Optical detection system for ultrasonic surface displacements

Transcription

1 Loughborough University Institutional Repository Optical detection system for ultrasonic surface displacements This item was submitted to Loughborough University's Institutional Repository by the/an author. Additional Information: A Doctoral Thesis. Submitted in partial fulfilment of the requirements for the award of Doctor of Philosophy at Loughborough University. Metadata Record: Publisher: c M.W. Godfrey Rights: This work is made available according to the conditions of the Creative Commons Attribution-NonCommercial-NoDerivatives 2.5 Generic (CC BY-NC- ND 2.5) licence. Full details of this licence are available at: Please cite the published version.

2 This item was submitted to Loughborough University as a PhD thesis by the author and is made available in the Institutional Repository ( under the following Creative Commons Licence conditions. For the full text of this licence, please go to:

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5 OPTICAL DETECTION SYSTEM FOR ULTRASONIC SURFACE DISPLACEMENTS by Martin William Godfrey A doctoral thesis. Submitted in partial fulfilment of the requirements for the award of Doctor of Philosophy of the Loughborough University of Technology May 1986 ~ by M.W. Godfrey 1986

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7 ACKNOWLEDGEMENTS I would like to thank all the members of the Physics Department for their encouragement, and particularly my supervisor David Emmony for his guidance. Thanks also go to Richard White who collaborated in much of the work. I would also like to thank Trevor Holroyd and those I worked with at Rolls Royce Ltd., Derby, for their help. The work was supported by SERC with a CASE studentship in association with Rolls Royce Ltd. The UKAEA at Risley and ANTE at Holton Heath also provided valuable assistance during the project. I would like to thank my parents for their support and for proof reading the typed texts. Special thanks go to Sarah Reed for her support during this work and for checking the original manuscripts. Finally I would like to thank Mrs. M.P. Ashwell for typing this thesis. i

8 ABSTRACT The work was carried out with the aim of developing an optical interferometric detection system. This was to be applied to the quantative measurement of low amplitude, high frequency surface displacements «lnm at several MHz). Two forms of interferometric detector are investigated. The performance and limitations in particular measurement situations are assessed for both types of interferometer. The first type of detector investigated is a miniature stabilised interferometer. The design of a stabilisation system is given, along with ways in which it can be optimised for a particular environment. The second type of detector studied is a quadrature interferometer. Various methods of processing the two channels of information from this device are discussed. The design of a new method of processing the signals is given, and its performance determined. The interferometric sensor is combined with a waveform digitiser and microcomputer to form an integrated detection system. Analysis of the waveforms obtained is performed by a system of Pascal programs developed for this purpose. The detection system is applied to tasks such as the calibration of other forms of transducer and the characterisation of artificial sources of acoustic emission. The results of experimental studies are given and the applications of such a system discussed. ii

9 CONTENTS Page ACknowledgements Abstract i ii INTRODUCTION 1.1 Introduction, an historical perspective 1.2 Review of previous work 1.3 Aims of the study STABILISED INTERFEROMETRIC' DETECTOR 2.1 Methods of interferometer stabilisation 2.2 Design of miniature interferometer 2.3 Fundamentals of the feedback system 2.4 Vibration level measurements 2.5 Stabilising transducers 2.6 Selection of photodetectors 2.7 Stabilisation system electronics 2.8 System performance 2.9 Summary QUADRATURE INTERFEROMETER SYSTEMS Principles of quadrature detection Construction of the quadrature interferometer Effect of focal spot size on frequency response Filtering requirements Interpretation of interferometer outputs 64

10 Page Square and add" quadrature processing Simulation of square and add operation F.E.T. square law unit Analog multiplier square law unit 3.7 Vector computer 3.8 Quadrature interferometer processor Summary System design concepts Circuit development Performance of signal processor SIGNAL ANALYSIS SYSTEM 4.1 Requirements of an analysis system 4.2 Selection of programming language 4.3 Choice of program standards 4.4 Transfer of waveform data to computer loo Method of data transfer Assembly language data transfer program Pascal data transfer program Output of waveform data Requirements of output routine Graph plotting facilities available on Apple Ire Graph plotting program Output of graphics on printer 4.6 Fourier transform routine Fourier transform fundamentals Pitfalls in the use of the discrete Fourier transform

11 Page Fourier transform program 4.7 Manipulation of waveform data 4.8 Digital filtering of waveforms 4.9 Processing of interferometer outputs 4.10 Summary of analysis system 5. APPLICATIONS OF THE DETECTION SYSTEM 5.1 Artificial source characterisation Pencil lead fracture Neodymium-YAG laser impact Fracture of hollow glass ba1atini 5.2 Transducer calibration 5.3 Transducer development 5.4 Summary 6. RECOMMENDATIONS AND CONCLUSIONS APPENDICES i) Derivation of an interference expression 170 ii) Electronics for the stabilised interferometer 175 iii) Electronics for the quadrature interferometer iv) File and data format standards. v) Listings of the disc file routines vi) REFERENCES Listing of the FFT routine BIBLIOGRAPHY 203

