Introduction to Displacement Measuring Interferometry

Introduction to Displacement Measuring Interferometry
ASPE 2008 Intro. to Displacement Interferometr

© 2008 Zygo Corporation. All rights reserved.
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. ASPE 2008 Intro. to Displacement Interferometr

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 ASPE 2008 Intro. to Displacement Interferometr

Displacement measurement
Outline Displacement measurement Basics of Displacement Measuring Interferometers (DMIs) Common interferometer configurations Introduction to uncertainty sources Specialized interferometer configurations Some application examples Summary ASPE 2008 Intro. to Displacement Interferometr

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 ASPE 2008 Intro. to Displacement Interferometr

Displacement Measurement

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 ASPE 2008 Intro. to Displacement Interferometr

Distance and displacement are two different things!
Target Retroreflector Two-frequency laser Cannot measure distance from beamsplitter! Can measure displacement of target ASPE 2008 Intro. to Displacement Interferometr

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 ASPE 2008 Intro. to Displacement Interferometr

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! ASPE 2008 Intro. to Displacement Interferometr

‘Absolute’ interferometers exist
Absolute measurements can be performed interferometrically Based on different working principle Multi-wavelength Frequency sweeping Tutorial restricted to displacement measuring interferometers ASPE 2008 Intro. to Displacement Interferometr

Many methods exist for the high-precision measurement of displacement
Displacement interferometers Optical probes Triangulation Encoders Chromatic aberration Capacitance gages Confocal Electronic indicators (LVDT, LVDI, etc.) Interferometric Fiber optic Ultrasonic And many others… ASPE 2008 Intro. to Displacement Interferometr

One way to compare these methods is based on range & resolution
10-6 10-7 Encoders LVDT 10-8 Resolution (m) Cap. Gauging 10-9 10-10 Interferometers 10-5 10-4 10-3 10-2 10-1 100 101 102 Max. Range (m) ASPE 2008 Intro. to Displacement Interferometr

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 ASPE 2008 Intro. to Displacement Interferometr

Physics of Optical Interference

Light waves are represented by sinusoids
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) The behavior of light waves as applied to interferometry may be explained by treating the electromagnetic (EM) disturbance as a transverse sinusoidal wave. The EM disturbance consists of varying electric and magnetic fields which are mutually orthogonal and also orthogonal to the direction of propagation. Most of the interactions of EM waves with one another and with matter are dominated by the electric or E field. This affords a further simplification in the representation. Hereafter, the EM disturbance will be represented by a transverse sinusoidal wave which depicts the variation of the E field. The EM disturbance is completely characterized by three quantities: Frequency or wavelength Amplitude Phase relative to some origin. These quantities are illustrated in the figure. The frequency and wavelength are related through the velocity of the disturbance in the medium. The amplitude is a measure of the strength of the disturbance with the irradiance (often referred to as intensity) of the disturbance being proportional to the square of the amplitude. The phase of the disturbance defines the position of the maxima or minima relative to some origin or reference. For the purposes of this tutorial, the phase difference between two disturbances  is far more significant than the absolute phase. Key concept: For most interferometric applications, phase difference is more significant than absolute phase. ASPE 2008 Intro. to Displacement Interferometr

Resultant wave E is given by sum of E1& E2
Equations of interference are derived by the Principle of Superposition Two light waves E1 & E2 of amplitude E10 & E20 with a phase difference d between them Resultant wave E is given by sum of E1& E2 irradiance of resultant wave I  E2 Consider two EM disturbances E1 and E2 with a phase difference  between them. Note that it is the phase difference that is critical and not the absolute phase. Applying the Principle of Superposition, the resultant disturbance at a point is given by the sum of the two electric fields. The observed irradiance is the time averaged value of the square of the amplitude and consists of three terms. The first two terms are the individual intensities of the disturbances (proportional to the square of E10 and E20). The third term exhibits a dependence on E10 and E20 and cosinusoidal dependence on . The first two terms are the irradiances of the individual disturbances. The first two terms confirm the intuitive notion that when two disturbances combine, the resulting irradiance is the sum of the individual irradiance. ASPE 2008 Intro. to Displacement Interferometr

Fundamental equation of Interference
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 The third term is the interference term which modulates or varies the sum of the intensities of the two individual disturbances. This modulation is a function of . An irradiance maxima results when the interference term is a positive maximum, i.e. when  is an integer multiple of 2. This implies that the peaks of the two sinusoidal disturbances line up and reinforce one another. This situation is termed constructive interference. Similarly, a irradiance minima is observed when  is an odd integer multiple of . This corresponds to the situation where the peaks of one disturbance line up with the troughs of another (or vice-versa). This is known as destructive interference. Irradiance maxima Irradiance minima ASPE 2008 Intro. to Displacement Interferometr

Constructive Interference
Interference of waves of unequal irradiance (amplitude) does not produce complete cancellation A+B A B In phase Constructive Interference A The above figure illustrates the general case of interference at a point between two waves (A and B) of the same frequency (or wavelength) but of unequal irradiance or amplitude. The two limiting cases are shown. In the first case, interference between the two waves when they are in phase results in constructive interference with the resultant amplitude being the sum of the two amplitudes. In the second case the waves are out-of-phase and the resultant amplitude is the difference of the two amplitudes. It can be seen that for the case of unequal amplitudes, complete cancellation is not observed. This means that while a intensity minima is observed, a completely dark interference region (complete cancellation) is not observed. The range of intensity variation between the situations of constructive and destructive interference is limited. This limited range of intensity variation results in an interference pattern where the distinction between the bright and dark regions is not marked. Such an interference pattern is said to have low contrast. A+B B Out of phase Destructive Interference ASPE 2008 Intro. to Displacement Interferometr

The special case of equal irradiance is of practical interest
Fundamental equation of Interference For the special case I1= I2 = I0 above equation reduces to In the special case of waves of equal amplitude, the situation is slightly different. The resulting interference pattern has a maxima when the waves are in phase, i.e., the phase difference is multiple of 2. Similarly, a irradiance minima is observed when  is an odd integer multiple of . In contrast to the previous case of waves of unequal amplitude, complete cancellation of the electric field now occurs with the result that the irradiance goes to zero at the minima. An interference pattern produced under such circumstances is said to have high contrast, i.e., the range of intensity values extends from a maximum down to minimum at zero intensity. This is in contrast to the previous case where the neither was the minimum zero, nor was the maximum at the highest intensity attainable. Irradiance maxima Irradiance minima ASPE 2008 Intro. to Displacement Interferometr

