Thickness measurement of coatings and characterization of surfaces with surface waves - Part 2: Guide to the thickness measurement of coatings by photothermic method

This document describes methods for the measurement of the thickness of coatings by means of thermal waves generated by a radiation source.
The method can be used for coatings whose thermal properties (e.g. thermal conductivity) are different from those of the substrates in a range from a few microns to some hundred microns.

Schichtdickenmessung und Charakterisierung von Oberflächen mittels Oberflächenwellen - Teil 2: Leitfaden zur photothermischen Schichtdickenmessung

Dieses Dokument legt ein Messverfahren fest, das eine Werkstoffprüfung mittels Wärmewellen erlaubt, die durch eine Strahlungsquelle erzeugt werden.
Das Messverfahren kann bei Beschichtungen angewendet werden, deren thermische Eigenschaften (z. B. Wärmeleitfähigkeit) sich von denen des Substrates unterscheiden, in einem Messbereich von einigen µm bis einige hundert µm.

Mesure de l'épaisseur des revêtements et caractérisation des surfaces à l'aide d'ondes de surface - Partie 2 : Guide pour le mesurage photothermique de l'épaisseur des revêtements

Le présent document décrit des méthodes de mesurage de l’épaisseur des revêtements à l’aide d’ondes
thermiques produites par une source de rayonnement.
La méthode peut être utilisée pour les revêtements dont les propriétés thermiques (par exemple, la
conductivité thermique) diffèrent de celles des substrats pour une plage d’épaisseur comprise entre quelques
microns et plusieurs centaines de microns.

Merjenje debeline nanosa prevlek in karakterizacija valovitih površin – 2. del: Vodilo za merjenje debeline prevlek s fototermično metodo

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2003-01.Slovenski inštitut za standardizacijo. Razmnoževanje celote ali delov tega standarda ni dovoljeno.Thickness measurement of coatings and characterization of surfaces with surface waves - Part 2: Guide to the thickness measurement of coatings by photothermic methodMesure de l'épaisseur des revetements et caractérisation des surfaces a l'aide d'ondes de surface - Partie 2 : Guide pour le mesurage photothermique de l'épaisseur des revetementsSchichtdickenmessung und Charakterisierung von Oberflächen mittels Oberflächenwellen - Teil 2: Leitfaden zur photothermischen SchichtdickenmessungTa slovenski standard je istoveten z:EN 15042-2:2006SIST EN 15042-2:2006en17.040.20ICS:SLOVENSKI

STANDARDSIST EN 15042-2:200601-september-2006

EUROPEAN STANDARDNORME EUROPÉENNEEUROPÄISCHE NORMEN 15042-2April 2006ICS 17.040.20 English VersionThickness measurement of coatings and characterization ofsurfaces with surface waves - Part 2: Guide to the thicknessmeasurement of coatings by photothermic methodMesure de l'épaisseur des revêtements et caractérisationdes surfaces à l'aide d'ondes de surface - Partie 2 : Guidepour le mesurage photothermique de l'épaisseur desrevêtementsSchichtdickenmessung und Charakterisierung vonOberflächen mittels Oberflächenwellen - Teil 2: Leitfadenzur photothermischen SchichtdickenmessungThis European Standard was approved by CEN on 2 March 2006.CEN members are bound to comply with the CEN/CENELEC Internal Regulations which stipulate the conditions for giving this EuropeanStandard the status of a national standard without any alteration. Up-to-date lists and bibliographical references concerning such nationalstandards may be obtained on application to the Central Secretariat or to any CEN member.This European Standard exists in three official versions (English, French, German). A version in any other language made by translationunder the responsibility of a CEN member into its own language and notified to the Central Secretariat has the same status as the officialversions.CEN members are the national standards bodies of Austria, Belgium, Cyprus, Czech Republic, Denmark, Estonia, Finland, France,Germany, Greece, Hungary, Iceland, Ireland, Italy, Latvia, Lithuania, Luxembourg, Malta, Netherlands, Norway, Poland, Portugal, Romania,Slovakia, Slovenia, Spain, Sweden, Switzerland and United Kingdom.EUROPEAN COMMITTEE FOR STANDARDIZATIONCOMITÉ EUROPÉEN DE NORMALISATIONEUROPÄISCHES KOMITEE FÜR NORMUNGManagement Centre: rue de Stassart, 36

