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Strengthen | Expand | Grow Introduction to Displacement Measuring Interferometry.

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Presentation on theme: "Strengthen | Expand | Grow Introduction to Displacement Measuring Interferometry."— Presentation transcript:

1 Strengthen | Expand | Grow Introduction to Displacement Measuring Interferometry

2 2 Information in this document is subject to change without notice. Portions of this document describe patented systems and methods and does not imply a license to practice patented technologies. No liability is assumed with respect to the use of the information contained in this documentation. No part of this document may be reproduced or transmitted in any form or by any means, electronic or mechanical, for any purpose, without the express written permission of Zygo Corporation. © 2008 Zygo Corporation. All rights reserved.

3 3 What is this presentation about? Who is it for? Restricted to interferometric measurement of displacement –Does not cover form, surface roughness Fundamentals Intended for an audience with a minimal background in displacement interferometry –Only knowledge of basic physics is assumed

4 4 Outline Displacement measurement Basics of Displacement Measuring Interferometers (DMIs) Common interferometer configurations Introduction to uncertainty sources Specialized interferometer configurations Some application examples Summary

5 5 Some terms that are used throughout this presentation DMIDisplacement Measuring Interferometer OPLOptical Path Length OPDOptical Path Difference f Split frequency ppmParts per million = multiplier of 1 X ppbParts per billion = multiplier of 1 X 10 -9

6 Strengthen | Expand | Grow Displacement Measurement

7 7 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

8 8 Distance and displacement are two different things! Target Retroreflector Two-frequency laser Cannot measure distance from beamsplitter! Can measure displacement of target

9 9 Another example of the distinction between distance & displacement Direct measurement of length is not possible with DMI Indirect measurements are possible by measuring displacement of a probing mechanism Transparent artifact whose length needs to be determined

10 10 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!

11 11 Absolute interferometers exist Absolute measurements can be performed interferometrically Based on different working principle –Multi-wavelength –Frequency sweeping Tutorial restricted to displacement measuring interferometers

12 12 Many methods exist for the high-precision measurement of displacement Displacement interferometers Encoders Capacitance gages Electronic indicators (LVDT, LVDI, etc.) Ultrasonic Optical probes –Triangulation –Chromatic aberration –Confocal –Interferometric –Fiber optic And many others…

13 13 One way to compare these methods is based on range & resolution Max. Range (m) Encoders Resolution (m) Cap. Gauging LVDT Interferometers

14 14 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

15 Strengthen | Expand | Grow Physics of Optical Interference

16 16 Light waves are represented by sinusoids 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) Phase difference A B Amplitude Phase ( 1 ) Phase ( 2 ) ( = ) Wavelength ( )

17 17 Equations of interference are derived by the Principle of Superposition Two light waves E 1 & E 2 of amplitude E 10 & E 20 with a phase difference between them Resultant wave E is given by sum of E 1 & E 2 irradiance of resultant wave I E 2

18 18 In the most general case the interfering waves have unequal irradiances Fundamental equation of Interference Resultant irradiance is the sum of the irradiances of the two waves combined with modulation due to interference term Irradiance maximaIrradiance minima

19 19 Interference of waves of unequal irradiance (amplitude) does not produce complete cancellation A B A B A+B Constructive Interference Destructive Interference In phase Out of phase

20 20 The special case of equal irradiance is of practical interest For the special case I 1 = I 2 = I 0 above equation reduces to Irradiance maxima Irradiance minima Fundamental equation of Interference

21 21 Waves of equal irradiance can produce complete cancellation A B A B A+B Constructive Interference Destructive Interference In phase Out of phase

22 22 Optical Path Difference (OPD) determines the phase difference between two waves 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 where n = refractive index of the medium of propagation l = physical path length traversed by beam Fundamental equation of Interference

23 23 Optical Path Difference (OPD) is the difference in OPL traversed by two waves A B l Air (n a ) Glass (n g ) A B l2l2 Air (n a ) l1l1

24 Strengthen | Expand | Grow Basics of Displacement Measuring Interferometry (DMI)

25 25 All displacement measuring interferometers have these basic components Split Recombine Target motion Reference beam Phase shifted beam Meas. beam Detector

26 26 The Michelson interferometer – a simple interferometer Fixed Mirror Monochromatic Light Source Beamsplitter Movable Mirror λ/4 Observed intensity at the detector Phase Measurement Electronics

27 27 The desired displacement d is related to raw phase output Assuming that the medium the interferometer is operating in has refractive index n and the vacuum wavelength of the light source is vac, the wavelength in the medium of operation is given by Also, 2 radians of phase corresponds to a path length change of, phase change corresponds to a path length change d given by

28 28 Three additional pieces of information are required to extract displacement d from the raw phase output Vacuum wavelength Refractive index of medium Additional scale factor which depends on interferometer configuration (½ in this case) must be taken into account

29 29 What does a DMI really measure? Displacement ? DMIs infer displacement from changes in optical path length (OPL) differences between measurement and reference arms Indeed, it is possible to build a displacement interferometer with no moving parts!

