JP5558127B2 - Misalignment measuring device, misalignment measuring method, and misalignment measuring program - Google Patents

Description

  The present invention relates to a technique for measuring a positional deviation of a pattern such as an image, for example.

  In various manufacturing apparatuses such as semiconductors and product inspection apparatuses, an apparatus for detecting and measuring a position (deviation) for positioning control (hereinafter also referred to as “position deviation measuring apparatus”) may be used.

  A method based on correlation between images (signals) may be used for the position shift measuring apparatus. For example, an image (hereinafter also referred to as “registered image”) captured in advance and stored in a memory or the like (hereinafter also referred to as “registered image”) and an image captured as a target for verification between the registered image (hereinafter also referred to as “matched image”). This is a method based on the correlation with For example, the correlation (coefficient) between both image patterns is calculated while shifting the relative positional relationship between the image pattern of the registered image and the image pattern of the verification image. Then, by obtaining the position where the correlation is maximized, the difference (positional deviation) between the positions of both images can be measured.

  One of the representative methods using correlation is a method based on a normalized correlation function or a method called a phase only correlation method. An example of a pattern matching apparatus using the phase only correlation method is described in Patent Document 1 below.

  The normalized correlation method is a method using a normal correlation coefficient. The phase only correlation method is a method of obtaining a correlation pattern in which phase components are emphasized by suppressing the amplitude in the frequency domain. The phase-only correlation method is known as a technique capable of measuring a positional deviation with higher detection sensitivity and higher accuracy than the normalized correlation method.

Japanese Patent Application Laid-Open No. 09-022406

  Filtering (band limitation) using a low-pass filter, a band-pass filter, or the like may be applied in the above-described pattern collation based on correlation or measurement of positional deviation. The noise component included in the image pattern can be removed or reduced by filtering, and the detection due to the noise component and the deterioration of measurement accuracy can be suppressed. Such a noise reduction effect can also be obtained by weighting with a frequency during correlation calculation between image patterns (for example, a relatively low weight at a high frequency).

  However, if filtering or weighting of frequency components is performed, not only the noise component but also the frequency component of the image pattern to be verified may be suppressed. As a result, the position resolution is lowered, and as a result, the accuracy of the position shift measurement may be deteriorated.

  One of the objects of the present invention is to improve the accuracy of positional deviation measurement based on the correlation between two patterns to be collated. Note that an N-dimensional pattern can be applied to the two patterns to be collated, where N = 2 corresponds to image matching (pattern matching), and N = 3 corresponds to three-dimensional pattern matching.

  However, the present invention is not limited to the above-described object, and other effects of the present invention can be achieved by the functions and effects derived from the respective configurations shown in the embodiments for carrying out the invention which will be described later. It can be positioned as one of

  One aspect of the positional deviation measuring apparatus of the present invention is m types (two types of pattern signals corresponding to two N-dimensional patterns (N is an integer of 2 or more) to be collated, which indicate phase traveling directions that are not parallel to each other. m is an integer satisfying m ≧ N), and correlation calculation means for performing signal processing corresponding to calculation for obtaining a correlation between m sets of pattern signals to which the same phase information is added, and the correlation Misregistration calculation means for obtaining a misregistration corresponding to the phase difference between the patterns based on m sets of correlation phase information obtained by the computing means.

  The positional deviation measuring device further includes positional deviation estimation means for comparing the pattern signals to estimate the positional deviation between the patterns, and the positional deviation calculation means is obtained by the positional deviation estimation means. The positional deviation may be determined based on the estimated value of the positional deviation and the phase information of the correlation obtained by the signal processing.

  Further, the positional deviation estimation means obtains a correlation value obtained by the amplitude correlation calculation unit for obtaining a correlation related to the amplitude of the pattern signal, a maximum value of the correlation obtained by the amplitude correlation calculation unit, and the positional deviation corresponding to the maximum value And a maximum value calculation unit obtained as an estimated value.

  The positional deviation estimation means may include a maximum value calculation unit that obtains a maximum value of the amplitude information of the correlation obtained in the signal processing and obtains a positional deviation corresponding to the maximum value as the estimated value. .

  Further, the correlation calculation means includes m types of complex filters each having a filter characteristic corresponding to each of the m types of phase information, and applies the m types of complex filters to each of the pattern signals. The m kinds of phase information may be added to each of the signals.

  Further, the correlation calculation means may perform the addition of the phase information and the calculation of the correlation in the signal processing in the frequency domain.

  Furthermore, a part or all of the complex filter may be a filter by continuous wavelet transform.

  Further, according to one aspect of the positional deviation measuring method of the present invention, m indicating phase traveling directions that are non-parallel to each of pattern signals corresponding to two N-dimensional (N is an integer of 2 or more) patterns to be collated. Obtained by the signal processing corresponding to an operation for adding a type (m is an integer satisfying m ≧ N) and obtaining a correlation between m sets of pattern signals to which the same phase information is added, and the signal processing. And a process for obtaining a positional shift according to the phase difference between the patterns based on the phase information of the m sets of correlations.

  Furthermore, one aspect of the misregistration measurement program of the present invention is a computer-readable misregistration measurement program that causes a computer to perform a predetermined misregistration measurement process by being read by a computer, M types (m is an integer satisfying m ≧ N) indicating phase traveling directions that are not parallel to each other are added to the pattern signals corresponding to the N-dimensional (N is an integer of 2 or more) pattern, and the same. Based on the signal processing corresponding to the calculation for obtaining the correlation between the m sets of pattern signals to which the phase information is added and the phase information of the m sets of correlations obtained by the signal processing, according to the phase difference between the patterns. And causing the computer to execute a process for obtaining the misalignment.

  According to the above aspect of the present invention, it is possible to improve the measurement accuracy of the positional deviation based on the correlation between patterns. For example, even if a band limitation such as filtering for noise reduction or frequency weighting is applied to a pattern such as an image used for correlation calculation, it is possible to improve the measurement accuracy of the positional deviation. In other words, both noise reduction and measurement accuracy improvement can be achieved.

It is a figure which shows an example of the contour-line map of a correlation value in order to explain the fall of position shift measurement accuracy. It is a figure which respectively shows an example of the waveform of the signal which shifted the 1-dimensional pattern signal and the said pattern signal by l. It is a figure explaining the waveform and phase difference of the signal which added phase information to the pattern signal illustrated in FIG. It is a figure which shows the change of the phase and absolute value of the cross correlation function between the pattern signals illustrated in FIG. It is a figure which shows an example of an equiphase line drawn on a complex plane by adding phase information to a pattern signal. It is a figure which shows an example of an equiphase line drawn on a complex plane by adding phase information to a pattern signal. It is a figure which shows an example of two equiphase lines drawn on a complex plane by adding two types of phase information to a pattern signal. It is a figure which shows an example of three equiphase lines drawn on a complex plane when three types of phase information are added to a pattern signal. It is a block diagram which shows an example of the position shift measurement system which concerns on one Embodiment of this invention. It is a functional block diagram which shows the 1st aspect of the signal processing apparatus shown in FIG. FIG. 11 is a functional block diagram of the signal processing apparatus shown in FIG. 10 when the number of dimensions of the pattern signal is N = 2. 12 is a functional block diagram illustrating a configuration example of a positional deviation approximate value estimation unit illustrated in FIGS. 10 and 11; FIG. It is a functional block diagram which shows the 2nd aspect of the signal processing apparatus shown in FIG. (A) And (B) is a figure which shows the example of the characteristic of the filter applied to the phase information addition filter part illustrated to FIG.10 and FIG.11, respectively. (A) And (B) is a figure which shows an example of the phase advancing direction of the pattern signal after the filter application illustrated to FIG. 14 (A) and FIG.14 (B), respectively. It is a functional block diagram which shows the 3rd aspect of the signal processing apparatus shown in FIG. It is a functional block diagram which shows the 4th aspect of the signal processing apparatus shown in FIG. It is a functional block diagram which shows the 5th aspect of the signal processing apparatus shown in FIG. (A) And (B) is a figure which shows an example of the pattern used for the position shift measurement by the signal processing apparatus of the 5th aspect shown in FIG. 18, respectively. (A) And (B) is a figure which shows an example of the complex correlation pattern obtained in the process of the position shift measurement by the signal processing apparatus of the 5th aspect shown in FIG. 18, respectively. It is a figure which shows an example of the equiphase line in the complex correlation pattern obtained in the process of the position shift measurement by the signal processing apparatus of the 5th aspect shown in FIG.

