BARBIER, Remi (University of Lyon 1 - IPNL) - NDIP 11 - IN2P3
BARBIER, Remi (University of Lyon 1 - IPNL) - NDIP 11 - IN2P3
BARBIER, Remi (University of Lyon 1 - IPNL) - NDIP 11 - IN2P3
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Part I: T. Hollenhorst, A theory <strong>of</strong> multiplication Noise, IEEE Transactions on electron devices Vol. 37. N0. 3. MARCH 1990<br />
M N, and f N : Gain and noise increment <strong>of</strong> a <strong>of</strong> the N identical stage device<br />
ΦN (z) Generating function <strong>of</strong> the N stage device<br />
φN (z) Generating function <strong>of</strong> the stage N<br />
[ ]<br />
Φ N +1 (z) = Φ N φ N +1 (z)<br />
[ [ ] ]<br />
ΦN (z) = φ1 φ2 …φN −1[ φN (z) ]…<br />
Recursion relations for M N and f N :<br />
M N +1 =<br />
M 01M N<br />
1 − (M N −1)(M 10 −1)<br />
fN +1 = f 01 + M 2<br />
10MN<br />
+1<br />
2<br />
M01MN [ f10(M N −1) + f N ]<br />
N<br />
(M 01 − M<br />
MN =<br />
10)M 01<br />
N N<br />
(M 01 −1)M 10 − (M10 −1)M 01<br />
fN = A( MN −1)<br />
+ B 1 − 1 ⎛⎛ ⎞⎞<br />
⎜⎜ ⎟⎟<br />
⎝⎝ ⎠⎠<br />
MN A = f01M 01 M10 −1 ( ) + f10M10( M01 −1)<br />
( M01 −1)<br />
2<br />
( M10 + M01) B = M 2<br />
01 f01( M01 − M10)<br />
+ f10M10( M01 −1)<br />
M10 + M01 [ ]<br />
( M01 −1)<br />
2<br />
( )<br />
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M01 N<br />
M€ N = M01 fN = f 01 1 − 1<br />
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⎛⎛ ⎞⎞<br />
⎜⎜ ⎟⎟<br />
⎝⎝ M01 ⎠⎠<br />
N stages : PMT / APD / EMCCD<br />
M N, and f N : PMT M N and f N : APD M and f: EMCCD<br />
M 01 = δ<br />
f01 = σ 2<br />
01<br />
2<br />
σ 01 = δ<br />
f01 = 1<br />
M01 M 10 =1<br />
f 10 = 0<br />
Rémi Barbier, <strong>NDIP</strong> 20<strong>11</strong>, <strong>Lyon</strong>, France, July 4-8 tutorial : photodetectors<br />
−1<br />
1 − 1<br />
€<br />
⎛⎛ €<br />
⎜⎜<br />
⎝⎝<br />
= 1<br />
(Poisson)<br />
δ<br />
M N = δ N<br />
fN = 1 1<br />
1 −<br />
δ −1 δ N<br />
⎛⎛ ⎞⎞<br />
⎜⎜ ⎟⎟<br />
⎝⎝ ⎠⎠<br />
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Do it as an exercise !<br />
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M N<br />
€<br />
⎞⎞<br />
⎟⎟<br />
⎠⎠<br />
M 01 =1+ µ<br />
f 01 = µ<br />
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k ≡ α<br />
β
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