I didn't plan to do a follow-up to yesterday's post about the optics of sending messages with lasers, but then I starting idly thinking about detection, prompted in part by a bunch of conversations with my summer students about single-photon detectors. which led to scribbling on the back of an envelope, which led to Googling, and suddenly, I have a follow-up post.
So: as we said yesterday, if you want to send messages over a distance of ten light years, a relatively efficient way to do this might be to send them via lasers. This results in the light being spread over a pretty big area, though-- the best you can do at a distance of 11 light-years is a spot around 160,000m radius-- so how easy would that be to detect?
Well, we have the ability to detect single photons, so a good way to think about this would be to ask how many photons from that laser spot we could expect to collect with a telescope. The number of photons per second sent out by a laser will be equal to the laser power in watts divided by the energy per photon (a watt is one joule per second, remember). The photon energy depends on the wavelength, and yesterday's estimates used a wavelength of 400nm, at the short end of the visible spectrum, which corresponds to around 5x10-19 joules per photon. So a one-watt laser would be sending out 2x1018 photons per second.
Yesterday, we said that the smallest spot you could hope to make at the far end is 1.6x105 meters in radius, so we need to spread those photons over that area, which works out to about 24,000,000 photons per square meter per second. If you were looking at that with a telescope having a mirror with a 10-meter radius, you'd expect to see something just under eight billion photons per second. That's a pretty substantial rate, something you would easily be able to detect even without going to fancy single-photon counters.
Of course, it's not quite as simple as just detecting those eight billion photons per second, because your communications laser is going to be coming from a region very close to your home star, so you'll need to pick it out from that background. which is where we have to turn to Google, which turned up this discussion at CosmoQuest giving two different values: a very bright star produces something like two million photons per second per square centimeter, and a very dim one about 0.2 photons per millisecond per square centimeter. Doing a bit of multiplication gets us a total photon flux for our imaginary telescope of somewhere between 6x108 and 6x1012 photons per second, depending on the magnitude of the star the signal is coming from. At the low end, that would make our 1W laser clearly detectable; at the high end, not so much.
But then, it's not as bad as it might seem, because a laser by definition is concentrated in a very narrow band of wavelengths, while the flux from a star is spread out in a black-body sort of spectrum. So if you were to focus on a very narrow region in the right range of wavelengths, the laser photons might very well stand out even against the background of light from the star. This will also depend somewhat on the character of the star-- a violet laser would be more clearly detectable coming from the neighborhood of a reddish star. I've had enough mucking around with weird astronomical unit conversions, though, so I'm not going to try to figure out the details-- call it extra-credit homework, which you can send to Rhett for grading.
Of course, that's the optimum case, where you're getting the smallest possible spot size at your distant target by launching your signal from a mirror with a radius of 100,000m, the size of a biggish asteroid. That might not be completely ludicrous for a civilization capable of launching an interstellar probe in the first place, but it's not going to work for the probe itself. So what would the return signal look like, assuming you used the 10-m-radius detection mirror to send the return signal?
Well, from yesterday's post, a 10m launch mirror gives you a beam at the far end with a radius of 1.3x109m. that's a factor of 8000 or so bigger than you would get with the asteroid-scale mirror, which corresponds to an increase in the beam area by a factor of 66,000,000. Which means a 10m telescope back on Earth would pick up just 114 photons/s from a space probe equipped with a 1W laser at 400nm. That's... more challenging. You might try using the same asteroid-scale mirror as a telescope to pick up the return signal, which would boost your laser photon counts back up to the same level as before. But, of course, that's going to boost the photon rate from the background star by that same factor of 66,000,000, so it doesn't actually help. If you wanted your laser flux to match the total background light from a dim star, you'd need to use a five megawatt laser to send the signal, which is a bit tricky. But I suppose you could run it off the magic compact fusion reactor you're using to power your relativistic space probe in the first place...
So, anyway, there's another blog post on the feasibility of using lasers to send messages between the stars. There are, of course, a lot of factors left out of this, chiefly the fact that I assumed perfect Gaussian beams for this (which you're probably not going to get) and that I've ignored any effects of stuff along the beam line. Even interstellar space isn't perfectly empty, and over the span of 11 light years, you might need to worry about that medium causing some distortion of your beam. In which case, you probably want to decrease all the laser photon count rates by an order of magnitude or so, probably more. But those calculations won't fit on the back of any envelopes I have handy, so this is what you get.
Typo: two million photons per millisecond -> second?
I don't think the signal has to compare with the star flux to be detected, only the noise. Between that and a very narrow spectral slit, signal detection would be quite a few orders of magnitude easier. The remaining problem, however, is what bitrate you'd be able to detect.
I second Lurker #753's comment: a zero-th magnitude star like Vega will send roughly one million photons per second through an area of one square cm through the common astronomical V-band filter.
