Compensation for the effect of substrate alloy

Abstract

A method is described for compensating for substrate variations in a measurement of a quantity of a material disposed on a substrate, the method including receiving detected X-ray signals for measurement of the material at a position on a surface of the substrate, and determining a quantity of material based on the received X-ray measurement signals and a predetermined set of compensation parameters for the substrate, the set of compensation parameters varying with position on the surface of the substrate.

Description

[Technical field]

[0001] (CROSS REFERENCE TO RELATED APPLICATIONS) This application claims the benefit of priority from U.S. Patent Application No. 63 / 269,852, filed March 24, 2023, which is hereby incorporated by reference in its entirety.

[0002] FIELD OF THEINVENTION The present disclosure relates to a method for compensating for substrate variations in X-ray measurements of a material quantity of a material disposed on a substrate, a method for determining compensation parameters for substrate variations in X-ray measurements of a material quantity of a material disposed on a substrate, and an X-ray analysis system. [Background technology]

[0003] X-ray scattering and X-ray fluorescence (XRF) analysis are used in a variety of non-contact industrial process measurements, particularly for thickness measurements. For example, these techniques can be used to monitor the thickness of materials such as webs transported on conveyor rolls and coatings applied to the web. The rolls may have a surface coating, and measurements may be made based on the uniformity of this surface coating across the entire surface of the roll.

[0004] 1, an exemplary X-ray sensor head configuration for a web measurement process is shown. The apparatus includes a rolling machine 10 and an X-ray sensor head 20. The X-ray sensor head 20 emits X-rays that are directed at a material, such as a web, passing over the rolling machine 10 and detects the returning scattered X-rays or fluorescent X-rays as a voltage signal. As the thickness of the material increases, the scattered radiation and X-ray fluorescence are modulated, such as increased or decreased.

[0005] During processing, the mill 10 rotates and the sensor 20 moves along the width (x) of the mill, whereby the detected voltage signal is a function of the mill's cylindrical coordinates (x,φ) and time (t). The detected voltage signal can then be correlated to the thickness or basis weight of a material, such as a web or coated web, by linearizing it according to a calibration curve. The voltage signal can also be compensated for temperature before any correlation based on the calibration curve is performed.

[0006] As industrial processes advance, maintaining and improving the accuracy of such measurements is a significant challenge. Summary of the Invention

[0007] This disclosure stems from a new realization that the surface coating of the substrate (e.g., a conveyor roll machine) that provides the surface on which the material to be measured by X-ray analysis is placed can be damaged. Typically, a filler material containing multiple elements (often different from the surface coating of the roll machine) can be used to repair the substrate. Such repairs can be necessary for industrial processes.

[0008] It was previously expected that the substrate surface during X-ray analysis would be smooth and have a uniform coating across the entire surface. However, it has been found that additional filler material affects the detected X-ray signal, such as the XRF or X-ray scattering signal, leading to measurement inaccuracies. The filler material may, for example, absorb the XRF signal or provide additional XRF signal, thereby changing the spectrum. Alternatively, the filler material may cause more or less X-ray scattering, which may change the X-ray signal. In one aspect, the present disclosure provides techniques to compensate for this inaccuracy.

[0009] Compensation is achieved by identifying a set of compensation parameters for the substrate surface. The parameters are position-dependent (i.e., they vary depending on the position on the substrate surface being measured). Since measurements are performed for multiple positions on the substrate surface, the set of compensation parameters typically covers multiple positions. The parameters are applied in a process that correlates (linearizes) the detected X-ray signal to a material amount, e.g., thickness, basis weight, or coating weight. This linearization typically uses a predefined calibration curve. If the substrate surface has a substantially cylindrical shape (e.g., a rolling mill or conveyor belt that can be seen as a squashed cylinder shape, or a cylinder with a slightly non-circular cross section), each position on the substrate surface can be defined by cylindrical coordinates (the position along the width of the substrate surface and the rotation angle of the substrate).

[0010] The X-ray signal may be a sampled voltage or an integrated charge. The signal is typically time-averaged over a (fixed) measurement period.

[0011] Specific parameters that may be used may include one or more of the following: (a) open circuit voltage (V 0,Sub ), (b) a spectral adjustment factor for the determined coating weight (a), and (c) a temperature compensation factor for the voltage signal (b). It is noted that the substrate may be subject to temperature variations, for example due to heating of the substrate (e.g., in the case of a rolling mill). Since these parameters are position dependent (i.e., they are different for each position on the substrate surface), a database of parameters for a particular substrate may be provided for compensation purposes, which may be stored in non-volatile memory.

[0012] In practice, the measured voltage may be normalized using a normalization factor or shutter-open signal by dividing the measured voltage by the normalization factor or shutter-open signal (both reduced by the saturation voltage before division). The measured voltage may be temperature compensated by applying a temperature compensation factor to the measured voltage (preferably together with a temperature compensation factor), preferably the measured voltage normalized by the normalization factor or shutter-open signal. A spectral tuning factor for the determined coating weight may be determined from the measured voltage, preferably multiplied by the coating weight, determined from the measured voltage normalized by the normalization factor or shutter-open signal and / or compensated by the temperature compensation factor.

