Method and apparatus for determining the layer thicknesses of a multilayer sample

Abstract

Method for determining the layer thicknesses of a sample with a known plurality N of superimposed layers S i , with i = 1, 2, 3, ..., N, with the steps: a) Generating pulses of electromagnetic high-frequency radiation with a predetermined frequency bandwidth, b) Irradiating the sample with electromagnetic high-frequency radiation and c) Time-resolved measurement of the electric field E P (t) the electromagnetic radiofrequency radiation reflected by or transmitted through the sample, d) Selecting a layer thickness d i , an absorption index k i and a refractive index n i for each layer S i , with i = 1, 2, 3, ..., N, e) Calculating a time-dependent electric field E M(t) for the electromagnetic high-frequency radiation reflected by or transmitted through the sample using a model, wherein the model defines a time-dependent electric field E according to the number N+1 interfaces between the measurement environment and the sample, as well as between the individual layers. j (t), with j = 0, 1, 2, 3, ..., N, taken into account, where the electric fields E j (t) depending on the layer thicknesses d i , the absorption indices k, which are assumed to be constant over the frequency bandwidth of the electromagnetic high-frequency radiation used i and the refractive indices n, which are assumed to be constant over the frequency bandwidth of the electromagnetic high-frequency radiation used. i to the time-dependent electric field E M (t) are added, f) Comparing the calculated electric field E M (t) with the detected electric field E P(t) g) when there is a deviation Q between the calculated electric field E M (t) and the detected electric field E P (t) is greater than a predetermined tolerance T, the layer thicknesses d i , the refractive indices n i and the absorption indices k i as long as the deviation Q is varied and steps e) to g) are repeated until the deviation Q is smaller than the tolerance T, and h) Providing the layer thicknesses d i as a result of the layer thickness determination, characterized in that initially for step d) and for a predetermined number of L repetitions of steps e) to g) the absorption index k i is selected from a range of values ​​that is small compared to the expected range of values ​​that the absorption index k represents. i for the respective shift S i a sample can assume and which is in relation to the maximum expected absorption index k ifor the respective layer includes small absorption indices.

Description

[0001] The present invention relates to a method and a device for determining the layer thicknesses of a sample with a known plurality N of superimposed layers S i , with i = 1, 2, 3, ..., N.

[0002] In many applications, such as automotive manufacturing, coatings are used that consist of several layers of different materials arranged on top of each other. Each layer can serve a different purpose. In automotive manufacturing, for example, a multi-layer coating might consist of a protective coating, a base coat, and a clear coat. A similar principle applies to the aerospace industry, where multi-layer coatings are also applied, for example, to an aircraft fuselage. For each individual layer of the coating to fulfill its purpose, it must be applied evenly and with a specified thickness. Therefore, being able to determine the thickness of each individual layer is essential, not only for quality control purposes.

[0003] For obvious reasons, the applied coating should not be damaged when determining the layer thickness. Furthermore, many coatings are sensitive to touch and may not be fully cured before the layer thickness of individual layers is to be determined during the production process. Therefore, the layer thicknesses must be determined non-destructively and without contact.

[0004] Known non-destructive and non-contact measuring methods for determining the layer thicknesses of a sample with a known plurality of N superimposed layers S i The experiments, where i = 1, 2, 3, ..., N, use electromagnetic high-frequency radiation to irradiate the sample. As the sample passes through the radio frequency radiation, its intensity varies depending on the distance traveled, i.e., the layer thickness d. i , and the absorption index k i the individual layers S i muted.

[0005] At interfaces between two layers with different refractive indices n i However, even at a transition between the measurement environment and the sample, the electromagnetic high-frequency radiation is partially reflected and partially transmitted according to Fresnel's laws. With thin coatings, which are usually coatings with a total thickness of less than 100 µm, the time interval between successive partial reflections can no longer be resolved with sufficient accuracy, making a simple time-of-flight measurement for determining the layer thickness impossible.

[0006] Upon closer examination, the refractive index and the absorption index of each layer S are also related. i The refractive index depends on the frequency of the electromagnetic radiation used. Therefore, previously known methods for determining layer thicknesses take frequency-dependent refractive indices into account. i(f) and frequency-dependent absorption indices k i (f).

[0007] In the article “Non-contact multi-layer thickness measurement of industrial coatings using THz measurement technology” by Volker KS Feige, Milan Berta, Stephan Nix, Frank Ellrich, Joachim Jonuscheidt and René Beigang, published in Technisches Messen: tm, Vol. 79, 2012, No. 2, pp. 87-94. – ISSN 0171-8096, such a non-destructive and non-contact measurement method for determining the layer thicknesses of a sample with a known plurality of N layers arranged one above the other is described.

