Advanced image processing and flaw reconstruction algorithms of eddy current data are based on alow noise level of the field response signal. Magnetometers such as SQUID and fluxgate sensors provide a high field sensitivity of between 0.1 pT/ÖHz and several pT/Ö
Hz, and an outstanding dynamic range due to their read out electronics based on a feed back loop. Therefore these sensors can measure the same maximum field amplitude of about a few 100 µT compared to conventional coil systems, which leads to a dynamic range of more than 150 dB/ÖHz. Eddy current (EC) measurements based on a usual 12-16 bit data recording often result in an effective dynamic range of less than 65 - 85 dB/ÖHz, due to the quantization noise of the ADC. In the case of typical eddy current signal processing algorithms, such as subtraction of reference signals or phase rotation a higher dynamic range is required. We, therefore, set up an eddy current system which covers an analog dynamic range of more than 160 dB/ÖHz. The measured field variations (in phase and quadrature channel) are recorded in a multimeter having a maximum dynamic range of 28 bit (170 dB/ÖHz). We report on EC measurements with real 21 and 24 bit field resolution, on several aluminium samples and modified signal processing for the separation of defect signals or the improvement of the spatial resolution.
Increasing requirements in quality control demand the reliable detection of very small or deep lying defects hidden in conductive samples. The development of new analysis techniques, based on both software algorithms and adapted hardware components, is thus becoming increasingly important for crack detection based on electromagnetic testing. The question whether the sophisticated hardware equipment of eddy current (EC) systems with higher field sensitivity and higher dynamic range actually meets these requirements is discussed with respect to special EC applications.
In standard EC testing, the field data are usually recorded in a 12 - 16 bit format, corresponding to an analog dynamic range of 65 - 85 dB/ÖHz. But when measuring samples with complicated geometrical structures and different materials, defect signals are superposed by, for example, edge effects, which often are more than several magnitudes larger than the field variation caused by the defect structure. Furthermore, in standard EC signal processing algorithms, such as subtraction methods and phase rotation, the defect signal must be separated from an artificial background, which requires, in the case of small defects, a dynamic range of more than 16 bit. Such sensitive EC measurements have been realized by using sensitive magnetometers such as SQUID or flux gate sensors for the detection of the response field caused by the crack [1-4].
However, the dynamic range and the linearity would be small, if the direct read-out of a SQUID or a flux-gate sensor were employed. For instance, the SQUID provides a periodic magnetic flux/voltage transfer function, which enables one to count the flux periods, but leads to a field resolution, which is too low. Therefore in most practical applications, the SQUID is used in a feedback circuit as a null detector of magnetic flux. A variation of the external field results in a non linear change in the output voltage of the SQUID. This voltage is amplified by an integrator, which is connected to a feed back coil located in close proximity to the SQUID. Therefore each external field variation is instantaneously compensated by the output voltage of the integrating amplifier. This linearized output voltage (current) is then a direct measure of the external field variation applied to the SQUID. The maximum dynamic range of a SQUID used in a so called flux-locked-loop (FLL) is mainly limited by both the voltage noise level of the integrator, and its maximum admissible drive current . Using low noise operational amplifiers with a few nV/ÖHz, which provide an outstanding analog dynamic range of up to 180 dB/ÖHz, enables one to measure very small magnetic fields, superposed by strong background field variation (movement in earth field or remanent field of ferromagnetic components).
2. Experimental setup
In our measurements, we have used both SQUID and flux gate sensors for the detection of the magnetic field variation caused by the sample under test.
To exploit the high analog dynamic range of the field sensor in an EC measurement, all further components, such as the excitation unit, demodulation and data recording have also been adapted to cover a large dynamic range.
Figure 1 shows the principle block diagram of the measurement setup. The excitation coil is connected to the low noise excitation unit, which generates eddy currents in the conductive sample under test.
