A point source has a spherical uniform intensity distribution. A typical LED has a Lambertion like distribution until they put some kind of collimating lens on it.
Ok here is a direct response to your post from the Physicist. No more translation error on my part:
"The argument proposed does not consider that actual nature of a laser. What makes a laser a laser is a property of photons that statistically makes similar ones attempt to be like each other rather than be different. This you will see as photons are often referred to as bosons (Bose-Einstein particles). It is this property that leads to stimulated emission, which is the operational heart of a laser. Energy is stored in a substance in a 'metastable' state (which means that it is very long lived compared to other high level energy states). When photons begin to appear in the substance as this state decays, if the geometry is conducive (i.e. a long crystal with parallel optically flat mirrored ends), the photons that happen to be emitted along the axis stimulate the metastable states to decay in resonance. The photon energy builds and builds. All of the photons have (ideally) the same wave function; they are in lockstep, propagating in the same direction as the impressed wave that dumped each molecule from its metastable state. In a way the energy bundle becomes one big photon.
As this laser light propagates through matter (e.g. atmosphere) it will scatter. That's why you can see a red or green laser beam that is not pointed at you. The act of scattering also causes the beam to expand. One of the mechanisms I mentioned yesterday, exploding aerosol particles, which result in 'unit index spheres,' which act as spherical bubble micro lenses on the laser's path. Even in empty space, the laser will eventually loose coherence because of quantum mechanical interactions. Laser beams do not obey a 1/r2 beam expansion because of internal coherence, but they do expand for other reasons and eventually loose their internal coherence.
If we were dealing with an incoherent source, there is a much simpler way to express the problem than the arithmetic you were quoting. It is just to compare the ratios that imply the angles in question. This works quite accurately for small angles. What is a small angle? Well, it is one that shows a minor change when comparing the Sine, Tangent, and Radian measure of the angle. For example, 5.72957795 degrees is 0.1000 Radian. The Sine of this angle is 0.09983342, and the Tangent is 0.10033467. As you can see for an angle of 6 degrees or so these functions (which are really ratios) round to the same answer at 4 decimal places. For smaller angles the agreement is even better. So, the angle implied by a beam diameter of 1 mm / 50 mm length is the same angle as 1 cm / 50 cm, or 10 cm / 500 cm ( 10 cm / 5 m), which gives a beam diameter of 10 cm.
Whether the source is infinitesimal (a star from our distant point of view), or a small element of an extended source (hot lava, or an iron bar in a forge), or diffuse reflection of a small element of a surface that is illuminated by some source (e.g. sun or auto head light), the light intensity falls off as 1/r2 in the direction from which you are viewing. For extended sources and diffuse reflection surfaces the intensity also falls off with the Cosine of the angle of the viewing direction from the perpendicular to the surface element. This is known as Lambert's Law, or Lambertian reflection. Reflections in mirrors, and curved mirrors, also follow the 1/r2 drop off, but you compute from the image in the mirror. The size of the image in the mirror becomes the size of the source in this calculation."
You are correct, all the measurements I make are always on the far side of the focal point and I understand now what you are saying. I think it also pretty rough problem to get the focal point to be at your target when working in an atmosphere. In my original post, my mind was on someone who was talking about the danger of reflections, eye damage, wavelengths, and more generally collateral damage. You would want the target if possible to be at or near the focal point. That being the circumstance, any reflections from hitting the target will fall off with 1/r^2. In summary, I was always talking about being on the far side of the focal point, which if I am correct, is true with a typical OTS laser pen as well. That may be the source of our disagreement as I did not pay close attention to your proposed experimental setup.
Well, I don't know what to tell you. I am just an engineer. I work with different light sources in the lab every day. Lasers, LED's, SLED's, incandescent sources, and they all behave the same with respect to the inverse square law. The farther you move a detector away from the source the lower the signal. The decrease can be defined by 1/r^2. I am quoting the following numbers from the top of my head without doing the calculations, so don't hold me to it. If you take a beam from a source that has a divergence of +/-60 degrees, and you use a lens to lower the divergence to +/-30 degrees, you will get a ~4x increase in intensity for a given measurement. Obviously this is due to the concentration of the energy into a smaller area. You can make any claims you want, but I have measured it in the lab. The signal will fall off with distance as a function of 1/r^2 relative to the intensity of the source. As far as the theoretical physics, I trust what the Phd I work with tells me.
The only corner case is a perfect laser in a vacuum. In ALL other cases the inverse square law applies. Ask a physicist... that is what I did after you tried to Jedi mind trick me.
Well if you want to get technical....:P A "perfectly" collimated (beam diameter remains precisely the same size no matter the distance) beam doesn't follow the inverse square law. Show me this device, I would love to see it.
Yes, and it is even more concerning because the eye's blink reflex will not occur, increasing the damage. Infrared laser == nasty.
It depends on the wavelength... The closer you get to the visible spectrum the more dangerous for the eye. However, there is a generally accepted cut-off in the near infrared region where you really stop worrying about it being to "bright" for your eyes to handle. At that cut-off point if the reflection or even direct beam isn't strong enough burn/vaporize flesh your good.
Funny you should mention the font. I didn't choose it, and thought it looked that way to show me it was my post. I hate it too. I looks to be "code mode" or something.
Slashdot Mirror
After I installed CoreAVC I can easily play 720p video, but youtube maxes the CPU. HQ doesn't work well and forget HD.
-bc
You must then consider left-wingers to live in a fantasy world?
In fact I do.....
-bc
A point source has a spherical uniform intensity distribution. A typical LED has a Lambertion like distribution until they put some kind of collimating lens on it.
-bc
Where do I sign up for that?