30 30 Phase changes in either reference or measurement beams contribute to measured displacement Split Recombine Target motion Surface deviation Index changes Reference Phase shifted beam Target Reference motion Surface deviation Index changes Detector

31 31 Laser Measured displacement is a function of OPL changes in both measurement and reference arms Beamsplitter Movable Mirror Reference Mirror

32 32 Good displacement metrology requires careful consideration of spurious terms l m is the desired term All other terms are sources of uncertainty in measurement Assumption that the reference arm is fixed should be evaluated carefully!

33 33 Another way to think of these effects is in terms of the metrology loop Metrology loop is an imaginary closed contour that passes through all components of the system that influence the measurement result Laser Beamsplitter Reference Mirror Movable Mirror Metrology Loop

34 34 Changes in the metrology loop affect the measurement Changes in index in measurement and reference arm Change in beamsplitter (BS) position –Expansion of mounts –Index changes in BS Changes in target and reference mirrors –Changes in surface shape (mounting, thermal) –Surface figure related changes

35 35 DMIs have several advantages over other methods Eliminate Abbé offsets –Measure directly at point of interest High resolution (< 0.5 nm) High velocity (> 5 m/sec) Long range capability (> 10 meters) Measure multiple degrees of freedom Non-contact Directly traceable to the unit of length

36 Strengthen | Expand | Grow Heterodyne Interferometers

37 37 Commercial systems come in two major flavors Homodyne or single frequency Heterodyne or dual frequency –ZYGO DMI Significant differences in –Light source –Detection electronics Focus of this tutorial is heterodyne systems

38 38 A short detour into homodyne systems Homodyne interferometers use a single frequency laser Based on measurement of intensity variation at detector

39 39 Homodyne systems use specialized detectors & electronics Provision for power normalization to mitigate sensitivity to spurious intensity variations Quadrature outputs to provide direction information Low noise electronics to compensate for operation near DC (in presence of large 1/f noise)

40 40 A simple homodyne interferometer system Basic system simply counts changes in intensity at detector No direction sense Sensitive to variations in intensity of source and changes in ambient light level Inefficient use of light from source Reference Retroreflector Target Retroreflector BS Single frequency laser Detector

41 41 A more robust commercial implementation Special optic produces a rotating plane of polarization depending on the OPD Detectors are polarization sensitive Multiple detectors produce quadrature outputs and power normalization functionality Reference Retroreflector PBS Single frequency laser Special optic Target Retroreflector Polarization sensitive detector

42 42 Heterodyne interferometers are based on the principle of heterodyning Heterodyne receivers used in radios Also known as AC interferometers Example of frequency shifting the signal into a more favorable part of the spectrum –Avoid 1/f noise at low frequencies –Eliminate sensitivity to low frequency intensity variations of light source –Enable use of sophisticated phase measurement techniques instead of intensity

43 43 Heterodyne systems extract displacement by making phase measurements Phase or frequency measurement –Equivalent methods –Direct measurement of frequency change (phase) using Doppler shifted signal Requires changes to the hardware –Two frequency laser source

44 44 Heterodyne systems are typically polarization encoded Polarization encoding requires special components but confers many advantages –More efficient use of light –More flexibility in routing of beams through interferometer –Potential for varied interferometer configurations –More measurement axes from a given source

45 45 What is polarization in this context? Polarization state of an electromagnetic disturbance defines the direction that the electric field is pointing Polarization states encountered in heterodyne DMI systems –Linear (horizontal and vertical) –Circular Left handed (LCP) Right handed (RCP)

46 46 We will make a slight detour to take a look at the various polarization states and some of the polarization components. I will be using software developed at the University of Mississippi for optics education and hereby acknowledge the WebTOP project. Software is available as a free download at

47 47 Special components are required to manipulate the polarization state and include polarizers… Basic element that converts unpolarized light to linearly polarized light Azimuthal orientation determines orientation of output polarization state Known as an analyzer when used to determine state of polarization Linear polarizer Unpolarized Light Linearly polarized Light Polarization plane of polarizer

48 48 beamsplitters… Polarization Beamsplitter (PBS) Non-polarizing Beamsplitter (NPBS) Splits incoming beam regardless of polarization Splits incoming beam based on polarization state

49 49 … and quarter-wave plates Left circ. pol. polarized light Right circ. pol. polarized light Vertical pol.Horizontal pol. 45 Linearly polarized light is turned into circularly polarized light by passage through a quarter-wave plate with its fast axis at 45 to the incoming polarization state. Vertical pol. RCPHorizontal pol. LCP Fast axis

50 50 Polarizers are also used to combine orthogonal pol. states Incoming orthogonal polarization states do not interfere Polarizer at 45 to both states produces a component of each state along polarization plane Interference can now occur Vertical pol. Horizontal pol. Polarization plane of polarizer Components of vertical and horizontal pol. 45

51 51 Another detour to examine the behavior of the polarization components discussed in the preceding slides.

