Contents

%%% pcount.m  Photon counting examples
%   by Chuck DiMarzio
%      Northeastern University
%      June 2009
%

Poisson Distribution

Low mean number (0.1)

nbar=0.1;n=[0:10];
p=exp(-nbar).*nbar.^n./factorial(n);
fig1=figure;bar(n,p);grid on;
xlabel('n, Number');
ylabel('P(n), Probability');

Moderate mean number (1)

nbar=1;n=[0:10];
p=exp(-nbar).*nbar.^n./factorial(n);
fig2=figure;bar(n,p);grid on;

xlabel('n, Number');
ylabel('P(n), Probability');

Moderate mean number (3.5)

nbar=3.5;n=[0:10];
p=exp(-nbar).*nbar.^n./factorial(n);
fig3=figure;bar(n,p);grid on;
xlabel('n, Number');
ylabel('P(n), Probability');

Moderate mean number (50)

nbar=50;n=[20:80];
p=exp(-nbar).*nbar.^n./factorial(n);
fig4=figure;bar(n,p);grid on;
xlabel('n, Number');
ylabel('P(n), Probability');

Probability of 1 or more

n=0;nbar=10.^[-2:.01:1];
p0=exp(-nbar).*nbar.^n./factorial(n); % probability of zero
n=1;p1=exp(-nbar).*nbar.^n./factorial(n); % probability of one
fig5=figure;loglog(nbar,1-p0,nbar,1-p0-p1);grid on;
xlabel('nbar, Mean number');
ylabel('P(n>0,1), Probability');
axis([1e-2,1e1,1e-4,1]);
text(3e-2,1e-2,'P(n>0)');
text(3e-1,1e-2,'P(n>1)');