[0008] The sample to be examined is irradiated with pulses of electromagnetic high-frequency radiation with a predetermined frequency bandwidth, whereby the electric field E P (t) the electromagnetic high-frequency radiation reflected by or transmitted through the sample is detected with time resolution. The detected, time-resolved electric field E P(t) is measured with a calculated, time-resolved electric field E M (t) compared, which is based on a physical model for the expected measurement signal. The model includes S for each interface between two layers. i with differing refractive indices n i as well as a time-dependent electric field E between the measurement environment and the first layer of the sample. j (t), with j = 1, 2, 3, ..., N, where the individual electric fields E j (t) taking into account an assumed layer thickness d i , previously known frequency-dependent absorption indices k i (f) and previously known frequency-dependent refractive indices n i (f) calculated and related to the time-dependent electric field E M (t) of the model are added.

[0009] The calculated electric field E M (t) and the measured electric field E P(t) are compared with each other. An iterative optimization procedure is used by varying the layer thicknesses d. i attempts to calculate the electric field E M (t) to the detected electric field E P (t) to approximate the sample. If there is sufficient agreement between the calculated electric field E M (t) and the detected electric field E P (t) the layer thicknesses d apply i as determined. The frequency-dependent refractive indices n i (f) and the frequency-dependent absorption indices k i(f) are currently determined experimentally in advance, i.e., by calibration measurements of individual layer thicknesses in a single-layer system. For a predetermined number of frequency points distributed across the frequency bandwidth of the electromagnetic high-frequency radiation used in the measurement procedure, the frequency-dependent refractive index n is determined for each individual layer of a known material composition. i (f) and the frequency-dependent absorption index k i (f) determined for this frequency point.

[0010] In practice, however, the individual layers are often applied to uncured and still moist layers, allowing the materials to mix at the interfaces. Furthermore, individual layers can swell in the presence of moisture. However, material mixing and changes in layer thickness are not taken into account when measuring the thickness of a single-layer system. The frequency-dependent refractive indices determined by such calibration measurements are therefore not considered. i (f) and absorption indices k i (f) and the model based on it therefore only inadequately reflect the actual properties of the coating of the sample.

[0011] Furthermore, previously known methods are computationally intensive, as the material parameters for each individual frequency point must be considered in the calculation. If the determination of the frequency-dependent material parameters is based, for example, on 125 frequency points, then for a sample with four layers, 4 x 125 frequency-dependent refractive indices, 4 x 125 frequency-dependent absorption indices, and 4 layer thicknesses must be taken into account when calculating the electric field E. M (t) must be taken into account. In this case, 1004 variables must be considered at each iteration step, so the computational effort per iteration step is large and the computation time is long.

[0012] US 2013 / 0204577A1 discloses an analytical model that simulates the propagation of electromagnetic radiation through a coated continuous path, where the layer thickness and the computation index determine the speed and direction of the transmitted radiation. The model predicts properties of the transmitted radiation based on properties of the incident radiation and initially assigned values ​​for the layer thicknesses. The layer thicknesses are assigned in a process in which incident radiation with known properties is directed onto a coated path, and then actual measurements of the transmitted radiation are compared with the predicted properties.Using a fitting algorithm, the assigned layer thicknesses of the model are adjusted, and the process is repeated until the actual and predicted values ​​are within the desired limits, so that the assigned thicknesses then represent the measured final dimensions. Radiation measurements are obtained using THz time-domain spectroscopy.

[0013] The article by VAN MECHELEN, JLM; KUZMENKO, AB; MERBOLD, H.: Stratified dispersive model for material characterization using terahertz time-domain spectroscopy. In: Optics Letters, Vol. 39, 2014, No. 13, pp. 3853–3856, discloses an approach to terahertz material analysis that provides highly accurate material parameters and can be used for industrial quality assurance. The method treats the material under investigation locally within its environment as a layered system and realistically describes the light-matter interaction of each layer.

[0014] Against this background, the object of the present invention is to provide a simple, preferably fast, and accurate method for determining the layer thicknesses of a sample with a known plurality of N layers arranged one above the other.

[0015] At least one of the aforementioned problems is solved according to the invention by a method for determining the layer thicknesses d i a sample with a known plurality of N layers arranged one above the other S i , with i = 1, 2, 3, ..., N, solved, which has the following steps: a) Generating pulses of electromagnetic high-frequency radiation with a predetermined frequency bandwidth, b) Irradiating the sample with electromagnetic high-frequency radiation and c) Time-resolved measurement of the electric field E P (t) the electromagnetic radiofrequency radiation reflected by or transmitted through the sample, d) Selecting a layer thickness d i , an absorption index k i and a refractive index n i for each layer S i , with i = 1, 2, 3, ..., N, e) Calculating a time-dependent electric field E M (t) for the electromagnetic high-frequency radiation reflected by or transmitted through the sample using a model, wherein the model defines a time-dependent electric field E according to the number N+1 interfaces between the measurement environment and the sample, as well as between the individual layers. j (t), with j = 0, 1, 2, 3, ..., N, taken into account, where the electric fields E j (t) depending on the layer thicknesses d i , the absorption indices k, which are assumed to be constant over the frequency bandwidth of the electromagnetic high-frequency radiation used iand the refractive indices n, which are assumed to be constant over the frequency bandwidth of the electromagnetic high-frequency radiation used. i to the time-dependent electric field E M (t) are added, f) Comparing the calculated electric field E M (t) with the detected electric field E P (t) g) when there is a deviation Q between the calculated electric field E M (t) and the detected electric field E P (t) is greater than a predetermined tolerance T, the layer thicknesses d i , the refractive indices n i and the absorption indices k i as long as the deviation Q is varied and steps e) to g) are repeated until the deviation Q is smaller than the tolerance T, and h) Providing the layer thicknesses d ias a result of the layer thickness determination, wherein initially for step d) and a predetermined number of L repetitions of steps e)-g), where L is preferably 5, 10, 15 or 20, the absorption index k i is selected from a range of values ​​that is smaller than the expected range of values ​​that the absorption index k represents. i for the respective shift S i a sample can assume and which is in relation to the maximum expected absorption index k i for the respective layer of small absorption indices.