52 52 What does a heterodyne system look like? How is it different from a homodyne system? Reference Retroreflector Target Retroreflector PBS Measurement signal Two frequency laser Fiber optic Pickup Reference signal Phase Interpolator Digital Position Data Optical fiber f2f2 f 2 f1f1 (f 1 ± f 1 ) f 2 - (f 1 ± f 1 ) f1f1

53 53 What happens when waves of two frequencies interfere? Consider two light waves E M & E R of equal amplitude E 0 and frequencies f 1 and f 2 in the reference and measurement arms of the interferometer respectively with a phase difference between them Interference between these waves produces a sinusoidal intensity variation with a difference frequency equal to the difference between the two frequencies

54 54 What are the implications of this result? For a constant phase intensity I varies with a frequency f (split frequency) Operating point of the system has been translated from 0 Hz (DC) to the split frequency If f =0, eq. reduces to homodyne case

55 55 Outputs of the two kinds of interferometers are different Reference Retroreflector Target Retroreflector Spectrum Analyzer Detector 0 Hz Split Frequency HOMODYNEHETERODYNE Translation of operating point

56 56 Why do we observe this? For a target moving with velocity v, phase change is given by for a double pass interferometer. Substituting for in expression for intensity and rearranging results in frequency shift is proportional to velocity.

57 57 Direction and magnitude of frequency shift contain information Magnitude of frequency shift is proportional to the velocity Direction of frequency shift depends on direction of motion Direction is encoded in sign of shift

58 58 Changes in frequency and phase are related Frequency shift gives us velocity Phase is the integral of the frequency, which corresponds to displacement Integral of frequency shift produces expression for displacement

59 59 Notation is required for interferometer ray diagrams Multiple attributes of the beam need to be represented Beam direction –Arrow direction Polarization state –Pol. symbol behind arrow Frequency (f 1 or f 2 or altered frequency) –Arrow color & notation Arrow color: base frequency Green = f 1 Red = f 2 Arrow color: base frequency Green = f 1 Red = f 2 Arrow head: direction of propagation Polarization symbol l = p pol. = s pol. Circular pol. Polarization symbol l = p pol. = s pol. Circular pol. f 1 ± f 1 Notation: Base or altered frequency Notation: Base or altered frequency

60 60 Reference for phase detection is optically generated in newer systems… Reference Retroreflector Target Retroreflector PBS Measurement signal Two frequency Laser Fiber optic Pickup Reference signal (optical) Phase Interpolator Digital Position Data Optical fiber f2f2 f 2 f1f1 (f 1 ± f 1 ) f 2 - (f 1 ± f 1 ) External Optical reference NPBS Internal Optical reference or f1f1 f 1 ± f 1 f2f2 f 1 - f 2

61 61 … and electrically generated in older systems Reference Retroreflector Target Retroreflector PBS Measurement signal Two frequency Laser Fiber optic Pickup Reference signal (electrical) Phase Interpolator Digital Position Data Optical fiber f1f1 f 2 f1f1 (f 1 ± f 1 ) f2f2 f 1 ± f 1 f2f2 f 2 - (f 1 ± f 1 )

62 62 Goal is to determine the phase shift between reference & measurement signals Measurement (Doppler shifted) Reference (Fixed split frequency)

63 63 FOP (Lens w/polarizer) Two frequency laser f 1, f 2 Target Linear Interferometer Reference Signal Measurement Signal Oscilloscope ZMI 4004 f ref = f 1 – f 2 f meas = f 2 - (f 1 ± f 1 ) ZMI phase measurement electronics convert phase shift into displacement Phase difference is determined by measurement electronics Reference

64 Strengthen | Expand | Grow Heterodyne DMI System Components

65 65 Components of a Heterodyne DMI System Laser source Beam directing optics Interferometers Measurement electronics Target

66 Strengthen | Expand | Grow Laser Source

67 67 Laser source fulfills multiple requirements Produce coherent radiation at a fixed wavelength –High stability Generate two overlapping beams –Linearly polarized –Orthogonal –At two slightly different frequencies Production of desired polarization state and stabilization may be coupled

68 68 Laser wavelength establishes the unit of length Interferometer measures phase Wavelength is required to convert phase difference to displacement Uncertainty in wavelength produces an uncertainty in displacement

69 69 Laser source is frequency stabilized to control wavelength Uncertainty in absolute wavelength is less critical is most applications, stability is more critical Scale factor is calibrated out in some applications Wavelength measured in some applications Wavelength stability 1-10 ppb Production of red light around 633 nm guarantees a level of traceability

70 70 Lasers consist of a resonator and a gain medium Radiation gains energy from the gain medium as it oscillates in resonator Each medium has a gain curve that defines the wavelength range of laser Actual wavelength is determined by resonator length Gain Medium Resonator mirrors Output k-1 k

71 71 Different techniques are used for stabilization Consider case where two modes (wavelengths) are under gain curve Two modes are orthogonal and linearly polarized Matching the intensity of the two modes provides feedback for stabilization Varying tube length provides the tuning mechanism k-1 k k Vary resonator length

72 72 Laser is stabilized by changing tube length Laser tube length determines wavelength Length is changed by varying temperature Stabilized by balancing intensity of two adjacent modes Heater power supply Controller - Detectors p s Beamsplitter Laser output Heater

73 73 Two frequencies are commonly generated by two methods Orthogonal linear polarizations Circular linear polarizations Axial magnetic field Zeeman effect f+ ff- f f f 1 = f + f f 2 = f f AOM Accousto- optic modulator Laser tube f 1 = f + f f 2 = f - f

