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Optical Sources, Detectors, and Systems by Robert H. Kingston

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4.6 Effective Input Noise Current, Responsivity, and Detectivity 91
network bandvs^idth required for effective detection of a pulse of width
T. Also shovy^n for comparison is a Gaussian pulse,
expi-lTtP'
/T^),
with
its associated power spectrum, expi-Ttft^) which also has area or first
moment, 1/2T. Thus, B = 1/2T is a reliable approximation for the
required network bandwidth for a typical current pulse.
4.6 Effective Input Noise Current, Responsivity, and
Detectivity
To this point we have characterized the preamplifier in terms of an
effective input resistance and noise temperature. From a system design
point of view, commercially available amplifiers are usually specified in
terms of the normalized or
"spof'
noise current measured in Ajs/Hz,
usually quoted in pAj^Hz, with 1 pA =
10'^'^
A, The effective input
noise current then becomes
and the quantity, fz„) rj can be found from Figure
4.11.
Example. The transimpedance amplifier example at the end of Sec-
tion
4.3
used an input resistance of JRJ = 10,000Q, and had an effec-
tive input noise temperature of T^
=
60 K. From Figure 4.11, the
effective input noise current density is 0.6 pA/^z. Assuming a
I MHz bandwidth, compatible with TV imaging rates, the net input
noise current is then
600
pA or approximately 4 x 10^
electrons/sec.
The sampling time corresponding to this bandwidth is 0.5
jjsec,
and
thus the noise or rms count fluctuation in any sample is 2000!
Thus,
even with the reduced effective temperature, the performance
is far removed from "photon'' counting.
Another descriptor for detectors is the responsivity % the current
output per unit optical power given by rj^//zv -
T]X
(ijm)/1.24 in A/W.
The amplifier noise limited NEP then becomes
92
Chapter 4 The Ideal Detector and Noise Limitations
100
w
0.1
10
100
1000
10000
100000
R, (ohms)
Figure 4.11 Normalized noise ctirrent 0„)J7, PsR^for
TKJ
= 10,30,100, and 300 K. lpA = 10^^ amp.
(NEP)j,i^
=(in)eff/^
=
(in)^^fB/9{
(4.23)
Finally we define detectivity D as the reciprocal of the NEP, with
dinnension Vf . This figure of merit increases when the sensitivity or
ability to detect signals increases Many detectors are also specified in
the literature in terms of their
specific
detectivity D*
(pronounced
D-star).
This quantity is D normalized to a standard detector area A oi
1
cnP;
and bandwidth, B, of 1 Hz. We may then write D
*
for the
background-linrdted and amplifier-limited cases as

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