[0013] In one aspect (which may be combined with any other aspect disclosed herein), the present disclosure provides a method for determining compensation parameters. This may be accomplished by obtaining a detected X-ray signal for each of a number of locations on a surface of a substrate (and generally multiple X-ray signals per location, with different conditions for each signal). A set of compensation parameters for each location on the surface of the substrate may then be established from the respective detected X-ray signal(s).

[0014] For example, a shutter open signal for a position on the substrate may be established by measuring the position of the surface of the substrate with no material placed on the substrate (e.g., no material placed between the sensor head and the substrate). The shutter open signal for a position may then include the detected X-ray signal obtained at that position. Effectively, in an implementation using a rolling mill, the bare rolling mill surface is mapped, i.e., each square centimetre of the rolling mill surface is measured by the X-ray sensor using a synchronous scanning motion across the rolling mill width and the rolling mill rotation angle.

[0015] In another embodiment, the spectral tuning ratio may be determined by measuring the X-ray signal for each location on the surface of the substrate when a known amount of material (e.g., thickness) is placed at a predetermined location (or distance) relative to the X-ray sensor. The spectral tuning ratio for each location may be established by comparing the amount of material (e.g., basis weight or weight of material) determined for each location and comparing it to the known amount of material. Preferably, a pre-established shutter open signal is used in determining the amount of material.

[0016] The temperature compensation factor may be established by measuring a surface of the substrate, with no material disposed on the substrate, at a different (typically higher) temperature than the measurement made to establish the shutter-open signal. A temperature compensation factor may be identified (typically calculated) for this temperature, and the temperature compensation factor may be established by comparing the shutter-open signal adjusted by the temperature compensation factor (or equivalently, another measurement made at the first temperature with no material on the substrate) to the measured x-ray signal.

[0017] Any aspect may be embodied as a computer program (e.g., software and / or firmware) that may be provided on a computer readable medium. Additionally or alternatively, the aspect may be found in hardware, for example, an X-ray analysis system. The system may comprise features configured to implement any of the method aspects and / or features. These may include an X-ray sensor and / or a processing unit (processor).

[0018] The present disclosure may be put into practice in many ways and a preferred embodiment may be described below, by way of example only, and with reference to the accompanying drawings. [Brief description of the drawings]

[0019] [Figure 1] 1 illustrates an exemplary X-ray sensor head configuration for a web metrology process. [Diagram 2]1 depicts a typical XRF calibration curve showing X-ray detector signal for different substrate basis weights. [Diagram 3] Measurements at different positions on a cylindrical substrate are illustrated. [Figure 4] 1 illustrates an approach for establishing a spectral tuning rate or tilt angle rate in one embodiment. [Diagram 5] 1 depicts a flowchart of a compensation algorithm, according to one embodiment. [Figure 6] 1 depicts a flowchart for substrate mapping, according to one embodiment. [Figure 7A] 1 depicts a flowchart of an algorithm for establishing a spectral adjustment parameter or tilt angle parameter, according to one embodiment. [Figure 7B] 1 depicts a flowchart of an algorithm for establishing a spectral adjustment parameter or tilt angle parameter, according to one embodiment. [Figure 8] 1 depicts a flowchart of an algorithm from establishing temperature compensation parameters, according to one embodiment. [Figure 9] 1 depicts a mapped substrate according to one embodiment. DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

[0020] Like reference numbers indicate corresponding features.All drawings are to be understood as schematic.

[0021] In the examples discussed here, XRF measurements of basis weight or coating weight on a cylindrical substrate are described. It will be understood that different X-ray techniques and / or different material amount measurements and / or different substrate geometries may alternatively be used. For example, the X-ray signal may be from X-ray scattering. It will be clear how to modify the approach disclosed below in such a situation. Also, measurements may be made in this example only at specific locations (called "binned" values ​​or locations) on the surface of the substrate.

[0022] The following table shows the parameters used in the particular embodiment considered at this stage.

[0023] [Table 1-1]

[0024] [Table 1-2]

[0025] Measurements of the material on the substrate (open beam measurements) are made at specific locations identified by cylindrical coordinates (x,φ) on the substrate, which may be correlated to binned locations (X,φ). The measurements are nominally made at a specific time, t, but in practice are made over a period of time (T), and the voltage values ​​are obtained from time-averaged integrated measurements over that period. This measured x-ray voltage signal is therefore identified as V(x,φ,t).

[0026] Referring now to FIG. 2, a typical XRF calibration curve is depicted showing the X-ray detector signal for different substrate basis weights. It can be seen that for all substrates, the detector signal decreases with increasing basis weight, but eventually saturates. This is due to the saturation voltage V s The saturation voltage depends on the material disposed on the substrate and typically does not change as the substrate composition is adjusted.