74 74 Two methods have some differences Zeeman method Small difference frequency (max. of ~ 4MHz) Variation in the split frequency from one laser to the next Low laser output power AOM –Bragg cell –RF drive at split frequency –Greater split frequency (~20MHz) –Small variation between lasers due to crystal oscillator

75 75 Polarization states of laser output are critical Heterodyne source produces two orthogonal linear polarizations at two slightly different frequencies (wavelengths) Polarizations are nominally perpendicular & parallel to laser head base States must be linearly polarized to prevent mixing Nominally to base plane Base plane

76 76 Polarization states have slightly different frequencies Two polarizations differ in frequency by 20MHz For ZYGO systems f 1 > f 2 f 1 corresponds to polarization to base f 2 corresponds to polarization // base Corresponding wavelengths are slightly different Base plane f1f1 f2f2

77 77 Split frequency determines the maximum target velocity Maximum velocity is limited by permissible drop in frequency Max. permissible drop corresponds to a Doppler shift that drives signal frequency to zero Usually limited to some fraction of f f f max Stationary target Target at max. velocity

78 78 Split frequency sets an upper bound on the target velocity The maximum frequency shift max is some fraction k of f The maximum velocity v max is related to max by N is an integer that depends on the interferometer configuration. For a single pass system, N=2 and for a double-pass system, N=4. One pass = one back-and-forth trip of the measurement beam

79 79 Large split frequencies enable high velocities For k=0.8 and f= 20MHz, max = 16 MHz For a single pass interferometer N=2 and a wavelength = 633 nm, v max 5 m/s For a double-pass system, N=4, leading to an increase in resolution but a decrease in v max to 2.5 m/s

80 80 Laser heads have several key features Two-frequency output Larger split frequencies enable higher velocities Two-frequencies are orthogonally polarized Polarization states are nominally linear Typical power output ~1.3 mW

81 Strengthen | Expand | Grow Beam directing optics

82 82 Beam directing optics split and direct the source beam Fold mirrors turn beam through 90 NPBS split incoming beams regardless of polarization –Various split ratios Orientations of f 1 and f 2 can change on passage through directing optics Designed for specific orientation Non-polarizing beam splitter (NPBS) Fold mirror Input Output Output 2 Output 1

83 83 Fibers route light from the source & to the detectors Polarization maintaining (PM) fibers convey source beam from a remote laser source to system Multi-mode fibers carry return signals from the interferometer output to remote electronics

84 84 Multi-axis systems require the source beam to be directed to multiple interferometers Delivery Module (DM) Interferometers Measurement Electronics Laser Module (LM) DM PM fiber NPBS Multi-mode fiber

85 Strengthen | Expand | Grow Optical Components – Basic Building Blocks

86 86 Most standard interferometers are composed of some basic optical components Polarization beams splitter (PBS) Quarter-wave plate Plane mirror Retroreflector (corner-cube) Plane mirrors and retroreflectors can also be used as targets

87 87 Polarization beamsplitter is the heart of an interferometer Creates reference & measurement beams Separates input polarization states Polarization states are called s & p & defined relative to plane of incidence Pneumonic: p passes Polarization Beamsplitter Splits incoming beam based on polarization state p at f 1 s at f 2 p at f 1

88 88 Retroreflectors (corner cubes) are insensitive to rotations Output beam parallel to input regardless of rotation about nodal point Output beam translates at twice the rate as retro Hollow or solid Coated retroreflectors if solid Can alter polarization state Output beam Input beam Offset

89 89 A quarter-waveplate is used to rotate polarization states Changes the polarization state of a linearly polarized beam to circular Two passes through it result in rotation of linear polarization state by 90 (from p to s in above example) LCP RCP p p s s /4 45

90 90 Plane mirrors are used both in the measurement and reference arms Allows for translation perpendicular to optical axis Surface figure is critical if target translates perpendicular to direction of measurement Deformed mirror produces spurious displacement Minimal tilt of the mirror is allowed Plane mirror Measurement beam Direction of travel Surface Figure (flatness) /4 = 158nm Direction of measurement

91 Strengthen | Expand | Grow Common Linear Displacement Interferometer Configurations

92 92 Common interferometer configurations are discussed Two common configurations are discussed in detail Emphasis is on understanding inner workings Provide a basis for understanding other configurations Not an exhaustive description of the multitude of configurations in existence (or possible)

93 93 The Michelson interferometer revisited Tilt sensitive and can accommodate very limited mirror tilt Mirror tilt causes reduced beam overlap Difficult to align and maintain alignment Does not make efficient use of light from source Monochromatic light source Fixed Mirror Beamsplitter Movable Mirror Detector

94 94 A typical linear displacement measuring system Reference Retroreflector Target Retroreflector PBS Measurement signal Two-frequency laser Fiber optic pickup (FOP) Reference signal Phase Interpolator Digital Position Data Optical fiber

95 95 Notation is required for interferometer ray diagrams Multiple attributes of the beam need to be represented Beam direction –Arrow direction Polarization state –Pol. symbol behind arrow Frequency (f 1 or f 2 or altered frequency) –Arrow color & notation Arrow color: base frequency Green = f 1 Red = f 2 Arrow color: base frequency Green = f 1 Red = f 2 Arrow head: direction of propagation Polarization symbol l = p pol. = s pol. Circular pol. Polarization symbol l = p pol. = s pol. Circular pol. f 1 ± f 1 Notation: Base or altered frequency Notation: Base or altered frequency

