JP5333143B2 - Shape measuring apparatus, shape measuring method and program - Google Patents

Abstract

<P>PROBLEM TO BE SOLVED: To provide a device and a method for measuring a shape, and a program which do not depend on an input image with respect to an operation load required for processing and which can prevent occurrence of an error due to the noise contained in a phase before connection. <P>SOLUTION: This device for measuring the shape includes an object imaging device which irradiates a measuring object with linear laser light consisting of a short-cycle wave modulated by a long-cycle wave and images the linear laser light reflected by the measuring object, and an arithmetic processing device which performs image processing of an image of the measuring object thus formed and specifies the shape of the measuring object. The arithmetic processing device includes a phase-calculating section which calculates the phases of the long-cycle wave and the short-cycle wave, respectively, based on the formed image; a phase connecting section which connects the phases of the long-cycle wave by a weighted least squares method, based on the calculated phases of the long-cycle wave, while the phases of the short-cycle wave are connected by the weighted least squares method, based on the connected phases of the long-cycle wave; and a shape-specifying section which specifies the shape of the measuring object based on the connected phases of the short-cycle wave. <P>COPYRIGHT: (C)2011,JPO&amp;INPIT

Description

  The present invention relates to a shape measuring device, a shape measuring method, and a program.

  Conventionally, in order to measure the shape of an object, an active three-dimensional image measurement method in which light controlled by a measurement device is projected onto an object has been used. This three-dimensional image measurement method is a method of measuring a shape of a moving object by generating a fringe image using, for example, a time-modulated laser light source and a delay integration type (Time Delay Integration: TDI) camera. This method can extract information on the shape of the measurement object from a single image, and the apparatus itself can be composed of a pattern projection device, a camera, and an image processing device, and thus can be widely applied to various industries. is there. In particular, a method of obtaining a fringe image using a time-modulated laser light source and a TDI camera is a useful method for inspecting minute irregularities on a steel sheet to be transferred.

  By the way, the above three-dimensional image measurement method is a method of generating a fringe image by irradiating a pattern with a predetermined period on the surface of an object. In the measurement process, the phase between adjacent pixels in the fringe image is measured. It is necessary to consider the connection. In order to match the phase between adjacent pixels, a process called phase connection process is often performed in the three-dimensional image measurement method.

  Various methods have been proposed as such phase connection processing. For example, in the following Patent Document 1 to Patent Document 3, the phase corresponding to a pixel whose phase is undetermined so that the phase difference between the pixel whose phase is fixed and the pixel to which phase connection will be performed is minimized A method of performing phase connection by adding integer multiples (0, ± 1, ± 2,...) Of 2π is disclosed. Further, in Patent Document 4 and Patent Document 5 below, an image to be processed is divided into regions in which the phase change between adjacent pixels is sufficiently small (that is, a region in which the phase can be considered to be continuous). A method of adding an integer multiple of 2π in units of regions to the phase of pixels included in the region is disclosed.

JP 2000-146543 A JP 2005-308539 A JP 2008-82869 A JP-A-10-90112 JP 2000-149024 A

  However, in the methods described in Patent Documents 1 to 3, when noise is included in the phase before phase connection, addition is performed even though 2π should not be originally added to the phase. There was a problem that an error may remain. Moreover, since these methods are sequential processes for all the pixels constituting the image, there is a problem that it is difficult to increase the processing speed by parallel computation.

  Further, in the methods described in Patent Document 4 and Patent Document 5, when the phase change of the image to be processed is large, the number of divisions increases, resulting in a problem that the processing time increases. . This means that the processing time varies depending on the image to be processed. Therefore, when there are restrictions on the processing time such as online processing, it is difficult to apply the methods described in these documents. turn into.

  Accordingly, the present invention has been made in view of the above problems, and irradiates the surface of the object to be measured with a pattern having a predetermined period, and measures the three-dimensional shape of the object to be measured from the generated fringe image. This is intended to enhance the phase connection processing between adjacent pixels in the fringe image. An object of the present invention is to provide a shape measuring device, a shape measuring method, and a shape measuring device capable of preventing an error caused by noise included in a phase before connection without depending on an input image and a calculation load required for processing. To provide a program.

In order to solve the above problems, according to an aspect of the present invention, a linear laser beam composed of a short-period wave having a relatively short period and modulated by a long-period wave having a relatively long period is measured. An object imaging device that images the linear laser light reflected by the measurement object, and performs image processing on a captured image of the measurement object generated by the object imaging device, An arithmetic processing device that identifies the shape of the measurement object, and the arithmetic processing device, based on a captured image of the measurement target, includes the phases of the long-period wave and the short-period wave included in the captured image. And a phase calculation unit for calculating the phase of the long period wave by a weighted least square method based on the phase of the long period wave calculated by the phase calculation unit, and the connected long period wave of phase A phase connecting portion connecting the phase of the short-period waves by weighted least square method on the basis of preliminary the phase calculation section wherein the short period waves the phase calculated by the short period waves coupled by the phase connecting portion based on the phase, have a, a shape identifying unit which identifies a shape of the measurement object, the phase calculation unit further calculates the amplitude of the long period wave and the short period waves, the phase connecting portion Is provided with a shape measuring device for determining a weight used in the weighted least square method based on the amplitude of the long period wave and the short period wave calculated by the phase calculation unit .

  It is preferable that the phase connection unit generates an initial value of the phase when the phase of the short period wave is connected based on a connection result of the phase of the long period wave.

  The phase connection unit sets the weight value corresponding to the position where the amplitude is equal to or smaller than a predetermined threshold in the captured image as a positive value equal to or smaller than a predetermined value, and the amplitude is equal to or smaller than the predetermined threshold. The weight value corresponding to a position other than the position may be 1.

  The phase connection unit, when performing the process of connecting the phases of the short period waves, the difference between the initial value of the phase of each position in the captured image and the initial value of the phase of the position adjacent to the position If the sum of absolute values of the differences exceeds a predetermined threshold, the weight value at the corresponding position may be set to zero.

  When the period of the long-period wave is K times the period of the short-period wave, the phase connection unit is obtained by multiplying the phase of the long-period wave after phase connection by K times the phase of the short-period wave. It may be an initial value.

In order to solve the above problem, according to another aspect of the present invention, a linear laser beam composed of a short-period wave having a relatively short period modulated by a long-period wave having a relatively long period is used. Imaging the linear laser beam reflected by the measurement object while scanning the measurement object, generating a captured image of the measurement object, and imaging the measurement object based on the captured image of the measurement object a phase of the long periodic wave and the short-period waves included in the image, and calculating the length and the amplitude of the periodic wave and the short period waves, respectively, based on the long periodic wave of the phase issued calculated The phase of the long period wave is connected by the weighted least square method, and the phase of the short period wave is calculated by the weighted least square method based on the phase of the connected long period wave and the calculated phase of the short period wave. Connect A step that, based on the connected the short-period wave phase by the step of connecting the phase, identifying a shape of the measurement object, seen containing an in step of connecting the phase is calculated Further, there is provided a shape measuring method for determining a weight used in the weighted least square method based on the amplitude of the long period wave and the short period wave .

In order to solve the above problems, according to still another aspect of the present invention, a linear laser beam composed of a short-period wave having a relatively short period and modulated by a long-period wave having a relatively long period To the computer that performs image processing on the captured image of the measurement object generated by the object imaging device that images the linear laser light reflected by the measurement object. Based on the image, the phase calculation function for calculating the phase of the long period wave and the short period wave included in the captured image, respectively, and the long square wave based on the calculated phase of the long period wave by the weighted least square method with connecting periodic wave phase, by the connected long period wave phase and weighted least-squares method on the basis of the calculated short-period wave phase by the phase calculation function of the short-period waves A phase connection function of connecting the phase, based on the short periodic wave phase after phase connection, a shape specifying function of specifying the shape of the measurement object, is realized, the phase calculation function, the long period The phase connection function is used in the weighted least squares method based on the amplitude of the long period wave and the short period wave calculated by the phase calculation function. program is provided for determining the weight to be.

  As described above, according to the present invention, when the surface of the object to be measured is irradiated with a pattern having a predetermined period and the three-dimensional shape of the object to be measured is measured from the generated fringe image, weighting is performed. By performing the phase connection process using the least square method, the phase connection process between adjacent pixels in the fringe image can be enhanced. Thereby, in the present invention, the calculation load required for processing can be made independent of the input image, and it is possible to prevent the occurrence of errors due to noise included in the phase before connection.

It is explanatory drawing for demonstrating the structure of the shape measuring apparatus which concerns on the 1st Embodiment of this invention. It is explanatory drawing for demonstrating a fringe image. It is explanatory drawing for demonstrating the fringe image in case a level | step difference exists in a measuring object. It is a block diagram for demonstrating the structure of the image process part which the arithmetic processing apparatus which concerns on the same embodiment has. It is explanatory drawing for demonstrating an example of the fringe image obtained in the case of 2 period addition. It is explanatory drawing for demonstrating the signal processing in a phase calculation part. It is a spectrum which shows the signal of 1 line of the fringe image by 2 period addition. It is a vector diagram regarding the signal after passing a low-pass filter. It is a spectrum which shows the signal of 1 line of the fringe image by 2 period addition. It is explanatory drawing for demonstrating the outline | summary of a phase connection process. It is explanatory drawing for demonstrating the change of the frequency of the fringe image according to the inclination of a measuring object. It is explanatory drawing for demonstrating the change of the frequency of the fringe image according to the inclination of a measuring object. It is explanatory drawing for demonstrating an example of the fringe image by AM modulation. It is explanatory drawing for demonstrating the signal processing in a phase calculation part. It is a spectrum which shows the signal of 1 line of the fringe image by AM modulation. It is a vector diagram regarding the signal after passing a low-pass filter. It is a flowchart for demonstrating the whole flow of the shape measuring method which concerns on the embodiment. It is explanatory drawing for demonstrating a phase connection process. It is explanatory drawing for demonstrating a phase connection process. It is explanatory drawing for demonstrating the phase connection process which concerns on the same embodiment. It is explanatory drawing for demonstrating the specific example of the phase connection process which concerns on the embodiment. It is explanatory drawing for demonstrating the specific example of the phase connection process which concerns on the embodiment. It is explanatory drawing for demonstrating parallel processing of the phase connection process which concerns on the same embodiment. It is a flowchart for demonstrating the phase connection method which concerns on the same embodiment. It is a flowchart for demonstrating the phase connection method by which the parallel processing which concerns on the embodiment was carried out. It is a block diagram for demonstrating the hardware constitutions of the arithmetic processing unit which concerns on embodiment of this invention. It is explanatory drawing for demonstrating the result of Example 1 of this invention. It is explanatory drawing for demonstrating the result of Example 2 of this invention. It is explanatory drawing for demonstrating the result of Example 2 of this invention. It is explanatory drawing for demonstrating the result of Example 2 of this invention. It is explanatory drawing for demonstrating the result of Example 2 of this invention. It is explanatory drawing for demonstrating the result of Example 2 of this invention. It is explanatory drawing for demonstrating the result of Example 2 of this invention. It is explanatory drawing for demonstrating the connection result by the conventional phase connection process.

  Exemplary embodiments of the present invention will be described below in detail with reference to the accompanying drawings. In addition, in this specification and drawing, about the component which has the substantially same function structure, duplication description is abbreviate | omitted by attaching | subjecting the same code | symbol.

(First embodiment)
<Overall configuration of shape measuring device>
First, the overall configuration of the shape measuring apparatus according to the first embodiment of the present invention will be described in detail with reference to FIGS.

  In the following description, a case where shape measurement is performed using a linear laser light source and a TDI camera is taken as an example. However, the shape measurement apparatus according to the present embodiment is not limited to such an example, and an object is measured. Alternatively, a light source capable of irradiating a spatial periodic pattern and an imaging device may be used.

  The shape measuring apparatus 10 according to the present embodiment is an apparatus that optically measures the shape of an object, and mainly includes, for example, an object imaging device 100 and an arithmetic processing device 200 as shown in FIG. . As an object of shape measurement (hereinafter also referred to as a measurement object), for example, a steel sheet S manufactured at a steel mill or the like is assumed. The steel plate S that is the measurement object is conveyed at a constant speed in the longitudinal direction of the steel plate (left and right direction in FIG. 1). The shape measuring apparatus 10 according to the present embodiment measures the shape of the steel sheet S during conveyance of the steel sheet S, and detects defects such as dents and wrinkles present on the surface of the steel sheet.

