2. • Interference
• Intensity
• Visibility
• Optical Path Length [OPL]
• Optical Path Difference [OPD]
• Coherence:
• Spatial coherence
• Temporal coherence

3. Optical Interfrometry is an optical measurement technique that provides extreme
precise measurements of distance, displacement or shape and surface of objects.
It exploits the phenomenon of light waves interference .
Where under certain conditions a pattern of dark and light bars called interference
fringes can be produced. Fringes can be analyzed to present accurate
measurements in the range of nanometer.
The recent developments in laser, fiber optics and digital processing techniques
have supported optical interferometry .
Applications ranging from the measurement of a molecule size to the diameters of
stars.

4. Light waves
 For many centuries, light was considered a stream of particles .
 Light wave exhibits various behaviours which can not interpreted
through the particles theory of light such as, refraction, diffraction
and interference.
 in19th
century the particles concept was replaced by the wave
theory .
 light waves are transverse waves with two components; magnetic
and electric field each one of them oscillating perpendicular to
the other and to the propagation direction.
 The visible light is part of the electromagnetic spectrum it
extends from 750nm for the red color to 380nm for the violet
color.
Light wave characteristics:
light speed in free space (c): C=300k (km/s)
C = λv
V = c/n
λn =λ /n
 Where: n is the refractive index of the medium in which the light travels.
λn is the wavelength in medium other than free space.
EM-wave propagation
Visible light spectrum
Refractive index

5. Interference
 Interference is a light phenomenon .It
can be seen in everyday life. e.g..
colures of oil film floating on water.
In electromagnetic waves , interference
between two or more waves is just an
addition or superposition process. It
results in a new wave pattern .

6. Superposition of two waves
 When two waves with an equal amplitudes are superposed the
output wave depends on the phase between the input waves.
Y = y1 + y2
Where: y1=A1 sin (wt + θ1 )
y2=A2 sin (wt + θ2)
 Since the energy in the light wave is intensity I ,which is proportional to
the sum of square amplitudes A^2
where: A=A1^2+A2^2+2A1A2 cos (θ1 – θ2)
If A1=A2=A then:
A=2A^2+2A^2 cos (θ1 – θ2)
If y1&y2 in phase ,cos(0)=1 hence,
Y = 4A^2 ,it gives a bright fringe.
If y1&y2 out of phase by (π) ,cos (π)=-1 hence,
Y = 0 ,it gives a dark fringe

7. Optical Path Length [OPL]
 When light beam travels in space from one point
to another, the path length is the geometric length
d multiplied by n (the air refractive index) which
is one:
OPL = d
 Light beam travels in different mediums will have
different optical path, depending on the refractive
index (n)of the medium or mediums.
OPL = n d

8. Optical Path Difference [OPD]
If two beams with the same wavelength i.e same
frequency, travel from two different points
towards the same destination ,taking different
paths there will be a difference in their optical
path this difference is called the optical path
difference [OPD].
it is very important factor in determining fringes
intensity.
OPD = mλ
Here, If m=0 or any integer values there will be a
bright fringe. Otherwise dark fringes (maximum
darkness when )
OPD= (m-1/2) λ

9. Intensity of Interference fringes
 Intensity of interference fringes depends on the phase
between the recombined waves i.e.
 Intensity I is the complex amplitude of the interferer
waves A given as: I=│A│^2
I = lAl^2 = I1+I2+2(I1I2) cos (Δθ) ^1/2
 When Δθ = 0
I max = I1 + I2 +2(I1I2)^1/2
if I1=I2 then
I max=4I
 When Δθ = π
I min = I1 + I2 – 2(I1I2)^1/2
if I1=I2 then
I min=0

10. Visibility of Interference fringes
Visibility determines the ability to resolve
interference fringes. It depends on the coherence
degree between the recombined light waves.
It is defined as:
V = I max - I min / I max + I min
maximum if Imin = 0 , V= 1
When Imin = Imax , V= 0
[ 0 ≤V≤1 ].

11. Coherence
Coherence of light wave is defined as the correlation
between the electric field values at different locations or
times. The coherent light source is able to produce a
coherent waves able to interfere with each other.
Ideal coherent source is a source with one wave length
only ‘‘monochromatic’’ which does not exist in practice.
Practically, there is no fully coherent light or fully
incoherent light, but there are light sources with deferent
coherence degree .

12. Spatial & Temporal Coherence
 Spatial coherence:
The degree of correlation between different points on the
same wave front at the same time.
Spatial coherence is light source dependent, as the source
size extends its spatial coherence degree deteriorate.
 Temporal coherence:
The correlation between the electric fields at the same
point but at different times.
Temporal coherence proportionate to the wave train
length. Monochromatic sources such as laser have a high
degree of temporal coherence, because of the long wave
trains.
 Coherence Length: ΔS = N λ.
where N is the waves number contained in one wave train.
 Coherence time :Δt = ΔS / C
where C is the light speed in space .

13. Interferometry refers to family of techniques where waves superimposed
to extract information about the waves

15. Interferometers classifications:
 Double path versus Common path interferometers
 Wave front splitting versus Amplitude division
interferometers

16. Interferometer
 Interferometer:
Is an optical instrument that can produced two
beams interference or multiple beam
interference.
 wave front division interferometers:
Two light beams from the same wave front are
made to interfere to produce an interference
fringe pattern. Eg :Rayleigh interferometer
Lloyd’s mirror
 Amplitude-division interferometers:
A light beam from one source point is divided
into two beams using a beam splitter.
e.g. Michelson’s interferometer
Fabry perot interferometer,Fizau interferometer

17. In Fizau interferometer,

18. Double path interferometer
- reference beam and sample beam travel along
divergent paths
eg: Michelson interferometer
Twymann Green interferometer
Mach Zehnder interferometer
Common path interferometer
- reference beam and sample path travel along same
path
Eg: Point diffraction interferometer
Sagnac interferometer
Fresnel’s biprism

19. In common path interferometer,

20. Michelson interferometer
 Configuration:
Michelson interferometer consists of a coherent light
source, a beam splitter BS a reference mirror ,a
movable mirror and a screen .
 Applications:
There are many measurements that Michelson
interferometer can be used for, absolute distance
measurements, optical testing and measure gases
refractive index.
 Work method:
The BS divides the incident beam into two parts one
travel to the reference mirror and the other to the
movable mirror .both parts are reflected back to BS
recombined to form the interference fringes on the
screen.

21. Twyman-Green interferometer
Configuration:
 A modified configuration of Michelson
interferometer ( rotatable mirror& a
monochromatic point source)
Applications: length measurements, optical testing
e.g. lenses ,prisms, mirrors.
Work method:
When the interferometer aligned properly, two images
of the light source S from the two mirrors M1&M2 will
coincide. The superposed waves are parallel and have a
constant phase difference. On the serene a uniform
illumination can be seen with a constant intensity
depends on the path difference.
Mirror imperfections test:
There will be an interference fringes due to the path
difference between W2 and the reference plan wave W1

22. APPLICATIONS
In science and industry for measurement of small
displacements,refractive index changes and surface
irregularities.
 Physics and Astronomy.
Engineering and applied science .
Biology and medicine.