  Embodiments of the present invention will be described below with reference to the drawings. However, the embodiment described below is merely an example, and there is no intention to exclude various modifications and technical applications that are not explicitly described below. In other words, the present invention can be implemented with various modifications (combining the embodiments, etc.) without departing from the spirit of the present invention. In the following description of the drawings, the same or similar parts are denoted by the same or similar reference numerals. The drawings are schematic and do not necessarily match actual dimensions and ratios. In some cases, the dimensional relationships and ratios may be different between the drawings.

[A] Outline Description It is generally said that pattern matching and positional deviation measurement methods using correlation are resistant to noise. For example, in pattern matching such as image matching, even if a random noise component (pattern) that changes each time matching is included in the pattern (signal) to be verified, the influence of the noise component can be reduced. This utilizes the fact that there is no or low correlation between the noise component and the pattern to be collated.

  However, when there is a correlation between the noise component and the pattern to be collated, the influence of the noise component cannot be ignored. For example, when two patterns to be collated are photographed by the same imaging device, the fixed pattern noise derived from the imaging device may be included in both patterns in common.

  In this case, since the same or substantially the same pattern noise is included in both patterns, a strong correlation occurs between the patterns. As a result, the measurement accuracy of misalignment decreases. For example, a result that there is no positional deviation may be obtained regardless of the actual positional deviation. This is because the pattern noise exists at the same position in each of the two patterns to be collated, and therefore, the positional deviation between the fixed pattern noises is measured instead of the positional deviation of the pattern to be originally measured.

  When the phase only correlation method is used for the correlation calculation, the high sensitivity of the phase only correlation method has an adverse effect and is easily influenced by the correlation (autocorrelation) between fixed pattern noises. In addition, when the normalized correlation method is used, it may be affected by fixed pattern noise.

  One of the methods for avoiding such a situation includes the above-described filtering and frequency weighting. While noise components are generally distributed widely from low to high frequencies, the pattern to be verified tends to be distributed in a low frequency region. Therefore, the influence of the noise component can be removed or reduced by removing or reducing the high frequency component included in the pattern by filtering or frequency weighting.

  However, if high frequency components are suppressed (band limitation) using filtering or frequency weighting, not only noise components but also high frequency components of the pattern to be matched may be suppressed. If the high-frequency component of the pattern to be matched is suppressed, the high-frequency component information is lost also from the correlation value (pattern) obtained by the correlation calculation, so that the position resolution is lowered and consequently the measurement accuracy of the positional deviation is improved. to degrade.

  For example, as schematically illustrated in the contour map of the correlation value (correlation pattern) in FIG. 1, when the high frequency component of the pattern is removed or suppressed by band limitation, the difference in the correlation value becomes gentle and position detection is performed. The accuracy of is reduced. As a result, the position where the correlation value shows a peak (maximum) and the true value of the actual positional deviation tend to be inconsistent.

  Therefore, in the present embodiment, phase information is added to each of the pattern signals corresponding to the two patterns to be collated, and the position corresponding to the phase difference between the two patterns based on the correlation of the pattern signal to which the phase information is added. We will ask for the deviation. By using the additional phase information in this way, it is possible to improve the position resolution, and thus the measurement accuracy of the positional deviation. Note that an N-dimensional pattern can be applied to the two patterns to be verified. For example, a case where N = 2 corresponds to an image pattern, and a case where N = 3 corresponds to a three-dimensional pattern.

(Viewpoints)
The positional deviation measurement method using the correlation can be considered as a problem of searching for the positional deviation that maximizes the value of the evaluation criterion based on the correlation. On the other hand, in measurement and signal processing, measurement accuracy and estimation accuracy can be improved by using the phase of a signal and the phase difference between signals.

  Therefore, it is considered that a method using a phase is applied to N-dimensional (N is an integer of 2 or more) pattern matching. First, phase information is added to each of pattern signals corresponding to two patterns to be verified. An example of a method for adding phase information is Hilbert transform. When the Hilbert transform is performed on the pattern signal, the real-valued pattern signal is converted into a complex value, and phase information corresponding to the complex argument is included in the pattern signal.

  Thus, by obtaining the correlation between the pattern signals to which the phase information is added, the phase difference between the two pattern signals can be obtained, and as a result, information on the positional deviation between the patterns can be obtained based on the phase difference. It becomes possible. However, when this method is applied to a two-dimensional or higher pattern (image or the like), the positional deviation cannot be specified from one phase information. For example, when the Hilbert transform is applied to a two-dimensional pattern, isophase lines are formed on the complexized pattern. That is, it can be seen that a point corresponding to the positional deviation is on a certain curve, but it cannot be specified as one point.

  Therefore, in the present embodiment, the phase information that is not parallel to the number of dimensions or more than that is generated, and these are combined so that the positional deviation can be specified as one point. For example, in the case of a two-dimensional case, if two different equiphase lines that are not parallel to each other are obtained, the positional deviation can be specified from the intersection. Since the measurement value of the positional deviation uses phase information, the accuracy is higher than the value obtained from the position of the maximum value of the evaluation criterion. That is, in the present embodiment, the point at which the value of the evaluation criterion based on the correlation is maximized is not used as the measurement value of the positional deviation as it is, but the phase information of the number of dimensions in the vicinity thereof or more. By using this, it is possible to improve the measurement accuracy of misalignment.

(Principle explanation of displacement measurement)
(One-dimensional case)
The present invention is intended for pattern signals of two or more dimensions, but as a first introduction, the principle for measuring the positional deviation between one-dimensional pattern signals will be briefly described. Consider a signal A (x) and a signal A (xl) obtained by shifting the signal A (x) by 1 in the negative direction of the axis x (see FIG. 2). However, both the signals A (x) and A (xl) are real signals.

Consider giving phase information to each of these signals A (x) and A (xl). The phase information can be added by using the Hilbert transform or the like, but the added phase is somewhat complicated. For the sake of simplicity, a complex sine wave with an angular frequency ω is used here.
The phase information is added by multiplying by.

Complex signals f (x) and g (x) obtained by giving phase information to the signal A (x) and the signal A (x−1), respectively, can be expressed by the following equation (1). J is an imaginary unit.

The phase difference between the two signals f (x) and g (x) shown in Equation (1) is ωl, which is proportional to the magnitude l of the deviation (see FIG. 3). A cross-correlation function φ _{f, g} between the two signals f (x) and g (x) is obtained by the following equation (2). Φ _A represents the autocorrelation function of the signal A (x).

The cross-correlation function φ _{f, g} and the autocorrelation function φ _A can be expressed by the following equation (3), respectively. In order to simplify the explanation, here, a definition that calculates without subtracting the average value is used. An asterisk (*) in the formula (3) represents a complex conjugate.

The plots of the phase (deflection angle) and absolute value of the cross-correlation function φ _{f, g} are shown in the upper and lower parts of FIG. φ _A is a real value,
Since the absolute value of is always 1, the absolute value of φ _{f, g} is equal to φ _A and the phase is
Match the phase. As illustrated in the upper part of FIG. 4, when α = 1, the phase becomes 0 (see point A). This corresponds to the fact that when the signal g (x) is shifted by 1 in the negative direction of the axis x, the phase of the signal f (x) coincides with the phase of the signal g (x) and the phase difference becomes zero. ing. In this way, after adding phase information to a signal and converting it to a complex value, calculating a cross-correlation function and examining its phase makes it possible to measure a positional shift between one-dimensional patterns.

In FIG. 4, the phase is 0 not only at point A (α = 1) but also at points B and C. This is due to the nature of the exponential function of complex numbers.
It is because it cannot be distinguished.

Therefore, although the phase alone cannot uniquely estimate the position shift, the phase is 0 near the maximum value of the absolute value (information on the magnitude of the correlation) of the cross-correlation function φ _{f, g} (see point A ′ in the lower part of FIG. 4). You can narrow down to one point by finding the point that becomes. Since the absolute value of the cross-correlation function φ _{f, g} is sufficiently small compared to the point A ′, the points B ′ and C ′ shown in the lower part of FIG. 4 can be excluded from the position deviation estimated value candidates. Note that it is not essential to use the maximum absolute value of the cross-correlation function to narrow down the points where the phase becomes zero. It is also possible to use a value of an evaluation standard used for other existing positional deviation estimation for the narrowing down.