[About object imaging device]
First, the object imaging apparatus 100 will be described.
The object imaging apparatus 100 according to the present embodiment mainly includes a laser light source 101, a rod lens 103, and a delay integration type (TDI) camera 105, for example, as shown in FIG.

  As the laser light source 101, for example, a CW laser light source that continuously performs laser oscillation can be used. The wavelength of light oscillated by the laser light source 101 is preferably a wavelength belonging to the visible light band of about 400 nm to 800 nm, for example. The laser light source 101 oscillates laser light based on an irradiation timing control signal sent from the arithmetic processing unit 200 described later.

  The rod lens 103 is a lens that spreads the laser light emitted from the laser light source 101 in a fan shape along the width direction (direction perpendicular to the paper surface of FIG. 1) of the steel sheet S that is the measurement object. As a result, the laser light emitted from the laser light source 101 becomes the linear laser light L, and the steel sheet S is irradiated. In the object imaging apparatus 100 according to the present embodiment, a lens other than the rod lens may be used as long as the laser light can be fanned out.

  Here, as shown in FIG. 1, the laser light source 101 and the rod lens 103 are arranged so that the linear laser light L is incident on the steel sheet S obliquely.

  In the portion irradiated with the linear laser beam L on the surface of the steel sheet S that is the measurement object, a linear bright portion is formed along the width direction of the steel sheet S. Further, since the steel plate S is conveyed along the longitudinal direction of the steel plate S, when viewed from the steel plate S, the linear bright part is also moved along the longitudinal direction of the steel plate S. The reflected light (linear reflection image) from the linear bright part is transmitted to the delay integration camera 105 and captured by the delay integration camera 105.

  The delay integration type (TDI) camera 105 captures a linear reflection image of the steel sheet S being conveyed. The TDI camera 105 includes a two-dimensional light receiving surface on which a large number of photoelectric conversion elements are arranged in a matrix. When the linear reflection image of the steel sheet S enters the photoelectric conversion element with a width of one column through the lens 107 of the TDI camera 105, each photoelectric conversion element of the TDI camera 105 converts the accumulated charge into the photoelectric conversion element. The data is transferred to the photoelectric conversion element located in the same row as the conversion element and located in the next column. The timing of this transfer is the same for all photoelectric conversion elements, and is controlled by a camera shift pulse signal sent from the arithmetic processing unit 200 described later. That is, each time a camera shift pulse signal is input, each photoelectric conversion element transfers the charge one column at a time. When the camera shift pulse signal is input, the photoelectric conversion elements located in the last column read out the accumulated charges and output them to the arithmetic processing unit 200 described later. As a result, a light section image corresponding to the linear reflection image is output to the arithmetic processing unit 200 described later.

  Here, since the steel plate S moves along the longitudinal direction of the steel plate, the steel plate S is irradiated with laser light from the laser light source 101, and a linear reflection image of the steel plate S is captured for a certain time using the TDI camera 105. Then, the light cutting image in each position of the longitudinal direction of the steel plate S can be obtained sequentially. An image representing the entire steel sheet S can be obtained by sequentially arranging the optically cut images thus obtained in the horizontal direction.

  In general, in the TDI camera 105, when light is incident on each photoelectric conversion element while charges are being transferred, a charge corresponding to the intensity of the incident light is added. However, in the shape measuring apparatus 10 according to the present embodiment, as described above, a linear reflection image having a width corresponding to one column is incident on the photoelectric conversion elements, so that charges are added to the photoelectric conversion elements during the transfer of charges. Little happens. An optical bandpass filter that transmits only the wavelength of the laser beam may be provided in front of the TDI camera 105.

  Further, since the linear laser beam L is periodically modulated and the intensity of the linear laser beam L changes with time, in each row on the light receiving surface of the TDI camera 105, the linear laser beam L is accumulated in each photoelectric conversion element in the column direction. The distribution of the amount of charge (that is, the received light intensity) also periodically changes. For this reason, an image obtained by sequentially arranging the light cut images output from the TDI camera 105 in the horizontal direction in the vertical direction is the density of each light cut image (that is, the horizontal direction of the image (that is, (Corresponding to intensity) is a fringe image that periodically changes.

  FIG. 2 shows an example of a fringe image generated as described above. Here, the stripe is a light section image corresponding to one period of density change. In such a fringe image, the longitudinal direction, that is, the direction parallel to the fringe corresponds to the width direction of the steel sheet S that is the measurement object, and the horizontal direction, that is, the direction orthogonal to the fringe is the steel sheet S that is the measurement object 2. Corresponds to the longitudinal direction. If the ratio of the camera shift frequency of the TDI camera 105 to the modulation frequency of the laser light is M: 1, M light-cut images, that is, M pixels in the horizontal direction form one stripe.

  Since the linear laser beam L is incident on the surface of the steel sheet S, which is an object to be measured, from an oblique direction, for example, when there is a recess in the steel sheet S, the reflection point of the linear laser beam L in FIG. As a result, the position of the light section image on the photoelectric conversion element of the TDI camera 105 is also shifted rightward, that is, in the column direction. For this reason, in the fringe image, the light cut image corresponding to the linear laser light L reflected by the concave portion is earlier in time than the light cut image corresponding to the linear laser light L reflected by the flat portion other than the concave portion. Will be output. Therefore, in the two-dimensional image obtained by sequentially arranging the one-dimensional images output from the TDI camera 105 in the horizontal direction, the concave portions present in the steel sheet S can be recognized as a stripe shift. For example, in FIG. 2, the portion where the stripe is bent corresponds to the concave portion present in the measurement object.

  The incident angle of the linear laser beam L to the steel sheet S can be set to an arbitrary value, but is preferably set to 45 degrees, for example. By setting the incident angle to 45 degrees, the amount of change in the depth of the steel sheet S as the measurement object becomes equal to the amount of movement of the stripes, and information on the depth of the recesses present in the steel sheet S can be easily obtained from the amount of movement of the stripes. This is because it can be obtained.

  By the way, as shown to Fig.3 (a), the case where the level | step difference 21 exists in the steel plate S which is a measuring object, for example, and the depth of the level | step difference 21 is a phase difference of a half cycle is considered. In this case, the striped image generated based on the measurement data obtained by irradiating the steel plate S with the intensity-modulated light from the laser light source 101 and being obtained from the TDI camera 105 is an image as shown in FIG.

  Referring to FIG. 3A, it can be seen that the correspondence relationship of the stripe a-a ′, the stripe b-b ′, the stripe c-c ′,... However, it is impossible to determine, for example, whether the stripe b is a stripe corresponding to the stripe a 'or a stripe corresponding to the stripe b' only by the camera image as shown in FIG. Further, since the signal information obtained from the TDI camera 105 is only the phase, if the depth of the step exceeds a half cycle, the continuity of the information is lost, making it difficult to measure the shape of the object surface. Such a problem relating to the continuity of fringes also occurs in the method of projecting fringe images.

  The problem of the level difference as described above is caused by the relationship between the intensity modulation period (the period of the stripes) used in the shape measuring apparatus 10 and the height of the level difference. It is conceivable to use a sine wave with a long period. However, when an object is measured using only a long-period wave, the spatial error of the long-period wave is low, so that a generated error becomes relatively large. Therefore, in the arithmetic processing device 200 included in the shape measuring apparatus 10 according to the present embodiment, the approximate height of the step is obtained using the long period wave, and the phase of the short period wave is obtained using the approximate height of the step. The surface shape can be measured with high accuracy.

[Overall configuration of arithmetic processing unit]
Next, the configuration of the arithmetic processing device provided in the shape measuring apparatus 10 according to the present embodiment will be described in detail with reference to FIG.

  For example, as illustrated in FIG. 1, the arithmetic processing device 200 according to the present embodiment mainly includes a timing signal generation unit 201, an image processing unit 203, a display unit 205, and a storage unit 207.

  The timing signal generation unit 201 is realized by, for example, a CPU (Central Processing Unit), a ROM (Read Only Memory), a RAM (Random Access Memory), a communication device, and the like. The timing signal generator 201 generates a sine waveform signal having a predetermined frequency ω, and sends the generated sine waveform signal to the laser light source 101. Since the laser light source 101 can continuously change the oscillation intensity by a signal input from the outside, it receives a sine waveform signal sent from the timing signal generator 201 and outputs it in a sine waveform. It is possible to oscillate laser light that changes. That is, the timing signal generator 201 can periodically modulate the laser light emitted from the laser light source 101 by sending the generated sine waveform to the laser light source 101.

More specifically, the timing signal generator 201 generates a sine wave having a normal period (frequency ω ₁ ) and a sine wave having a longer period than the sine wave having the frequency ω ₁ (frequency ω ₂ ). Two types of sine waves are added to modulate the laser beam. Hereinafter, a sine wave having a normal cycle and a relatively short cycle (frequency ω ₁ sine wave) will be referred to as a “short cycle wave”, and a sine wave having a longer cycle than the normal cycle frequency (frequency ω). ₂ ) is referred to as a “long-period wave”. Here, the timing signal generator 201 modulates the laser beam so that the period of the long-period wave is K times the period of the short-period wave.

The timing signal generation unit 201 generates a sine waveform having a frequency M times the frequency ω ₁ as a camera shift pulse signal, and transmits the generated camera shift pulse signal to the TDI camera 105.

  As described above, the timing signal generation unit 201 can be said to be a drive control unit that controls driving of the laser light source 101 and the TDI camera 105 provided in the object imaging apparatus 100.

  The image processing unit 203 is realized by, for example, a CPU, a ROM, a RAM, a communication device, and the like. The image processing unit 203 connects a phase to a fringe image generated by using imaging data acquired from the object imaging apparatus 100 (more specifically, the TDI camera 105 of the object imaging apparatus 100) (hereinafter, referred to as “phase imaging”). Image processing including a phase connection process) is performed, and the shape of the steel sheet S that is the measurement object is specified. When the image processing on the striped image corresponding to the steel plate S is completed, the image processing unit 203 transmits information about the obtained shape of the steel plate S to the display unit 205.

  The image processing unit 203 will be described in detail later again.

  The display unit 205 is realized by, for example, a CPU, a ROM, a RAM, an output device, and the like. The display unit 205 displays the measurement result of the steel sheet S, which is the measurement object, transmitted from the image processing unit 203 on an output device such as a display provided in the arithmetic processing device 200. Thereby, the user of the shape measuring apparatus 10 can grasp the measurement result of the surface shape of the measurement object (steel plate S) being conveyed on the spot.

  The storage unit 207 is an example of a storage device included in the arithmetic processing device 200. The storage unit 207 appropriately records various parameters, the progress of processing, or various databases that need to be saved when the arithmetic processing apparatus 200 according to the present embodiment performs some processing. The The storage unit 207 can be freely read and written by the timing signal generation unit 201, the image processing unit 203, the display unit 205, and the like.

[About the image processing unit]
Next, the image processing unit 203 included in the arithmetic processing apparatus 200 according to the present embodiment will be described in detail with reference to FIG. FIG. 4 is a block diagram for explaining a configuration of an image processing unit included in the arithmetic processing apparatus according to the present embodiment.

  For example, as illustrated in FIG. 4, the image processing unit 203 according to the present embodiment mainly includes a signal acquisition unit 211, a phase calculation unit 213, a phase connection unit 215, and a shape identification unit 217.

  The signal acquisition unit 211 is realized by, for example, a CPU, a ROM, a RAM, a communication device, and the like. The signal acquisition unit 211 acquires signal data corresponding to the light section image transmitted from the TDI camera 105 of the object imaging apparatus 100. Moreover, the signal acquisition part 211 produces | generates the signal data showing the fringe image of the steel plate S which is a measuring object using the signal data corresponding to the acquired light cutting image. The signal acquisition unit 211 transmits signal data representing the generated fringe image to a phase calculation unit 213 described later. The signal acquisition unit 211 may record signal data acquired from the TDI camera 105, signal data representing the generated fringe image, and the like in the storage unit 207 and the like.