Waves of equal irradiance can produce complete cancellation
A+B B In phase Constructive Interference A In contrast to the general case described earlier, the special case of equal radiance results in the doubling of the amplitude of the resultant during constructive interference and a complete cancellation during destructive interference. This leads to a much larger range in the intensity variation. An interferogram obtained under these conditions exhibits much higher contrast, i.e., difference between the minimum and maximum irradiance is larger. This larger range of intensity variation results in an interference pattern where the distinction between the bright and dark regions is marked. This is a highly desirable situation and interferometric arrangements try to maximize this contrast. Key concept: Interferometer arrangements try to match intensities of the interfering beams to maximize contrast. A+B B Out of phase Destructive Interference ASPE 2008 Intro. to Displacement Interferometr

Optical Path Difference (OPD) determines the phase difference between two waves
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 What is ? The phase difference  between interfering waves is dependent on the optical path difference (OPD). The OPD is the difference in the optical path length (OPL) and not the difference in physical path length. The OPL is the product of the physical path length and the index of refraction of the medium through which the wave propagates. The OPL and the physical path length are identical only in a medium of refractive index one, i.e., in vacuum. where n = refractive index of the medium of propagation l = physical path length traversed by beam ASPE 2008 Intro. to Displacement Interferometr

Optical Path Difference (OPD) is the difference in OPL traversed by two waves
Air (na) B Glass (ng)  l l1 The above figures illustrate the concepts of OPL and OPD. Consider two waves A and B. In the upper figure, the two waves are initially in phase and pass through air and glass of equal physical path length. The two waves emerge out-of-phase by virtue of the different indices of refraction of the two materials. In the lower figure, a contrasting situation is illustrated where the path difference originates from the difference in physical path length rather than from a difference in index. The product of the index and the physical path length is a measure of the delay resulting from the beam traveling through a particular path. The equations alongside each illustration express the phase difference in radians. Key concept: OPL and OPD depend on both index and physical path length.Variation in either results in a change in OPL. A Air (na) B Air (na)  l2 ASPE 2008 Intro. to Displacement Interferometr

Basics of Displacement Measuring Interferometry (DMI)

All displacement measuring interferometers have these basic components
Reference beam Source Split Recombine Detector Meas. beam Target motion  Phase shifted beam ASPE 2008 Intro. to Displacement Interferometr

The Michelson interferometer – a simple interferometer
Fixed Mirror Movable Mirror Monochromatic Light Source Beamsplitter λ/4 λ/4 This is the basic Michelson interferometer. Monochromatic light is directed at a half-silvered mirror that acts as a beam splitter. The beam splitter transmits half the beam to a movable mirror and reflects the remainder at 90 degrees to a fixed mirror. The reflections from the movable and fixed mirrors are recombined at the beam splitter where their interference is observed. With the mirrors exactly aligned and motionless, so that the recombined beams are parallel, an observer will see a constant intensity of light. When one of the mirrors is displaced in a direction parallel to the incident beam the observer will see the intensity of the recombined beams increasing and decreasing as the light waves from the two paths constructively and destructively interfere. A cycle of intensity change of the interference of the recombined beams represents a half wavelength displacement of movable mirror travel (because the change in path length of the light corresponds to two times the displacement of the movable mirror). If the wavelength of the light is known the displacement of the movable mirror can be accurately determined. An important characteristic of interferometry is that only the displacement is measured, not the absolute position. Therefore; the initial distance to the movable mirror is not measured, only the change in position of the mirrors with respect to each other can be determined. Observed intensity at the detector Phase Measurement Electronics  ASPE 2008 Intro. to Displacement Interferometr

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 ASPE 2008 Intro. to Displacement Interferometr

Refractive index of medium
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 ASPE 2008 Intro. to Displacement Interferometr

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! ASPE 2008 Intro. to Displacement Interferometr

Phase changes in either reference or measurement beams contribute to measured displacement
Reference motion Surface deviation Index changes Source Detector Split Recombine Target Target motion Surface deviation Index changes  Phase shifted beam ASPE 2008 Intro. to Displacement Interferometr

Measured displacement is a function of OPL changes in both measurement and reference arms
Reference Mirror Movable Mirror Laser Beamsplitter ASPE 2008 Intro. to Displacement Interferometr

All other terms are sources of uncertainty in measurement
Good displacement metrology requires careful consideration of spurious terms lm is the desired term All other terms are sources of uncertainty in measurement Assumption that the reference arm is ‘fixed’ should be evaluated carefully! ASPE 2008 Intro. to Displacement Interferometr

Another way to think of these effects is in terms of the metrology loop
Reference Mirror Metrology Loop Movable Mirror Laser Beamsplitter Metrology loop is an imaginary closed contour that passes through all components of the system that influence the measurement result ASPE 2008 Intro. to Displacement Interferometr

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 ASPE 2008 Intro. to Displacement Interferometr

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 Due to their inherent accuracy, DMI’s have become an attractive tool for the most demanding displacement measuring applications. The fundamental accuracy of a DMI system is based on the precise knowledge of the wavelength of light. A DMI allows the user to minimize geometrical errors, such as Abbé offset error and opposite axis error, that are associated with mechanical displacement measuring techniques. Depending on the system configuration, a DMI can resolve displacements to 0.08 nanometers and track velocities up to 5.1 meters per second over a large displacement range. DMI’s allow the user to measure displacements at the point of interest. With the simple detection scheme of a heterodyne system, multiple axes can be measured simultaneously (X, Y,  & more). Most DMI systems are easy to use and align. Using interferometers with application specific designs, the measured optical path change can be related to physical quantities such as linear displacement, angular displacement, straightness of travel, flatness, squareness, and parallelism, as well as changes in the refractive index of air. ASPE 2008 Intro. to Displacement Interferometr

Heterodyne Interferometers

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 ASPE 2008 Intro. to Displacement Interferometr

A short detour into homodyne systems
Homodyne interferometers use a single frequency laser Based on measurement of intensity variation at detector Homodyne = single frequency = DC ASPE 2008 Intro. to Displacement Interferometr

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) ASPE 2008 Intro. to Displacement Interferometr

A simple homodyne interferometer system
Reference Retroreflector Target Retroreflector Single frequency laser Detector BS 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 A homodyne interferometer system is made up of a laser source, polarization optics, photodetector(s) and measurement electronics. Depending on the features the user requires from a homodyne system (direction sensing, power normalization, etc), the detector configuration can become complex. A homodyne source is typically a HeNe laser that outputs a single frequency beam consisting of two opposing circularly polarized components. The beam is split into the reference and measurement legs of the interferometer by a beam splitter. Following a reflection off their respective targets, the beams return back to the beam splitter. In order to observe interference, the two beams must have the same polarization. This is accomplished using a linear polarizer oriented at 45° to the two polarization's prior to the photodetector. The signal is run through a Schmidt trigger or similar electronics to locate the zero crossings. Counting the zero crossings is equivalent to counting every half fringe. Some limitations to a simple homodyne system shown include the inability to detect the direction sense of the target and sensitivity to changes in the beam power and system alignment. ASPE 2008 Intro. to Displacement Interferometr