[0016] Surprisingly, it has turned out that for the calculation of the time-dependent electric field E M (t) for the electromagnetic high-frequency radiation reflected by or transmitted through the sample is sufficient based on a model if the model is sufficient for each individual layer S i a refractive index n that is constant over the frequency bandwidth iand an absorption index k that is constant over the frequency bandwidth i assumes. Regarding the use of frequency-dependent refractive indices n i (f) and frequency-dependent absorption indices k i (f) can thus be omitted. For thin coatings, preferably coatings with a total thickness of less than 100 µm, particularly less than 70 µm, it has been found that the interaction path for the electromagnetic high-frequency radiation penetrating the sample is so short that the frequency dependence of the refractive indices and the frequency dependence of the absorption indices are negligible. Both the refractive index and the absorption index can be approximated by a value that is constant for each layer over the frequency bandwidth of the high-frequency radiation used.

[0017] The model is based on the assumption that the refractive indices n i and the absorption indices k iThe conditions that are constant over the frequency bandwidth used are met for a sample if the materials used for the layers do not exhibit dispersion in the frequency bandwidth of the electromagnetic high-frequency radiation used, i.e., are non-dispersive, or if the thicknesses d i the individual layers S i are so small that the influence of dispersion on the measurement result is negligible.

[0018] Based on this consideration, the number of unknowns to be determined per layer can be significantly reduced. This also applies to a prior determination of the refractive indices n. i and the absorption indices k iThis can be dispensed with. The determination of the layer thicknesses of a sample with a known plurality of N superimposed layers can be carried out in this way without prior calibration. Determination of the layer thicknesses, refractive indices, and absorption indices is possible. Therefore, it is also unnecessary to know the material composition of the coating, as is otherwise required for calibration measurements. Since calibration errors are avoided, it has been possible in experiments to achieve a minimum detection limit for the layer thickness of approximately 5 µm. In comparison, the minimum detection limit for comparative measurements using conventional measuring methods is about 20 µm.

[0019] In one embodiment, the generated electromagnetic high-frequency radiation lies in a frequency range from 1 GHz to 30 THz, the so-called THz frequency range.

[0020] In one embodiment, the calculation of the time-dependent electric field E takes into account M (t) in step e) for a given number R of multiple reflections in the layers S i Additionally, each has a time-dependent electric field E r (t), with r = 1, 2, 3, ..., R, which are associated with the electric fields E j (t) depending on the layer thicknesses d i , the absorption indices k, which are assumed to be constant over the frequency bandwidth of the electromagnetic high-frequency radiation used i and the refractive indices n, which are assumed to be constant over the frequency bandwidth of the electromagnetic high-frequency radiation used. i to the electric field E M (t) are added.

[0021] It is understood that the time-resolved electric fields E P (t), E M (t), E j (t) and / or E r(t) can be represented in both time and frequency domains. Switching between time and frequency domain representations is possible by applying a corresponding Fourier transform to the electric field to be represented.

[0022] In one embodiment, steps e) and / or f) are performed in the frequency domain. The electric fields E j (t) and / or E r (t) are therefore in step e) depending on the layer thicknesses d i , the absorption indices k, which are assumed to be constant over the frequency bandwidth of the electromagnetic high-frequency radiation used i and the refractive indices n, which are assumed to be constant over the frequency bandwidth of the electromagnetic high-frequency radiation used. i in the frequency domain to the electric field E M (t) of the model is added. Accordingly, the calculated electric field E M(t) in step f) with the measured electric field E P (t) of the sample in the frequency domain. An advantage of carrying out steps e) and / or f) in the frequency domain is that a phase shift occurring during a transition of the electromagnetic high-frequency radiation from an optically thinner layer to an optically denser layer is not reflected in the frequency domain representation of the electric fields E. j (t) and / or E r (t) can be represented by a phase shift of 180°.

[0023] In one embodiment, step h) further comprises providing the refractive indices n i and / or absorption indices k i as a result. In addition to the layer thicknesses d i The refractive indices can also be used. i and / or the absorption indices k i for each layer S i the sample is determined and provided.

