JP2001153797A - Method for unwrapping phase data - Google Patents

Abstract

PROBLEM TO BE SOLVED: To improve a success ratio for unwrapping phase distribution images by improving a conventional cut line method. SOLUTION: In a stage in which images having the residue of different codes are combined thereby setting a cut line, pixels are sequentially ordered irrespective of the codes of the residue from the pixel having the non-zero residue which is closest to the center of the image, and are combined according to the order, thereby setting the cut line. Moreover, the cut line is shaped in a stairway form. In the case where an isolated region appears by a plurality of cut lines, the phase unwrapping is carried out by the pixel with the non-zero residue of a certain angle in the isolated region and two pixels in an unwrapped region adjacent to the pixel.

Description

DETAILED DESCRIPTION OF THE INVENTION

[0001]

The present invention relates to a method of calculating phase data of a pixel of a phase distribution image from an interferogram, wherein the range of the phase of the pixel output by the arc tangent operation included in the process is from -π to + π. The present invention relates to a method for obtaining phase data of pixels of a true phase distribution image from a wrapped image which is (or 0 to 2π), and is useful as, for example, a method for processing an X-ray phase distribution image. It is.

[0002]

2. Description of the Related Art Methods for obtaining phase data of pixels of a phase distribution image from interference fringe intensity include a Fourier transform method and a fringe scanning method. Either method involves calculating the arc tangent in the process of determining the pixel phase data,
Therefore, as shown in FIG. 1, the phase data of the pixel of the phase distribution image obtained by the inverse tangent value range is 0 despite that it originally has a continuous phase (the straight line denoted by reference numeral 101). Has a phase indicated by a line folded (wrapped) in the range from
(A broken line with a). Obtaining the continuously changing original phase data from the phase data of the pixels of the phase distribution image folded in the range of 0 to 2π is called phase data unwrapping.

In general, a point

[0004]

[Outside 1]

[0005] The complex scalar wave field U of monochromatic light at

[0006]

[Outside 2]

And phase

[0008]

[Outside 3]

Then, it can be expressed as (Equation 1).

[0010]

(Equation 1)

Here, i is an imaginary unit. At this time, the ray vector field directed in the direction perpendicular to the wavefront

[0012]

[Outside 4]

Can be written as (Equation 2).

[0014]

(Equation 2)

Here, λ is the light wavelength, and n is the refractive index of the medium (usually air). Since the ray vector field is a conserved field without vortices, (Equation 3) holds.

[0016]

(Equation 3)

The phase between a certain pixel P and a certain pixel Q satisfies the relationship of (Equation 4).

[0018]

(Equation 4)

Here, it can be said that the integration path can be arbitrarily selected from (Equation 3).

Now, the phase data of the pixel of the phase distribution image wrapped in the range of 0 to 2π is

[0021]

[Outside 5]

Will be described as follows. When each pixel of the phase distribution image is viewed by folding, when a phase step occurs between the phases of adjacent pixels, the difference has a value close to ± 2π. In order to obtain data of the original phase that changes continuously, it is necessary to add or subtract a phase of 2π to the phase of one pixel. Hereinafter, a method of unwrapping the phase data of an arbitrary pixel based on a certain pixel of the phase distribution image will be described.

Now,

[0024]

[Outside 6]

Is defined as (Equation 5).

[0026]

(Equation 5)

Here,

[0028]

[Outside 7]

Is the m-th point on the unwrapped path,
The symbol Rd means that the value in the angle brackets is rounded off to the decimal point. The threshold value is a parameter for checking whether or not there is a phase difference between the (m-1) th pixel and the mth pixel.

(Equation 5)

[0031]

[Outside 8]

The phase of the pixel Q with respect to the pixel P using

[0033]

[Outside 9]

Can be written as (Equation 6).

[0035]

(Equation 6)

Here, the second term on the right side means the sum along the path from the pixel P to the pixel Q.

With a gentle and smooth phase distribution image, no particular problem occurs in the unwrapping process. But,
When the phase gradient is steep compared to the pixel size, when the noise in the image is remarkable, and when the image is distorted, the interference fringe becomes unclear, and the error that the unwrap result differs depending on the path is generated. appear. For example, in FIG. 2, a case may occur where the result differs between the case where the unwrapping is performed along the path A from the pixel P to the pixel Q and the case where the unwrapping is performed along the path B. From a mathematical point of view, this event can be considered to occur because (Equation 3) is not satisfied in a part of the image.

