Prism coupling system and method with improved strength transition location detection and tilt compensation

Abstract

Prism coupling systems and methods include using a prism coupling system to collect 2D digital mode spectra of IOX articles. The location and orientation of the mode lines and critical angle are found by performing a weighted fit to the mode lines and critical angle images, and are used to define a compensated mode spectrum. If a mode line tilt is found, it is removed from the 2D digital mode spectrum to define the compensated mode spectrum. The compensated mode spectrum is then processed using techniques known in the art to provide a more accurate estimate of the stress-related properties of the IOX sample relative to the uncompensated mode spectrum. A derivative-based method using derivative spectra and curve fitting to accurately establish the location of intensity transitions in the mode spectrum of an IOX sample is also disclosed.

Description

[0001] This application claims priority to U.S. Provisional Patent Application No. 62 / 929,351, filed November 1, 2019, the contents of which are incorporated herein by reference in their entirety.

[0002] This disclosure relates to prism coupling systems and methods for characterizing stress in glass-based chemically strengthened articles, and more specifically to such systems and methods with improved strength transition position detection and tilt compensation. Background Technology

[0003] Chemically strengthened glass substrates are formed by subjecting a glass substrate to chemical modification to improve at least one strength-related property, such as hardness, fracture resistance, etc. Chemically strengthened glass substrates have been specifically used as cover glass for display-based electronic devices, particularly handheld devices such as smartphones and tablets.

[0004] In one method, chemical strengthening is achieved through an ion exchange (IOX) process, whereby ions in the matrix of the glass substrate (“primary ions” or “substrate ions”) are replaced by ions introduced from outside the molten pool (i.e., replacement ions or inwardly diffused ions). Strengthening typically occurs when the replacement ions are larger than the primary ions (e.g., Na+). + Or Li + Ions are K + (Ion substitution). The IOX process creates an IOX region in the glass that extends from the surface of the article into the matrix. The IOX region defines a refractive index distribution within the matrix with a depth of layer (DOL), which represents the size, thickness, or "depth" of the IOX region measured relative to the surface of the article. The refractive index distribution also defines stress-related properties, including: stress distribution, knee stress, center tension, tensile-strain energy, birefringence, peak depth, layer depth, and refractive index distribution. The refractive index distribution can also define an optical waveguide in the glass-based article, which, when the refractive index distribution meets certain criteria conventional in the art, supports a guiding mode for a given wavelength of light of a number m.

[0005] Prism coupling systems and methods can be used to measure the spectra of guided modes of flat optical waveguides formed in glass-based IOX articles to characterize one or more properties of the IOX region, such as refractive index distribution and the aforementioned stress-related characteristics. This technique has been used to measure the properties of glass-based IOX articles for various applications, such as chemically strengthened coatings for displays (e.g., smartphones). Such measurements are used for quality control purposes to ensure that, for each of the selected characteristics for a given application, the IOX region exhibits the expected characteristics and falls within the selected design tolerances.

[0006] Measurements of stress-based properties using prism coupling rely on the formation and detection of transverse magnetic (TM) and transverse electrical (TE) mode spectra, which have corresponding intensity transitions in the form of TM and TE mode lines and TM and TE critical angle transitions. The TM and TE mode lines need to be relatively sharp (i.e., have high contrast) to allow for accurate determination of their positions. Similarly, the critical angle transition also needs to be relatively sharp to allow for accurate determination of its position. This is because the positions of the mode lines and critical angle transitions are used in calculations to determine the stress-based properties of IOX articles, and any error in the position of the mode lines or critical angle transitions (which may be caused by mode line tilting and reduced contrast) will translate into errors in the calculated stress-based properties.

[0007] Unfortunately, the prism coupling system used to characterize the stress-based properties of IOX products is imperfect, resulting in incomplete formation of TM and TE mode lines, leading to reduced contrast and tilt. Therefore, there is a need for improved prism coupling systems and methods that provide accurate estimates of the position and orientation of mode line and critical angle transitions, leading to more accurate calculations of the stress-related properties of the measured sample. Summary of the Invention

[0008] The prism coupling systems and methods described herein include using a prism coupling system to collect 2D digital mode spectra of IOX articles. The mode spectra have mode lines that may be tilted relative to their ideal orientation due to system defects. Such tilting can introduce errors in estimating stress-based properties of the IOX articles. These methods include the following steps: accurately determining the amount of tilt in the mode lines by performing a weighted fit on the 2D digital mode spectrum for each mode line around the intensity extrema associated with each mode line. The determined tilt is then used to adjust the measurement system via either hardware or software to reduce or eliminate the average tilt that causes the 2D digital mode spectrum to be tilted, thereby defining a compensated mode spectrum. The compensated mode spectrum is then processed using techniques conventional in the art to estimate one or more stress-related properties of the IOX article. This provides a more accurate estimate of the stress-related properties of the IOX article compared to using uncompensated mode spectra with tilted mode lines.

[0009] The weighted fitting method disclosed in this paper is based on analytical (closed-form) solutions that determine the position and tilt angle (orientation) of the mode lines with high accuracy. The fitted lines are then used to define an updated or “compensated” digital mode spectrum for estimating at least one stress-based property of the IOX article.

[0010] Weighted fitting methods use 2D mode spectral images to directly find the slope and intercept of each mode line, rather than using 1D averaged grayscale intensity to directly find only the position of the mode lines. The accuracy of 1D averaging methods is limited because averaging the mode spectrum prevents the extraction of the mode line details and information needed to accurately determine the slope and intercept.

[0011] According to aspect (1), a method is provided for estimating at least one stress-based characteristic of an ion-exchange (IOX) article having a waveguide region. The method includes the steps of: using a prism coupling system, irradiating the IOX article with a coupling prism to generate a transverse magnetic (TM) guiding mode and a transverse electrical (TE) guiding mode in the waveguide region of the IOX article; capturing a digital two-dimensional (2D) mode spectrum, the digital 2D mode spectrum including mode lines representing the TM guiding mode and the TE guiding mode of the waveguide region, wherein each mode line is defined by a 2D intensity distribution having intensity values ​​and intensity extrema and having a tilt measured relative to an ideal reference orientation in a first direction; and locating the mode line by fitting it in a region near the intensity extrema of at least one of these mode lines. The fitting step is performed using a weighted least squares regression method in the region near the intensity extrema; the tilt is measured by determining the fitting line of at least one of the mode lines in the 2D mode spectrum by using weighted least squares regression to fit the 2D intensity distribution in the region near the intensity extrema; the tilt is substantially removed from the mode lines by adding the measured tilt in a second direction opposite to the first direction to define at least one of a tilt-compensated TM mode spectrum and a tilt-compensated TE mode spectrum; and the at least one of the tilt-compensated TM mode spectrum and the tilt-compensated TE mode spectrum is used to estimate the at least one stress-based characteristic of the IOX article.

[0012] According to aspect (2), a method according to aspect (1) is provided, wherein the intensity extreme value includes the intensity minimum value.

[0013] According to aspect (3), a method according to any one of aspects (1) to (2) is provided, further comprising the steps of: averaging the 2D mode spectrum to form a one-dimensional (1D) spectrum having an average intensity extremum for each mode line, and using the average intensity extremum to determine the initial position of each mode line.

[0014] According to aspect (4), a method according to any one of aspects (1) to (3) is provided, wherein the 2D mode spectrum includes a digital mode spectral image having a grayscale intensity distribution based on pixel intensity values, and wherein the weighted least square regression method includes the following steps for each mode line: defining a weight that emphasizes pixel intensity values ​​closer to the intensity extremum to force the fitted line to follow the 2D intensity extremum more closely.

[0015] According to aspect (5), a method according to aspect (4) is provided, wherein the weighting is limited by an exponential weighting function.

[0016] According to aspect (6), a method according to any one of aspects (1) to (5) is provided, further comprising the steps of: determining the average variance of the fitted line of the 2D intensity distribution in the vicinity of the intensity extremum; and applying the average variance to each mode line to evaluate whether each mode line is a true mode line or a false mode line.

[0017] According to aspect (7), a method according to any one of aspects (1) to (6) is provided, wherein there are K mode lines, and the method further includes the steps of: determining the slope a of each mode line and the average slope of the slope a based on these mode lines. and standard deviation With limiting slope change parameters

[0018]

[0019] and; a threshold parameter T, where for a given mode line, a zk <T means that the pattern line is a true pattern line.

[0020] According to aspect (8), a method according to aspect (7) is provided, where T≤2.

[0021] According to aspect (9), a method according to any one of aspects (1) to (8) is provided, wherein the at least one stress-related characteristic includes at least one of the following: stress distribution, knee stress, central tension, tensile-strain energy, birefringence, peak depth, layer depth, and refractive index distribution.

[0022] According to aspect (10), a method according to any one of aspects (1) to (9) is provided, wherein the 2D mode spectrum is captured on a rotatable detector, and wherein the action of substantially removing the tilt amount from these mode lines by adding the measured tilt amount is performed by rotating the rotatable detector.

[0023] According to aspect (11), a method according to any one of aspects (1) to (9) is provided, wherein the 2D mode spectrum is captured on a digital detector, and wherein the action of substantially removing the tilt amount from these mode lines by adding the measured tilt amount is performed by digitally rotating the mode spectrum.

[0024] According to aspect (12), a method is provided for compensating for tilt deviation in a prism coupling system for estimating at least one stress-based characteristic of an ion-exchange (IOX) article having a waveguide region. The method includes the steps of: capturing a digital two-dimensional (2D) mode spectrum for each of a plurality of IOX articles, the digital 2D mode spectrum including mode lines of the TM-guided mode and the TE-guided mode representing the waveguide region, wherein each mode line is defined by a 2D intensity distribution having intensity extrema and a tilt amount measured relative to an ideal reference orientation in a first direction; measuring the tilt amount in each mode line by determining a fitted line of the 2D mode spectrum for each mode line using a weighted fit of the 2D intensity distribution in a region near the intensity extrema; averaging these tilts of the mode lines to determine the tilt deviation of the prism coupling system; and adjusting the measurement system to reduce or eliminate the determined tilt deviation from at least one of the captured mode spectra, thereby reducing the tilt amount in each mode line and defining the compensated mode spectrum for at least one of the plurality of IOX articles.

[0025] According to aspect (13), a method according to aspect (12) is provided, further comprising the steps of: adjusting the measurement system to reduce or eliminate the determined tilt bias from the subsequently captured mode spectrum of the additional IOX article, thereby reducing the amount of tilt in each mode line and the compensated mode spectrum defining the additional IOX article.

[0026] According to aspect (14), a method according to any one of aspects (12) to (13) is provided, further comprising the steps of: measuring the variance of the tilts of the pattern lines, and comparing each tilt with the variance to determine whether each pattern line is a true pattern line or a false pattern line.

[0027] According to aspect (15), a method according to any one of aspects (12) to (14) is provided, wherein the amount of tilt is measured as either the tilt angle or the tilt slope.

[0028] According to aspect (16), a method according to any one of aspects (12) to (15) is provided, wherein the at least one stress-related characteristic includes at least one of the following: stress distribution, knee stress, central tension, tensile-strain energy, birefringence, peak depth, layer depth, and refractive index distribution.

[0029] According to aspect (17), a method according to any one of aspects (12) to (16) is provided, wherein the 2D mode spectrum is captured on a rotatable detector, and wherein the action of subtracting the established tilt bias is performed by rotating the rotatable detector.

[0030] According to aspect (18), a method according to any one of aspects (12) to (16) is provided, wherein the 2D mode spectrum is captured on a digital detector, and wherein the action of subtracting the established tilt bias is performed by digitally rotating the mode spectrum.

[0031] According to aspect (19), a method according to any one of aspects (12) to (18) is provided, further comprising the step of calculating the tilt deviation variance in the tilt deviation based on the tilt amount of each mode line.

[0032] According to aspect (20), a method according to any of aspects (12) to (19) is provided, wherein, when capturing the 2D mode spectrum from these IOX samples, the tilt bias and the tilt bias variance are respectively calculated as runn I ng) tilt deviation and current tilt deviation variance.

[0033] According to aspect (21), a method is provided for estimating at least one stress-based characteristic of an ion-exchange (IOX) article having a waveguide region. The method includes the steps of: irradiating the IOX article with a coupling prism using a prism coupling system to generate a transverse magnetic (TM) guiding mode and a transverse electrical (TE) guiding mode in the waveguide region of the IOX article; capturing a digital two-dimensional (2D) mode spectrum comprising mode lines representing the TM and TE guiding modes of the waveguide region, wherein the 2D mode spectrum extends generally in the y-direction, and each mode line has a long scale extending generally in the x-direction and a two-dimensional grayscale intensity distribution I(x,y) based on pixel intensity values; and averaging these pixel intensity values ​​in the x-direction for each mode line to obtain a value. A one-dimensional grayscale intensity distribution I(y) is generated; the initial position of the given pattern line is approximated by locating the extreme values ​​among these pixel intensity values ​​of the one-dimensional grayscale intensity distribution for each pattern line; wherein these pixel intensity values ​​of the one-dimensional grayscale intensity distribution include pixel intensity values ​​in the vicinity region of the extreme value; and a weighted least squares fit is performed for each pattern line, wherein pixel intensity values ​​closer to the extreme value in the one-dimensional grayscale intensity distribution are weighted more than those pixel intensity values ​​farther from the extreme value in the one-dimensional grayscale intensity distribution to identify the best-fit line defining the estimated position of the given pattern line; and these estimated positions of the pattern lines are used to estimate the at least one stress-based characteristic of the IOX article.