[0024] In one embodiment, the electric fields Ej (t) and / or E r(t) a time-dependent electric field E0 of the generated electromagnetic high-frequency radiation, preferably acquired by a blank measurement. In the blank measurement, a measurement is performed without a sample positioned in the beam path of a device for determining the layer thicknesses of a multilayer sample. In a reflection geometry, the sample is replaced by a simple mirror. In a transmission geometry, the measurement is performed without a sample. The time-resolved electric field E0 acquired by a blank measurement corresponds to the electric field of the electromagnetic high-frequency radiation used, which strikes the sample, and also represents the receiving characteristics of the measuring device used to acquire the high-frequency radiation reflected or transmitted by the sample. The electric field E0 determined in this way serves as the starting point for the calculation taking into account the layer thicknesses d. i, the refractive indices n i and the absorption indices k i calculated electric fields E j (t) and / or E r (t).

[0025] The method itself can be used in a preliminary step to determine selected material parameters of individual layers, whereby the material parameters thus determined can be used as input variables in a subsequent execution of the method according to the invention. The method presented here can therefore also be used for self-calibration.

[0026] The refractive index n i and the layer thickness d i have a decisive influence on the phase information of the time-dependent electric field. The absorption index k i and the layer thickness d i In contrast, they influence the amplitude of the time-dependent electric field. Based on the refractive indices n i and the layer thicknesses d iThe phase information of the electric fields E j (t) and / or E r (t) is intended for the coating. This results in destructive and constructive superpositions of the individual fields E. j (t) and / or E r (t), which is the calculated electric field E M (t) results, which is characterized by the phase and amplitude. However, the phase also depends on the thicknesses d. i and the refractive indices n i This means that several combinations of these two material parameters can lead to an identical phase shift. If the refractive index of the model does not match the actual refractive index of the individual layer S i If the values ​​on the sample agree, then the momentum amplitude of the calculated time-resolved electric field E deviates. M (t) partly considerably from the measured time-resolved electric field E P(t) ab. To eliminate ambiguities, the influence of the amplitude can be reduced by initially assuming smaller absorption indices k. i Ambiguities can be suppressed. For the first iteration steps, reducing the possible range of values ​​for the absorption indices can decrease the probability of ambiguities and thus increase the convergence of the optimization.

[0027] Therefore, initially, i.e. at the beginning of the process, in step d) and for a predetermined number of L repetitions of steps e) to g), where L is preferably 5, 10, 15 or 20, the absorption index k is determined. i selected from a range of values ​​that is small compared to the actually expected range of values ​​that the absorption index k represents. i for the respective shift S i the sample can assume and which is in relation to the maximum expected absorption index k i for the respective layer includes small absorption indices.

[0028] In another embodiment, k i in step d) and for a predetermined number of L repetitions of steps e) to g), where L is preferably 5, 10, 15 or 20, selected from the range of 0 to 0.01, preferably from the range of 0 to 0.05 and particularly preferably from the range of 0 to 0.1. This initial restriction of the search space for the absorption indices k i has proven particularly advantageous in determining paint layers with actual absorption indices in the range of 0 to 1.5.

[0029] In one embodiment, the permissible value range for each layer S can be i be adapted.

[0030] In one embodiment, a genetic optimization algorithm is used such that in step d) a plurality X of possible solution candidates I s , with s = 1, 2, 3, ..., X, for the layer thicknesses d i , refractive indices ni and absorption indices k i is selected from predefined value ranges, whereby in a further step d') is based on the plurality X of possible solution candidates I s (n i , k i , d i ) an equal number X of mutated solution candidates K s (n i , k i , d i ) is calculated, where in step e) for each of the X solution candidates I s (n i , k i , d i ) and K s (n i , k i , d i ) an electric field E M (t) is calculated and these calculated electric fields E M (t) in step f) with the measured electric field E P (t) of the sample are compared, where if for each electric field E M (t) the deviation Q from the measured electric field E P(t) is greater than a predetermined tolerance T, in step g) those solution candidates I s (n i , k i , d i ) or K s (n i , k i , d i ) as I s (n i , k i , d i ) are adopted for which the deviation Q is smaller, whereby the X solution candidates thus retained are I s (n i , k i , d i ) can be further varied by repeating steps d') to g) until the deviation Q for at least one solution candidate is smaller than the tolerance T.

[0031] In one embodiment, in step d') the mutated solution candidates K are s (n i , k i , d i ) from three randomly selected solution candidates I s (n i , k i , d i ) calculated.

[0032] In one embodiment, the majority of solution candidates is X = 128.

[0033] In one embodiment, the layers are paint layers of a vehicle coating, wherein preferably for steps b) and c) the paint layers are not yet cured.

[0034] In another embodiment, the deviation Q between the calculated and measured electric fields E M (t), E P (t) the mean squared error.