Such a pixel can be examined as follows. Pixel coordinate point (i, j)

[0039]

[Outside 10]

Can be calculated by (Equation 7).

[0041]

(Equation 7)

That is, it can be said that a pixel whose value of (Expression 7) is not zero causes inconsistency in the unwrap operation. Hereinafter, the amount calculated by (Equation 7) is referred to as a residue. Here, an example of calculation of the residue by (Equation 7) is shown in FIGS. 3 (a) to 3 (c). Here, for the four pixels of the phase distribution image, the respective coordinate points are (i, j) on the lower left side and (i, j) on the upper left side.
j + 1), the upper right side is (i + 1, j + 1), and the lower right side is (i + 1, j).
Are shown in the box of each pixel. For example, in the example of FIG.
_d [0.0−0.8] + R _d [0.3−0.0] + R _d [0.6
−0.3] + R _d [0.8−0.6] = − 1, and the residue−
Similarly, it can be seen that the examples of FIGS. 3B and 3C have the residues 0 and +1, respectively.

If a non-zero residue is detected at the coordinate point (i, j) of a pixel, the result of unwrapping the pixel via the right side and the result via the left side of the pixel will be different. Therefore, by defining a path (cut line) connecting pixels having residues of different signs and prohibiting an unwrap path that crosses the path, it is possible to solve the problem that the unwrap results differ depending on the path. However, at the stage of determining the cut line, a degree of freedom remains in the method of combining pixels having different sign residues. The combination is usually a method of selecting the pixel with the closest residue of the different sign (for example,
JM Huntley, Noise-immune phase unwrapping algori
thm, Appl. Opt. Vol. 28, No. 15, 3268-3270, August,
1989 and its modifications R. Cusack, JM Huntley and HT
Goldrein, Improved noise-immune phase-unwrapping a
lgorithm, Appl. Opt. Vol. 34, No. 5 781-789, 1995).

FIG. 4 shows a conventional example of setting a cut line connecting pixels having the same residue of different codes. In FIG. 4A,
A coordinate point M (x ₁ ,
y ₁ ) and a coordinate point N having a negative residue to be paired with y ₁ )
A cut line 401 is set for (x ₂ , y ₂ ).
FIGS. 4B and 4C show a state in which the cut line 401 is set as data on a computer and the horizontal mask array H (x,
y) and the vertical mask array V (x, y) (eg, JM Huntley, Noise-immune phase
unwrapping algorithm, Appl. Opt. Vol. 28, No. 15, 3
268-3270, August, 1989).

The cut line 401 is mathematically defined as (Equation 8) and (Equation 9).

[0046]

(Equation 8)

[0047]

(Equation 9)

Other elements are set to zero. By adding the above restrictions, errors in the unwrap operation are reduced.

[0049]

The conventional cut line method in which the residue of the pixel is considered is considerably improved from the unwrapping method in which the residue of the pixel is not considered. Are not sufficiently considered when the number of pixels having the residue is different and when the isolated region of the residue surrounded by a plurality of cut lines occurs. The present invention is intended for such a case, and an object of the present invention is to further improve the success rate of unwrapping compared to the conventional cut line method.

[0050]

A method of combining pixels having positive and negative residues is as follows. First, a pixel having a positive or negative residue closest to the center of the image is selected as a reference. Next, from this reference pixel, all pixels having non-zero residues are ordered in the order of proximity to the reference pixel regardless of the sign of the residue. Next, a cut line is defined by selecting a pair of pixels having the nearest residue of the opposite sign in this order. Also, as shown in FIG. 5 (a), the shape of the cut line is assumed to be a stepwise connection between pixels having residues of different signs instead of the conventional right-angled one.

FIG. 5 shows an example of setting a cut line according to the present invention. FIG. 5A shows a coordinate point M (x ₁ , y ₁ ) having a certain positive residue on a phase distribution image and a coordinate point N (x ₂ , y ₂ ) having a negative residue corresponding thereto. On the other hand, cut line 5
This shows a state where 01 has been set. FIGS. 5B and 5C show a state in which the cut line 501 is set as data on a computer when the horizontal mask array H (x, y) and the vertical mask array V are used.
(X, y). However, if the combination of coordinate points of pairs of residues of different signs is not the same size in the x-axis direction and the y-axis direction, even if it is said to be step-like,
As shown in FIG. 5 (a), it does not increase or decrease step by step in the x direction and the y direction. In this case as well, instead of a simple polygonal line as shown in FIG. 4, for example, as shown in FIG.