96 96 # passes = 1 Scale factor = 1/2 N = 2 A closer look at the linear displacement interferometer Most common linear interferometer Thermally balanced – same glass path lengths Retroreflector confers immunity to rotation Easy to align Reference Retroreflector Target Retroreflector f2f2 f 2 f1f1 (f 1 ± f 1 ) f 2 - (f 1 ± f 1 ) f1f1 f1f1 f2f2

97 97 # passes = 1 Scale factor = 1/2 N = 2 A more compact variation – the single beam interferometer Similar to previous configuration Smaller target retro More compact optics Small beams subject to loss at retro apex Polarization state varies over beam Reference Retroreflector Target Retroreflector f2f2 f 2 f1f1 (f 1 ± f 1 ) f 2 - (f 1 ± f 1 ) /4 f1f1

98 98 Retroreflector based interferometers are unsuitable in some applications Retro interferometers can tolerate very limited motion to measurement axis Unsuitable for applications where target moves to measurement (beam) direction –X-Y stages –Straightness measurement Plane mirrors are ideally suited Many interferometer configurations have been designed for plane mirror targets

99 99 Plane mirrors interferometers (PMI) are designed be used with plane mirrors Plane mirror target permits translation to measurement direction Ref. arm is retro-reflected within interferometer Two passes through /4 rotates pol. state 90 Reference retroreflector f1f1 f 2 f1f1 f 1 ± 2 f 1 f 2 - (f 1 ± 2 f 1 ) f1f1 f 1 ± f 1 f 1 ± f 1 Plane mirror # passes = 2 Scale factor = ¼ N = 4 f2f2

100 100 PMI design confers tilt tolerance on interferometer Tilt of mirror results in shear of measurement and reference beams rather than misalignment Double pass interferometer Scale factor of ¼ (N=4) Not a symmetric design, beams travel different paths and hence not as stable as HSPMI (to be discussed) Temperature coefficient of ~300 nm/°C

101 101 # passes = 2 Scale factor = ¼ N = 4 f1f1 High Stability PMI (HSPMI) is based on a symmetric design Reference plane mirror f 2 - (f 1 ± 2 f 1 ) Target plane mirror f2f2 f 2 f1f1 f 1 ± 2 f 1 f1f1 f 1 ± f 1

102 102 Symmetric design results in high stability Same resolution as PMI Thermally stable design; unlike PMI reference path and measurement path traverse the same amount of glass (but not exactly the same path) Tolerates mirror tilt; results in shearing of beams rather than misalignment Temperature coefficient 18 nm/°C

103 103 f2f2 Outgoing primary (First-pass beam) Returning secondary (Second-pass beam) To FOP f1f1 Mirror tilt is transformed to beam shear Beams shown separated for visualization

104 104 Beam overlap & signal strength change as the target mirror tilts The measurement and reference beams must overlap in order to provide a signal to the electronics As the target mirror rotates, the measurement beam will shear across the reference beam –Less overlap = decreased AC signal Near Full Signal ~50% No signal

105 105 Observed AC signal decreases with increasing beam shear Loss depends of beam size Larger beam, smaller signal loss

106 106 Tilt also contributes a displacement error

107 107 Tilt error is function of distance of target mirror from PBS Larger target mirror distance results in larger error Error is symmetrical, i.e., direction of tilt does not matter Error is ~ few nm for typical mirror tilts (~ a few seconds) characteristic of good quality stages

108 Strengthen | Expand | Grow Measurement Electronics

109 109 Measurement board measures phase change between measurement and reference signals Converts phase change into digital output Electronic resolution up to /1024, i.e., subdivides 2 radians of phase into 1024 parts With one-pass interferometer: System resolution = ( /1024)*(1/2) = / nm Maximum velocity 5 m/s Real time data rates >20MHz

110 110 Electronics can accommodate multiple axes Current technologies permit up to 64 channels from one laser source Each channel requires 70 nW for operation Electronics have low data age uncertainty –Enable synchronization of axes for coordinated motions

111 111 Interferometer output is optical Interference requires the two beams to have the same polarization state Orthogonally polarized measurement and reference beams combine at the exit of the interferometer Orthogonal polarization states are combined by a polarizer to create interference Detectors convert optical output to electrical signals

112 112 Output of interferometer is coupled to electronics via fiber Numerous advantages –Eliminate heat –Less cost –Smaller size Consist of –Lens –Polarizer oriented relative to base –Connector for multi- mode fiber Polarizer at 45 to incoming polarization states Focusing lens Multi-mode fiber Fiber optic pickup (FOP) Beam input Fiber connector

113 113 Polarization states are combined prior to launch into fiber Fiber optic cables commonly used for transfer of mixed signal to measurement electronics Specialized fibers are needed to maintain polarization states Above requirement is avoided by combining the polarization states with a polarizer before launch