In this example, since a signal that can be easily explained is used, it may seem that the positional deviation can be measured even with the position of the absolute value of the cross-correlation function φ _{f, g} alone in FIG. Not so. For example, as described above, when the cross-correlation function φ _{f, g} is obtained from a signal in which the pattern signal is band-limited to remove or suppress the high-frequency component as described above, since the position resolution is reduced, the cross-correlation function φ _f, It is not easy to measure the positional deviation accurately with the absolute value of _g alone.

  On the other hand, when the phase information is used as described above, it is possible to improve the measurement accuracy of the positional deviation even when the original pattern signal is band-limited and smooth. Therefore, the accuracy of measurement is determined by measuring the true misregistration using phase information after narrowing the misregistration (search) range to some extent based on the absolute value of the cross-correlation function between patterns and existing evaluation criteria. Can be improved. In this method, if the conditions are good, it is also possible to measure a positional deviation or delay more detailed than, for example, the sampling interval of the pattern signal.

(2D case)
Next, consider the case of a two-dimensional pattern signal such as an image signal. As in the one-dimensional case, consider two simplified signals f (x, y) and g (x, y) represented by the following equation (4). Note that x and y represent horizontal and vertical coordinates in a two-dimensional pattern such as an image, respectively.

The cross-correlation function φ _{f, g} of the two signals f (x, y) and g (x, y) shown in the equation (4) can be expressed by the following equation (5), for example.

Here, in the case of a two-dimensional signal, unlike the case of a one-dimensional signal,
Is 0 at all points on the line where α + β = k + 1. In other words, when phase information is given by applying Hilbert transform or the like to a two-dimensional pattern signal, for example, as schematically shown in FIGS. 5 and 6, phase = 0 on the pattern converted into a complex value One equiphase line can be defined. That is, it can be specified (estimated) that a point corresponding to the positional deviation exists on the equiphase line.

  However, it is difficult to specify (restrict to one point) where the point corresponding to the positional deviation exists on the equiphase line. This is because the number of unknowns is greater than the number of constraint conditions, so the solution is not uniquely determined. In other words, if another isophase line that is non-parallel to (intersects with) the equiphase line can be determined on the pattern converted to the complex value, the position corresponding to the misalignment can be determined. It can be uniquely estimated as an intersection (see FIG. 7).

Therefore, another phase information is added to the signals f (x, y) and g (x, y) by a method different from the above equation (4) to obtain another cross-correlation function. For example, the phase information is added to the signals f (x, y) and g (x, y) as represented by the following formula (6).

In this case, the cross-correlation function φ _{r, s} of the two signals r (x, y) and s (x, y) shown in the equation (6) can be expressed by the following equation (7).

The phase of the cross-correlation function φ _{r, s} becomes 0 on a line where α−β = k−1 is satisfied. Therefore, as schematically illustrated in FIG. 6, the positional deviation is uniquely determined by obtaining the intersection point between the isophase line where α−β = k−1 and the isophase line where α + β = k + 1 is satisfied. Can be estimated.

  In this way, phase information is added to a two-dimensional (for example, image) pattern signal by two methods, and an intersection of equiphase lines (a straight line or a curve with a phase of 0) of the cross-correlation function between the pattern signals is obtained. This makes it possible to measure the positional deviation between patterns. However, if two equiphase lines are coincident or parallel to each other, no intersection of equiphase lines is generated. Therefore, the phase information added to the pattern signal may be devised so that an intersection of equiphase lines is produced. A specific example will be described later.

  To summarize the above, for each of the two-dimensional pattern signals to be verified, phase information is added to the complex values by the two methods, and the phase components of the cross-correlation between the pattern signals converted into complex values are obtained. By obtaining the intersection of two equiphase lines whose value (phase) corresponds to 0 in (phase pattern), it is possible to obtain a positional deviation between two-dimensional patterns (for example, images).

  In the above example, the pattern signal is converted into a complex value by two methods, but the conversion may be performed by three or more methods. However, if the number of obtained equiphase lines is larger than the number of dimensions, the number of constraint conditions is larger than the number of unknowns. Therefore, for example, as schematically shown in FIG. There are cases where multiple items are generated and cannot be fixed at a single point. In such a case, for example, the positional deviation can be uniquely estimated by using the least square method or obtaining the centroids of a plurality of intersections.

(N dimension)
The above-described method can be extended to an N-dimensional pattern with N ≧ 3. For example, for each of two given N-dimensional pattern signals, phase information is added in m ways (where m is an integer of m ≧ N) and converted into a complex value. Then, in the phase component (phase pattern) of the cross-correlation between m sets of pattern signals converted into complex values, m sets of hypersurfaces or hyperplanes (hereinafter referred to as “equal phase regions”) whose values (phases) respectively correspond to 0. "Is collectively referred to as". ", The deviation between the N-dimensional patterns can be obtained.

  In the case of m> N, when a plurality of intersections in the equiphase region are generated and cannot be determined at one place, for example, by using the least square method or obtaining the center of gravity of the plurality of intersections, It is possible to uniquely estimate the deviation.

[B] Description of Specific Example Hereinafter, a specific example of the above-described displacement measurement will be described in detail with reference to FIGS.

(System configuration example)
FIG. 9 is a block diagram illustrating an example of a misregistration measurement system according to an embodiment of the present invention. The measurement system illustrated in FIG. 9 includes, for example, a pattern generation device 1 that generates an N-dimensional pattern signal and a signal processing device 2 that processes the pattern signal generated by the pattern generation device 1. For example, the two-dimensional pattern in the case of N = 2 is an image pattern. In this case, the pattern generation device 1 corresponds to an imaging device such as an image sensor or a CCD camera.

  The signal processing device 2 exemplarily shows a pattern matching device (position displacement measuring device) that compares two pattern signals given from the same or different pattern generation devices 1 and measures the pattern displacement (position displacement) of both patterns. (Hereinafter also referred to as “positional displacement measurement function”). Note that the two pattern signals to be collated may be generated by the same pattern generation device 1 or different pattern generation devices 1.

  The signal processing device 2 includes, for example, a CPU (Central Processing Unit) 21, a ROM (Read Only Memory) 22, a RAM (Random Access Memory) 23, a hard disk drive (HD) 24, a memory (FM) 25, And an interface (I / F) 26.

  The CPU 21 is an example of a computer (arithmetic processing unit), and is a CISC (Complex Instruction Set Computer) or RISC (Reduced Instruction Set Computer) CPU, MPU (Micro Processing Unit). , DSP (Digital Signal Processor), ASIC (Application Specific Processor), etc.

  The ROM 22, RAM 23, HD 24, and memory 25 are all examples of a storage unit, and various data such as a predetermined program and parameters can be stored in any storage area (exemplarily ROM 22). The program includes a misalignment measurement program that causes a computer to perform misalignment measurement according to the present embodiment. Note that the storage unit may be an internal or external storage device. In addition, an SSD (Solid State Drive), a flash memory, an SRAM (Static Random Access Memory), or the like may be used as the storage unit. If a high-speed writing and reading speed is not required, a lower-speed magnetic tape device An optical disk device or the like may be used.

  The misregistration measurement program can be provided in a form recorded on a computer-readable recording medium. Examples of recording media include flash memory, flexible disk, CD-ROM, CD-R, CD-R, CD-RW, DVD, Blu-ray disk, magnetic disk, optical disk, magneto-optical disk, IC card, ROM cartridge, SSD And various computer-readable media. The computer reads the misregistration measurement program from the recording medium, appropriately transfers it to the hard disk 24 or RAM 23, and uses it.

  Further, the misregistration measurement program may be recorded in an internal or external storage device such as RAM 23, HD 24, or a recording medium, and provided to the computer from the storage device or storage medium via a communication line such as the Internet. it can.

  Here, the computer is a concept including, for example, hardware and an operating system (OS), and may mean hardware that operates under the control of the OS. Further, when the OS is unnecessary and the hardware can be operated by the program alone, it can be considered that the hardware corresponds to a computer. The hardware can include an arithmetic device such as a CPU and a reading device that can read a program recorded on a recording medium.

  The misregistration measurement program includes program code for causing the above-described computer to realize the misregistration measurement function described above. Some of the functions may be realized by the OS instead of the program.

  The ROM 22 is an example of a nonvolatile storage medium. The CPU 21 reads the program and data stored in the ROM 22 and sets the microcode of the CPU 21, initializes each part, starts the OS and the like from the HD 24, and executes the misregistration measurement program. Or give instructions.

