s the mean?
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
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
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.
Can I comment on that? You were capitalizing on the fact that you didn't
have any photons in those other slots.
You're not getting something for nothing. That's part of the statistics
you are dealing with.
If you start adding noise photons in there, yes it does deteriorate and
it goes down.
Not necessarily that you are lost, because you have to actually know
then what is that intensity.
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?
That is correct.
So it works in a dark field, but not in a bright field.