Project Cyclops, A Design... - Department of Earth and Planetary ...

If the output filter is very wide compared with HQ)
and H*H so that G(f) _ G(0) over the significant range
of integration, then for the incoherent case equation
(D7)
becomes
S Ps 2 (D9)
N hv fGdf
Po + Po 2
n a(o)
those expressions that may apply to photon detection as
well.
No Postdetection filtering
If shot noise is negligible; expression (D5) becomes
simply
S Ps2 _ ( Ps 12 (DI3)
while for the coherent case, equation (D8) becomes
s
-- = (DIO)
N hv fGdf 2
(Pr + Po)
n G(0)
+ --
m
PrPo + Po 2
If the output filter is very narrow compared with H00
and H*H so that H0') _ H(0) and H*H = [H*H]f_ 0
over the significant range of integration, then for the
incoherent case equation (D7) becomes
which is always less than unity unless there is no receiver
noise. The receiver bandwidth and band shape do not
affect
the SIN ratio.
Ideal RF Bandpass Filter of Width B, Ideal Low Pass
Postdetection Filter of Cutoff Frequency W
In this case:
H0O =
' • H,H =
0, 1 [IqB/2 {B-Oq,_B
S G(0) Ps 2
_
N [- hv (H*H)f = 0-]
(Dll)
If W > B, the case of no postdetection filtering
applies, since the output filter is too wide to have any
effect.
If W < B, and we neglect shot noise we find from
equation
(D7)
while for the coherent case, equation (D8) becomes:
S Ps B 1 (DI4)
N
_TO_ 2
W 2- (W/B)
S
N
o( o) Pr_
I Pr + Po ) -- hv + 2PrPo
r_
f H(O) Hdf
For W