B-1050 Brussels© 2006 CENAll rights of exploitation in any form and by any means reservedworldwide for CEN national Members.Ref. No. EN 15042-2:2006: E

EN 15042-2:2006 (E) 2 Contents Page Foreword..............................................................................................................................................................3 1 Scope......................................................................................................................................................4 2 Normative references............................................................................................................................4 3 Terms and definitions...........................................................................................................................4 4 Symbols and abbreviation....................................................................................................................6 5 Foundations of photothermal materials testing.................................................................................6 6 Photothermal measuring methods....................................................................................................12 7 Applications in layer thickness measurements...............................................................................17 Bibliography......................................................................................................................................................22

EN 15042-2:2006 (E) 3 Foreword This document (EN 15042-2:2006) has been prepared by Technical Committee CEN/TC 262 “Metallic and other inorganic coatings”, the secretariat of which is held by BSI. This European Standard shall be given the status of a national standard, either by publication of an identical text or by endorsement, at the latest by October 2006, and conflicting national standards shall be withdrawn at the latest by October 2006.

According to the CEN/CENELEC Internal Regulations, the national standards organizations of the following countries are bound to implement this European Standard: Austria, Belgium, Cyprus, Czech Republic, Denmark, Estonia, Finland, France, Germany, Greece, Hungary, Iceland, Ireland, Italy, Latvia, Lithuania, Luxembourg, Malta, Netherlands, Norway, Poland, Portugal, Romania, Slovakia, Slovenia, Spain, Sweden, Switzerland and United Kingdom.

EN 15042-2:2006 (E) 4 1 Scope This document describes methods for the measurement of the thickness of coatings by means of thermal waves generated by a radiation source. The method can be used for coatings whose thermal properties (e.g. thermal conductivity) are different from those of the substrates in a range from a few microns to some hundred microns. 2 Normative references The following referenced documents are indispensable for the application of this document. For dated references, only the edition cited applies. For undated references, the latest edition of the referenced document (including any amendments) applies. ISO/DGuide 99998, Guide to the expression of uncertainty in measurement (GUM) – Supplement 1: Numerical methods for the propagation of distributions 3 Terms and definitions For the purposes of this document, the following terms and definitions apply. 3.1 amplitude of the thermal wave

∆∆∆∆T0

maximum local temperature variation of the oscillating part for periodic-harmonic heating processes NOTE See Equation 2. 3.2 penetration depth of thermal waves depth at which the temperature variation below a modulated heated surface is still measurable. NOTE In general, the penetration depth is of the order of magnitude of the thermal diffusion length 3.3 modulation frequency

f frequency at which the intensity of the heating radiation varies periodically 3.4 phase (phase shift) of the thermal wave

∆ - measure of the temporal delay of the temperature oscillation relative to the excitation for periodic-harmonic heating processes NOTE See Equation 3. 3.5 photothermal efficiency

η proportion of the incident radiation intensity that is converted into heat NOTE

In most technical applications it is approximately identical to the absorption.
EN 15042-2:2006 (E) 5 3.6 thermal diffusion length

µ characteristic length of the thermal diffusion with pulsed heating or periodically modulated heating, where the temperature amplitude has decreased to about 1/e or 37 %

NOTE 1 1/e, with natural number e = 2,71828. NOTE 2 See Equation 4. 3.7 thermal diffusion time

τ characteristic time that a thermal wave or a temperature pulse requires for penetrating a layer of finite thickness NOTE See Equation 7. 3.8 thermal diffusivity

