[Laser] heliograph vs. laser indeed!

[Tim Toast]

 I'm unsure of the math right now, but i was thinking about
the comparison between the heliograph and laser. And to try
to get someone more inclined to do the math, to do the
math, i thought i would point out some similarities between
the heliograph and a laser that may help put them on more
equal footing with each other first - to lessen the "apples
and oranges" aspect of trying to compare them. 

 I think most people will realize a mirror reflecting
sunlight will have a beam divergence of about 8.3
milliradians (about 1/2 degree) no matter what the diameter
of the mirror, due to the angular size of the sun in the
sky. A flat mirror can be thought of as a "pinhole lens".
Like a pinhole, a flat mirror will project an image of the
sun at whatever you point it at. The further away the
target is, the bigger will be the image (remember it's
spreading out at that 8.3 milliradian rate). The mirror can
be thought of as a point source that emits N power
collected from the sun. The sun shining on the mirror has X
amount of power - i think it's close to 1000 watts per
square meter. So a one meter sized flat mirror will emit a
1 kw beam and have a divergence of 8.3 milliradians (1/2
degree).

 At 100 miles away, the spot from the mirror will be a
certain size. So the 1000 watts will be spread out in the
spot size Z. Apparently it would be visible to the naked
eye without much trouble. Someone should be able to
calculate the power recovered from that beam by a given
size lens knowing the spot size at the receiving
site.(someone who's not hating the math as much as me :)

 Now, the laser. I'm going to go out on a limb and say a 5
milliwatt laser would definitely be visible 100 miles away.
It's just a matter of how collimated you can make the beam
(and point it). If the 5 mw laser had a divergence the same
as the heliograph mirror (8.3 milliradians) i would say it
would probably not be visible at such a distance. But as
you narrow the laser beam with the collimator, eventually
you will reach a point where the laser is visible. Maybe it
requires a better collimation than the normal 1 milliradian
beams from unmodified laser pointers, maybe not. 
So it's just a matter of some math (which i hate) to
determine at what point the laser (degree of collimation
and power level) and heliograph (diameter) will be of equal
intensity as seen from a given distance away. 

some conclusions:
 I'm going to go ahead and say most any laser, 5mw or
above, can be equal in brightness to any normal sized
heliograph depending on the laser optics, and those optics
need not be any larger than the heliograph mirror. All this
ignores the fact the mirror beam will be spread out over
the whole visible spectrum whereas the laser is a narrow
band device. I'm sure that gives the laser an additional
advantage since you can use bandpass filters at the
reciever to help isolate it from the background. 

some other power levels:
 I assume that 15 kw Imax projector lamp being visible from
the moon, is un-collimated - just the bare bulb with no
more focusing than the tube itself provides (i guess most
of the energy comes out one side of it) - so it has a
divergence of  45 to 90 degrees?? and as seen from earth, a
magnitude of 5 or 6, or "just visible by naked eye". 
 And Charles Pooley's statement that a 30 milliwatt laser
with 10 microradian collimation would be seen as a 5th
magnitude star from lunar distance. Or in other words by
naked eye by an order of magnitude or so. 
 I know the low frequency atmospheric scintillation from
6th magnitude stars can be detected on PGP rx's and 22 cm
apertures (F1AVY). Just imagine that 5th or 6th magnitude
star 100% modulated... and how much smaller the telescope
could be and still detect it. So there you go, for better
or worse.
now somebody do some math 8)



-----------------------------------------------
James n5gui wrote:

I still consider the "gold" standard to be the heliograph.
That was a device that was intended to be used in daylight
and received by the human eye.  The rule of thumb was that
the effective range of a heliograph mirror was 10 miles for
each inch of mirror diameter.  Perhaps some of you can
translate that into something equivalent to the devices we
are using today.  




       
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