[0034] According to aspect (22), a method according to aspect (21) is provided, wherein the weighting function is a function of these pixel intensity values, and the weighting function places greater weight on those pixel intensity values ​​that are closer to the extreme value in the one-dimensional grayscale intensity distribution compared to those pixel intensity values ​​that are farther away from the extreme value in the one-dimensional grayscale intensity distribution.

[0035] According to aspect (23), a method according to aspect (22) is provided, wherein the weighting function includes an exponential function.

[0036] According to aspect (24), a method according to any one of aspects (21) to (23) is provided, wherein the at least one stress-related characteristic includes at least one of the following: stress distribution, knee stress, center tension, tensile-strain energy, birefringence, peak depth, layer depth, and refractive index distribution.

[0037] According to aspect (25), a method according to any of aspects (21) to (24) is provided, further comprising the step of removing any false mode lines by comparing the best-fit line with at least one expected mode line characteristic.

[0038] According to aspect (26), a method according to any one of aspects (21) to (25) is provided, wherein the at least one expected mode line characteristic is selected from a group of mode line characteristics including: position, width, variance relative to average tilt, tilt angle, and tilt slope.

[0039] According to aspect (27), a method according to any one of aspects (21) to (26) is provided, wherein the mode lines are tilted, and the method further comprises the steps of: estimating the tilt amount of each of the tilted mode lines before estimating the at least one stress-based characteristic of the IOX article; and rotating the mode spectrum to a negative of the tilt amount to substantially remove the tilt from the mode lines.

[0040] According to aspect (28), a method according to aspect (27) is provided, wherein estimating the tilt angle of each of these tilted pattern lines comprises the steps of: calculating the slope a of each of these pattern lines as a fitting parameter of the best-fit line, wherein the slope a defines the amount of tilt.

[0041] According to aspect (29), a method according to any one of aspects (27) to (28) is provided, wherein the step of capturing the digital 2D mode spectrum is performed by a rotatable detector, and wherein the step of rotating the mode spectrum is accomplished by rotating the rotatable detector.

[0042] According to aspect (30), a method according to aspect (29) is provided, wherein rotating the rotatable detector includes the steps of: performing a precise rotation of a rotatable stage that rotatably supports the rotatable detector.

[0043] According to aspect (31), a method according to aspect (29) is provided, wherein the step of rotating the mode spectrum is accomplished by digitally rotating the digital 2D mode spectrum.

[0044] According to aspect (32), a method according to any one of aspects (21) to (26) is provided, wherein the mode lines are tilted, and the method further comprises the step of: before estimating the at least one stress-based characteristic of the IOX article: rotating the mode spectrum to a negative number of the deviation tilt to substantially remove the tilt from the mode lines, wherein the deviation tilt is defined as the arithmetic mean of the tilts of the mode lines measured using the prism coupling device for different IOX articles.

[0045] According to aspect (33), a prism coupling system is provided for measuring at least one stress-related characteristic of an ion-exchange (IOX) article having a waveguide region. The prism coupling system includes: a light source system configured to generate input light along an input optical axis; a coupling prism configured to dock with the IOX article to define a coupling interface, wherein the input light is incident on and reflected from the coupling interface to form reflected light, the reflected light leaving the coupling prism and traveling along an output optical axis, wherein the reflected light includes a guided mode spectrum, the guided mode spectrum including mode lines having positions defined by the waveguide region; and a digital sensor including pixels and configured to detect the TM guided mode spectrum and the TE guided mode spectrum and form the TM guided mode spectrum and the TE guided mode spectrum based on the TM guided mode spectrum and the TE guided mode spectrum. A two-dimensional (2D) digital image of the TM-guided mode spectrum and the TE-guided mode spectrum; a controller configured to receive the 2D digital image of the TM-guided mode spectrum and the TE-guided mode spectrum, the controller having instructions stored in a non-transitory computer-readable medium, the instructions causing the controller to perform the following actions: determining a tilt amount for each mode line; determining an average tilt amount and a tilt variance based on the tilt amounts of the mode lines; subtracting the average tilt amount from the mode spectrum to define a tilt-compensated mode spectrum, the tilt-compensated mode spectrum having a reduced tilt amount for each of the mode lines; and using the tilt-compensated mode spectrum to estimate the at least one stress-based characteristic of the IOX article.

[0046] According to aspect (34), a prism coupling system according to aspect (33) is provided, wherein the digital sensor is rotatable about the output optical axis, and wherein the action iii) of subtracting the average tilt amount from the mode spectrum includes the step of rotating the digital sensor.

[0047] According to aspect (35), a prism coupling system according to aspect (34) is provided, wherein the rotatable digital sensor is operably supported by a rotation drive system configured to rotate the digital sensor in precise angular increments.

[0048] According to aspect (36), a prism coupling system according to aspect (35) is provided, wherein the precise angle increment is in the range of 0.0026 radians to 0.0009 radians.

[0049] According to aspect (37), a prism coupling system according to aspect (33) is provided, wherein the action iii) of subtracting the average tilt amount from the mode spectrum includes the step of digitally rotating the 2D digital image.

[0050] According to aspect (38), a prism coupling system according to any of aspects (33) to (37) is provided, wherein the action ii) of establishing the average tilt and tilt variance based on these tilts of the mode lines includes the following steps: performing the current tilt average and current tilt variance.

[0051] According to aspect (39), a prism coupling system according to aspect (38) is provided, wherein the action iii) of subtracting the average tilt amount from the mode spectrum is performed only when the current average tilt amount exceeds a threshold tilt amount.

[0052] According to aspect (40), a prism coupling system according to aspect (39) is provided, wherein the threshold tilt amount is in the range of 0.006 to 0.001 radians.

[0053] According to aspect (41), a method is provided for estimating the position of intensity transitions in a mode spectrum of an ion-exchange (IOX) article. The method includes the steps of: calculating a derivative spectrum based on the mode spectrum to form corresponding derivative intensity transitions based on these intensity transitions; for each derivative intensity transition, determining a fitted line representing the position of that derivative intensity transition to define a set of fitted lines having the corresponding position in the mode spectrum; performing an error check on each fitted line in the set of fitted lines to assess whether the associated derivative intensity transition corresponds to a mode line or noise in the mode spectrum, and discarding any fitted lines found to be caused by noise, thereby determining a set of checked fitted lines; and defining the estimated positions of these intensity transitions in the mode spectrum as the corresponding positions of the set of checked fitted lines to define a corrected mode spectrum.

[0054] According to aspect (42), a method according to aspect (41) is provided, wherein these intensity transitions include mode lines and critical angle transitions, and wherein these derivative intensity transitions include derivative lines and derivative critical transition lines.

[0055] According to aspect (43), a method according to any of aspects (41) to (42) is provided, wherein the step of determining the fitted line is performed using a weighted linear regression method.

[0056] According to aspect (44), a method according to aspect (43) is provided, wherein the weighted linear regression method uses an exponentially weighted function of intensity in these derivative intensity transitions.

[0057] According to aspect (45), a method according to any of aspects (43) to (44) is provided, wherein the step of determining the fitted line is performed using a two-level weighted regression method.

[0058] According to aspect (46), a method according to aspect (45) is provided, wherein the two-level weighted regression method includes an exponentially weighted function of these derivative strength transitions.

[0059] According to aspect (47), a method according to any one of aspects (41) to (46) is provided, wherein the intensity transitions have lengths, and the method further comprises the steps of: averaging the mode spectrum along the length of the intensity transitions to form an average mode spectrum; and using the average mode spectrum to form the derivative spectrum.

[0060] According to aspect (48), a method according to any one of aspects (41) to (47) is provided, wherein the step of calculating the derivative spectrum utilizes a finite difference method, which includes the step of performing intensity normalization such that the derivative intensity transitions of the derivative spectrum are in the range between 0 and 1.

[0061] According to aspect (49), a method according to any one of aspects (41) to (48) is provided, wherein the step of performing the error check includes the steps of: comparing the intensity value of the candidate points of the fitted line with a threshold distance relative to the fitted line; and excluding those candidate points that exceed the threshold distance.

[0062] According to aspect (50), a method according to aspect (49) is provided, wherein the threshold distance is based on the standard deviation of the distance between the candidate points used to form the fitted line and the fitted line.

[0063] According to aspect (51), a method according to any one of aspects (41) to (50) is provided, further comprising the step of: using the corrected mode spectrum to estimate at least one stress-based characteristic of the IOX article.

[0064] According to aspect (52), a method for estimating the location of a critical angular intensity transition in a mode spectrum of an ion-exchange (IOX) article includes the following steps: a) calculating the derivative of the critical angular intensity transition by taking the derivative of the original image of the mode spectrum to form a derivative critical transition line; b) determining the fitted line of the derivative critical transition line; c) identifying the extreme values ​​of the fitted line as representing the location of the critical angular intensity transition in the mode spectrum.

[0065] According to aspect (53), a method according to aspect (52) is provided, wherein the mode spectrum includes a TM mode spectrum having a TM critical angle intensity transition and a TE mode spectrum having a TE critical angle intensity transition, and the method includes the steps of: performing actions a) to c) for each of the TM critical angle transition and the TE critical angle transition to determine the TM critical angle transition position and the TE critical angle transition position in the mode spectrum; calculating the difference between the TM critical angle position and the TE critical angle position; and using the difference between the TM critical angle transition position and the TE critical angle transition position in the mode spectrum to calculate the knee stress in the IOX article.

[0066] According to aspect (54), a method is provided for estimating the positions of mode lines in a mode spectrum of an ion-exchange (IOX) article. The method includes the steps of: approximating an initial position in the mode spectrum for a given mode line by locating the intensity extrema of each mode line; calculating the derivative of the mode spectrum to define a derivative spectrum having derivative lines corresponding to the mode lines, each derivative line having an intensity transition; and for each mode line, determining a fitted line of the mode line by performing a weighted least-squares fit using the initial position of the mode line and the intensity transition of the mode line to define a set of fitted lines having corresponding positions in the mode spectrum, wherein these corresponding positions of the fitted lines are used as estimated positions of the mode lines in the mode spectrum.

[0067] According to aspect (55), a method according to aspect (54) is provided, wherein the mode lines include TE mode lines and TM mode lines, and the method further includes the step of using the corresponding positions of these fitted mode lines to estimate at least one stress-based characteristic of the IOX article.

[0068] According to aspect (56), a method according to any one of aspects (54) to (55) is provided, further comprising the steps of: averaging the mode spectrum in a direction along the length of the mode lines to form an average mode spectrum; and using the average mode spectrum for the step of locating the intensity extremum of each mode line and for the step of calculating the derivative spectrum.

[0069] According to aspect (57), a method according to any of aspects (54) to (56) is provided, wherein the weighted least squares fit includes a weighting function that depends on the difference between the intensity extremum and the intensity transition.

[0070] According to aspect (58), a method according to aspect (57) is provided, wherein the weighting function includes an exponential function.

[0071] According to aspect (59), a method according to any one of aspects (54) to (58) is provided, further comprising the steps of performing an error check by the following steps: for each mode line, comparing the intensity value of a candidate point of the fitted line of the mode line with a threshold distance relative to the fitted line; and excluding those candidate points that exceed the threshold distance.

[0072] According to aspect (60), a method according to aspect (59) is provided, wherein the threshold distance is based on the standard deviation of the distance between the candidate points used to form the fitted line and the fitted line.

[0073] Additional features and advantages are set forth in the following “Examples”, and those skilled in the art will understand some of these features and advantages through this specification and the accompanying drawings, or through practicing the embodiments as described herein and in the accompanying drawings. It should be understood that both the foregoing general description and the following “Examples” are merely exemplary and intended to provide an overview or framework to understand the nature and characteristics of the claims. Attached Figure Description

[0074] The accompanying drawings are included to provide further understanding and are incorporated in and constitute a part of this specification. These drawings illustrate one or more embodiments and, together with the “Examples”, explain the principles and operation of various embodiments. Thus, this disclosure will be more fully understood according to the following “Examples” in conjunction with the accompanying drawings, in which:

[0075] Figure 1A This is a top-down view of an example IOX article including a flat glass substrate.

[0076] Figure 1B yes Figure 1A A close-up cross-sectional view of the IOX article taken in the xy plane, and the close-up cross-sectional view illustrates an example IOX process that is performed across the substrate surface and into the body of the substrate.