A more robust commercial implementation
Reference Retroreflector Target Retroreflector Single frequency laser Polarization sensitive detector PBS Polarization sensitive detector Polarization sensitive detector Special optic 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 To minimize errors caused by fluctuations in laser intensity detectors can be added. The example depicts a homodyne system with quadrature output and an additional detector for normalizing the laser intensity (Io). Some homodyne systems will use more than one detector. For this scheme to work it is necessary to have a good signal to noise ratio at each of the detectors. Since Homodyne systems detect changes in intensity, the following conditions can also cause errors: Beam intensity profile changes during displacement Measurement and reference beam overlap changes during motion Non-ideal characteristics of the photodiodes ASPE 2008 Intro. to Displacement Interferometr

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 Heterodyne = two frequency = AC ASPE 2008 Intro. to Displacement Interferometr

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 ASPE 2008 Intro. to Displacement Interferometr

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 ASPE 2008 Intro. to Displacement Interferometr

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) For two beams of light to interfere, the beams must have the same polarization state. In a DMI system this is achieved through the use of a mixture of polarizing and non-polarizing optical components. Only a single polarization state can transmit through a polarizer. The orientation of the transmitted polarization state is based on the angle of the polarizer in the optical path. Waveplates or retarders change the polarization state of the light. A quarter waveplate converts linearly polarized light to a circular polarization state. A half waveplate will rotate the plane of polarization from horizontal to vertical. Polarizing and non-polarizing beam splitters are used in DMI applications. The non-polarizing beam splitters are used to split portions of the source beam to accommodate multiple axes of measurement. Polarization beam splitters are an integral part of the interferometer. A polarization beam splitter separates the source beam into its measurement and reference legs. ASPE 2008 Intro. to Displacement Interferometr

Software is available as a free download at
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 ASPE 2008 Intro. to Displacement Interferometr

Known as an analyzer when used to determine state of polarization
Special components are required to manipulate the polarization state and include polarizers… Polarization plane of polarizer 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 Linearly polarized Light Unpolarized Light Linear polarizer Create and insert solid model ASPE 2008 Intro. to Displacement Interferometr

Polarization Beamsplitter (PBS) Non-polarizing Beamsplitter (NPBS)
beamsplitters… Insert solid models Polarization Beamsplitter (PBS) Non-polarizing Beamsplitter (NPBS) Splits incoming beam regardless of polarization Splits incoming beam based on polarization state ASPE 2008 Intro. to Displacement Interferometr

… and quarter-wave plates
Vertical pol. Horizontal pol. Fast axis 45 45 Right circ. pol. polarized light Left circ. pol. polarized light Vertical pol.  RCP Horizontal pol.  LCP 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. ASPE 2008 Intro. to Displacement Interferometr

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. Polarization plane of polarizer 45 Horizontal pol. Components of vertical and horizontal pol. ASPE 2008 Intro. to Displacement Interferometr

Another detour to examine the behavior of the polarization components discussed in the preceding slides. ASPE 2008 Intro. to Displacement Interferometr

What does a heterodyne system look like
What does a heterodyne system look like? How is it different from a homodyne system? Reference Retroreflector f2 f1 f1 f2 Two frequency laser Optical fiber Target Retroreflector (f1 ± D f1) Fiber optic Pickup PBS f2- (f1 ± Df1) A typical system. Point out components. Measurement signal Digital Position Data Reference signal Phase Interpolator ASPE 2008 Intro. to Displacement Interferometr

What happens when waves of two frequencies interfere?
Consider two light waves EM & ER of equal amplitude E0 and frequencies f1 and f2 in the reference and measurement arms of the interferometer respectively with a phase difference d between them Interference between these waves produces a sinusoidal intensity variation with a difference frequency equal to the difference between the two frequencies ASPE 2008 Intro. to Displacement Interferometr

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 ASPE 2008 Intro. to Displacement Interferometr

Outputs of the two kinds of interferometers are different
Reference Retroreflector Target Retroreflector Detector Spectrum Analyzer Translation of operating point 0 Hz 0 Hz Split Frequency HOMODYNE HETERODYNE ASPE 2008 Intro. to Displacement Interferometr

For a target moving with velocity v, phase change  is given by
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. ASPE 2008 Intro. to Displacement Interferometr

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 ASPE 2008 Intro. to Displacement Interferometr

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 ASPE 2008 Intro. to Displacement Interferometr

Notation is required for interferometer ray diagrams
Polarization symbol l= p pol. = s pol. Circular pol. Multiple attributes of the beam need to be represented Beam direction Arrow direction Polarization state Pol. symbol behind arrow Frequency (f1 or f2 or altered frequency) Arrow color & notation Arrow head: direction of propagation f1 ± D f1 Arrow color: base frequency Green = f1 Red = f2 Notation: Base or altered frequency ASPE 2008 Intro. to Displacement Interferometr

Reference for phase detection is optically generated in newer systems…
External Optical reference Reference Retroreflector or f1 - f2 Internal Optical reference f2 f1 f2 f1 Two frequency Laser NPBS Target Retroreflector f2 f2 - (f1 ± Df1) (f1 ± D f1) Fiber optic Pickup PBS f1 ± Df1 The source for a Heterodyne interferometer system is a highly stabilized, two frequency HeNe laser whose output beam contains two frequency components, each with a unique linear polarization. In a typical Heterodyne system the laser beam is split into a reference and measurement leg at a polarization beam splitter (PBS). In the single pass interferometer example shown above, one of the frequency components (f1) is used as the measurement beam and reflects from the moving target back to the beam splitter. The other frequency component (f2) acts as the reference and reflects from a fixed target back to the beam splitter. At the beam splitter, the measurement and reference beams recombine. The recombined beams pass through a polarizer and are sent to the detection electronics where the optical interference signal is monitored. If the movable target remains stationary, the frequency of the optical interference signal (the beat frequency) will be the exact difference between the lasers two frequencies (f2 - f1). When the target moves, the frequency of the optical interference signal will be shifted up or down by the Doppler effect (f1 ± Df1), depending on the direction of target motion. Optical fiber Measurement signal Digital Position Data Reference signal (optical) Phase Interpolator ASPE 2008 Intro. to Displacement Interferometr

