Method for localizing a thermal source and computer program

Abstract

The invention relates to a method comprising the following steps for localizing a thermal source (2) in a substrate (1) having a first surface (11): cyclically exciting the thermal source (2) with an excitation signal having at least one excitation frequency Φ; detecting in a spatially resolved manner a pixel intensity IP(tP,x,y) of the infrared radiation at the first surface, where IP denotes the measured intensity, tP denotes the time and x, y denotes the lateral position on the first surface (11), and correlating the pixel intensity IP(tP,x,y) with a signal having the excitation frequency Φ in order to obtain the amplitude A(x,y) and the phase θ(x,y) of the pixel intensity IP for each lateral position on the first surface (11), wherein the amplitude A(x,y) and the phase θ(x,y) are converted into an intensity distribution IM(t,x,y), where IM denotes the intensity, t denotes the time and x, y denotes the lateral position; and determining a reconstructed intensity distribution IR(x,y,z) from the intensity distribution IM(t,x,y), where x, y denotes the lateral position and z denotes the depth in the substrate (1) below the first surface (11). The invention furthermore relates to a computer program for carrying out the method.

Description

[0001] FRIESE GOEDEN Patent Attorneys PartGmbB Widenmayerstraße 49 80538 Munich Our reference: 32026 PWO GO Applicant: Fraunhofer-Gesellschaft eV ─────────────────────────────────────────────────────────────────────── Method for localizing a thermal source and computer program The invention relates to a method comprising the following steps for localizing a thermal source (2) in a substrate (1) with a first surface (11): cyclic excitation of the thermal source (2) with an excitation signal having at least one excitation frequency Φ; spatially resolved detection of a pixel intensity I P (t P ,x,y) of the infrared radiation at the first surface, where I P the measured intensity, t P denote time and x, y the lateral position on the first surface (11), and correlate the pixel intensity I P (t P,x,y) with a signal with the excitation frequency Φ, to determine the amplitude A(x,y) and the phase θ(x,y) of the pixel intensity I Pto obtain for each lateral position on the first surface (11). The invention further relates to a computer program for carrying out such a method. A non-destructive testing method for locating defects in electronic components is known from US 2011 / 0297829 A1. This known method takes advantage of the fact that defects in electronic components often lead to increased contact resistances, which in turn lead to locally increased heating. With cyclic excitation, the heat emanating from the defect propagates as a wave through the volume of the semiconductor component and can be detected at a surface using an infrared camera.To determine the depth below the substrate surface at which the heat source lies, the known method proposes simulating the heat propagation of defects at different depths using finite element analysis and accepting as correct the depth at which the simulation best agrees with the measured values. This method has the disadvantage that the three-dimensional localization of the defects within the semiconductor device requires a large computational effort and nevertheless yields only unreliable results. According to one aspect of the invention, a method for localizing a thermal source in a substrate is proposed. In some embodiments of the invention, the substrate can be an unpackaged electronic component, in particular an integrated circuit that integrates a plurality of electronic components in a small space.In other embodiments, the substrate can be an enclosed component, i.e., at least one semiconductor chip or integrated circuit, which is mounted in a metal and / or plastic housing equipped with connection contacts. In yet other embodiments, the substrate can be a printed circuit board, in particular a multilayer board. The thermal source to be localized can be a defect in the component or in a connection of the housing or the circuit board. In particular, such a defect can exhibit electrical resistance, which leads to a locally increased electrical power dissipation and thus to heat generation.The defect can be, for example, a reduced conductor cross-section of a conductor track, an incorrectly dimensioned electrical resistor, a gate dielectric with increased conductivity, a short-circuited diode, or any other defect occurring during the processing of integrated circuits. In some embodiments, the object of the invention may be not only to mark and reject the integrated circuit or printed circuit board as defective, but also to determine the exact location of the defect within the integrated circuit or printed circuit board in order to obtain information for optimizing the manufacturing process of the integrated circuit. The method disclosed herein comprises at least the following steps: First, the thermal source within the substrate is cyclically excited.In the simplest case, the thermal source can be excited by an excitation signal containing exactly one excitation frequency Φ, and therefore following a sinusoidal waveform. In other embodiments, the excitation signal can simultaneously contain a plurality of excitation frequencies Φ. In this case, the excitation signal can exhibit a defined cyclic signal in the time domain, for example, a square wave with a predefinable duty cycle. In other embodiments, the cyclic excitation can be achieved by gradually increasing the supply voltage to a maximum value and subsequently switching off or reducing the supply voltage, resulting in a sawtooth or triangular waveform. In still other embodiments, the cyclic excitation can be achieved by an arbitrary function that contains or consists of a plurality of discrete excitation frequencies Φ.The largest period of the excitation signal in the time domain is subsequently referred to as the lock-in frequency Ψ. The excitation frequency Φ used for the subsequent evaluation of the