Outline • Displacement measurement • Basics of Displacement Measuring Interferometers (DMIs) • Common interferometer configurations • Introduction to uncertainty sources • Specialized interferometer configurations • Some application examples • Summary 2
Some terms that are used throughout this presentation DMI Displacement Measuring Interferometer OPL Optical Path Length OPD Optical Path Difference f Split frequency ppm Parts per million = multiplier of 1 X 10-6 ppb Parts per billion = multiplier of 1 X 10-9 3
What does ‘displacement’ mean in this context? • Denotes a change in position – How far something has moved • Implies a – Start point and an end point – Relative motion • Distinguished from ‘distance’ – Absolute separation between two points • Displacement measurement tools can establish distance indirectly 5
Distance and displacement are two different things! Target Retroreflector Two-frequency laser Cannot Can measure measure displacement distance from of target beamsplitter! 6
Another example of the distinction between distance & displacement Transparent artifact whose length needs to be determined • Direct measurement of length is not possible with DMI • Indirect measurements are possible by measuring displacement of a probing mechanism 7
Consequences of relative nature of measurement • If the beams of a DMI are broken and signal is lost, system loses track of target position • When beam is reestablished, system starts counting from current position of target • System has no knowledge of the new position relative to the beamsplitter • Critical that beam not be interrupted! 8
‘Absolute’ interferometers exist • Absolute measurements can be performed interferometrically • Based on different working principle – Multi-wavelength – Frequency sweeping • Tutorial restricted to displacement measuring interferometers 9
Many methods exist for the high-precision measurement of displacement • Displacement • Optical probes interferometers – Triangulation • Encoders – Chromatic • Capacitance gages aberration – Confocal • Electronic indicators (LVDT, LVDI, etc.) – Interferometric – Fiber optic • Ultrasonic • And many others… 10
One way to compare these methods is based on range & resolution 10-6 10-7 Encoders 10-8 10-9 Resolution (m) 10-10 Interferometers 10-5 10-4 10-3 10-2 10-1 100 101 102 Max. Range (m)11
DMIs and encoders are unique • Most displacement measuring devices have a relatively fixed resolution/range ratio – Gain one at the cost of the other • DMIs and encoders do not suffer from this trade-off – Same resolution regardless of range • Encoders are limited in range by maximum length that can be manufactured • Encoders often suffer from location conflicts 12
Light waves are represented by sinusoids A Phase (1) Phase difference (=2- 1) B Amplitude Phase (2) Wavelength () • Electric field of an electromagnetic (EM) disturbance can be represented as a sinusoid • Three parameters completely define the wave – Amplitude (Typically of the electric or E field) – Frequency () or wavelength (λ) – Phase (phase difference more significant than absolute phase) 14
Equations of interference are derived by the Principle of Superposition Two light waves E1 & E2 of amplitude E10 & E20 with a phase difference between them E = E sin(t) 1 10 E = E sin(t +) 2 20 Resultant wave E is given by sum of E1& E2 E = E + E = E sin(t)+ E sin(t +) 1 2 10 20 irradiance of resultant wave I E2 I = (E + E )2 = (E sin(t) + E sin(t +))2 1 2 T 10 20 I = I + I + 2 I I cos( ) 1 2 1 2 15
In the most general case the interfering waves have unequal irradiances I = I + I + 2 I I cos() 1 2 1 2 Sum of irradiances Interference term Fundamental equation of Interference Resultant irradiance is the sum of the irradiances of the two waves combined with modulation due to interference term Irradiance maxima Irradiance minima I = I + I + 2 I I I = I + I -2 I I 1 2 1 2 1 2 1 2 when = 2m when =m m = 0,1,2,... m = 1,3,5... 16
Interference of waves of unequal irradiance (amplitude) does not produce complete cancellation A A+B B In phase Constructive Interference A A+B B Out of phase Destructive Interference 17
The special case of equal irradiance is of practical interest I = I + I + 2 I I cos() 1 2 1 2 Sum of irradiances Interference term Fundamental equation of Interference For the special case I1= I2 = I0 above equation reduces to I = 4I cos2 0 2 Irradiance maxima Irradiance minima I = 4I I = 0 0 when = 2m when = m m = 0,1,2,... m = 1,3,5... 18
Waves of equal irradiance can produce complete cancellation A A+B B In phase Constructive Interference A A+B B Out of phase Destructive Interference 19
Optical Path Difference (OPD) determines the phase difference between two waves I = I + I + 2 I I cos() 1 2 1 2 Sum of irradiances Interference term Fundamental equation of Interference Phase difference () is a function of the optical path difference Optical path difference (OPD) is the difference in optical path length as distinct from the physical path length Optical path length (OPL) is defined as OPL= n*l where n = refractive index of the medium of propagation l = physical path length traversed by beam 20
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