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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