[0077] Figure 1C schematically depicting the formation Figure 1A and 1B The result of the IOX process on the IOX article is that the IOX article has a near-surface peak region (R1) and a deep region (R2).

[0078] Figure 1D yes Figures 1A to 1C The figure shows an example refractive index distribution n(x) for an IOX product.

[0079] Figure 2A and Figure 1CSimilarly, an example IOX product formed using a single exchange ion species is illustrated.

[0080] Figure 2B and Figure 1D Similar, and is Figure 2A The example refractive index distribution n(x) of IOX products is represented.

[0081] Figure 3A This is a schematic diagram of an example prism coupling system according to the present disclosure, and the example prism coupling system is used to measure IOX articles using the methods disclosed herein.

[0082] Figure 3B yes Figure 3A A close-up image of the photodetector system of the prism coupling system.

[0083] Figure 3C This is a close-up, top-down view of a photodetector system, showing the detector supported by a rotatable support platform driven by a rotation drive system to perform a precise amount of rotation of the detector around the output optical axis of the prism coupling system.

[0084] Figure 3D and Figure 3C Similarly, an alternative arrangement of the rotary drive system is shown.

[0085] Figure 4A It is a schematic representation of an idealized 2D mode spectrum (mode spectral image), which includes a system composed of an ideal prism coupling system... Figure 3B The TM and TE mode spectra captured by the photodetector system show intensity variations appearing as dark features against a light (bright) background.

[0086] Figure 4B Is using Figure 3A An example image of a 2D mode spectral image captured by a prism coupling system, showing intensity variations in the form of mode lines and critical angle transitions.

[0087] Figure 4C It is based on Figure 4B The derivative spectrum is calculated from the example mode spectrum, and the derivative spectrum is plotted as the derivative intensity variation in the form of derivative lines and derivative critical transition lines.

[0088] Figure 5A and 5B yes Figure 4B Example of a mode spectrum: TM mode spectrum ( Figure 5A ) and example TE mode spectra ( Figure 5B The row average standardized 1D intensity distribution I TM-A (y) and I TE-AThe relationship between (y) and y position (number of pixels i).

[0089] Figure 6A and 6B These are the TM mode spectrum and the TE mode spectrum, respectively. Figure 4C The graph showing the relationship between the row-averaged normalized 1D intensity change rate I' (relative units) and the y-position (relative units) of the derivative spectrum.

[0090] Figure 7A This is a close-up of the example mode line (TM or TE), where the peaks and valleys identified in the corresponding derivative line of the derivative spectrum are indicated by transition lines TL to mark the intensity transitions in the example mode line.

[0091] Figure 7B This is a close-up of an example critical angle transition (TM or TE), which is marked by the transition line TL1 and indicates the range of maximum intensity change from light to dark. The transition line is marked by the valley point or critical angle transition point obtained from the derivative critical transition line of the derivative spectrum.

[0092] Figure 8A This is a schematic representation of the example mode spectrum, showing mode line tilt and reduced mode line contrast. Each of these factors complicates determining the accurate mode line positions required for accurately calculating the stress-based parameters of the measured IOX article.

[0093] Figure 8B It is used to calculate the slope (a) and tilt angle (a) of a given mode line in the mode spectrum when using the weighted least squares method described in this paper. A close-up schematic diagram of the local xy coordinate system.

[0094] Figure 8C This is a schematic representation of the mode spectrum of an IOX article measured using a prism coupling system, where the TM mode spectrum has three tilted TM mode lines and the TE mode spectrum has two tilted TE mode lines.

[0095] Figure 9A and 9B They are Figure 8C Normalized 1D intensity distribution of example TM mode spectrum and example TE mode spectrum I TM-A (y) and I TE-A The graph shows the relationship between (y) and y position (number of pixels i), where the 1D intensity distribution is obtained by averaging the intensity values ​​in the x direction ("row average").

[0096] Figure 10A yes Figure 4CA close-up of an example segment of the 2D grayscale intensity distribution near the TM mode line of the TM mode spectrum, showing the fitted line FL of the intensity extrema (e.g., the lowest intensity).

[0097] Figure 10B This is a close-up image illustrating an example of using fitted lines to determine the position and orientation of pattern lines. The pattern line image is noisy, with white dotted lines indicating uncorrected fitted lines and white solid lines indicating error-corrected fitted lines.

[0098] Figure 11 It is a histogram, plotted as count N and tilt angle. The relationship (expressed in degrees) is used to plot the distribution of tilt angles calculated for 1295 mode spectra taken from different IOX products and different prism coupling systems, where the arithmetic mean of the tilt angles is called the bias tilt angle.

[0099] Figure 12A and 12B It is a schematic drawing of the measured mode spectrum with tilted mode lines, in which Figure 12B Showing the average tilt angle of the pattern line Rotation in the relative direction makes the pattern lines substantially perpendicular (i.e., without significant tilting (e.g., residual tilt)). )) mode spectrum. Detailed Implementation

[0100] Reference will now be made in detail to various embodiments of the present disclosure, examples of which are illustrated in the accompanying drawings. The same or similar reference numerals and symbols are used throughout the drawings to refer to the same or similar parts whenever possible. The drawings are not necessarily to scale, and those skilled in the art will recognize where the drawings have been simplified to illustrate key aspects of the present disclosure.

[0101] Cartesian coordinates are shown in some of the accompanying figures for reference only, and these Cartesian coordinates are not intended to restrict direction and / or orientation.

[0102] The abbreviation μm stands for micrometer, which is 10 -6 rice.

[0103] The abbreviation nm stands for nanometer, which is 10 -9 rice.

[0104] Depending on the context, the acronym IOX can mean either "ion exchange" or "ion-exchanged". "IOX article" refers to an article formed using at least one IOX process. Therefore, an article formed by a DIOX (double IOX) process is referred to herein as an IOX article; however, it can also be called a DIOX article.

[0105] The term “glass substrate” is used herein to describe materials, articles, matrices, substrates, etc., and means that such materials, articles, matrices, materials, substrates, etc. may include or be composed of any of glass, glass crystals, or glass ceramics.

[0106] Space xyz Cassette holder for glass substrates and IOX products is marked in Figure 1A , 1B In 1C, x is the direction into the main body of the IOX article.

[0107] The compressive stress distribution of an IOX product is denoted as CS(x), and is referred to as stress distribution in this paper. The surface compressive stress or simply "surface stress" of the stress distribution is denoted as CS, and is the value of the compressive stress distribution CS(x) at x = 0, i.e., CS = CS(0), where x = 0 corresponds to the surface of the IOX product.

[0108] The compression line depth (DOC) is the x-distance from the surface of an IOX article into the IOX article, at which the compressive stress CS(x) or CS'(x) intersects zero.

[0109] Knee stress is represented as CS k It is the compressive stress at the knee transition point (depth D1) between the peak region (R1) and the deep region (R2), i.e., CS(D1) = CS k .

[0110] The peak region R1 has peaks denoted as D1 and DOL relative to the substrate surface. SP The peak depth, also known as the peak layer depth, is the region of peak depth. The peak region is also called the "near-surface peak region" to distinguish it from the deep region.

[0111] The deep region R2 has a depth D2, which is also represented as the total layer depth DOL of the entire IOX region. T .

[0112] "Mode spectrum" includes transverse magnetic (TM) mode spectrum with TM mode lines and transverse electrical (TE) mode spectrum with TE mode lines. Mode lines are also referred to as "stripes" in the art. Mode spectrum can be described as including the mode lines and the critical angle transition (i.e., the coupling angle θ changes to a critical angle θ associated with light coupled to the waveguide of the IOX substrate and traveling as a guiding mode in that waveguide). C The intensity transition is formed by the location of the point.

[0113] A “compensated mode spectrum” or “corrected mode spectrum” or “improved mode spectrum” is a mode spectrum in which the location and / or orientation of intensity variations in the mode spectrum are defined using the methods disclosed herein, and the mode spectrum may include fitted mode lines in which any tilt is substantially removed, and the mode spectrum may include the location of intensity variations defined using derivative-based methods disclosed herein.

[0114] The tilt angle of individual pattern lines is expressed as And it is measured relative to the x-direction of the local xy Cartesian coordinates, such as... Figure 4C As shown in the diagram. The tilt angle measured counterclockwise relative to the x-direction. It is positive, and the tilt angle measured clockwise relative to the x-direction is positive. It is negative. The slope or rotation of individual mode lines is... And for small tilt angles, .

[0115] The term "tilt" refers to the rotation of the model line relative to its ideal orientation, which in the local coordinate system is in the x-direction. Tilt can be measured using either the tilt angle or the slope, and note that, as just noted above, these two measurements may be substantially the same for small angles.

[0116] The average slope is expressed as It is the average or arithmetic mean of all slopes of all mode lines in a given mode spectrum (i.e., TM and TE mode spectra), calculated by summing all slopes and dividing by the total number of slopes added. The variance of the slopes is denoted as υ, and the average variance is denoted as... Unless otherwise specified, variance is calculated as standard deviation.

[0117] The slope of the deviation is represented by a B Furthermore, it is the arithmetic mean or average of all slopes measured using a single prism coupling device for the mode spectra of different IOX products. Therefore, the deviation slope a can be... B The bias slope variance is considered a property of a given prism coupling device that reflects the tendency of the given prism coupling device to have a tilted mode spectrum. The bias slope variance (or just the slope variance) is a measure of the extent of the distribution of slope measurements used to calculate the bias slope, and is measured as the standard deviation unless otherwise stated.

[0118] Tilt bias describes the tendency of a prism coupling system to produce mode spectra with tilted mode lines. Tilt bias variance describes the degree of consistency or inconsistency of the tilt bias.

[0119] The claims set forth below are incorporated into and constitute a part of this "Embodiment".

[0120] Example prism coupling systems and measurement methods are described, for example, in the following document: entitled "METHODS OF CHARACTERIZING ION-EXCHANGED CHEMICALLY STRENGTHENED GLASSES CONTAIN", published on December 8, 2016. I U.S. Patent Application Publication No. 2016 / 0356760 (also published as WO 2016 / 196748 A1) entitled "METHODS OF CHARACTERIZING ION-EXCHANGED CHEMICALLY STRENGTHENED GLASSES CONTAIN" was published on February 20, 2018. I U.S. Patent No. 9,897,574, “Characterization Methods of Lithium-Containing Ion-Exchange Chemically Strengthened Glasses Contained”; and U.S. Patent Application Publication No. 2019 / 0033144, “METHODS OF IMPROVING THE MEASUREMENT OF KNEE STRESS IN ION-EXCHANGED CHEMICALLY STRENGTHENED GLASSES CONTAIN”. I The following documents are cited in this document: “NG LITHIUM (Improved method for measuring knee stress in lithium-containing ion-exchange chemically strengthened glass)”; U.S. Patent No. 9,534,981, published January 3, 2017, “PRISM-COUPLING SYSTEMS AND METHODS FOR CHARACTERIZING ION-EXCHANGE WAVEGUIDES WITH LARGE DEPTH-OF-LAYER (Prism-coupled systems and methods for characterizing ion-exchange waveguides with large depths)”; and U.S. Patent Application Publication No. 2019 / 0301952, entitled “PRISM-COUPLING STRESS METER WITH WIDE METROLOGY PROCESS WINDOW (Prism-coupled stress meter with a wide measurement process window)”.

[0121] IOX products

[0122] Figure 1AThis is a top-down view of example IOX article 10. IOX article 10 includes a glass substrate 20 having a matrix 21 defining a (top) surface 22, wherein the matrix has a basic (bulk) refractive index n. S and surface refractive index n0. Figure 1B This is a close-up cross-sectional view of the IOX article 10 taken in the xy plane, and illustrates an example IOX process performed across surface 22 and in the x direction into matrix 21 to form an example IOX article.

[0123] Reference Figure 1B The glass substrate 20 includes substrate ions IS in the matrix 21, which exchange with first ions I1 and second ions I2. The first ions I1 and second ions I2 can be introduced into the matrix 21 sequentially or in parallel using known techniques. For example, the second ion I2 can be a K+ ion introduced via a KNO3 bath for strengthening before the introduction of the first ion I1. + The first ion can be introduced via a bath containing AgNO3 to add antimicrobial Ag to the vicinity of surface 22. + ion. Figure 1B The circles representing ions I1 and I2 are for illustrative purposes only, and their relative sizes do not necessarily represent any actual relationship between the sizes of the actual ions involved in ion exchange. Figure 1C The result of the IOX process that forms IOX article 10 is schematically illustrated, wherein for ease of explanation, ... Figure 1C Substrate ions IS are omitted, and substrate ions IS are understood to constitute matrix 21. The IOX process forms IOX region 24, which includes a near-surface peak region R1 and a deep region R2, as explained below. IOX region 24 defines optical waveguide 26.

