O'Reilly logo

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

Stay ahead with the world's most comprehensive technology and business learning platform.

With Safari, you learn the way you learn best. Get unlimited access to videos, live online training, learning paths, books, tutorials, and more.

Start Free Trial

No credit card required

4.7 General Signal-to-Noise Expression 93
NEP
(D%r= I
^—VAB=
^ (4.24)
using Eq. (4.19). In the background-limited case we see that D* is con-
trolled by the background power density striking the detector. There is
thus a family of hmiting curves for D* in the long-wavelength region
where the background is typically at 300 K and the background intens-
ity is a function of the optical system
//#,
or the numerical aperture, NA
(see Kingston, 1978). The amplifier-limited expression is particularly
applicable to photovoltaic detectors discussed in Chapter 5, where the
so-called RA
product
becomes a figure of merit.
4.7 General Signal-to-Noise Expression for Combined
Signal, Background, and Amplifier Noise
We have thus far treated detection systems as operating in one of
three distinct regimes: signal or photon noise limited, background noise
limited, or amplifier noise limited. In some important cases, however,
the signal-induced noise can become comparable or greater than the
amplifier noise at high values of (S/N)y, Under these conditions, it is no
longer correct to set the (S/N)y equal to P^NEP, although the NEP is
still a qualitative figure of merit. This is an especially important
consideration in communications and radar systems, where high (S/N)y
is required for extremely low error rates and high detection probabilities.
In addition, avalanche photodiodes and optical amplifiers usually have a
strong signal-dependent noise output component.
For the most general expression for signal to noise we take into
account all noise current contributions and write
i.) -Js_- is
(4_25)
^)v ^ 42qiB+(4kT^BIRi„)
94 Chapter
4
The Ideal Detector and Noise Limitations
and using i = riq(P^P^)/hv, we obtain, after some manipulation,
= (4.26)
S^ ^
i
V ^ V ^U^J ^in
This result may now be written in terms of our previous definitions of
(NEP)BI and (NEP)^y and the quantity (NEP)si=
2hvB/ri,
yielding
^ (4.27)
.NJv ^P^
X (NEP)si +
(NEP)li^
+
(NEP)
We use this expression in Chapter 7.
2

With Safari, you learn the way you learn best. Get unlimited access to videos, live online training, learning paths, books, interactive tutorials, and more.

Start Free Trial

No credit card required