  The phase calculation unit 213 adds a phase corresponding to each pixel based on a fringe image obtained by irradiating the steel sheet S with a laser beam modulated by adding two types of sine waves of a short period wave and a long period wave. Is calculated. Hereinafter, the function of the phase calculation unit 213 will be described with reference to FIGS. 5 and 6, taking as an example a case where processing is performed on a fringe image captured by two-frequency addition that adds a long-period wave and a short-period wave. explain.

The diagram shown in FIG. 5 (a) irradiates the steel sheet S with a laser beam modulated by adding a short period wave with a frequency ω ₁ and a long period wave with a frequency ω ₂ having a longer period than the short period wave. It is an example of the fringe image obtained in this way. When one line of the input image of the fringe image is taken out, a signal shown in FIG. 5B is obtained.

FIG. 6 shows an outline of the signal processing operation in the phase calculation unit 213 according to the present embodiment. The signal obtained by the two-frequency addition shown in FIG. 5B is input to the short cycle signal processing unit 221 and the long cycle signal processing unit 223. The short-period signal processing unit 221 multiplies the input signal by the real part (Re) and imaginary part (Im) of the complex carrier having the same frequency ω ₁ as the short-period wave, and the multiplication result is a low-pass filter. Input to (LPF) 225. Further, the short cycle signal processing unit 221 inputs the output from the low-pass filter 225 to the coordinate conversion unit 227, performs coordinate conversion, and calculates the amplitude r1 and the phase θ1 of the short cycle signal. The phase amount obtained by the phase θ1 of the short-period signal, and the magnitude of the phase amount reflects the surface shape of the steel sheet S as the measurement object with high accuracy and corresponds to, for example, the depth of the step.

The long-cycle signal processing unit 223 is similar to the short-cycle signal processing unit 221 in that the real part (Re) and imaginary part (Im) of the complex carrier having the same frequency ω ₂ as the long-period wave with respect to the input signal. , The multiplication result is input to the low pass filter 229. Further, the long cycle signal processing unit 223 inputs the output from the low pass filter 229 to the coordinate conversion unit 231 to perform coordinate conversion, and calculates the amplitude r2 and the phase θ2 of the long cycle signal. The obtained phase θ2 shows a rough surface shape, and in this example, as will be described below, the phase connection unit 215 uses the phase θ1 of the short-period wave to correctly connect the phase θ2.

Here, the signal processing shown in FIG. 6 will be described using a general formula. The short-period waves and cosine waves of frequency omega _1, the long period waves and cosine waves of frequency omega _2, a displacement of the fringes and dx. In this case, the short period wave and the long period wave are respectively expressed as follows.

Here, when the short-period wave and the long-period wave described above are simply added, the observed waveform I _add is expressed as the following Expression 1.

Here, the reason why 2 is added in the above formula 1 is to satisfy the condition that the light intensity never becomes negative. Furthermore, since the complex carrier C for calculating the phase of the short-period wave is C = exp (jω ₁ x), in the case of simple addition, I _add × C, which is the result obtained by multiplying the complex carrier, is The following equation 2 is obtained.

As described above, when the multiplication result is expressed as a sum of components, the direct current component + (ω ₁ −ω ₂ ) + ω ₁ + (ω ₁ + ω ₂ ) + 2ω ₁ is obtained.

FIG. 7 shows, in the spectral domain, a process in which the short period signal processing unit 221 shown in FIG. 6 takes out the frequency ω ₁ of the short period wave with a low pass filter. FIG. 7A shows the spectrum of the signal of one line of the fringe image. Spectra of one line of the signal of the fringe image includes a component ± omega ₁ complex frequency short period waves, the component ± omega ₂ of the complex frequency of the long cycle signal, a DC component, a. This DC component is the result of applying a bias so that the sign of the signal is always positive because the observed brightness has only a positive value.

Next, as shown in FIG. 7B, the short period signal processing unit 221 multiplies the sine wave C having the complex frequency component ω ₁ of the short period wave. moving only ω ₁ in. By passing the result through a low-pass filter, the short-period signal processing unit 221 can extract the short-period wave component ω ₁ before the complex carrier multiplication. However, looking at the passband of the low-pass filter shown in FIG. 7B, the component of ω ₁ −ω ₂ is in the passband of the low-pass filter. That is, with this low-pass filter, it is not possible to extract only the short-period wave component ω ₁ before the complex carrier multiplication, and the component ω ₁ −ω ₂ is included.

This effect will be described with reference to FIG. FIG. 8 is a vector diagram of the signal after passing through the low-pass filter. The vector v0, which is a zero-frequency component on the real axis, corresponds to the short-period wave component ω1 before complex carrier multiplication, and this component does not vary. However, since the frequency of the ω ₁ −ω ₂ component is not zero, the corresponding vector v2 rotates on the vector diagram. Since the observed vector is the vector v1, which is the sum of the vector v0 and the vector v2, when the vector v2 rotates, the vector v1 changes and its phase (the angle of the vector v1) also changes. As a result, an error occurs in the phase calculation processing by the phase calculation unit 213.

  As described above, a low-pass filter is used to separate a signal with a long and short cycle from one image, but depending on the low-pass filter used, necessary information may not be separated. However, as shown in FIG. 9, necessary information can be obtained by narrowing the bandwidth of the low-pass filter. As a result, only a short-period wave frequency can be extracted, although a slight burden is imposed on the arithmetic processing. The phase calculation unit 213 according to the present embodiment uses a low-pass filter having a narrow pass band through which only a short period wave can pass.

  The phase calculation unit 213 according to the present embodiment transmits the phases θ1 and θ2 calculated in this way to the phase connection unit 215 described later. Further, the phase calculation unit 213 preferably transmits the calculated amplitudes r1 and r2 to the phase connection unit 215.

  The phase connection unit 215 is realized by, for example, a CPU, a ROM, a RAM, and the like. The phase connecting unit 215 performs processing for connecting the phases so that the phase transmitted from the phase calculating unit 213 accurately corresponds to information on the surface shape such as the depth of the step.

  Since the phase of the short-period wave calculated by the phase calculation unit 213 as described above is calculated using an inverse trigonometric function (more specifically, arctan) by the coordinate conversion unit, it is −π to π. Takes values up to. However, if the phase changes by more than π or -π in the corresponding phase, such as the depth of the step, the calculation result is obtained even though it actually has a phase of ± π or more. , From −π to π. As a result, the phase calculated by the phase calculation unit 213 changes discontinuously as shown in the upper part of FIG.

  Therefore, the phase connecting unit 215 performs a process of connecting the phases so that the phase transmitted from the phase calculating unit 213 accurately corresponds to the surface shape information such as the depth of the step. As a result, for example, the phase that changes discontinuously as shown in the upper part of FIG. 10 becomes a phase that represents an actual phase change as shown in the lower part of FIG. The phase connecting unit 215 transmits the phase after the phase connecting process to the shape specifying unit 217 described later.

  The phase connection process performed by the phase connection unit 215 will be described in detail later.

  The shape specifying unit 217 is realized by, for example, a CPU, a ROM, a RAM, and the like. Based on the phase after the phase connection process transmitted from the phase connecting unit 215, the shape specifying unit 217 calculates the depth d of the dent existing on the surface of the measuring object, and specifies the shape of the measuring object.

  Here, when the imaging resolution in the column direction of the photoelectric conversion elements in the TDI camera 105 is s (mm / pixel) and the incident angle of the linear laser light L is θ, the reflection point of the linear laser light L is in the longitudinal direction. The shifted distance h = d · tan θ corresponds to h / s pixels in the striped image. When the ratio between the camera shift frequency of the TDI camera 105 and the modulation frequency of the laser beam is M: 1, M pixels in the horizontal direction form one stripe in the stripe image. That is, when the fringes are shifted by M pixels, the phase shift is 2π. Therefore, the phase shift Δφ in the fringe image data when the reflection point of the linear laser beam L is shifted by the distance h in the longitudinal direction is expressed by the following formula 3 from the relationship M / 2π = (h / s) / Δφ. It becomes like this.

  d = {M · s / (2π · tan θ)} · Δφ (Expression 3)

  Therefore, the shape specifying unit 217 sets the setting value of the object imaging device 100 such as the imaging resolution of the TDI camera 105 and the incident angle θ of the linear laser light L, the frequency ratio M acquired from the timing signal generating unit 201, and the phase connection. Using the phase φ transmitted from the unit 215 and the above equation 3, the depth d of the dent existing on the surface of the measurement object can be calculated.

  Strictly speaking, when a normal lens is used, the imaging resolution s changes according to the depth d, and thus correction is necessary. However, as in the case of measuring the dent of the steel plate, the lens working distance is not affected. When the depth change is very small, the change in the imaging resolution s can be ignored in practice. If a telecentric lens is used, the imaging resolution s can be made constant regardless of the depth d.

  When the calculation of the depth of the dent existing on the surface of the measurement object is completed, the shape specifying unit 217 transmits a calculation result representing the shape of the measurement object to the display unit 205.

[Modification of Arithmetic Processing Unit]
The configuration of the image processing unit 203 according to the present embodiment has been described in detail above.
Note that the arithmetic processing device 200 according to the present embodiment described above can measure a deep step that cannot be measured by a conventional method with high accuracy by using a narrow-band low-pass filter. However, when the measurement object has an inclination, a change in phase difference increases according to the inclination, and a desired phase may not be extracted well.

  FIG. 11 is an explanatory diagram for explaining that the frequency changes depending on whether the measurement object is flat or tilted. The projection light L from the laser light source is incident on the flat measurement object p1, and the periodic signal s1 is obtained. Here, when the measurement target is tilted, when the projection light L from the laser light source is incident on the tilted measurement target p2 using the same measurement apparatus, the displacement amount of the periodic pattern changes depending on the location. Therefore, as shown in FIG. 11, the frequency of the obtained periodic signal s2 changes compared to the case where it is incident on the flat measurement object p1. This result is the same in the method of projecting the fringe pattern.

When the measurement object is tilted as shown in FIG. 11, the fringe displacement dx can be expressed as dx = αx (α is a proportional constant) using the position x. Therefore, in the case of simple addition, the observed waveform formula I _add is expressed by the following formula 4. As is apparent from the following Equation 4, the frequencies ω ₁ and ω ₂ are multiplied by (1 + α) due to the presence of the slope.

  The spectrum of this observed waveform is shown in FIG. It can be seen that the frequency is (1 + α) times compared to the spectrum of the observed waveform in the flat case shown in FIG. FIG. 12B shows a process in which this signal is processed by the image processing unit 203 and passed through the narrow band low pass filter shown in FIG. As can be seen from FIG. 12B, in the low pass filter having a narrow pass band as shown in FIG. 9, the short pass wave is not included in the pass band of the filter, and the short pass wave component cannot be extracted.

  As described above, when the periodic pattern is configured by simple addition of a short period and a long period, if the object to be measured is flat, a low-pass filter with a narrow pass band can be used to create a deep step. Even if it exists, the depth of the step can be measured. However, when the measurement object is inclined, the depth of the step may not be accurately obtained.

  Below, the modification of the arithmetic processing apparatus 200 which concerns on this embodiment which can measure the depth of a level | step difference correctly, without using a low-pass filter of a narrow band is demonstrated. The arithmetic processing unit according to the present modification performs amplitude modulation (AM modulation) on the short period wave and superimposes the long period signal.

  First, as shown in FIG. 13A, a linear laser beam L that has been AM-modulated by the timing signal generator 201 is irradiated onto a moving steel plate S that is a measurement object, and is imaged by a TDI camera 105. A striped image is obtained from the processed image. The waveform for one line of the fringe image is shown in FIG. FIG. 13B shows a waveform when one line x of the stripe image of FIG. 13A is extracted. Here, the short period wave is 1/4 (0.25 times) the sampling frequency, and the long period wave is 1/16 (0.0625 times) the sampling frequency. That is, the period of the long period wave is four times that of the short period wave.