… and electrically generated in older systems
Reference Retroreflector f2 f1 f1 f2 Two frequency Laser Target Retroreflector f2 f2 - (f1 ± Df1) (f1 ± D f1) Fiber optic Pickup PBS f1 ± Df1 Optical fiber Measurement signal Digital Position Data Reference signal (electrical) Phase Interpolator ASPE 2008 Intro. to Displacement Interferometr

(Fixed split frequency)
Goal is to determine the phase shift between reference & measurement signals Measurement (Doppler shifted) Reference (Fixed split frequency)  ASPE 2008 Intro. to Displacement Interferometr

Phase difference is determined by measurement electronics
Linear Interferometer Target f1 , f2 Two frequency laser FOP (Lens w/polarizer) ZMI 4004 Oscilloscope Measurement Signal Dfmeas = f2 - (f1 ± Df1) ZMI phase measurement electronics convert phase shift into displacement The source for a Heterodyne interferometer system is a highly stabilized, two frequency HeNe laser whose output beam contains two frequency components, each with a unique linear polarization. In a typical Heterodyne system the laser beam is split into a reference and measurement leg at a polarization beam splitter (PBS). In the single pass interferometer example shown above, one of the frequency components (f1) is used as the measurement beam and reflects from the moving target back to the beam splitter. The other frequency component (f2) acts as the reference and reflects from a fixed target back to the beam splitter. At the beam splitter, the measurement and reference beams recombine. The recombined beams pass through a polarizer and are sent to the detection electronics where the optical interference signal is monitored. If the movable target remains stationary, the frequency of the optical interference signal (the beat frequency) will be the exact difference between the lasers two frequencies (f2 - f1). When the target moves, the frequency of the optical interference signal will be shifted up or down by the Doppler effect (f1 + δ), depending on the direction of target motion. Heterodyne detection makes a phase comparison between a measurement signal of unknown frequency to a reference signal of known frequency at discrete time intervals. The zero crossings of the reference signal (in this case the positive zero crossings) are used to indicate the phase of the measurement signal. The change of measurement phase from one reference cycle to another indicates a measurable shift in frequency. The phase change represents the Doppler shifted frequency that results with movement of the target optic. This shift is monitored by a photodetector and converted to an electrical signal. The Doppler shifted signal will have a frequency of: f = f2 - (f1 ± Df1), where Df1 is the Doppler shift. The phase difference between the two signals is measured every cycle and any phase changes are digitally accumulated. For accurate measurement it is important that the phase interpolation scheme (manufacturer specific) be linear to within the required tolerances of the application. Dfref = f1 – f2 Reference Reference Signal ASPE 2008 Intro. to Displacement Interferometr

Heterodyne DMI System Components

Components of a Heterodyne DMI System
Laser source Beam directing optics Interferometers Measurement electronics Target A typical heterodyne system consists of a frequency stabilized laser, interferometer optics, a target mirror and measurement electronics. Some recent milestones in DMI technology include: Very high velocity measurements >5m/s Linear resolution of 0.15nm System synchronization Fiber optic signal transfer The output power of a heterodyne frequency stabilized HeNe laser head is typically less than 700Watts. This limits a heterodyne system to about six axes of measurement. Multiple lasers operating at the exact same frequency allow for an unlimited number of measurement axes. Linear resolution of 0.15 nanometer ( microinch) with a 2-pass interferometer and angular resolution of arc seconds can be achieved with the latest electronics packages. Velocities of up to 4 meters per second can be tracked with a 0.3 nanometer linear resolution using a linear interferometer. The latest DMI electronics packages have the detection electronics on the measurement board. This allows for fiber optic transfer of the measurement and reference signals. ASPE 2008 Intro. to Displacement Interferometr

Laser Source ASPE 2008 Intro. to Displacement Interferometr

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 ASPE 2008 Intro. to Displacement Interferometr

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 ASPE 2008 Intro. to Displacement Interferometr

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 Helium Neon (HeNe) lasers are the most common frequency stabilized source with a typical wavelength around 633 nanometers. The frequency of a DMI laser must be highly stable. If the laser frequency drifts the unequal path length of the interferometer changes its length and the system detects what it believes to be motion of the target. The primary mechanism for drift of the frequency is change of the laser tube length due to temperature fluctuations. One method of laser stabilization is to wrap a heating coil around the laser tube and then monitor and stabilize the laser output using this coil. Below, the error in nanometers is shown for different values of laser stabilization over various unequal path lengths between the reference and measurement beams of the interferometer. ASPE 2008 Intro. to Displacement Interferometr

Lasers consist of a resonator and a gain medium
Resonator mirrors Gain Medium Output k-1 k 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 ASPE 2008 Intro. to Displacement Interferometr

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 Vary resonator length k-1 k ASPE 2008 Intro. to Displacement Interferometr

Laser is stabilized by changing tube length
Heater power supply Controller - Detectors s p Laser output Beamsplitter Heater Laser tube length determines wavelength Length is changed by varying temperature Stabilized by balancing intensity of two adjacent modes One method of stabilizing a laser tube is to ensure the laser operates at a uniform temperature. The method used for stabilization will be dependent on the required laser frequency stability. --Need block diagram here and more detail on feedback mechanism ASPE 2008 Intro. to Displacement Interferometr

Two frequencies are commonly generated by two methods
Circular linear polarizations Axial magnetic field f 1= f + f f 2= f - f Zeeman effect Orthogonal linear polarizations f+Df f-Df Laser tube f 1= f + f AOM Accousto-optic modulator For a DMI system to operate in optical heterodyne mode, the beam from the laser head must have two components that are orthogonally linearly polarized and differ in frequency by a fixed amount. The frequencies must be known and need to remain stable over the lifetime of the laser. Two different methods of generating the frequency split are used in industry; Zeeman technology and an accousto optic method. The Zeeman technique produces two frequencies by applying an axial magnetic field to the laser tube. The resultant output from the laser consists of a dual frequency beam whose frequency states are circularly polarized in opposite directions. Limitations of the Zeeman effect are : Small difference frequency (maximum of  4MHz) Variation in the split frequency from one laser to the next Low laser output power The acousto-optic method uses a frequency shifter, such as a Bragg cell, to produce the frequency difference. This technique yields a frequency split that is much greater than that of the Zeeman technique (20MHz). The split also remains constant because the Bragg cell is driven by a stable quartz oscillator. f f 2= f f ASPE 2008 Intro. to Displacement Interferometr