When a crack is located in the material, the field distribution above the test object changes. This field deviation, emanatinf from the distortion of the eddy current flow, is detected either by a fluxgate [6,7] or an HTc - rf -SQUID made from YBCO [8,9]. A lock-in-amplifier having a dynamic range of up to 130 dB/ÖHz then compares the reference excitation signal with the measured field and its changes in amplitude and phase. Each of the two output channels (in phase and quadrature) are connected with a high resolution multimeter, covering a digital dynamic range of up to 28 Bit (170 dB/Ö
Hz). The sample rate depends on the required field resolution. When scanning with a resolution of 21 Bit (126 dB) and a velocity of, say, 30 mm/s, the sample rate is limited to 600 Hz, leading to a distance between the recorded field values of 50 µm. The measured field data are synchronized with the position of the x/y -stage.
All parameters such as scanning range, velocity, dynamic range, bandwith etc, can be controlled by a PC. The system includes, in conjunction with an EC software - based on Labview programs- features such as extraction of line scans, phase rotation and standard filters.
Fig 1: Scheme of the measurement setup, including a digital field resolution of more than 25 Bit.|
The EC measurement was performed with a circular excitation coil and a fluxgate magnetometer to detect the response field. In order to preserve the total dynamic range of the lock-in amplifier for the detection of the response field variation, the excitation field was compensated by either an additional local compensation coil, attached in close proximity to the sensor, or an electronically adapted subtraction of the excitation field .
3. Signal-to-noise ratio of the system
For a first determination of the attainable signal-to-noise ratio we performed a measurement with 25 bit resolution of the output voltage of a 9V battery.
Figure 2 shows 100 samples of the input voltage, in which small fluctuations of the last bits can be observed. A dynamic range of ±10 Volts and a voltage amplitude of the last bit of approximately 900 nV was obtained for an integration time of 1s (bandwidth of about 1Hz), leading to a maximum dynamic range of 147 dB/ÖHz. The noise level of these measurements did not change when a resolution of 28 bit was used. We therefore assume that the voltage fluctuations are induced by external noise sources.
Fig 2: Measurement of the output voltage of a 9V battery, using the multimeter with a 25 bit mode. Integration time: 1s, sample rate 50 Hz.|
To demonstrate an EC measurement with high signal-to-noise ratio, we used a simple specimen, consisting of two aluminium sheets with a total thickness of 2.6 mm. The upper sheet has a thickness of 2 mm and covers a 0.6 mm thick sheet, which contains a defect having a length of 20 mm and a height of 0.6 mm.
The probe makes use of a circular excitation coil and a flux gate sensor for the detection of the vertical component, Bz , of the response field. In fig. 3a, a typical crack signal with an amplitude of about 9 µT can be observed. The bandwidth was adjusted to be 1 Hz.
The field values were recorded in a 21 bit mode with a sample rate of about 600 Hz. The output voltage of the flux gate was demodulated by a lock-in amplifier with low dynamic range, leading to a step-like response signal. This effect can be observed in the left diagram (fig 3b), which is a magnification of the interval of the response field indicated by the dotted rectangle in fig 3a. Due to the low pass filter of the lock-in amplifier, the step-like change of the output voltage is superposed by transient oscillations (fig 3c). Fig. 3d shows the magnification of the last periods of the damped oscillations, having an amplitude of about 20 pT. The noise amplitude is about 5 pT/ÖHz, leading to a signal-to-noise ratio of about 125 dB/ÖHz, which nicely corresponds to the digital dynamic range of 21 bit data recording.
|Fig. 3: EC measurement (2 kHz, circular coil) of a defect in a depth of 2 mm, using a resolution of 21 Bit.