In the case of an image in which many cut lines are laid, that is, an image having many pairs of residues of different codes, an isolated area surrounded by the cut lines may be generated. FIG. 6 shows an example in which the cut lines 602 and 603 are set, so that the region 601 is surrounded by two cut lines and becomes an isolated region. The following procedure was used to unwrap such an isolated area.

As shown in FIG. 6, the cut line 602,
A coordinate point Q (x ₃ , y ₃ ) of a pixel having a non-zero residue at a certain corner in the isolated area 601 surrounded by 603 is determined based on a predetermined rule (for example, as a point closest to the image center). ), And focus on the coordinate points P (x ₁ , y ₁ ) and R (x ₂ , y ₂ ) of two pixels in the unwrapped area adjacent thereto.
By allowing unwrapping only between the pixels QP or between the pixels QR, unwrapping within the isolated region 601 can be started. Regarding whether to select between the pixels QP or between the pixels QR, a secondary difference along each direction is checked, and a small absolute value is used as a criterion.

If there is some prior knowledge about the image, it can be used for unwrapping. Here, phase-type tomography (Atsushi Hyakuo, Akira Fukuhara,
4-348262, phase tomography apparatus) will be described.

In the phase tomography, as shown in FIG. 7B, the X-ray irradiated to the xy plane 703 is used.
The phase distribution image 703 is measured for each rotation angle θ _i while rotating the subject 701 placed on the line 702 little by little. A sinogram is an individual image 704 seen on the (x, θ) plane of a three-dimensional data set obtained by superimposing a plurality of measured phase distribution images in the order of rotation angles θ _i.
(See FIG. 7A).

In the phase tomography, unwrapping may be performed on a phase distribution image, but may be performed on a sinogram. Here, a sinogram that uses the physical fact that the spatial integration value of the true phase distribution image is constant irrespective of the irradiation angle of an X-ray or the like to the subject as preliminary knowledge is used as the preliminary knowledge in the unwrapping. Will be described. That is, when the unwrapping result is insufficient even with the algorithm using the cut line, correction is performed using the above-mentioned prior knowledge so as to obtain a more correctly unwrapped phase distribution image.

[0057]

DESCRIPTION OF THE PREFERRED EMBODIMENTS Embodiments of the present invention will be specifically described below.

The wrapped phase data of the phase distribution image of the subject is generally unwrapped according to the procedure shown in FIG. In this procedure, first, phase data of the wrapped phase distribution image of the subject is read (step 801), coordinate points of pixels having non-zero residues are detected (step 802), and all non-zero residues are detected. The order of the coordinate points of the pixels having a number is performed (step 803). The coordinate point of a pixel having a non-zero residue is represented by C (x ₀ , y ₀ ) and the position of a pixel having a certain non-zero residue is R (x, y), where C is the coordinate point of the pixel at the center of the phase distribution image. The distance D between the point and the coordinate point of the central pixel was defined as (Equation 10), and the order was determined based on the magnitude of D. Here, a and b are the sizes of the phase distribution image in the x-axis direction and the y-axis direction.

[0059]

(Equation 10)

Next, a pixel having a higher non-zero residue according to the above-mentioned ordering, and a sign opposite to the coordinate point,
In addition, another pixel having a non-zero residue is combined with the highest pixel having a non-zero residue that has not been combined (step 804). This procedure is continued until all non-zero residue pixels are combined. If the number of pixels with positive and negative residues is different, there will be pixels with non-zero residues that remain uncombined, but pixels with such non-zero residues will necessarily be Since it is considered that the pixel having the non-zero residue is virtually present at the end of the phase distribution image closest to the pixel having the non-zero residue, the pixels having the opposite sign are virtually present, and the two are combined. Was.

Next, a mask arrangement is introduced, and a cut line connecting pixels having the combined positive and negative residues is set (step 805). At this time, instead of the perpendicular cut line described in the related art, the cut line is formed in a step shape as shown in FIG.

