report on wave diffraction

1. Systems & Biomedical Engineering Department
Physical optics
Project on waves diffraction
Presented for : ph Mohammed Hesham
Presented by :​ ​Abdelrhman Aboubakr
Section : 1
Bench Number: 42

2. Diffraction​ :
Diffraction pattern of red laser beam made
on a plate after passing through a small
circular aperture in another plate
Diffraction refers to various phenomena
that occur when a wave encounters an
obstacle or a slit. It is defined as the
bending of waves around the corners of an
obstacle or aperture into the region of
geometrical shadow of the obstacle. In
classical physics, the diffraction
phenomenon is described as the
interference of waves according to the
Huygens–Fresnel principle that treats each
point in the wave-front as a collection of
individual spherical wavelets. These
characteristic behaviors are exhibited when

3. a wave encounters an obstacle or a slit that
is comparable in size to its wavelength.
Similar effects occur when a light wave
travels through a medium with a varying
refractive index, or when a sound wave
travels through a medium with varying
acoustic impedance. Diffraction has an
impact on the acoustic space. Diffraction
occurs with all waves, including sound
waves, water waves, and electromagnetic
waves such as visible light, X-rays and radio
waves.
Since physical objects have wave-like
properties (significantly at the atomic level,
invisibly at macro level), diffraction also
occurs with matter and can be studied
according to the principles of quantum
mechanics. Italian scientist Francesco Maria
Grimaldi coined the word "diffraction" and

4. was the first to record accurate
observations of the phenomenon in 1660.
While diffraction occurs whenever
propagating waves encounter such changes,
its effects are generally most pronounced
for waves whose wavelength is roughly
comparable to the dimensions of the
diffracting object or slit. If the obstructing
object provides multiple, closely spaced
openings, a complex pattern of varying
intensity can result. This is due to the
addition, or interference, of different parts
of a wave that travel to the observer by
different paths, where different path
lengths result in different phases (see
diffraction grating and wave superposition).
The formalism of diffraction can also
describe the way in which waves of finite
extent propagate in free space. For

5. example, the expanding profile of a laser
beam, the beam shape of a radar antenna
and the field of view of an ultrasonic
transducer can all be analyzed using
diffraction equations.
Application​ :
The effects of diffraction are often seen in
everyday life. The most striking examples of
diffraction are those that involve light; for
example, the closely spaced tracks on a CD
or DVD act as a diffraction grating to form
the familiar rainbow pattern seen when
looking at a disc. This principle can be
extended to engineer a grating with a
structure such that it will produce any
diffraction pattern desired; the hologram
on a credit card is an example. Diffraction in

6. the atmosphere by small particles can cause
a bright ring to be visible around a bright
light source like the sun or the moon. A
shadow of a solid object, using light from a
compact source, shows small fringes near
its edges. The speckle pattern which is
observed when laser light falls on an
optically rough surface is also a diffraction
phenomenon. When deli meat appears to
be iridescent, that is diffraction off the meat
fibers.All these effects are a consequence of
the fact that light propagates as a wave.
Diffraction can occur with any kind of wave.
Ocean waves diffract around jetties and
other obstacles. Sound waves can diffract
around objects, which is why one can still
hear someone calling even when hiding
behind a tree. Diffraction can also be a
concern in some technical applications; it

7. sets a fundamental limit to the resolution of
a camera, telescope, or microscope.
History​ :
The effects of diffraction of light were first
carefully observed and characterized by
Francesco Maria Grimaldi, who also coined
the term diffraction, from the Latin
diffringere, 'to break into pieces', referring
to light breaking up into different
directions. The results of Grimaldi's
observations were published posthumously
in 1665.Isaac Newton studied these effects
and attributed them to inflexion of light
rays. James Gregory (1638–1675) observed
the diffraction patterns caused by a bird
feather, which was effectively the first
diffraction grating to be discovered. Thomas
Young performed a celebrated experiment

8. in 1803 demonstrating interference from
two closely spaced slits. Explaining his
results by interference of the waves
emanating from the two different slits, he
deduced that light must propagate as
waves. Augustin-Jean Fresnel did more
definitive studies and calculations of
diffraction, made public in 1815 and 1818,
and thereby gave great support to the wave
theory of light that had been advanced by
Christiaan Huygens[13] and reinvigorated
by Young, against Newton's particle theory.
Mechanism​:
In traditional classical physics diffraction
arises because of the way in which waves
propagate; this is described by the
Huygens–Fresnel principle and the principle
of superposition of waves. The propagation