Two methods have some differences
Zeeman method AOM Small difference frequency (max. of ~ 4MHz) Bragg cell RF drive at split frequency Variation in the split frequency from one laser to the next Greater split frequency (~20MHz) Small variation between lasers due to crystal oscillator Low laser output power ASPE 2008 Intro. to Displacement Interferometr

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 Nominally  to base plane Base plane Base plane ASPE 2008 Intro. to Displacement Interferometr

Polarization states have slightly different frequencies
Two polarizations differ in frequency by 20MHz For ZYGO systems f1 > f2 f1 corresponds to polarization  to base f2 corresponds to polarization // base Corresponding wavelengths are slightly different f1 f2 Base plane ASPE 2008 Intro. to Displacement Interferometr

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 Stationary target max  f Target at max. velocity ASPE 2008 Intro. to Displacement Interferometr

Split frequency sets an upper bound on the target velocity
The maximum frequency shift max is some fraction k of f The maximum velocity vmax is related to max by The greater the split frequency, the greater the possible target slew rate. Typical Zeeman frequency split = 3.65Mhz Therefore, maximum possible target slew rate  578mm/s * Typical AOM frequency split = 20Mhz Therefore, maximum possible target slew rate  3165mm/s * * Maximum velocity values assume 2-pass interferometer configuration. NOTE: The actual maximum slew rate may be less than the maximum possible slew rate calculations shown due to the design of the system electronics. 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 ASPE 2008 Intro. to Displacement Interferometr

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, vmax  5 m/s For a double-pass system, N=4, leading to an increase in resolution but a decrease in vmax to  2.5 m/s ASPE 2008 Intro. to Displacement Interferometr

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 ASPE 2008 Intro. to Displacement Interferometr

Beam directing optics ASPE 2008 Intro. to Displacement Interferometr

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 f1 and f2 can change on passage through directing optics Designed for specific orientation Input Output 1 Output 2 Non-polarizing beam splitter (NPBS) Non-polarizing optics steer the source beam to the target of interest. The number of measurement axes and location of measurement target determine the quantity and type of non-polarizing optics in a DMI system. The interferometer consists of polarizing optics. The polarizing optics are required to generate the two separate beam paths required for displacement calculation; reference and measurement. Input Output Fold mirror ASPE 2008 Intro. to Displacement Interferometr

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 ASPE 2008 Intro. to Displacement Interferometr

Multi-axis systems require the source beam to be directed to multiple interferometers
Delivery Module (DM) PM fiber Measurement Electronics Laser Module (LM) Interferometers PM fiber NPBS DM Multi-mode fiber ASPE 2008 Intro. to Displacement Interferometr

Optical Components – Basic Building Blocks

Polarization beams splitter (PBS) Quarter-wave plate Plane mirror
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 ASPE 2008 Intro. to Displacement Interferometr

Polarization beamsplitter is the heart of an interferometer
p at f1 Creates reference & measurement beams Separates input polarization states Polarization states are called s & p & defined relative to plane of incidence Pneumonic: p passes s at f2 p at f1 s at f2 A polarization beamsplitter is at the heart of every heterodyne interferometer. The polarization beamsplitter separates the dual frequency source beam into two beams of different polarizations. The two beams become the reference and measurement legs of the interferometer. Polarization Beamsplitter Splits incoming beam based on polarization state ASPE 2008 Intro. to Displacement Interferometr

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 The output beam always exits the retroreflector parallel to the input beam. Accuracy of parallelism dependent on retro fabrication specifications. Typical accuracy < 10 arc seconds. Retroreflector output beam parallelism is independent of tilt of the retroreflector but results in translation of the return beam which is twice the translation of the retro apex.. The output beam separation from the input is equal to twice the distance of the input to the retroreflector apex. A retroreflector is used as a target for single pass interferometer configurations. It is also an integral part of other interferometer designs that require multiple passes of the measurement and reference beams. << Insert solid model << Solid and hollow retros << Nodal point and rotations about nodal point Offset ASPE 2008 Intro. to Displacement Interferometr

A quarter-waveplate is used to rotate polarization states
/4 45 LCP s s RCP A quarter waveplate converts linear polarization into circular. Quarter waveplates are used at the output of all PMI’s. Two passes through a quarter waveplate result in a 90 rotation of the beam’s polarization state and allows for the measurement beam to make a second pass to the target for increased resolution. << Show how this setup will flip the polarization state 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) ASPE 2008 Intro. to Displacement Interferometr

Plane mirrors are used both in the measurement and reference arms
Surface Figure (flatness) /4 = 158nm Plane mirror Measurement beam Direction of travel Direction of measurement 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 If a target mirror is translating in a direction parallel to the reflective surface, the flatness (surface figure) of the mirror becomes critical. Translation across a deformed mirror will result in the electronics outputting a value that can be read as an apparent displacement of the target. Example of a stage mirror. A target mirror is allowed only minimal tilt during a measurement because as the target tilts, the measurement beam becomes displaced from the reference beam at the receiver. Parasitic motions can produce coupling ASPE 2008 Intro. to Displacement Interferometr

Common Linear Displacement Interferometer Configurations

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) ASPE 2008 Intro. to Displacement Interferometr

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 Fixed Mirror Movable Mirror Monochromatic light source Beamsplitter Simple interferometer. Tilt sensitive, difficult to align. Very limited angular range – need a number. Not a practical configuration. Detector ASPE 2008 Intro. to Displacement Interferometr

A typical linear displacement measuring system
Reference Retroreflector Two-frequency laser Target Retroreflector Optical fiber Fiber optic pickup (FOP) PBS A typical system. Point out components. Measurement signal Digital Position Data Reference signal Phase Interpolator ASPE 2008 Intro. to Displacement Interferometr

Notation is required for interferometer ray diagrams
Polarization symbol l= p pol. = s pol. Circular pol. Multiple attributes of the beam need to be represented Beam direction Arrow direction Polarization state Pol. symbol behind arrow Frequency (f1 or f2 or altered frequency) Arrow color & notation Arrow head: direction of propagation f1 ± D f1 Arrow color: base frequency Green = f1 Red = f2 Notation: Base or altered frequency ASPE 2008 Intro. to Displacement Interferometr

A closer look at the linear displacement interferometer
# passes = 1 Scale factor = 1/2 N = 2 Reference Retroreflector f2 f1 f2 f1 Target Retroreflector f2- (f1 ± Df1) f1 f2 (f1 ± D f1) Most common linear interferometer Thermally balanced – same glass path lengths Retroreflector confers immunity to rotation Easy to align Explain the optics Beam routing – polarization and frequency Angle insensitivity Similar path lengths in glass Scale factor ASPE 2008 Intro. to Displacement Interferometr