When the setting of the cut line is completed,
For example, all pixels are sequentially unwrapped using the pixel at the center of the phase distribution image as a reference point (step 806). Thus, the unwrapping of the entire phase distribution image is completed, and the data is updated (step 807).

FIG. 9 shows details of the unwrap process in step 806 of FIG. First, a coordinate point Q of a pixel to be unwrapped is determined (step 901). Next, the coordinate point P of the reference pixel is determined (step 902). In addition, in order to shorten the calculation time, a pixel that has been unwrapped at a coordinate point of a pixel adjacent to the coordinate point Q is preferably selected as a reference point. Next, the presence or absence of a cut line between the pixels P and Q is checked (step 903). If there is no cut line there, an arbitrary path connecting the pixels P and Q (usually the shortest path is selected) , (Equation 6), and proceeds to the unwrapping of the next pixel. If there is a cut line between the pixels P and Q, a detour is made along the cut line from the pixel P (step 904), and if a path to the pixel Q is determined (step 905),

[0064]

[Outside 11]

Is calculated (step 906), and the phase of the pixel Q is calculated based on (Equation 6).

[0066]

[Outside 12]

Is calculated (step 907). In this embodiment, the threshold parameter in (Equation 5) is 1.7π.
Was used. Thereafter, the process proceeds to unwrap of the next pixel. If the unwrapping of the pixel Q succeeds, the pixel Q can be set as an unwrapped point and can be used as a subsequent reference point.

When the pixel Q does not reach the pixel Q and returns to the pixel P again due to the detour around the cut line, it can be determined that the pixel Q is in an isolated area when viewed from the pixel P. At this time, a flag of the isolated area is set to the pixel Q (step 908), the unwrap is suspended, and the process proceeds to the unwrap of the next pixel. It is checked whether the unwrapping of all the pixels except for the isolated area is completed (step 909), and the unwrapping of the isolated area is performed (step 91).
Go to 0). The order of the pixels to be unwrapped may be any method as long as the whole phase distribution image can be examined. For example, the image may be sequentially advanced along the rows and columns of the phase distribution image, or may be advanced spirally from the first reference coordinate point.

Next, a method of unwrapping an isolated area will be described with reference to FIG. A flag is set for pixels in an area that has not been unwrapped in the processing so far, that is, an isolated area (step 908). If an isolated area exists (step 1001), a pixel Q at a certain corner in the isolated area that is in contact with the unwrapped area is selected (step 1002). Here, attention is paid to P and R of two pixels in the unwrapped area adjacent to the pixel Q. Pixel QP
By allowing unwrapping between the pixels or between the pixels QR, the pixel Q can be used as a reference point for unwrapping the inside of the isolated area. At this time, the phase of the pixel Q when unwrapped with respect to the pixel P

[0070]

[Outside 13]

Alternatively, the phase of pixel Q when unwrapped with reference to pixel R

[0072]

[Outside 14]

Which one to select is based on the following determination method.

The secondary differences Δ ^k _xx and Δ ^k _yy at the pixel Q are calculated by ( _Equation 11) and ( _Equation 12) (step 100).
3).

[0075]

[Equation 11]

[0076]

(Equation 12)

The sum of the absolute values of Δ ^k _xx and Δ ^k _yy is compared on the basis of the pixel P and the pixel R (step 1004).
The direction in which the value becomes smaller is selected (steps 1005 and 1006). For example, if (Equation 13),

[0078]

(Equation 13)

Phase

[0080]

[Outside 15]

Is selected as the phase of the pixel Q.

In (Equation 11) and (Equation 12), the coordinate point (i, j) belongs to the pixel Q, and the adjacent coordinate point is unwrapped with respect to the pixel Q or already unwrapped (or (The pixels P and R themselves).

In this manner, the reference pixel in the isolated area is determined. Thereafter, the inside of the isolated area is unwrapped again based on FIG. 9 (step 1007). The flag of the unwrapped portion is reset (step 1008), and the isolated area is searched again (step 1001). By repeating this, the entire image can be unwrapped even when isolated regions are nested.

Next, a case will be described in which a sinogram obtained in the process of phase tomography using X-rays is unwrapped. There is no particular problem if unwrapping is successful using the above method, but if the unwrapping process is incomplete even using the above method, supplement the unwrapping process by using physical facts as preliminary knowledge Can be. That is, the spatial integration of the true phase distribution image is constant irrespective of the irradiation angle of the subject such as X-rays. This process is performed after the end of step 806 in FIG. FIG. 11 shows the procedure.

