Re: Laser ranging to moon begs questions


John C. Polasek <jpolasek@xxxxxxxxxx> writes:

On 21 Oct 2007 14:21:10 -0400, Craig Markwardt
<craigmnet@xxxxxxxxxxxxxxxxxxxxxxxxxx> wrote:


John C. Polasek <jpolasek@xxxxxxxxxx> writes:
On 20 Oct 2007 08:32:03 -0400, Craig Markwardt
<craigmnet@xxxxxxxxxxxxxxxxxxxxxxxxxx> wrote:


Yep, for example:
http://ilrs.gsfc.nasa.gov/stations/sitelist/MDOL_sitelog.html

Pulsed ND Yag laser, pulsed at 10 Hz with a 200 ps duty cycle. Those
parameters appear to be pretty standard (though the peak power varies
from one station to another).

Also, the beam-width of most laser systems reported on that page
appear to be in the 10's of arcsecond range, not the 0.075 microrad
values previously reported.

Craig
This spec says divergence is adjustable from 0-20 seconds. It also
says "final beam diameter .75m ". This latter is probably as adjusted
out of the telescope which may have a final mirror of .75m.

snip

This is really valuable information that straightens things out
considerably:
From Dickey et al. 1994,
Ranging to the moon is technically challenging. An outgoing pulse
of laser light transmitted from the a collimating telescope with a
beam divergence of 3 to 4 s of arc, consistent with atmospheric
seeing, spreads to an area of approximately 7 km in diameter on the
lunar surface. ...

[Corner cube ] arrays intercept only 10^{-9} of the area of the
impinging light beam. The angular spread of the returning pulse is
set by diffraction, polarization properties, and irregularities of
the array's individual corner cubes. In the case of the the 3.8 cm
diameter Apollo corner cube, the spread is approximately 10 sec of
arc. Thus, the diameter of the spot produced on the Earth is
approximately 20 km. A 1 m diameter receiving telescope would
collect only 2 x 10^{-9} of the returning photons. A variety of
practical matters, such as quantum efficiencey, mirror reflectance,
optical performance under thermal stress, and velocity aberration
(which slightly shifts the center of the returning beam from the
location of the transmitting and receiving telescope), make the
product of the transmitting, lunar retroreflecting, and receiving
efficiences considerably less than unity. The overall signal loss
of approximately 10^{-21} puts a premium on the detailed design of
ground stations to minimize their losses.
...


With 20 seconds of beamwidth, (which I doubt, since, if it's
adjustable, what would be the point?) we reduce the photon count from
6.43e22 to 4.02e16 photons/s/m^2. The field strength would go down by
sqrt(1.6e6) or1265 to 1.9millivolts/meter.

According to Shelus et al, approx 3 x 10^{17} photons are launched per
pulse, which is reduced by the losses to significantly less than one
returned photon per pulse (approx 1/3rd of a return per minute, at a
10 Hz pulse rate). I have read elsewhere that under the best
conditions (rather than average), the McDonald station can return 1
photon per minute.

On the other hand, newer stations like APOLLO (Apache Point) can
return several photons per pulse.

CM


References

Dickey et al., "Lunar Laser Ranging: A Continuing Legacy of the Apollo
Program," Science, 1994, Vol. 265. no. 5171, pp. 482 - 490

Shelus et al. "McDonald Observatory Lunar Laser Ranging: Beginning the
Second 25 Years," IAU Symp, 1996, v.172, p. 409
Thank you Craig for getting some real data.

Using their figures, the attenuation, as I figure it, is 7.7x10^-28
yielding a "robust" 15 photons per pulse m/l in line with their
"several photons per pulse".

They use much smaller mirror 3.8cm., and first patch of 7 km vs 28m

You are mistaken. The area of a *single reflector* is 3.8 cm
diameter, but the assembly has multiple reflectors. However, the 3.8
cm number is relevant for the returned diffraction pattern.

from a 3 second divergence and not microradians. They reckon the
return patch 21km vs the first patch of 7 km arose from divergence
angle tripling from 3 sec to 10 seconds on the way back. Twice would
be better.
My calculations:
WL = 532nm
Ep = hc/WL = 3.7e-19J per photon
Ebeam = 1.75J Pwide = 200ps

N = photons/pulse = Ebeam/Ep = 4.02e18 photons/pulse Shelus:3e17
(Shelus figure is 13 times lower (wd make 15ppp go to 1ppp). I will
argue for my figure: 1.75joules, 3.73-19J/photon.

You of course are assuming peak power output which appears to be
incorrect.

Phorate = N/Pwide = 2e28 ph/sec 1 pulse

Calculating the photon rate "per pulse" is not relevant here, only the
total number of photons per pulse.

Calculate attenuations starting from the .75m scope, their 7km patch
At1 = bexit/patch1 = (.75m/7km)^2 = 1.15e-8 7km patch not 28m
At2 = mirror/patch1 = (3.8cm/7km)^2 = 2.95e-11 3.8cm not 50
At3 = receiver/patch2 =( 1m/21km)^2 = 2.6e-9 1m vs .1m
Atoveral = 7.67e-28

Even if one were to assume pure geometric calculations (which are
incorrect), your calculations are still incorrect. The number of
photons received at the retroreflector are,

N_retro = N_transmitted * (A_retro/A_lunar_spot)
= N_transmitted * (1100 cm^2 / 38 km^2)
= N_transmitted * (~2 x 10^{-9})

which is in line with the Dickey quotation. The number received at
earth is,

N_received = N_retro * (A_receiver / A_earth_spot)
= N_retro * (0.44 m^2 / 346 km^2)
= N_retro * (~1 x 10^{-9})

again comparable to the Dickey estimates. However, what you *don't*
account for by the geometry-only approach is the other loss factors
described above. The true attenuation is around 10^{-21}, but this
actual value depends on observing angles and other factors.

So for 3e17 photons launched per pulse, about 0.0003 photons are
received. Thus, it takes about 300 sec to receive one photon (my
previous estimate was incorrect).

The Apache Point observatory (which is *different* than McDonald) is
much more capable because of the much larger aperture area on the
earth.

CM
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