[0035] The present invention also includes a device for determining the layer thicknesses of a sample with a known plurality N of superimposed layers S i , with i = 1, 2, 3, ..., N, exhibiting: - a source that is set up and designed in such a way that it generates pulses of electromagnetic high-frequency radiation with a predetermined frequency bandwidth during the operation of the device, - a device that is set up and designed in such a way that, during operation of the device, it irradiates the sample with electromagnetic high-frequency radiation, - a measuring device which is set up and designed in such a way that it measures the electric field E during operation of the device P (t) time-resolved detection of the high-frequency electromagnetic radiation reflected by or transmitted through the sample, - a control and evaluation unit that is set up and designed to perform the following steps during operation of the device: d) Selecting a layer thickness d i , an absorption index k i and a refractive index n i for each layer S i , with i = 1, 2, 3, ..., N, e) Calculating a time-dependent electric field E M(t) for the electromagnetic high-frequency radiation reflected by or transmitted through the sample using a model, wherein the model defines a time-dependent electric field E according to the number N+1 interfaces between the measurement environment and the sample, as well as between the individual layers. j (t), with j = 0, 1, 2, 3, ..., N, taken into account, where the electric fields E j (t) depending on the layer thicknesses d i , the absorption indices k, which are assumed to be constant over the frequency bandwidth of the electromagnetic high-frequency radiation used i and the refractive indices n, which are assumed to be constant over the frequency bandwidth of the electromagnetic high-frequency radiation used. i to the time-dependent electric field E M (t) are added, f) Comparing the calculated electric field E M (t) with the detected electric field E P(t) g) when there is a deviation Q between the calculated electric field E M (t) and the detected electric field E P (t) is greater than a predetermined tolerance T, the layer thicknesses d i , the refractive indices n i and the absorption indices k i as long as the deviation Q is varied and steps e) to g) are repeated until the deviation Q is smaller than the tolerance T, and h) Providing the layer thicknesses d i as a result of the layer thickness determination, wherein the control and evaluation device is further set up and designed such that initially for step d) and a predetermined number of L repetitions of steps e)-g) the absorption index k i is selected from a range of values ​​that is small compared to the expected range of values ​​that the absorption index k represents. i for the respective shift S ia sample can assume and which is in relation to the maximum expected absorption index k i for the respective layer includes small absorption indices.

[0036] In one embodiment, the evaluation unit includes a graphics card that is configured and designed to perform steps d) to f), so that all optimization calculations can be carried out on the graphics card, preferably in parallel. This reduces the computation time.

[0037] In a further embodiment, the source comprises a laser for generating short electromagnetic pulses in the infrared spectral range and a beam splitter that divides the pulses into two spatially separated pulses, wherein a device is set up and designed such that, during operation of the device, it directs the first pulse to generate a pulse of electromagnetic high-frequency radiation onto a target, while directing the second pulse to the measuring device in such a way that the second pulse occurs simultaneously with the generated pulse of electromagnetic high-frequency radiation on the measuring device.

[0038] Further advantages, features, and applications of the present invention will become clear with reference to the following description of preferred embodiments and the accompanying figures. These show: Fig. 1. A sketchy cross-section through an exemplary sample, Fig. 2 a flowchart illustrating the process steps according to an embodiment of the present invention, Fig. 3. A comparison between the measured electric field E P (t) and the calculated electric field E M (t) from a comparative experiment, Fig. 4 a comparison of the thicknesses d i the individual layers of the comparison experiment Fig. 3, and Fig. 5 a sketchy representation of a device according to the invention for carrying out the method.

[0039] In the Fig. Figure 1 shows a sketched cross-section through an exemplary sample. The sample has a coating of N = 4 superimposed layers. Each layer consists of a different material and is distinguished by its refractive index n. i , their layer thickness d i and their absorption index k icharacterized. When the sample is irradiated with pulses of electromagnetic high-frequency radiation with a predefined frequency bandwidth, the incident radiation is partially reflected at each interface, i.e., between the measurement environment and the sample, as well as between two adjacent layers. The partial reflections are described in the Fig. 1 according to their respective origin by E P0 (t), E P1 (t), E P2 (t), E P3 (t) and E P4 (t) indicated, where the time-resolved electric field of the high-frequency radiation used for irradiation is in the Fig. 1 is labelled as E'0(t). The time-resolved electric fields of these partial reflections superimpose to form the time-resolved electric field E. P (t) of the sample, which is recorded during the measurement. Upon closer examination, the electric field E comprises P(t) of the sample also exhibits multiple reflections, which arise from repeated reflections of the radiofrequency radiation at the interfaces. In the Fig. These multiple reflections are not shown in Figure 1. The temporal sequence of the partial reflections, their amplitudes, and their phases depend on the material parameters of the layers.

[0040] In the Fig. 2 are the steps of the procedure for determining the layer thicknesses of a sample with a plurality of N layers arranged one above the other S i , with i = 1, 2, 3, ..., N, according to one embodiment of the present invention, is represented as a flowchart. In a first step a), pulses of electromagnetic high-frequency radiation with a predetermined frequency bandwidth are generated. In a subsequent step b), the generated electromagnetic high-frequency radiation is used to irradiate a sample which has a coating consisting of a plurality of N superimposed layers S iEach of these layers has a refractive index n. i , an absorption index k i and a layer thickness d i which affect the reflection and transmission properties of the layers for the electromagnetic high-frequency radiation used.

