fourier-space thing that shows up like that? or is it just a simple microlens? What is it? It can't be something too crazy since they got to be pumping these things out for a few pennies a piece.

If those attachments are the same as the ones I have on my laser pointer (they look like a clear plastic disk), then it's a phase grating. The plastic is etched in thickness, creating a diffractive optical element. The specific pattern is essentially the Fourier transform (meaning the thickness function t(x,y) gives a phase delay equal to the FT of the far-field intensity) of the far-field pattern you want. These gratings are really easy to design and fabricate, and the fidelity of the grating is proportional to the number of discrete thickness levels allowed (the number of 'bits' of the grating). Another trick is to remove the undiffracted component by an overall phase shift of the wavefront. If you look closely at yours, you may notice the projection is periodic, corresponding to the 1, 2, 3... diffraction orders.

Here's a magnified image of oa phase grating- the far-field pattern is a "no smoking" sign:

[PLAIN]http://img194.imageshack.us/img194/1617/dsc6170x.jpg

It's not the best image- the grating is tilted so it goes in and out of focus- but you get the idea.