From - Tue Dec 10 11:02:50 1996
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From: Bill Simpson
Newsgroups: sci.physics,sci.optics
Subject: Re: photon statistics for LEDs and diode lasers?
Date: Tue, 10 Dec 1996 09:22:49 -0600
Organization: University of Winnipeg
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On Fri, 6 Dec 1996, Wayne Shanks wrote:
> a wrote:
> >
> > > I believe that laser photon statistics and LED photon statistics are
> > > Poisson statistics.
> > >
> > > The only difference between a laser and an incandesent source is that
> > > all the photons in a laser are of the same frequency and phase locked to
> > > each other. these two properties are what makes a laser a laser. A LED
> > > is like a laser except that the light is not all the same phase.
> > > Incadesent light is of many frequencies and random phase. If you are
> > > just talking about the the photon counting statistics then the laser the
> > > LED and the lamp are the same.
> > >
> > > Wayne S
> >
> > A single-frequency laser source will exhibit poisson statistics. However,
> > an LED will have a Gaussian distribution. This is related to the fact
> > that there are many uncorrelated random processes happening. According to
> > the Central Limit Theorem, whenever you add up the contributions of many
> > random processes (regardless what distribution they are, in our case
> > Poissonian) you'll end up with a Gaussian distribution (assuming that the
> > processes are uncorrelated.)
Incandescent light is also "random" ("chaotic" is the term Louden uses),
yet its photon statistics are not normal. I don't get it.
> >
> > If you have a multi-longitudinal mode laser you'll also get Gaussian statistics.
> >
> > Jeff
>
>
> Very interesting....so you mean to say that the interval between photons
> hitting a counter is normally distributes about some mean interval for
> light emitted by a LED? or are you talking about some other coralation?
>
> Wayne
>
By "Poisson distributed" one means:
"the number of photons delivered by a particular flash is a realization of
a Poisson random variable with some mean"
To measure this you would have a histogram with the count on the y-axis
and the number of photons delivered on the x-axis.
By "normally distributed" one means "the number of photons delivered by a
particular flash is a realization of a normal random variable with some
mean and variance". I hope this is what was meant.
The statement about interevent intervals is wrong, it seems to me.
(For example, Poisson distribution does NOT refer to distribution of
interevent times for Poisson process. Interevent times for Poisson
process distributed as exponential! Not sure how normal distribution for
photons would affect interevent times)
BTW I realized after posting initially that incandescent light is not
Poisson distributed, strictlt speaking. It is approx Poisson only if the
observation interval is much longer than the coherence time (whatever that
is).
Where can I read more about LEDs and photon statistics?
Thanks for all the responses.
Bill Simpson