
416 OPTICS FOR ENGINEERS
13.2.1 Mean and Standard Deviation
We will consider a light source that we would think of as “constant” in the classical sense, with
apower,P. If we consider a very short time interval, dt, there are only two possibilities. First
there is a small probability that a photon will be detected. We assume that this probability is
• Independent of time (the source is constant)
• Independent of previous photon detections
• Proportional to the source power
• Proportional to the duration of the interval, dt
Therefore, we call this probability α dt where α is a constant. The only other possible result
is that no photon is detected. The