114 114 Phase interpolation electronics convert optical output to digital data Convert optical signals into electrical signals and digitize them Measure the phase difference between a reference signal and measurement signal Output phase change which corresponds to displacement in units of counts Output of board needs to be scaled to provide displacement in units of length

115 115 Electronics also provide additional functionality Outputs in various formats Programmable digital filters Provision for synchronization with other devices –Clock –Digital I/O Cyclic error correction (CEC) Error checking Absolute phase

116 Strengthen | Expand | Grow Calculation of Displacement

117 117 Displacement calculation requires additional information Integer based on number of passes # of counts/2 of phase Refractive index of medium Vacuum wavelength Phase in counts from phase meter Desired displacement

118 118 Phase value is obtained from measurement electronics Phase output from electronics is in units of counts Electronics outputs the accumulated phase from user specified zero

119 119 Phase value from measurement electronics is converted to phase through a constant k is a constant that depends on measurement electronics Represents the number of phase meter counts/2 radians of phase Typical values of k are 512 or 1024

120 120 Vacuum wavelength is obtained from laser head specs. Wavelengths for the two frequencies from a two-frequency laser are slightly different Appropriate wavelength value based on which frequency is in the measurement arm

121 121 Appropriate wavelength must be used to scale data Wavelength used for scaling depends on which frequency (f 1 or f 2 ) is in the measurement arm Use 1vac & 2vac for f 1 & f 2 respectively Use of incorrect wavelength results in displacement error f2f2 f 2 f1f1 (f 1 ± f 1 ) f1f1 f 1 f2f2 (f 2 ± f 2 ) 1vac = nm 2vac = nm f2f2 f1f1

122 122 Direction sense is determined by the frequencies in the two arms Disposition of frequencies in each arm depends on –Laser head orientation –Orientation of beam directing optics –PBS orientation Interchanging frequencies reverses the direction sense Can be set in software f1f1 f 2 f1f1 (f 1 ± f 1 ) f2f2 f 1 f2f2 (f 2 ± f 2 ) Phase readout increases Phase readout decreases f1f1 f2f2

123 123 Two passes N is a constant that depends on the interferometer config. N depends on the number of passes of the measurement beam One pass is one back-and-forth trip of the beam N = 2 and 4 for linear & plane mirror interferometer respectively One pass N=2 Pass 1 Pass 2 N=4

124 124 Changes in the refractive index change the wavelength Wavelength in the medium of operation is equal to vac only in a vacuum (n=1) For operation in a medium other than vacuum, n must be known n is usually determined from an analytic expression

125 125 Index of air is not a constant & depends on many factors Index depends on –Pressure –Temperature –Humidity –Composition Very sensitive to presence of hydrocarbons Hydrocarbon content is typically not factored into analytic expressions

126 126 Index of air may be calculated using Edlens equation Relationship between the index and pressure, temperature, humidity and wavelength is given Edlens equation Complex equation Pressure, temperature, humidity and wavelength must be known to calculate index Typically obtained from measurements

127 127 Index of air may also be calculated from the following approximation Index values can also be obtained using the index calculator at

128 128 Environmental inputs are typically obtained from a weather station Weather station contains instrumentation to measure environmental parameters Weather station may communicate directly with measurement system Station location is critical Should be located close to measurement beam path in order to sense environmental factors in the space occupied by measurement beam

129 129 Another method of tracking index changes is a wavelength tracker Interferometric arrangement that utilizes fixed length beam paths of known lengths Measurement beam passes through medium of interest Reference beam passes through a vacuum path Measures index changes relative to initial environmental conditions Initial conditions provided by other means

130 130 Wavelength tracker is a differential interferometer Unlike a typical weather station used in conjunction with Edlens equation, tracker also tracks index changes due to composition changes Spacer Interferometer Vacuum Air L

131 131 Measurement beam is in air while reference is in vacuum Beam in air Beam in vacuum Input beam Fiber optic pickup DPMI Cell

132 132 Tracker does not measure absolute index, only changes L is length of the cell As before, appropriate vac must be used depending on the frequency in the measurement arm Sign of measured phase corresponding to a change in index also depends on disposition of frequencies Initial index is calculated by other means

133 Strengthen | Expand | Grow Uncertainty Sources and Analysis

134 134 Interferometric displacement measurements have low uncertainty compared to other methods While uncertainty is low in a relative sense it is finite and can be estimated Number of contributors Example of a simple uncertainty analysis to develop a feel for main sources Analysis based on the ISO Guide to Expression of Uncertainty in Measurement (GUM)

135 135 We will consider an uncertainty analysis of a displacement measurement of a linear stage Stage base dsds Stage L Abbé Deadpath L deadpath Measurand is the displacement of the stage as measured at point indicated at the surface of the stage and indicated by d s

136 136 We will include the following sources of uncertainty Wavelength Refractive index Phase meter output Deadpath error Abbe offset Cosine error

137 137 We will neglect the following sources of uncertainty Cyclical errors due to mixing Data age uncertainty Thermal expansion –Interferometer –Target mount Air turbulence Effect of parasitic motions Change in index of target Beam shear Surface figure of target Index gradients Inertia loading Vibration And a host of others…

138 138 We will assume the following uncertainty values & parameters S. No.ParameterNominal value 1Stage travel250 mm 2Deadpath250 mm 3Abbé offset100 mm