α thermal parameter characterizing heat propagation in a body with time-dependent heating NOTE See Equation 6. 3.9 thermal effusivity

e thermal parameter determining the surface temperature of a body with time-dependent heating NOTE See Equation 5. 3.10 thermal wave spatiotemporally variable temperature field that is set up in a body (or medium) with time-dependent heating and is described by the heat conduction equation NOTE 1 see Equation 1. NOTE 2 The thermal wave is generated in one limiting case by a periodic-harmonic excitation, in the other limiting case by a pulsed excitation. 3.11 thermal reflection coefficient

Rls

thermal parameter that is a degree of the reflection of the thermal wave at the boundary interface between two layers of different effusivity and thus describes the heat transfer across this boundary interface NOTE See Equation 8.

EN 15042-2:2006 (E) 6 4 Symbols and abbreviation

Symbol Unit Description See Equation ∆T(x,t) K amplitude of the temperature oscillation of the thermal wave 1 ∆T0(x) K amplitude of the temperature oscillation of the thermal wave at the surface (x = 0) 2 ∆ -

rad phase of the temperature oscillation of the thermal wave

3 µ m thermal diffusion length 4 e Ws1/2/(m2K) thermal effusivity 5 α m2/s thermal diffusivity 6 τ s thermal diffusion time 7 F0 W/m2 heat flow/excitation power density 7 η

photothermal efficiency
k W/(m⋅K) thermal conductivity
12 ρ Kg/m3 mass density 13 c J/(kg⋅K) specific heat capacity
13 f s-1 modulation frequency
i0 W/m2 incident radiant power density
2 x m location below the boundary interface
t s time

5 Foundations of photothermal materials testing 5.1 Physical foundations 5.1.1 Thermal waves The concept "thermal wave(s)" describes a spatially and temporally variable temperature field that is generated in a body by time-dependent heating. Besides the concept thermal wave the term "temperature wave" is also used in technical literature. The excitation of the spatiotemporally variable temperature field mathematically described by a diffusion equation - the heat conduction equation - can occur in the one limiting case periodic-harmonically and in the other limiting case pulsed.

The physical foundations [1], [5], [6], [7] can be derived both for the harmonic excitation and for the pulsed excitation, and are related by a Fourier transformation. This clause considers primarily the harmonic excitation; the derivation for the pulsed excitation can be found in [8].

EN 15042-2:2006 (E) 7 An example of thermal waves observable in nature is the temperature distribution in the ground. This distribution is dependent on the time of day and year, with the daily variation in temperature reaching a penetration depth of nearly 30 cm and the variation in the course of the year penetrating up to several meters [9]. The example of thermal waves [10] excited by the harmonic-periodic and large-area irradiation of homogeneous, semi-infinite bodies absorbing only at the surface, can be used to describe the most important properties of thermal waves and to identify the physical variables and parameters that are measurable by means of thermal waves during materials testing. ()()()()xftxTtxTφ∆π∆∆+⋅=20cos, (1) NOTE Terms are defined in Clause 4. ()()µπη/exp200xfeixT−=∆ (2) ()4πµφ−−=∆xx (3) fηαµ= (4) The amplitude of the thermal wave (Equation 1) decreases exponentially with the depth, if the heated surface is taken to be x = 0. The measurable penetration depth has the order of magnitude of the thermal diffusion length µ. Conditioned by the frequency-dependency of the thermal diffusion length µ (Equation 4), the penetration depth can be adjusted by precisely varying the modulation frequency f of the heating. The amplitude of the thermal wave ∆T0(x) (Equation 2) and the phase shift ∆φ(x) (Equation 3) depend on the following thermal properties:

The thermal effusivity (thermal penetration coefficient), e, is given by the equation:

ckeρ= (5) and the thermal diffusivity, ., is given by the equation: ()ckρα= (6) Accordingly, frequency-dependent measurements of the amplitude and phase of the thermal wave provide depth-resolved information on these combined thermal parameters. In Equations (5) and (6), k is the thermal conductivity, ρ the mass density and c the specific heat capacity. The amplitude of the thermal wave measurable at the surface is proportional to the photothermal efficiency η, which specifies the proportion of the incident radiant power converted into heat. With layered systems the amplitude and the phase shift of the temperature oscillation are determined on the one hand by the ratio of the thermal effusivity of layer and substrate elayer/esubstrate, and on the other hand by the thermal diffusion time for the layer: layerlayerlayerlατ2= (7)

EN 15042-2:2006 (E) 8 where
llayer
is the geometrical thickness of the layer; .layer

is the thermal diffusivity of the layer. Given a known value of the thermal diffusivity of the layer and a sufficiently large thermal contrast, describable according to [11] by the thermal reflection coefficient:

substratelayersubstratelayerlseeeeR+−= (8) contactless and non-destructive layer thickness determination is possible by means of thermal waves (see Clause 6). 5.1.2 Thermal Properties The significance of the thermal effusivity and the thermal diffusivity can be made especially clear by means of special time-dependent heating (step function). According to [12], the thermal effusivity e (Equation 5) is a measure of the time-dependent heating of a surface: ()teFtxTπ02,0==∆ (9) where F0 is the constant heat flow absorbed at the surface and ∆T(x = 0,t) represents the heating of the surface at time t after the start of heating. The thermal effusivity determines the contact temperature between bodies and layers having different thermal properties. An example is the contact temperature: ()()212211eeTeTeTcontact+⋅+⋅= (10) occurring at the boundary interface between two semi-infinite bodies having different thermal effusivity e1 and e2 and different initial temperatures T1 and T2, after these bodies have been brought into contact with one another. The thermal diffusivity α (Equation 6) is a measure of the propagation of the temperature through a homogenous body:

()()=∆=−=∆∫txtxTtttxeFtxTαπαπ4,0''/'4exp,020ierfcd (11) Given measurements of the thermal effusivity and thermal diffusivity by means of thermal waves, the heat conductivity and the heat capacity per unit volume can be determined using Equations (5) and (6): ek⋅=α (12) ()αρec= (13)

EN 15042-2:2006 (E) 9 Here it shall be kept in mind that with Equations (12) and (13) effective parameters shall be determined for the actual test object that include the influence of porosity, surface roughness and anisotropy on the heat transfer [13]. 5.1.3 Thermal depth profiling The thermal diffusion length µ (Equation 4) is a measure of the penetration depth of the thermal wave. Since the thermal diffusion length and hence the penetration depth can be varied via the modulation frequency of the heating, a depth-resolved measurement of thermal properties is possible. The resolution limits basically depend on the thermal contrast of the individual layers, on the detection procedure used and on the technical quality of the detectors. 5.1.4 Measurable variables and possibilities of measurement In principle, thermal waves can be used to measure any physical variable that affects the heat transfer and temperature distribution in a body, i.e. the spatial distribution of the thermal effusivity and of the thermal diffusivity or the layer thickness in layered systems with different thermal properties. Accordingly, it is possible to measure directly or infer other characteristic data, such as the hardness of metallic materials, porosity and moisture in solid bodies, if these variables affect heat transfer properties. In these cases, however, the correlation of, for example, the porosity, moisture [13], [14] or hardness [15] with the effective thermal properties shall be determined through calibration. Optical variables, such as the photothermal efficiency η and the absorption coefficient β for electromagnetic radiation, which affect the intensity and depth profile of the heat sources can also be determined. In addition, the processing and modification of technical surfaces (e.g. by plasma etching, ion implantation, heat treatment, machining, friction wear, etc.) can be determined by means of thermal waves, if these surfaces have a measurable reactive effect on the optical or thermal properties. Using photothermal methods of measurement facilitates on the one hand quantitative determination of the features of the test object, such as coating thickness, thermal diffusivity, thermal effusivity, absorption coefficient, adhesion of layers or cracks, etc. On the other hand, monitoring of the production process, such as uniform coating thickness or implantation dose is possible.