A more compact variation – the single beam interferometer
# passes = 1 Scale factor = 1/2 N = 2 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 /4 f2 f1 f2 f1 The single beam interferometer is a variation of the linear interferometer that allows the beam to enter the center of the polarization beamsplitter and reflect off the apex of the retroreflector. If the source beam is too small (3mm diameter or less) this design may result in large efficiency losses at the retroreflector unless knife edge retroreflectors are utilized. (f1 ± D f1) f2- (f1 ± Df1) Target Retroreflector ASPE 2008 Intro. to Displacement Interferometr

Plane mirrors are ideally suited
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 ASPE 2008 Intro. to Displacement Interferometr

Plane mirror target permits translation  to measurement direction
Plane mirrors interferometers (PMI) are designed be used with plane mirrors # passes = 2 Scale factor = ¼ N = 4 Reference retroreflector f2 f1 f1 f1 f2 f1 ± D f1 Plane mirror f1 ± D f1 f1 ± 2D f1 f2- (f1 ± 2Df1) l/4 Explain the optics Beam routing – polarization and frequency Angle insensitivity Similar path lengths in glass Scale factor Plane mirror target permits translation  to measurement direction Ref. arm is retro-reflected within interferometer Two passes through /4 rotates pol. state 90 ASPE 2008 Intro. to Displacement Interferometr

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 ASPE 2008 Intro. to Displacement Interferometr

High Stability PMI (HSPMI) is based on a symmetric design
Reference plane mirror # passes = 2 Scale factor = ¼ N = 4 f2 l/4 l/4 f1 f1 f1 ± 2D f1 f1 ± D f1 Target plane mirror f2- (f1 ± 2Df1) ASPE 2008 Intro. to Displacement Interferometr

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 ASPE 2008 Intro. to Displacement Interferometr

Mirror tilt is transformed to beam shear
Beams shown separated for visualization Returning secondary (Second-pass beam) To FOP f1 f2 Outgoing primary (First-pass beam) ASPE 2008 Intro. to Displacement Interferometr

Beam overlap & signal strength change as the target mirror tilts
Near Full Signal ~50% No signal 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 ASPE 2008 Intro. to Displacement Interferometr

Observed AC signal decreases with increasing beam shear
Loss depends of beam size Larger beam, smaller signal loss ASPE 2008 Intro. to Displacement Interferometr

Tilt also contributes a displacement error

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 ASPE 2008 Intro. to Displacement Interferometr

Measurement Electronics

Converts phase change into digital output
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) =  /2048  0.31 nm Maximum velocity  5 m/s Real time data rates >20MHz The function of the measurement board in a Heterodyne DMI system is to convert a measurement signal from an interferometer and a reference signal from the laser head into measurement data. The displacement information can be read in parallel format from a P2 or VME interface as an 8, 16 or 32 bit 2’s complement word. A P2 interface typically provides real time position data at a rate of up to 10 MHz. A VME bus interface outputs data at a rate of up to 3 MHz. Data from the VME bus can be delayed by the operating system software running in parallel to DMI acquisition. Serial data is available in quadrature or up/down pulse format. Quadrature is usually the easiest data format to integrate to a closed loop system. A disadvantage to quadrature and up-down interfaces is the applications but the speed of the moving target is directly proportional to the output data rate. ASPE 2008 Intro. to Displacement Interferometr

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 ASPE 2008 Intro. to Displacement Interferometr

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 ASPE 2008 Intro. to Displacement Interferometr

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 Fiber connector Beam input Fiber optic pickup (FOP) The original DMI systems used bulky electrical receivers to convert the optical signal produced by the overlapping measurement and reference beams. The receivers had a tendency to produce heat and cause electrically induced errors. Fiber optic couplers were developed to eliminate electrically induced errors and a heat source. The size and convenience of the fiber optic coupler allow for reduced cost and package size. Focusing lens Polarizer at 45 to incoming polarization states Multi-mode fiber ASPE 2008 Intro. to Displacement Interferometr

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 Most heterodyne systems utilize fiber optic technology for transmission of the measurement signal from the interferometer to the measurement board and for sending the reference signal frequency from the laser to the measurement board. ASPE 2008 Intro. to Displacement Interferometr

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 ASPE 2008 Intro. to Displacement Interferometr

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 ASPE 2008 Intro. to Displacement Interferometr

Calculation of Displacement

Displacement calculation requires additional information
Phase in counts from phase meter Vacuum wavelength Desired displacement Refractive index of medium Integer based on number of passes # of counts/2 of phase ASPE 2008 Intro. to Displacement Interferometr

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 ASPE 2008 Intro. to Displacement Interferometr

k is a constant that depends on measurement electronics
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 ASPE 2008 Intro. to Displacement Interferometr

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 ASPE 2008 Intro. to Displacement Interferometr

Appropriate wavelength must be used to scale data
f2 f1 (f1 ± D f1) Wavelength used for scaling depends on which frequency (f1 or f2) is in the measurement arm Use 1vac & 2vac for f1 & f2 respectively Use of incorrect wavelength results in displacement error 1vac = nm f1 f2 (f2 ± D f2) f2 f1 2vac = nm ASPE 2008 Intro. to Displacement Interferometr

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 f1 f2 (f1 ± D f1) Phase readout increases f1 f2 (f2 ± D f2) f2 f1 Phase readout decreases ASPE 2008 Intro. to Displacement Interferometr

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 Two passes N=4 Pass 2 ASPE 2008 Intro. to Displacement Interferometr

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 ASPE 2008 Intro. to Displacement Interferometr

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 ASPE 2008 Intro. to Displacement Interferometr

Index of air may be calculated using Edlen’s equation
Relationship between the index and pressure, temperature, humidity and wavelength is given Edlen’s equation Complex equation Pressure, temperature, humidity and wavelength must be known to calculate index Typically obtained from measurements ASPE 2008 Intro. to Displacement Interferometr

Index of air may also be calculated from the following approximation
Index values can also be obtained using the index calculator at emtoolbox.nist.gov ASPE 2008 Intro. to Displacement Interferometr

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 ASPE 2008 Intro. to Displacement Interferometr

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 ASPE 2008 Intro. to Displacement Interferometr

Wavelength tracker is a differential interferometer
Air Interferometer Spacer Vacuum Spacer Air L Unlike a typical weather station used in conjunction with Edlen’s equation, tracker also tracks index changes due to composition changes ASPE 2008 Intro. to Displacement Interferometr