139 139 Uncertainty in input values contributes to uncertainty in measured displacement Refractive index uncertainty Vacuum wavelength uncertainty Phase meter uncertainty Uncertainty in measured displacement Temp uncertainty Pressure uncertainty Humidity uncertainty

140 140 Uncertainty in vacuum wavelength Represents the lack of knowledge of the actual value of the wavelength Frequency stabilization of laser guarantees that wavelength is stable Does not guarantee any particular value For critical measurements wavelength should be measured or otherwise accounted for

141 141 Bounding uncertainty can be estimated from physics of HeNe laser If no other information is available and the HeNe laser produces red light, then the wavelength uncertainty is ~ 3 ppm Consequence of the fact that the width of the laser gain curve above the threshold is ~ 2 X m k-1 k Laser threshold 2 X m

142 142 Some rules of thumb for index dependence on environment At Temperature T = 20 C, Pressure P = 760 mmHg and Relative humidity H = 50% 1 ppm change in index is caused by: T 1 C P 3 mm Hg H 100%RH

143 143 Change in the index of air can be calculated from the following approximation

144 144 Cosine error results from misalignment of beam and axis of motion Measured displacement d m Actual displacement d a Direction of motion

145 145 Measured displacement is less than actual displacement Not significant for typical applications until misalignment is large Misalignment also causes shear of measurement beam as a function of displacement Beam shear reduces overlap between measurement and reference beams resulting in reduction in signal

146 146 Abbé error results from an offset between measurement axis and axis of interest L Abbé Pitch Measured displacement d m Stage displacement d s Measurement axis Displacement axis

147 147 Abbé principle is a fundamental principle of metrology Axis of measurement must pass through the axis of interest, i.e., the line along which we wish to measure displacement If there is an offset, angular error motions of the stage couple into the measurement Magnitude of uncertainty contributed scales linearly with offset for a given angular error

148 148 Abbé principle is a fundamental principle of metrology Axis of measurement must pass through the axis of interest, i.e., the line along which we wish to measure displacement If errors of parallax are to be avoided, the measuring systems must be placed coaxially to the line in which displacement is to be measured on the workpiece. Dr. Ernest Abbé, late 1800s

149 149 Deadpath = Length between PBS and target retro at interferometer zero Dead path L deadpath Measuring Path Point at which interferometer zero is set PBS Index variation n

150 150 Dead path should be as small as possible Minimize errors due to refractive index variations during a measurement Causes changes in separation between zero point and PBS Consequence of fact that any compensation only applies to displacement from zero Deadpath contribution can be minimized by –Short deadpath –Minimizing changes in index

151 151 Deadpath can be minimized by simple strategies Addition of a fold mirror can help move interferometer to a more advantageous position Fold mirror Range of motion Deadpath

152 152 Uncertainty analysis is based on this model equation

153 153 Results of uncertainty analysis

154 154 Dominant source of uncertainty is a function of setup Contribution from the pitch error motion dominates as a result of the Abbé offset This contribution applies to any metrology technique Index contribution dominates contributions linked to interferometer –Compensation can make a large difference Deadpath contribution is significant and scales linearly with deadpath

155 155 Index contributions can be reduced Measure environment and compensate Uncertainty in environmental variables is replaced with uncertainty in the measurement of these variables

156 156 In critical applications, index effects can be reduced further Operate system in a helium atmosphere –Helium has lower index sensitivity to environmental variables Operate system in vacuum –Consider all systems issues associated with transition to vacuum

157 157 Compensation reduces index contribution drastically

158 158 Uncertainty analyses are a tool to identify significant contributors Uncertainties associated with refractive index typically dominate in uncompensated system Setup related contributions can usually be reduced by careful alignment –Abbé offset –Deadpath –Beam alignment to direction of motion Capability of a measurement technique should be judged in the context of the measurement uncertainty

159 Strengthen | Expand | Grow Specialized Interferometer Configurations

160 160 Specialized configurations extend the capability of linear displacement interferometers Utilize the principles of linear displacement interferometry to make other measurements –Relational (differential) measurements –Angle –Straightness Emphasis is on introducing configurations, not on detailed analysis

161 161 Column reference interferometers perform a differential measurement between two parts of a machine

162 162 Column reference interferometer monitors relative displacement between stage and lens column ColumnColumn reference interferometer (CRI) Stage Stage mirror Column mirror

163 163 Column reference interferometer (CRI) Performs a differential measurement Reduces deadpath error Steering wedges facilitate beam alignment Folded HSPMI Target and Reference Mirrors Steering Wedges /4 waveplates Retroreflector PBS Fold Mirror Compensating Plugs

164 164 Differential PMI makes meas. between two plane mirrors

165 165 DPMI can be configured to make differential displacement measurement PBS Target Reference /4 /2 Shear plate

166 166 Some features of the linear DPMI Measurement is differential and permits a short metrology loop Resolution is same as a two-pass PMI

167 167 …or differential angular measurements Reference PBS Target /4 /2 Shear plate

168 168 Some features of the angular DPMI Measurement is differential and permits a short metrology loop Range is limited and varies inversely with distance of target mirror from interferometer and typically < ±1 Sub 0.01 arc-second resolution achievable