For the surface study of test objects, thermal imaging methods are used; here, thermal waves are used pointwise to form a surface raster, or in the case of large-area modulated heating, to make time-dependent recordings with an IR camera. 5.2 Structure of a photothermal measuring system A photothermal measuring instrument comprises components to carry out the following functions: excitation, detection and measured value processing. As a rule, the measurement data are compared with calibration data, so that quantitative statements on deviations in the production process or on deviations from the desired functional properties can be made. The only requirement on the test object (besides optical accessibility) is the supply of energy (through the absorption of radiation, for example) and its conversion into a detectable form (by increasing the thermal radiation to the level of IR detection, for example). The detectable signals (amplitude and phase) then provide information on material properties and/or their modifications in layers near the surface. Figure 1 shows one possible way of integrating a photothermal measuring system in a production line or in the production process. Feedback coupling serves to control the production process and ensure the functional properties of a component. As a non-destructive and contactless procedure, thermal waves are suitable for testing materials and components. They can be used as an on-line measuring procedure for production monitoring and quality testing.

EN 15042-2:2006 (E) 10 Key 1. Blank raw material 2. Production process 3. Material flow 4. Photothermal measuring system 5. Excitation system 6. Application in subassembly 7. Product 8. Test object 9. For materials testing 10. Detector system 11. Measured value processing including comparison with calibration data 12. Process control 13. Diagnosis 14. Functional property 1234576891011121314 Figure 1 — Block diagram with the components required for photothermal materials testing

5.3 General information on measuring methods with thermal waves Common to all photothermal studies is the precise periodic or pulsed introduction of a quantity of heat into a test body and the detection of local heating. Because of their special properties, light sources are especially suitable for efficient excitation (i.e. heating) of the test object. In the following, therefore, the optical excitation is considered to exemplify the possible ways of introducing heat into the test object.

The various photothermal methods of measurement differ in the temporal structure of the excitation and in the manner in which the thermal response is measured (e.g. surface temperature, heat flow or changes of other physical effects). In the case of periodic-harmonic excitation, the amplitude and phase are registered as accessible variables. In the case of pulsed excitation, the temporal development of the temperature is determined. As shown in Figure 2, the introduction of thermal energy (excitation) in areas near the surface of a test object leads to a series of effects that directly or indirectly can be used for testing material properties. These effects include the thermal and acoustic waves emitted at the surface of the test object and in the surrounding medium, increased thermal radiation, deformation of the surface, modification of the reflectivity as well as changes in the magnetic, electric and dielectric properties.

EN 15042-2:2006 (E) 11 Key 1. Heat radiation 2. Modulated excitation source 3. Acoustic waves 4. Thermal waves 5. Surface absorption 6. Volume absorption 7. Acoustic waves 8. Sample 9. Thermal waves 10. Surface deformation 12346789105 Figure 2 — Interaction of radiation with the material as the basis for photothermal materials testing

The introduced heat is diffused through the test object, causing changes in temperature, the propagation of which through the interior of the material can be described by Equation (1). The diffusion process itself depends on the thermal properties of the material and is described in terms of the thermal diffusivity α and the thermal effusivity e, which can be computed from the thermal conductivity k, the heat capacity c and the density ρ of the material according to Equations (5) and (6).

Owing to the severe damping, the amplitude of the temperature oscillation in the material depth strongly decreases. This feature is described by the thermal diffusion length µ (Equation 4). For measuring techniques with thermal waves, the thermal diffusion length µ approximately and intuitively describes the range in which information from the interior of the material is contained in the surface temperature. The characteristic feature of this form of materials testing thus lies in changing the thermal diffusion length through the selection of the modulation frequency (compare Figure 3). This provides an overview of the photothermally accessible measuring range. Key X Thermal diffusion length, µ [m] Y Frequency, f, [Hz] 1. 1 Ag, Cu, Al, Si,

SiC, Zn,
Cr, air, steel Si3N4 2. Silica, ceramics 3. PE, water, paint

10-310-410-510-11101021031014123XYFigure 3 — Diffusion length as a function of the frequency (data from [17]; further data can be found in [18] and [13])

In the case of pulsed excitation, the measurable depth range basically depends on the time delay of detection following excitation.