FIG. 14 shows an outline of the signal processing operation in the phase calculation unit 213 included in the image processing unit 203 of the arithmetic processing device 200 according to this modification. First, the signal shown in FIG. 13B is input to the short period signal processing unit 221 of the phase calculation unit 213. The short-period signal processing unit 221 multiplies the input signal by the real part (Re) and imaginary part (Im) of a complex carrier having the same frequency ω ₁ as the short-period wave, and the multiplication result is a low-pass filter. Input to (LPF) 225. Further, the short cycle signal processing unit 221 inputs the output from the low-pass filter 225 to the coordinate conversion unit 227, performs coordinate conversion, and calculates the phase θ1 and the amplitude r1 of the short cycle wave. The obtained phase θ1 is the phase of the short period wave, and is information reflecting the surface shape with high accuracy.

The amplitude r1 obtained by the short cycle signal processing unit 221 is input to the long cycle signal processing unit 223 of the phase calculation unit 213. Since the calculated amplitude r1 changes periodically with the frequency ω ₂ of the long-period wave, the long-cycle signal processing unit 223 has the same frequency ω _{2 as the} long-period wave with respect to the input phase r1. Multiplying the real part (Re) and imaginary part (Im) of the complex carrier having, and the multiplication result is input to the low-pass filter 229. Further, the long cycle signal processing unit 223 inputs the output from the low pass filter 229 to the coordinate conversion unit 231 to perform coordinate conversion, and calculates the amplitude r2 and the phase θ2 of the long cycle signal. The obtained phase θ2 is a rough indication of the surface shape of the steel sheet S that is the object to be measured, and is used by the phase connecting portion 215 to correctly connect the phase θ1 of the short period wave.

Here, the signal processing shown in FIG. 14 will be described using a general formula. The AM-modulated observation waveform I _am is expressed as the following Expression 5. Here, in the following formula 5, A is a parameter representing the degree of modulation, and takes a value of 0 to 1.

Here, the reason why 2 is added in the above formula 5 is to satisfy the condition that the light intensity never becomes negative. Furthermore, since the complex carrier C when calculating the phase of the short-period wave is C = exp (jω ₁ x), I _am × C, which is the result obtained by multiplying the complex carrier, is given by become that way.

As described above, when the multiplication result is expressed as a sum of components, −ω ₂ + DC component + ω ₂ + ω ₁ + (2ω ₁ −ω ₂ ) + 2ω ₁ + (2ω ₁ + ω ₂ ) is obtained.

FIG. 15 shows the spectrum of the signal of one line of the fringe image. FIG. 15A shows the spectrum of the observed waveform I _am that has undergone AM modulation. Here, the direct current component is a result of applying a bias so that the obtained signal does not become negative because the intensity of the observation light does not become negative.

As a result of AM modulation, sidebands appear on both sides of the short-period wave, separated by the long-period wave frequency (0.625). FIG. 15B shows the result of multiplying the complex carrier C. The spectrum shown in FIG. 15B is shifted to the right by 0.25 from the spectrum shown in FIG. At this time, ± ω ₂ components are included in the passband of the low-pass filter, but unlike the case of simple addition, these appear symmetrically at the origin.

FIG. 16 is a vector diagram of signals in the low-pass filter passband. The zero-frequency component on the real axis, that is, the phase θ1 of the short period wave does not change. In addition, although the component ± ω ₂ of the long-period wave oscillates, it is considered to be a vector rotating in the opposite direction, so that they cancel each other and do not affect the phase θ 1 of the short-period wave. Therefore, the image processing unit 203 according to the present modification can determine the phase θ1 of the main carrier without using a narrow-band low-pass filter.

Here, the amplitude r1 is the rotation of components ± omega ₂ vector long period waves, expands and contracts. That is, the amplitude r1 obtained by the short period signal processing unit 221 periodically varies at the frequency ω ₂ of the long period wave. Therefore, the processing for obtaining the phase of the signal r1 is performed by the long period signal processing unit 223 as described above. Similarly to the short cycle signal processing unit 221, the long cycle signal processing unit 223 multiplies a sine wave having the same frequency as the long cycle wave, and inputs the obtained multiplication result to the low pass filter 229. Further, the long cycle signal processing unit 223 can perform coordinate conversion on the output from the low pass filter 229 to obtain the phase θ2 of the long cycle signal. In this case, this corresponds to extracting the phase of a single sine wave. Therefore, in this process, a low-pass filter having a normal pass region is used instead of a narrow-band filter in this modification. It is possible to use. A low-pass filter having a normal pass region can be configured at low cost, and the amount of calculation required for processing can be reduced.

  The phase calculation unit 213 according to the present modification transmits the phases θ1 and θ2 calculated in this way to the phase connection unit 215. Further, the phase calculation unit 213 preferably transmits the calculated amplitudes r1 and r2 to the phase connection unit 215.

  Similarly to the phase connection unit 215 according to the first embodiment, the phase connection unit 215 according to the present modification uses the phase transmitted from the phase calculation unit 213 based on the phase connection process described in detail later. Then, phase connection processing is performed so as to accurately correspond to information on the surface shape such as the depth of the step.

  As described above, in the arithmetic processing device 200 according to the present modification, by using the amplitude-modulated laser beam, the depth of the step can be accurately measured even when the measurement target is tilted. is there.

  Heretofore, an example of the function of the arithmetic processing apparatus 200 according to the present embodiment has been shown. Each component described above may be configured using a general-purpose member or circuit, or may be configured by hardware specialized for the function of each component. In addition, the CPU or the like may perform all functions of each component. Therefore, it is possible to appropriately change the configuration to be used according to the technical level at the time of carrying out the present embodiment.

  A computer program for realizing each function of the arithmetic processing apparatus according to the present embodiment as described above can be produced and installed in a personal computer or the like. In addition, a computer-readable recording medium storing such a computer program can be provided. The recording medium is, for example, a magnetic disk, an optical disk, a magneto-optical disk, a flash memory, or the like. Further, the above computer program may be distributed via a network, for example, without using a recording medium.

<Overall flow of shape measurement method>
Next, the overall flow of the shape measuring method performed by the shape measuring apparatus according to the present embodiment will be described in detail with reference to FIG. FIG. 17 is a flowchart for explaining the overall flow of the shape measuring method according to the present embodiment.

  First, the object imaging apparatus 100 provided in the shape measuring apparatus 10 according to the present embodiment images a moving object (for example, a steel plate S) irradiated with the linear laser light L with the TDI camera 105. The image processing unit 203 (more specifically, the signal acquisition unit 211) of the arithmetic processing device 200 provided in the shape measuring apparatus 10 acquires a signal corresponding to the captured image captured by the TDI camera 105, and acquires one sheet. A fringe image is generated (step S11). Thereafter, the signal acquisition unit 211 transmits the generated fringe image signal to the phase calculation unit 213.

  The phase calculation unit 213 of the arithmetic processing device 200 performs signal processing as shown in FIG. 6 or 14 on the fringe image signal transmitted from the signal acquisition unit 211, and the short period wave included in the signal and The amplitude and phase of the long period wave are calculated (step S13). The phase calculation unit 213 transmits the calculated short period wave and the phase of the long period wave to the phase connection unit 215.

  The phase connection unit 215 of the arithmetic processing device 200 performs the phase connection process of the short period wave using the phase of the long period wave based on the phase transmitted from the phase calculation unit 213 (step S15). This phase connection process will be described in detail later. The phase connection unit 215 transmits the phase of the short-period wave after connection to the shape specifying unit 217.

  The shape specifying unit 217 of the arithmetic processing device 200 uses the equation 3 described above to determine the depth of the step existing in the moving object, using the phase of the short-period wave after connection transmitted from the phase connection unit 215. (Step S17). Thereby, the arithmetic processing apparatus 200 can measure the shape (surface shape) of moving objects, such as a measured steel plate, with high precision.

<About phase connection processing>
Next, the phase connection process performed in the arithmetic processing device 200 according to the present embodiment (more specifically, the phase connection unit 215) will be described in detail with reference to FIGS.

[Outline of phase connection processing]
First, an outline of the phase connection process will be described with reference to FIGS. 18 and 19. 18 and 19 are explanatory diagrams for describing the phase connection processing.

  The phase connection processing performed by the phase connection unit 215 is performed by observing the observed phase (this is a value in the range of −π to π regardless of the true phase size as shown in the upper part of FIG. 10. Is used to determine the true phase gradient (that is, the difference between the true phases at positions adjacent to each other in the fringe image).

In the following description, for example, in the striped image as shown in FIG. 2, two coordinate axes i and j are considered for the sake of convenience in order to specify the positions of the pixels constituting the strip. Here, the coordinate axis i and the coordinate axis j are axes orthogonal to each other. For example, in the striped image as shown in FIG. 2, one of the vertical direction and the horizontal direction can be the coordinate axis i, and the other can be the coordinate axis j. In the following description, the notations i and j are also used as parameters representing positions on the coordinate axes.

In the following description, an actually observed phase (hereinafter also referred to as an observed phase) is represented as ψ _{i, j} (−π ≦ ψ _{i, j} <π), and the true value to be obtained by the phase connection process. _Is expressed as φ _{i, j} . Further, two types of differences Δx _{i, j} and Δy _{i, j} of the observation phase ψ _{i, j} are defined as in the following Expression 101 and Expression 102.

Δx _{i, j} = R (ψ _{i + 1, j} −ψ _{i, j} ) (Equation 101)
Δy _{i, j} = R (ψ _{i, j + 1} −ψ _{i, j} ) (Formula 102)

  Here, in the above formulas 101 and 102, R (•) is obtained by adding or subtracting an integer multiple of 2π to the substituted value, and setting the value within the range [−π, π) (−π or more and less than π). ). For example, when (−4π / 3) is substituted for R (•), R (−4π / 3) = (2π / 3) is output.

Note that in the following description, the suffixes _{i and j in} the notation ψ _{i, j} , φ _{i, j} , Δx _{i, j} , and Δy _{i, j} may be omitted.

○ Relationship between observation phase ψ _{i, j} and true phase φ _{i, j As} described above, the phase connection processing performed in phase connection unit 215 is true based on observation phase ψ _{i, j.} This is a process for determining the difference between the phases φ _{i, j} . In performing this process, a condition for determining whether or not the calculated true phase φ _{i, j} is a correct value is necessary. This condition is that “there is no noise in the observation phase ψ, and the absolute value of the phase difference between adjacent positions is smaller than π with respect to the true phase φ”. When this condition is satisfied, Δx and Δy, which are the differences in the observation phase ψ, are respectively equal to the X-direction difference and the Y-direction difference of the true phase φ.

For example, consider the case where the calculated true phase φ _{i, j} is equal to the observed phase ψ _{i, j} as shown on the upper side of FIG. At this time, it is assumed that the observation phase ψ _{i, j + 1 of} the position (i, j + 1) adjacent to the position (i, j) along the j direction is ψ _{i, j + 1} = φ _{i, j} + α-2π. As is apparent from FIG. 18, the difference in the observation phase ψ along the j direction is ψ _{i, j + 1} −ψ _{i, j} = α−2π. Therefore, Δy _{i, j} = R (ψ _{i, j + 1} −ψ _{i, j} ) = α.

Here, if α is a value smaller than π, Δyi, j is equal to the true phase difference in the Y direction under the conditions described above. As shown in the lower side of FIG. , J + 1), the true phase φ _{i, j + 1} is φ _{i, j + 1} = φ _{i, j} + α.

  Therefore, the phase connection unit 215 can obtain the true phase φ by integrating the differences starting from an arbitrary point and using the conditions described above.

However, when there is noise in the observation phase ψ, there may be no true phase φ whose difference matches the calculated Δx, Δy. For example, suppose i × j = 3 × 3 lattice points, the observation phase ψ at each j is as shown on the left side of FIG. 19, and noise is present at the center i = 2 and j = 2 of the lattice points. Suppose that exists. It is assumed that the observation phase ψ _{2,2 at} i = 2 and j = ₂ has a large negative value due to the presence of this noise.

Here, when ψ _2,2 −ψ _1,2 is a negative value larger than −π, Δx _1,2 is negative. In addition, ψ _3,2 −ψ _2,2 is a positive value larger than + π, and Δx _2,2 is also negative. In this way, Δx and Δy are calculated and the gradient direction is illustrated as shown on the right side of FIG. As is apparent from the figure, when the integration path (order) performed by the phase connection unit 215 changes, the integration value becomes a positive value or a negative value. The value of the phase φ will be different.