signals can be the fundamental frequency of the excitation signal or a harmonic of the excitation signal. If the excitation signal simultaneously contains a plurality of excitation frequencies Φ, an excitation frequency Φ can thus be selected for localizing the thermal source. In some embodiments, the excitation frequency Φ can be identical to the lock-in frequency Ψ. Excitation of the thermal source can be achieved, in the case of a semiconductor device, by switching the supply voltage on and off. In the case of a printed circuit board, a test current can be passed through at least one conductor to excite the thermal source.The at least one excitation frequency Φ can, in some embodiments of the invention, be between 0.1 Hz and approximately 120 Hz, or between approximately 1 Hz and approximately 12 Hz, or between approximately 0.1 Hz and approximately 6 Hz, or between approximately 6 Hz and approximately 25 Hz, or between approximately 90 Hz and approximately 120 Hz. The substrate can have a polygonal shape and a comparatively large surface area with a comparatively small thickness. The substrate can be homogeneous. In other embodiments of the invention, the substrate can have a multilayer structure and consist of several layers of one or more semiconductor materials, metals, alloys, and / or insulators. During the cyclic excitation of the thermal source in the substrate, the substrate is located within the detection range of a two-dimensional infrared detector, for example, an infrared camera.The surface of the substrate facing the infrared camera is referred to as the first surface for the purposes of the following description. The first surface, together with the opposite second surface, can constitute the largest boundary surface of the substrate. The infrared camera can include a lens that images at least part of the first surface onto the camera's field of view. The infrared camera can be a known infrared camera with a two-dimensional detector. The two-dimensional detector can have between approximately 300 and approximately 1000 pixels in each dimension. The detector can be cooled to improve the signal-to-noise ratio. The infrared camera can have a relatively short integration time of approximately 0.2 ms to approximately 10 ms or of approximately 0.5 ms to approximately 2 ms. The image acquisition rate of the infrared camera can be higher than the excitation frequency Φ.For example, the image acquisition rate can be more than 2 times, more than 4 times, more than 10 times, more than 20 times, or more than 40 times greater than the excitation frequency Φ. The infrared camera is designed and intended to acquire a sequence of spatially resolved images of the infrared radiation at the first surface that is time-synchronized with the excitation frequency Φ. The infrared camera thus provides data on the pixel intensity I. P (t P ,x,y) as a function of the lateral position x, y on the first surface of the substrate and the time t P In some embodiments, the pixel intensity I P (t P ,x,y) are acquired in a time-synchronous manner with the lock-in frequency Ψ. In some embodiments of the invention, the pixel intensity I measured at the first surface can be P (t PThe amplitude A(x,y) and the phase θ(x,y) relative to the excitation frequency Φ are correlated with the excitation signal. This determines the amplitude A(x,y) and the phase θ(x,y) relative to the excitation frequency Φ for each lateral position x, y. The conversion of the pixel intensity I P (t P The amplitude A(x,y) and the phase θ(x,y) can be derived from the excitation signal and integrated over the lock-in periods. In some embodiments of the invention, an intensity distribution I can be derived from the amplitude A(x,y) and the phase θ(x,y). M (t,x,y) are determined, where t denotes time and x, y the lateral position on the first surface of the substrate. From the intensity distribution I M (t,x,y) in turn can be a reconstructed intensity distribution I R(x,y,z) are calculated, where x and y denote the lateral position on the first surface of the substrate and z the depth in the substrate below the first surface. The intensity distribution I M The amplitude (t,x,y) of the thermal wave propagating from the thermal source at the first surface is thus calculated layer by layer back into the substrate. The location in the substrate where this wave converges can be considered the origin of the thermal wave and therefore the location of the desired thermal source in the substrate. In some embodiments of the invention, the amplitude A(x,y) and the phase θ(x, y) can be converted into the intensity distribution I. M(t,x,y) includes the following steps: For each lateral position, a time vector can be generated which has a predefinable length or duration. In some embodiments of the invention, the length can correspond to the period of the lock-in frequency Ψ, i.e., the maximum duration L is 1 / Ψ. In other embodiments, the duration of the time vector can correspond to the period of the excitation frequency Φ, i.e., the length L is 1 / Φ. For each location, a time delay t can be derived from the phase angle θ(x,y). D The time vector between the excitation of the thermal source and the detection of infrared radiation at the first surface can be determined. Then the time vector at position t can be calculated. D , which corresponds to the travel time of the wave from the thermal source to the point on the surface under consideration, a Gaussian monopulse with the intensity A(x,y) of the respective pixel determined in the previous step as maximum amplitude is used to create an intensity distribution IM (t,x,y) to obtain. In some embodiments of the invention, the time delay t can be D The following formula can be used to determine the phase θ(x,y) and excitation frequency Φ for each pixel from the measured values: This allows the easily determined phase shift θ(x,y) between the excitation frequency and the detection of the thermal wave at the surface to be converted into the time difference required for reconstructing the depth information. In some