[0124] Furthermore, ions I1 may be abundant in regions R1 and R2 (see Figure 2, which will be described and discussed below), just like ions of type I2. Even using a single-step ion exchange process, the formation of two IOX regions R1 and R2 can be observed, in which the relative concentrations of ions I1 and I2 differ significantly. In one example, using ion exchange of Na-containing or Li-containing glasses in a bath containing a mixture of KNO3 and AgNO3, a high concentration of Ag can be obtained. + and K + The peak region R1 also has a high concentration of Ag. + and K + The deep region R2, but compared to the deep region R2, Ag + Relative to K + The relative concentration of may be significantly higher in the peak region R1.

[0125] Figure 1DFor example Figure 1C The example refractive index distribution n(x) of the example IOX article 10 shown in the figure illustrates a peak region R1 associated with shallower ion exchange (ion I1) and a peak region having a depth D1 (or DOL) penetrating into the matrix 21. SP The deep region R2 is associated with deeper ion exchange (ion I2) and has a defined total depth (DOL). T The depth D2. In one example, the total DOL T The thickness is at least 50 μm, and in one example it can be as high as 150 μm or 200 μm. As described below, the transition between the peak region R1 and the deep region R2 defines the knee KN in the refractive index distribution n(x) and also in the corresponding stress distribution CS(x).

[0126] In practice, a deeper region R2 can be generated before the peak region R1. The peak region R1 is adjacent to the substrate surface 22 and is relatively steep and shallow (e.g., D1 is a few micrometers), while the deeper region R2 is less steep and extends relatively deep into the substrate to the aforementioned depth D2. In one example, the peak region R1 has a maximum refractive index n0 at the substrate surface 22 and decreases sharply to an intermediate refractive index n I (This can also be called the "knee refractive index"), while in the deeper regions R2 gradually decreases from the intermediate refractive index to the substrate (body) refractive index n. S It is emphasized here that other IOX processes can cause steep and shallow near-surface refractive index changes, and the DIOX process is discussed here in an illustrative manner.

[0127] Figure 2A and Figure 1C Similarly, an example IOX process is illustrated using a single exchange ion I3 to form IOX article 10. Figure 2B and Figure 1D Similar, and is Figure 2A The example refractive index distribution n(x) of the IOX article 10 is shown. The example refractive index distribution n(x) smoothly transitions from the relatively high surface refractive index n0 to the substrate or body refractive index n of the matrix 21. S Therefore, the optical waveguide 26 (also referred to herein as the waveguide region) is defined by an IOX region 24, which has a gradient distribution of ions I3 in the glass matrix in the x direction from the surface 22 into the matrix 21.

[0128] Prism coupling system

[0129] Figure 3AThis is a schematic diagram of an example prism coupling system 28 that can be used to implement aspects of the methods disclosed herein. The prism coupling method using prism coupling system 28 is non-destructive. This feature is particularly useful for measuring fragile IOX articles for research and development purposes and for quality control during manufacturing.

[0130] The prism coupling system 28 includes a support stage 30 configured to operably support the IOX article 10. The prism coupling system 28 also includes a coupling prism 40 having an output surface 42, a coupling surface 44, and an output surface 46. The coupling prism 40 has a refractive index n. P >n0. By making the coupling prism coupling surface 44 into optical contact with the surface 22, the coupling prism 40 docks with the measured IOX article 10, thereby defining a coupling interface 50, which in one example may include a docking (or refractive index matching) fluid 52.

[0131] The prism coupling system 28 includes an input optical axis A1 and an output optical axis A2, which pass through the input surface 42 and the output surface 46 of the coupling prism 40, respectively, and converge approximately at the coupling interface 50 after refraction at the prism / air interface.

[0132] The prism coupling system 28 includes a light source system 60 sequentially along the input optical axis A1, which emits measurement light 62 in a general direction along the input optical axis A1. A focusing optical system 80 is located between the coupling prism 40 and the light source system 60 and is used to focus the measurement light to form a focused light 62F, which passes through the input surface 42 and is incident on the coupling surface 44 and coupling interface 50 of the coupling prism 40.

[0133] The prism coupling system 28 also includes, in sequence from the coupling prism 40 along the output optical axis A2, a collection optics system 90, a TM / TE polarizer 100, and a photodetector system 130, the collection optics system having a focal plane 92 and a focal length f and receiving reflected light 62R as explained below.

[0134] The input optical axis A1 defines the center of the input optical path OP1 between the light source system 60 and the coupling surface 44. The input optical axis A1 also defines the coupling angle θ relative to the surface 22 of the measured IOX article 10.

[0135] The output optical axis A2 defines the center of the output optical path OP2 between the coupling surface 44 and the photodetector system 130. Note that due to refraction, the input optical axis A1 and the output optical axis A2 may be bent at the input surface 42 and the output surface 46, respectively. They can also be decomposed into subpaths by inserting a mirror (not shown) into the input optical path OP1 and / or the output optical path OP2.

[0136] In one example, the photodetector system 130 includes a detector (camera) 110 and a frame capture device 120. In other embodiments discussed below, the photodetector system 130 includes a CMOS or CCD camera. Figure 3B This is a close-up top-down view of the TM / TE polarizer 100 and the detector 110 of the photodetector system 130. In one example, the TM / TE polarizer includes a TM segment 100TM and a TE segment 100TE. The photodetector system 130 includes a photosensitive surface 112.

[0137] The photosensitive surface 112 is located on the focal plane 92 of the collecting optical system 90, wherein the photosensitive surface is substantially perpendicular to the output light axis A2. This is used to convert the angular distribution of the reflected light 62R leaving the output surface 46 of the coupling prism into a lateral spatial distribution of light at the sensor plane of the detector 110. In one example embodiment, as... Figure 3B As shown in the close-up illustration, the photosensitive surface 112 includes pixels 112P. In one example, the detector 110 is a digital detector, such as a digital camera, CMOS, sensor, etc.

[0138] like Figure 3B The diagram illustrates how dividing the photosensitive surface 112 into TE and TM segments allows for the simultaneous recording of a digital image of a two-dimensional (2D) angular reflectance spectrum (mode spectrum) 113, comprising individual TE and TM mode spectra 113 of the TE and TM polarizations of the reflected light 62R. This simultaneous detection eliminates measurement noise sources that could arise from TE and TM measurements performed at different times, considering that system parameters may drift over time. The digital image thus captured is hereinafter referred to as the “raw image” or “mode spectrum image.”

[0139] Figure 3C This is a close-up top-down view of detector 110, shown operably supported by a rotatable support platform 131 having a front side 132, a periphery 133, and a rear side 134. Detector 110 is shown supported at the front side 132 and is shown with an angular orientation β = N relative to the vertical reference line VL. Β ·δβ, where δβ is the rotation increment, and N ΒThis is the number of rotation angle increments. The rotatable support stage 131 can be supported at the rear side 134 by a support shaft 135. The rotatable support stage 131 is configured to rotate about the output optical axis A2, such that the detector 110 and its photosensitive surface 112 can rotate relative to the output optical axis. In one example, the rotatable support stage 134 is operatively connected to a rotary drive system 136. In one example, the rotary drive system 136 includes a first drive gear 137 operatively attached to a rotary drive motor 138 that drives the first drive gear. The rotary drive motor 138 is operatively connected to a motor controller 138C that controls the operation of the rotary drive motor.

[0140] In one example, the first drive gear 137 engages a groove 133G on the periphery 133 of the rotatable support 131 to cause the rotatable support to rotate when the rotary drive motor 138 drives the first drive gear 137. In one example, the rotary drive motor 138 is a precision motor that can rotate the first drive gear 137 in small, precise rotational increments δβ under the control of the motor controller 138C, such that the photosensitive surface 112 of the detector 110 is used with a number of N... Β Small, precise rotation increments δβ rotate to the selected angular orientation β = N. Β •δβ. In one example, the rotary drive motor 138 includes a commercially available rotary piezoelectric motor or a similar high-resolution rotary positioner.

[0141] In an alternative embodiment shown in close-up illustration IN1, the rotary drive motor 138 can be replaced by a manually precision-driven component 140 (e.g., a precision drive screw, a precision worm gear, or a worm gear combined with a differential micrometer). In one example, the angular increment δβ can be in the range of 0.15 degrees to 0.05 degrees.

[0142] Figure 3D and Figure 3C Similarly, an alternative arrangement of the rotary drive system 136 is illustrated, wherein the support shaft 135 includes a second drive gear 139 that engages a first drive gear 137 to rotate the rotatable support platform 131 and thus the detector 110. The photodetector system 130, including the rotatable support platform 131 and the rotary drive system 136, includes a rotatable photodetector system 130R.

[0143] Continue to refer to Figure 3AThe prism coupling system 28 includes a controller 150 configured to control the operation of the prism coupling system. The controller 150 is also configured to receive and process image signals SI representing the captured (detected) raw images (i.e., TE and TM mode spectra 113) from the photodetector system 130. The controller 150 includes a display 151, a processor 152, and a memory unit (“memory”) 154. The controller 150 can control the activation and operation of the light source system 60 via a light source control signal SL, and receive and process image signals SI from the photodetector system 130 (as shown, for example, from the frame capture unit 120). In one example, a motor controller 138C is controlled by the controller 150 via a motor controller signal SMC to initiate the rotation of the detector 110 for reasons explained in more detail below.

[0144] The controller 150 is programmable (e.g., programmed to have instructions implemented in a non-transitory computer-readable medium) to perform the functions described herein, including operating the prism coupling system 28 and performing signal processing of the image signal SI to obtain measurements of one or more of the aforementioned stress characteristics of the IOX article 10. Furthermore, the controller is also configured to implement the methods described herein for determining the mode line position and removing any tilting of mode lines 115TM and 115TE (refer to the description and discussion below). Figure 4A , 4B ).

[0145] mode spectra

[0146] Figure 4A This is a schematic representation of the idealized mode spectrum 113 captured by the photodetector system 130. Figure 4B The actual mode spectrum 113 is captured by the photodetector system 130. Local Cartesian coordinates are x and y. Mode spectrum 113 has TM and TE total internal reflection (TIR) ​​segments 114TM and 114TE, respectively associated with TM and TE guided modes, and non-TIR segments 117TM and 117TE, respectively associated with TM and TE radiation and leakage modes. TIR segment 114TM includes one or more TM mode lines 115TM, ​​while TIR segment 114TE includes one or more TE mode lines 115TE. TM mode lines 115TM and TE mode lines 115TE are generally aligned in the x-direction and spaced apart in the y-direction.

[0147] The measured TM mode spectrum 113TM has a discrete 2D intensity distribution I TM (x,y), while the TE mode spectrum 113TE has a discrete 2D intensity distribution ITE(x,y), where the discreteness is caused by digital capture of the mode spectrum 113 using a detector 110 including a two-dimensional pixel array 112P.

[0148] The transitions 116TM and 116TE between the TIR segments 114TM and 114TE and the non-TIR segments 117TM and 117TE define the critical angles for optical coupling into and out of the optical waveguide 26 of the IOX article 10, and are referred to as the critical angle transition 116. The difference in the starting position of the critical angle transitions 116TM and 116TE of the TM mode spectrum 113TM and the TE mode spectrum 113TE is related to the knee stress CS. k Proportional, and this proportion is Figure 4A The middle is composed of "~CS" k As instructed.

[0149] The mode line 115 and the critical angle transition 116 each constitute an intensity transition in the mode spectrum 113. Therefore, in the following description, unless otherwise indicated, the reference to "intensity transition" in the mode spectrum 113 may refer to either the mode line 115 or the critical angle transition 116.

[0150] Depending on the configuration of the prism coupling system 28, the TM mode line 115TM and the TE mode line 115TE can be either bright lines or dark lines. Similarly, depending on the configuration of the prism coupling system 28, the critical angle transitions 116TM and 116TE can be transitions from bright to dark or from dark to bright.

[0151] exist Figure 4A In the other mode spectra discussed below and shown in other figures, for ease of illustration, the TM mode line 115TM and the TE mode line 115TE are shown as dark lines, while the corresponding critical angle transitions 116TM and 116TE are shown as intensity transitions from bright to dark.

[0152] exist Figure 4B In the original text, the TM mode line 115TM and the TE mode line 115TE are also dark, but the contrast of the mode lines is not particularly high, making it difficult to accurately determine the location of the TM and TE mode lines. The various systems and methods disclosed herein involve determining the position of the TM mode line 115TM and the TE mode line 115TE with improved accuracy, resulting in more accurate calculations of the characteristics of the generated IOX article 10.

[0153] Stress characteristics are calculated based on the difference in the x-position of the TM mode line 115TM and the TE mode line 115TE in mode spectrum 113. Birefringence B is the difference between the effective refractive indices of the TM and TE polarizations, where the effective refractive index is represented by the y-position of the mode line. The surface compressive stress CS or compressive line depth is calculated by the y-distance between the mode line (effective refractive index) and the ratio B / SOC, where SOC is the stress optical coefficient. At least two TM mode lines 115TM and TE mode lines 115TE are required to calculate the surface stress CS. Additional mode lines are needed to calculate the compressive stress distribution CS(x). Layer depth DOL T It is a measure of the stress penetration length or ion penetration length of the matrix 21 entering the glass substrate 20, and in the case of the IOX process, it can also be calculated by the position and number of the TM mode line 115TM and the TE mode line 115TE. Therefore, the position of the TM and TE mode lines along the x-axis is the most basic measurement for inferring the stress-related characteristics of the IOX article 10.