169 169 Routing of beams is complex and three-dimensional DPMI - Angular DPMI - Linear

170 170 Larger angular motions are handled by a dual-retro config. Beam bender Angular Retroreflector PBS f 2 f1f1 f2f2 f 1 ± f 1 f 2 ± f 2 f1f1 f 1 ± f 1 f 2 ± f 2 R

171 171 Some features of the angular interferometer Range of ± 10 Resolution < 0.1 arc-second Insensitive to pure displacement Commonly used in machine tool metrology applications Used for rotary table calibrations with appropriate fixturing Care required in setup to achieve lowest uncertainty

172 172 DMI can be used to measure straightness of an axis Wollaston prism Dihedral mirror Straightness error motion f1f1 f 1 ± f 1 f 2 ± f 2 f1f1 f 1, f 2 f 2 ± f 2 f 1 ± f 1

173 173 Some features of a straightness interferometer Wollaston prism is a birefringent prism that splits the two polarization states at an angle Different sets of optics for short and long travel ranges Dihedral angle is typically ~1.6 and ~0.16 for short and long travel ranges respectively

174 174 Optical probe config. is ideally suited for small targets Single-pass interferometer Reference beam reflects off vertex of retro Beam routing behavior same as single beam interferometer Target mirror Lens PBS /4 Reference retroreflector

175 175 Some features of the optical probe configuration Ideal when only a small target mirror can be used Range is determined by depth of focus of lens and can be as large as ± 5 mm (f = 150 mm) Focal length determines standoff Spot size ~ 100 m Signal strength is a strong function of displacement from focus

176 176 Fiber fed interferometers have advantages in some applications Remote laser source Laser radiation is transported to system via optical fibers Eliminates heat load from laser Improves flexibility in terms of optical plumbing

177 177 Fiber fed heterodyne interferometers must preserve the input polarization states Heterodyne Laser Source Polarization Maintaining (PM) Fiber Expanded beam to optics Delivery Module Beam expander Remote Laser Head Split frequency generator/polarizer

178 178 Other configurations abound Literally hundreds of interferometer designs exist Many different approaches to same measurement problem Once the basics are understood, the basic building blocks can be used to create numerous custom designs.

179 Strengthen | Expand | Grow Application Examples

180 180 Typical DMI Applications Calibration (static) –Machine tools –Stage calibration –X/Y stages –CTE Production (dynamic) –Semiconductor instruments –Feedback for diamond turning –X/Y stage control

181 181 Use as feedback sensors for motion control is a very common application X-Y wafer stage X-Y reticle stage Interferometers

182 182 Wafer processing requires measurement of multiple DOF Accurate monitoring of X and Y position and rotation Require simultaneous measurement of multiple degrees of freedom –Many lithography tools use ~30 axes of DMI per system

183 183 Used as feedback for machine tools & measuring machines Large Optics Diamond Turning Machine (LODTM) at Lawrence Livermore

184 184 Interferometer system for the LODTM

185 185 Stage calibration is another common application Determination of stage errors Generation of an error maps DMI Calibration Data Commanded Position (mm) DMI Position (mm) Stage Error Commanded Position (mm) Position Error ( m)

186 186 Machine stage Another application involves use as an indicator HSPMI Reference mirror Laser in Laser out Straightedge

187 187 Machine tool metrology is an example of strap-on metrology Characterize various error motions of a machine tools Many different types of interferometers Numerous accessories Measurements made between tool & workpiece Laser Head DMI Target

188 188 Many machine parameters may be evaluated Linear displacement accuracy Straightness Angular error motions with exception of roll Squareness when used with appropriate accessories –Optical square Dynamic performance can be measured

189 189 Rotary tables may be calibrated with DMIs Variety of configurations depending on range of angle Extremely high angular resolutions (< 0.1 arc-sec) All interferometer configurations require specialized fixturing if calibration is required over 360 –Hirth coupling based indexer

190 190 Dilatometry and material stability measurements use DMIs Used in setups for measurement of –Thermal expansion –Material stability –Stability of epoxy joints Very stable when operated in vacuum High resolution critical for sensing small changes

191 191 A setup for the measurement of material stability* Interferometric metrology for the measurement of material stability Interferometers operate in vacuum * Patterson, SR., Interferometric Measurement of the Dimensional Stability of Superinvar, UCRL-53787, LLNL,1988.

192 192 Other applications Actuator calibration –PZT, electrostrictive, linear motors, capstan drives, etc. Gage calibration –LVDT –Capacitance gages –Encoders Vibration analysis

193 193 Some general comments about DMI applications Only a sampling of possible applications Numerous other applications possible Setup & procedure are critical to good results Minimize geometric errors by design –Abbé, cosine & deadpath Stable environment Minimize total measurement time Compensate for index change

194 Strengthen | Expand | Grow Summary

195 195 DMIs are versatile devices Measure at the point of interest –Eliminate Abbé offsets High resolution, velocity & low uncertainty Non-contact Directly traceable to the unit of length Many commercial configurations exist Configured for many geometries Measure multiple degrees of freedom simultaneously (64 with one laser head)

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