embodiments of the invention, only pixels that meet a predefined inclusion criterion can be used to localize the thermal source. This can reduce noise, allowing the calculation to be performed faster and with higher accuracy. In some embodiments of the invention, only pixels whose intensity I Mabove a predefined threshold. This means that the inclusion criterion is specified such that the intensity or amplitude must exceed a certain value. Pixels whose intensity is below the threshold are considered noise, which contains no usable information. This enables automated application of the inclusion criterion. In some embodiments of the invention, only pixels whose amplitude A(x,y) is greater than approximately 40%, 30%, or 20% of the measurable maximum value of the infrared detector used can be included in the calculation. Such an inclusion criterion allows for simple, automated determination of the area of ​​interest within the measurement range captured by the infrared camera.In some embodiments of the invention, the inclusion criterion can be specified such that only pixels forming a contiguous area are included in the calculation. This excludes the consideration of individual pixels that only happen to exhibit a high intensity. Unphysical reconstructed intensity distributions can thus be suppressed or at least occur less frequently. In some embodiments of the invention, the determination of the reconstructed intensity distribution I. R (x,y,z) by a time-based method. This means that the calculation takes place in the time or space domain. Such a method can be easily implemented. In other embodiments of the invention, the determination of the reconstituted intensity distribution I can be R(x,y,z) can be determined using a Fourier-based method. This can increase the accuracy of the reconstruction and thus the accuracy of the localization of the thermal source in the substrate. In some embodiments of the invention, the determination of the reconstructed intensity distribution I can be performed using a Fourier-based method. R The determination of the reconstructed intensity distribution can be carried out by a delay-and-sum method or by an inverse boundary scattering transformation. These methods are easy to implement due to their simplicity. In other embodiments of the invention, the determination of the reconstructed intensity distribution can be carried out by a phase-shift migration or by an omega-k migration. These methods can be characterized by high numerical stability and high accuracy. In some embodiments of the invention, the method for determining the reconstructed intensity distribution I R (x,y,z) include the following steps: Providing the intensity distribution I M(t,x,y)[Z0] at the first surface of the substrate, discretizing the time information t with a time increment Δt, discretizing the position information x, y with position increments Δx, Δy respectively, discretizing the depth information z with a depth increment Δz, and determining the propagation speed of the thermal waves in the substrate between the desired thermal source and the first surface of the substrate from the thermal conductivity α of the substrate. By discretizing the depth information z with a depth increment Δz, a plurality of planes Δz are generated. l defined in the substrate, with l = 0, 1, 2, …. The planes Δz l can run parallel to the plane defined by the first surface of the substrate. The intensity distribution at the first surface is then calculated backwards in time, so that the intensity distribution for each of the planes Δz is determined. lThe process is as follows: First, a Fourier transform of the intensity distribution I can be performed. M to be carried out in order to obtain a transformed intensity distribution Î M (ω,k x ,k y ) to obtain. Here, ω denotes the inverse or frequency information of the time information t. The lateral position x, y is given by the corresponding wavenumbers or spatial frequencies k. x and k y The transformed intensity distribution is subsequently subjected to phase migration. Phase migration is performed by multiplying the transformed intensity distribution by a phase factor. ^^^∆௭^ , in order to obtain a migrated intensity distribution at a time earlier than the measurement. Then, all frequencies ω of the migrated intensity distribution are summed and the resulting intensity distribution is inversely transformed by Fourier to obtain the reconstructed intensity distribution I.R (x,y,z0+Δz l ) at a distance Δz l to obtain a focused plane below the first surface of the substrate. In simpler terms, the wave field at the surface is Fourier-transformed, extrapolated in the z-direction (i.e., at a depth Δz from the substrate surface), integrated over ω, and then inversely Fourier-transformed. This results in a focused plane at a predefined depth Δz of the substrate. This calculation is performed for each plane Δz. l within the substrate, the thermal wave is repeatedly calculated. This allows the thermal wave at the first surface to be gradually reconstructed back to its point of origin, resulting in a three-dimensional representation of the wave field within the substrate. The point within the substrate where the reconstructed wave image I RThe point where the wave field converges or forms a focal point can be considered the starting point of the wave field and thus the location of the thermal source to be determined. In some embodiments, the spatial frequency k required for calculating the phase factor can be determined. z in the z-direction can be determined as follows: w obei ^^௪ = √4 ⋅ α ⋅ π ⋅ Φ represents the propagation speed of the thermal wave in the substrate. The spatial frequency k z depends on ω, k x , k y . For each point in the wave field, a different k results. z The thermal conductivity α can be easily measured or obtained from tables. The angular frequencies ω, which relate to the frequency components of the time dimension t of the intensity distribution I M (t,x,y) after applying Fourier analysis are calculated as: 2 ⋅ N^ N^ N^ where N tthe total number of time