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Re: Coherence
Dear all,
I have made an error of my own in this piece which I just
discovered:
> Here is the lowdown from the horse's mouth:
>
> According to the 1990 ITS Notes (p2-7, 2-8) :
>
>
> "How long does it take for caollapsing initially stored energy
> to build up a standing wave on a distributed resonator? For that
> matter, how long does it take for light to interfere and form a
> diffraction pattern? (And what happens if the light is not
> monochromatic?) The answer is not what is commonly called the
> resonator fill time, which corresponds to the time for standing waves
> to build up when forced by a sinewave generator (Tfill = 2Q/w),
> Furthermore, other things being equal, why is the voltage rise far
> less on a resonator driven by a bandpass signal than the rise
> produced on the same resonator by a narrowband source?"
>
> NOTE: I take the notion of a sinewave generator and a narrowband
> signal to be the same thing. That leaves us with a clear oxymoron!!
>
> "The bottom line on our analyses was that the time taken for the
> waves to build up, from initial uniform energy storage (at the
> primary spark quenching instant), is inversely related to the
> spectral width of the resonator. This is the famous Fourier
> reciprocity relation:
>
> dt.df >= 1/(4.PI)
>
> where df is related to the cavity Q as Q = df/fo," (NOTE ????????)
> "and dt is the coherence time. We interpret the latter as the time
> duration required for coherent oscillations to build up on a
> distributed resonator and a standing wave pattern to form."
>
> NOTES: There is a glaring formulaic error in there. In fact we know
> that Q = fo/df.
That is what was said in the piece. However, they have used to correct
formula for Q in deriving:
> Working things out using their stuff,
>
> df = fo/Q
> => dt.fo/Q >= 1/(4PI)
> => dt >= Q/(4.PI.fo)
this formula since it is obvious df = fo/Q is the correct formula.
In fact had I used Q = df/fo I should have obtained
dt >= 1/(4.PI.Q.fo) which would be garbage.
My math in the next bit is wanting as well....
> If we take the correct formula for Q,
>
> df = Q/fo
> => dt.Q/fo >= 1/(4PI)
> => dt >= fo/(4.PI.Q)
In fact the first line is completely wrong.
The upshot is that their coherence time formula is quite correct
despite the wrong formula for Q being given. Howver, the sight of
coherence on the scope remains as elusive as ever. My sincere and red-
faced apologies.
Malcolm
<snip>