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Old 12-08-2009, 02:55 PM #1
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Default Size of a focused spot

I was curious as to size of a focused spot. Does anybody know how to work it out (at least to a rough approximation)? I guess it must be limited only by diffraction, since the image size is effectively zero, but I can't find the answer anywhere.

Thanks

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Old 12-08-2009, 04:01 PM #2
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Default Re: Size of a focused spot

You need to determine the wavelength first, then the lens you're using. Then, the distance you're going to point it at and what surface you're going to point it at.
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Old 12-09-2009, 09:29 AM #3
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Default Re: Size of a focused spot

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Originally Posted by nikokapo View Post
You need to determine the wavelength first, then the lens you're using. Then, the distance you're going to point it at and what surface you're going to point it at.
405, 405-G-1 (Jayrob modification), ~ 10cm, wood or paper ....
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Old 12-09-2009, 02:34 PM #4
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Default Re: Size of a focused spot

with perfect lens its wawelengths sideways length
am i correct?
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Old 12-09-2009, 05:41 PM #5
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Default Re: Size of a focused spot

Wikipedia gives the formula for determining angular resolution as sin theta = 1.22*(wavelength/aperture)

Angular resolution - Wikipedia, the free encyclopedia

I think (but am not sure) that the angular resolution gives the diffraction limited spot size.

It seems that for laser beams, one should use the beam width rather than the aperture. Fortunately they are both about the same = ~ 4mm so nothing much turns on that.

So wavelength is 0.405 microns, beam width/aperture is ~ 4mm = 4000 microns
Thus sin theta = 0.000124
Thus theta = ~ 0.1mrad

So with a focused point at 10cm, the spot would be 0.01 mm across.

But this can't be right because then a focused 1mm green would produce the same power per unit area as a 10 watt 1mm beam set to infinity.

And that aint' so .....

Stuck ......
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Old 01-19-2010, 09:08 AM #6
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Default Re: Size of a focused spot

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Originally Posted by davidgdg View Post
So with a focused point at 10cm, the spot would be 0.01 mm across.

But this can't be right because then a focused 1mm green would produce the same power per unit area as a 10 watt 1mm beam set to infinity.

And that aint' so .....

Stuck ......
Hah ha, pulling 10 watts out of a 1mw laser, I'd buy those optics.
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Old 01-19-2010, 03:52 PM #7
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Default Re: Size of a focused spot

davidgdg;

I have previously done some focus size experiments for some of my Hi-Power lens assembly customers.

These are the results I got with a BR laser diode:

Quote:
Measured the focused beam size for my Blu-Ray w/ a microscope...
by checking the hole size after burning thru paper in several trials.

It measured 0.006" or 0.15mm .

That seems like a well-focused spot for a single AR lens.
I have read several papers on focus size,
but the actual results are always larger than the equations predict.

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Old 01-19-2010, 05:50 PM #8
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Default Re: Size of a focused spot

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Originally Posted by davidgdg View Post

But this can't be right because then a focused 1mm green would produce the same power per unit area as a 10 watt 1mm beam set to infinity.

And that aint' so .....

Stuck ......
It could easily be so, since we're talking about a focused spot. If you're talking W/cm^2 then the unfocused 1mm spot at 10W could be putting the same amount of power into a 1 mcron spot as a 100mW beam focused to 1 micron. (I haven't done the actual math so this is just a description)

Also, beam quality is a key factor in determining the smallest size that the spot can be focused. A TEM00 beam will focus to a much smaller size than a less perfect beam. The higher the m^2 factor of the beam, the larger the focused spot. In theory, a perfectly gaussian TEM00 beam can be focused to a spot 1 wavelength across, but this is never seen in real life since a truly gaussian, diffraction-limited beam is impossible.
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Old 01-22-2010, 02:17 AM #9
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Default Re: Size of a focused spot

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Also, beam quality is a key factor in determining the smallest size that the spot can be focused. A TEM00 beam will focus to a much smaller size than a less perfect beam. The higher the m^2 factor of the beam, the larger the focused spot. In theory, a perfectly gaussian TEM00 beam can be focused to a spot 1 wavelength across, but this is never seen in real life since a truly gaussian, diffraction-limited beam is impossible.
There are actually a few papers in the recent years where people are able to focus the beam down below the diffraction limit using interference techniques and some nano scale electro optics. I can possibly look up some references for you if you wish.