12 1. INTRODUCTION 1.1 Introduction, an Historical Perspective. Acoustics, which Comes from the Greek word for hearing, has its origins in the work of Greek philosophers, who around the 6th Century BC studied the origins of sound. Research into sound progressed in an haphazard manner throughout the following centuries, with the work of people like Galileo Galilei, Euler, etc. In 1877 the publishing of "The Theory of Sound" by J.W. strutt (Lord Rayleigh) [1], marked a turning point in the history of acoustics. This book pulled together much of the work which had been done in the field of acoustics up to that time, along with a sizeable contribution from Lord Rayleigh himself. This book laid the foundations of the science of acoustics, providing a firm theoretical basis for much of the subsequent work in this field. Ultrasonics is the study of sound with frequencies above those in the audible range. A large number of applications of ultrasonics have been investigated, and many are widely used. These applications include Fault Location (non-destructive testing). Acoustic emission (fault monitoring) Surface acoustic wave signal processing devices. Cleaning. Medical imaging (a version of fault location). Welding. Velocity detectors. It is the first two of these categories with which this work is concerned, i.e. the use of ultrasonics in non-destructive testing. The first category involves the sending out of a pulse of ultrasound, and listening for returned echoes, or the degree of transmission. The second method involves using passive listening devices to detect sounds or shock waves emanating from within the material being studied. This method developed rapidly after work carried out by Kaiser [2] in the early 50's. Both of the methods described above involve the detection of a transient stress wave. This stress wave is detected at a surface, after propagating through the material under study. Early studies of shock wave propagation, were carried out with the aim of trying to interpret the signals from earth tremors and siesmic studies. Confirmation of the -1-

13 theoretical studies was fairly easily carried out at the low frequencies connected with such phenomenon. Confirmation of the theories at the higher frequencies involved in ultrasonics is not as easy. Ultrasonic studies generally require a wider bandwidth of detection. This wider. bandwidth will increase the levels of noise present on the detector output. As the ultrasonic signals are often very weak, the development of transducers has concentrated on resonant types, which have the ability to detect these small signals. These resonant transducers distort the detected signal, making it difficult or impossible to interpret the output [31. It is to the development of transducers which do not possess this drawback, that this study is directed. 1.2 Review of Previous Work. The use of ultrasonics for flaw detection began with the work of Firestone [4,5J. The method used involves projecting a short pulse train of ultrasonic waves into the object. Any signal returned to the transducer represents ultrasound reflected from flaws, irregularities etc. This technique depends on the amplitude and time of travel of the reflected pulse, but does not use the effect of the flaw on the waveform of the reflected pulse train. Recently work has been carried out on analysing the form of the reflected/transmitted pulse [6,7J. This is achieved by excitation of the material with an impulse response, and noting the effect of the flaw on wave propagation. Acoustic emission is the phenomenon of sound generation in a material under stress. The sound is the result of stress relief at a point/points in the material, and the subsequent redistribution of those stresses. Acousticemission is released from a number of sources, such as crack motion in a metal, or the breaking of a fibre in a composite material. By monitoring the acoustic emission one can detect a growing flaw, but not a static one. Therefore acoustic emission can be used as a means of monitoring the dynamic behaviour of cracks and flaws. The stress wave released by the source of acoustic emission, propagates through the material to the surface where it can be monitored. Therefore the detected signal will contain the following information: 1. Rate of acoustic emission. 2. Information about the source of acoustic emission. 3. Information about the medium through which the stress wave has propagated. -2-

14 Initial work in this field concentrated on detecting the rate of acoustic emission. by Mason et al [81. mechanical twinning of tin. One of the first experimental studies was performed The acoustic emission was observed during the studies were then carried out to find a relationship between acoustic emission and applied stress. Kaiser [2] observed that acoustic emission activity did not occur until the material was stressed beyond a particular level. to which the material had previously been subjected. has now become known as the Kaiser effect. This level is the maximum stress This phenomenon Considerable interest has been shown towards the use of acoustic emission for indicating impending failure of a component. Some the failure of fatigue-cracked success has been obtained in indicating specimens [9]. However, the technique is not sufficiently refined to allow unambiguous warning of failure. It is possible to obtain several waveforms from each acoustic emission event by placing an array of transducers around the Source of acoustic emission. These waveforms will be similar in shape, but will be displaced in time relative to each other. By knowing the velocity of sound in the material, it is possible to determine the location of the source of acoustic emission [loj. This technique is well established and a number of commercial instruments based on this principle are available. These systems are often used for assessing the integrity of engineering structures [11]. Recently Costack [12] has used a small array to determine the bearing of a source from a single detector location. All of these systems involve the detection of the acoustic emission. Various attempts have been made to obtain information about the source of acoustic emission from the detected signals [13, l4j. Transducers used for detecting acoustic emission have tended to be developments of the type used in ultrasonic flaw detection work. These transducers are resonant in nature, and pruduce outputs which bear little relation to the input waveform. The output which is produced is highly dependent on the transducer and sample resonances, and is of the form shown in Figure Typical measurements carried out by commercial equipment on the detected signal are shown in Figure These measurements are useful in discriminating between true sources of acoustic emission, and noise sources [15]. However, the relationship between the input and output signals is complicated. Therefore it is difficult to determine -3-

