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optical interferometry and its applications in absolute distance measurements. by: KHALED ALZAHRANI Liverpool John Moores University GERI. Outlines. Interferometry Concepts Popular inteferometric configurations Absolute distance measurement (ADI). Interferometry Concepts.
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by: KHALED ALZAHRANI
Liverpool John Moores University
Popular inteferometric configurations
Absolute distance measurement (ADI)
Optical Path Length [OPL]
Optical Path Difference [OPD]
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.General Concepts
light speed in free space (c): C=300k (km/s)
C = λv
V = c/n
λnis the wavelength in medium other than free space.
Visible light spectrum
Y = y1 + y2
Where: y1=A1 sin (wt + θ1 )
y2=A2 sin (wt + θ2)
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
OPL = d
OPL = n d
OPD = mλ
OPD= (m-1/2) λ
I= lAl^2 = I1+I2+2(I1I2) cos (Δθ) ^1/2
I max = I1 + I2 +2(I1I2)^1/2
if I1=I2 then
I min = I1 + I2 – 2(I1I2)^1/2
if I1=I2 then
V = I max - I min / I max + I min
maximum if Imin= 0 , V= 1
When Imin = Imax , V= 0
[ 0 ≤V≤1 ].
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.
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.
where N is thewaves number contained in one wave train.
where C is the light speed in space .
Interferometers classifications:wave front division interferometers Amplitude division interferometer
Is an optical instrument that can produced two beams interference or multiple beam interference.
Two light beams from the same wave front are made to interfere to produce an interference fringe pattern.
A light beam from one source point is divided into two beams using a beam splitter.
e.g. Michelson’s interferometer
Michelson interferometer consists of a coherent light source, a beam splitter BS a reference mirror ,a movable mirror and a screen .
There are many measurements that Michelson interferometer can be used for, absolute distance measurements, optical testing and measure gases refractive index.
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.
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.
There will be an interference fringes due to the path difference between W2 and the reference plan wave W1
consists of a light source, a detector, two mirrors to control the beams directions and two beam splitters to split and recombine the incident beam.
consisting of two parallel high reflecting glass plates separated several millimeters , a focusing lens and a display screen.
Developments in laser techniques and digital image processing have made distance measurement by optical techniques very attractive at variety of applications in industrial fields e.g. tool calibration, aircraft industry and robotics.
Two measurement techniques:
Measurement accuracy larger than a 1mm
based on interferometry, enable high precision measurements of distances or displacements.
commonly used for high-resolution displacement measurements. Resolution better than 100 nm .Drawback of this technique is the incremental manner of measuring, resulting from the counting of optical fringes.
ADI cannot be covered by classical interferometry since the range of non-ambiguity is limited to half the optical wavelength
offers great flexibility in sensitivity by an appropriate choice of the different wavelengths
Example: conceder two optical wavelength λ1&λ2 with PD=L .the phases φ1 and φ2 corresponding to the wavelengths λ1 and λ2
∆φ1 =(2π/ λ1) 2L & ∆φ2=(2π/ λ2) 2L
∆φ12= (∆φ1- ∆φ2) = 2π/[1/ λ1 - 1/ λ2] 2L = [2π/ λs]2L
λs= [λ1λ2/(λ1- λ2)]this synthetic wavelength is much longer than λ1 or λ2.
The range of non-ambiguity of the phase difference Δφ12, which is also known as the synthetic phase, is therefore increased compared to the range of non-ambiguity of classical interferometry. Moreover, the sensitivity of the measurement is reduced.
Adjust laser toλ1
Adjust laser toλ2