Therefore, if there is noise in the observed phase, the phase connection unit 215 cannot calculate the true phase φ such that the difference between Δx _{i, j} and Δy _{i, j} matches at all positions. In order to calculate the phase φ, the least square method, which is a process for minimizing the difference error, is performed.

○ Phase connection processing using weightless least square method In the phase connection unit 215 according to the present embodiment, the observation phase is connected using the weighted least square method, and the phase connection using the weighted least square method is used. Prior to explaining the processing, the phase connection processing using the weightless least square method, which is the basis of the weighted least square method, will be described first.

In order to minimize the difference error, a function expressed by the difference between the value to be obtained and the observed value is generated, with the value to be obtained as a variable and the observed value as a constant, and this function is minimized. You should think about becoming. Therefore, when performing the phase connection process using the weightless least square method _, the difference of the true phase φ _{i, j} that is the value to be obtained is used as a variable, and the observed phase ψ _{i, j} that is the observed value is You can think of a function with the difference as a constant. Here, as a function represented by a difference between a value to be obtained and an observed value, a function J using a square sum of differences represented by the following Expression 11 is used. Hereinafter, this function J will be referred to as an evaluation function J.

As is apparent from the right side of Equation 11 above, the first term on the right side is the true phase difference (φ _{i + 1, j} −φ _{i, j} ) treated as a variable and Δx which is an observation phase treated as a constant. It is the square of the difference between _{i and j} (that is, the error between the true phase difference and the observed phase difference). Similarly, the second term on the right side is the square of the difference between the true phase difference (φ _{i, j + 1} −φ _{i, j} ) treated as a variable and Δy _{i, j} which is the observation phase. Further, the summation in the above equation 11 is performed for all lattice points (i, j).

  As is clear from Expression 11, the evaluation function J is a function that always takes a value of 0 or more, and this evaluation function J is minimum (that is, J = 0) that all the lattice points (i, j) When the true phase difference coincides with the observed phase difference. Therefore, by obtaining the value of a variable that minimizes the value of the evaluation function J, it is possible to obtain the true phase φ difference that correctly reflects the actual observation phase difference.

  In the above equation 11, the evaluation function J is expressed in the form of a difference, but this evaluation function J can also be expressed in the form of integration. In this case, the evaluation function J is expressed as the following Expression 12.

Here, in the above equation 12, φ _x and Δ _x are the x-direction derivative of the true phase to be obtained and the x-direction derivative of the difference between the observed phases, respectively, and φ _y and Δ _y are the true _values to be obtained, respectively. Y-direction differentiation of the phase and the y-direction differentiation of the difference between the observation phases.

  When the evaluation function J is expressed in an integral form, the process of obtaining the variable to be minimized in Expression 12 results in a problem of obtaining the unknown function φ (x, y) using a variational method. The evaluation function J is a function that always takes a positive value because it is expressed as the sum of squares of the difference, and the processing using this variation method is performed with respect to a minute change of the unknown function φ (x, y). This results in a problem of obtaining φ (x, y) at which the fluctuation amount of the evaluation function J becomes zero. If this problem is expressed by a mathematical expression, the Euler-Lagrange equation shown in the following Expression 13 is obtained. Therefore, the problem of obtaining a variable that minimizes the Expression 12 is eventually expressed by the following Expression 14. This results in a Poisson equation.

Here, in the above equation 14, φ _xx and Δ _xx are second-order derivatives of the true phase φ and the difference Δ of the observation phase Δ by the variable x, and φ _yy and Δ _yy are the true phase φ, respectively. And second-order differentiation of the observation phase difference Δ by the variable y. When these second-order derivatives are expressed in the form of differences, the following equations 15 to 18 are obtained.

φ _xx : (φ _{i + 1, j} −φ _{i, j} ) − (φ _{i, j} −φ _{i−1, j} ) (Equation 15)
φ _yy : (φ _{i, j + 1} −φ _{i, j} ) − (φ _{i, j} −φ _{i, j−1} ) (Expression 16)
Δ _xx : Δx _{i, j} −Δx _{i−1, j} (Expression 17)
Δ _yy : Δy _{i, j} −Δy _{i−1, j} (Expression 18)

Therefore, when the Poisson equation represented by the equation 14 is expressed in the form of a difference, the following equation 19 is obtained. In order to find a solution of this equation, it is only necessary to solve the simultaneous equations for all φ _{i, j.} Become.

φ _{i + 1, j} + φ _{i−1, j} + φ _{i, j + 1} + φ _{i, j−1} −4φ _{i, j}
= Δx _{i, j} −Δx _{i−1, j} + Δy _{i, j} −Δy _{i, j−1} (Equation 19)

  Here, as a method for solving the simultaneous equations represented by Equation 19, for example, a so-called iterative method or a direct method can be used. Examples of the iterative method include a Jacobi method, a Gauss-Seidel method, a successive over relaxation (SOR) method, and a conjugate gradient method (Conjugate Gradient Method). Moreover, LU decomposition (Lower-Upper decomposition) etc. can be mentioned as an example of a direct method. Note that these methods are merely examples, and solutions other than those described above can be used as appropriate. Further, in the following description, a case where the simultaneous equations represented by Expression 19 are solved using an iterative method will be described, but the present invention is not limited to such a case.

Here, consider a case where the simultaneous equations represented by the above equation 19 are solved by an iterative operation using the Gauss-Seidel method. Assuming that the unknown function φ _{i, j} in the k-th iteration is expressed as φ _{i, j} (k), in the iterative operation in the Gauss-Seidel method, the subscript includes i−1 or j−1. Can use the (k + 1) -th value. Therefore, when solving the equation 19 using the Gauss-Seidel method, the equation 19 can be transformed into the following equation 20.

When solving Equation 20, if the number of lattice points in the X direction is Nx, i = 1 to Nx, and if the number of lattice points in the Y direction is Ny, j = 1 to Ny, so the boundary (ie, i = 1 or It is necessary to consider the handling of values outside the boundary necessary for the calculation of i = Nx or j = 1 or j = Ny), that is, φ _0,1, φ _{Nx + 1,1 and the} like. As the handling of the boundary, it is preferable to use any one of the following conditions 1) or 2).

1) At the boundary, the phase slope is zero.
φ _0,1 = φ _1,1 = φ _0,1 , Δx _0,1 = Δy _1,0 = 0, etc. 2) The following symmetry holds at the boundary.
φ _0,1 = φ _2,1 , φ _1,0 = φ _1,2 , Δx _0,1 = −Δx _1,1 , Δy _1,0 = −Δy _1,1

By solving Equation 20 using such conditions, the true phase φ _{i, j} can be calculated in a lump.

○ Phase connection processing using the weighted least squares method The phase connection processing using the weightless least squares method described above, but there are steps on the surface of the measurement object. The location where the condition that the absolute value of the phase difference between adjacent positions is smaller than π is not satisfied, or there are black parts such as dirt on the surface of the object to be measured, which are partially striped. When there is a place where an image cannot be acquired (that is, a portion where the noise component of the phase is large), an error occurs in the connected phase around the place. Therefore, the phase connection unit 215 according to the present embodiment performs a phase connection process using a weighted least square method as described below, so that even in a place where an error occurs in the phase as described above, The true phase can be calculated with high accuracy.

  For example, consider a measurement object such as a steel plate as shown in FIG. A cut as shown in FIG. 20A is present at one end of the measurement object, and the measurement object has a region that warps upward (region A) and a region that warps downward (region). B) exist. The phase image in such a case (for example, a grayscale image in which the image becomes white when the phase is + π and the image becomes black when the phase is −π), as shown in FIG. And at the left end where the region B is connected, the images are displayed with similar darkness. In the region A, the darkness decreases as it goes to the right end, and in the region B, the darkness increases as it goes to the right end. Presumed to be.

  In order to be able to calculate the phase as shown in FIG. 20B, the phase connection unit 215 according to the present embodiment has a physical break as shown in FIG. A mathematical break as shown in FIG. 20C is introduced to the corresponding mathematical expression, and the place where the error occurs is excluded from the processing target area.

  In order to introduce the mathematical break as described above, the phase connecting unit 215 according to the present embodiment changes the evaluation function J described above to the following Expression 103.

  Here, in Expression 103 above, φ, Δx, and Δy are the same as in the case of the weightless least square method, and W (i, j) (0 ≦ W (i, j) ≦ 1) is the position (i , J). By changing the value of the weight W (i, j) for each position (i, j), the phase connecting unit 215 according to the present embodiment introduces a mathematical break for the evaluation function J. That is, the phase connection unit 215 calculates the value of the weight W (i, j) for a place where the condition regarding the absolute value of the phase difference is not satisfied due to the presence of a step or the like, or a place where the phase noise component is large. Within a range of 0, a positive value that is less than or equal to a predetermined value that can be regarded as almost 0 compared to 1 is set to a value close to 0, such as 0.001, and a normal location (location as described above) In the portion other than), the value of the weight W (i, j) is set to 1.

  By introducing such weights W (i, j), the expression of the evaluation function J that expresses the differential type (an expression that gives a discretized solution of the evaluation function J) is expressed by each lattice point as shown in Expression 104 below. The weight W (i, j) is applied.

The phase connection unit 215 according to the present embodiment, from the phase calculation unit 213, observes the long-period wave observation phase ψ (θ2 in FIG. 6 or FIG. 14) and the short-period wave observation phase ψ (θ1 in FIG. 6 or FIG. 14). These two types of observation phases are transmitted. Therefore, the phase connection unit 215 performs phase connection processing based on the weighted least square method shown in the above equation 104 for each of the observation phase ψ _{i, j} of the long period wave and the observation phase ψ _{i, j} of the short period wave. Do. In the following description, a case where the simultaneous equations represented by Expression 104 are solved using an iterative method will be described, but the present invention is not limited to such a case.

Hereinafter, the phase connection process performed by the phase connection unit 215 will be specifically described.
First, the phase connection unit 215 performs phase connection processing based on Expression 104 using the observation phase ψ _{i, j} of the long-period wave transmitted from the phase calculation unit 213. At this time, the phase connecting unit 215 performs the weighted least square method with the initial value of the true phase φ _{i, j} of the long-period wave as 0.

  Further, the phase connecting unit 215 uses the weight W (i, j) of each lattice point (i, j) of the long-period wave in Expression 104 as the amplitude of the long-period wave transmitted from the phase calculation unit 213 (FIG. 6 or It is set in advance based on r2) in FIG. For example, the phase connecting unit 215 refers to the amplitude r2 of the long-period wave at each lattice point (i, j) and determines whether or not the amplitude r2 is equal to or less than a predetermined threshold value thr1. When the amplitude r2 satisfies the above conditions, the phase connecting unit 215 determines that the corresponding lattice point (i, j) is a part to be excluded, and sets the value of the weight W (i, j) to 0. Set to a close value. Further, when the amplitude r2 does not satisfy the above condition, the phase connecting unit 215 determines that the corresponding lattice point (i, j) is not a part to be excluded, and the weight W (i, j) The value of 1 is assumed to be 1.

  Here, the phase connecting unit 215 may continuously change the weight W (i, j) according to the amplitude of the long-period wave, and the value 0 based on whether or not the above condition is satisfied. A value close to 1 or 1 may be used. When the value of the weight W (i, j) is set to a value close to 0 or a binary value of 1, the phase connection unit 215 sets the weight W (i, j) close to 0 when the above condition is satisfied. The weight W (i, j) is 1 when the condition is not satisfied.

Based on the weight W (i, j) determined in this way and the initial value of the true phase φ _{i, j} , the phase connecting unit 215 observes the observation phase ψ of the long-period wave transmitted from the phase calculating unit 213. The phase connection process of _{i, j} is performed, and the true phase φ _{i, j} of the long period wave is calculated.

When the phase connection process of the long period wave is completed, the phase connection unit 215 subsequently performs the phase connection process of the short period wave. Here, in the shape measuring apparatus 10 according to the present embodiment, the timing signal generator 201 modulates the period of the long period wave so that it is K times the period of the short period wave. As a result, since one cycle of the long period wave corresponds to the K period of the short period wave, a phase obtained by multiplying the phase of the long period wave after phase connection by K is the phase after connection of the short period wave under ideal conditions. (That is, the true phase φ to be obtained). Therefore, the phase connection unit 215 K times the true phase φ _{i, j} obtained by the phase connection process of the long period wave (phase connection process using the weighted least squares method) The initial value of the true phase φ _{i, j} is assumed. By setting the initial value of the phase in this way, it is possible to reduce the number of iterations rather than repeating the calculation by the iterative method from the initial value 0.