  The memory 25 temporarily stores, for example, a pattern signal generated by the pattern generation device 1. The CPU 21 stores the pattern signal stored in the memory 25 in the HD 24, for example. The stored pattern signal can be used as a template (registered pattern signal) that is referred to during the positional deviation measurement process. In addition, the CPU 21 uses a pattern signal to be collated stored in the memory 25 (hereinafter also referred to as “collation pattern signal”) and a registered pattern signal stored as a template in the HD 24 in accordance with the positional deviation measurement program. Match.

  The I / F 26 is, for example, an external connection I / F that can connect peripheral devices (peripherals) such as a display device or a printing device, or a network such as a LAN (local area network) or a WAN (wide area network). Communication I / F that enables connection to The external connection I / F, for example, provides an interface such as USB, IEEE 1394, serial, parallel, infrared, and wireless. As the communication I / F, for example, WiMAX (registered trademark), c. A device that conforms to a connection method such as Link (registered trademark), HDMI (registered trademark), wired / wireless LAN, telephone line, mobile phone network, PHS network, power line network, IEEE1394, or the like can be applied.

  The signal processing device 2 outputs, for example, a positional deviation measurement result to the display device or the printing device through the external connection I / F, or communicates with another signal processing device 2 or a server through the communication I / F. Can do. Therefore, the signal processing device 2 can also provide a part of the program and various data to other signal processing devices 2 that are communicably connected.

(First aspect)
FIG. 10 illustrates a functional configuration (first aspect) of the signal processing device 2 realized by the CPU 21 reading and executing the above-described misregistration measurement program.

  The signal processing device 2 illustrated in FIG. 10 exemplarily includes a misalignment approximate value estimation unit 3 and m sets (two integers satisfying m ≧ N, which convert each of the two pattern signals to be verified into complex values. M = 2) complex filter sections 4A-i and 4B-i (#i) (i = 1, 2,..., M). Further, the signal processing device 2 includes m correlation calculation units 5-i (#i), m phase component extraction units 6-i (#i), and m equal phase information calculation units 7-i. (#I) and an intersection calculation unit 8. In addition, in FIG. 11, the structural example of the signal processing apparatus 2 in the case of N = 2 and m = 2 is shown.

  The approximate position deviation estimation unit (hereinafter, also simply referred to as “positional displacement estimation unit”) 3 compares two patterns to be collated (for example, a registered pattern and a collation pattern) and roughly determines how much they are deviated from each other. The misalignment is estimated. Any method may be applied as long as a rough positional deviation can be estimated. For example, it is possible to apply a known displacement measurement method to the displacement estimation unit 3.

  The input to the misregistration estimation unit 3 may be a pattern signal to which a filtering process for removing or suppressing noise components such as fixed pattern noise is applied as will be described later, or a pattern signal to which the filtering process is not applied. Good. Alternatively, a pattern signal that has been subjected to amplitude suppression processing in the phase-only correlation method may be used as an input to the positional deviation estimation unit 3.

  As a non-limiting example of a method for estimating a rough positional deviation, a method for estimating a positional deviation based on amplitude information of cross-correlation between pattern signals will be described below. For example, as shown in FIG. 12, the method can be realized by including an amplitude correlation calculation unit 31, a maximum value search unit 32, and a search center determination unit 33 as an example of the positional deviation estimation unit 3.

The amplitude correlation calculation unit 31 calculates a non-normalized cross-correlation function φ _{f, g} of f (p, q) and g (p, q) represented by the following formula (8), for example.

Here, f (p, q) and g (p, q) represent a two-dimensional registration pattern signal and a collation pattern signal, respectively. P and q represent discretized coordinate values, and correspond to the horizontal axis (x) and the vertical axis (y) in the plane, respectively. Therefore, the signal g (κ + α, λ + β) is obtained by shifting the signal g (κ, λ) by −α in the horizontal direction and −β in the vertical direction, and Expression (8) shows the shifted signal and the signal f ( The magnitude of correlation with (κ, λ) is obtained. In other words, the magnitude of the correlation with g (κ, λ) is obtained after the signal f (κ, λ) is shifted by α in the horizontal direction and β in the vertical direction. Also,
Represents the average values of f (p, q) and g (p, q), respectively.

Next, the maximum value search unit (maximum value calculation unit) 32 obtains the position (coordinates) of the maximum value of the cross-correlation function φ _{f, g} obtained by the equation (8) in the amplitude correlation calculation unit 31. Since the position of the maximum value obtained here can be determined to be close to the position corresponding to the true positional deviation between the two patterns, the search center determining unit 33 determines the position of the maximum value as a rough estimated value of the positional deviation. To do. The approximate estimated value is used in the intersection calculation unit 8 to determine the center position of the search range for the intersection of equiphase lines.

  Note that one or both of the two pattern signals to be collated may contain noise. For example, if the above-described fixed pattern noise is included in both pattern signals, there is a possibility that even a rough positional deviation cannot be estimated. Such a situation can be avoided by providing the misregistration estimation unit 3 with a filter unit 30 for filtering the two pattern signals to be collated, as indicated by a broken line in FIG.

  That is, the noise component included in each pattern signal is removed or suppressed in advance by filtering each pattern signal with the filter unit 30 before obtaining the cross-correlation between the pattern signals. Here, the concept of “filtering” includes a process of performing weighting by frequency at the time of correlation calculation between pattern signals (for example, relatively reducing the weight of a high frequency with a high ratio of noise components). That's good.

  If a noise component (for example, a high frequency component) is removed or suppressed from the pattern signal by filtering, the frequency component of the pattern may be removed or suppressed as described above, and the accuracy of the approximate estimated value may deteriorate. However, in the present embodiment, as will be described later, since the positional deviation can be estimated with high accuracy using the phase information, the deterioration can be tolerated.

Filtering by the filter unit 30 can be realized by, for example, a convolution operation of the filter coefficient of the filter unit 30 and each of the registered pattern signal and the collation pattern signal. For example, when the filter coefficient of the filter unit 30 is expressed by h _R (p, q), the convolution operation can be expressed by the following equation (9).

f _A (p, q) and g _A (p, q) represent pattern signals after applying amplitude filtering to f (p, q) and g (p, q), respectively. The filter coefficient h _R (p, q) may be either a real number or a complex number, and f (p, q) and g (p, q) (hereinafter simply abbreviated as “f” and “g”, respectively). It is sufficient if the noise can be removed or suppressed. The filter unit 30 may use different filters for the registered pattern signal and the matching pattern signal, but it is preferable to use the same filter.

After filtering by the filter unit 30, the amplitude correlation calculation unit 31 calculates a cross-correlation function between f _A (p, q) and g _A (p, q). In this calculation, f (p, q) and g (p, q) represented by Expression (8) are converted into f _A (p, q) and g _A (p, q) represented by Expression (9), respectively. Replace it. When the filter (coefficient) h _R (p, q) is a complex number, the cross-correlation function is also a complex function. In this case, the maximum value search unit 32 can obtain the absolute value or the maximum value of the real part of the cross-correlation function φ _{f, g} and set the position as a rough estimated value of the positional deviation.

Note that the method for obtaining the rough estimated value is not limited to the method based on the amplitude information of the cross-correlation function of the two pattern signals as described above. For example, as shown in the following equation (10), the sum of the absolute values of the differences between the two pattern signals is used as the evaluation function, and the position corresponding to the minimum value of the evaluation function is used as the rough estimated value. There is also a method to seek.

  Next, the complex filter units 4A-i and 4B-i, the correlation calculation unit 5-i, the phase component extraction unit 6-i, the equiphase information calculation unit 7-i, and the intersection calculation unit 8 will be described. These parts are responsible for the process of estimating a more accurate positional shift based on the phase information of the cross correlation between the pattern signals. Hereinafter, when the complex filter units 4A-i and 4B-i are not distinguished, they are simply expressed as “complex filter unit 4-i”.

The complex filter unit 4-i adds phase information to the input pattern signal. The addition of the phase information can be realized by a convolution operation of a complex value filter (coefficient), a registered pattern signal, and a matching pattern signal. When a filter applied to the complex filter unit 4-i is represented by h _i (p, q), this calculation can be represented by the following equation (11). _{However, f F (p, q)} , g F (p, q) represents a pattern signal after filtering.