a: Crack signal; b: Magnification of an interval indicated by the dotted line - voltage steps of the lock-in amplifier; c: Superposed oscillation by the low pass filter; d: Noise amplitude of about 5 pT/ÖHz. |
4. Measurements of riveted multilayer samples
At the left side of Figure 4, a sketch shows a riveted multi-layer test sample, consisting of four aluminium sheets bolted together by a titanium rivet. The upper three layers have a thickness of 5 mm and the bottom layer has a thickness of 10 mm. The third layer contains an exchangeable sheet, in which defects with different lengths (2, 5, 10, 15 mm) have been introduced. The optimum excitation frequency was calculated to be 180 Hz . The EC measurement was performed with standard 12 bit data recording, covering an effective dynamic range of about 65 dB/Ö
Hz due to the fluctuations of the last bits of the ADC. In order to prevent the ADC from being saturated by too strong eddy current response signals (+10V corresponds to 212= 4096 counts of the ADC), the maximum response signal, caused by the bolt and the adjacent crack, was smaller than 4 V (»
For the separation of the defect signals from the disturbing background, several steps in signal processing have to be performed. Firstly, the Lift-Off effect has to be eliminated by subtracting a linear function (see Fig. 4, line 1). The second step contains an adapted phase rotation, which minimizes the large bolt signal caused by the upper part of the bolt, and enlarge the response signal of the depth as the crack is located (see Fig. 4, line 2). However, the defect signal is still superposed by the residue of the bolt signal, caused by the current distortions at the bolt, which occur in the same depth where the crack is located. Therefore, as a third step for a total separation of the crack signal from substantial background signals, subtraction of a reference bolt signal is required (see Fig. 4, line 3).
Fig 4 : Measurement of a bolted multilayer sample using 180 Hz excitation frequency.The 5 mm long crack was located in a depth of 10 mm. Line 1: Total signal containing both bolt signal and crack signal. Line 2: Suppression of the bolt signal by rotating the phase. Line 3: Subtracting the residual bolt signal for a total separation of the crack response field|
Each of these signal processing operations yield a reduction of signal amplitude of up to one order of magnitude. Especially when measuring very deep lying defects, the crack signal could be smaller than 3 orders of magnitude compared to the total eddy current response signal of the bolt, which results in small voltage variations of a few mV. As an example, a magnification of the totally separated crack signal (5 mm height, 5 mm length, covered by 10 mm aluminium) is show in Fig. 5. Due to the small size of the crack, and an excitation coil having a diameter of 20 mm, the crack signal contains two local minima. However, the crack separation procedure results in a reduced SNR smaller than 6.
Fig 5 : Magnification of line 3: Subtracting the residue bolt signal for a total separation of the crack response field|
Modern software algorithm such as neural network techniques, allow for the classification of the defect geometry [12-14] by extracting mathematical features, such as amplitude, width, slope, position of the maxima and the integral function from the response signal. However, the reliable determination of a feature vector, inspecting the detected response field, also depends on a sufficiently high signal-to-noise ratio, especially when measuring very small and deep lying defects located in close proximity to bolts, rivets and edges. Fig. 6 shows a measurement of cracks with different lengths located in the third layer (covered by 10 mm aluminium). The response field was measured with both 16 bit resolution (Fig. 6 left ) and 21 bit resolution (Fig. 6, right). The crack signal was separated from the Lift-Off effect and bolt signal by phase rotation and subtraction as described above. The remaining crack signal shows a higher amplitude of the response signal when cracks with larger lengths are measured, due to a larger volume in which the eddy current distortion occurs. However, for too low digital resolution, in conjunction with small cracks, the determination of features, such as the positions of the maxima proves to be very uncertain. Therefore, in the case of too low digital resolution, the influence of this quantization noise inevitably gives rise to a diminished probability of detection (POD).