[0027] The curve (particularly its slope, which defines the bare substrate mass attenuation rate and open beam voltage) varies for different substrate compositions. As can be seen from the figures shown, for a particular signal (e.g., measured voltage), the correct basis weight can be identified if the correct curve is used. Note that the curve may differ between measured locations on the substrate. The compensation techniques disclosed herein allow the correct curve to be identified for a particular substrate and a particular location on the substrate.

[0028] Compensation for substrate composition is performed in the following manner (algorithmically depicted in the flow chart of FIG. 5, as described below).

[0029] First, the open beam measurements are compensated by normalization so that they are the same for all substrates after saturation voltage subtraction. This is done according to the following equation (1):

[0030]

number

[0031] After substrate compensation, the measurements may now be temperature compensated using equation (2) below.

[0032]

number

[0033] This is the (position-independent) temperature compensation coefficient

[0034]

number

[0035]

number

[0036] Here, the detected voltage can be compensated and linearized using a first order calibration curve based on a polynomial regression of the mass decay rate according to equation (4) below.

[0037]

number

[0038] However, the actual mass attenuation rate is different compared to the primary calibration curve, therefore compensation for the spectral changes is performed using the following equation (5):

[0039]

number

[0040] Therefore, the compensation parameter to be established is the normalized shutter open voltage V 0,Sub (x,φ), temperature compensation rate b(x,φ), and spectral change rate a(x,φ). All of these are position dependent (i.e., may vary depending on the position on the substrate). For use during production, they are preferably stored in a database, typically provided in a non-volatile memory. Methods for establishing these compensation parameters are described below.

[0041] Generally speaking, a method for compensating for substrate variations in the measurement of the amount of material of a material disposed on a substrate can be envisaged. The method includes receiving an X-ray signal detected for the measurement of a material at a position on a surface of a substrate (particularly a material on and, optionally, in contact with the substrate), and determining the amount of material based on the received X-ray measurement signal and a predefined set of compensation parameters for the substrate, the set of compensation parameters varying according to the position on the surface of the substrate. The determination of the material quality may be based on any form of X-ray analysis, for example, XRF analysis or X-ray scattering analysis. In some implementations, the amount of material indicates a material thickness, a coating weight, and / or a basis weight. In some implementations, the material characteristic may also be a thickness of a chemical vapor deposition or an electrodeposition, such as on a metal sheet or foil. The steps of receiving and determining are advantageously repeated for multiple positions on the surface of the substrate.

[0042] Any of the aspects disclosed herein may be embodied as a computer program configured to perform any of the methods disclosed herein (or having steps corresponding to each of the method steps disclosed herein and causing the processing device to perform the method steps) when executed by a processing device. The processing device may be coupled to an X-ray analysis system to receive suitable signals and / or to control the system according to the methods.

[0043] In another aspect, an X-ray analysis system for measuring a quantity of a material disposed on a substrate may be considered. The system may include an X-ray sensor configured to detect X-ray signals for measurement of the material at a location on a surface of a substrate, and a processing device for compensating for substrate variations in the measurement, the processing device configured to determine a material quantity based on the detected X-ray measurement signal and a predefined set of compensation parameters for the substrate, the set of compensation parameters varying according to the location on the surface of the substrate. The system may have features according to any other aspect disclosed herein and / or the processing device may be configured according to any other aspect disclosed herein.

[0044] Some optional and / or advantageous features according to any of the embodiments are described below.

[0045] In some embodiments, the substrate surface has a cylindrical shape. Each position on the surface of the substrate may then be defined by a position along the width (x) of the substrate surface and a rotation angle (φ) of the substrate.

[0046] The detected x-ray signal may comprise the sensor output of either a sampled voltage or an integrated charge. Typically, the x-ray signal is then time-averaged over a measurement period (e.g., of predetermined and / or fixed duration).

[0047] In one embodiment, determining the amount of material includes adjusting the received X-ray measurement signal according to a set of compensation parameters. The adjusted X-ray measurement signal may then be correlated with the amount of material according to a calibration relationship (between the signal and the amount of material). The calibration relationship may be represented by a curve, and parameters of the curve may be selected, for example, according to a standard.

[0048] In an embodiment, the set of compensation parameters includes a predefined shutter opening signal for the substrate (or more specifically, for each position on the substrate). The received X-ray measurement signal may then be adjusted by normalizing it according to the predefined shutter opening signal (for the measured position). In an embodiment, the set of compensation parameters includes a predefined temperature compensation factor. The received X-ray measurement signal may then be adjusted by compensating it for temperature and applying the predefined temperature compensation factor. In an embodiment, the set of compensation parameters includes a predefined spectral adjustment factor. The material quantity may then be determined by applying the predefined spectral adjustment factor to the material quantity determined by correlating according to the (standard) calibration relationship.

[0049] Further references to general terms of the present disclosure continue below: First, specific details of the method for establishing compensation parameters will now be described.

[0050] An exemplary process for determining the compensation parameters includes the following steps: First, perform a shutter open voltage mapping of the substrate at room temperature. Next, perform a simulated measurement of an equivalent sample at room temperature to determine the tilt adjustment parameters or curve correction parameters. Finally, perform a simulated measurement of an equivalent sample for the rolling mill at an elevated temperature to determine the temperature compensation adjustment parameters. These steps are preferably performed in this order so that the previously established parameters can be used to properly establish the other parameters.

