Optics deal with light in a classical way
(i.e, without quantum concepts) using one of two viewpoints:
- Geometrical optics
is based on the concept of light rays
propagating in a straight line according to the classical laws of reflection
(angle of reflexion = angle of incidence) and refraction
Both of these where unified as consequences of the principle of least time
postulated by Pierre de Fermat iaround 1635 and confirmed experimentally in 1851
(when it was finally established that the celerity of light is indeed inversely proportional
to the index of refraction of the medium).
The wave theory of light, on the other hand,
(as well as the laws of reflexion and refraction of geometrical optics, incidentally).
It was first championned by Christiaan Huygens and
received experimental support from Thomas Young in 1803.
The idea that light is a form of electromagnetic wave is due to
who was later vindicated mathematically by James Clerk Maxwell
(Maxwell's equations, 1864).
quantum optics (fundamental research)
photonics (applied science)
are based on the explicit idea that light consists of
packets of energy proportional to its frequency
(the coefficient of proportionality being
This idea was formally put forth in 1905 by
Albert Einstein to explain the
(in 1900, Max Planck
had paved the way by showing that the blackbody spectrum
could be explained by postulating that
all energy exchanges between radiation and matter
could only occur in quanta of energy proportional to the frequency).
So, the key difference between optics and photonics is that the latter deals primarily
quantization of light which is ignored by the former.
Also, in optics we consider light to consist either
of particles (explaining the
light rays and sharp shadows
on which geometrical optics is based)
or waves (which explain diffraction using Huygens principle).
In photonics, we integrate the quantum notion that the light quanta
(photons) have properties characteristic of both waves and particles.
vs. Geometrical optics.
This imposes a lower limit on the noise of the image sensors used on modern digital cameras.
Those are composed of a digital array consisting of millions of individual sensors
of the type analyzed below: One per pixel for a black-and-white sensor,
up to four per pixel
for color photography.
The arrival of photons in a monochromatic light beam is essentially a
Poisson process whose activity
a is equal to the radiant power
of the beam (in watts, W) divided into the
energy of each photon (in joules, J).
For standard yellow-green light (540 THz)
the luminous power in lumens (lm) is, by definition,
683 times the radiant power in watts (W).
A surface area of S square meters receiving an illumination of L
(expressed in lx, a lux being defined as a lumen per square meter)
thus receives an average number of photons per second equal to the activity
in becquerels (Bq) of the aforementioned Poisson process, namely:
S (L / 683) / (h 5.4 1014 Hz)
= L S 4.092 1015
If we express
a in Bq,
L in lx and S in square microns, we have:
a = 4092 L S
In a Poisson process
with an activity of a becquerels,
the probability of observing exactly n arrivals in t seconds is given by:
exp(-lt) (at) n / n!
The average number of arrivals is
at. Let N be the RMS of the noise:
N 2 + (at) 2
Pn n 2
For the right-hand-side summation, we use the following remarks:
S n x n / n!
= exp (x)
S n n x n / n!
= x d/dx exp (x) = x exp (x)
S n n 2 x n / n!
= x d/dx [ x exp (x) ]
= x exp (x) + x 2 exp(x)
Applying this to the above with x = at yields:
N2 + (at) 2
(at) + (at) 2
So, the RMS value of the noise is
N = Ö(at).
and the signal to noise ratio is:
at / N =