  Similarly to the case of the long-period wave, the phase connection unit 215 transmits the weight W (i, j) of each lattice point (i, j) of the short-period wave in Expression 104 from the phase calculation unit 213. It is set in advance based on the amplitude of the short-period wave (r1 in FIG. 6 or FIG. 14). For example, the phase connecting unit 215 refers to the amplitude r1 of the short period wave at each lattice point (i, j) and determines whether or not the amplitude r1 is equal to or less than a predetermined threshold value thr2. When the amplitude r1 satisfies the above conditions, the phase connecting unit 215 determines that the corresponding lattice point (i, j) is a part to be excluded, and sets the value of the weight W (i, j) to 0. Set to a close value. Further, when the amplitude r1 does not satisfy the above condition, the phase connecting unit 215 determines that the corresponding lattice point (i, j) is not a part to be excluded, and the weight W (i, j) The value of 1 is assumed to be 1.

  Here, as in the case of the long-period wave, the phase connection unit 215 may continuously change the weight W (i, j) according to the magnitude of the amplitude of the short-period wave. A value of either 0 or 1 may be used based on whether or not the above is satisfied.

In addition, the phase connection unit 215 not only determines the weight W (i, j) according to the amplitude of the short period wave, but also the true phase of the short period wave calculated based on the true phase of the long period wave. It is preferable to determine the weight W (i, j) according to the initial value of. For example, the phase connection unit 215 calculates a change in the initial value of the true phase of the calculated short period wave, and a portion where the change in the initial value of the phase is large (the change in the initial value of the phase is equal to or greater than a predetermined threshold value). Is identified). As a value representing a change in the initial value of the phase, for example, the sum of absolute values of differences between the phase at the lattice point (i, j) and the phase at the lattice point adjacent to the lattice point (i, j) | Φi _{+ 1, j−} φi _{, j} | + | φi _{, j + 1−} φi _{, j} | can be used.

  The phase of the long-period wave (true phase) reflects the outline of the surface shape of the measurement object. Therefore, a large change in the initial value calculated based on the true phase of the long-period wave suggests that there may be a large step or the like at the corresponding position (i, j). Yes. Therefore, the phase connection unit 215 sets the weight W (i, j) at a location where the change in the initial value of the phase is large to a value close to zero. Also in this case, the phase connection unit 215 may continuously change the weight W (i, j) according to the change of the initial value, and may be a value close to 0 or 1 depending on the relationship with the predetermined threshold value. It may be set to any of the values. As described above, the phase connection unit 215 determines the value of the weight W (i, j) in accordance with the change in the initial value of the phase as well as the amplitude of the short period wave, regarding the phase connection process of the short period wave.

  In addition, when calculating the weight W related to the short period wave, the phase connection unit 215 calculates the product W1 × the weight W1 calculated from the amplitude of the short period wave and the weight W2 calculated from the absolute value sum of the above differences. W2 may be used. In this case, the phase connection unit 215 sets the weight W (i, j) to a value close to 0 at a place where the amplitude of the short-period wave is small or a large step may exist, and otherwise In this case, the weight W (i, j) is set to 1.

The phase connection unit 215 determines the initial value and the weight W (i, j) of the short period wave as described above, performs the phase connection process by the weighted least square method based on Expression 104, and The true phase φ _{i, j} is calculated together. Since the true phase φi, j of the short-period wave calculated in this way is a phase to be obtained that represents the surface shape of the measurement object, the phase connecting unit 215 calculates the calculated short-period wave after connection. The phase φ is transmitted to the shape specifying unit 217.

Further, when the phase connection unit 215 solves the equation represented by Expression 104 using the iterative method, the phase φ _{i, j} obtained in the k-th iteration and the (k−1) -th iteration are obtained. The difference from the phase φ _{i, j} may be calculated, and when the calculated difference is equal to or less than a predetermined threshold, it is determined that the value of the phase φ _{i, j} has converged, and the iteration may be terminated. The phase connecting unit 215 may end the iteration regardless of whether or not the phase φ _{i, j} has converged after iterating the phase φ _{i, j by a} predetermined number of iterations. In this case, the upper limit of the number of iterations can be set in advance using various statistical processes.

By repeating until the value of the phase φ _{i, j} converges, the phase connecting unit 215 can calculate the phase φ _{i, j} to be obtained with extremely high accuracy. In addition, by setting an upper limit of the number of iterations in advance and ending the iteration regardless of convergence when the upper limit is exceeded, the cost required for computation can be made constant regardless of the input fringe image. . In addition, since the calculation time required for one phase connection process can be estimated, the shape measuring apparatus 10 according to the present embodiment can be used on the production line.

  When solving the equation 104, the method for solving the equation, the handling of the boundary, and the like are the same as the phase connection processing using the weightless least square method.

  Further, in the above description, a place where the condition regarding the absolute value of the phase difference is not satisfied due to the presence of a step or the like or a place where the phase noise component is large is specified based on the magnitude of the amplitude calculated by the phase calculation unit 213. Although the case has been described, the method for specifying such a place is not limited to the above-described method. For example, the phase connection unit 215 may identify the place as described above by differentiating the phase waveform of the long-period wave calculated by the phase calculation unit 213 and analyzing the obtained differential waveform. Further, the phase connecting unit 215 may specify the place as described above based on the pixel value of the captured image obtained by capturing the measurement object.

[Specific example of one-dimensional phase connection processing]
Next, with reference to FIGS. 21 and 22, the phase connection process using the weighted least square method according to the present embodiment will be described in detail using an example in which the observation phase and the true phase are one-dimensional. Explained. 21 and 22 are explanatory diagrams for describing a specific example of the phase connection processing according to the present embodiment.

  In the following, for comparison, both the case of using the unweighted least square method and the case of using the weighted least square method will be described.

Calculation Conditions Here, it is assumed that the actual phases (correct phases) φ1 to φ5 and the observation phases φ1 to φ5 have the following values as shown in FIG.

[Φ1, φ2, φ3, φ4, φ5]
= [0, (2/3) π, (4/3) π, (6/3) π, (8/3) π]
[Ψ1, ψ2, ψ3, ψ4, ψ5]
= [0, (2/3) π,-(2/3) π, 0, (2/3) π]

  From the observation phases ψ1 to ψ5 described above, Δx1 to Δx4 are as follows.

[Δx1, Δx2, Δx3, Δx4]
= [(2/3) π, (2/3) π, (2/3) π, (2/3) π]

  In the boundary, the following conditions are given based on the condition 2) (symmetric condition) described above.

  φ0 = φ2, φ6 = φ4, Δx0 = −Δx1, Δx5 = −Δx4

In the case of the unweighted least square method From Equation 14 described above, the equation to be considered is φ _xx = Δ _xx . Therefore, in the case of this example, an expression that gives a discretized solution of the evaluation function J is as shown in Expression 21 below.

φ _{i + 1} + φ _i−1 −2φ _i = Δx _i −Δx _i−1 (Expression 21)

  Therefore, when the equation 21 is solved by an iterative method such as the Gauss-Seidel method, the iterative equation becomes the following equation 22.

φ _i (k + 1)
= (1/2) × (φ _{i + 1} (k) + φ _i−1 (k + 1) −Δx _i + Δx _i−1 )
... (Formula 22)

  In the case of this example, the above formula 22 is specifically written as follows.

φ1 (k + 1) = (1/2) (2φ2 (k) −2Δx1)
= Φ2 (k) − (2/3) π (Expression 23)
φ2 (k + 1) = (1/2) (φ1 (k + 1) + φ3 (k)) (Equation 24)
φ3 (k + 1) = (1/2) (φ2 (k + 1) + φ4 (k)) (Equation 25)
φ4 (k + 1) = (1/2) (φ3 (k + 1) + φ5 (k)) (Equation 26)
φ5 (k + 1) = (1/2) (2φ4 (k + 1) + 2Δx3)
= Φ4 (k + 1) + (2/3) π (Expression 27)

As an initial value of the true phase φ,
φ1 (0) = φ2 (0) = φ3 (0) = φ4 (0) = φ5 (0) = 0
Shall be given.

  When Expressions 23 to 27 were iteratively calculated based on the above initial values, φ1 to φ5 converged to the following values, respectively.

φ1 (∞) = − (5/3) π
φ2 (∞) = − π
φ3 (∞) = − (1/3) π
φ4 (∞) = (1/3) π
φ5 (∞) = π

  Comparing the convergence value with the actual phase φ value shows that the obtained convergence value is correct except for a constant. That is, when (5/3) π is uniformly added to the obtained convergence value, the value of the actual phase φ is obtained.

  As described above, in the phase connection process based on the Poisson equation as shown in Expression 14, the calculation is performed by giving only the difference between the observation phases as Δx1 to Δx4, and the obtained result is that the slope between the two points is Δx Since it converges to a value that matches, there is an arbitrary number of constants.

In the case of the weighted least square method In the example of the weighted least square method, it is assumed that there is a step at the position of φ3 and the calculation is performed. The weight W is assumed to be a binary value of 0 or 1. In this case, the weights W are W1 = W2 = W4 = W5 = 1 and W3 = 0. Further, in consideration of a symmetric condition with respect to the weight W, it is assumed that W0 = W1.

  In the case of this example, an expression that gives a discretized solution of the evaluation function J from Expression 104 is as follows.

W1 (φ2-φ1) −W0 (φ1-φ0) = W1Δx1-W0Δx0
→ φ2−φ1 = Δx1 (Formula 105)
W2 (φ3-φ2) −W1 (φ2-φ1) = W2Δx2-W1Δx1
→ φ3 + φ1-2φ2 = Δx2−Δx1 (Formula 106)
W3 (φ4-φ3) −W2 (φ3-φ2) = W3Δx3-W2Δx2
→ φ2−φ3 = −Δx2 (Formula 107)
W4 (φ5-φ4) −W3 (φ4-φ3) = W4Δx4-W3Δx3
→ φ5-φ4 = Δx4 (Formula 108)
W5 (φ6-φ5) −W4 (φ5-φ4) = W5Δx5-W4Δx4
→ φ4-φ5 = −Δx4 (Formula 109)

  As is clear from the above formulas 105 to 109, there are no variables φ4 and φ5 in formulas 105 to 107 relating to φ1 to φ3, and φ1 to φ3 in formulas 108 and 109 relating to φ4 and φ5. You can see that the variable does not exist. In this way, by setting the weight W3 = 0, the relationship between φ1 to φ3 and φ4 and φ5 is eliminated, and the processing target is divided into the regions φ1 to φ3 and the regions φ4 and φ5. be able to.

  Here, as initial values, φ1 = φ2 = φ3 = 0, φ4 = φ5 = 4π (that is, an initial value indicating that a height difference of 4π exists between φ3 and φ4), and iterative calculation is performed. The following convergence values were obtained. Further, the obtained convergence value is schematically shown in FIG.

φ1 (∞) = − π
φ2 (∞) = − (1/3) π
φ3 (∞) = (1/3) π
φ4 (∞) = (10/3) π
φ5 (∞) = 4π

  As is clear from FIG. 22, it can be seen that the difference between the phases coincides with (2/3) π, which is the difference between the given observation phases. Further, comparing φ1 to φ3 with φ4 and φ5, it can be seen that the phase difference between these two regions is about 4π. From this result, it is understood that when the phase connection process using the weighted least square method is performed, the step given by the initial value is preserved.

  In the phase connection processing by the phase connection unit 215 according to the present embodiment, when the phase of the short period wave is connected, the phase after the connection of the long period wave reflecting the outline of the surface shape of the measurement object is used. The initial value of the phase is generated. For this reason, in the phase connection process by the phase connection unit 215, an initial value including appropriate step information is set when the phase connection process of the short period wave is performed. Therefore, as is clear from the above specific example, the phase connection unit 215 appropriately selects the weight W and performs the phase connection process by the weighted least square method, thereby causing a large step or the like on the surface of the measurement object. Even if it exists, the phase connection can be performed accurately.