[0051] Referring now to FIG. 3, measurements at different positions of a cylindrical substrate (roll) are illustrated. The roll has a width (L) and a circumference (U). Thus, each measurement at a specific point along the width (x) and at a specific orientation angle (φ) of the roll can be converted to a two-dimensional position on a plane. The measurements require relative movement between the sensor and different positions on the cylindrical substrate. In one embodiment, the sensor is held at a specific position on the width and the roll is rotated in angular steps of 360 degrees so that multiple angular positions relative to that width point are measured. In another implementation, the roll may be rotating continuously (e.g., for standard operating conditions, the sensor is moved along the width and the roll rotation is repeated).

[0052] Shutter opening voltage mapping of the substrate is performed by measuring a bare roll machine (ie, a roll machine with no material on the substrate and / or between the substrate and the X-ray sensor).

[0053] Time-averaged, normalized substrate voltage V 0,Sub (x,φ) (shutter open voltage) is established for a defined time window T at a specific position on the mill according to the following equation (6): In other words, the shutter open voltage is established as the voltage measurement determined when no material is placed on the substrate.

[0054]

number

[0055] As described above, the sensor remains in the same horizontal position until all data points are filled in for φ. Then the horizontal position of the sensor is moved in for all data points, and this is repeated for each binned value of X.

[0056] Next, an approach for establishing the spectral tuning rate or tilt angle rate is presented. As mentioned above, this procedure is advantageously performed after the shutter opening voltage has been mapped to the substrate (as described above). This procedure is performed with the substrate at room temperature, without any material disposed on the substrate.

[0057] Optionally, the first process is to check the coating deviation. This is done by measuring the coating weight without a sample at any position on the mill after the 2D shutter opening voltage adaptation. For all positions, the measurements are Δcw meas If the coating deviation is small enough, it is possible to determine the linear regression parameters for each location and then the process can continue.

[0058] The primary process for establishing the spectral tuning rate or tilt angle rate is carried out with the substrate at room temperature with no material disposed on the substrate.

[0059] Instead, a material is interposed between the substrate and the sensor, as described below: The substrate is rotated at standard production speed.

[0060] Other substrate surfaces that present a periodically repeating surface to the X-ray head may also be treated similarly. For example, the surface of an elongated conveyor belt on which the object to be analyzed is placed may be described as substantially cylindrical, with a "pseudo" angular position (φ') defined by using a cylinder with a circumference U equal to the conveyor belt length. Stationary substrates (e.g., planar substrates) may be analyzed using a Cartesian coordinate system rather than cylindrical coordinates.

[0061] 4, an approach for establishing the spectral tuning rate or tilt angle rate in one embodiment is shown. It shows a sensor head 100, a measurement sample 110, and a substrate (roll machine) 120. One or more known samples 110 are measured at each roll machine position due to spectral changes that may be caused, for example, by the varying composition of the substrate 120 and therefore different at different substrate positions. The number of samples 110 may be production dependent and may vary significantly based on the application.

[0062] It is highly desirable to have the same sample 110 at each measurement location on the mill. Therefore, the sample 110 is advantageously positioned at a fixed position (or distance) relative to the sensor head 100 during scanning, for example by directly attaching the sample 110 to the sensor head 100.

[0063] The sensor then performs the same mapping operation as shown with respect to Figure 3 for the bare roll machine case. The following sequence is performed: the coating weight of the sample is mapped and a linear regression of the parameter set a(x,φ) is performed at each location according to equation (7) below. The 2D array a(x,φ) thus defines the spectral change at each location in the measurement space, without requiring any additional information about the chemical composition of the different substrates.

[0064]

number

[0065] This process may be repeated for multiple samples 110. Several example numbers of samples may be considered based on the characteristics of the production line under consideration. For example, if the line runs only a single basis weight of a single coating material, it may be sufficient to use only this basis weight for a single sample. If the line runs different thicknesses or different coating materials, then the samples should cover the entire measurement range to perform appropriate Gain / Offset adjustments. In the case of very large production ranges, it may be desirable to split the measurement range and parameters into subsets. In the case where the sample material 110 is fragile and cannot be directly attached to the sensor head 100 or otherwise securely positioned, it may be possible to use a similar material (in terms of XRF or Compton response) to simulate production. As a result, multiple sets of spectral tuning ratios or tilt angle ratios may be established for different thickness ranges and / or different materials.

[0066] The resulting set(s) of spectral adjustment factor (coefficient) or tilt angle factor (coefficient) parameters (a(x,φ)) are then beneficially stored in a non-volatile memory database.

[0067] We now consider an approach to establishing the temperature compensation factor. Desirably, this approach is performed after both the shutter-open voltage and the tilt adjustment have been successfully mapped to the substrate. Similar to the process for establishing the shutter-open voltage, the substrate is measured without any material placed on it and without any material between the substrate and the sensor (in other words, any sample material used to establish the tilt adjustment is removed). The substrate (e.g., a rolling mill) is heated to a temperature above room temperature and typically rotated at standard production speed.

