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- 1. • Interference • Intensity • Visibility • Optical Path Length [OPL] • Optical Path Difference [OPD] • Coherence: • Spatial coherence • Temporal coherence
- 2. 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.
- 3. 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
- 4. 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 .
- 5. 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
- 6. 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
- 7. 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
- 8. 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
- 9. 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 ].
- 10. 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 .
- 11. 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 .
- 12. Interferometry refers to family of techniques where waves superimposed to extract information about the waves
- 13. Interferometers classifications: Double path versus Common path interferometers Wave front splitting versus Amplitude division interferometers
- 14. 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
- 15. In Fizau interferometer,
- 16. 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
- 17. In common path interferometer,
- 18. 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.
- 19. 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
- 20. 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.

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