[0041] The electric field E reflected or transmitted by the sample P (t) of the electromagnetic high-frequency radiation is recorded in time-resolved step c). In step d), for each layer S i a layer thickness d i , a refractive index n i and an absorption index k i The initial values ​​are selected. In a subsequent step e), a time-dependent electric field E is generated. M(t) for the electromagnetic high-frequency radiation reflected by or transmitted through the sample is calculated using a model. The model includes a time-dependent electric field E corresponding to a number N+1 interfaces between the measurement environment and the sample, as well as between the individual layers. j (t), with j = 0, 1, 2, 3, ..., N, where the electric fields E j (t) to the time-dependent electric field E M (t) of the model as a function of the layer thicknesses d i , the refractive indices n i and the absorption indices k i The refractive index n is added. The model is based on the assumption that the refractive index n i and the absorption index k i each layer S i is constant over the frequency bandwidth of the high-frequency radiation used, i.e., independent of the frequency of the high-frequency radiation.

[0042] Then, in step f), the calculated electric field E is determined. M (t) of the model with the detected electric field E P (t) of the sample compared, wherein in step g) if there is a deviation Q between the calculated electric field E M (t) and the detected electric field E P (t) is greater than a predetermined tolerance T, the layer thicknesses d i , the refractive indices n i and the absorption indices k i This process is varied and steps e) to g) are repeated until the deviation Q is smaller than the tolerance T.

[0043] If the deviation Q is smaller than the tolerance T, the layer thicknesses d are determined in one step h). i provided as a result of the layer thickness determination.

[0044] An exemplary comparison of a measured, time-resolved electric field E P (t) and a calculated, time-dependent electric field EM (t) after determining the material parameters n i , k i and d i is in Fig. 3 shown. The relative deviation between the normalized electric fields E P (t) and E M (t) lies within + / - 5%, which corresponds to the existing tolerance T.

[0045] The one in Fig. The result shown in section 3 was based on a sample with N = 4 superimposed layers, as is also the case in the Fig. 1 is indicated. A primer (i = 1) is coated with a layer of filler (i = 2), a layer of basecoat (i = 3), and a layer of clearcoat (i = 4). The layer thicknesses d, determined by cross-section using a light microscope as a reference value, are shown below. i are in the Fig. 4 compared to the layer thicknesses determined by the application of the inventive method.

[0046] Fig. Figure 5 schematically shows the structure of a device 1 according to the invention, which is used to carry out the inventive method for determining the layer thicknesses of a sample with a known plurality of N layers arranged one above the other. i , with i = 1, 2, 3, ..., N, is set up and designed, in which the electromagnetic high-frequency radiation 2 in a frequency range of 1 GHz to 30 THz is generated and detected with photoconductive switches as source 3 and detector 4 for the high-frequency radiation 2.

[0047] The device 1 comprises a laser 5 for generating short electromagnetic pulses in the infrared spectral range. The pulse duration of the pulses generated by the laser 5 is approximately 100 fs. Each pulse generated by the laser 5 is split into two spatially separated pulses of approximately equal power (not in the Fig. 5 not shown) and coupled into source 3 and detector 4.

[0048] In the illustrated embodiment, the source 3 and the detector 4 each consist of a high-frequency component configured as a photoconductive switch, each with a dipole structure serving as an antenna for the high-frequency radiation 2. Each dipole antenna has a break in its center, which, together with a photoconductive semiconductor substrate located beneath the antenna structure, forms a photoconductive switch. The electromagnetic radiation generated by the laser 5 in the form of short pulses is focused onto these photoconductive switches. Alternatively, as shown here, it is also possible to guide the electromagnetic radiation generated by the laser 5 onto the photoconductive switches using optical fibers 6, 7. In such an embodiment, it may be necessary to pre-compensate for the dispersion that the individual pulses experience in the fiber.

[0049] In the illustrated embodiment, the semiconductor substrate for the photoconductive switch is a gallium arsenide grown at low temperatures, exhibiting short charge carrier lifetimes or charge carrier capture times. The electromagnetic high-frequency radiation 2 generated by the source 3 is focused onto the sample 12, for example, via a THz beam splitter 9 and a lens 11. The electromagnetic high-frequency radiation 2 reflected from the sample 12 is then directed onto the detector 4, for example, again via the THz beam splitter 9 and a mirror 10.

[0050] Both source 3 and detector 4 have two feed lines for their respective dipole antennas (in the Fig.(5 not shown). During operation of the device 1, a rectangularly modulated bias voltage is applied to the high-frequency component used as source 3 via the antenna leads. The rectangular modulation serves to enable the electromagnetic radiation to be detected by a lock-in amplifier, whose reference signal is phase-coupled to the modulation of the bias voltage of source 3. The brief closing of the photoconductive switch causes a short current pulse across the antenna, which leads to the emission of a broadband high-frequency pulse 2 from the antenna.