  Even in the phase connection process using the weighted least square method, the obtained calculation result has an arbitrary number of constants as in the case of the phase connection process using the weightless least square method. . However, if the reference phase magnitude (that is, the correct phase magnitude at a certain position) is known, the connected phase can be determined.

  As another method of combining the two frequencies, the values ΔxL and ΔyL corresponding to Δx and Δy of the short period wave are calculated from the difference between K times the phase after connection of the long period wave, and the short period wave Compared to the original Δx and Δy calculated from the observation phase ψ, it may be considered that ΔxL is used instead of Δx in a portion corresponding to a step (that is, a portion where Δx and ΔxL are far apart). However, in this case, the phase φ may not be smoothly connected at the switching point between ΔxL and Δx. Further, when the phase connection process is performed using the iterative method, if the value of Δx is large, it is necessary to set a large number of iterations, which may increase the time required for the phase connection process.

[Parallel processing of phase connection processing]
Next, parallel processing of the phase connection process performed by the phase connection unit 215 according to the present embodiment will be described with reference to FIG. FIG. 23 is an explanatory diagram for explaining parallel processing of the phase connection processing.

  Since the phase connection process performed by the phase connection unit 215 according to the present embodiment is not a sequential process as in the conventional phase connection process, the processing target area for performing the phase connection process is divided into several partial areas. By performing the processing, parallel processing of the phase connection processing can be realized.

  For example, as shown in FIG. 23, a case is considered in which a certain processing target region is processed in parallel by an iterative method (Gauss-Seidel method) using four processors. In this case, the phase connection unit 215 divides the processing target region into four, and causes one processor to perform the phase connection processing in each region. For example, as shown in the upper part of FIG. 23, the phase connection unit 215 causes the processor 1 to handle the upper left area A, causes the processor 2 to handle the upper right area B, and causes the processor 3 to handle the lower left area C. The processor 4 is in charge of the lower right area D.

  When the region to be processed is divided as shown in the lower part of FIG. 23 and the iterative process is performed by the Gauss-Seidel method, each processor repeats the grid point of interest and the grid point adjacent to this grid point. The phase connection process is performed using

  The processor 1 in charge of the area A can perform the phase connection process using only the repetition result of the grid points existing in the area A. However, the processor in charge of the other area needs to obtain the kth iteration result of the grid point adjacent to the grid point located at the boundary from the processor in charge of the area adjacent to its own area. Specifically, as shown in the lower part of FIG. 23, for the regions B to D, from the processor in charge of the regions located on the left side and the upper side of the lattice points located at the boundaries indicated by the oblique lines, Obtain the kth iteration result.

  At this time, in the (k + 1) -th iteration of the Gauss-Seidel iteration, the phase connection unit 215 strictly requests φ (k + 1) belonging to the adjacent region, but instead of φ (k + 1), φ (k + 1) k) is used to perform the phase connection process.

  Although it is a part of the area in charge, since the calculation is performed using φ (k) where φ (k + 1) should be originally calculated, there is a possibility that the convergence of the calculated value is slightly reduced. However, the number of grid points included in the entire processing target area is practically tens of thousands to several millions, and in the case of dividing into about 4 to 16, the decrease in convergence can be ignored.

  As described above, in the phase connection method according to the present embodiment, it is easy to divide the processing target area into several areas and allow a plurality of processors to perform parallel processing, and to increase the calculation speed of the plurality of processors. Can be easily realized.

  The phase connection process using the weighted least square method performed by the phase connection unit 215 according to the present embodiment has been described in detail above. Hereinafter, such a phase connection method will be described along an actual flow.

<Flow of phase connection method using weighted least square method>
First, the flow of the phase connection process using the weighted least square method performed by the phase connection unit 215 will be described in order with reference to FIG. FIG. 24 is a flowchart for explaining the phase connection method according to the present embodiment.

  First, the phase connection unit 215 determines the value of the weight W used for the phase connection process of the long period wave, as described above, based on the amplitude r2 of the long period wave transmitted from the phase calculation unit 213. (Step S101). Subsequently, the phase connecting unit 215 uses the calculated weight W to connect the phases of the long-period wave by the weighted least square method with the initial value of the true phase being 0 (step S103). Thereby, the phase connection part 215 can obtain the phase of the long-period wave after the connection in which the phases are correctly connected.

Subsequently, the phase connecting unit 215 calculates the initial value of the phase of the short period wave using the calculated phase of the long period wave and the period ratio K between the long period wave and the short period wave (step S105). ). More specifically, the phase connection unit 215 multiplies the calculated phase φ _{i, j} of the long-period wave by K to obtain an initial value of the phase of the short-period wave at the lattice point (i, j).

  Next, the phase connection unit 215 determines the phase of the short period wave based on the amplitude r1 of the short period wave transmitted from the phase calculation unit 213 and the initial value calculated using the phase after the connection of the long period wave. The value of the weight W used for the connection process is determined (step S107). More specifically, the phase connection unit 215 has a predetermined location where the amplitude r1 of the short-period wave satisfies a predetermined condition and a change in the initial value of the phase (for example, the sum of absolute values of the differences between the initial values of the phases). A place satisfying the condition is specified, and the value of the weight W corresponding to the place is set to a value close to 0, and set to 1 in other places.

  After that, the phase connecting unit 215 connects the phase of the short-period wave by the weighted least square method using the calculated initial value of the phase and the determined value of the weight W (step S109). Thereby, the phase connection part 215 can obtain the phase of the short-period wave after the connection in which the phases are correctly connected.

  In the above description, the case of determining the value of the weight W used for the phase connection process of the short period wave after calculating the initial value of the phase of the short period wave has been described. However, the phase connection method according to the present embodiment The order of the processes performed in is not limited to this order. For example, the initial value of the phase may be calculated after determining the value of the weight W used for the phase connection process of the short period wave, and the determination of the weight W and the calculation of the initial value of the phase are performed in parallel. You may go.

<Flow of parallel connection phase connection method>
Next, the flow of the phase connection method that has been parallelized will be described with reference to FIG. FIG. 25 is a flowchart for explaining the parallel connection phase connection method according to the present embodiment.

  When the phase connection process described above is performed in parallel processing, the phase connection unit 215 first sets initial values for all processing target areas to be subjected to the phase connection process in the procedure described above. Set (step S201). Subsequently, the phase connection unit 215 divides the processing target area into a plurality of areas in accordance with the number of processors available for the phase connection process, and determines a processor in charge of the phase connection process in each area. In addition, the phase connecting unit 215 calculates the weight W necessary for the phase connecting process in advance.

  Subsequently, the processor in charge of processing in each region acquires the boundary value in the kth iteration from the processor in charge of the region located on the left side and the upper side of the region in charge thereof (step S203). When the processor in charge of each region acquires the boundary value in the kth iteration, the processor performs phase connection processing of the assigned region for each processor, and calculates the phase value in the (k + 1) th iteration (step S205).

  Subsequently, each processor waits until all processors performing parallel processing finish the (k + 1) -th iterative operation (step S207). When the (k + 1) th iteration operation of all the processors is completed, each processor sets a parameter k representing the number of iterations to (k + 1) (step S209), and determines whether or not the predetermined number of iterations has been completed. (Step S211).

  If the iterative operation has not been performed for the predetermined number of iterations, each processor returns to step S203 again to perform the iterative operation. Further, when iterative calculations have been performed for a predetermined number of iterations, each processor ends the iterative calculation and outputs the calculation result at that time.

  By performing processing in such a flow, the phase connection unit 215 can perform parallel processing on the phase connection processing using the iterative method.

(About hardware configuration)
Next, the hardware configuration of the arithmetic processing apparatus 200 according to the embodiment of the present invention will be described in detail with reference to FIG. FIG. 26 is a block diagram for explaining the hardware configuration of the arithmetic processing apparatus 200 according to the embodiment of the present invention.

  The arithmetic processing device 200 mainly includes a CPU 901, a ROM 903, and a RAM 905. The arithmetic processing device 200 further includes a bus 907, an input device 909, an output device 911, a storage device 913, a drive 915, a connection port 917, and a communication device 919.

  The CPU 901 functions as an arithmetic processing device and a control device, and controls all or a part of the operation in the arithmetic processing device 200 according to various programs recorded in the ROM 903, the RAM 905, the storage device 913, or the removable recording medium 921. The ROM 903 stores programs used by the CPU 901, calculation parameters, and the like. The RAM 905 primarily stores programs used in the execution of the CPU 901, parameters that change as appropriate during the execution, and the like. These are connected to each other by a bus 907 constituted by an internal bus such as a CPU bus.

  The bus 907 is connected to an external bus such as a PCI (Peripheral Component Interconnect / Interface) bus via a bridge.

  The input device 909 is an operation unit operated by the user, such as a mouse, a keyboard, a touch panel, a button, a switch, and a lever. The input device 909 may be, for example, remote control means (so-called remote control) using infrared rays or other radio waves, or may be an external connection device 923 such as a PDA corresponding to the operation of the arithmetic processing device 200. May be. Furthermore, the input device 909 includes, for example, an input control circuit that generates an input signal based on information input by a user using the operation unit and outputs the input signal to the CPU 901. The user of the arithmetic processing device 200 can input various data and instruct processing operations to the arithmetic processing device 200 by operating the input device 909.

  The output device 911 is configured by a device that can notify the user of the acquired information visually or audibly. Examples of such devices include CRT display devices, liquid crystal display devices, plasma display devices, EL display devices and display devices such as lamps, audio output devices such as speakers and headphones, printer devices, mobile phones, and facsimiles. The output device 911 outputs results obtained by various processes performed by the arithmetic processing device 200, for example. Specifically, the display device displays results obtained by various processes performed by the arithmetic processing device 200 as text or images. On the other hand, the audio output device converts an audio signal composed of reproduced audio data, acoustic data, and the like into an analog signal and outputs the analog signal.

  The storage device 913 is a data storage device configured as an example of a storage unit of the arithmetic processing device 200. The storage device 913 includes, for example, a magnetic storage device such as an HDD (Hard Disk Drive), a semiconductor storage device, an optical storage device, or a magneto-optical storage device. The storage device 913 stores programs executed by the CPU 901, various data, various data acquired from the outside, and the like.

  The drive 915 is a recording medium reader / writer, and is built in or externally attached to the arithmetic processing unit 200. The drive 915 reads information recorded on a removable recording medium 921 such as a mounted magnetic disk, optical disk, magneto-optical disk, or semiconductor memory, and outputs the information to the RAM 905. The drive 915 can also write a record on a removable recording medium 921 such as a magnetic disk, an optical disk, a magneto-optical disk, or a semiconductor memory. The removable recording medium 921 is, for example, a CD medium, a DVD medium, a Blu-ray medium, or the like. The removable recording medium 921 may be a CompactFlash (registered trademark) (CompactFlash: CF), a flash memory, an SD memory card (Secure Digital memory card), or the like. Further, the removable recording medium 921 may be, for example, an IC card (Integrated Circuit card) on which a non-contact IC chip is mounted, an electronic device, or the like.

  The connection port 917 is a port for directly connecting a device to the arithmetic processing device 200. Examples of the connection port 917 include a USB (Universal Serial Bus) port, an IEEE 1394 port, a SCSI (Small Computer System Interface) port, and an RS-232C port. By connecting the external connection device 923 to the connection port 917, the arithmetic processing apparatus 200 acquires various data directly from the external connection device 923 or provides various data to the external connection device 923.

  The communication device 919 is a communication interface configured with, for example, a communication device for connecting to the communication network 925. The communication device 919 is, for example, a communication card for wired or wireless LAN (Local Area Network), Bluetooth (registered trademark), or WUSB (Wireless USB). The communication device 919 may be a router for optical communication, a router for ADSL (Asymmetric Digital Subscriber Line), or a modem for various communication. The communication device 919 can transmit and receive signals and the like according to a predetermined protocol such as TCP / IP, for example, with the Internet and other communication devices. The communication network 925 connected to the communication device 919 is configured by a wired or wireless network, and may be, for example, the Internet, a home LAN, infrared communication, radio wave communication, satellite communication, or the like. .

