archive: Re: SETI A hair-brained idea

Re: SETI A hair-brained idea

Dr. H. Paul Shuch ( (no email) )
Thu, 17 Sep 1998 16:08:32 -0400

At 07:47 PM 9/17/98 +0100, Colin Crook wrote:

>Ok first,light is a form of radiation.So are radio waves.Now if a telescope
>can magnafify light 400x,couldn't it also do the same with radio waves?You
>could focus your telescope on a star,put your reciver at the eye piece,and
>get a signal 400x more powerful!If this would work,it would cost less than
>a dish,and take up less space.So,would it work?

Colin,
You have just described exactly how both (Newtonian) optical telescopes
and (parabolic dish) radio telescopes work. The reason the optical
telescope mangifies light hundreds or thousands of times is that its mirror
is large relative to the wavelength of light being gathered. A radio
telescope similarly "magnifies" its "light" hundreds or thousands of times,
because *its* mirror (the parabolic dish -- which focuses light to *its*
eyepiece, the feedhorn) is large relative to the wavelength it is focusing.
The only problem is, the radio telescope is dealing with electromagnetic
radiation about half a million times longer that visible light wavelengths,
so for equivalent performance, its "mirror" needs to be about half a
million times larger than the equivalent optical telescope's.
Now that we agree on the basics, let's run the numbers. A reflecting
telescope (optical or radio, it doesn't matter) has a "magnification" which
can be described in terms of power gain. At 100% efficiency (which we can
never achieve, because the real world isn't perfect), we can calculate that
power gain. It's actually easier to calculate voltage gain, and then
square it, since power ratio varies with the square of voltage ratio. The
relationship is:
Voltage gain ~ (Reflector circumference) / (wavelength)
where both are measured in the same units. Of course, circumference equals
diameter times pi (for a round mirror), and diameter is twice radius, which
is why all the textbook formulae contain a (2 pi * r) factor.
Next, power gain = (voltage gain)^2. This is your "magnification" of light.
Finally, in radio we usually convert power gain to dBi, a logarithmic
shorthand. dBi means deciBels compared to an isotrope. An isotropic
radiator is a theoretical (can't actually build one, buy one, or find one
in nature) ideal omnidirectional antenna. Omnidirectional means it
radiates equally poorly in all directions. Anyway, the conversion is:
dBi = 10 * log (power ratio)
where we use a base 10 logarithm.

So let's put all this together and run some examples.

First: my optical telescope (a Celestron) has 100 mm radius reflector.
That mirror has a circumference of (2 * pi * 100 mm) ~ just over a half
meter. I use it to magnify visible light which has a 500 nanometer
wavelength. The voltage gain is (1/2 m)/(500 nm) = 1,000,000!
Theoretical power gain is (1,000,000)^2 = 1,000,000,000,000! Converting to
dBi, that's 10 log (10^12) = +120 dBi (only I won't really get anywhere
near that performance, because my eyepiece and mirror are quite imperfect.)

Next: let us consider Arecibo at the hydrogen line. The mirror at Arecibo
has a 152 meter radius. Its circumference is (2 * pi * 152 meters) ~ just
under 1 kilometer. I use it to receive "light" at a wavelength of 21 cm.
So the voltage gain is (1 km)/(21 cm) ~ 5,000. Theoretical power gain is
(5,000)^2 = 25,000,000. Converting to dBi, that's 10 log (2.5 * 10^7) ~
+74 dBi (only Arecibo won't really get anywhere near that performance,
because its eyepiece {the feedhorn} and mirror {the reflector} are quite
imperfect.)

Conclusion? In terms of power gain, my Celestron telescope is tens of
thousands of times more sensitive than Arecibo. Which explains why optical
SETI is so appealing.


-----------------------------------------------------------------
H. Paul Shuch, Ph.D. Executive Director, The SETI League, Inc.
433 Liberty Street, PO Box 555, Little Ferry NJ 07643 USA
voice (201) 641-1770; fax (201) 641-1771; URL http://www.setileague.org/
email work: n6tx@setileague.org; home: drseti@usa.net

"We Know We're Not Alone!"