15 rise time : peak amplitude.' rise time-: slope ---. :.;l "" ' ~ -;... HI ringdown counts /1 ~ - - threshold event duration Figure Typical acoustic emission waveform detected with a conventional piezoelectric transducer. amplitude electromagnetic interference response from true signal mechanical noise flow noise o frequency MHz Figure Frequency spectra of noise sources [18]. -4-

16 the true nature of the source from the detected waveform. To obtain information about the source of acoustic emission, or the effect of a flaw on a transmitted pulse, a transducer which will respond accurately to a transient stress wave is required. Theoretical studies of the frequency content of the signals from acoustic emission sources have been carried out by Pao et al [16]. These studies indicate that the signal contains components up to several megahertz. This has been borne out by experimental studies by Wadley and Scruby using a capacitive transducer [17J. Therefore transducers which will produce an output which accurately represents the acoustic emission waveform, will have bandwidths of several megahertz. Birchon [18J investigated the frequency content of signals from nonacoustic emission sources (Figure 1.2.2). These noise sources will interfere with the acoustic emission signal, and will often determine the minimum detectable signal. Birchon found that the mechanical noise rapidly decreased in amplitude above 100 Hz. However, cavitation noise from flowing liquids can have frequency contents up to 2 MHZ. Therefore it is necessary to use high pass filtering to remove the noise from the ultrasonic signals. Transducers used for detecting acoustic emission usually use a piezoelectric crystal as the sensing element. Theoretical models of the operation of such transducers have been developed [19, 20J. These models have been used to optimise the response of the transducer, to the ultrasonic signal returned from a flaw. This has lead to transducers which are very sensitive to ultrasonic stimuli, but which only respond over a narrow bandwidth. Therefore this type of transducer is well suited to locating sources of acoustic emission. However, they are not suitable for determining the waveform of an ultrasonic pulse returned from a flaw, or of an acoustic emission signal. Accurate representation of transient stress waves, can be achieved by using thick crystals of piezoelectric material with low resonant frequencies [21J. However, the length of pulses which can be detected in this way, is limited to the transit time of the piezoelectric block. Large diameters of piezoelectric crystal ('15mm) are needed to provide adequate sensitivity. This severely limits the bandwidth, except when it is used directly opposite the emission source. For practical -5-

17 reasons it is not usually possible to operate in this epicentre mode. Therefore a detector with a small frontal area is required to give an accurate response to surface acoustic waves. A transducer which possesses these properties has been described by Proctor [22, 23]. This transducer, Figure 1.2.3, uses a conical piezoelectric sensing element. This arrangement avoids mechanical resonances of the piezoelectric element, and gives the transducer a fairly flat response up to 1 MHz (Figure 1.2.4). The transducer is simple to construct. However, it is limited to operating on near horizontal surfaces, which has limited its range of applications. It is well suited for use as a secondary standard and other laboratory work, but is not very suitable for use on engineering structures. The design has been adapted to enable this form of transducer to be used in any orientation [24J. A spring is used to load the sensing element onto the surface, instead of relying on gravity. However, the lifetime of the transducer is reduced each time the transducer is detached and replaced On a surface [23J. In the case of a spring loaded transducer, a change in calibration is usually noted after a couple of uses in new locations. The frequency response of these transducers is limited by the area in contact with the surface. Unfortunately the area cannot be reduced to extend the response to surface waves up to 10 MHz, as this will increase the pressure on the tip to unacceptable levels. An alternative detection method is to use the inverse magnetostrictive effect [25J. This effect has been used for ultrasonic transducers, and its suitability for detecting acoustic emission has recently been assessed [26J. Practical considerations usually necessitate the need for a waveguide made from a material with a high magnetostrictive coefficient. The diameter of this waveguide will restrict the bandwidth of response to surface waves. In addition the extended area of interaction of the stress wave with the detection coil, limits the frequency response to around 4.4 MHz [26J. One detection method which offers the possibility of very wide bandwidth detection, is capacitive sensing. A number of groups have investigated the use of capacitive transducers for detecting acoustic emission [27, 28, 29]. Capacitive sensing is essentially an electrical -6-

18 output ampl,ifier brass backing \ \ nylon skirt piezoelectric sensing element I conductive sample Figure NBS transducer [22J. magni tude db (ref lv/m) Figure frequency MIlz Frequency response of NBS transducer [22J. -7-