Each complex filter unit 4-i adds phase information such that the equiphase lines obtained by the equiphase information calculation unit 7-i are not parallel to each other (in other words, an intersection of equiphase lines is generated). . The filter operation of the complex filter unit 4-i having such a relationship is realized by using, for example, a set of filters represented by the following expression (12) if N = 2 (two-dimensional). it can. More specifically, when performing the calculation of Expression (11), h ₁ (p, q) is applied when i = 1, and h ₂ (p, q) is applied when i = 2. It can be realized.

Here, the reason why phase information that does not become parallel between h ₁ (p, q) and h ₂ (p, q) can be simply described. The exp 1 (jω ₀ p) of h ₁ (p, q) is a complex sine wave whose phase advances in the horizontal direction. On the other hand, exp (jω ₀ q) of h ₂ (p, q) proceeds in the vertical direction even with the same complex sine wave. Since the phase advance direction of these two is orthogonal, the phase advance direction of the pattern after filtering is also different. In this way, phase information that is not parallel to each other can be added.

By the way, the equation (12) shows a combination of h ₁ (p, q) and h ₂ (p, q) in which the phase traveling directions are orthogonal to each other. In this case, the finally obtained equiphase line ( In the case of generalized N dimensions, equi-phase surfaces that are hypersurfaces or hyperplanes) intersect with each other in a nearly orthogonal manner, and the intersections can be easily obtained with high accuracy. Therefore, it is preferable to select the filter coefficients of the complex filter units 4-i so that the traveling directions of the phases are orthogonal to each other.

Note that ω ₀ is the frequency of the complex sine wave. h ₁ (p, q) is a filter that passes only a component with a horizontal frequency of ω ₀ and a vertical frequency of 0, and h ₂ (p, q) is a horizontal frequency of 0 and a vertical frequency. Each function as a filter that allows only components with ω ₀ to pass. Therefore, it is preferable to select a frequency for ω _{0 such} that the matching pattern signal and the registered pattern signal are sufficiently higher in power than the noise component. This is because if the frequency at which the verification pattern signal and the registered pattern signal have no power is selected as ω ₀ , it becomes difficult to measure the positional deviation based on the phase information.

Further, the above-described filters h ₁ (p, q) and h ₂ (p, q) are merely examples, and other filters can be applied as long as they have similar characteristics. For example, a filter represented by the following equation (13) may be applied.

On the other hand, when a set of filters represented by the following expression (14) is selected, the phase advance direction is exactly opposite, so the added phase information becomes parallel. Therefore, the set of filters represented by the following equation (14) may be excluded from candidates.

Further, a set of filters represented by the following equation (15) may be excluded from candidates.

The two filters represented by Expression (15) can satisfy different phase equivalence lines as long as the passing frequencies are different from each other, assuming that ω ₁ ≠ ω _2. This is because the point of intersection cannot be obtained.

  Note that the filters (coefficients) applied to the sets of the complex filter units 4A-i and 4B-i corresponding to the registered pattern signal and the collation pattern signal may be different from each other, but it is easier to implement the same filter. . Further, it is preferable that characteristics of the complex filter unit 4-i other than the filter characteristics (characteristics relating to the phase information added to the pattern signal), for example, gain characteristics with respect to the frequency, are aligned with the other complex filter units 4-i.

  Further, the complex filter unit 4-i can be provided with functions of a low-pass filter and a band-pass filter. This is convenient, for example, when the noise component of the pattern signal is not removed or suppressed and the noise component is removed or suppressed.

Next, the correlation calculation unit 5-i calculates a cross-correlation function between complex pattern signals converted into complex values by the complex filter unit 4-i and added with phase information. The correlation calculation here may be to obtain a normalized cross-correlation function or to obtain a non-normalized cross-correlation function. For example, a two-dimensional non-normalized cross-correlation function can be expressed by the following equation (16).

  Since the correlation calculation target is a complex-valued pattern signal, m correlation pattern signals (hereinafter also referred to as “complex correlation patterns”) having complex values are obtained by the m correlation calculation units 5-i.

  In other words, the complex filter unit 4-i and the correlation calculation unit 5-i described above add phase information to each of the two pattern signals to be collated, and calculate the correlation between the pattern signals to which the phase information is added. An example of a correlation calculation unit that performs signal processing corresponding to the calculation to be obtained.

  The phase component extraction unit 6-i extracts a phase component from the complex correlation pattern and generates a phase pattern. The phase pattern is obtained, for example, by calculating a complex phase (deflection angle).

  The equiphase information calculation unit 7-i is an equiphase line with a phase value of 0 in each phase pattern (in the case of three or more dimensions, it is an equiphase surface that is a hypersurface or hyperplane, and so on. ). It is sufficient to obtain the equiphase line around the search center. The search center can be set to a rough estimated value obtained by the misalignment rough value estimating unit 3.

  The intersection calculation unit 8 obtains an intersection of equiphase lines closest to the search center. The obtained intersection is a measured value of the positional deviation. In the case of m = N, the intersection point may be simply obtained. When m> N, the number of isophase lines required is larger than the number of dimensions of the pattern, so that there may be a plurality of intersections. In that case, the intersection point may be determined according to some rule, such as using the center of gravity of the obtained plurality of intersection points as a measurement value.

  In other words, the phase component extraction unit 6-i, the equal phase information calculation unit 7-i, and the intersection calculation unit 8 described above are the complex filter unit 4-i and the correlation calculation unit 5-i that are examples of the correlation calculation unit. This is an example of a positional deviation calculation means for obtaining a positional deviation according to the phase difference between patterns based on the obtained phase information of the correlation.

  In the above description, specific mathematical expressions are exemplified only in the case of N = 2 (two-dimensional), but the above-described processing can be implemented even when extended to a general case of three or more dimensions. is there. Examples of applications in the case of three or more dimensions include measurement of positional deviation between three-dimensional patterns, alignment between high-dimensional patterns obtained by a plurality of means, and the like.

(Second aspect)
The above-described processing until obtaining the cross-correlation function (complex correlation pattern) between the registered pattern signal and the verification pattern signal may be performed in the frequency domain. In the frequency domain, processes such as filtering and correlation calculation can be realized by simple multiplication and complex conjugate calculation, so that, for example, the efficiency of the calculation process can be improved. A functional configuration example of the signal processing device 2 in this case is shown as a second mode in FIG.

  The signal processing apparatus 2 illustrated in FIG. 13 exemplarily includes a positional deviation approximate value estimation unit 3, m phase component extraction units 6-i, m equiphase information calculation units 7-i, and Fourier transform. Units 11A and 11B, a synthesis operation unit 12, m phase information addition filter units 13-i, and m phase inverse Fourier transform units 14-i. Further, the positional deviation approximate value estimation unit 3 includes an amplitude filter unit 34, an amplitude inverse Fourier transform unit 35, a maximum value search unit 32, and a search center determination unit 33.

  The Fourier transform units 11A and 11B generate a frequency domain signal (Fourier transform pattern signal) by Fourier transforming the two pattern signals (registered pattern signal and collation pattern signal) to be collated. The “Fourier transform” may be a discrete Fourier transform (DFT) or a fast Fourier transform (FFT). When each pattern signal that has already undergone Fourier transform is input to the signal processing device 2, one or both of the Fourier transform units 11A and 11B may be deleted.

The synthesis operation unit 12 multiplies the complex conjugate of the Fourier transform pattern signal of the registered pattern signal and the Fourier transform pattern signal of the verification pattern signal. For example, the angular frequencies in the horizontal direction and the vertical direction are expressed by ω _x and ω _y , respectively, and two-dimensional Fourier transform pattern signals obtained by Fourier transforming the two-dimensional pattern signals are respectively represented by F (ω _x , ω _y ) and G ( omega _x, expressed as _{ω y), F (ω x} , complex conjugate of F * (ω _x of ω _y), ω _y) and is expressed, the synthesis result of the _{operation, F * (ω x, ω} y) G (Ω _x , ω _y ). The synthesis operation corresponds to an operation for obtaining a cross-correlation between both signals. The calculation result by the synthesis calculation unit 12 is given to the positional deviation approximate value estimation unit 3 and each phase information addition filter unit 13-i.

In the positional deviation approximate value estimation unit 3, the amplitude filter unit 34 plays the same role as the filter unit 30 in the first aspect, and removes or reduces the influence of noise when estimating a rough positional deviation. Used for. Accordingly, if noise removal or suppression has already been performed for each pattern signal, the filter unit 34 may be deleted. Note that at least one type of filtering (function) applied to the filter unit 34 may be used. When expressing the filtering _{H R (ω x, ω y} ) , the filtering result by the filter unit _{34, F * (ω x, ω} y) G (ω x, ω y) H R (ω x, ω y) and Can express.