[0154] Derivative-based methods

[0155] In the example method (referred to herein as the "derivative-based method"), the location of the TM mode line 115TM and the TE mode line 115TE is determined by detecting the intensity transition in each of the mode lines in the derivative image (represented as the normalized derivative of the original grayscale intensity of the image). Specifically, the exact location where the transition occurs is where the rate of change of the grayscale intensity of the spectrum (or image) is at an extreme value, which is the maximum intensity for bright lines and the minimum intensity for dark lines.

[0156] Figure 4C yes Figure 4B The derivative of the mode spectrum 113, referred to herein as the "derivative spectrum" 113D, has a "derivative intensity transition" consisting of a "derivative line" 115D and a "derivative critical transition line" 116D. Specifically, the derivative spectrum 113D has a TM segment 113D-TM, which has a "TM derivative intensity transition" consisting of a "TM derivative line" 115D-TM and a "TM derivative critical transition line" 116D-TM. The derivative spectrum 113D also has a TE segment 113D-TE, which has a "TE derivative intensity transition" consisting of a "TE derivative line" 115D-TE and a "TE derivative critical transition line" 116D-TE. The numerical methods discussed below are used according to... Figure 4B The derivative spectrum 113D of the mode spectrum 113 is calculated numerically.

[0157] The TM and TE derivative lines 115D of the derivative spectrum 113D represent the TM mode line 115TM and TE mode line 115TE in the "derivative space". In the derivative space, each pixel has an intensity value proportional to the derivative of the grayscale intensity of the original image, and the derivative intensity transition is represented as the darkest / brightest pixel. The term "derivative line" is used herein as a shorthand for the rate of change of mode line intensity with respect to the position associated with the actual mode line. The derivative line is not a line in the original image (mode spectrum), but becomes a "line" in the derivative space representing the rate of change of grayscale intensity. The intensity can be the full range of grayscale pixel intensity, such as 0 to 255, or normalized to 0 to 1 in increments of 1 / 256. Similarly, the term "derivative critical transition line" is used herein as a shorthand for the rate of change of critical angle intensity with respect to the position associated with the critical angle transition in the mode spectrum. The derivative critical transition line is not a line in the original image (mode spectrum); rather, it is the location where the original image transitions from bright to dark, that is, the intensity "edge" that becomes a "line" in derivative space.

[0158] Compared to attempting to detect intensity transitions directly in the “image space” of the captured mode spectrum 113, analyzing the derivative intensity transitions in mode spectrum 113D makes it easier to estimate the actual location of the intensity transitions in mode spectrum 113.

[0159] The derivative spectrum 113D can be calculated from the mode spectrum 113 as follows. First, assume that the grayscale intensity at column I and row j of the digital image of the mode spectrum 113 is p. ij There are a total of m pixel rows, and the distance between each pixel on the horizontal axis is Δh. At column i and row i, the derivative d of the grayscale intensity with respect to the horizontal axis / row is... ij It can be expressed as a finite difference formula:

[0160]

[0161] To plot the derivative strength transition to produce, for example... Figure 4C The derivative spectrum 113D shown is obtained by standardizing the derivative so that its value lies between 0 and 1.

[0162]

[0163] Reference Figure 4CThe derivative lines 115D-TM and 115D-TE represent the locations where grayscale intensity changes. Thus, for each mode line 115, the transition from high to low grayscale intensity occurs towards the front of the mode line, while the transition from low to high intensity occurs towards the rear of the mode line. Therefore, the derivative intensity transition appears as a line / band in the derivative space, because, as discussed above, the derivative spectrum 113D shows the rate of change of grayscale intensity with position, where the highest / lowest rate of change of grayscale intensity in a local region appears as the brightest or darkest pixel in that region.

[0164] The example derivative method uses the following three main steps to process the derivative spectrum 113D: 1) isolating the sub-segments of the derivative spectrum 113D where derivative intensity transitions occur to identify derivative lines 115D-TM and 115D-TM and critical angle transition lines 116D-TM and 116D-TE; 2) locating the derivative intensity transitions using either a weighted linear regression method or a two-layer weighted regression shape detection method, as described in more detail below; and 3) checking to confirm that the detected derivative intensity transitions are associated with mode lines 115 or critical angle transitions 116 in the mode spectrum 113 and are not artifacts from the original mode spectral image.

[0165] The first major step can be performed by analyzing the row averaging of the derivatives of the grayscale intensity of the TM derivative spectrum 113D-TM and the TE derivative spectrum 113D-TE. Here, "row" refers to the direction along the length of the mode line 115. In the row averaging plot described herein, the "peak point" or "peak value" in the curve is denoted as PP, and the "valley point" or "valley value" is denoted as VP, where the subscripts for TM and TE are used for plotting TM and TE, respectively. The TM and TE critical angle transition points of the TE critical angle transition 116TM and the TE critical angle transition 116TE are denoted as CP, respectively. TM and CP TE .

[0166] Figure 5A and 5B yes Figure 4B Example of a mode spectrum: TM mode spectrum 113TM ( Figure 5A ) and example TE mode spectrum 113TE ( Figure 5B The row average standardized 1D intensity distribution I TM-A (y) and I TE-A A graph showing the relationship between (y) and y position (number of pixels i). The minimum intensity of the TM mode line 115TM and the TE mode line 115TE is shown as a dark circle, and the critical angle transitions 116TM and 116TE are also indicated by dark circles.

[0167] Figure 6A and 6B yes Figure 4C The average row intensity I′ of the derivative spectrum 113D, the TM derivative spectrum 113D-TE, and the TE derivative spectrum 113D-TM TM-A (y) and I′ TE-A The relationship between (y) and y-position (number of pixels i). See reference... Figure 6A and 6B The valley point VP′ and the peak point PP′ (located within the dashed circle) correspond to the derivative lines 115D-TM and 115D-TE in the derivative space and are used to identify... Figure 5A and 5B The intensity transition points (points) TP (dark circles) in the corresponding mode lines 115TM and 115TE of the mode spectra 113TM and 113TE shown are denoted as CP′. The critical transition lines are respectively represented as CP′. TM and CP′ TE And with Figure 5A and 5B The critical angle transitions in the mode spectra 113TM and 113TE correspond to 116TM and 116TE.

[0168] The curves in mode spectrum 113 and derivative spectrum 113D are based on average grayscale intensity, and the average derivative of grayscale intensity is generally not smooth. Therefore, an example aspect of the method involves smoothing the mode spectrum curves and derivative spectrum curves using a smoothing operation (e.g., moving average or smoothing function) before using the curves to pre-select / isolate possible locations of mode line transitions. Even though the transitions are typically located at valleys / peaks in the average derivative of grayscale intensity, image defects can create valleys / peaks in the curves and introduce errors in the calculations used to determine the characteristics of the IOX article 10 under consideration.

[0169] Assuming the average derivative of grayscale intensity is s, the following steps can be used to find possible locations of derivative intensity transitions.

[0170] The first step involves targeting a given derivative spectrum, either 113D-TM or 113D-TE (see reference). Figure 6A , 6B The derivative intensity transition in the equation seeks points at the bottom of the valley VP′ and the top of the peak pp′, where these points satisfy the following condition:

[0171] S i ≤-S m S i ≥S M (3A)

[0172] Where S m and S MThese are two parameters, which can be selected using a first percentage (e.g., ~30%) of the negative average derivative data for the selected trough and a second percentage (e.g., ~15%) of the positive average derivative data for the selected peak. The example first and second percentages described above are based on experimental sample values ​​and can be adjusted as needed to obtain optimal results.

[0173] The second step involves using equation (1A) to group the discovered data points. In one example, this is done by the following steps: linking all successive data points into separate groups, then finding the minimum value from each negative group and the maximum value from each positive group, and then retaining only the minimum and maximum data points that are likely to be peak / valley locations.

[0174] The third step is to retain only the valley point VP′ that follows the peak point PP′ in the data set above if the valley value is not the last data point in the data set above.

[0175] The last (rightmost) valley point VP' is associated with the critical transition line of the derivative, so it is denoted as VP' and CP'. Other valley points VP' (followed by peak points PP') of a given derivative line indicate that the transition occurs at the beginning of the given mode line, while peak points PP' indicate that the transition occurs at the end of the given mode line.

[0176] Figure 7A This is a close-up of an example mode line 115 (TM or TE) that uses transition lines TL to identify intensity transitions. The position of the transition line TL is based on the valley point VP' and peak point PP' of the corresponding derivative line 115D of the corresponding derivative spectrum 113D. The region between adjacent transition lines TL constitutes a transition region or transition segment.

[0177] The dotted white line is the first transition line TL1, where the image grayscale intensity changes most rapidly from high to low. The dashed white line is the second transition line TL2, where the image grayscale intensity transitions most rapidly from low to high. Solid white lines indicate the points where the grayscale intensity reaches its lowest point. These lowest points can be used to determine the fitted lines FL using the methods discussed below, including weighted regression and two-level weighted regression methods.

[0178] Figure 7B and Figure 7A Similarly, a close-up of example critical angle transition 116 is shown, where the transition line TL1 is based on the derivative spectrum 113D (e.g., referencing...). Figure 6A and 6BThe valley point of the derivative critical transition line is VP' = CP'. Unlike mode line 115, at the critical angle transition 116, the grayscale intensity of the original image changes to its lowest position without changing back to its initial grayscale intensity position, resulting in only a single transition line TL = TL1 associated with the derivative critical angle transition line. This transition line is used to determine the estimated location of the critical angle transition 116 in the mode spectrum 113.

[0179] The transition line TL is then applied to mode spectrum 113, and particularly to mode line 115 and critical angle transition 116, to determine an estimate of the position of mode line 115 and critical angle transition. The estimated positions of mode line 115 and critical angle transition 116 are then used to calculate one or more optical properties of the IOX article 10 (e.g., at least one stress-based property).

[0180] In summary, the derivative-based method includes the following main steps: 1) Calculating the derivative spectrum from the mode spectrum to form a derivative intensity transition including the derivative line (associated with the mode line) and the derivative critical transition line (associated with the critical angle transition) based on the intensity transition defined by the mode line 115 and the critical angle transition 116; 2) Determining a fitted line for each derivative intensity transition to define a set of fitted lines having the corresponding position in the mode spectrum; 3) Performing an error check on each fitted line in the set to evaluate whether a given derivative intensity transition corresponds to an intensity transition in the mode spectrum or noise in the mode spectrum, and discarding any fitted lines found to be caused by noise, thereby defining a set of checked fitted lines; 4) Limiting the estimated position of the intensity transition in the mode spectrum to the corresponding position defined by the set of checked fitted mode lines in the derivative spectrum, thereby forming a "corrected" or "improved" mode spectrum; 5) Using the corrected or improved mode spectrum to estimate at least one stress-based characteristic of the IOX article 10.

[0181] Methods for estimating the position and tilt angle of the model line

[0182] Figure 8A and Figure 4A Similarly, an example mode spectrum 113 is plotted, wherein mode lines (mode lines) 115TM and 115TE are tilted relative to the x-axis of the local xy coordinate system of mode spectrum 113 by an angle. tilt. Figure 8B This is a schematic diagram of a local xy coordinate system, illustrating how to measure the tilt angle. And the slope 'a' and intercept 'b' of example pattern lines 115TM or 115TE. Figure 8B In the diagram, the local xy coordinate system has been rotated so that the y-axis is perpendicular.

[0183] The tilt angle shown It is positive because it involves a counterclockwise rotation relative to the x-axis. The slope 'a' is also positive because both Δy and Δx are positive. In one example, different TM mode lines 115TM and different TE mode lines TE can all have slightly different tilt angles. Or slope a. In the following discussion and calculations, slope a is used to describe the tilt or rotation of a given mode line. It will be understood by those skilled in the art that the tilt angle can also be used without loss of generality, because And for small angles, Therefore, the term "inclination," as used in this article, can refer to either the angle of inclination or the slope, as each is a measure of the amount of inclination.

[0184] Therefore, in one example, the average slope The slope α is defined as the average of all slopes α of all TM mode lines 115TM and TE mode lines 115TE for a given mode spectrum 113. In some of the following discussion, for ease of interpretation, it is sometimes assumed that the different slopes α of TM mode lines 115TM and TE mode lines 115TE are substantially constant, such that for a given mode spectrum,

[0185] The tilt of the TM mode line 115TM and the TE mode line 115TE significantly complicates the measurement of the mode line positions (i.e., y-positions) used to calculate the stress-based properties of the IOX article 10. Furthermore, the reduced contrast of the TM mode line 115TM and the TE mode line 115TE can make determining the exact center of each mode line substantially more difficult, especially since the reduction in contrast may not (and generally is not) symmetrical with respect to an ideal mode line. This ambiguity in the mode spectrum 113 precludes simple methods for determining the mode line positions and tilt. For example, a simple method for determining the tilt would be to measure the relative positions of the top and bottom of a given mode line and then use simple trigonometric geometry to obtain the tilt. The problem with this method is that it assumes the precise position is known when it may not be readily determined from the raw data (i.e., the digital image of the mode spectrum, also known as the mode spectral image). Thus, the simple method described above leads to inaccurate calculations of the stress-related properties of the measured IOX article 10.