9. of a wave can be visualized by considering
every particle of the transmitted medium
on a wavefront as a point source for a
secondary spherical wave. The wave
displacement at any subsequent point is the
sum of these secondary waves. When
waves are added together, their sum is
determined by the relative phases as well as
the amplitudes of the individual waves so
that the summed amplitude of the waves
can have any value between zero and the
sum of the individual amplitudes. Hence,
diffraction patterns usually have a series of
maxima and minima.
In the modern quantum mechanical
understanding of light propagation through
a slit (or slits) every photon has what is
known as a wavefunction which describes
its path from the emitter through the slit to

10. the screen. The wavefunction (the path the
photon will take) is determined by the
physical surroundings such as slit geometry,
screen distance and initial conditions when
the photon is created. In important
experiments (A low-intensity double-slit
experiment was first performed by G. I.
Taylor in 1909, see double-slit experiment)
the existence of the photon's wavefunction
was demonstrated. In the quantum
approach the diffraction pattern is created
by the distribution of paths, the observation
of light and dark bands is the presence or
absence of photons in these areas (no
interference!). The quantum approach has
some striking similarities to the
Huygens-Fresnel principle, in that principle
the light becomes a series of individually
distributed light sources across the slit

11. which is similar to the limited number of
paths (or wave functions) available for the
photons to travel through the slit.
There are various analytical models which
allow the diffracted field to be calculated,
including the Kirchhoff-Fresnel diffraction
equation which is derived from wave
equation, the Fraunhofer diffraction
approximation of the Kirchhoff equation
which applies to the far field and the
Fresnel diffraction approximation which
applies to the near field. Most
configurations cannot be solved analytically,
but can yield numerical solutions through
finite element and boundary element
methods.
It is possible to obtain a qualitative
understanding of many diffraction
phenomena by considering how the relative

12. phases of the individual secondary wave
sources vary, and in particular, the
conditions in which the phase difference
equals half a cycle in which case waves will
cancel one another out.
The simplest descriptions of diffraction are
those in which the situation can be reduced
to a two-dimensional problem. For water
waves, this is already the case; water waves
propagate only on the surface of the water.
For light, we can often neglect one direction
if the diffracting object extends in that
direction over a distance far greater than
the wavelength. In the case of light shining
through small circular holes we will have to
take into account the full three-dimensional
nature of the problem.
Examples​ :

13. ·Single-slit diffraction
·Diffraction grating
·Circular aperture
·General aperture
·Propagation of a laser beam
·Diffraction-limited imaging
·Speckle patterns
Coherence​:
The description of diffraction relies on the
interference of waves emanating from the
same source taking different paths to the
same point on a screen. In this description,
the difference in phase between waves that
took different paths is only dependent on
the effective path length. This does not take

14. into account the fact that waves that arrive
at the screen at the same time were
emitted by the source at different times.
The initial phase with which the source
emits waves can change over time in an
unpredictable way. This means that waves
emitted by the source at times that are too
far apart can no longer form a constant
interference pattern since the relation
between their phases is no longer time
independent.
The length over which the phase in a beam
of light is correlated, is called the coherence
length. In order for interference to occur,
the path length difference must be smaller
than the coherence length. This is
sometimes referred to as spectral
coherence, as it is related to the presence
of different frequency components in the

15. wave. In the case of light emitted by an
atomic transition, the coherence length is
related to the lifetime of the excited state
from which the atom made its transition.
If waves are emitted from an extended
source, this can lead to incoherence in the
transversal direction. When looking at a
cross section of a beam of light, the length
over which the phase is correlated is called
the transverse coherence length. In the
case of Young's double slit experiment, this
would mean that if the transverse
coherence length is smaller than the
spacing between the two slits, the resulting
pattern on a screen would look like two
single slit diffraction patterns.
In the case of particles like electrons,
neutrons and atoms, the coherence length

16. is related to the spatial extent of the wave
function that describes the particle.
References​:
●Wireless Communications: Principles
and Practice, Prentice Hall
communications engineering and
emerging technologies series
●"A History of Physics in its Elementary
Branches, including the evolution of
physical laboratories."
●Andrew Norton (2000). Dynamic fields
and waves of physics

17. ●The complete version of Fresnel's paper
on diffraction was published in 1821.
Table Of Contents​:
1.Diffraction
2.Applications
3.History
4.Mechanism
5.Examples
6.Coherence
7.References