points (sampling points) in the time vector, assuming that N t is an even number. The wave numbers k x as spatial frequency components of the spatial dimension x of the intensity distribution I M (t,x,y) after applying Fourier analysis are calculated as follows: 2 ⋅ π NNN k = Δ ^− ^ , − ^^ + 1.0, … , ^x ⋅ N − 1൨ ^ 2 2 2 where N x The total number of pixels of the detector in the x-direction is, assuming that this is the number of pixels N. x is straight. The wave numbers k y as spatial frequency components of the spatial dimension y of the intensity distribution I M (t,x,y) after applying Fourier analysis are calculated as follows: where N y The total number of pixels of the detector in the y-direction is, assuming that this is the number of pixels N yis straight. In some embodiments of the invention, the reconstructed intensity distribution at a distance Δz can be l below the first surface of the substrate, starting from the intensity distribution measured at the first surface for all Δz l The calculation is thus performed for all depths of the substrate based on the measured values, so that error propagation can be avoided. In other embodiments of the invention, the reconstructed intensity distribution can be performed at a distance Δz. l+1 below the first surface of the substrate, starting from the reconstructed intensity distribution at a distance Δz l, i.e., calculated recursively from the preceding layer. This saves computation time, so the result is obtained more quickly. In some embodiments of the invention, the substrate can contain a plurality of material layers, each exhibiting a different thermal conductivity α, where the reconstructed intensity distribution I R(x,y,z) is determined separately for each material layer. The reconstructed intensity distribution of the first material layer, whose upper surface borders the first surface of the substrate, can be calculated as described above. For the second material layer, whose upper surface borders the lower surface of the first material layer, the reconstructed intensity distribution at the interface replaces the measured intensity distribution. The reconstructed intensity distribution of the preceding material layer thus forms the starting value for calculating the intensity distribution in the subsequent material layer. In some embodiments of the invention, the position increment Δx, Δy for discretizing the position information x,y can be greater than or equal to the size of a detector pixel on the first surface of the substrate. For this purpose, a calibration standard can be imaged onto the infrared detector by means of optical imaging through a lens.Thus, the known structure size of the calibration standard can be specified in terms of the number of pixels of the infrared detector. The resulting pixel spacing in the image plane can then be calculated. In other embodiments of the invention, the spatial increment Δx, Δy can also be larger than a detector pixel on the first surface of the substrate, so that the measurement signals of several pixels are added to obtain the desired spatial increment Δx, Δy. In some embodiments of the invention, the time increment Δt can be determined as follows: Here, n can be chosen between approximately 16 and approximately 2048, or between approximately 16 and approximately 1024, or between approximately 512 and approximately 2048, or between approximately 512 and 1024. In some embodiments of the invention, n can alternatively or additionally meet the condition n = 2. mfulfillment, where m is a positive integer. This can simplify the computer implementation of the method. In some embodiments of the invention, the depth increment Δz can be chosen to be smaller for lower thermal conductivity α and larger for higher thermal conductivity α. This ensures that high resolution is achieved in the back-calculation of the intensity distribution only where necessary. In other layers, which have only a minor influence on the reconstructed intensity distribution I, the depth increment Δz can be chosen to be smaller. RHaving a higher thermal conductivity allows for faster calculations, thus saving overall computing time. In some embodiments of the invention, the depth increment Δz can be constant over the entire depth of the substrate and is independent of the thermal conductivity α. The method is particularly suitable for implementation in a computer program, so the procedure described here is carried out when the computer program runs on a microprocessor. A microprocessor within the meaning of this description can be any device capable of executing the computer program. In particular, this can be a CPU, a GPU, a DSP, or an FPGA. The computer program itself can be stored on a data carrier. Alternatively or additionally, the computer program can be transmitted via a computer network in the form of a data-representing signal sequence.The invention will now be explained in more detail with reference to figures, without limiting the general concept of the invention. Figure 1 shows a schematic representation of a device usable for the method according to the invention. Figure 2 shows an exemplary substrate in section. Figure 3 shows the amplitude A(x,y) in an embodiment. Figure 4 shows the phase θ(x,y) in an embodiment. Figure 5 shows the generation of a plurality of time vectors from the amplitude and phase information according to Figures 3 and 4. Figure 6 illustrates the structure and designations of a substrate with several material layers in section. Figure 7 shows a flowchart of the proposed method for determining the reconstructed intensity distribution. Figure 8 shows the result of the localization of a thermal source. Based on the figures...1 An embodiment of a device is described with which the pixel intensity data I used for the method according to the invention is used. Pcan be obtained. Fig. 1 shows a substrate 1. The substrate 1 can be a homogeneous substrate, which may consist of a single layer of material. In other embodiments of the invention, the substrate 1 can be a semiconductor device, in particular an