EN 15042-2:2006 (E) 12 6 Photothermal measuring methods 6.1 Excitation methods for photothermal materials testing 6.1.1 Radiation sources Various sources of radiation are used for photothermal materials testing. The specifically directed periodic-harmonic or pulsed introduction of heat into the object to be tested is decisive. 6.1.2 Excitation with optical sources of radiation The introduction of a quantity of heat by an optical process presupposes that the test object under study absorbs the excitation light. Accordingly, sources of radiation from the ultraviolet to infrared ranges of the spectrum are used. Because of non-radiative transitions, energy can thereby be deposited in the test object. The following sources are used:  Wide band emitters: white light sources (Xe high pressure lamps and other gas discharge lamps, flash lamps, halogen lamps, etc.);  Laser light sources (excimer, gas, solid state lasers or laser diodes, dye lasers) and light diodes. Here it is crucial whether and how the excitation source can be modulated. Different methods can be used:  Mechanical modulation for all light sources in the range of approximately 1 Hz to 10 kHz;  Acoustic-optical modulators (usually 0,01 Hz to 10 MHz) or electro-optical modulators (usually 0,1 Hz to 100 MHz) with laser beam sources;  Direct current modulation with light and laser diodes (usually 0,01 Hz to 100 MHz) or with diode-pumped solid state lasers (usually 0,01 Hz to 20 kHz). Depending on the application, the excitation power density ordinarily lies between a light power density of 1 and 100 kW/m2. It is also possible to introduce heat energy into the test object by means of pulsed sources of radiation. For this purpose laser radiation sources (solid state, excimer or dye lasers) are available for photothermal materials. Depending on the control method, a pulse duration of microseconds (10-6 s) to nanoseconds

(10-9 s) is attained. With a pulse duration of 100 microseconds (10-4 s) to seconds, white light sources can also be used.

The excitation energy here is usually 10 to 1000 J/m2 per pulse. 6.1.3 Excitation with microwaves Microwaves can be used to introduce heat into the test object via dielectric and magnetic interactions. With magnetic resonance methods, energy from a microwave field is absorbed by the magnetic dipoles of the probe. Usually an additional external magnetic field is required in order to fulfil the prerequisites for resonance absorption. 6.1.4 Other excitation methods Thermal waves can also be excited by X-ray radiation. Because of the required power, synchrotron sources of radiation have had to be used in the past. Electron and ion beams are used for the high-resolution imaging of probe areas near the surface (electron/ion beam acoustic microscopy).

EN 15042-2:2006 (E) 13 With electrically conducting test objects, heat can be introduced directly via the current flow (Joule effect, resistance heating, eddy current heating). Also strong acoustic fields can introduce heat, produced in the sample particularly at interfaces having mechanically contact, but not strong adhesion, for example at cracks. 6.2 Photothermal detection methods 6.2.1 Photo-acoustic detection With the photo-acoustic effect, the thermal waves in the test object are indirectly detected via pressure oscillations in the surrounding gas compartment by means of a microphone. Two mechanisms are used to generate the pressure signal:  the periodically modulated heat flow that penetrates the gas volume from the solid/gas boundary interface and causes the pressure in the chamber to increase;  and the thermoelastic deformation of the material. Generally the microphone is attached to a closed chamber of a few cubic centimetres (see Figure 4). Key 1. Excitation beam 2. Microphone 3. Emitted sound wave 4. Test object 1234 Figure 4 — Diagram of a photo-acoustic measurement cell

6.2.2 Detection of thermal radiation: photothermal radiometry With radiometric detection, the temporal oscillation of the surface temperature is observed by measuring the emission of thermal radiation. A radiometric set-up is shown schematically in Figure 5. A part of the emitted thermal radiation (infrared radiation) is imaged via the appropriate optics (mirror and/or transmission optics) at a suitable infrared detector (IR detector).