Ok here is a direct response to your post from the Physicist. No more translation error on my part:
"The argument proposed does not consider that actual nature of a laser. What makes a laser a laser is a property of photons that statistically makes similar ones attempt to be like each other rather than be different. This you will see as photons are often referred to as bosons (Bose-Einstein particles). It is this property that leads to stimulated emission, which is the operational heart of a laser. Energy is stored in a substance in a 'metastable' state (which means that it is very long lived compared to other high level energy states). When photons begin to appear in the substance as this state decays, if the geometry is conducive (i.e. a long crystal with parallel optically flat mirrored ends), the photons that happen to be emitted along the axis stimulate the metastable states to decay in resonance. The photon energy builds and builds. All of the photons have (ideally) the same wave function; they are in lockstep, propagating in the same direction as the impressed wave that dumped each molecule from its metastable state. In a way the energy bundle becomes one big photon.
As this laser light propagates through matter (e.g. atmosphere) it will scatter. That's why you can see a red or green laser beam that is not pointed at you. The act of scattering also causes the beam to expand. One of the mechanisms I mentioned yesterday, exploding aerosol particles, which result in 'unit index spheres,' which act as spherical bubble micro lenses on the laser's path. Even in empty space, the laser will eventually loose coherence because of quantum mechanical interactions. Laser beams do not obey a 1/r2 beam expansion because of internal coherence, but they do expand for other reasons and eventually loose their internal coherence.
If we were dealing with an incoherent source, there is a much simpler way to express the problem than the arithmetic you were quoting. It is just to compare the ratios that imply the angles in question. This works quite accurately for small angles. What is a small angle? Well, it is one that shows a minor change when comparing the Sine, Tangent, and Radian measure of the angle. For example, 5.72957795 degrees is 0.1000 Radian. The Sine of this angle is 0.09983342, and the Tangent is 0.10033467. As you can see for an angle of 6 degrees or so these functions (which are really ratios) round to the same answer at 4 decimal places. For smaller angles the agreement is even better. So, the angle implied by a beam diameter of 1 mm / 50 mm length is the same angle as 1 cm / 50 cm, or 10 cm / 500 cm ( 10 cm / 5 m), which gives a beam diameter of 10 cm.
Whether the source is infinitesimal (a star from our distant point of view), or a small element of an extended source (hot lava, or an iron bar in a forge), or diffuse reflection of a small element of a surface that is illuminated by some source (e.g. sun or auto head light), the light intensity falls off as 1/r2 in the direction from which you are viewing. For extended sources and diffuse reflection surfaces the intensity also falls off with the Cosine of the angle of the viewing direction from the perpendicular to the surface element. This is known as Lambert's Law, or Lambertian reflection. Reflections in mirrors, and curved mirrors, also follow the 1/r2 drop off, but you compute from the image in the mirror. The size of the image in the mirror becomes the size of the source in this calculation."
You are correct, all the measurements I make are always on the far side of the focal point and I understand now what you are saying. I think it also pretty rough problem to get the focal point to be at your target when working in an atmosphere. In my original post, my mind was on someone who was talking about the danger of reflections, eye damage, wavelengths, and more generally collateral damage. You would want the target if possible to be at or near the focal point. That being the circumstance, any reflections from hitting the target will fall off with 1/r^2. In summary, I was always talking about being on the far side of the focal point, which if I am correct, is true with a typical OTS laser pen as well. That may be the source of our disagreement as I did not pay close attention to your proposed experimental setup.
-bc
Sounds like we agree now.
-bc
Well, I don't know what to tell you. I am just an engineer. I work with different light sources in the lab every day. Lasers, LED's, SLED's, incandescent sources, and they all behave the same with respect to the inverse square law. The farther you move a detector away from the source the lower the signal. The decrease can be defined by 1/r^2. I am quoting the following numbers from the top of my head without doing the calculations, so don't hold me to it. If you take a beam from a source that has a divergence of +/-60 degrees, and you use a lens to lower the divergence to +/-30 degrees, you will get a ~4x increase in intensity for a given measurement. Obviously this is due to the concentration of the energy into a smaller area. You can make any claims you want, but I have measured it in the lab. The signal will fall off with distance as a function of 1/r^2 relative to the intensity of the source. As far as the theoretical physics, I trust what the Phd I work with tells me.
-bc
The only corner case is a perfect laser in a vacuum. In ALL other cases the inverse square law applies. Ask a physicist... that is what I did after you tried to Jedi mind trick me.
-bc
Well if you want to get technical.... :P
A "perfectly" collimated (beam diameter remains precisely the same size no matter the distance) beam doesn't follow the inverse square law. Show me this device, I would love to see it.
-bc
Actually, it drops off according to the inverse square law. The atmospheric effects are secondary.
-bc
Yes, and it is even more concerning because the eye's blink reflex will not occur, increasing the damage. Infrared laser == nasty.
It depends on the wavelength... The closer you get to the visible spectrum the more dangerous for the eye. However, there is a generally accepted cut-off in the near infrared region where you really stop worrying about it being to "bright" for your eyes to handle. At that cut-off point if the reflection or even direct beam isn't strong enough burn/vaporize flesh your good.
-bc
Funny you should mention the font. I didn't choose it, and thought it looked that way to show me it was my post. I hate it too. I looks to be "code mode" or something.
-bc
I'll see your mwave and raise you a zipzoomfly.com... I have had good luck with both actually.
-bc
How can you say that! BSG 1984 was some awesome TV!
-bc
Exactly.... segmented memory was left behind with real mode (8086). Protected mode drop the segmentation.
-bc
That is funny. Thanks for the belly laugh. -B