integrated circuit or a printed circuit board. In this case, the substrate contains a multilayer structure made of different semiconductor materials, alloys, metals, and dielectrics. The substrate can contain a thermal source 2, for example, in the form of a defect or manufacturing flaw in the component used as substrate 1. The defect can be, for example, a reduced conductor cross-section of a conductor track, an incorrectly dimensioned electrical resistance, a gate dielectric with increased conductivity, a short-circuited diode, or any other defect occurring during the processing of the substrate.A power supply 4 is used to cyclically excite the thermal source 2 with an excitation frequency Φ. The power supply 4 can generate an electrical excitation signal which has a predefinable current and / or a predefinable voltage and / or a predefinable time structure. In the simplest case, the time structure can have a single excitation frequency Φ, so that the excitation signal represents a sinusoidal waveform in the time domain. In other embodiments, the time structure can have a plurality of excitation frequencies Φ simultaneously. In this case, the excitation frequencies Φ can form a defined cyclic signal in the time domain, for example, a square wave with a predefinable duty cycle, a sawtooth waveform, or a triangular waveform.In other embodiments, the excitation frequencies Φ in the time domain can form an arbitrary function containing or consisting of a plurality of discrete excitation frequencies Φ. The largest period in the time domain of the signal used to excite the thermal source is subsequently referred to as the lock-in frequency Ψ. The excitation frequency Φ used for subsequent signal evaluation can be the fundamental frequency of the signal used to excite the thermal source or a harmonic of this signal. In the illustrated embodiment, the thermal source is excited by cyclically switching the voltage, resulting in a square wave signal with a 50% duty cycle. The substrate 1 also has a first surface 11, which forms the interface with the hemisphere surrounding the substrate 1. The first surface 11 is detected using an infrared camera.The infrared camera 3 can have a two-dimensional infrared detector with a plurality of pixels in two spatial directions. The first surface 11 can be imaged, at least partially, onto the infrared detector by means of a lens 35. The infrared detector can be cooled to increase the signal-to-noise ratio. The infrared camera 3 thus detects the infrared radiation emanating from the first surface 11 of the substrate 1 as a function of the lateral position on the first surface 11, which can be specified by the coordinates x, y along its length and width. Furthermore, the infrared camera 3 is operated in a time-synchronous manner with the lock-in frequency Ψ, for example by means of a lock-in method or a boxcar integrator.The acquisition rate of the infrared camera is a multiple of the lock-in frequency Ψ and / or the excitation frequency Φ, so that the infrared camera acquires time information for every location on the first surface 11 of the substrate 1. The output of the infrared camera 3 thus contains the pixel intensity I. P (t P Provides a digital or analog signal representing ,x,y). An example measurement signal of pixel intensity I P (t PThe diagram (x, y) is superimposed next to the infrared camera 3 in Fig. 1. It schematically illustrates that the emission of infrared radiation from the first surface follows the application of the electrical voltage with a time delay. Likewise, the infrared radiation decreases again with a time delay after the electrical voltage is switched off. The duration of the delay and the maximum amplitude for each pixel depend on the number, thickness, and thermal conductivity of the covering layers, and thus on the structure of the substrate 1 and the depth of the thermal source within the substrate. To increase the signal-to-noise ratio, the infrared camera 3 can record more than approximately 100, 1,000, 10,000, or 100,000 on / off cycles of the lock-in frequency Ψ. In some embodiments of the invention, the infrared camera 3 can record fewer than approximately 3,000,000 or fewer than approximately 1,000.Record 000 on / off cycles of the lock-in frequency Ψ. The measurement principle is explained again with reference to Fig. 2. Fig. 2 shows a substrate 1 with a first surface 11 and an opposing second surface 12. Furthermore, the sectional view in Fig. 2 shows a thermal source 2, for example, a defect in a conductor track or a gate dielectric with increased conductivity of a field-effect transistor. Naturally, the type of thermal source is not limited. The invention does not disclose the detection of a specific thermal source or a particular defect as a solution principle. Fig. 2 further shows that the substrate 1 can consist of a plurality of material layers. By way of example, four material layers 101, 102, 103, and 104 are shown in Fig. 2. In other embodiments of the invention, the number of material layers 101, 102, 103, and 104 can be greater or lesser.The material layers 101, 102, 103, and 104 can be semiconductors, metals, alloys, or dielectrics. Each material layer can have a different thermal conductivity α. Fig. 2 further illustrates how thermal energy from the thermal source 2 penetrates the covering layers and leads to the emission of infrared radiation 25 at the first surface 11. Due to the cyclic excitation of the thermal source 2, the thermal energy is emitted cyclically in the form of a thermal wave, so that the infrared radiation 25 has a different travel time or phase shift and can also have a different amplitude or maximum value depending on the layers covering the thermal source 2 and depending on the lateral localization within the plane defined by the substrate. Figs. 3 and 4 show how the pixel intensity I measured at the first surface P (tP The pixel intensity I is converted into an amplitude image A(x,y) and a phase image θ(x,y), where A is the amplitude, θ the phase angle relative to the excitation frequency Φ, and