[0068] The spectral changes may result in different temperature compensation parameters for each position (x,φ), which may result in different absorptivities of air. The spectra at each position are unknown and are measured using a heated mill without an external sample.

[0069] The following sequence is performed: First, the voltage is measured without a sample at each position of the mill after the 2D shutter open voltage adaptation (according to equation (6) above). Then, the temperature compensation adjustment parameters (b(x,φ)) are established for each position (x,φ) according to equation (8) below, where:

[0070]

number

[0071]

number

[0072] The resulting set of temperature compensation parameters b(x,φ) is beneficially stored in a non-volatile memory database.

[0073] Returning to the general terms above, further aspects may be considered (which may be provided independently or in combination with other aspects disclosed herein). This provides a method for determining compensation parameters for substrate variations in measuring the amount of material disposed on a substrate. The method includes acquiring at least one detected X-ray signal for each of a plurality of positions on a surface of the substrate, and establishing a set of compensation parameters for each position on the surface of the substrate based on the respective at least one detected X-ray signal. In one aspect, the acquiring step may result in one detected X-ray signal for each of a plurality of positions on the surface of the substrate (at specific different conditions). The establishing step may then result in one compensation parameter for each position on the surface of the substrate. The acquiring and establishing steps may then be repeated for different types of compensation parameters. As will be appreciated in alternative respects, the acquiring step may result in multiple detected X-ray signals for each of a plurality of positions on the surface of the substrate (generally acquired at different times and under different conditions). The establishing step may then result in multiple compensation parameters for each position on the surface of the substrate.

[0074] All of the details discussed above (e.g., with reference to the general terms of this disclosure) may be applied to this aspect. For example, the acquired detected x-ray signal may include a sensor output of either a sampled voltage or an integrated charge. Typically, the x-ray signal is then time-averaged over the measurement period. Possible compensation parameters are now described.

[0075] For example, the set of compensation parameters may include a shutter open signal for the substrate. The at least one detected X-ray signal may then include an X-ray signal obtained for each location on the surface of the substrate when no material is disposed on the substrate (at a first temperature, e.g., room temperature). Establishing the set of compensation parameters may then include defining a shutter open signal for each location on the surface of the substrate by each obtained detected X-ray signal (which may include a sensor output, which may be either a sampled voltage or an integrated charge; typically, the X-ray signal is then time averaged over a measurement period, as described above).

[0076] In another embodiment, the set of compensation parameters includes a spectral adjustment factor for the substrate. The at least one detected X-ray signal may then include an X-ray signal obtained for each location on the surface of the substrate when a known amount of material is placed at a predetermined position (or distance) relative to the X-ray sensor. For example, the known amount of material may be attached to the X-ray sensor. Establishing the set of compensation parameters may then include establishing a spectral adjustment factor for each location on the surface of the substrate by identifying an amount of material for each location from correlating an X-ray measurement signal derived from the acquired X-ray measurement signal for each location with the amount of material according to a calibration relationship, and comparing the identified amount of material with the known amount of material. Advantageously, the X-ray measurement signal derived from the acquired X-ray measurement signal includes an acquired X-ray measurement signal for each location with a shutter open signal for each location.

[0077] In a further embodiment, the set of compensation parameters includes a temperature compensation factor for the substrate. The at least one detected X-ray signal may then include an X-ray signal acquired for each location on the surface of the substrate when no material is disposed on the substrate at a second, different temperature (typically higher than the first temperature). Establishing the set of compensation parameters may then include calculating a temperature compensation factor for the second temperature and establishing a temperature compensation factor for each location on the surface of the substrate by comparing the X-ray signal acquired for each location at the first temperature adjusted by the temperature compensation factor with the acquired X-ray signal acquired for each location at the second temperature.

[0078] 5, a flow chart of the compensation algorithm is depicted. It can be seen that this follows the above discussion of the method of voltage measurement compensation. It includes the steps of measuring the voltage while the system is measuring online, determining the measured sensor head position (x,φ) and calculating the position (V 0,sub The steps include: compensating the voltage for the substrate measurement using an open shutter voltage vs. (x,φ)), temperature compensation using a temperature compensation factor (tuning parameter), b(x,φ), linearizing the measurement using a standard calibration curve, performing spectral tuning of the measurement using a spectral tuning factor, a(x,φ), and data post processing (profile, interface updates, etc.). The system then stops the online measurement and proceeds to a standby position. Although a voltage measurement is shown in this regard, the same techniques can be used equally well for charge measurements.

[0079] FIG. 6 depicts a flow chart of substrate mapping according to the above procedure. First, the system determines that a new substrate map is being generated and that the roll machine scan is at operating speed. The first loop iterates over the size X step In the process, X=X min From X maxWithin the first loop, a second loop performs an angle scan, but the number of iterations (i(φ)) is less than the integration time divided by the sampling rate. For each execution of the second loop, the following steps are performed: raw The angle roll position (φ) is determined. The iteration number (i(φ)) is incremented. The voltage measurement is incremented from V0 to V norm and V(x,φ) is V norm Within the first loop, after the second loop is completed, the following further steps are performed: V(x,φ) is defined as V(x,φ) / i(φ), and V(x,φ) is then stored in a database.