I do this sort of calculation for a living, so feel free to ask additional questions.
I had typed both of the stellar fluxes as "per second" then noticed that one was supposed to be "per millisecond." And, of course, when I went back to fix it, I corrected the wrong one, making both figures wrong.
One thing you didn't mention - that the lunar laser rangers also take advantage of - is that you can concentrate your photons in a narrow pulse. The laser ranging folks use 100 picosecond pulses. Compared to a continuous laser this gives you a 10^10 increase in the rate of photons (during the pulse) that makes it much more easily detectable over continuous sources like stars.
I'm wondering how the figures change if you use microwave or radio frequencies instead. I played around with the equations in yesterday's post -- one immediate conclusion is that the minimum size of the spot, and the size of the transmitter required, both monotonically increase as wavelength increases. But it may be practical to equip the probe with a much larger transmitter than it would for visible frequencies, and it may also be easier to detect a beam aimed directly at the receiving star and allowed to spread to, say, the diameter of Jupiter's orbit, against the background of the sending star. I can't find good figures for radio-frequency emissions for main sequence G/K/M dwarfs.
If one does stick to visible light, another thing that might help is picking a laser frequency corresponding to one of the strong absorption lines in the star's emission profile. Background there wouldn't be zero, but it would be a lot lower than elsewhere.
You could improve detectability by temporally modulating the beam at high frequency relative to the signal modulations imposed on that carrier. Then you've got a narrow band in temporal frequency as well as photon energy.
And you don't have to lock onto the signal in real time like it was a phone call or something. You can record the signal from your detector during the prearranged communication window and then analyze it offline, take a good long time figuring out the synchronization of the whole transmission before trying to extract the actual symbols.
The problem wieth concentrating the beam too much is that you can only detect it whe you're right there. That's not much use if you' ve got a 160 km radius spot, but are orbiting the star at a useful distance. You'd have to know exactly where the probe was in it's orbit - 10 years in advance (not as easy as simply predicting where the star system will be in 10 years).
So better stick with a more spread out beam I think.
Laser guy here. Why stop at one watt? I work on industrial green pulsed lasers that will put out 350W of average power in 20ns pulses at 10khz. That's a pretty prominent signal.
No reason to stop at one watt. It's just a nice round number for back-of-the-envelope calculations. You can certainly scale up the laser power by whatever factor you like, and the photon counts will go up by a corresponding amount.
Using pulsed lasers for communicating might raise some interesting issues. Most of the low-intensity pulsed communication experiments I know of rely on regular timing to boost their efficiency-- that is, since they know the repetition rate of the laser, they know exactly when to look, and aren't integrating background counts during times when the pulse isn't on.
If you're talking about something like an interstellar space probe, though, you might need to start worrying about relativistic effects on the timing of the pulse train. It's not going to be a huge effect-- you need to be at about 0.14c before you slow time by 1% (homework question)-- but might add up over the long time such a mission would involve.
One way of mitigating this problem would be to have a second transmitter some distance away from the actual star to rebroadcast.
On this end it wouldn't be too hard (for a civilization capable of sending out probes) to stick a few transmitters orbiting the sun a light-year or so away. (You need a few because otherwise there is a reasonably likelihood the transmitter will be in line with the sun when you actually want a transmission.)
On the other end, let's suppose you had a second probe which takes a signal (probably radio, since otherwise you just have the same glare problem for the second probe to see the first) from the first probe and rebroadcasts the message in laser. Is there any distance between the probes for which this would actually be something helpful to do? Or is it the case that the second probe would have to be so far away from the first probe in order to mitigate the glare that the first probe would not be able to communicate to the second?
To my layperson's mind this seems to support the conclusions that:
a) Laser communication is viable for interstellar purposes, from robotic probe missions to inhabited planets in an interstellar civilization.
b) A wide beam at the destination (e.g. Jupiter orbit size) is preferable for ease of aiming, and the reception issues can be overcome within presently-known & existing technologies.
c) It is not likely that our solar system would coincidentally happen to lie within the beam paths of another civilization's communications network. But even so, it is worthwhile to support SETI efforts at detecting any such beam, due to the importance of the potential discovery.
Yes? No? and/or what have I missed?
Back a few days to Fermi Fallacies (see also my comment at #14 and correction at #15 there):
I'm inclined to think that the belief that we are alone & unique, has historically been associated with certain kinds of theology, and has become associated with our collective sense of self-worth or importance.
Conversely it is possible that, not only are we not-alone and not-unique, but "they" won't consider us important enough to be worth communicating with, until we achieve some threshold of development such as interstellar (or even interplanetary) civilization. "You're barely an embryo; call us after you hatch" is not exactly ego-gratifying, but as long as we're speculating about the Fermi paradox, it's not unreasonable either.
Howsabout building some sort of giant lens in space, and focusing the sun's light into a beam?