19 detection method, so is free from the mechanical resonances associated with the previous detection methods. In addition the output from such sensors is capable of being calibrated in terms of absolute displacement. However, the relatively large diameters of electrode used (typically 6mm), limits the bandwidth of response when used to detect surface waves. A capacitive transducer with a point like a probe has been developed to overcome this' limitation [30}. However, such a transducer requires highly polished surfaces, and the ability to maintain the electrode! surface spacing constant to within a few hundred nanometres. This limits the instrument to operation in a controlled laboratory environment, on carefully prepared test specimens. A detection method which offers a number of advantages, is optical detection. By using a beam of light as the probe, the detector is not in contact with the surface at the point of study. Therefore the detector will not disturb the propagation of ultrasonic waves. This non-contacting nature also offers the possibility of scanning the sample, or the study of rotating components. AS sensing is performed by a photodetector, the response of the transducer is not dominated by mechanical resonances. The transducer response can be designed to meet. particular requirements of bandwidth, by using the appropriate design of photodetector. Optical detection methods which are based on interferometry, offer the advantage of being able to measure the movement of a surface in units of displacement. This feature makes it suitable for quantatative studies of ultrasonic signals. It is also useful for calibrating other forms of transducer. Interferometric techniques have been used by a number of workers to measure the movement of surfaces. Large scale movements (>l~m) are measured by counting the passage of interference fringes past a point [31]. This technique is well established, and commercial instruments which use it are available [32J. As the expected surface displacements are of the order of Inm, such systems do not have sufficient sensitivity. A Michelson interferometer with a minimum detectable displacement of 3pm has been developed by Kahanna and Tann [33J. The bandwidth of this system (20 Hz - 20 KHz) is insufficient for ultrasonics work. The -8-

20 sample and interferometer are mounted rigidly on a granite block. This obviously limits the applications to which such a device can be put. An additional limitation is that it must be operated in an acoustically quiet environment. Studies have been carried out into the possibility of using an interferometer to detect the ultrasonic pulses from acoustic emission sources [34, 35J. These studies used a Michelson interferometer, which is actively stabilised against low frequency environmental disturbances (Figure 1.2.5). This device uses bandwidths up to 6MHz, and has a minimum detectable displacement of 5Opm. The interferometer was used to study several types of acoustic emission events (Figure 1.2.6). However, these measurements were taken with the sample securely clamped [35 J Therefore the environmental vibrations were minimised, reducing the requirements of the stabilisation system. An interferometric method which is capable of monitoring small high frequency signals in the presence of large low frequency vibrations, is quadrature interferometry. An interferometer of this type has been describeq by Vilkomerson [36J. This device was used to monitor ultrasonic pulses many cycles in length. It could also be used to measure transient pulses. Therefore, a quadrature interferometer should be suitable for making quantatative measurements of the stress wave released by acoustic emission SOurces. It could also be used for quantatative measurements of other ultrasonic phenomenon. As well as a device for the wide bandwidth detection of acoustic waveforms a system for quantatatively assessing the results is required. Conventional acoustic emission instrumentation measures various parameters of the transducer output, such as peak amplitude, event duration, etc. [15] (Figure 1.2.1). These measurements are very dependent on the properties of the transducer. Therefore this method does not provide sufficient information to determine the true nature of the acoustic waveform. other methods of analysing acoustic waveforms have been investigated [37, 38J. These studies used conventional acoustic emission transducers, and measured properties such as frequency content. The analysis is performed on digitised detector outputs using a specialised software system -9-

21 DETECTOR ~. SPECIMEN M.O. S I I ~c BEAM EXPANDER ~, ~,, ~. M. ~ /,p PIEZO ORIVE Figure stabilised Michelson interferometer [35J. optical,\ ~ I transducer J ~. Piezoelectri=-~ fi transducer ~ \I ~~ , ~.. tt-+++~_..., I f horizontal 50~S/div Figure Real acoustic emission waveforms in indium [35J. -10-

22 written for this purpose [39J. The analysis techniques applied by this system were used to discriminate between different types of acoustic emission source. 1.3 Aims of the study The considerations in the previous section lead to a project with a number of different aims. These aims include: i) Development of optical interferometric sensors. These sensors needed to be capable of detecting displacements of Inm, at frequencies up to 10 MHz. Also they would be expected to operate in conditions typical of a non-destructive testing facility. ii) Development of a signal analysis system. This system would be required to take the output from the above sensors, and provide the operator with quantatative information about their performance. iii) Use of the optical sensors and the signal analysis system to study ultrasonics and acoustic emission. This work would include the study of artifical sources of acoustic emission, and the development of ultrasonic transducers. -11-

23 2., STABILISED INTERFEROMETRIC DETECTOR 2.1 Methods of Interferometer Stabilisation As stated in the previous chapter, optical interferometric sensors possess a number of advantages over conventional ultrasonic detectors. A correctly designed interferometric sensor will produce an output which is an accurate representation of the ultrasonic waveform. For quantatative studies of ultrasonics, a detector which is capable of producing an absolutely calibrated output is required. Thus an interferometric sensor would form an important part of a system for studying ultrasonic waveforms. Interference is the combination of two or more waves. This process forms a resultant wave which depends on the amplitude and phase characteristics of the constituent waves. Optical interferometers can be split into two categories. 1. Wave front splitting interferometers. 2. Amplitude splitting interferometers. Wave front splitting interferometers were the first type of interferometer to be devised. This category includes devices such as Young's slits, Fresnel's biprism, and Lloyd's mirror. However, such devices suffer from disadvantages such as high light loss, which limits their practical application. One of the simplest forms of amplitude splitting interferometer is the Michelson interferometer [40] (Figure 2.1.1). The incident light is split by a beam splitter, which usually consists of a partially reflecting film on a glass plate. A compensating plate is sometimes placed in one of the interferometer arms, to make the passage through glass and air equal in'each arm. This is important when the,light is not monocromatic. The need to do this is avoided if a cube beam splitter is used. The light is reflected off the two mirrors m and m, and interferes on the l 2 surface of the beam splitter. This interference pattern may be observed or detected at A. An interference pattern which is out of phase (due to the phase change on reflection at a boundary), is sent back along the path of the incident light. The Michelson interferometer has the advantage that it is simple to construct, and the various optical components are easily accessible. A number of other geometries of interferometer exist [40J, each of which -12-