[0051] The path lengths of the optical and radio frequency signals on the path from the laser via the source 3 and the object 12 to the detector 4 on the one hand, and from the laser via a delay line 8 to the detector 4 on the other hand, are arranged such that the radio frequency signal 2 hits the detector 4 simultaneously with the second part of the optical pulse, the first part of which caused the generation of the radio frequency pulse 2 in the source 3.

[0052] Considering the high-frequency component 4 used on the detector side, the current flowing through the antenna and the photoconductive switch formed by it is detected and measured there. For this purpose, the high-frequency component 4 is connected to a control and evaluation unit (not shown here). For example, the control and evaluation unit can be a conventional industrial PC. The control and evaluation unit can also be connected to a monitor to display the measurement results.

[0053] The electromagnetic field of the high-frequency pulse 2, which strikes the antenna of detector 4, causes charge carriers to flow across the antenna or the switch, thus generating a current. However, the current can only flow through the antenna when the photoconductive switch is closed by the arrival of an electromagnetic pulse from the laser 5. Since the electromagnetic pulse used to close the photoconductive switch on the detector side is short in time compared to the high-frequency pulse striking the antenna, the electric field of the high-frequency pulse 2 can be sampled with temporal resolution by shifting the arrival times of the two relative to each other using the delay line 8.

[0054] In the illustrated embodiment, the evaluation and control unit calculates the time-resolved electric field E. M(t) and compares this with the measured, time-resolved electric field E P (t) of the sample. Is there a deviation Q between the calculated electric field E M (t) and the detected electric field E P If (t) is greater than a predetermined tolerance T, the control and evaluation unit varies the layer thicknesses d. i , the refractive indices n i and the absorption indices k i and repeats steps e) to g) until the deviation Q is smaller than the tolerance T. The control and evaluation unit then sets the determined layer thicknesses d. i ready so that they can be displayed on a monitor, for example.

[0055] For the purposes of the original disclosure, it is pointed out that all features as they can be deduced by a person skilled in the art from the present description, the drawings, and the claims, even if they are specifically described only in connection with certain other features, can be combined individually or in any combination with other features or groups of features disclosed herein, unless this has been expressly excluded or technical circumstances render such combinations impossible or pointless. A comprehensive, explicit description of all conceivable combinations of features is omitted here solely for the sake of brevity and readability.

[0056] While the invention has been illustrated and described in detail in the drawings and the preceding description, this illustration and description are merely exemplary and are not intended to limit the scope of protection as defined by the claims. The invention is not limited to the disclosed embodiments.

[0057] Variations of the disclosed embodiments are obvious to a person skilled in the art from the drawings, the description, and the accompanying claims. In the claims, the word "have" does not exclude other elements or steps, and the indefinite article "a" or "an" does not exclude multiple features. The mere fact that certain features are claimed in different claims does not preclude their combination. Reference numerals in the claims are not intended to limit the scope of protection. Reference symbol list 1 Device for carrying out the method according to the invention 2 High-frequency radiation 3 Source 4 Detector 5 lasers 6 optical fibers 7 optical fiber 8 Delay unit 9 THz beam splitter 10 mirrors 11 Lens 12 Sample