Measurement beam is in air while reference is in vacuum
Input beam Cell Fiber optic pickup DPMI Beam in vacuum Beam in air ASPE 2008 Intro. to Displacement Interferometr

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 ASPE 2008 Intro. to Displacement Interferometr

Uncertainty Sources and Analysis

Number of contributors
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) ASPE 2008 Intro. to Displacement Interferometr

We will consider an uncertainty analysis of a displacement measurement of a linear stage
Deadpath Ldeadpath  LAbbé Stage Stage base ds Measurand is the displacement of the stage as measured at point indicated at the surface of the stage and indicated by ds ASPE 2008 Intro. to Displacement Interferometr

We will include the following sources of uncertainty
Wavelength Refractive index Phase meter output Deadpath error Abbe offset Cosine error ′ ASPE 2008 Intro. to Displacement Interferometr

We will neglect the following sources of uncertainty
Change in index of target Cyclical errors due to mixing Beam shear Data age uncertainty Surface figure of target Thermal expansion Interferometer Index gradients Target mount Inertia loading Air turbulence Vibration Effect of parasitic motions And a host of others… ASPE 2008 Intro. to Displacement Interferometr

We will assume the following uncertainty values & parameters
S. No. Parameter Nominal value 1 Stage travel 250 mm 2 Deadpath 3 Abbé offset 100 mm S. No. Uncertainty Source Uncertainty 1 Wavelength 10 ppb 2 Temperature 2 C 3 Pressure 15 mm Hg 4 Humidity 20% RH 5 Pitch amplitude 5 arc-sec 6 Index in deadpath 2 ppm 7 Phase meter 1 LSB ASPE 2008 Intro. to Displacement Interferometr

Uncertainty in input values contributes to uncertainty in measured displacement
Vacuum wavelength uncertainty Phase meter uncertainty Uncertainty in measured displacement Refractive index uncertainty Pressure uncertainty Temp uncertainty Humidity uncertainty ASPE 2008 Intro. to Displacement Interferometr

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 ASPE 2008 Intro. to Displacement Interferometr

Bounding uncertainty can be estimated from physics of HeNe laser
2 X 10-6 m Laser threshold k-1 k 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 10-6 m ASPE 2008 Intro. to Displacement Interferometr

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 STP = Standard Temperature and Pressure T = 20°C P = 760 mm Hg RH = 50% Changes in the environment over the time of measurement are typically the largest error source in a DMI metrology system. Controlling the climate, monitoring the pressure, temperature and humidity changes and/or reducing the measurement time will minimize these errors. Edlèn published the first paper detailing wavelength compensation calculations. Shown above is Edlèn's formula with a power series expansion for the water vapor pressure term and an alternate formulation using an exponential fit. Other versions of Edlèn's formula exist. For more precise work, it is possible to incorporate molecular concentrations of the air, such as the partial pressure of CO2, into the calculation. ASPE 2008 Intro. to Displacement Interferometr

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

Cosine error results from misalignment of beam and axis of motion
Measured displacement dm  Direction of motion Actual displacement da ASPE 2008 Intro. to Displacement Interferometr

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 A cosine error results from an angular misalignment between the measurement laser beam and the axis of motion. For optimum alignment of a DMI system the optical path and axis of motion must be parallel. Cosine error is generally negligible until the angle becomes quite large. A cosine error will cause the interferometer to measure a displacement shorter than the actual distance traveled. As cosine error occurs the measurement and reference beams will shear resulting in a loss of signal efficiency. ASPE 2008 Intro. to Displacement Interferometr

Measured displacement dm
Abbé error results from an offset between measurement axis and axis of interest Measured displacement dm Pitch  Measurement axis LAbbé Displacement axis Stage displacement ds When the axis of measurement is offset from the axis of interest, Abbé errors will occur. As first described by Dr. Ernst Abbé of Zeiss: “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.” ′ ′ ASPE 2008 Intro. to Displacement Interferometr

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 ASPE 2008 Intro. to Displacement Interferometr

Abbé principle is a fundamental principle of metrology
“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 Axis of measurement must pass through the axis of interest, i.e., the line along which we wish to measure displacement ASPE 2008 Intro. to Displacement Interferometr

Deadpath = Length between PBS and target retro at interferometer zero
Point at which interferometer ‘zero’ is set Index variation n PBS Dead path Ldeadpath Measuring Path ASPE 2008 Intro. to Displacement Interferometr

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 ASPE 2008 Intro. to Displacement Interferometr

Deadpath can be minimized by simple strategies
Range of motion Addition of a fold mirror can help move interferometer to a more advantageous position Deadpath Deadpath Fold mirror The upper example is using a right angle configured interferometer that is positioned a long distance from the target’s travel. The lower example shows how adding a fold mirror and changing the interferometer to a straight thru configuration can minimize the potential dead path error. ASPE 2008 Intro. to Displacement Interferometr

Uncertainty analysis is based on this model equation
′ ′ ASPE 2008 Intro. to Displacement Interferometr

Results of uncertainty analysis

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 ASPE 2008 Intro. to Displacement Interferometr

Index contributions can be reduced
S. No. Parameter Uncertainty Compensated Uncompensated 1 Temp uncertainty 0.1C 2C 2 Pressure uncertainty 1 mm Hg 15 mm Hg 3 Humidity uncertainty 5% RH 20% RH Measure environment and compensate Uncertainty in environmental variables is replaced with uncertainty in the measurement of these variables ASPE 2008 Intro. to Displacement Interferometr

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 ASPE 2008 Intro. to Displacement Interferometr

Compensation reduces index contribution drastically

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 ASPE 2008 Intro. to Displacement Interferometr

Specialized Interferometer Configurations

Emphasis is on introducing configurations, not on detailed analysis
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 ASPE 2008 Intro. to Displacement Interferometr

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

Column reference interferometer (CRI)
Column reference interferometer monitors relative displacement between stage and lens column Column mirror Column reference interferometer (CRI) Column Stage Stage mirror ASPE 2008 Intro. to Displacement Interferometr

Column reference interferometer (CRI)
Target and Reference Mirrors Steering Wedges /4 waveplates Retroreflector PBS Fold Mirror Compensating Plugs A column reference design allows for the measurement of the relative displacement between two active mirrors, while reducing a system’s dead path error. The configuration shown depicts a two-pass column reference design. The resultant measurement is a linear displacement that represents the difference between a reference and a target mirror. Performs a differential measurement Reduces deadpath error Steering wedges facilitate beam alignment ‘Folded’ HSPMI ASPE 2008 Intro. to Displacement Interferometr