First, in the sinogram unwrapped by the method described above, the integral value of the phase value of each row (in the direction of the spatial axis) is calculated, and the intermediate value is assumed to be close to the integral value of the true phase distribution image. Then, a reference value for the following comparison is set (step 1101).

Next, the difference between the phase integral value and the intermediate value of each row is calculated, and it is checked whether or not the difference exceeds a threshold value (step 1102). In this embodiment, the threshold value is the standard deviation of the integrated value of each row.

When the difference between the integral value and the intermediate value exceeds the threshold value, correction is made in the following procedure. The value of the corresponding pixel is compared between the adjacent corrected row and the current row of interest, and an integer multiple of 2π is added or subtracted from the one with the larger difference, and the difference is made closer to zero, so that the overall The process is continued until the difference between the integral values falls within the threshold (step 1103).

This correction method is repeated for each row exceeding the threshold (step 1104).

Hereinafter, the effect of the present invention will be verified using an actual phase distribution image.

FIG. 12 (a) illustrates a wrapped sinogram of a phase distribution image measured for a biological specimen, in which the coordinate points of all pixels with non-zero residues are ordered by the procedure of the present invention, and FIG. 12B is an example of a phase distribution image obtained by unwrapping the cut line using the conventional cut line method described with reference to FIG. 4. As is apparent from a comparison between the two, the result of FIG. 12B shows that the effect of the processing by the cut line appears in the lower center part of the image, and it cannot be said that the phase distribution image has been sufficiently processed.

FIG. 13A shows a sinogram of a phase distribution image measured for another biological specimen, unwrapped in the same manner as the processing performed in FIG. 12A, and further integrating the X-ray phase distribution image. It is an example of the phase distribution image by the result corrected based on the fact that the value is constant. FIG. 13B is an example of a sinogram before correction based on the fact that the integral value is constant. As is clear from comparison between the two, the result of FIG. 13B shows a shadow of insufficient unwrapping processing in the middle part on the left side of the image, and cannot be said to be a phase processing image that has been sufficiently processed.

In phase tomography, the X-ray phase distribution image does not directly observe itself, but observes a tomographic image reconstructed from it. According to the present invention, since the result of unwrapping the sinogram is good, it has been confirmed that the image quality of the tomographic image reconstructed from the result is improved. This example will be described with reference to FIG.

FIG. 14A shows an example of a sinogram unwrapped by the present invention, and FIG. 14B shows an example of a case where the same sinogram is unwrapped by a conventional method. FIG. 14 (c) shows an example of a tomographic image reproduced from FIG. 14 (a), and FIG. 14 (d) shows an example of a tomographic image reproduced from FIG. 14 (b). As is apparent from a comparison between FIG. 14C and FIG. 14D, in FIG. 14D, a line that flows from the middle part on the right side of the image to the lower part on the left side appears. 14C, a better tomographic image was reproduced in FIG. 14C.

[0094]

According to the improvement of the cut line method according to the present invention, the success rate of the unwrapping process is improved.

[Brief description of the drawings]

FIG. 1 is a view for explaining an original phase of phase data of a phase distribution image and a phase wrapped in a range of 0 to 2π.

FIG. 2 is a diagram showing an example of a path when a pixel Q is unwrapped based on a pixel P.

FIGS. 3A to 3C are diagrams illustrating calculation examples of the residue of a pixel.

FIG. 4A shows an example of setting a conventional cut line;
(B) and (c) are horizontal mask arrangements H for that purpose.
The figure which shows (x, y) and the vertical mask arrangement | sequence V (x, y).

FIG. 5A shows an example of setting a cut line according to the present invention, and FIGS. 5B and 5C show a horizontal mask arrangement H (x, y) and a vertical mask arrangement V (x, y) therefor. FIG. (D) is a diagram showing another example of setting a cut line according to the present invention.

FIG. 6 is a diagram showing an example of an isolated area surrounded by cut lines.

FIG. 7A is a three-dimensional data structure of a phase distribution image in phase-type tomography, and FIG. 7B is an explanatory diagram for acquiring a phase distribution image therefor.