[0186] Current mode line detection methods rely on iterative calculations and computer-fitting of the grayscale intensity distribution of a given mode line (115TM or 115TE). Iterative fitting is performed using a Gaussian function or some other functional form of the mode line intensity distribution shape and fitting parameters to define the mode line position. While such fitting methods can work fairly well, they require iteration to converge and are therefore slow, even when implemented computer-based. Furthermore, they do not always achieve optimal accuracy. From a commercial perspective, the slowness is problematic because it reduces the measurement throughput of IOX articles. In a manufacturing environment, reduced measurement throughput directly translates to increased manufacturing costs. Inaccurate determination of mode line position is also a problem, as it directly translates to errors in the calculated stress-based characteristics, which in turn translates to reduced quality control and increased manufacturing costs.

[0187] One aspect of this disclosure relates to methods for finding the location and tilt of mode lines. These methods are called estimations because the digital nature of the captured mode spectrum makes it difficult, if not impossible, to determine the exact location of the mode lines.

[0188] The mode line estimation method disclosed in this paper can be divided into three main steps: 1) using a one-dimensional (1D) average grayscale intensity curve to approximately locate the TM mode line 115TM and the TE mode line 115TE based on the two-dimensional digital mode spectral image; 2) using machine learning methods (more specifically, a modified type of weighted least squares method) to determine / estimate the mode line position on the two-dimensional mode spectra 113TM and / or 113TE; and 3) removing any “false” mode lines that are not true mode lines, wherein the removal is based on criteria related to the estimated position, slope, and width of typical mode lines.

[0189] Step 2) can be broken down into the following two sub-steps: i) Setting up a total loss function using weights based on grayscale intensity. For dark mode lines, the error at darker pixels is weighted more heavily than the error at lighter pixels to force the fitted line through darker pixels. For light or bright mode lines, the error at lighter pixels is weighted more heavily than the error at darker pixels to force the fitted line through lighter pixels; ii) Analytically minimizing the loss function using a modified weighted least squares method, which takes into account the mode line position and tilt angle. The best estimate provides an analytical solution.

[0190] Figure 8CThis is a schematic representation of the actual mode spectrum 113 of the IOX article measured using prism coupling system 28, wherein the TM mode spectrum 113TM has three mode lines 115TM, ​​and the TE mode spectrum 113TE has two mode lines 115TE. The TM mode lines 115TE and the TE mode lines 115TM are almost perpendicular, i.e., they have a small (positive) tilt angle. And therefore it has a small but positive slope a. For ease of explanation, the slope of the pattern lines 115TM and 115TE in Figure 4D is exaggerated compared to the actual data.

[0191] As discussed above, the measured TM mode spectrum 113TM has a discrete 2D intensity distribution I TM (x, y), while the TE mode spectrum 113TE has a discrete 2D intensity distribution ITE(x, y), where the discreteness is caused by digital capture of the mode spectrum 113 using a detector 110 including a two-dimensional pixel array 112P.

[0192] To determine the initial positions of mode lines 115TM and 115TE, in one example, intensity I is set in the x-direction. TM Averaging (x, y) and ITE(x, y) to constrain the corresponding y-average ("row average") 1D discrete intensity distribution I TM-A (y) and I TE-A (y), as mentioned above and Figure 5A and 5B This was discussed in conjunction with other discussions.

[0193] Figure 9A and 9B They are Figure 8C Normalized (averaged) 1D intensity distribution of the TM and TE modes of mode 113. TM-A (y) and I TE-A A graph showing the relationship between (y) and y-position (in the number of pixels i). Intensity distribution I TM-A (y) and I TE-A (y) has a concave D (denoted as D respectively) TM and D TE These depressions are assumed to be approximate positions of the TM mode line 115TM and the TE mode line 115TE, respectively.

[0194] In order to find the average intensity distribution I with sufficient accuracy TM-A (y) and I TE-A (y) concave D TM Or D TEThe y-position needs to be calculated accurately enough for the stress-related characteristics of the measured IOX article 10, requiring a method to provide sufficient information about whether the depression D has been found. TM Or D TE A deterministic method for the true bottom (i.e., the best estimate). The above discussion presents an example method based on the derivative spectrum of the truncated mode spectrum and the use of derivative lines to identify transition sub-regions in the mode spectrum to be processed.

[0195] Another example procedure for accurately determining the location of the bottom of a given concave depression D has selected constraints based on intensity averaging. In the following calculations, for ease of representation, I... TM-A (y) or I TE-A The discrete x-mean intensity defined by (y) is given by z. i The symbol represents the pixel, where the subscript i represents a pixel.

[0196] One constraint is that, given the bottom of the concave D, on either side ("left and right") of pixel i, within a given pixel range, it has the lowest average grayscale intensity z given by the following equation. i :

[0197] z i ≤min(z i+k k = 1, 2...m r ); zi≤min(z) i-k k = 1, 2...m l (1B)

[0198] Another constraint is the grayscale intensity z at the bottom of the concave D. i The average value is less than the average grayscale intensity of a given number of neighboring pixels. The width to be averaged is given as m. r and m l (Number of pixels measured) and the corresponding intensity margin is given as z. mr and z ml Then z i Given by the following equation:

[0199]

[0200] Another constraint is that the grayscale intensity at the bottom of the concave D is at least one given value lower than the average peak grayscale intensity from the left to the valley. The backward width is given as m. lo And the margin is given as z pl We got

[0201] z i ≤max(z i-k k = 1, 2...m lo )-zpl (3B)

[0202] After all the concave Ds in a given 1D discrete intensity distribution of the row-averaged TM mode spectrum 113TM and TE mode spectrum 113TE have been located and all (possible) mode lines have been approximately determined, a more precise mode line location is determined by fitting a line to the lowest (minimum) intensity (for dark mode lines) of a sub-segment of the original 2D image around each approximate mode line, including slope and intercept.

[0203] Figure 10A This is a close-up of the example segment SM, taken from the example 2D grayscale intensity distribution (mode spectral image 113TM), around the example TM mode line 115TM, ​​showing the fitted line FL with the lowest intensity.

[0204] Single-layer weighted regression detection method

[0205] As mentioned above, it is assumed that the model line being analyzed has a slope and intercept given by the following standard line formula (in local xy coordinates):

[0206] y = ax + b (4B)

[0207] Where 'a' is the slope (i.e., the rotation that causes the tilt), and 'b' is the intercept (refer to...). Figure 8B The pattern line is the best fit for the darkest pixels (assuming the pattern line is a dark line), giving the darkest pixels more weight than the lighter ones. Therefore, in one example, a weighted least squares method is used to determine the best-fit line FL.

[0208] Suppose n is the total number of points to be fitted, then the objective function (or "loss function" in machine learning) F is constrained as follows:

[0209]

[0210] To find the best-fit line, the objective function is minimized by taking the derivative of the objective function with respect to the slope 'a' and the cutoff 'b' and then making it vanish.

[0211]

[0212] The solutions to these equations are given by the following equations:

[0213]

[0214]

[0215] in

[0216]

[0217] The weighting function w can be used i To emphasize that darker pixels are more important than lighter pixels, the weighting function w i In the total loss, the same distance between the fitted line and the pixel coordinates of the darker pixels is weighted more at the lighter pixels to force the line through the darker pixels.

[0218] Therefore, the weighting function w i This makes the fitted line follow the intensity extremum more closely, which in this example is the intensity minimum. For examples with bright mode lines, the intensity extremum could also be the intensity maximum.

[0219] The example weighting function F is an exponential function of the difference between the grayscale pixel intensity pi and the minimum grayscale intensity (i.e., the darkest pixel). Example exponential weighting function w i Given by the following equation:

[0220]

[0221] Where α is a positive constant.

[0222] According to equation (9B), the darkest pixel (p i =min(p k Pixels of color k (k = 1, 2, ..., n) have a weight equal to 1, while lighter pixels have a smaller weight. The exponent constant α determines how much more weight darker pixels have compared to lighter pixels. To make the weight decrease quickly from dark to light pixels, the value of the exponent constant α is increased. Alternatively, other weighting functions w can be used that provide a relatively fast weight change from dark to light pixels. i Note that for mode spectra with bright lines, the weighting is reversed. Therefore, the weighting is generally based on the local extrema of the intensity associated with a given type of mode line (i.e., bright or dark).

[0223] Two-level weighted regression detection method

[0224] Another example method for pattern line fitting and detection includes a two-layer weighted regression detection method. This method is similar to the single-layer method, except that it incorporates derivative information regarding grayscale pixel intensity, as discussed above in derivative-based methods. Therefore, the name "two-layer" reflects the application of intensity extrema and transition intensities to each pattern line 115 during the weighting process that defines the fitted line for each pattern line, as described below.

[0225] against Figure 10AFor each column (or row for a horizontal or substantially horizontal line) of the intensity distribution segment SM, this method finds the row (or column for a horizontal line) location where the transition is most likely to occur by finding the intensity-related weighted average of the pixel y-positions in that column. Assuming pixel (x... i y j The derivative of the grayscale intensity at point () is d ij And also assume that the total number of points at column i is m. i Then the most likely row / column position and the generated pixel intensity of columns / rows for:

[0226]

[0227]

[0228] Among them, the weighting coefficient It is related to the intensity derivative. In order to find dark shapes in the derivative space, the weighting coefficients give more weight to dark pixels than to light pixels, and in order to find bright shapes, the weighting coefficients give more weight to bright pixels.

[0229] An example weighting function is the grayscale intensity p at the pixel. ij The minimum / maximum grayscale intensity d of any column or the entire image min =min[d ij j = 1, 2...m i ] or d max =max[d ij j = 1, 2...m i The exponential function of the difference between the darkest or brightest point at column i (which depends on the type of line being searched).

[0230] Dark shapes (transition from light to dark);

[0231] or Bright shapes (transition from dark to light); (3C)

[0232] Where β is a given positive constant. According to equation (3C), it can be seen that when searching for dark shapes in the derivative space (the transition from light to dark in the original image space), the darkest pixel (d) is the one that determines the shape. ij =d min The lightest pixel will have a weight equal to 1, and lighter pixels will have a smaller weight. On the other hand, when searching for bright shapes (transitions from dark to light) in derivative space, when determining transition shapes (e.g., lines), the brightest pixel (d) will have a weight equal to 1. ij =dmax ) will have a weight equal to 1, and darker pixels will have a smaller weight.

[0233] The exponential constant β determines how differently the weights of darker points differ from those of lighter points in the derivative space. To make the weights decrease rapidly with the derivative of grayscale intensity, the value of the exponential constant β can be increased. Another possible weighting function is the Dirac delta function, where the weight is 1 at the darkest / brightest pixel in the column and zero at all other pixels. The purpose of the weights is to distinguish the role of the derivative of grayscale intensity when determining where the transition shape will most likely pass through each column / row.

[0234] From the most likely point in all columns (or rows for horizontal lines). Weighted regression is used to find the best-fit shape. For example, for an FSM image, the goal is to find the points most likely to connect. The fitted line, these points define a given TM mode line 115TM or TE mode line 115TE or critical angle transition 116TM or 116TE. The equation for the fitted line is:

[0235] y = ax + b (4C)

[0236] Where 'a' is the slope (rotation) and 'b' is the intercept of the fitted line. Assume 'n' is the total number of most likely points to fit (the total number of columns, or, for a horizontal line, the total number of rows with generating points). To find the best-fit line, the loss function F, commonly known in machine learning, is constrained as follows:

[0237]

[0238] Next, the loss function F is minimized. To minimize the loss function F (which best fits the darkest point), the derivative of the loss function is taken with respect to a and b, with the loss function set to zero:

[0239]

[0240] And the solution is:

[0241]

[0242]

[0243] in

[0244]

[0245] To find the dark line in the derivative space (the transition from light to dark in the original image space), the weighting function w should make the most likely location... Dark-generated pixels at the location It has more weight than lighter pixels. One weighting function is the same exponential function form given in equation (3C). The constant can have different values ​​(and is therefore denoted as α below), where the value depends on the grayscale generation intensity at the pixel. The difference between the derivative of the value and the minimum gray level intensity (the darkest point) in all columns:

[0246]

[0247] Where α is a given non-negative constant. According to equation (9C), it can be seen that, when determining the fitted line, the darkest generated pixel is... Darker pixels will have a weight equal to 1, while lighter pixels will have a smaller weight. The exponential constant α determines how much more weight darker pixels will have compared to lighter pixels. To make the weight decrease rapidly from dark pixels to light pixels, the value of the exponential constant α can be increased. When α = 0, one weight is applied to all generated pixels, meaning the line will be equally likely to be near both dark and light generated pixels. Similarly, a similar weighting function can be used to find the bright line in the derivative space (the transition from dark to bright in the original image space).