  The inverse Fourier transform unit 35 for amplitude applies inverse Fourier transform (IDFT or IFFT) to the Fourier transform pattern signal after filtering. By the inverse Fourier transform, information (amplitude pattern) relating to the magnitude of cross-correlation between pattern signals can be obtained.

  In FIG. 13, the processing order of the correlation calculation realized as the calculation by the synthesis calculation unit 12 and the filtering by the filter unit 34 is opposite to the order shown in the first mode (for example, see FIG. 12). However, there is no difference in the effect obtained. Since both correlation calculation and filtering can be realized by multiplication and complex conjugate calculation in the frequency domain, it is easy to exchange the calculation order. However, also in the second mode, as in the first mode, it is possible to perform correlation calculation after filtering. Such commutability of the calculation order is similarly applied to the processing order of the calculation by the synthesis calculation unit 12 and the filtering by the phase information addition filter unit 13-i described later.

  Similar to the first aspect, the maximum value search unit 32 obtains the maximum value of the cross-correlation function (see, for example, the equation (8)) obtained through the synthesis calculation unit 12 and the filter unit 34 as described above, and the maximum value The position (coordinates) corresponding to is obtained.

  The search center determination unit 33 sets the position of the maximum value as a rough estimated value of positional deviation. The approximate estimated value is also used in the second mode to determine the center position of the search range for the intersection of equiphase lines in the intersection calculation unit 8.

  In the second aspect, the rough calculation of the positional deviation is obtained based on the result of the correlation calculation in the frequency domain (calculation by the synthesis calculation unit 12), thereby effectively using the correlation calculation in the frequency domain. Can do. This is preferable because it can speed up the arithmetic processing, but is not limited to this. You may obtain | require the rough estimated value of position shift by the method shown by the 1st aspect.

  Next, the phase information addition filter unit 13-i, the phase inverse Fourier transform unit 14-i, the phase component extraction unit 6-i, the equal phase information calculation unit 7-i, and the intersection calculation unit 8 will be described. These parts are responsible for processing for estimating a more accurate positional shift based on the phase information of the cross-correlation function obtained as a calculation result by the synthesis calculation unit 12.

  First, in the phase information addition filter unit 13-i, the equiphase lines (equiphase surface that is a hypersurface or hyperplane in the case of three or more dimensions) obtained by the equiphase information calculation unit 7-i are not parallel to each other. Such phase information is added to the calculation result of the composition calculation unit 12.

For example, in the case of N = 2 (two-dimensional), two filters (functions) H ₁ (ω _x , ω _y ) and H ₂ (ω _x , ω _y ) represented by the following expression (17) are expressed. The present invention can be applied to the calculation result [F ^* (ω _x , ω _y ) G (ω _x , ω _y )] of the synthesis calculation unit 12.

That is, the filter H ₁ (ω _x , ω _y ) corresponds to the first quadrant in the coordinate plane in which the horizontal and vertical axes are respectively defined by ω _x and ω _y as illustrated in FIG. The frequency component corresponding to the second to fourth quadrants is blocked and the frequency component corresponding to the second to fourth quadrants is blocked. On the other hand, as illustrated in FIG. 14B, the filter H ₂ (ω _x , ω _y ) passes the frequency component corresponding to the fourth quadrant on the same coordinate plane, and the first to third quadrants. Each of the frequency components corresponding to is cut off.

A signal obtained by applying the filter H _i (ω _x , ω _y ) to the calculation result of the synthesis calculation unit 12 is F ^* (ω _x , ω _y ) G (ω _x , ω _y ) H _i (ω _x , ω _y ). The filtering is the same as the filtering performed by the complex filter unit 4-i exemplified in the first aspect except that the calculation is performed in the frequency domain. Moreover, the point which can apply a low-pass filter and a band pass filter collectively to the phase information addition filter part 13-i is the same as that of a 1st aspect.

The phase information is expressed by the filters H ₁ (ω _x , ω _y ) and H ₂ (ω _x , ω _y ) (hereinafter simply abbreviated as “H ₁ ” and “H ₂ ”, respectively) represented by Expression (17). The reason why it can be added to the cross-correlation function (correlation pattern) will be described below. There are positive and negative frequencies, which are the same for angular frequencies. The meaning of the positive and negative will be described with a sine wave function of the following equation (18).

  When the frequency is positive, that is, when ω> 0, the phase of S (x) advances as x increases. On the other hand, when ω <0, the phase of S (x) is delayed (returned) as x increases. For example, in FIGS. 7A and 7B, the phase proceeds from left to right on the horizontal axis when the frequency is positive, and from right to left when the frequency is negative. The same applies to the vertical direction (Y axis), and the phase advances from the bottom to the top in FIGS. 7A and 7B if the frequency is positive, and from the top to the bottom if it is negative.

By the way, the original pattern signal to be verified usually includes both positive and negative frequency components. However, when the filters H ₁ and H ₂ represented by the expression (17) are applied to the pattern signal, each of the signals after the filter application includes only one of positive and negative frequency components.

For example, applying the filter H _1, only the horizontal and vertical directions are positive frequency component remains. Therefore, when both are combined, for example, as indicated by a broken line arrow in FIG. 15A, the phase advances obliquely from the lower left to the upper right of the page. In contrast, when applying the filter H _2, horizontal only positive frequency components in the vertical direction only negative frequency components remain, respectively. Therefore, when both are combined, the phase advances obliquely from the upper left to the lower right of the page, as indicated by the dashed arrow in FIG. In this manner, by using the filters H ₁ and H ₂ , phase information having phase advance directions that are orthogonal to each other can be added to the calculation result of the synthesis calculation unit 12.

  Next, the phase inverse Fourier transform unit 14-i illustrated in FIG. 13 performs an inverse Fourier transform (IDFT or IFFT) on the signal to which the phase information is added by the phase information addition filter unit 13-i as described above. ) Apply. Thereby, m sets of “complex correlation patterns” as referred to in the first aspect can be obtained.

  In other words, the Fourier transform units 11A and 11B, the synthesis operation unit 12, the phase information addition filter unit 13-i, and the inverse Fourier transform unit 14-i described above are respectively the pattern signals corresponding to the two patterns to be verified. This is an example of a correlation calculation means for performing signal processing corresponding to a calculation for adding phase information to and obtaining a correlation between pattern signals to which the phase information is added.

  The remaining processes by the phase component extraction unit 6-i, the equiphase information calculation unit 7-i, and the intersection calculation unit 8 are the same as or similar to those in the first mode, and are obtained by the inverse Fourier transform unit 14-i, respectively. The phase component is extracted from the obtained complex correlation pattern to obtain an equiphase line (equal phase surface that is a hypersurface or hyperplane in the case of three or more dimensions), and the intersection of the obtained isophase lines is located. The measured value of deviation. Further, the setting of the search center and the determination of the measurement value when m> N may be the same as in the first mode.

(Third aspect)
In the first and second aspects described above, a cross-correlation function (amplitude information) for estimating a rough displacement and a cross-correlation function with phase information added to estimate the displacement more accurately are obtained separately. However, filtering for obtaining both cross-correlation functions and cross-correlation calculation may be made common. In this case, since it is not necessary to obtain the cross correlation function individually, the calculation efficiency can be improved.

  A functional configuration example of the signal processing apparatus 2 in this case is shown as a third aspect in FIG. For example, the signal processing device 2 illustrated in FIG. 16 includes a positional deviation approximate value estimation unit 3a, complex filter units 4A-i and 4B-i (#i), a correlation calculation unit 5-i, and an amplitude / phase. A separation unit 6a-i, an equiphase information calculation unit 7-i, and an intersection calculation unit 8 are provided.

  The complex filter unit 4-i adds phase information to the pattern signal by converting each of the registered pattern signal and the matching pattern signal into a complex value. The addition of the phase information can be realized by a convolution operation of a complex value filter coefficient, a registered pattern signal, and a matching pattern signal. That is, if N = 2, the complex filter unit 4-i performs the calculation according to the equation (11) exemplified in the first aspect.

At least one of the filters (calculations) applied to the complex filter unit 4-i is preferably designed so that the positional deviation approximate value estimation unit 3a functions properly. As a non-limiting example, a filter (coefficient) represented by the following equation (19) is applied to the complex filter unit 4-i.