24 compensating plate mirror \ incident m ~~~~--~~~--~ 1 light A Figure Arrangement of Miche1son Interferometer. intensity phase difference ~ Figure Variationbf Intensity with Phase Difference. -13-

25 has particular advantages and disadvantages. However, all these forms of interferometer are based on the principles inherent in a Michelson in terferometer. Expressions for the interference of two beams of light are given in a number of publications [41, 42J. These give the intensity of the resultant interference pattern under certain conditions (constant light frequency, phase, etc.). expression is derived in appendix I. A general form of the interference The intensity produced by interfering two spherically divergent waves, is given by expression 1.11 of appendix I. Response of detector to the resultant of two waves ~ ( where 2.1 A/r and A /r are the amplitudes of the two beams at the l 2 2 point of interference. W l and w are the frequencies of the two beams, with wave 2 numbers (2n/A) of r and r are the distances travelled by the beams from sources l 2 with initial phases of El and E. 2 If the term in the square brackets is denoted by a phase angle ~ (the phase difference between the two beams), then 2.1 may be written as: Response of detector 2.2 As ~ is varied this takes the form of an offset cosine wave as shown in Figure For studying ultrasonic waveforms, the sensor is required to detect the small displacements of a surface resulting from the passage of the ultrasonic wave. These displacements will generally be much less than the wavelength of light [24J. The sensitivity of an interferometer to small surface displacements, is found by differentiating expression 2.1 with respect to a change in r (or r l 2 ). Response of detector to small surface displacements di ~ K 2 dr 1 l

26 Thus the sensitivity is dependent on the value of 0, and varies between -1 and +1. The positions of maximum sensitivity are indicated by A, B and C in Figure Maximum sensi ti vity occurs when I sin [0J I = 1. Thus to maintain high sensitivity 0 has to remain constant, so that this condition is maintained. Unfortunately environmental disturbances often give phase changes of several radians. This would completely mask the small acoustic waves one is trying to detect. It would also move the interferometer from a position of high sensitivity to displacement. Thus it is necessary to use a ~ystem which is stable to, or stabilise. against environmental disturbances. An interferometer which is stable to environmental disturbances, is the differential interferometer (Figure 2.1.3) This differential arrangement has been used by a number of workers [42, 43], to reduce the sensitivity of an interferometer to surface orientation and position. The tw~ beams in a differential interferometer are focussed onto the same surface. As both arms of the interferometer are reflected by the same surface, both beams remain parallel, making it less sensitive to surface alignment. The interferometer is sensitive to the relative surface displacement between the two focal points. Unfortunately this sensitivity varies with acoustic wavelength as shown in Figure However, with the correct design this can result in a wide or narrow bandwidth response. This makes it suitable for detecting signals with restricted bandwidths, but makes it unsuitable for detecting wide bandwidth ultrasonic signals. Various other arrangements of interferometer exist which are capable of detecting surface displacement with high sensitivity. These may be divided into two categories. 1. Heterodyne techniques 2. Homodyne techinques. Heterodyne techniques involve shifting the frequency of light in one of the interferometer arms. The resultant interference pattern varies in intensity at the beat frequency between the two beams. When one of the mirrors in the interferometer moves, light reflected from the mirror is Doppler shifted. This frequency shift will cause a shift in the beat frequency. The shift in beat frequency can be detected, and -15-

27 detector IL...J grating-c] t Cl t Cl t CJ surface being monitored light d Figure lens beam splitter Differential interferometer arrangement. o BW ''''~Il,..'0 ~ ~.'oll----:~, ' " '-- O~ 1.0 I~ 2.0 h.-q~ell(, MM: d = 1/2 A a at 1 MHz i~nnn'~-' 20 ' i:mn '. d = 3/2 A a at 1 MHz d = 5/2 A a at 1 MHz '<>+---~o.:----!::.--.-:':"o,-!=--,'::."-----:-.:-o f q.u-"t~ -..z Figure Variation of sensitivity with frequency [42]. -16-