[0248] Once the best-fit line (fit line) FL is found, the error checking process described below can be performed to ensure that noise does not adversely affect the determination of the fit line FL.

[0249] Error Check

[0250] As described above, once the fitted line FL of the mode line 115 is determined according to the two-layer method described above, the fitted line can be examined to determine whether the determined fitted line is prone to generating noise that may cause errors.

[0251] Figure 10B This is a close-up view of an example segment SM of the mode line 115 in the mode spectrum (image) 113, illustrating an example of determining the position and orientation of the mode line 115 when the mode line image has noise or an "image anomaly" IA. This noise or image anomaly is indicated by white x for clarity and may take the form of dirt gauges DS, which appear as small dark areas in the brighter parts of the mode line image. As described above, once the fitted line FL of the mode line 115 is determined according to the two-layer method described above, the fitted line can be examined to determine whether the determined fitted line FL is prone to generating noise that may cause errors.

[0252] The error checking step can be performed by examining each possible (candidate) point. This is achieved by adjusting the distance (error) between the current line and the fitted line FL. If the distance is too large (i.e., exceeds the threshold distance), such as... Figure 10B As shown, candidate points can be associated with dirt specifications DS and are not actually associated with a portion of pattern line 115, and therefore can be omitted when calculating the fitted line. This "distance check" can be performed by defining the following equation (1D) as follows for the error e associated with the distance between points on the fitted line FL:

[0253]

[0254] Where σ is the standard deviation of the error, and k is a constant that depends on how closely the points are wanted to fit the fitted line; this constant can be in the range of 2 to 4. Therefore, in one example, the threshold distance (kσ) is based on the standard deviation of the distance between the candidate points used to form the fitted line and the fitted line itself. The process of removing outliers from the fitted line FL using equation (1D) can be iterated until no obvious outliers remain in the set and an accurate fitted line FL is achieved.

[0255] exist Figure 10B In the diagram, the white dotted line represents the initially determined fitted line FL without error correction, while the white solid line represents the more accurate error-corrected fitted line FL using an error correction method based on Equation 1D. ec Note how the initially determined fitted line FL is "pulled apart" from the actual pattern line position by the (dark) image anomaly IA.

[0256] Tilt mode line

[0257] The method also includes the following step: finding the slope of the mode line. In one example, this is done by calculating the average slope based on the slope 'a' of the mode line in a given mode spectrum 113. Before averaging the slope α of individual mode lines, one aspect of the method involves ensuring that the mode lines identified using the above equations (1B) to (3B) are real mode lines and not spurious mode lines (e.g., some other features unrelated to the guiding mode of the optical waveguide 26 defined by the IOX article 10).

[0258] The following example method can be used to identify and remove any false pattern lines. First, calculate the pattern spectrum from, for example, 50% of the pixels (see...). Figure 8A The mean variance of the fitted line FL for the darker portion of the segment. Assuming the number of pixels is m, the average variance is derived from... Given:

[0259]

[0260] Mean variance It is a measure of how well the fitted line FL fits the darker pixels, with larger numbers indicating poor fitting. Poor fitting can indicate that the fitted pattern line is actually a false pattern line (e.g., dark features caused by imaging errors, debris, detector problems, etc.) or perhaps a very wide pattern line.

[0261] Second, analyze the calculated slope 'a' of the mode lines (i.e., the value of slope 'a' found according to equation (6B) or equation (7C). Assuming there are a total of K mode lines (for both TM mode spectrum 113TM and TE mode spectrum 113TE), the "z-fraction" of the slope of each mode line can be calculated as follows:

[0262]

[0263] in It is the average and It is the slope α of all mode lines 115TM and 115TE from mode spectrum 113. k The standard deviation. The z-score indicates how many standard deviations the angular rotation of the mode line deviates from the mean. A z-score equal to + / -2 means that the quantity is 2 standard deviations from the mean. An anomaly in parameter a relative to the parameter expected based on typical mode spectrum 113 and the typical mode lines 115TM and 115TE therein is a sign that the indicated mode line may be a false mode line.

[0264] If the average variance of a mode line Very large z-fraction a with a slope zk If the slope deviates too far from the average slope compared to what is expected for an actual or "true" mode line, the mode line can be removed from the group of measured mode lines. The combination of these two conditions can be used to ensure that only spurious mode lines are removed from the analyzed mode spectrum. As mentioned above, spurious mode lines may be caused, for example, by debris or markings on the IOX article 10, or by inoperable or faulty portions (e.g., pixel regions) of the detector 110 that appear as dark features on the measured mode spectrum 113.

[0265] In one example, removing false pattern lines includes the following steps: comparing the best-fit line with at least one expected pattern line characteristic selected from a group of pattern line characteristics that includes: position, width, variance of position relative to dark pixels, tilt angle, and slope.

[0266] The method described in this paper for determining the position and tilt angle of a given mode line utilizes closed-form analytical expressions and direct calculations, rather than open-form equations involving iterative calculations requiring convergence. Therefore, the method disclosed herein for determining the position and tilt of mode lines in a mode spectrum is substantially faster than prior art methods involving iterative calculations. The use of the weighted least squares method also leads to a more accurate determination of the stress-related properties of the measured IOX article 10, as the mode line position is estimated more accurately.

[0267] Experiments were conducted, with measurements performed using different prism coupling systems 28 and different IOX artifacts 10. The mode line positions and slopes α were calculated using the method described above for a total of 1295 mode spectra. Figure 11 It is a histogram, plotted as count N and tilt angle. The relationship (expressed in degrees) is used to plot the angle of inclination. The distribution within. This is used to determine the position and tilt angle of the mode lines. The above method uses the following parameters for calculation:

[0268] m r =m l =20

[0269] z mr =z ml =0.005

[0270] z pl =0.04

[0271] m l0 =50

[0272] α = 20

[0273] |a zk |≤1.7

[0274]

[0275] Figure 11 The histogram shows the tilt angle. The distribution has a mean of -0.133° and a standard deviation of 0.227°. This means that the prism coupling systems 28 used to capture the mode spectra of IOX articles have non-zero tilt bias in their mode spectra. Careful examination of the tilt angles of 1295 mode spectra revealed that those exceeding 3 standard deviations from the mean were not due to false positives or analytical errors. When compiling such data for a single prism coupling system 28, the resulting average tilt angle is expressed as... This is called the deviation tilt angle. A similar quantity can be defined using the slope 'a' as a measure of tilt.

[0276] In another experiment, mode spectrum 113 with tilted TM mode line 115TM and TE mode line 115TE was captured and is shown in Figure 12A In this process, the average tilt angle is calculated using the method described above. The measurement was -2.788°. Then, the digital mode spectrum 113 was rotated (i.e., the digital mode spectrum image was rotated under the operation of controller 150) to +2.788° (e.g., ...). Figure 12B (As shown), to vertically align the TM mode line 115TM and the TE mode line 115TE. Note that because the mode spectrum 113 is digital and therefore includes a grid of discrete image pixels 112P (see Figure 115TM). Figure 3B Therefore, residual tilt angles may exist when tilt angle correction is applied. In this example, the residual tilt angle It is 0.061 degrees. In most (if not all) cases, this size (e.g., a percentage of one degree) results in a residual tilt angle of 0.061 degrees. This will not introduce significant errors into subsequent calculations of the stress-related properties of the measured IOX article 10, making... .

[0277] The methods described above are very fast and accurate because they allow for the relatively quick calculation of one or more stress-related properties of the measured IOX article 10.

[0278] Correcting tilt deviation in prism coupling system

[0279] like Figure 11 As shown in the histogram, a given prism coupling system 28 may have a bias tilt (e.g., bias tilt angle). Or the slope of the deviation a B Furthermore, different prism coupling systems tend to have different bias tilts. Therefore, it is desirable to improve the prism coupling system 28 by adjusting the measurement system via either hardware or software to substantially reduce or remove this bias tilt, so that calculations of stress-related characteristics based on the compensated mode spectrum obtained using the system provide more accurate estimates of one or more stress-related characteristics of the measured IOX article 10.

[0280] One aspect of this disclosure relates to a method for substantially compensating for or correcting a bias tilt of a given prism coupling system 28 to obtain a tilt-compensated mode spectrum 113. An example method includes the following steps: determining a tilt angle based on past measurements of the IOX article 10, particularly captured mode spectra. Or the average or mean of the slope 'a' and the corresponding variance (e.g., standard deviation) of the angle or slope. The mean and standard deviation of the tilt angle or slope can be calculated, for example, from the stored tilt angles or slopes of all measured mode spectra of all IOX articles measured from a specific prism coupling system 28. The tilt angle can be... The slope α and the measured mode spectrum 113 are stored in the memory 154 of the controller 150. Because a given prism coupling system 28 can measure hundreds of IOX articles 10 in a relatively short time, the number of available mode spectra 113 is sufficient to produce statistically significant values ​​for the mean and standard deviation of the tilt angle, i.e., the number of samples is statistically significant.

[0281] In an alternative embodiment of this method, based on the current (runn) I The tilt angle is calculated using the ng value instead of the stored pattern spectral data. Alternatively, the mean and standard deviation of the slope 'a'. The advantage of this alternative embodiment is that it uses only two existing statistical parameters (plus the number of measurements already performed by the prism coupling system), requiring significantly fewer computing resources and less time to access stored data. The following explains the existing methods for calculating the mean and standard deviation while performing new measurements.

[0282] From Figure 11 The histogram data produces a mean tilt angle of -0.133° and a standard deviation of 0.227° for the tilt angle, indicating the deviation of the tilt angle. Non-zero. Substantially compensates for or removes the deviation tilt angle. The efficiency of the prism coupling system was improved by enhancing the quality of the captured mode spectra, which led to more accurate measurements of the stress-related properties of the measured IOX article.

[0283] Tilt bias is likely largely caused by hardware bias, i.e., dynamic interactions and defects in the various components of the prism coupling system. Tilt bias can also originate from the measurement itself, and it is best to minimize bias from both sources to produce high-quality mode spectra. Reducing tilt bias from the prism coupling system 28 by improving the hardware (system components) can be expensive and complex, ultimately resulting in diminishing returns on effort and cost.

[0284] Similar to tilt bias, tilt variance / standard deviation can be caused by instrument hardware variations. Tilt variance can also be caused by variations between IOX items 10 (e.g., variations in sample warpage and sample warpage orientation relative to the input optical axis A1 measured by the prism coupling system). Minimizing measurement variance is also desirable. Tilt variance / standard deviation is an indicator of measurement consistency, and if it exceeds a selected tolerance, it indicates a hardware and / or measurement problem.

[0285] As mentioned above, there are two main methods for calculating tilt bias and tilt variation: using all stored pattern spectral data or retaining current records of three parameters (variables): 1) the average current tilt angle of the last image produced by the test sample; 2) the current standard deviation of the tilt angle of the last image produced by the test sample; and 3) the number of images produced / analyzed.

[0286] By using these three variables, the mean and standard deviation can be calculated / updated when a new measurement is taken, eliminating the need to store all tilt angle data.

[0287] The slope a after the nth mode spectrum i average slope and standing difference σ - Limited to:

[0288]

[0289] The mean and standing difference of the (n+1)th image are given by the following equation:

[0290]

[0291] According to equation (4E), in order to update the current mean / deviation of the slope when a new measurement (n+1) is completed, and its standard deviation σ + Only a new slope a is needed n+1 And three previous current variables: the mean / deviation of the slope. and its standard deviation σ - And how many images n have been analyzed. It is not necessary to retain all tilt data to update / find the new current average at the (n+1)th image after analyzing new images. and its standard deviation σ + .

[0292] After several measurements have been performed on a given prism coupling system 28 and the mode spectrum has been analyzed, and once the calculations of the current average and standard deviation have stabilized, tilt bias can be compensated via either hardware or software. In one example, the prism coupling system 28 is adjusted to a tilt bias amount (but in the opposite direction) using the methods discussed below, such that the resulting mode spectrum has a tilt with a substantially zero average value. It should be noted that due to the discrete / digital nature of mode spectra, some residual tilt may exist as discussed above. A substantially tilt-free mode spectrum simplifies the accurate determination of the mode line positions, which, as described above, translates into an accurate estimate of the stress-based properties of the measured IOX article.

[0293] The standard deviation of the tilt angle or slope is a measure of the consistency of tilt between mode spectra. A large standard deviation of tilt indicates instability in the prism coupling system 28, inconsistent site / contact position of the IOX article 10 within the prism coupler system, or a substantial change in one or more key physical properties of the IOX article (e.g., warpage). When the standard deviation / variance of tilt exceeds a selected threshold, the prism coupling system 28 and / or the IOX article 10 need to be evaluated to identify one or more sources of measurement bias.

