f. mccullough, m. hill, j.w. mcbride€¦ · f. mccullough, m. hill, j.w. mcbride university of...

Review of optical techniques for three-

dimensional surface measurement

F. McCullough, M. Hill, J.W. McBride

University of Southampton, Department of Mechanical Engineering,Highfield, Southampton, SO 17 1BJ, UKE-mail: [email protected], [email protected], [email protected]

Abstract

Optical measurement techniques for high precision three-dimensional formmeasurement are reviewed. The systems investigated include interferometry,auto focus techniques and triangulation systems. The configurations of theseinstruments and their methods of operation are described. Optical based systemshave a number of limitations when applied to high precision measurement ofcurved surfaces. The performance of these systems are discussed and assessed. Arecommended system for three-dimensional form measurement is described.

1 Introduction

This paper is concerned with optical systems for high precision three-dimensional(3-D) form measurement. The systems investigated include interferometry, autofocus techniques and triangulation systems. Optical techniques have theadvantage of being a non-contact measurement. Three-dimensionalmeasurements provide more information about a surface than two-dimensionalmeasurements, however a higher performance is required from hardware andsoftware [1]. For 3-D roughness measurements only vague recommendationshave been published. These recommend that a raster scan of 128x128 or256x256 data points should be used. No recommendations have been publishedfor form measurement. It is clear that form measurements cannot be used togenerate roughness data as widely spread data can result in aliasing [2].

To examine the performance of the various systems a number of criteria areused, including resolution, gauge range, repeatability, spot size and angular

Transactions on Engineering Sciences vol 23, © 1999 WIT Press, www.witpress.com, ISSN 1743-3533

298 Laser Metrology and Machine Performance

tolerance. The resolution of the system is the smallest increment that can bemeasured. The gauge range is the maximum distance over which themeasurement is reliable. The repeatability is the spread of the data resulting fromthe repeat measurement of the same quantity. The spot size is the size of the laserspot on the surface and is a factor in the uncertainty is the XY position of thepoint measured. The angular tolerance is often the critical factor especially oncurved or rough surfaces. It is the maximum angle of inclination of the surfacethat can be tolerated before the measurement is lost or liable to be wrong.

A number of applications are considered as part of this work, these arecontact lens moulds, joint replacements, electrical contacts, and aspheric lenssurfaces; each places different demands on the system. As an example, electricalcontacts require good edge handling because of the discontinuities caused byboth the geometry and the erosion.

2 Non-contact instruments

This section is a description of various non-contact instruments that can be usedin high precision surface measurement. Optical techniques do not require contactwith the surface so eliminate the risk of damage or contamination. This can be asignificant advantage in many applications. Optical instrument frequently find itdifficult to distinguish the optical and physical properties of the surface resultingin a lower accuracy. As there is no need to remain in contact with the surface, themeasurement can be made at greater speed. A number of instruments arediscussed such as: interferometers, auto-focus-based systems and triangulationprobes.

2.1 Interferometers

Interferometers are widely used to measure distance in a number of situations.They are used extensively to calibrate Co-ordinate Measurement Machines(CMMS) and machine tools [3]. They can also be used to measure a number ofdifferent physical properties such as refractive index [4]. Laser interferometersfunction using the wave characteristic of light to measure a phase differencebetween two different light beams. The phenomenon of interference is describedin [5]. Unfortunately the resulting signal is the same if the path differenceincreases or decreases, this creates difficulties when trying to use this method asthe signals are non-directional. If the path difference is greater than half thewavelength then the interferometric signal starts to repeat. This is called A/2ambiguity and is a fundamental limitation. It can be overcome in somecircumstances which will be discussed later.


Laser Metrology and Machine Performance 299

2.1.1 Frequency modulated continuous wave systems (FMCW)The frequency modulated continuous wave systems use standard interferometerconfigurations [6]. The main difference is that these systems use a syntheticwaveform rather than using the waveform of the laser light to measure the pathdifference [7] [8]. Once the synthetic waveform is generated it can be used in thesame manner as a normal waveform. This has a major advantage that by selectinga suitable wavelength the gauge range and resolution achievable can beoptimized for any given application.

Onodera and Ishii [9] describe a frequency-modulated system that uses twolaser diodes to generate a synthetic wavelength of 4.7 microns. This is used in aFabry Perot configuration with an optical path difference of 60 mm. The systemalso uses a phase stepping algorithm to extract the phase of the interferometricsignal. The synthetic wavelength is given by 'k\K2/\Kl-K2\ where XI and K2 arethe wavelengths of the laser diodes. The system is complex and uses electronicsto adjust the system for differing path differences. The paper shows that thegauge range is 1/2 where 1 is the synthetic wavelength, it does not describe theresolution achieved.