@ the OP: One of the above posters is correct that it is limited by both the aperture and the wavelength of light you use. In the case of a parallel beam the "aperture" would be the beam diameter. Its because of this if anyone plans to use super tight focal points one always expands a beam then re collapses it with a short focal length lens. Check out a few articles on Gaussian optics.

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Old 01-22-2010, 02:49 AM #10
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Default Re: Size of a focused spot

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There are actually a few papers in the recent years where people are able to focus the beam down below the diffraction limit using interference techniques and some nano scale electro optics. I can possibly look up some references for you if you wish.

Love to see them! Technology these says is pretty incredible.. it's impossible to keep up if you don't work in the field. I wonder if such a beam could be focused down smaller than a gaussian beam, or if it's impossible to get any smaller.
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Old 01-22-2010, 02:56 AM #11
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Default Re: Size of a focused spot

Focusing Beyond the Diffraction Limit with Far-Field Time Reversal -- Lerosey et al. 315 (5815): 1120 -- Science

ScienceDirect - Optics Communications : Propagation and focusing of Gaussian laser beams beyond conventional diffraction limit

Science paper using microwaves (if you dont have access I can technically cant post the full article because of copyright BS)

Dimple lens goes beyond the diffraction limit (Photonics Spectra | Nov 2009 | Tech News) another more general article


All different methods but I cant find the nano scale electronic paper now. Its been 3 years so it might be buried now and out of date.
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Old 01-22-2010, 03:32 AM #12
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Default Re: Size of a focused spot

Wow.. That's some impressive stuff. Too bad the articles aren't free, but I'll probably try to buy one or two. Should be a good read.
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Old 01-23-2010, 03:08 AM #13
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Default Re: Size of a focused spot

Airy disk - Wikipedia, the free encyclopedia

Worth taking a peek, even if you skip the math and look at the pictures...

I really like this forum, threads go from "what can i burn" to wave theory in 4 posts!
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Old 01-26-2010, 12:52 AM #14
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Default Re: Size of a focused spot

I have no measurement, but what I always hear or am told is that it is about the size of a human hair. Which is pretty good, but of course you cant actually see this, as the light reflecting off the object will always make the dot look to be about the diameter of pencil lead. (or bigger)
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Old 05-13-2010, 01:43 AM #15
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Default Re: Size of a focused spot

I'd like to add my thoughts to this thread.

Assuming a perfect lens, the size of the spot would be the size of the emitting area on the facet of the semiconductor for a diode-based laser.
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Old 07-06-2010, 06:19 PM #16
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Default Re: Size of a focused spot

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Originally Posted by davidgdg View Post
Wikipedia gives the formula for determining angular resolution as sin theta = 1.22*(wavelength/aperture)

Angular resolution - Wikipedia, the free encyclopedia

I think (but am not sure) that the angular resolution gives the diffraction limited spot size.

It seems that for laser beams, one should use the beam width rather than the aperture. Fortunately they are both about the same = ~ 4mm so nothing much turns on that.

So wavelength is 0.405 microns, beam width/aperture is ~ 4mm = 4000 microns
Thus sin theta = 0.000124
Thus theta = ~ 0.1mrad

So with a focused point at 10cm, the spot would be 0.01 mm across.

But this can't be right because then a focused 1mm green would produce the same power per unit area as a 10 watt 1mm beam set to infinity.

And that aint' so .....

Stuck ......
Using this formula and a high numerical aperture lens you can best expect to be in the order of the wavelength in terms of spot size, but that is the ideal case. In terms of power density (power per area), yeah, a 10 mW laser can be focused to a very tight spot and have a high power density; it is practically what I am doing to expose photoresist which normally requires a few watts of UV light (not focused) and I am only using 10 mW of power off of a 405 nm blu-ray laser diode that is very tightly focused (~1 um achieved, getting it smaller).
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