Claims

[1] Method for determining the layer thicknesses of a sample with a known plurality N of layers S arranged one above the other i , with i = 1, 2, 3, ..., N, with the steps: a) Generating pulses of electromagnetic high-frequency radiation with a predetermined frequency bandwidth, b) Irradiating the sample with electromagnetic high-frequency radiation and c) Time-resolved measurement of the electric field E P (t) the electromagnetic radiofrequency radiation reflected by or transmitted through the sample, d) Selecting a layer thickness d i , an absorption index k i and a refractive index n i for each layer S i , with i = 1, 2, 3, ..., N, e) Calculating a time-dependent electric field E M(t) for the electromagnetic high-frequency radiation reflected by or transmitted through the sample using a model, wherein the model defines a time-dependent electric field E according to the number N+1 interfaces between the measurement environment and the sample, as well as between the individual layers. j (t), with j = 0, 1, 2, 3, ..., N, taken into account, where the electric fields E j (t) depending on the layer thicknesses d i , the absorption indices k, which are assumed to be constant over the frequency bandwidth of the electromagnetic high-frequency radiation used i and the refractive indices n, which are assumed to be constant over the frequency bandwidth of the electromagnetic high-frequency radiation used. i to the time-dependent electric field E M (t) are added, f) Comparing the calculated electric field E M (t) with the detected electric field E P(t) g) when there is a deviation Q between the calculated electric field E M (t) and the detected electric field E P (t) is greater than a predetermined tolerance T, the layer thicknesses d i , the refractive indices n i and the absorption indices k i as long as the deviation Q is varied and steps e) to g) are repeated until the deviation Q is smaller than the tolerance T, and h) Providing the layer thicknesses d i as a result of the layer thickness determination, characterized by , that initially for step d) and for a predetermined number of L repetitions of steps e) to g) the absorption index k i is selected from a range of values ​​that is small compared to the expected range of values ​​that the absorption index k represents. i for the respective shift S i a sample can assume and which is in relation to the maximum expected absorption index k ifor the respective layer includes small absorption indices. [2] Method according to claim 1, characterized by , that the calculation of the time-dependent electric field E M (t) in step e) for a given number R of multiple reflections in the layers S i Additionally, each has a time-dependent electric field E r (t), with r = 1, 2, 3, ..., R, takes into account which are associated with the electric fields E j (t) depending on the layer thicknesses d i , the absorption indices k, which are assumed to be constant over the frequency bandwidth of the electromagnetic high-frequency radiation used i and the refractive indices n, which are assumed to be constant over the frequency bandwidth of the electromagnetic high-frequency radiation used. i to the electric field E M (t) are added. [3] Method according to claim 1 or 2, characterized by, that steps e) and / or f) are based on a representation of the electric fields E P (t), E M (t), E j (t) and / or E r (t) are based in the frequency domain. [4] Method according to any one of claims 1 to 3, characterized by , that step h) continues to provide the refractive indices n i and / or the absorption indices k i as a result. [5] Method according to any one of claims 1 to 4, characterized by , that the electric fields E j (t) and / or E r (t) is based on a time-dependent electric field E0 of the generated electromagnetic high-frequency radiation, preferably measured with a blank measurement. [6] Method according to any one of claims 1 to 5, characterized by that L is 5, 10, 15 or 20. [7] Method according to any one of claims 1 to 6, characterized by , that k ifor step d) and the number of L repetitions of steps e) to g) is selected from the range of 0 to 0.01, preferably from the range of 0 to 0.05 and particularly preferably from the range of 0 to 0.

1. [8] Method according to any one of claims 1 to 7, characterized by , that the layers are paint layers of a vehicle coating, wherein for steps b) and c) the applied paint layers are preferably not yet cured. [9] Method according to any one of claims 1 to 8, characterized by , that the deviation Q between the calculated and measured electric fields E M (t), E P (t) is the mean squared error. [10] Device for determining the layer thicknesses of a sample with a known plurality of N layers arranged one above the other S i , with i = 1, 2, 3, ..., N, exhibiting: - a source that is set up and designed in such a way that it generates pulses of electromagnetic high-frequency radiation with a predetermined frequency bandwidth during the operation of the device, - a device that is set up and designed in such a way that, during operation of the device, it irradiates the sample with electromagnetic high-frequency radiation, - a measuring device which is set up and designed in such a way that it measures the electric field E during operation of the device P (t) time-resolved detection of the high-frequency electromagnetic radiation reflected by or transmitted through the sample, and - a control and evaluation unit that is set up and designed to perform the following steps during operation of the device: d) Selecting a layer thickness d i , an absorption index k i and a refractive index n i for each layer S i, with i = 1, 2, 3, ..., N, e) Calculating a time-dependent electric field E M (t) for the electromagnetic high-frequency radiation reflected by or transmitted through the sample using a model, wherein the model defines a time-dependent electric field E according to the number N+1 interfaces between the measurement environment and the sample, as well as between the individual layers. j (t), with j = 0, 1, 2, 3, ..., N, taken into account, where the electric fields E j (t) depending on the layer thicknesses d i , the absorption indices k, which are assumed to be constant over the frequency bandwidth of the electromagnetic high-frequency radiation used i and the refractive indices n, which are assumed to be constant over the frequency bandwidth of the electromagnetic high-frequency radiation used. i to the time-dependent electric field E M (t) are added, f) Comparing the calculated electric field E M (t) with the detected electric field E P (t) g) when there is a deviation Q between the calculated electric field E M (t) and the detected electric field E P (t) is greater than a predetermined tolerance T, the layer thicknesses d i , the refractive indices n i and the absorption indices k i as long as the deviation Q is varied and steps e) to g) are repeated until the deviation Q is smaller than the tolerance T, and h) Providing the layer thicknesses d i as a result of the layer thickness determination characterized by , that the control and evaluation unit is further set up and designed such that initially for step d) and a predetermined number of L repetitions of steps e) to g) the absorption index k iis selected from a range of values ​​that is small compared to the expected range of values ​​that the absorption index k represents. i for the respective shift S i a sample can assume and which is in relation to the maximum expected absorption index k i for the respective layer includes small absorption indices. [11] Device according to claim 10, characterized by, that the source comprises a laser for generating short electromagnetic pulses in the infrared spectral range and a beam splitter that divides the pulses into two spatially separated pulses, wherein a device is set up and designed such that, during operation of the device, it directs the first pulse to generate a pulse of electromagnetic high-frequency radiation onto a target, while directing the second pulse to the measuring device in such a way that the second pulse occurs simultaneously with the generated pulse of electromagnetic high-frequency radiation onto the measuring device.

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