Fischer [10] describes a frequency-modulated interferometer that is used forabsolute distance measurement. A frequency modulation (FM) demodulationtechnique is used to extract the phase of the interferometric signal. A single laserdiode is modulated to supply a synthetic wavelength. The system gives aresolution of 1.6|im with a measurement range of 50 mm. Unfortunately, therepeatability is poor at 50um, which limits the usefulness of the instrument.

One of the problems with modulating the input current to a laser diode is thatintensity of the light emitted changes as well as the wavelength. In some instancestemperature control is also required to keep the system stable [11]. This situationcauses several problems when trying to examine the intensity variation in aninterferometric signal. Sandoz [12] describes a method of correcting for theseintensity fluctuations that allow phase shifting algorithms to be used withoutincurring errors. The paper does not describe what this improved method wouldyield in terms of resolution and gauge range but does mention that it comparesfavourably with that achieved by the phase algorithms.

These instruments seem to have significant advantages over some of theothers but unfortunately, it would be difficult to increase the resolutionsignificantly because very fast data acquisition and analysis would be needed.This is currently not possible at a reasonable cost:

2.1.2 Fringe counting interferometersFringe counting interferometers work not by measuring the phase differencebetween two different light beams but by counting the number of phase changesfrom in phase to anti-phase and vice versa [13]. This allows the interferometer tomeasure over a larger range, but with a resolution of X/2. This type of system isnon-directional and the interferometric signal must be highly repeatable in orderfor the phase changes to be counted successfully. If the interferometric signal islost it results in lost counts and the measurement is no longer reliable.


300 leaser Metrology and Machine- Performance

There have been a number of improvements made, such as the use of twointerferometric signals in phase quadrature (a quarter X phase difference)[14].This improves the resolution and gives directionality to the interferometric signal.The directionality is achieved by keeping track of which signal was in-phase oranti-phase last. A reliable interferometric signal allows the resolution to beimproved by calculating what portion of a phase change has been detected. Thisis called fringe sub-division and can divide a phase change as many as 50 times[15]. The paper by Downs and Birch [16] describes a refractiometer that uses abi-directional fringe counting method. In a later paper Birch describes a methodto correct for a non-ideal signal this is a modified version of that first used byHeydemann [17]. Using this technique allows a fringe to be sub-divided such thatthe resolution is approximately 1 nm. This resolution is achieved with a randomvariation of 10 per cent on the interferometric signal.

Another fringe counting technique is used by Martin [18] to measure positionand velocity of gas valves. Two interferometric signals in approximate phasequadrature are used. An acousto-optical modulator is used to step the phase ofthe reference beam, this allows the correction to be determined avoiding A/2ambiguity. Amplitude modulation is also used to avoid false counts.

This high resolution combined with the large gauge range of fringe countinginterferometers make these systems extremely useful. The need for a repeatableinterferometric signal means the signal beam must be returned with very littledistortion. A corner cube prism would normally be used for this purpose. Itwould not therefore be sensible to measure the surface directly using thesesystems but they could be used to measure other parts of the system

2.1.3 Fibre optic interferometersThese systems work on the same principle as standard interferometers [6]. Thebeam splitters are replaced by fibre couplers and the fibres are used as wave-guides. These systems have several advantages over standard interferometersystems they generally are cheaper and more robust. This type of system has beenused for surface profiling by Carolan [19]. A Fizeau configuration was usedwhere the reference signal was reflected from the cleaved end of the fibre. Adiagram of this configuration is shown in figure 2.1. The probe consists of theend of the fibre and a graded index (GRIN) lens [20]. The light reflected from thesurface is collected by the GRIN lens and is fed back into the fibre. The phase ofthe interferometric signal is calculated from the intensities. The computer alsocontrols the movement of the probe by controlling a D C motor driver. A pulseshaping circuit is used to modulate the diode power supply in order to create themodulated output. A passive phase stepping technique is used to recover thedisplacement, which involves switching between different values of phase bymodulating a laser output frequency. The speed of the profiler must be such thatthe phase stepping cycle is completed before a movement of the profiler iscarried out. The results obtained were compared with measurements taken on aRTH Talysurf [21] and the profiles produced were very similar.