28 integrated to produce a signal giving surface displacement [44J. Homodyne techniques involve keeping the frequency in the interferometer arms the same. to keep the phase difference (~) The interference expression (expression 2~1) ways. This is performed by various means, in order between the interferometer arms constant. may be interpreted in two One interpretation is that the expression gives a 'snapshot' description of the interference process. The various expressions in the square brackets, give the phase difference between the two beams at a particular instant in time. The change over a period of time, is found by finding the phase at the end of the period, and subtracting from it the conditions at the start of the period. The other interpretation is to consider the expression as a 'dynamic' description of interference. The various terms in the bracket, give the phase difference between the interfering beams at the start of the time period. After this time a change in w, K, r or E will be perceived as a frequency shift at the detector. Thus the (w - w )t term gives the variatiqn of phase I 2 difference with time. If the frequency difference is not constant with time then the above term should be written as an integral. T2 time dependent phase shift ~(t) = f (w I - w 2 )dt. 2.4 It can be shown that this gives identical results to those from the 'snapshot' interpretation. Movement of the mirror in one of the interferometer arms, will Doppler shift the frequency of light in that arm (w ). To keep the I phase difference ~(t) constant with time (expression 2.4), the frequency in the other arm must be shifted by the same amount (homodyne detection). This frequency shifting, or stabilisation may be produced by a variety of techniques. The simplest technique for stabilisation, is to produce an equal Doppler shift in the frequency of light in the other interferometer arm. This is achieved by moving the mirror in this arm, at the same rate as the mirror which is subjected to environmental disturbances. This technique has been used by a number of workers to stabilise an interferometer [34, 45J. This method is used to stabilise against low -17-

29 frequency vibrations due to environmental disturbances. Disturbances due to the signal of interest are outside the bandwidth of stabilisation, and hence are still present on the photodetector output. Another approach to stabilisation, is to change the frequency of light in one of the interferometer arms, by altering the refractive index in that arm. Whilst the refractive index is changing the frequency of light is shifted, by an amount dependent on the rate of change of refractive index. Koyuncu [46] used an electro-optic cell to stabilise a Michelson interferometer in this manner. However, this method can only stabilise against low levels of environmental disturbance. This is due to the limited range over which the refractive index of the crystal can be varied. Jackson et al [47J used the frequency shift caused by a change in refractive index and path length, to stabilise a fibre optic interferometer. This method provides a greater range of stabilisation, as the refractive index changes are produced over long lengths of fibre wrapped around a piezo-electric fibre stretcher. Another approach is to compensate for the Doppler shift in the sample arm, by changing the frequency of light used in the interferometer. The process is most conveniently explained using the 'snapshot' interpretation of the interference expression 2.1. The method involves keeping the term Kl.r - K.r of expression 2.1 constant. If the wave l 2 2 number K is independent of direction, and the same in each arm, then this expression may be written as: Thus if the wavelength is made proportional to the path length difference, the interferometer can be stabilised. Olsson et al [48} used a tunable dye laser, to stabilise an interferometer by this method. An interferometer may also be stabilised by frequency shifting the light in one of the arms of the interferometer. The frequency shift may be applied to the non Doppler shifted beam, so that the frequency of this beam tracks that of the Doppler shifted beam. Alternatively the frequency shift may be applied to the Doppler shifted beam, to return it to its original frequency. This method has been used by Harwell in a versatile interferometer system [32J. The range of environmental -18-

30 disturbances which may be stabilised against is not limited by the stabilising transducer. However, the stabilisation system itself is rather complex and difficult to set up. For detection of the amplitude ultrasonic waves, it would be necessary to stabilise the interferometer. Each of the above methods have particular advantages and disadvantages. For the building of a small interferometric sensor, stabilisation by moving the reference mirror was selected as being the most suitable. This method allows the construction of a simple stabilisation system, without the bulky optics required by some of the other methods. 2.2 Design of the Miniature Interferometer. One of the first requirements of the project, was the design and construction of a miniature stabilised interferometer. This interferometer was to be used for the quantatative study of acoustic emission. Previous interferometric systems for studying acoustic emission had tended to be big and bulky [34J. limited the range of practical applications. The large size of these interferometers had Miniaturisation of such a device would make it portable, and thus applicable to a wider range of situations, such as those not found in the laboratory environment. A stabilised interferometer system had been developed at Loughborough This instrument was based on a Mirau, or Fizeau in line inter-, ferometer, using a 1:j5 mm camera lens (Figure 2.2.1). A mirror mounted on a piezoelectric crystal, was used to stabilise the interferometer against vibrations experienced on an optical bench. miniaturise this instrument. The aim of the work was to It was also to be capable of operating in environments other than those experienced on an optical bench. A microscope objective containing a Mirau interferometer is available from Vickers Instruments Ltd. [50]. This contains all the optical components for a Mirau interferometer in an objective 48 mm long, and 23 mm in diameter. interferometer system. This would form an ideal interferometer head for a miniature Unfortunately, the reference mirror of the interferometer lies in the centre of the focussing lens (Figure 2.2.1). Therefore to stabilise the interferometer, a stabilising transducer has to be placed in the centre of this lens. A stabilising transducer placed Alternatively the interferometer could be stabilised by in this position would block out most of the light entering the interferometer. -19-

31 incident light detector mirror c::::::!~±=f=:::l-beam sp li t ter Figure 2.2_1 Mirau interferometer arrangement. cube beam splitter frosted face object -H--II Figure 2_2.2 bimorph stabilising transducer Michelson interferometer objective_ - -' r T ~nterferometer head Figure ~detector '/ A V - /f V f'\ - beam beam laser sphtter expander Arrangement of miniature interferometer. -20-