Note that W is a function that is symmetrical with respect to the origin, called a window function, and has a maximum value at the origin and decreases as the distance from the origin increases. An example of such a function is a triangular window function represented by the following equation (20).

Here, w _d represents the width of the window function W. The width w _d of the window function W may be selected so that, for example, the window function W includes 2 to 20 periods of complex sine waves. If the width w _d of the window function W is too large, positional deviation approximate value estimating section 3a there may not function properly. Conversely, if the width w _d of the window function W is too small, there is a possibility that the complex filter unit 4-i is not function described in the first embodiment. For example, if one period of a complex sine wave does not appear to be included in the window function W, phase information cannot be successfully added to the pattern signal.

The reason why phase information that is not parallel can be added to the pattern signal by the filters h ₁ (p, q) and h ₂ (p, q) represented by Expression (19) is the same as the reason described in the first aspect. It is almost the same. Even if the window function W is added, there is no significant difference in its function.

In addition, h ₁ (ω _x , ω _y ) passes the frequency components around (ω _x , ω _y ) = (ω ₀ , 0), and h ₂ (ω _x , ω _y ) becomes (ω _x , ω _y). ) = (0, ω ₀ ), each functioning as a band-pass filter that passes surrounding frequency components. Therefore, it is preferable to select a frequency for ω _{0 such} that the matching pattern signal and the registered pattern signal are sufficiently higher in power than the pattern noise.

However, the above-mentioned filters h ₁ (p, q) and h ₂ (p, q) are merely examples, and other filters can be applied as long as they have similar characteristics. In the third aspect, the filters (coefficients) applied to the set of complex filter units 4A-i and 4B-i corresponding to the registered pattern signal and the matching pattern signal may be different, but the same. It is easier to implement.

  Further, it is preferable that characteristics of the complex filter unit 4-i other than the filter characteristics (characteristics relating to the phase information added to the pattern signal), for example, gain characteristics with respect to the frequency, are aligned with the other complex filter units 4-i. Further, the complex filter unit 4-i can be provided with functions of a low-pass filter and a band-pass filter. This is convenient, for example, when the noise component of the pattern signal is not removed or suppressed and the noise component is removed or suppressed.

  Next, the correlation calculator 5-i calculates the cross-correlation between the pattern signals converted into complex values and added with the phase information. The correlation calculation here may be to obtain a normalized cross-correlation function or to obtain a non-normalized cross-correlation function. For example, in the case of N = 2 (two dimensions), the cross-correlation function that is not normalized can be obtained by the above equation (16). What is obtained by the correlation calculation is a complex correlation pattern, and a total of m patterns are obtained by the m correlation calculation units 5-i.

  The amplitude / phase separation unit 6a-i separates the complex correlation pattern obtained by the correlation calculation unit 5-i into amplitude information (amplitude pattern) and phase information (phase pattern). The amplitude pattern is obtained by taking the absolute value or real part of the complex correlation pattern. The phase pattern is obtained by obtaining the phase (deflection angle) of the complex correlation pattern. The amplitude pattern is provided to the maximum value search unit 32 of the positional deviation approximate value estimation unit 3, and the phase pattern is provided to the subsequent equiphase information calculation unit 7-i.

  In the positional deviation approximate value estimation unit 3, the maximum value search unit 32 obtains a position (coordinates) where the amplitude pattern given from the amplitude / phase separation unit 6a-i has the maximum value. At that time, only one amplitude pattern may be employed, or a maximum value search may be performed for all available amplitude patterns.

  Based on the position of the maximum value of the amplitude pattern obtained by the maximum value search unit 32, the search center determination unit 33 determines the center of the range (search range) in which the positional deviation measurement is performed using the phase pattern. When one amplitude pattern is employed alone, the position of the maximum value is directly used as the search center. When a plurality of amplitude patterns are employed, the search center can be determined by, for example, employing a position where the sum of the correlation functions is maximized or obtaining a centroid of the position of the maximum value of each amplitude pattern.

  The rest of the processing by the equiphase information calculation unit 7-i and the intersection calculation unit 8 is the same as or similar to the first mode, and the phase = 0 in the phase pattern obtained by the amplitude / phase separation unit 6a-i. Isophase lines (equiphase planes that are hypersurfaces or hyperplanes in the case of three or more dimensions) are obtained, and the intersection of the obtained isophase lines is used as a measurement value of positional deviation. Further, the setting of the search center and the determination of the measurement value when m> N may be the same as in the first mode.

(Fourth aspect)
The processing until obtaining the cross-correlation function (complex correlation pattern) between the registration pattern signal and the verification pattern signal described above in the third mode can be performed in the frequency domain as described in the second mode. . As described in the second mode, in the frequency domain, processing such as filtering and correlation calculation can be realized by simple multiplication and complex conjugate calculation, so that the calculation process can be made more efficient.

  A functional configuration example of the signal processing device 2 in this case is shown as a fourth mode in FIG. The signal processing apparatus 2 illustrated in FIG. 17 has a second mode (see FIG. 13) in which the complex filter units 4A-i and 4B-i and the correlation calculation unit 5-i in the configuration illustrated in FIG. In the same manner as the above, this is equivalent to a block provided with Fourier transform units 11A and 11B, a synthesis operation unit 12, a filter unit 15-i, and an inverse Fourier transform unit 14-i.

  The Fourier transform units 11A and 11B generate a frequency domain signal (Fourier transform pattern signal) by performing Fourier transform (DFT or FFT) on the two pattern signals to be collated (registered pattern signal and collation pattern signal), respectively. When each pattern signal that has already undergone Fourier transform is input to the signal processing device 2, one or both of the Fourier transform units 11A and 11B may be deleted.

  The synthesis operation unit 12 multiplies the complex conjugate of the Fourier transform pattern signal of the registered pattern signal and the Fourier transform pattern signal of the verification pattern signal. Thereby, the cross correlation of both signals is calculated | required. The calculation result by the synthesis calculation unit 12 is given to the phase information addition filter unit 13-i.

  The filter unit 15-i obtains phase information such that the equiphase lines (equiphase surfaces that are hypersurfaces or hyperplanes in the case of three or more dimensions) obtained by the equiphase information calculation unit 7-i are not parallel to each other. It adds to the calculation result of the synthetic | combination calculating part 12.

Here, at least one of the filter units 15-i has both functions of the amplitude filter unit 34 and the phase information addition filter unit 13-i exemplified in the second mode. For example, in the case of N = 2 (two dimensions), the filters H ₁ and H ₂ exemplified in Expression (17) have such a function (characteristic), so at least one of the filters H ₁ and H ₂ is selected. What is necessary is just to apply to the filter part 15-i.

  The inverse Fourier transform unit 14-i applies inverse Fourier transform (IDFT or IFFT) to the signal to which the phase information is added by the phase information addition filter unit 13-i as described above. As a result, the aforementioned “complex correlation pattern” can be obtained.

  The remaining processes by the positional deviation approximate value estimation unit 3a, the amplitude / phase separation unit 6a-i, the equiphase information calculation unit 7-i, and the intersection calculation unit 8 may be the same as or similar to those in the third mode.

  In the fourth aspect described above, all complex correlation patterns are obtained by calculation in the frequency domain, but a part of them can also be obtained by the method shown in the third aspect (see FIG. 16). is there. However, if importance is placed on improving the calculation efficiency, the fourth mode is preferable.

(5th aspect)
The addition of phase information to each of the two pattern signals to be verified (registered pattern signal and verification pattern signal) may be performed using continuous wavelet transform. A functional configuration example of the signal processing apparatus 2 in this case is shown as a fifth aspect in FIG.

  The signal processing device 2 illustrated in FIG. 18 includes the complex filter units 4A-1 to 4A-m and 4B-1 to 4B-m in the configuration illustrated in FIG. 16 as continuous wavelet transform units 16A-1 to 16A-m and It corresponds to the one replaced with 16B-1 to 16B-m. In the following description, when the continuous wavelet transform units 16A-i and 16B-i are not distinguished, they are abbreviated as continuous wavelet transform units 16-i.

  The continuous wavelet transform units 16A-i and 16B-i perform continuous wavelet transform on the registered pattern signal and the collation pattern signal, respectively. The wavelet used for the continuous wavelet transform is illustratively a complex function wavelet for adding phase information to the pattern signal.

For example, in order to add phase information to a two-dimensional pattern signal, two Gabor wavelets represented by the following equation (21) can be applied.

