Download Noise_and_Detection

NOISE
N. Libatique
ECE 293
2nd Semester 2008-09
Optical Detection: Biomolecular Signaling
http://universe-review.ca
11-cis-retinal  trans-retinal  rodopsin changes shape  makes opsin sticky to transducin 
GDP from transducin falls off and replaced by GTP  activated opsin binds to phosphodiesterase
which aqcuires the ability to cut cGMP  lower cGMP conc. causes ion channels to close lowering
Na concentration in cell and lowers cell potential  current transmitted down optic nerve to brain
http://universe-review.ca
Optical Detection


Opto-electronic Detection vs. Others
(Biomolecular Signalling)
Limits of communication, bit error rate
Shot Noise


Shot Noise, Johnson Noise, 1/f Noise
Shot Noise ~ Poisson Process
Dt very small







P(0,Dt) + P(1,Dt) = 1
P(1,Dt) = a(Dt); a = rate constant
No arrivals over t + D t ; P(0, t + D t)
P(0, t + D t) = P(0,t) P(0,D t)
What is P(0, t)?
In a pulse of width t, what is the probability of
it containing N photons?
P(N)
t
What is the detection limit?
A perfect quantum detector is used to receive an
optical pulse train of marks and spaces. If even one
photon arrives, it will be detected and counted as a
mark. The absence of light over a clock period is a
space. Every pulse will have a random number of
photons. On average, how many photons should be
sent per pulse, if it is desired that only 1 ppb be
misinterpreted as a space when in fact it is a mark?
Poisson





dP(0,t)/dt = - a P(0, t)
P(0, t) = e- a t ;
What about P(N)? N photons at a time?
It can be shown that this is a Poisson process
P(N) = (Nm)N e –N / N!
m
Poisson Distribution
Optical Shot Noise
N = 6; Only 16%
of pulses have 16
photons;
e-6 probability of
having no photons
P(N) = (Nm)N e –Nm / N!
Variation is fundamental
Signal to Noise Ratio
Shot Noise on a Photocurrent
Other Sources





Aside from photon shot noise
Background radiation: blackbodies
Johnson Noise: thermal motion of electrons
1/f Noise: conductivity fluctuations
Amplifier Noise
Background Radiation



Ptotal = Psignal + Pbackground
MeanSquareCurrentshot proportional to Ptotal
I(W/cm2) = (T/645)4 (T in K)
4.7x10-2 W/cm2 at 300 K
 Human Body 2 m2  1 kW


Spectrally distributed
3K
1,000 oC
http://en.wikipedia.org/wiki/Black_body
Spectral Distribution
http://en.wikipedia.org/wiki/Black_body
Bit Error Rates






Analog Signals: SNR ratio
Digital Signals: BER
Telco Links = 10-9
Datacomms and Backplanes
= 10-12
Quality Factor
Power required to achieve Q
and BER? 0.1 dB significant
as fiber losses are low…
http://zone.ni.com/devzone/cda/tut/p/id/3299
Probability Distribution Function
• Signal + Noise results in
bit errors…
• Noise statistics of signal,
detector, amplifier determine
PDF
Output
Current
A01
2s1
Id
s(1) = expectation current value
Decision Level
2s0
s(0) = expectation current value
A10
Probability
Probability of Error






p(0) = probability that a space is transmitted
p(1) = probability that a mark is transmitted
A01 = probability that space is seen as mark
A10 = probability that mark is seen as space
P(E) = p(0) A01 + p(1) A10
Assume Gaussian statistics 
P(E) = Integral[Exp[-x2/2],{x,Q,Infinity}]/Sqrt[2 p]
BER vs Q
BER
10-5
10-7
10-9
6
Q
Design



Assume a perfect quantum detector. Amplifier
input impedance is 50 Ohms. Shunt Capacitance
2 pF. Design a 100 Mbps link at 1.5 mm. Design
for a BER 10-12.
Assume the effective bandwidth required would
be 200 MHz (Nyquist Criterion).
Optimize the detector. Minimize the power
required to achieve BER.  reducing the BW
via changing RC, reduce ckt noise, etc……
Show…
Poisson Statistics: Show value of mean:
Summation [k p(k,n), {k,0,Infinity}]
 Poisson Statistics: Expectation value for k2
(Note: p(k,) = nk e-n / k!
 Mean[(k-n)^2] = n
 Simulate a current governed by Poisson Noise