32 moving the objective relative to the sample surface. However, the relatively high mass of the objective would make such an approach difficult. Thus the Mirau microscope objective was not suitable for use in a miniature interferometer. Vickers Instruments also manufacture interference objectives based on a Michelson interferometer configuration. As the reference arm of such an interferometer is off axis, it is accessible for placing a stabilising transducer in (Figure 2.2.2). The complete objective is 47 mm long and 35 mm in diameter, so could form a miniature interferometer head. To provide an electrical output from the interferometer, a photodetector is usually placed in the remaining arm of the interferometer. Unfortunately the output face of the cube beam splitter used in the objective is frosted (Figure 2.2.2). Thus it was not possible to use a photodetector at the output from this arm of the interferometer. In the miniature interferometer, the arrangement shown in Figure was used. This enabled a photodetector output to be obtained. However, this method has the disadvantage that the intensity of light at the photodetector, is 1/4 of that in a conventional Michelson arrangement. In addition to the interferometer head a source of light is required. Low power (~ 1 mw) Helium Neon gas lasers are in the region of 30 cm in length, and 5 cm in diameter. Thus such a light source would be much larger than the interferometer head. The use of a solid state light source would allow the size of the complete instrument to be reduced considerably. Solid State lasers tend to have wide line widths, due to the high current densities needed to produce lasing action. In addition the majority of devices originally available were for pulsed operation, and thus unsuitable for continuous operation. Some edge emitting LED's were obtained which did not possess these limitations. These operate around 800nm, with a linewidth of approximately 40nm [51}. As this is in the infra red region of the spectrum, it would not be visible. Experiments with a video camera system, showed that it is possible to observe the distribution of light from the LED. Thus it would be possible to set up the interferometer using the camera system. A possible restriction on the use of such devices is their coherence length. The coherence length would determine the accuracy to which the interferometer has to be aligned, and the path lengths made equal. -21-

33 ,,2 Coherence length 6X = 6" [s2j where " is the wavelength of light and 6" is the linewidth. of 16 llm. For the LED's used this gives a coherence length This is too small for practical use, so a Helium Neon gas laser was used as the light source. Recent developments have lead to CW semi conductor lasers, with linewidths of 0.01 nm at 840 nm becoming available Is3]. This would give a coherence length of 70 mm, which would allow their use in a wide variety of interferometer systems. As an alternative to making the source of light small, the light can be channelled to the interferometer head from a remote light source using fibre optics. This would have the advantage that the relatively fragile gas laser can be remote from any vibrating object. However, multimode fibres do not preserve the coherent properties of the laser light, and produce a speckle pattern at the output. Monomode fibres at 633 nm are difficult to obtain, and coupling of light into these fibres difficult to achieve. This would lead to large power losses on coupling light into the fibre, so this approach was not used. Instead the interferometer head and a Helium Neon gas laser were used to produce the interferometer system (Figure 2.2.3). 2.3 Fundamentals of the Feedback System As was shown in Section 2.1, in order to obtain constant high sensitivity to surface displacement it is necessary to stabilise the interferometer. This is achieved by using some form of feedback system to keep the path length difference between the interferometer arms constant. Therefore before designing a stabilisation system some consideration of the principles of feedback is required. A feedback control system is a combination of elements which cooperate to maintain a physical quantity termed the output, approximately equal to an ideal output that is related to other physical quantities termed inputs [54]. For stabilising the interferometer the feedback system should keep the mirror spacing approximately constant, when subjected to various environmental disturbances. The block diagram of a simple feedback system is shown in Figure The output of the system C(s) is the response of a system with a transfer function G(s) to a signal E(s). The signal E(s) (error signal) is in turn derived by subtracting the feedback signal F(s) from the input signal -22-

34 R (s) E (sl c (s) G (sl F (sl H(sl Figure Basic feedback control system. beam spli tter, /, IL,,,, re ference mirror s tabilising t ransducer Figure T (jw) A(jw) < amplifier Interferometer feedback control system. R \...,...1 photodet ector Im increasing frequencies -1.0 Re negative frequency Figure Locus of function in the complex plane. -23-

35 R (s) This feedback signal is derived from the output C(s) via feedback components with a transfer function H(s). In a stabilised interferometer the output signal C(s), is the position on an interference fringe. This output is the response of the optical system to the relative mirror spacing (all other factors being assumed constant). This relative mirror spacing is the difference between the sample mirror position R(s), and the reference mirror position F(s). The reference mirror is driven by feedback components, which complete the feedback control system. The feedback components will consist of a photodetector, electronic amplification and stabilising transducer (Figure ) From Figure one can write the following expressions [SSJ: C(s) = G(slE(s) F(s) = H(s)C(s) E(s) = R(s) - F(sl Substituting for F(s) in 2.7: E(s) = R(s) - H(s)G(s) Using this to substitute for E(s) in 2.5: C(s) = G(s)R(s) - G(s)H(s)C(s) Rearranging C(s) (1 + H(s) G(s» = G(s)R(s) or C(s) G(s) R(s) = 1 + H(s)G(s) 2.8 This is called the closed loop transfer function, and relates the output signal to the input. Expression 2.8 gives performance for large disturbances of the system. If the system is stabilised only small disturbances of the system will occur. One can derive a similar expression to expression 2.8, to give the response to small disturbances. The optical transfer function for large disturbances has the form [S6J: C(s) = I = PCl(l + C cos [ 4~D )) = G(s)E(s)