[0080] 7A and 7B depict a flow chart of an algorithm for establishing the spectral tuning or tilt angle parameters. This follows the procedure described above. The first loop performs a surface mapping in the measurement space without any additional sample. For each position, a voltage is measured, which is compensated using the open shutter voltage for that position. The compensated voltage is calculated based on the measured fundamental width cw meas To find, the magnitude of the elementary width, |cw meas | is the maximum allowable measured coating weight difference Δcw before compensation is made meas If so, the process is stopped (and restarted). Otherwise, the process continues with the procedure for each sample, starting with the sample being placed in front of the sensor holder (as shown in FIG. 4). The second loop performs surface mapping in the measurement space with the sample placed, using the following steps for each position: the voltage is measured, the measured voltage is compensated using the open shutter voltage for that position, the compensated voltage is linearized according to the base calibration, and the measurement mapping is performed cw i (x,φ). Once the second loop is completed for all samples, a coating weight regression is performed to determine a(x,φ) and the determined parameters are stored in the database.

[0081] 8 depicts a flow chart of an algorithm from establishing temperature compensation parameters according to one embodiment. This also follows the procedure described above. Surface mapping is performed for each position in the measurement space without a sample in place using the following steps: voltage is measured, the measured voltage is compensated using the open shutter voltage for that position, and temperature compensation adjustment parameters (b(x,φ)) are established for the position according to equation (8) above. Once the loop is completed, the determined parameters are stored in a database.

[0082] The time taken for calibration (determination of compensation parameters) can be estimated as follows: The first step (eg bare roll machine mapping according to the flow chart of FIG. 6) may have a duration according to the following formula:

[0083]

number

[0084] This may actually be around 3 hours.

[0085] The second step (eg, spectral adjustment according to the flowchart of FIGS. 7A and 7B) may have a duration for each sample according to the following formula:

[0086]

number

[0087] This may actually be around 3 hours.

[0088] The third step (eg, temperature compensation adjustment according to the flowchart of FIG. 8) may have a duration for each sample according to the following formula:

[0089]

number

[0090] This may actually be around 3 hours.

[0091] So in practice, the total time estimate for N samples is 3h+N * 3h + additional warm-up time for the substrate may be given if necessary.

[0092] FIG. 9 illustrates a 2D array of spectral tuning parameters (a(x,φ)) and temperature tuning parameters (b(x,φ)) stored in a database according to one embodiment. The figure is for a mill having a width of 100 length units (e.g., mm, cm, m). For measurement purposes, the width is subdivided into 10 equal parts between 5 and 95, and the circumference is subdivided into 10 equal angular parts between 18 and 342. The first two columns, corresponding to x=5 and x=15, are filled for mill orientation angles φ=18°-342°. It is understood that when the mapping is completed, all cells are filled with specific values ​​of a(x,φ) and b(x,φ).

[0093] As used herein, including in the claims, the singular form of a term herein is to be construed as including the plural form, and vice versa, unless the context indicates otherwise. For example, a singular reference, including in the claims, such as "a" or "an" (e.g., an analog-to-digital converter) means "one or more" (e.g., one or more analog-to-digital converters), unless the context indicates otherwise. Throughout the specification and claims of this disclosure, words such as "comprise," "including," "having," and "contain," as well as variations of words such as "comprising" and "comprises" or the like, mean "including but not limited to" and are not intended to exclude other elements.