x, y the lateral position. P (t P ,x,y) into the amplitude A(x,y) and the phase θ(x,y) can be correlated with the pixel intensity I P (t PThe correlation is performed using the excitation signal or a sine wave signal with excitation frequency Φ and integration over the lock-in periods. Figures 3 and 4 show the camera image processed by the correlation, with two spatial coordinates x and y, which denote the width and length of the substrate 1 at the first surface 11, respectively. Figure 3 shows the amplitude A(x,y) of the infrared radiation for each pixel. Figure 4 shows the time delay as the phase angle θ(x,y) of the infrared radiation at the first surface 11 of the substrate 1. The measured values ​​shown in Figures 3, 4, and 5 were obtained with a nominally homogeneous titanium substrate. The titanium substrate has a total thickness of 0.955 mm and may have a thin, natural oxide layer on its surface. In the illustrated embodiment, the thermal source 2 to be located was realized by a probe tip made of an alloy, which contacts the second side 12 of the homogeneous substrate.To cyclically excite the thermal source, an electric current flows through the probe tip into the substrate, resulting in a slightly increased power loss at the contact point due to the contact resistance. This allows thermal waves to be emitted from the contact point during periodic electrical excitation. These waves propagate through the titanium substrate to the first surface 11 of the substrate and can be detected there as described with reference to Fig. 1. The results of the method described below for determining a reconstructed intensity distribution I. R (x,y,z) are explained in more detail with reference to Fig. 8. With reference to Fig. 5, it is explained how the values ​​of the amplitude A(x,y) and the phase θ(x, y) shown in Fig. 3 and Fig. 4 are transformed into an intensity distribution I. M(t,x,y). First, pixels are selected from the pixel intensities detected by the infrared camera that meet a predefined inclusion criterion. In the illustrated embodiment, a region to be evaluated, or ROI (region of interest), was marked by user intervention, so that pixels within the marked area are used to locate the thermal source, and pixels outside the marked area are not. In other embodiments of the invention, only pixels whose detected intensity I M is greater than a predefined limit or trigger threshold. This limits the evaluation of the phase information to the area of ​​actual interest, thus reducing computation time and simultaneously increasing the quality of the reconstruction. In the subsequent process step, the time delay t DThe phase θ and excitation frequency Φ are determined for each pixel from the previously measured or determined values. This can be done using the following formula: Then, for each pixel within the area to be evaluated, a time vector with length or maximum duration L = 1 / Φ is generated, which is placed at position t. D It contains a Gaussian monopulse with the intensity of the respective pixel, recorded in the previous step, as its maximum amplitude. Fig. 5 shows an example of such a monopulse at position t in the central part of the image. D, where time is plotted on the abscissa and intensity on the ordinate. The right part of Fig. 5 shows a three-dimensional representation of a plurality of such time vectors, with the time vector plotted on the vertical axis and its localization within the first surface 11 on the two abscissas x and y. Fig. 5 thus also shows that the travel time of the thermal wave is longer in the edge regions due to the greater distance the heat has to travel between the thermal source and the surface. Pixels that are located directly above the thermal source, on the other hand, exhibit a shorter travel time. This can be verified with reference to Fig. 2. The method for the three-dimensional localization of the thermal source 2 is explained in more detail with reference to Figs. 6 and 7. Figure 6 illustrates the structure and designations of an exemplary substrate 1 with four material layers in cross-section.Each layer of material has a different thermal conductivity α and therefore a different propagation speed v. w the thermal wave emanating from heat source 2. Furthermore, each material layer has a different thickness d. An interface forms between the underside of one material layer and the topside of a subsequent layer at greater depth. Figure 6 further shows the discretization of the depth information z with a depth increment Δz. This results in a plurality of planes Δz l defined in the substrate, with l = 0, 1, 2, …. The planes Δz l can run parallel to the plane defined by the first surface of the substrate. It should be noted that the planes Δz lThis represents a conceptual, mathematical idea and not any real existing interfaces within substrate 1. Finally, Figure 6 shows that the depth increment Δz is chosen to be smaller for lower thermal conductivity α and larger for higher thermal conductivity α. For example, the thickness d1 of the first material layer in four planes Δz l1 , Δz l2 , Δz l3 and Δz l4 discretized. The thickness d2 of the second material layer in only three planes Δz 21 , Δz 22 and Δz 23 discretized. This ensures that high resolution is applied during the back-calculation of the intensity distribution only where necessary. In other layers, which have only a minor influence on the reconstructed intensity distribution I, RHaving this information allows for faster calculations, thus saving overall computing time. The intensity distribution I determined on the first surface 11 is described below. M calculated backwards in time, so that the intensity distribution for each of the levels Δz l This is determined and is shown in Figure 7: First, the inner repetition region A is explained, which allows the back-calculation of the reconstructed intensity distribution I. R (x,y,z) for a layer within a material layer. For this purpose, a Fourier transform of the intensity distribution I is used. M (t,x,y) on the first surface 11 to obtain a transformed intensity