Figure 2.1 Fibre optic Fizeau interferometer

This work was then extended [22] by developing a new system figure 2.2.This system was designed for non-contact profile measurement of machinedmetal surfaces, where profile of the surface was required rather than averageroughness parameters. This system allows the profile to be measured withouthaving to control the probe height above the surface. This instrument generates adifferential profile corresponding to the difference in surface heights at the twospots as they are traversed across the surface. A five-phase step interferometricsignal-processing algorithm is used to extract the displacement. The systemclaims to be immune to the changes in the optical properties of the surface. Theconfiguration of this system is more complex and overcomes the problem ofphase ambiguity by using two laser diodes with different wavelengths. Thisallows the displacement to be measured unambiguously over a range of 16 fim,which is much better than many of the other interferometric systems. The paperdoes not describe the resolution obtained, but the algorithm used would normallyyield a resolution of 1 run. The papers do not describe the angular toleranceobtained and the gauge range is small so these systems are not ideally suited toform measurement.

PHOTODIODE -ISOLATOR

Figure 2.2 Configuration of fibre optic interferometer



2.1.4 Phase stepping interferometersPhase stepping is one of the most common ways of overcoming ambiguities. Theprinciple is that the phase of the source or reference signal is changed a numberof times for a certain path difference. The interferometric signals from each phasestep are analysed together. This extends the measurement range by examining theinterferometric signals with a number of phase changes. The phase changes canbe introduced in a number of different ways. One method used extensively is tomount the reference mirror on a pizeo stage [23]. Pizeo stages can be movedextremely accurately over small distances. Another method used with laserdiodes is to change the input current as this changes the phase of the lightemitted. Changing the input current to the laser diode has the side effect that thewavelength of light emitted changes as well. This technique can be applied to fullfield, discrete and fibre optic interferometers.

Caber [24] uses a laser diode to step the phase of the reference beam to makethree-dimensional profiles of rough machined metal surfaces. These surfaceswould normally be difficult to measure using interferometry as the steep localsurface gradients would be more than the A/2 ambiguity. The system is claimedto produce fast accurate results with a resolution of 2 rim.

2.2. Auto-focus based systemsThese systems [23] work on the principle of maintaining the focus of a laser spoton a surface. The laser and light is focused by a lens, which is moved by anactuator positioned by a control system to maintain the focus. Once focus isachieved, the distance of the lens from the surface is always the same. Bymeasuring the displacement of the lens, the distance of the probe from the surfacecan be calculated. The focus error signals are generated in a number of differentways

2.2.1 The prismatic Foucault knife methodThe prismatic Foucault knife is illustrated on the diagram in figure 2.3 generateda directional error signal, which is sensed twice with two photo diode pairs. Asthe focus is lost the distribution of light on, each of the photo diode pairs isaltered; the two error signals are then combined. The range of disfocus that canbe tolerated controls the gauge range of the instrument.

Figure 2.3 Illustration of prismatic Foucault knife method of focus detection, leftsurface in focus, middle surface below focus position, right surface above focusposition.



A confocal method of focus detection is used by Schults [26] to estimate theeffect of temperature on lens performance. At best focus the light passes througha pinhole at the confocal position as focus is lost less light hits the photo detector.This type of error signal is non-directional so is difficult to employ.

The system described by Fainman [27] is similar to an auto-focus system. Ithas a resolution of 0.1 micron with a spot size less than two microns. This systemfunctions by placing a filter in the paths of the two beams. If the beam is correctlyfocused, a portion of the light will be transmitted to both detectors. As the focusis lost the amount of light transmitted decreases to one detector and increases toanother. This gives a directional error signal, which is amplified by a differentialamplifier. A feedback control system then adjusts the position of the objectivelens. The vertical resolution and spot size obtained are strongly dependent on thefocusing properties of the objective lens. Fainman states that it is quite possibleto obtain a spot size of 1 micron. The resolution obtained is dependent on thepositioning accuracy of the objective lens and is approximately 0.1 micron.Further experiments by Fainman indicated that a sensitivity of 50 nm waspossible, however the noise present was the same order of magnitude. Thissystem seems quite promising the resolution is good, the gauge range is not statedbut these systems have a relatively large gauge range when feedback control isused.

Murai [28] used an auto focus probe in an interesting way. Rather thanadjusting-the position of the objective lens, the whole probe is moved on a piezostage. The position of the stage is measured using a fringe countinginterferometer, which gives a high resolution and a relatively large gauge range.The interferometer has a resolution of 2.5 nm and the stage can move over adistance of 10 jim.

The probe that was developed by Mitsui [29] uses an astigmatic method offocus detection, figure 2.4.

QUARTER WAVE PLATE POLARISING BEAM SPLTER

QUADRENT DETECTORS

Figure 2.4 System of optical probe as used by Mitsui.