  Heretofore, an example of the hardware configuration capable of realizing the function of the arithmetic processing device 200 according to the embodiment of the present invention has been shown. Each component described above may be configured using a general-purpose member, or may be configured by hardware specialized for the function of each component. Therefore, it is possible to change the hardware configuration to be used as appropriate according to the technical level at the time of carrying out this embodiment.

(Example)
Hereinafter, the shape measuring apparatus and the shape measuring method according to the embodiment of the present invention will be described in detail with reference to examples. In addition, the Example shown below is an example of the shape measuring apparatus and shape measuring method which concern on embodiment of this invention to the last, Comprising: The shape measuring apparatus and shape measuring method which concern on this invention are limited to the following examples. Do not mean.

<Example 1>
First, a 256 × 256 point AM-modulated image having four short-period wave periods and 32 long-period wave periods is created, and a quarter portion (i and j are both 128 to 256) of this region. The artificial data in the case where a 5π plane is placed with a short period wave is generated. Therefore, in this artificial data, the cycle ratio K = 8. A phase connection process using the weighted least square method according to the present embodiment was performed on the artificial data. In this example, the weights of the least-squares method for long-period waves are all 1. Further, the weight of the short-period wave is the absolute value of the difference between the initial values of repetitions obtained by multiplying the phase after the connection of the long-period wave by 8 | φ _{i + 1, j} −φ _{i, j} | + | φ _{i, j + 1} The portion where −φ _{i, j} | exceeds 0.2π is set to 0.001, and the other portions are set to 1.

  For comparison, a phase connection process using the weighted least square method with only a short period wave was performed on the same input data. In this case, all the weights are set to 1, and the phase connection process using the least-square method with substantially no weight is used.

  The obtained results are shown in FIGS. 27 (a) and 27 (b). FIG. 27A shows the phase connection result when the phase connection processing is performed using only the short period wave, and FIG. 27B shows the present embodiment using the long period wave and the short period wave. It is a phase connection result at the time of performing the weighted least square method which concerns.

  As is clear from FIG. 27A, in the case of only a short period wave, the behavior is such that the height once becomes a negative value and then becomes a positive value in the vicinity of i = j = 128. It can be seen that the level difference of 5π cannot be accurately reproduced with respect to the level of. Conversely, when the phase connection processing according to the present embodiment is performed using the long period wave and the short period wave, it can be seen that a step of 5π (about 16) can be reproduced.

<Example 2>
Next, an example in which the phase connection process according to the present embodiment is performed on an actual steel plate will be described. The edge part (periphery) of this steel plate is covered with the adhesive tape, and the dent exists in the surface of the steel plate, and the paper is affixed.

  Moreover, the striped image of this steel plate was imaged using a TDI camera. The resolution of the TDI camera was 0.3 mm, the incident angle of the laser light source to the steel plate was 45 degrees, and the TDI camera was installed at a position perpendicular to the surface of the steel plate.

  In addition, the timing signal generator 201 sets the timing signal so that the period of the short period wave is a period corresponding to four pixels of the fringe image and the period of the long period wave is a period corresponding to 32 pixels of the fringe image. Was generated. That is, the ratio of the period of the long period wave to the short period wave was set to 8: 1.

  28A and 28B show a part of the fringe image actually obtained. In the coordinate axes shown in FIG. 28A, the x direction corresponds to the width direction of the steel plate, and the y direction corresponds to the conveyance direction of the steel plate. FIG. 28B is a graph obtained by cutting out the stripe image shown in FIG. 28A by one line along the y-axis. As is clear from FIG. 28B, it can be seen that the short period wave has a period corresponding to 4 pixels, and the long period wave has a period corresponding to 32 pixels.

  An image over the entire region of the steel sheet including the stripe image shown in FIG. 28A was processed using the arithmetic processing device 200 according to the present embodiment. FIG. 28C is an image (amplitude image) showing the behavior of the amplitude, generated using the amplitude of the short period wave calculated by the phase calculation unit 211. This amplitude image is an image in which the magnitude of the amplitude is represented by color shading. Note that a low frequency AM modulation component is superimposed on the amplitude image.

  As is clear from FIG. 28C, the image has a different color density at the periphery of the image (ie, the periphery of the steel plate) and the center of the image, and the periphery is covered with adhesive tape. It can be seen that is reflected. In addition, it can be seen that there is a substantially rectangular region having a color shade different from the surroundings in a portion surrounded by a dotted line located in the lower left of FIG. 28C, and paper is pasted on this portion. In addition, the portion surrounded by the dotted line located on the right side of FIG. 28C includes a white color portion in the surrounding dark color portion, and it is assumed that there is a dent.

  28D is an image illustrating the phase of the short-period wave calculated by the phase calculation unit 211 (an image showing the observation phase), and FIG. 28E is an image of the long-period wave calculated by the phase calculation unit 211. It is the image which illustrated the phase.

  Looking at FIG. 28D, three portions where the color of the image changes from black to white are seen from the left side to the right side of FIG. 28D. In the phase image, when the color of the image changes from black to white indicates that the phase difference is 2π, the phase image of the short period wave shown in FIG. 28D has a level of about 6π. It can be seen that the phase difference is illustrated.

  Further, as is clear from FIG. 28D, it is possible to clearly grasp the surrounding adhesive tape, paper attached to the surface, dents existing on the surface, and the like.

  When FIG. 28E is seen, although it is not as clear as the phase image of a short period wave, presence of the surrounding adhesive tape, the paper attached to the surface, etc. can be grasped | ascertained. Further, when the phase difference from the white portion located above the portion where the paper is present to the black portion on the lower right in FIG. 28E is examined, the phase difference is about (3/4) π, which is short. It is about 1/8 of the phase difference 6π in the phase image of the periodic wave.

Using the amplitude image and the phase image as described above, the phase connection process using the weighted least square method according to the present embodiment as described above was performed. Here, the weighted least square method performs an iterative operation using an iterative method (Gauss-Seidel method), and the iteration termination condition is that the amount of change for each iteration is less than 0.01 for all φ _{i, j.} The condition was to be.

  In the phase connection process of the short period wave, the initial value is obtained by multiplying the calculated phase of the long period wave by 8 times. In addition, regarding the weight W used for the phase connection processing of the short period wave, when the product of the amplitude of the short period wave and the sum of absolute values of the differences exceeds 0.2π, the weight W is set to 0.001. The weight W is set to 1 when it is less than 2π.

  The obtained result is shown in FIG. 29A. The image shown in the upper part of FIG. 29A is a phase image of a short-period wave after phase connection obtained by the phase connection process according to the present embodiment. The graph shown in the lower part of FIG. 29 is a graph showing the cross-sectional shape when the image shown in the upper part is cut along the y-axis at the portion indicated by the arrow.

  As is clear from FIG. 29A, by performing the phase connection process according to the present embodiment, it is possible to perform the phase connection process with high accuracy even for a fringe image including noise due to the presence of a step. It can be seen that a good image without noise can be obtained.

  FIG. 29B is obtained by phase-connecting the images shown in FIGS. 28C to 28E using a conventional phase connection method. The conventional phase connection method used is a method of adding ± 2π if the phase change amount of the adjacent pixel exceeds π in the phase image of the short period wave.

  As is clear from FIG. 29B, when phase connection is performed using the conventional phase connection method, there are many noises parallel to the x-axis direction in FIG. It can be seen that there are many.

  As described above, by using the phase connection method according to the present embodiment, even a fringe image including noise caused by a step or the like is extremely good while preventing errors due to the noise and occurrence of erroneous connection. A phase image after phase connection can be obtained. Thereby, in the shape measuring apparatus according to the present embodiment, the shape (surface shape) of the measurement object can be accurately measured.

  The preferred embodiments of the present invention have been described in detail above with reference to the accompanying drawings, but the present invention is not limited to such examples. It is obvious that a person having ordinary knowledge in the technical field to which the present invention pertains can come up with various changes or modifications within the scope of the technical idea described in the claims. Of course, it is understood that these also belong to the technical scope of the present invention.

DESCRIPTION OF SYMBOLS 10 Shape measuring device 100 Object imaging device 101 Laser light source 103 Rod lens 105 Delay integration type camera 107 Lens 200 Arithmetic processing device 201 Timing signal generation unit 203 Image processing unit 205 Display unit 207 Storage unit 211 Signal acquisition unit 213 Phase calculation unit 215 Phase Connection part 217 Shape specifying part S Steel plate

Claims (7)

The linear laser beam which is irradiated with a linear laser beam consisting of a short-period wave with a relatively short period modulated by a long-period wave with a relatively long period and reflected by the measurement object An object imaging device for imaging light;
An arithmetic processing device that performs image processing on a captured image of the measurement object generated by the object imaging device and identifies the shape of the measurement object;
With
The arithmetic processing unit includes:
A phase calculation unit that calculates phases of the long-period wave and the short-period wave included in the captured image based on the captured image of the measurement object;
Based on the phase of the long-period wave calculated by the phase calculation unit, the phase of the long-period wave is connected by a weighted least square method, and the phase of the connected long-period wave and the phase calculation unit are calculated. A phase connection unit that connects the phases of the short-period waves by a weighted least square method based on the phase of the short-period waves
Based on the phase of the short period wave connected by the phase connection unit, a shape specifying unit for specifying the shape of the measurement object;
I have a,
The phase calculation unit further calculates the amplitude of the long-period wave and the short-period wave,
The shape measuring apparatus, wherein the phase connecting unit determines a weight used in the weighted least square method based on amplitudes of the long-period wave and the short-period wave calculated by the phase calculation unit .   The shape measuring apparatus according to claim 1, wherein the phase connection unit generates an initial value of the phase when the phase of the short period wave is connected based on a connection result of the phase of the long period wave. The phase connection part is
In the captured image, the weight value corresponding to the position where the amplitude is equal to or less than a predetermined threshold is a positive value equal to or less than a predetermined value,
The amplitude is 1 the value of the weight corresponding to the position other than the position equal to or less than a predetermined threshold, the shape measuring apparatus according to claim 1 or 2. The phase connection unit, when performing the process of connecting the phases of the short period waves, the difference between the initial value of the phase of each position in the captured image and the initial value of the phase of the position adjacent to the position The shape measuring device according to claim 3 , wherein the sum of absolute values is calculated, and when the sum of absolute values of the differences exceeds a predetermined threshold, the weight value at the corresponding position is set to zero. When the period of the long period wave is K times the period of the short period wave,
The shape measuring apparatus according to claim 4 , wherein the phase connecting unit sets an initial value of the phase of the short period wave to K times the phase of the long period wave after phase connection. The linear laser beam reflected by the measurement object while scanning the measurement object with a linear laser beam consisting of a short period wave with a relatively short period modulated by a long period wave having a relatively long period And generating a captured image of the measurement object;
Calculating the phase of the long-period wave and the short-period wave included in the captured image, and the amplitude of the long-period wave and the short-period wave, respectively, based on the captured image of the measurement object;
With connecting phase of the long periodic wave by weighted least square method on the basis of the calculated the issued the long periodic wave of phase, based on the attached long period waves the phase and calculated the short periodic wave phase Connecting the phase of the short period wave by a weighted least square method;
Identifying the shape of the measurement object based on the phase of the short period wave connected by connecting the phase;
Only including,
The shape measuring method , wherein in the step of connecting the phases, a weight used in the weighted least square method is determined based on the calculated amplitudes of the long-period wave and the short-period wave . The linear laser beam which is irradiated with a linear laser beam consisting of a short-period wave with a relatively short period modulated by a long-period wave with a relatively long period and reflected by the measurement object In a computer that performs image processing on a captured image of a measurement object generated by an object imaging device that captures light,
A phase calculation function for calculating the phases of the long-period wave and the short-period wave included in the captured image based on the captured image;
The phase of the long period wave is connected by a weighted least square method based on the phase of the calculated long period wave, and the phase of the connected long period wave and the short period wave calculated by the phase calculation function A phase connection function for connecting the phases of the short-period waves by a weighted least square method based on the phase of
Based on the phase of the short period wave after phase connection, a shape specifying function for specifying the shape of the measurement object;
Realized ,
The phase calculation function further calculates the amplitude of the long period wave and the short period wave,
The phase connection function, on the basis of the the long periodic wave and the amplitude of the short-period waves calculated by the phase calculation function, determines a weight to be used in the weighted least squares method, program.