[0094] The following numbered paragraphs 1-24 provide various examples of the embodiments disclosed herein. Paragraph 1. A method for compensating for substrate variations in measuring a quantity of a material disposed on a substrate, the method comprising: receiving detected X-ray signals for measurement of the material at a position on a surface of the substrate; and determining a quantity of material based on the received X-ray measurement signals and a predetermined set of compensation parameters for the substrate, the set of compensation parameters varying according to the position on the surface of the substrate. Paragraph 2. The method of paragraph 1, wherein the substrate surface has a substantially cylindrical shape, and each position on the surface of the substrate is defined by a position along a width of the substrate surface and a rotation angle of the substrate. Paragraph 3. The method according to paragraph 1 or paragraph 2, wherein the material quantity indicates material weight and / or material basis weight. Paragraph 4. The method of any one of Paragraphs 1 to 3, wherein the amount of material indicates a weight, basis weight, or thickness of a deposit or coating. Paragraph 5. The method of any one of paragraphs 1 to 4, wherein the detected X-ray signal is a sensor output, including either a sampled voltage or an integrated charge, and a sensor output time-averaged over a measurement period. Paragraph 6. The method of any one of paragraphs 1 to 5, wherein the receiving and determining steps are repeated for multiple locations on the surface of the substrate. Paragraph 7. A method according to any one of paragraphs 1 to 6, wherein the step of determining the amount of material comprises adjusting the received X-ray measurement signal in accordance with the set of compensation parameters and correlating the adjusted X-ray measurement signal with the amount of material in accordance with a calibration relationship. Paragraph 8. A method according to any one of paragraphs 1 to 7, wherein the set of compensation parameters includes a predetermined shutter opening signal for the substrate, and adjusting the received X-ray measurement signal includes normalizing the received X-ray measurement signal in accordance with the predetermined shutter opening signal. Paragraph 9. The method of any one of paragraphs 1 to 8, wherein the set of compensation parameters includes a predetermined temperature compensation factor, and adjusting the received X-ray measurement signal includes compensating the received X-ray measurement signal for temperature and applying the predetermined temperature compensation factor. Paragraph 10. The method of any one of paragraphs 1 to 9, wherein the set of compensation parameters includes a predetermined spectral adjustment factor, and determining the amount of material includes applying the predetermined spectral adjustment factor to the amount of material determined by correlating according to the calibration relationship. Paragraph 11. A method for determining compensation parameters for substrate variations in measuring a material quantity of a material disposed on a substrate, the method comprising: obtaining at least one detected X-ray signal for each of a plurality of locations on a surface of the substrate; and establishing a set of compensation parameters for each location on the surface of the substrate based on the respective at least one detected X-ray signal. Paragraph 12. The method of paragraph 11, wherein the set of compensation parameters includes a shutter open signal for the substrate, and the at least one detected X-ray signal includes an X-ray signal acquired for each location on the surface of the substrate when no material is disposed on the substrate at a first temperature, and establishing a set of compensation parameters includes defining the shutter open signal for each location on the surface of the substrate by the respective acquired detected X-ray signal. Paragraph 13. The method of paragraph 11 or paragraph 12, wherein the set of compensation parameters includes a spectral tuning ratio for the substrate, and the at least one detected X-ray signal includes an X-ray signal obtained for each location on the surface of the substrate when a known amount of material is placed at a predetermined position relative to an X-ray sensor, and establishing a set of compensation parameters includes correlating an X-ray measurement signal derived from the obtained X-ray measurement signal for each location with an amount of material according to a calibration relationship, thereby identifying an amount of material for each location and comparing the identified amount of material to the known amount of material. Paragraph 14. A method according to any one of paragraphs 11 to 13, wherein the X-ray measurement signals derived from the acquired X-ray measurement signals include the acquired X-ray measurement signals for the respective positions due to the shutter opening signals for the respective positions. Paragraph 15. The method of any one of Paragraphs 11-14, wherein the set of compensation parameters includes a temperature compensation factor for the substrate, and the at least one detected X-ray signal includes an X-ray signal obtained for each location on the surface of the substrate when no material is disposed on the substrate at a second, different temperature, and establishing a set of compensation parameters includes calculating a temperature compensation factor for the second temperature, and establishing the temperature compensation factor for each location on the surface of the substrate by comparing the X-ray signal obtained for the respective location at the first temperature adjusted by the temperature compensation factor to the X-ray signal obtained for the respective location at the second temperature. Paragraph 16. The method of any one of Paragraphs 1 to 10, further comprising the method of any one of Paragraphs 11 to 15. Paragraph 17. A computer readable medium comprising a computer program, the computer program being configured to perform the method of any one of paragraphs 1 to 10 when executed by a processing device. Paragraph 18. An X-ray analysis system for measuring a quantity of a material disposed on a substrate, the system comprising: an X-ray sensor configured to detect X-ray signals for a measurement of the material at a position on a surface of the substrate; and a processing device for compensating for substrate variations in the measurement, the processing device configured to determine a material quantity based on the detected X-ray measurement signals and a predetermined set of compensation parameters for the substrate, the set of compensation parameters varying depending on the position on the surface of the substrate.

[0095] Although the embodiments according to the present disclosure are described with reference to particular types of equipment and applications (particularly XRF analysis of a rolling mill-based industrial process), and the embodiments have particular advantages in such cases, as discussed herein, the approach according to the present disclosure may be applied to other types of equipment and / or applications. The specific construction details of the X-ray system, while potentially advantageous (particularly considering the constraints and capabilities of known X-ray systems), may be significantly modified to arrive at a device having a similar or identical operation. Each feature disclosed herein may be replaced by an alternative feature serving the same, equivalent, or similar purpose, unless otherwise specified. Thus, unless otherwise specified, each feature disclosed is merely an example of a generic series of equivalent or similar features.

[0096] The use of any and all examples or exemplary language (such as "for instance," "such as," "for example," and the like) provided herein is merely to better describe the invention and does not imply a limitation on the scope, which is within the scope of the invention unless otherwise asserted. No language in the specification should be construed as indicating any element not claimed as essential to the practice of the invention.

[0097] Any steps described herein can be performed in any order, or simultaneously, unless otherwise stated or required otherwise by context.