distribution Î M (ω,k x ,k y to obtain ). Here, ω denotes the inverse or frequency information of the time information t. D The lateral position x, y is defined by the corresponding wave numbers or spatial frequencies k. x and k yExpressed. The transformed intensity distribution is subsequently subjected to phase migration. The phase migration is performed by multiplying the transformed intensity distribution by a phase factor. ^^^∆௭^ , in order to obtain a migrated intensity distribution at a time earlier than the measurement. The spatial frequency k required for calculating the phase factor can be used in this process. z in the z-direction can be determined as follows: wobei ^^௪ = √4 ⋅ α ⋅ π ⋅ Φ represents the propagation speed of the thermal wave in the substrate as a function of the thermal conductivity α. The spatial frequency k z depends on ω, k x , k y . For each point in the wave field, a different k results. z The angular frequencies ω, which relate to the frequency components of the time dimension t of the intensity distribution I M (t,x,y) after applying Fourier analysis are calculated as: where N t the total number of time points (sampling points) in the time vector, assuming that N t an even number The wave numbers k x as spatial frequency components of the spatial dimension x of the intensity distribution I M (t,x,y) after applying Fourier analysis are calculated as follows: 2 ⋅ π NN Nk^ = ^− ^ , − ^ + 1,0, … , ^Δx ⋅ N^ 2 2 2 − 1൨where N x The total number of pixels of the detector in the x-direction is, assuming that this is the number of pixels N. x is straight. The wave numbers k y as spatial frequency components of the spatial dimension y of the intensity distribution I M (t,x,y) after applying Fourier analysis are calculated as follows: where N y The total number of pixels of the detector in the y-direction is, assuming that this is the number of pixels N. yThe result of multiplying the transformed intensity distribution is Î M (ω,k x ,k y ) with the phase factor ^^ ^^^∆௭^ is the migrated intensity distribution Î M (ω,k x ,k y )[Z0+Δz l ] in the plane Δz l Then, all frequencies ω of the migrated intensity distribution Î are summed. M (ω,k x ,k y )[Z0+Δz l ] and the Fourier inverse transformation of the intensity distribution thus obtained, to obtain the reconstructed intensity distribution I R (x,y,z0+Δz l ) at a distance Δz lto obtain below the first surface of the substrate. In simpler terms, the measured wave field at the surface is Fourier-transformed, extrapolated in the z-direction (i.e., at a depth Δz from the substrate surface), integrated over ω, and then inversely Fourier-transformed. This results in a focused plane at a predefined depth Δz of the substrate. This calculation is performed for each plane Δz. l within the substrate. In the example shown, these steps are thus repeated four times in the repeating region A to generate the wave field in the four planes Δz. l1 , Δz l2 , Δz l3 and Δz l4 to determine the first material layer, thereby creating a three-dimensional representation of the wave field within the material layer. In the outer repetition region B, the reconstruction of the intensity distribution I is performed. RThe recursive process was carried out for all material layers of substrate 1, whereby the reconstructed intensity distribution I R (x,y,z) is determined separately for each material layer. The reconstructed intensity distribution of the second material layer in the planes Δz 21 , Δz 22 and Δz 23 , which borders the underside of the first material layer with its upper side, is achieved by 3 times the inner repeat area A, whereby the reconstructed intensity distribution at the interface Δz 14instead of the intensity distribution at the first surface 11. The reconstructed intensity distribution of the preceding material layer thus forms the starting value for the recursive calculation of the intensity distribution in the subsequent material layer. The evaluation of the measured values ​​shown in Figures 3, 4, and 5 using the method explained with reference to Figure 7 is shown in Figure 8. Figure 8 shows a cross-section through the titanium substrate 1 in the left part of the image, with the width y plotted on the abscissa and the depth z on the ordinate. The zero point is located at the top of Figure 8 and thus corresponds to the position of the first surface 11 of the substrate 1. From the left part of Figure 8, it can be seen that the thermal source is located approximately 1 mm below the first surface 11 and thus on the underside of the titanium substrate, which has a thickness of 0.955 mm.The proposed method is thus able to locate the thermal source on the second surface 12, even though the measurement data from the infrared camera 3 were only acquired on the first surface 11. The right-hand portion of Fig. 8 shows a section through the thermal source in a plane parallel to the first surface 11, with the length of the substrate x on the abscissa and the width y on the ordinate. Due to the location of the thermal source on the second surface 12 opposite the first surface 11, the right-hand portion of Fig. 8 can also be interpreted as a view of the second surface 12. As Fig. 8 shows, the location of the thermal source 2 on the underside of the titanium substrate and its point-like contact area could be depicted with high resolution from the measurement values ​​shown in Figs. 3 and 4. Of course, the invention is not limited to the embodiments shown.The foregoing description is therefore not to be regarded as limiting, but rather as explanatory. The following claims are to be understood as meaning that a named feature is present in at least one embodiment of the invention. This does not preclude the presence of further features. The following claims are not to be understood as meaning that a named feature is present in every embodiment of the invention. Insofar as the claims and the foregoing description define "first" and "second" embodiments, this designation serves to distinguish between two similar embodiments without establishing a hierarchy.