36 where I is the intensity of the interference pattern. p is the intensity of light entering the interferometer. Cl is an attenuation factor due to light losses. C is a contrast ratio, to take account of the unequal intensities in the interferometer arms (see Appendix I). D is the relative displacement of the interferometer mirrors. The optical transfer function for small disturbanc~s is found by differentiating this expression c(s) III p C411 S. [ e(s) = LID = ClT ~n 411D 1 -A- = g(s) 2.10 If the small signal response of the feedback components is denoted by h(s), then the small signal closed loop transfer function is C(s) g(s) res) = 1 + h(s)g(s) 2.11 For the output to be independent of the input r(s), the closed loop transfer function is required to be zero. is determined by the physics of the optical arrangement. The transfer function g(s) This will only be zero (insensitive to mirror movement) at the top and bottom of an interference fringe. However, as these positions are insensitive to surface displacement, one would not wish to stabilise at these points. Alternatively the closed loop transfer function can be made zero by making h(s) infinite. possess infinite gain. input to some extent. from the ideal stabilised output. However, practical feedback components do not Thus the output will always be dependent on the This dependency takes the form of a deviation The deviation, or error is due to the finite gain of the feedback components, and may be reduced by increasing the gain of the feedback components. In practice the transfer functions in the feedback control system are dependent on frequency. expression 2.10 is not dependent on frequency. The optical transfer function given by However, the feedback function h(s) will be dependent on the frequency response of the photodetector, amplifier and stabilising transducer. expression 2.11 as: Thus one may write c (j w ) = -=----.:g:!,-:-:--: r(jw) 1 + gh(jw)

37 If gh(jwl 1>1 then the gain of the system is reduced by the feedback, i.e. negative feedback. If 11 + gh(jw) 1<1 the gain of the system is being increased by positive feedback. If a frequency exists at which gh(jw) = -1, then the closed loop transfer function (expression 2.11) tends to infinity. This is an unstable situation and the system will oscillate. The product gh(jw) is a complex number, which will vary with frequency. If this product is plotted on the complex plane as frequency varies, a curve is traced out (Figure 2.3.3). The Nyquist stability criterion [57J states that if this curve encloses the point -1 + jo, then the system is unstable. An alternative way of stating this is, in order for a system to be stable, when the phase shift of gh(jw) becomes 180 0, the gain of the system Ih(jw)gl must be less than 1. The optical transfer function is given by expression The response of the feedback components is formed by the product of the responses of the individual feedback components (Figure 2.3.2). h(jw) = R A(jw) T(jwl 2.13 where R is the responsivity of the photodetector (volts per unit power), and is assumed to be independent of frequency. A(jw) is the small signal response of the amplifiers (which may contain filtering). T(jwl is the small signal response of the stabilising transducer (displacement per volt) which will be frequency dependent. The product h(jw)g is formed by combining expressions 2.10 and h(jw)g = pete ~1T Sin ( 4~D JR A(jW)T(jw) 2.14 For stability the locus of this expression in the complex plane must not enclose the point -1 + jo. The last two terms are frequency dependent, the preceding terms acting as constant multipliers. It is the last two terms which determine if the feedback becomes positive. Thus these two terms are important in determining the stability of the system. The factor A(jw) can be controlled by careful design of the electronic amplification system. Thus, it is necessary to find the response of -26-

38 the stabilising transducer T(jw), to determine the stability of the feedback system. 2.4 Vibration Level Measurements. The final interferometer was required to operate in a normal bench type environment, rather than on a stable optical bench. To determine the requirements,of a stabilising transducer, measurements were performed to find the vibration levels encountered on a normal laboratory bench. These measurements were performed using a quadrature interferometer, which rested on an aluminium block placed on the bench. As this is an unstabilised interferometer, observation of the change in the interference pattern gives information relating to the vibration levels experienced. A technique described in section 4.7 was used to calculate the surface displacement. This method combines the quadrature outputs, to produce an output waveform directly scaled in units of displacement (Figure 2.4.1). These measurements were carried out for various levels of environmental disturbance. 'For the interferometer resting on an undisturbed bench (Figure 3.4.2), vibrations around 50 nm in amplitude were observed. These 'vibrations' consist of path length changes caused by low frequency ('20 Hz) atmospheric disturbances. Superimposed on these variations is a smaller loo Hz component, due to mechanical hum from the equipment resting on the bench. The vibration levels observed with moderate disturbances of the bench are shown in Figure This consists of a sinusoidal vibration with an amplitude of around 600 pm at 75 Hz. This appears to be the natural frequency of the bench/interferometer combination. The vibrations observed with heavy disturbances of the bench are shown in Figure This is again in the region of 75 Hz, but with an amplitude of 2500 nm. It should be noted that these measurements determined the vibration levels observed over a time period of 40 ms. It is possible that in the long term much larger changes in path length are possible. The output was observed after the interferometer had been allowed to settle for an hour. This indicated that the path length drift over a period of several minutes, was negligible in comparison with the vibration levels observed above. -27-