Fig 6: EC measurement of a bolted multilayer sample, using 180 Hz excitation frequency. The 5 mm or 10 mm long crack was located at a depth of 10 mm. Suppression of the bolt signal by rotating the phase and subtracting the residual bolt signal for a total separation of the crack response field.Left: 12 bit resolution used, right: 21 bit resolution used.|
5. Improvement of the spatial resolution
When measuring samples with large thicknesses, containing deep lying defects, the spatial resolution is inevitably reduced, despite a close proximity between the sensor and the surface of the sample to be tested. Two deep lying defects located within a small horizontal distance of each other -smaller than the vertical distance between sensor and the location of the defects- might result in a field distribution, mistakenly indicating the presence of only a single defect. To prevent such false interpretation of the measured magnetic response field, caused by large material depths, additional software algorithms should be used. A very simple method is given by the derivatives of the 2nth order of the defect signal. With this method, a defect located very close to another defect structure can be separated from the superposed defect signal. The drawback of such a rough mathematical method is given by the strong loss of SNR, depending on the sample rate. However, the achieved number of derivatives with a SNR still larger than 2 depends on the available SNR of the original crack signal, as shown in Fig. 7. We note that the quantization noise of the ADC, as well as a too high analog noise level of the components of the EC system, affects the SNR of the derivatives in like manner. Therefore this method particulary can be applied when SQUID- or flux gate systems with large analog dynamic ranges are used in conjunction with a sufficiently high digital resolution of the recorded field values.
As an example of the increasing noise level of the derivatives, Fig. 7 demonstrates a crack signal and its derivatives using different digital resolution. The sample to be measured consists of two aluminium sheets, each of which contains a crack with a height of 40 mm and a length of 0.6 mm. The parallel aligned cracks are arranged at a distance of 8 mm from each other and were covered by an additional aluminium sheet with a thickness of 2 mm. The vertical distance between the field sensor - for this measurement we used a SQUID, mounted horizontally to the insert of the cryostat- and the sample, was about 16 mm. The two parallel cracks were measured with a circular excitation coil and an excitation frequency of 1 kHz.
As shown in Fig.7a the field distribution above the defect consists of a single symmetric peak, without any traces of two different defects. In the case of only one single defect, this symmetry is preserved when derivatives of higher order are calculated. The number of zero points of the derived defect signal then corresponds with the number of the nth order of derivative. However, this symmetry of the derivatives is broken when two cracks with a small distance from each other are measured. As an example, for the two cracks described above this symmetry is broken, when calculating the 4th derivative (Fig 7 d, e). The left part of Fig. 7 shows the derivative when a 25 bit data recording was used without any influence of quantization noise. In the case of standard EC devices using a digital resolution not larger than 16 bit, the effect of quantization noise already occurs in the second derivative. Thus, the broken symmetry of the 4th derivative almost vanishes due to the superposition of significant noise. The SNR of the 6th derivative is smaller than 1 (Fig 7 g).
|Abb. 7: EC measurement of two parallel cracks with a horizontal distance of 8 mm from each other. Diagram b,d,f: Derivatives of the original crack signal, using 25 bit digital resolution. Diagram c,e,g: Derivatives of the original crack signal, using 16 bit digital resolution. |
The employment of Eddy Current systems equipped with sensitive magnetometer to measure the response field is suitable for the detection of deep lying defects, where high field sensitivity at low frequencies is required. However, the strong attenuation of the response field in the case of deep lying defects (skin effect) often results in very noisy crack signals. Especially, when measuring complicated samples containing different materials and uneven geometry, the small crack signals are superposed by a background which often is more than several orders of magnitude larger compared to the defect signal. Due to the insufficient digital resolution of a usual 12 bit or 16 bit ADC, such small field variations are barely detectable in presence of edges, bolts or different materials, or entirely disappear in the quantization noise of the ADC.
An EC system was created, which provides an outstanding analog and digital dynamic range with an digital resolution of the recorded field values of up to 28 bit. Several Eddy current measurements were carried out on simple test samples and aircraft multi-layer structures to demonstrate the advantages of using EC systems with a high dynamic range.
The authors are grateful to V. Vengrinowich of IAP (Minsk) and H.-J. Krause of Research Center Jülich for stimulating discussions. This work is supported by the German Federal Ministry of Education and Research (BMBF).
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