EN 15042-2:2006 (E) 14 Key 1. IR detector 2. Excitation beam 3. Thermal radiation 4. Test object 1234 Figure 5 — Diagram of radiometric detection

6.2.3 Detection by changing the refractive coefficient

The heat flow from the test object into the surrounding air layer causes a local change in the refractive coefficient. This change can be detected by optical methods.

With photothermal beam deflection (Figure 6), a probe laser beam is deflected and guided across the heated probe surface (via a thermal lens or thermal bell). The deflection is registered by a position-sensitive detector (PSD). The deflection angle θ depends on the mean refractive coefficient gradient dn/dT across which the laser beam passes in the thermal bell. Key 1. Excitation beam

2. Thermal bell 3. PSD: 4 quadrant photodiode 4. Probe beam 5. Test object 13524θ Figure 6 — Diagram of photothermal beam deflection

Photothermal interferometry (Figure 7) makes use of the difference in the optical path traversed by a detection laser beam as it passes through the thermal lens, relative to a reference distance. The change in the refractive coefficient is manifested as an optical phase shift between the measurement and reference beams. The phase shift is detected from the interference signal.

EN 15042-2:2006 (E) 15 Key 1. Excitation beam

2. First beam splitter 3. Reference beam 4. Deflecting mirror 5. Thermal bell 6. Probe beam 7. Interference 8. Second beam splitter 9. Test object 135246789 Figure 7 — Diagram of photothermal interferometry

6.2.4 Other forms of detection Other forms of detection used in non-destructive photothermal materials testing are pyroelectric detection for measuring the heat flow and piezoelectric detection (Figure 8) for registering acoustic waves caused by the thermoelastic effect in the test object. The latter procedure is generally used with pulsed excitation. Key 1. Excitation beam

2. Piezodetector 3. Acoustic waves 4. Test object 2134 Figure 8 — Diagram of the piezodetection of acoustic waves

With optically reflecting test bodies, the thermoelastic deformation of the surface can be detected by means of the optical beam deflection of a detection laser beam, as shown in Figure 9.

EN 15042-2:2006 (E) 16 Key 1. Excitation beam

2. Detection laser 3. Position detector 4. Surface deformation 5. Test object 21345 Figure 9 — Diagram of optical beam deflection

In the case of thermo-reflection measurement (Figure 10), the reflectivity of a test object is observed by directing the beam from a detection laser on the test object and measuring the change in intensity of the reflected beam. This methods exploits the temperature dependence of the reflection coefficient. In addition, changes in the charge-carrier concentration in semi-conductors contribute to changing the reflectivity.

In the case of thermo-reflection measurements, a double modulation process can be used, i.e., the thermal waves are excited via two partial beams with different modulation frequencies. Key 1. Excitation beam

2. Detection laser 3. Photo detector 4. Test object 2134 Figure 10 — Diagram of thermo-reflection

6.3 Signal processing and calibration

Depending on the type of excitation — periodic-harmonic or pulsed — different components are used for analysis. Generally a low-noise preamplifier is introduced after the detector. With periodic-harmonic excitation, lock-in amplifiers (phase-sensitive amplifiers) are ordinarily used for this purpose. With pulsed excitation, digital transient recorders or analog boxcar integrators are employed. The lock-in amplifier is a narrow-band AC voltage amplifier followed by a rectifier. The lock-in amplifier provides two measurable variables: the amplitude, which is a measure of the amplitude of the generated temperature oscillation, and the phase, which reflects the temporal interval between the excitation and the temperature response.

EN 15042-2:2006 (E) 17 Transient recorders or boxcar integrators record the signal as of a reference time (e.g. start of the excitation pulse) in definable temporal intervals. With the transient recorder, the excitation signal may be periodically repeated, with the boxc

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