[0098] All of the aspects and / or features disclosed herein may be combined in any combination, except combinations in which at least some of such features and / or steps are mutually exclusive. There may be certain combinations of aspects that are of further benefit, such as the aspect of determining a set of compensation parameters and applying the set of compensation parameters to measurements as described herein. In particular, preferred features of the present invention are applicable to all aspects of the present invention and may be used in any combination. Similarly, features described in non-essential combinations may be used separately (not in combination).

Claims

1. 1. A method for compensating for substrate variations in measurements of a quantity of material disposed on a substrate, the method comprising: receiving a detected X-ray measurement signal of the material at a location on a surface of the substrate; determining a quantity of material based on the received X-ray measurement signals and a predetermined set of compensation parameters for the substrate, the set of compensation parameters varying according to the position on the surface of the substrate.

2. 2. The method of claim 1, wherein the surface of the substrate has a substantially cylindrical shape, and each location on the surface of the substrate is defined by a position along a width of the surface of the substrate and a rotation angle of the substrate.

3. The method of claim 1 , wherein the material amount indicates a material weight and / or a material basis weight.

4. The method of claim 1 , wherein the amount of material indicates a weight, basis weight, or thickness of a deposit or coating.

5. The method of claim 1 , wherein the detected x-ray measurement signal comprises a sensor output, either a sampled voltage or an integrated charge, and a time-averaged sensor output over a measurement period.

6. The method of claim 1 , wherein the receiving and determining are repeated for a plurality of locations on a surface of the substrate.

7. 2. The method of claim 1 , wherein determining the amount of material comprises adjusting the received X-ray measurement signals in accordance with the set of compensation parameters and correlating the adjusted X-ray measurement signals with the amount of material in accordance with a calibration relationship.

8. 2. The method of claim 1 , wherein the set of compensation parameters includes a predetermined shutter-opening signal for the substrate, and adjusting the received X-ray measurement signal includes normalizing the received X-ray measurement signal according to the predetermined shutter-opening signal.

9. 2. The method of claim 1 , wherein the set of compensation parameters includes a predetermined temperature compensation factor, and adjusting the received X-ray measurement signal includes compensating the received X-ray measurement signal for temperature and applying the predetermined temperature compensation factor.

10. 2. The method of claim 1, wherein the set of compensation parameters includes a predetermined spectral adjustment factor, and determining a material amount includes applying the predetermined spectral adjustment factor to a material amount determined by correlating according to the calibration relationship.

11. 1. A method for determining compensation parameters for substrate variations in measuring a quantity of a material disposed on a substrate, the method comprising: obtaining at least one detected x-ray signal for each of a plurality of locations on a surface of the substrate; and establishing a set of compensation parameters for each location on a surface of the substrate based on each of the at least one detected X-ray signal.

12. 12. The method of claim 11 , wherein the set of compensation parameters includes a shutter open signal for the substrate, and the at least one detected X-ray signal includes an X-ray signal obtained for each location on a surface of the substrate when no material is disposed on the substrate at a first temperature, and establishing a set of compensation parameters includes defining the shutter open signal for each location on a surface of the substrate by each of the obtained detected X-ray signals.

13. 12. The method of claim 11 , wherein the set of compensation parameters includes a spectral tuning ratio for the substrate, and the at least one detected X-ray signal includes an X-ray signal obtained for each location on a surface of the substrate when a known amount of material is disposed at a predetermined position relative to an X-ray sensor, and establishing a set of compensation parameters includes correlating the X-ray measurement signal with an amount of material derived from the X-ray measurement signals obtained for each of the locations according to a calibration relationship, thereby identifying an amount of material for each of the locations and comparing the identified amount of material to the known amount of material.

14. The method of claim 11 , wherein the x-ray measurement signals derived from the acquired x-ray measurement signals include the x-ray measurement signals acquired for each of the positions with the shutter open signal for each of the positions.

15. 12. The method of claim 11 , wherein the set of compensation parameters includes a temperature compensation factor for the substrate, and the at least one detected X-ray signal includes an X-ray signal obtained for each location on a surface of the substrate when no material is disposed on the substrate at a different second temperature, and establishing a set of compensation parameters includes: calculating a temperature compensation factor for the second temperature; and establishing the temperature compensation factor for each location on a surface of the substrate by comparing the X-ray signal obtained for each of the locations at the first temperature adjusted by the temperature compensation factor to the X-ray signal obtained for each of the locations at the second temperature.

16. The method of claim 1 further comprising the method of claim 10.

17. 13. A computer readable medium containing a computer program, the computer program being configured to perform the method of claim 1 when executed by a processor.

18. 1. An X-ray analysis system for measuring a quantity of a material disposed on a substrate, the system comprising: an X-ray sensor configured to detect an X-ray measurement signal of the material at a location on the surface of the substrate; 1. An X-ray analysis system for measuring a quantity of a material disposed on a substrate, comprising: a processing device for compensating for substrate variations in the measurement, the processing device being configured to determine a material quantity based on a detected X-ray measurement signal and a predetermined set of compensation parameters for the substrate, the set of compensation parameters varying according to the position on a surface of the substrate.

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