[0294] In one example, the controller 150 of the prism coupling system 28 is configured (e.g., configured to have instructions implemented in a non-transient computer-readable medium) to calculate and store the current average and standard deviation of the tilt angle of the mode lines, as well as the number of mode spectra used to obtain the current average. When the absolute value of the current average tilt angle deviates from 0 by a selected amount (i.e., a tilt angle threshold), the prism coupling system 28 is adjusted to reduce the average tilt (or tilt deviation) to be less than the tilt angle threshold and preferably equal to or close to zero. An example tilt angle threshold may be in the range of 0.001 rad to 0.006 rad. An example method for adjusting the prism coupling system 28 is discussed below.

[0295] In another example, controller 150 includes instructions (e.g., software) implemented in a non-transient computer-readable medium that implement adjustments to the tilt. In one example, the tilt observed on display 151 is magnified to allow for more precise elimination of tilt angle deviations. For example, during the calibration procedure, the image of the mode spectrum can be vertically contracted to magnify the tilt, thereby allowing the end user of prism coupling system 28 to visually observe the tilted mode lines. Furthermore, reference lines can be displayed simultaneously to further emphasize the tilt of the mode lines.

[0296] Adjusting the prism coupling system

[0297] The prism coupling system 28 can be adjusted in various ways to reduce or remove tilt from the mode spectrum. In one example, this is achieved by using the methods discussed above. Figure 3C and 3D The rotation drive system 136 rotates the detector 110 around the output optical axis A2. The rotation drive system 136 is configured to provide a selected number N. ΒThe precise angular rotation increment δβ is used to change the angular orientation β of detector 110 to at least substantially compensate for the tilt deviation of the prism coupling system. The accuracy of the rotational adjustment of detector 110 using the aforementioned rotational drive system 136 is substantially better than the standard deviation of the tilt angle. For example, as described above, the angular increment δβ provided by the rotational drive system 136 can be in the range of 0.15 degrees to 0.05 degrees (i.e., 0.0026 radians to 0.0009 radians).

[0298] As described above, the tilt compensation amount is calculated based on the tilt angle deviation measured by the prism coupling system. Then, the rotation drive system 136 is activated to change the rotational orientation of the detector 110 relative to the coupling prism 40 (i.e., relative to the output optical axis A2 or equivalently relative to a reference line perpendicular to it) by an appropriate amount N. Β The angular increment δβ) is the amount β=N that substantially compensates for or offsets the measured tilt deviation. Β •δβ. Then, without significant tilting deviation, the prism coupling system 28 is operated forward, which translates into a more accurate estimate of the stress-related characteristics of the measured IOX article.

[0299] In another example, when the tilt of an individual mode spectrum is measured, if the absolute value (magnitude) of the tilt falls within a selected tilt threshold limit, the mode spectrum is used for rapid processing. In this case, any compensation for tilt of a given mode spectrum is omitted to save time.

[0300] In one example, controller 150 can use the existing methods described above to monitor tilt bias in the mode spectrum. These methods calculate and store the current average of the tilt, the standard deviation of the tilt, and the number of mode spectra used to calculate the current average and standard deviation. When the absolute value of the current average of the tilt exceeds a selected tilt threshold, the controller automatically applies software correction to the tilt of subsequently measured mode spectra. Example thresholds for the tilt angle can be in the range of 0.006 to 0.001 rad (i.e., from approximately 0.0034 degrees to approximately 0.057 degrees). When using a slope α instead of a tilt angle, a corresponding threshold can be applied.

[0301] Software-based methods for correcting tilt are schematically illustrated in the sections introduced and discussed above. Figure 12A and 12B In this process, the digitally captured mode spectrum 113 is rotated such that mode lines 115TM and 115TE are substantially aligned with the vertical direction (i.e., the local y-direction associated with zero tilt angle). Figure 12BThe mode spectrum 113 is denoted as 113' (with mode spectra 113'TM and 113'TE) because it is a tilt-compensated mode spectrum. The tilt-compensated mode spectrum 113' can be processed using techniques conventional in the art to estimate one or more stress-related characteristics of a given IOX article 10. This provides a more accurate estimate of the stress-related characteristics of the IOX article 10 compared to using an uncompensated mode spectrum with tilted mode lines.

[0302] Those skilled in the art will understand that various modifications can be made to the preferred embodiments disclosed herein without departing from the spirit or scope of this disclosure as defined in the appended claims. Therefore, this disclosure covers any modifications and variations that fall within the scope of the appended claims and their equivalents.

Claims

1. A method of estimating at least one stress-related property of an ion-exchanged article having a waveguide region implemented by a prism coupling system, the method comprising: illuminating the ion-exchanged article through a coupling prism to generate a transverse magnetic guided mode and a transverse electric guided mode in the waveguide region of the ion-exchanged article; capturing a digital two-dimensional mode spectrum comprising mode lines of a transverse magnetic mode spectrum and a transverse electric mode spectrum representing the transverse magnetic guided mode and the transverse electric guided mode of the waveguide region, wherein each mode line is defined by a two-dimensional intensity profile having an intensity value and an intensity extremum and having a measured amount of tilt in a first direction relative to an ideal reference orientation; locating the mode lines by fitting at least one fitting line to at least one of the mode lines in a vicinity of the intensity extremum of the at least one of the mode lines, the fitting step being performed using a weighted least squares regression calculation in the vicinity of the intensity extremum; measuring the amount of tilt using the at least one fitting line; substantially removing the amount of tilt from the mode lines by adding the measured amount of tilt in a second direction opposite the first direction to define at least one of a tilt-compensated transverse magnetic mode spectrum or a tilt-compensated transverse electric mode spectrum; and using at least one of the tilt-compensated transverse magnetic mode spectrum and the tilt-compensated transverse electric mode spectrum to estimate the at least one stress-related property of the ion-exchanged article.

2. The method of claim 1, wherein the intensity extremum comprises an intensity minimum.

3. The method of claim 1, further comprising: averaging the two-dimensional mode spectrum to form a one-dimensional spectrum having an average intensity extremum for each mode line; and using the average intensity extremum to determine an initial position for each mode line.

4. The method of claim 1, wherein the two-dimensional mode spectrum comprises a digital mode spectrum image having a gray scale intensity distribution based on pixel intensity values, and wherein the weighted least squares regression calculation comprises for each mode line: defining a weighting that emphasizes pixel intensity values closer to the intensity extremum to force the fitting line to more closely follow the two-dimensional intensity extremum.

5. The method of claim 4, wherein the weighting is defined by an exponential weighting function.

6. The method of any one of claims 1 to 5, further comprising: determining an average variance of the fitting line of the two-dimensional intensity profile in the vicinity of the intensity extremum; and using the average variance for each mode line to assess whether each mode line is a true mode line or a false mode line.

7. The method of claim 6, wherein there are K mode lines, and the using the average variance for each mode line to assess whether each mode line is a true mode line or a false mode line comprises: using the at least one fitted line to determine a slope of the tilt of each pattern line k a k an average slope of the slope of the tilt and a standard deviation to define a slope variation parameter a zk , and Defining threshold parameters T wherein for a given pattern line means that the corresponding pattern line is a true pattern line.

8. The method of claim 7, wherein T < 2.

9. The method of any one of claims 1 to 5, wherein the at least one stress-related property comprises: Stress distribution, knee stress, central tension, tensile-strain energy, birefringence, peak depth, layer depth, refractive index distribution, or combinations thereof.

10. The method of any one of claims 1 to 5, wherein the two-dimensional mode spectrum is captured on a rotatable detector, and wherein substantially removing the tilt from the mode line by adding the measured tilt amount comprises rotating the rotatable detector.

11. The method of any one of claims 1 to 5, wherein the two-dimensional mode spectrum is captured on a digital detector, and wherein substantially removing the tilt from the mode line by adding the measured tilt amount comprises digitally rotating the mode spectrum.

12. A method for compensating tilt deviation in a prism coupling system for estimating at least one stress-related characteristic of an ion exchange article, the ion exchange article having a waveguide region, the method comprising: For each of the multiple ion exchange articles, a digital two-dimensional mode spectrum is captured, the digital two-dimensional mode spectrum including mode lines of transverse magnetic guiding mode and transverse electrical guiding mode representing the waveguide region, wherein each mode line is defined by a two-dimensional intensity distribution having intensity extrema and a tilt measured relative to an ideal reference orientation in a first direction. The tilt in each mode line is measured by using a weighted fit on the two-dimensional intensity distribution in the region near the intensity extrema to establish a fitted line for the two-dimensional mode spectrum for each mode line. The tilt of the mode line is averaged to establish the tilt deviation for the prism coupling system; as well as The measurement system is adjusted to reduce or eliminate the established tilt bias from at least one of the captured transverse electrical mode spectrum or transverse magnetic mode spectrum, thereby reducing the amount of tilt in each mode line and defining a compensated mode spectrum for at least one of the plurality of ion exchange articles.

13. The method of claim 12, further comprising: The measurement system is adjusted to reduce or eliminate the established tilt bias from the subsequently captured mode spectra of the additional ion exchange article, thereby reducing the amount of tilt in each mode line and defining a compensated mode spectrum for the additional ion exchange article.

14. The method of claim 12, further comprising: Measure the variance of the tilt of the pattern line; And compare each tilt with the variance to determine whether each pattern line is a true pattern line or a false pattern line.

15. The method of claim 12, wherein the tilt amount is measured as either a tilt angle or a tilt slope.

16. The method of claim 12, wherein the at least one stress-related characteristic includes at least one of the following: stress distribution, knee stress, central tension, tensile-strain energy, birefringence, peak depth, layer depth, or refractive index distribution.

17. The method of any one of claims 12 to 16, wherein the two-dimensional mode spectrum is captured on a rotatable detector, and wherein the action of subtracting the established tilt bias is performed by rotating the rotatable detector.

18. The method of any one of claims 12 to 16, wherein the two-dimensional mode spectrum is captured on a digital detector, and wherein the action of subtracting the established tilt bias is performed by digitally rotating the mode spectrum.

19. The method of any one of claims 12 to 16, further comprising: The tilt deviation variance in the tilt deviation is calculated based on the tilt amount of each mode line.

20. The method of claim 19, wherein when the two-dimensional mode spectrum from the ion-exchange sample is captured, the tilt bias and the tilt bias variance are calculated as current tilt bias and current tilt bias variance, respectively.

21. A prism coupling system for measuring at least one stress-related characteristic of an ion-exchanged article having a waveguide region, the prism coupling system comprising: A light source system configured to generate input light along an input optical axis; A coupling prism configured to dock with the ion exchange article to define a coupling interface, wherein input light incident on the coupling interface is reflected from the coupling interface to form reflected light, the reflected light leaving the coupling prism and traveling along an output optical axis, the reflected light including a guiding mode spectrum, the guiding mode spectrum including mode lines of a transverse magnetic guiding mode spectrum and a transverse electrical guiding mode spectrum having positions defined by the waveguide region; A digital sensor, comprising pixels and configured to detect the lateral magnetic guidance mode spectrum and the lateral electrical guidance mode spectrum, and to form a two-dimensional digital image of the lateral magnetic guidance mode spectrum and the lateral electrical guidance mode spectrum based on the lateral magnetic guidance mode spectrum and the lateral electrical guidance mode spectrum; A controller configured to receive the two-dimensional digital images of the transverse magnetic guidance mode spectrum and the transverse electrical guidance mode spectrum, the controller having instructions stored in a non-transient computer-readable medium, the instructions causing the controller to perform the following actions: i) Establish the tilt amount for each mode line; ii) Establish the average tilt and tilt variance based on the tilt of the model line; iii) Subtract the average tilt from the mode spectrum to define a tilt-compensated mode spectrum, the tilt-compensated mode spectrum having a reduced tilt for each of the mode lines. as well as iv) Use the tilt-compensated mode spectrum to estimate the at least one stress-related characteristic of the ion exchange article.

22. The prism coupling system of claim 21, wherein the digital sensor is rotatable about the output optical axis, and the controller is configured to rotate the digital sensor as part of subtracting the average tilt amount from the mode spectrum.

23. The prism coupling system of claim 22, wherein the rotatable digital sensor is operably supported by a rotation drive system configured to rotate the digital sensor in precise angular increments.

24. The prism coupling system of claim 23, wherein the precise angle increment is in the range of 0.0026 radians to 0.0009 radians.

25. The prism coupling system of claim 21, wherein the act iii) of subtracting the average tilt amount from the mode spectrum comprises: The two-dimensional digital image is rotated digitally.

26. The prism coupling system of any of claims 21 to 25, wherein the act ii) of establishing a mean tilt and a tilt variance from the tilt amounts of the mode lines comprises: Apply the current tilt mean and current tilt variance.

27. The prism coupling system of claim 26, wherein the action iii) of subtracting the average tilt from the mode spectrum is performed only when the current average tilt exceeds a threshold tilt.

28. The prism coupling system of claim 27, wherein the threshold tilt amount is in the range of 0.006 to 0.001 radians.

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