Claims

Claim 1. A method comprising the following steps for localizing a thermal source (2) in a substrate (1) with a first surface (11): cyclic excitation of the thermal source (2) with an excitation signal having at least one excitation frequency Φ; spatially resolved detection of a pixel intensity I P (t P ,x,y) of the infrared radiation at the first surface, where I P the measured intensity, t P denote time and x, y the lateral position on the first surface (11), and correlate the pixel intensity I P (t P ,x,y) with a signal with excitation frequency Φ, to determine the amplitude A(x,y) and the phase θ(x,y) of the pixel intensity I P to obtain for each lateral position on the first surface (11), characterized in that the amplitude A(x,y) and the phase θ(x,y) are converted into an intensity distribution I M (t,x,y) are transformed, where I Mdenote intensity, t time, and x, y lateral position; and determining a reconstructed intensity distribution I R (x,y,z) from the intensity distribution I M (t,x,y), where x, y denote the lateral position and z the depth in the substrate (1) below the first surface (11).

2. Method according to claim 1, characterized in that the conversion of the amplitude A(x,y) and the phase θ(x,y) into the intensity distribution I M (t,x,y) includes the following steps: Determining the time delay t D between the excitation of the thermal source (2) and the detection of the Intensity at the first surface (11) from the phase θ(x,y); generating a time vector for each lateral position (x,y) on the first surface (11) with duration L = 1 / Φ, where the time vector at position t Da Gaussian monopulse with the amplitude A(x,y) of the respective pixel as its maximum amplitude, as determined in the previous step.

3. Method according to claim 2, characterized in that the time delay t D The following formula is used to determine the phase θ(x,y) and excitation frequency Φ for each pixel:

4. A method according to any one of claims 1 to 3, characterized in that only pixels are used to localize the thermal source (2) which meet a predefinable inclusion criterion and / or that only pixels whose detected amplitude A(x,y) is above a predefinable limit value and / or that only pixels whose detected amplitude A(x,y) is greater than approximately 40% of the maximum value, or greater than approximately 30% of the maximum value, or greater than approximately 20% of the maximum value are included in the calculation.

5. A method according to any one of claims 1 to 4, characterized in that the determination of the reconstructed intensity distribution I R (x,y,z) by a time-based method or by a Fourier-based method, or that the determination of the reconstructed intensity distribution- lung I R(x,y,z) by a delay-and-sum method, or by an inverse boundary scattering transformation, or by a phase-shift migration, or by an omega-k migration.

6. Method according to any one of claims 1 to 4, characterized in that the method for determining the reconstructed intensity distribution I R (x,y,z) contains the following steps: Providing the intensity distribution I M (t,x,y)[Z0] at the first surface (11); Discretizing the time information t with a time increment Δt; Discretizing the position information x, y with position increments Δx, Δy, respectively; Discretizing the depth information z with a depth increment Δz; Determining the propagation speed of the thermal waves in the substrate (10) to Φ = √4 ⋅ α ⋅ π ⋅ Φ, where α denotes the thermal conductivity; Performing a Fourier transform of the intensity distribution I M (t,x,y) to create a transformed intensity distribution Î M(ω,k x ,k y to obtain ), where ω denotes the frequency information of the time information t, and k x , k y The spatial frequencies of the lateral positions x, y are denoted; a phase migration is performed by multiplying the transformed intensity distribution Î M (ω,k x ,k y ) with a phase factor ^^ ^^^∆௭^ , to obtain a migrated intensity distribution Î M (ω,k x ,k y )[Z0+ Δz l ] to obtain at a time earlier than the measurement, where k z the spatial frequency in the z-direction and Δz l denotes the distance of the l-th layer from the first surface (11) of the substrate (1); summation of all frequencies ω of the migrated intensity distribution Î M (ω,k x ,k y )[Z0+ Δz l ] and Fourier inverse transformation of the intensity distribution thus obtained Î M (k x ,k y)[Z0+ Δz l ], to determine the intensity distribution I R (x,y,Z0+ Δz l ) at a distance Δz l to obtain below the first surface (11) of the substrate (1).

7. Method according to claim 6, characterized in that the spatial frequency k z in the z-direction is determined as follows:

8. Method according to one of claims 6 or 7, characterized in that the reconstructed intensity distribution I R (x,y,Z0+ Δz l ) at a distance Δz l below the first surface (11) of the substrate (1) starting from the intensity distribution I M (t,x,y)[Z0] on the first surface (11) for all Δz l 9. Method according to one of claims 6 or 7, characterized in that the reconstructed intensity distribution I R (x,y,Z0+ Δz l+1 ) at a distance Δz l+1below the first surface (11) of the substrate (1) starting from the reconstructed intensity distribution I R (x,y,Z0+ Δz l ) at a distance Δz l is calculated recursively.

10. Method according to one of claims 1 to 9, characterized in that the substrate (1) contains a plurality of material layers (101, 102, 103, 104), each of which has a different thermal conductivity α exhibit, where the reconstructed intensity distribution I R (x,y,z) is determined separately for each material layer (101, 102, 103, 104).

11. Method according to any one of claims 6 to 10, characterized in that the position increment Δx, Δy for discretizing the position information x, y is greater than or equal to the size of a detector pixel on the first surface (11) of the substrate (1).

12. Method according to any one of claims 10 to 11, characterized in that the time increment Δt is determined as follows: where n is chosen between approximately 16 and approximately 1024 or between approximately 512 and 2048 and / or n = 2 . m is selected, where m is a positive integer.

13. Method according to any one of claims 10 to 12, characterized in that the depth increment Δz is selected to be smaller for smaller thermal conductivity α and larger for larger thermal conductivity α.

14. Computer program for carrying out a method according to any one of claims 1 to 13, wherein the computer program is executed on a microprocessor.

15. Data carrier with data stored thereon or signal sequence suitable for transmission via a computer network, representing data, wherein the data represents a computer program for carrying out a method according to any one of claims 1 to 13.

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