Here, x and y are horizontal and vertical coordinates, ω ₀ is the center frequency of the wavelet, and γ is a parameter that determines the spread of the wavelet. The center frequency ω _{0 of the} wavelet can be arbitrarily selected, but if it is set to 1 or 2π, subsequent processing can be simplified. γ affects the spatial resolution and frequency resolution as a result of the wavelet transform, and if it is small, the spatial resolution is important, and if it is large, the frequency resolution is important. In general, a value between π and 4π is appropriate.

The traveling direction of the phase of Ψ ₁ (x, y) is the direction illustrated in FIG. 15A, and the traveling direction of the phase of Ψ ₂ (x, y) is the direction illustrated in FIG. . That is, it is possible to add phase information such that the traveling directions of the phases are not parallel by the combination of these two wavelets.

The continuous wavelet transform of the input pattern signal f (x, y) can be exemplarily expressed by the following equation (22). When a discretized pattern signal is input, numerical integration may be used.

Here, a _x is the horizontal direction of the scale parameter, a _y is the scale parameter, b _x vertical shift parameters in the horizontal direction, the b _y represent the shift parameter in the vertical direction, respectively. The scale parameter is a parameter corresponding to the inverse of the scale or frequency. The shift parameter is a parameter corresponding to the position. i = 1,..., m represents the number (#i) of the continuous wavelet transform unit 16-i.

  Since the wavelet transform functions as a bandpass filter, noise can be suppressed together by appropriately selecting a scale parameter. When the scale parameter is decreased, the frequency is increased, and when the scale parameter is increased, the frequency is decreased. If the value is set too small, the position shift cannot be measured correctly due to the influence of noise, so it is desirable to set the value so as not to be affected by the noise.

The correlation calculation unit 5-i can be calculated by the following equation (23), for example, if it is a non-normalized cross-correlation function.

  The remaining processes by the positional deviation approximate value estimation unit 3a, the amplitude / phase separation unit 6a-i, the equiphase information calculation unit 7-i, and the intersection calculation unit 8 may be the same as or similar to those in the third mode.

  Wavelet transform and correlation operation can be exchanged under certain conditions (Tetsuya Tahara and Seiichi Shin, "Correlation between correlation wavelet transform and wavelet transform", IEEJ Industrial Measurement and Control Study Group materials) (IIC-03-76), pp. 13-18 (2003)). Therefore, a function equivalent to the above can also be realized by performing the wavelet transform after obtaining the cross-correlation function.

  Further, a part of the continuous wavelet transform unit 16-i may be replaced with the complex filter unit 4-i exemplified in the third mode (FIG. 16).

(Example of simulation results)
An example of the result of the simulation of the displacement measurement performed by the signal processing device 2 according to the fifth aspect described above is shown in FIGS.

  FIG. 19 shows an example of two patterns to be collated. Pattern B illustrated in FIG. 19B is 40 pixels in the right direction (horizontal direction) of the pattern A illustrated in FIG. The pattern is shifted by 15 pixels in the direction (vertical direction). In the simulation, the positional deviation was obtained. Both patterns contain common fixed pattern noise.

FIG. 20 is a diagram obtained by performing continuous wavelet transform on the pattern signals of both patterns, obtaining a normalized cross-correlation function from the result of the transformation, and contour plotting the absolute value of the obtained cross-correlation function. When FIG. 20A shows the correlation after the continuous wavelet transform of the pattern signal with Ψ ₁ in the expression (21), FIG. 20B shows the case where the same processing is performed with Ψ ₂ in the expression (21). Respectively. The scale at the time of continuous wavelet transform is set so that the center frequency of the passband is low in order to suppress the influence of fixed pattern noise. In this example, the position of the maximum value of the absolute value of the cross-correlation function is shifted by one pixel from the true value, resulting in an error.

FIG. 21 is a diagram in which isophase lines are plotted such that the phase of the cross-correlation function is zero. If equiphase lines # 1 continuous wavelet transform pattern signal in the [psi _1, the equiphase lines # 2 respectively correspond to the case of continuous wavelet transform a pattern signal in the [psi _2. In FIG. 21, there are intersections of two equiphase lines # 1 and # 2 in the vicinity of the maximum value of the absolute value. When the coordinates of the intersections are rounded to an integer, they coincide with the true value. As described above, by using the phase information in combination, the measurement accuracy of the positional deviation between the patterns can be improved.

  DESCRIPTION OF SYMBOLS 1 ... Pattern production | generation apparatus (imaging apparatus), 2 ... Signal processing apparatus, 3, 3a ... Position shift approximate value estimation part, 4A-1-4A-m, 4B-1-4Bm ... Complex filter part, 5-1 ˜5-m ... correlation calculation unit, 6-1 to 6-m ... phase component extraction unit, 6a ... amplitude / phase separation unit, 7 ... equal phase information calculation unit, 8 ... intersection point calculation unit, 11A, 11B ... Fourier transform Part, 12 ... synthesis operation part, 13 ... filter part, 13-1 to 13-m phase information addition filter part, 14-1 to 14-m ... inverse Fourier transform part, 15-1 to 15-m ... filter part, 16A-1 to 16A-m, 16B-1 to 16B-m: continuous wavelet transform unit, 24 ... hard disk, 25 ... memory, 30, 34 ... filter unit, 31 ... amplitude correlation calculation unit, 32 ... maximum value search unit, 33 ... Search center determination unit, 35 ... Inverse Fourier transform unit

Claims (9)

Phase information of m types (m is an integer satisfying m ≧ N) indicating phase traveling directions that are not parallel to each other of pattern signals corresponding to two N-dimensional patterns (N is an integer of 2 or more) to be collated. And a correlation calculation means for performing signal processing corresponding to a calculation for obtaining a correlation between m sets of pattern signals to which the same phase information is added,
A positional deviation calculating means for obtaining a positional deviation according to the phase difference between the patterns based on phase information of the m sets of correlations obtained by the correlation calculating means;
A misalignment measuring apparatus. A positional deviation estimation means for comparing the pattern signals and estimating a positional deviation between the patterns;
The misregistration calculation means includes
The misregistration measuring apparatus according to claim 1, wherein the misregistration is determined based on the estimated misregistration value obtained by the misregistration estimation means and the phase information of the correlation obtained by the signal processing. The positional deviation estimation means is
An amplitude correlation calculation unit for obtaining a correlation related to the amplitude of the pattern signal;
A maximum value calculating unit for obtaining a maximum value of correlation obtained by the amplitude correlation calculating unit, and obtaining a positional shift corresponding to the maximum value as the estimated value;
The position shift measuring device according to claim 2, comprising: The positional deviation estimation means is
The positional deviation measuring device according to claim 2, further comprising a maximum value calculation unit that obtains a maximum value of the amplitude information of the correlation obtained in the signal processing and obtains a positional deviation corresponding to the maximum value as the estimated value. The correlation calculation means includes
M complex filters having filter characteristics corresponding to the m types of phase information,
The misregistration measuring apparatus according to claim 1, wherein the m kinds of phase information are added to each of the pattern signals by applying the m kinds of complex filters to each of the pattern signals.   The positional deviation measuring apparatus according to claim 1, wherein the correlation calculation unit performs the addition of the phase information and the calculation of the correlation in the signal processing in a frequency domain.   The position shift measuring device according to claim 5, wherein a part or all of the complex filter is a filter based on continuous wavelet transform. Phase information of m types (m is an integer satisfying m ≧ N) indicating phase traveling directions that are not parallel to each other of pattern signals corresponding to two N-dimensional patterns (N is an integer of 2 or more) to be collated. Signal processing corresponding to an operation for obtaining a correlation between m sets of pattern signals to which the same phase information is added;
Based on the phase information of the m sets of correlations obtained by the signal processing, a process for obtaining a positional shift according to the phase difference between the patterns;
A method for measuring misalignment. A computer-readable misregistration measurement program that causes a computer to perform a predetermined misregistration measurement process by being read by a computer,
Phase information of m types (m is an integer satisfying m ≧ N) indicating phase traveling directions that are not parallel to each other of pattern signals corresponding to two N-dimensional patterns (N is an integer of 2 or more) to be collated. Signal processing corresponding to an operation for obtaining a correlation between m sets of pattern signals to which the same phase information is added;
Based on the phase information of the m sets of correlations obtained by the signal processing, a process for obtaining a positional shift according to the phase difference between the patterns;
A computer-readable misregistration measurement program for causing the computer to execute.