Differential PMI makes meas. between two plane mirrors

DPMI can be configured to make differential displacement measurement
PBS The Differential Plane Mirror Interferometer (DPMI) can be used to measure linear displacements or small angular displacements. The light entering in the interferometer is split into two parallel beams by the polarization shear plate. The polarization of one of these beams is then rotated by a half wave plate to match the polarization of the other beam. In this way, the two beams travel the same path through the interferometer except that they are now displaced by a few millimeters. The reference mirror is fabricated with holes in it so that the measurement beam passes through the mirror and the reference beam is reflected. Each beam travels to/through the reference mirror twice and the beam footprint is a square arrangement of non-overlapping beams. In the linear displacement application the two paths of the measurement beam are oriented diagonally across the square pattern. This interferometer design is good for remote or vacuum applications and has minimal thermal effects. However, it tends to be expensive due to the number and type of components required. Target Shear plate l/4 l/2 Reference ASPE 2008 Intro. to Displacement Interferometr

Some features of the linear DPMI
Measurement is differential and permits a short metrology loop Resolution is same as a two-pass PMI ASPE 2008 Intro. to Displacement Interferometr

…or differential angular measurements
PBS The DPMI can be configured for an angular measurement by simply changing the reference mirror. The angular displacement reference mirror has two holes that are positioned such that the second pass of the beams is directed to the opposite mirror it reflected from on the first pass. The resultant output is and angular displacement whose resolution is based on the separation between the beams on the target mirror (less than 0.1 arc second). Plus - resolution Target Shear plate l/4 l/2 Reference ASPE 2008 Intro. to Displacement Interferometr

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 ASPE 2008 Intro. to Displacement Interferometr

Routing of beams is complex and three-dimensional
DPMI - Linear DPMI - Angular ASPE 2008 Intro. to Displacement Interferometr

Larger angular motions are handled by a dual-retro config.
Beam bender f2 ± f2 f1 f2 f1  R f1 ± f1 f2 ± f2 f1 ± f1 PBS Angular Retroreflector ASPE 2008 Intro. to Displacement Interferometr

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 ASPE 2008 Intro. to Displacement Interferometr

DMI can be used to measure straightness of an axis
Dihedral mirror f1 f1 ± f1 f1, f2 Straightness error motion  f1 ± f1  f2 ± f2 Wollaston prism f2 ± f2 f1 ASPE 2008 Intro. to Displacement Interferometr

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 ASPE 2008 Intro. to Displacement Interferometr

Optical probe config. is ideally suited for small targets
Target mirror Lens PBS /4 Reference retroreflector Single-pass interferometer Reference beam reflects off vertex of retro Beam routing behavior same as single beam interferometer The optical probe allows measurement at a small beam: ~ 100 µm diameter. The range of motion is limited by the depth of focus of the objective lens. Thus, the lens should be optimized for the application. This interferometer is unusual, because it is aligned with no axial offset for the retro. The reference beam is centered on the apex of the retro and the measurement beam is centered on the objective lens. The optical probe can accommodate a wide range of target reflectivity. ASPE 2008 Intro. to Displacement Interferometr

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 ASPE 2008 Intro. to Displacement Interferometr

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’ ASPE 2008 Intro. to Displacement Interferometr

Fiber fed heterodyne interferometers must preserve the input polarization states
Heterodyne Laser Source Remote Laser Head Polarization Maintaining (PM) Fiber Split frequency generator/polarizer Beam expander Expanded beam to optics Delivery Module ASPE 2008 Intro. to Displacement Interferometr

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. ASPE 2008 Intro. to Displacement Interferometr

Application Examples ASPE 2008 Intro. to Displacement Interferometr

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 Static Applications acquire position data on a point by point basis. Examples of static measurements include the measurement of the radius of curvature of an optic and calibrations of machine tools and micrometer driven stages. Dynamic applications involve the active monitoring a process. Vibration measurements, calibration of the motion of a piezo-electric transducer (PZT) and closed loop stage control are typical dynamic applications. ASPE 2008 Intro. to Displacement Interferometr

Use as feedback sensors for motion control is a very common application
X-Y reticle stage Interferometers X-Y wafer stage ASPE 2008 Intro. to Displacement Interferometr

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 Wafer processing is a popular OEM (Original Equipment Manufacturer) application for a DMI. An OEM will integrate a DMI into the metrology sub-system of their tool. Lithography instruments, which include wafer steppers, scanners, CD-SEM’s, memory repair tools and mask development tools make-up the largest market of DMI users. ASPE 2008 Intro. to Displacement Interferometr

Used as feedback for machine tools & measuring machines
Large Optics Diamond Turning Machine (LODTM) at Lawrence Livermore ASPE 2008 Intro. to Displacement Interferometr

Interferometer system for the LODTM

Stage calibration is another common application
DMI Calibration Data Commanded Position (mm) DMI Position (mm) 250 500 Stage Error Position Error (m) 5 10 15 20 100 200 300 400 The stage calibration data can be used to create a look-up table to correct for errors inherent in the machine. The first plot shows the position as measured by the DMI as a function of indicator position. The difference between the indicator position and DMI position define the error in the machine. The second plot is the resultant stage calibration data. Position Error = DMI Position - Indicator Position Determination of stage errors Generation of an error maps ASPE 2008 Intro. to Displacement Interferometr

Another application involves use as an indicator
HSPMI Reference mirror Laser in Laser out Straightedge Machine stage ASPE 2008 Intro. to Displacement Interferometr

Machine tool metrology is an example of ‘strap-on’ metrology
Laser Head DMI Target Characterize various error motions of a machine tools Many different types of interferometers Numerous accessories Measurements made between tool & workpiece Machine tool calibration is a static application with many sample points. Here the position of the machine tool is measured and compared with the machine programmed position. A correction table can be formed or a correction function can be fit to the measured data. ASPE 2008 Intro. to Displacement Interferometr

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 ASPE 2008 Intro. to Displacement Interferometr

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 ASPE 2008 Intro. to Displacement Interferometr

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 ASPE 2008 Intro. to Displacement Interferometr

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. ASPE 2008 Intro. to Displacement Interferometr

Actuator calibration Gage calibration Vibration analysis
Other applications Actuator calibration PZT, electrostrictive, linear motors, capstan drives, etc. Gage calibration LVDT Capacitance gages Encoders Vibration analysis ASPE 2008 Intro. to Displacement Interferometr

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 ASPE 2008 Intro. to Displacement Interferometr

Summary ASPE 2008 Intro. to Displacement Interferometr

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) ASPE 2008 Intro. to Displacement Interferometr

Introduction to Displacement Measuring Interferometry

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Introduction to Displacement Measuring Interferometry

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