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The Search for Extraterrestrial Intelligence (SETI) in the

Optical Spectrum


Barney Oliver: Can you explain the e-lambda? What are you talking about there?

Jim Lesh: e-lambda is simply saying that if I have a Poisson distribution of two or any number, lambda, then the probability that the number of photons that I receive is zero, is given by e-lambda.

Barney Oliver: Then
lambda i
s the mean?

Jim Lesh: Right.

To put things into perspective, a lot of people talk about the quantum limit of communication. If you take a look at Yariv's book, Yariv talks about coherent detection of optical signals, he then works out what happens if you turn the local oscillator power up to infinity, or almost there, you get to the point where you wipe out all the thermal noise in the detector and you get quantum-limited performance. It sounds wonderful.

Ten years ago at JPL, we demonstrated a system in the laboratory that could transmit over 2.5 bits of information per detected photon at the receiver. Now, let me remind you that if you calculate the quantum limit for a heterodyne system, it's 1.4 bits per detected photon. So, that's the ultimate limit that no system can exceed. And yet in the laboratory with a direct detection system we demonstrated something that was about twice that good. The reason is that the quantum limit is based on that earlier noise model that I showed on a previous viewgraph, where you have a mean signal and a fluctuation. There are certain models for the noise, and certain models for the detection statistics that you have to be very concerned about as to whether or not they still apply, and in some of these weak signal transmission systems, they do not apply. In fact, we proved it.

Now, how conceptually can you do that? Some people think that it is not possible to do it, so I will show it with this viewgraph. If I take a time interval shown right here, and divide it up into a number of little time slots, and if I put one pulse in one of those time slots, then basically I'm saying it's the third message out of eight. So I have sent you now three bits of information because there are eight choices, and I can represent eight by three bits of information. If I take that same pulse, and transmit it over a link, and it gets diluted, I'm showing it right here, and if that pulse has three photons in it on the average, then the average throughput of that system is three bits of information for three photons detected at the receiver.

In our demonstration, we did not have eight bins, but we had 256 bins. In other words, eight bits of information transmitted, and we did have an average intensity of three photons at the receiver. We don't violate any of the fundamental physical principles. We just utilize the fact that the statistics aren't the same kind of statistics as in some of the other arenas.

My point of all of this is to caution you that it is important to not look at signal-to-noise ratios. It's important to say if you have certain kinds of signals coming back, what are the best ways of detecting them? I think that may apply to not only the optical versions, but also the RF as well.

Barney Oliver: Can I comment on that? You were capitalizing on the fact that you didn't have any photons in those other slots.

Jim Lesh: That's correct.

Barney Oliver: You're not getting something for nothing. That's part of the statistics you are dealing with.

Jim Lesh: If you start adding noise photons in there, yes it does deteriorate and it goes down.

Barney Oliver: You're lost.

Jim Lesh: Not necessarily that you are lost, because you have to actually know then what is that intensity.

Barney Oliver: I want to ask another question about this photon-bucket. It seems to me you oversold it a little bit. If you have lost phase information because of a poor surface, another way of stating that is you are going to get a larger image of a point source out here. It's going to be spread out over an area, and if you have a sensitive detector over that entire area you are going to be receiving photons all over that detector. Various points on that detector could correspond to different beams out here. So, what you are saying is that you have a much poorer directivity pattern then you would have if it were a good optical surface. Right?

Jim Lesh: That is correct.

Barney Oliver: So it works in a dark field, but not in a bright field.


Copyright , 1993, SPIE

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