The configuration is slightly more complex; it uses two beam splitters andmeasures two signals on two quadrant detectors. The aim of using two focussignals is to reduce the sensitivity to the diffraction caused by the surface. Theobjective used is a standard microscope objective with a numerical aperture (Na)of 0.8 and a magnification of x60. The strength of the cylindrical lenses allowssome control of the sensitivity and the linear range. The objective has the largest



effect on the gauge range and resolution, an objective with a 0.8 numericalaperture (Na) gives a linear range of 1 jim. An objective with Na of 0.65 gives alinear range of 3 pn. The resolution of the system was at least 1 run andmeasured profiles agree closely with those measured with a stylus instrument.

2.3 Triangulation

Laser triangulation works by focusing light onto a surface and examining theposition of the reflected light onto an array of photo detectors. There are twomain configurations used in laser triangulation, these are specular and diffusethese are illustrated in figure 2.5, and are described by Slazas [30].

DIFFUSE CONFIGURATION SPECULAR CONFIGURATION

Figure 2.5 Configurations of laser triangulation probes

The specular configuration is usually used on highly reflective surfaces suchas metals. The diffuse configuration is usually used on less reflective surfaces andcan be used in more situations. The specular configuration involves shining afocused beam of laser light on to the surface at a known angle. The directreflection of that beam is then collected by the receiving optics. Depending onthe position of the surface the reflected beam hits a photo diode array at aspecific position. The diffuse configuration shines the laser light perpendicular tothe surface. The receiving optics collects the scattered light and focuses it on to aphoto diode array. Again, the position of the focused light on the array gives theposition of the surface. The diffuse configuration is less susceptible to theinclination of the surface.

Costa [31] describes two laser triangulation systems. The first is anexperimental rig designed for use in a laboratory environment. The second is aprototype system, which has been designed from the experimental rig. Theprototype system uses a CCD camera to collect the imaged spot and uses adiffuse configuration. The system is unusual in that the incident light is at anangle but the observation plane is positioned perpendicular to the surface. Thepaper claims that sub-micron resolution is possible. The system is controlled by acomputer which moves the sample via an X Y stage. The results of calibrationshow a very low noise level with a reasonable resolution. A movement of the spotfrom one pixel to the next corresponds roughly with a movement of 1 fim in thesurface height.



3 Comparison of instruments

There is a significant variation depending on the precise implementation of thesystem, some may perform well under certain circumstance but the performancemay be poor in less ideal circumstances. Table 3.1 summarises the typicalperformance of the different types of system. These are compared in the contextof the applications identified in the introduction. Each application placesdifferent demands on the measurement system, despite these differences twocrucial criteria can be identified. The spot size and the angular tolerance.

System

Resolution(um)Gauge Range (urn)Angular ToleranceRepeatability

Spot Size(um)

Auto-Focus0.015-100050.220Good

2

SurfaceInterferometer0.00185°Good

2-30

FMCW

506000005°Poor

50+

InterferometerFringe counting0.00150000+PoorSignalDependant50+

Triangulation

0.00150-2005°Surfacedependant20+

TableS. 1 Summary of performance of different types of system.

The electrical contacts examined during this work were cylindrical in shape witha domed top; they were approximately 3mm in diameter with a height of 0.4 mm.Identifying the edges and height of the contact is important so the volume can becalculated; therefore, the spot size is the critical criteria. Replacement hip jointsneed to be measured over large section of their area, making angular tolerancethe important factor. Contact lens moulds require a good angular tolerance so theentire optical zone (5mm diameter) can be measured. Aspheric Lens surfaces canhave relatively large curvatures in the optical region so angular tolerance isimportant, a larger gauge range may also be required.

The triangulation and FMCW systems have spot sizes that are too large andangular tolerances that are too low. The surface interferometers have too smallgauge range and poor angular tolerances. The auto focus system combine a largeangular tolerance with a high resolution and small spot size so could be used. Thefringe counting interferometer cannot measure the surface directly but would beuseful in a configuration such as Murai [28] to measure the position of the probewhich has a similar resolution but is limited in range.

4 Conclusions

A range of optically based systems have been compared, in the context of theapplications identified in the introduction. Each application places differentdemands on the measurement system, despite these differences two crucialcriteria can be identified: the spot size and the angular tolerance. The resolutionis also important as it effects the accuracy of measurement. The gauge range isnot normally critical when measuring curved surfaces of small radius as the



angular tolerance is exceeded before the gauge range. The system most able tomeet these criteria is an auto focus system designed primarily for formmeasurement.

5 References

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f. mccullough, m. hill, j.w. mcbride€¦ · f. mccullough, m. hill, j.w. mcbride university of...

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