FIG. 8 is a flowchart showing an overall procedure of a phase distribution image unwrapping process according to the embodiment of the present invention.

FIG. 9 is a flowchart showing details of an unwrap procedure according to the embodiment of the present invention.

FIG. 10 is a flowchart showing details of an unwrapping procedure of an isolated area according to the embodiment of the present invention.

FIG. 11 is a flowchart showing details of an unwrap correction procedure when a physical fact is used as preliminary knowledge for sinogram unwrap.

FIG. 12 (a) orders a wrapped sinogram of a phase distribution image measured for a biological specimen to coordinate points of all pixels of a non-zero residue according to the procedure of the present invention, and FIG. 12B is a diagram showing an example of a phase distribution image obtained by unwrapping a cut line in a stepped manner, and FIG.
FIG. 5 is a diagram showing an example of a phase distribution image as a result of unwrapping by the conventional cut line method shown in FIG. 4.

FIG. 13 (a) shows a sinogram of a phase distribution image measured for another biological specimen, unwrapped in the same manner as the processing performed in FIG. 12 (a), and further, an X-ray phase distribution image 13B is an example of a phase distribution image based on the result of correction based on the fact that the integral value is constant, and FIG. 13B is a diagram illustrating an example of a sinogram before correction based on the fact that the integral value is constant.

FIG. 14A shows an example of a sinogram unwrapped according to the present invention, and FIG. 14B shows an example of the same sinogram unwrapped by a conventional method. FIG. 14C shows a tomographic image reproduced from FIG. 14A, and FIG. 14D shows a tomographic image reproduced from FIG. 14B.

[Explanation of symbols]

101: original phase signal, 102: wrapped phase signal, 401: cut line, 501: cut line, 70
1: subject, 702: X-ray, 703: phase 704: sinogram.

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[Procedure amendment]

[Submission date] November 25, 1999 (1999.11.
25)

[Procedure amendment 1]

[Document name to be amended] Drawing

[Correction target item name] FIG.

[Correction method] Change

[Correction contents]

FIG.

[Procedure amendment 2]

[Document name to be amended] Drawing

[Correction target item name] FIG.

[Correction method] Change

[Correction contents]

FIG. 13

[Procedure amendment 3]

[Document name to be amended] Drawing

[Correction target item name] FIG.

[Correction method] Change

[Correction contents]

FIG. 14

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Claims (5)

[Claims] In a method of unwrapping phase data of a phase distribution image, a phase jump of 2π is detected and corrected from a phase distribution image represented by wrapping a phase value in a range of 0 to 2π and unwrapped. The point where the phase jump becomes unclear is detected as a pixel having a non-zero residue, and the detection and correction of the phase jump of 2π is prohibited while traversing a cut line connecting pixels having different sign residues. The order is determined regardless of the sign of the residue from the pixel having the non-zero residue closest to the center of the image, and the cut line connecting the pixels having the residue with the different sign is defined and processed according to the priority order according to the order. A method of unwrapping phase data of a phase distribution image. 2. The cutting line according to claim 1, wherein said cutting line has a stepped shape.
Unwrapping method of the described phase data. 3. When a plurality of cut lines are present in the phase distribution image and an isolated area surrounded by the cut lines is present, a pixel at a certain corner in the isolated area;
Unwrap is permitted only for the pixel having the smaller absolute value of the secondary difference value of the phase difference between the pixel and two pixels outside the adjacent isolated region, and then unwrapping is performed within the isolated region. Unwrapping method of the phase data of the phase distribution image. 4. Acquiring a phase distribution image in a plurality of projection directions,
A phase data unwrapping method for processing a sinogram obtained in the process of phase tomography for reconstructing a tomographic image by the method according to any one of claims 1 to 3, wherein the unwrapped sinogram has a spatial axis direction. A phase data unwrapping method for correcting the phase data of each pixel row with known knowledge. 5. An intermediate value of an integral value of phase data of each pixel row in a spatial axis direction of a sinogram subjected to the unwrapped correction is examined, and when an integrated value of a certain pixel row is greatly deviated from the intermediate value. , The phase signal of the pixel in this pixel row is 2
5. The phase data unwrapping method for a phase distribution image according to claim 4, wherein a correction is made by adding or subtracting an integral multiple of π so that the integral value of the pixel row approaches the intermediate value.