JP2003232605A - Method and device for unwrapping phase data - Google Patents

Abstract

<P>PROBLEM TO BE SOLVED: To correctly unwrap phase data in measuring a subject with noise or local unevenness or inclination to the incoming light. <P>SOLUTION: A reference point P, which is one of the phase data, and at least three adjacent points Q are locally unwrapped so that the phase difference is within ±π (S2). If the error between the phase data of the reference point P and a fitting expression expressing the approximation to the locally unwrapped data of the points Q exceeds a permissible error, the reference point P is determined to be ineffective (S5). The determination process is repeated with one of the adjacent points Q as a new reference point P, and the effectiveness/ineffectiveness of the whole data are determined. After that, an extrapolated value of an adjacent point C adjacent to the one of the adjacent points Q is found by the fitting expression of a reference point A, which is one of the effective data, and the point C is unwrapped so that the phase difference from the extrapolated value is within ±π (S8). Then, the similar unwrapping process is repeated with a point adjacent to the reference point A as a new reference point A to unwrap the whole effective data. <P>COPYRIGHT: (C)2003,JPO

Description

Detailed Description of the Invention

[0001]

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to a method and apparatus for unwrapping two-dimensional phase data obtained by measuring a surface to be measured with an interferometer.

[0002]

2. Description of the Related Art Conventionally, there is an apparatus for obtaining the surface shape from phase data obtained by an interferometer when measuring the surface shape (displacement) of an object such as an electronic substrate (wafer). That is, the reflected light from the measured surface (surface) of the subject and the reflected light from the reference surface that serves as a reference are combined and caused to interfere with each other to form interference fringes. The shape of the measurement surface is obtained. A Fourier method, a fringe scanning method (fringe scan method), a heterodyne method, or the like is used as a method of analyzing the intensity data of the interference fringes. The fringe scanning method is described in detail in Japanese Patent Laid-Open No. 10-221033 (publication 1), which discloses a shape meter using the fringe scanning method for an oblique incidence interferometer.

Here, the surface shape measurement based on the fringe scanning method will be described with reference to FIG. FIG. 1 shows a schematic structure of a wafer surface shape measuring apparatus Z using a Michelson interferometer 1. The surface shape measuring device Z includes an interferometer 1, a signal processing circuit 11, a computer 12, and a monitor 13.
Composed of. The interferometer 1 includes a light source device 2 that emits a laser beam of parallel light flux, and a beam splitter 3 that receives the laser beam from the light source device 2, reflects a part of the incident light, and transmits the remaining part. , A reference reflecting mirror 4 having a reference surface 4a for reflecting the laser light transmitted through the beam splitter 3, a drive unit 5 for moving the reference reflecting mirror 4 in the optical axis direction, and a reflection surface 4a, Further, an imaging lens 6 arranged on the optical path of the light reflected by the beam splitter 3.
And a camera 7 such as a CCD for picking up an image formed by the image forming lens 6. A subject 8 is arranged on the optical path of the laser light reflected by the beam splitter 3, and the reflected light from the measured surface 8a (the subject surface) is incident on the beam splitter 3. As a result, interference fringes are formed on the camera 7 due to the interference of the light from the measured surface 8a and the light from the reference surface 4a,
This interference fringe is imaged by the camera 7.

The image picked up by the camera 7 is processed by a signal processor.
It is input to the logic circuit 11, where amplification, analog →
Signal processing such as digital conversion is performed, and each two-dimensional position (image
Interference fringe intensity data is generated for each
Data is entered into computer 12. Computer
Reference numeral 12 controls the drive unit 5 to set the reference reflecting mirror 4 at the set position.
By λ / 8 (where λ is the wavelength of light) in 4 steps (0,
λ / 8, 2λ / 8, 3λ / 8) and set each position
Interference fringe intensity data of each pixel from the signal processing circuit 11 for each
If you take in and perform arithmetic processing such as unwrap described later
Both of them, if necessary, display data and characteristic diagrams on the monitor 13.
indicate. The setting positions of the four stages of the reference reflecting mirror 4
The interference fringe intensity data for each of the
What is displayed on the Nita 13 is shown in FIGS.
It In the fringe scanning method, the setting position of the reference reflecting surface 4 is 0, λ /
When changing to 8, 2λ / 8, 3λ / 8, to the camera 7
The phase of the arriving light is 0, π / 2, 2π / 2, 3π / 2
And changes. The predetermined pixel (point) in the camera 7
The interference fringe intensity data corresponding to the four-stage setting positions are I
₀, I₉₀, I₁₈₀, I₂₇₀Then, according to the following equation (1),
The phase data θ of the pixel (point) is obtained.     θ = tan^-1{(I₉₀-I₂₇₀) / (I₀-I₁₈₀)}… (1) As a result, the phase data θ is wrapped in the range of −π to π.
Will be done. From the images of FIGS. 2 (a) to 2 (d),
The monitor uses the phase data θ obtained in (1) as an image.
What is displayed in 13 is FIG. 2 (e1). Figure 2 (e
2) is the x-axis direction in the image of FIG.
Change the phase data θ on a predetermined straight line
Lofeel). However, the original shape of the measured surface 8a
The image of the phase data showing the shape is as shown in Fig. 2 (f1).
It changes continuously. Figure 2 (f2) is a diagram
Phase on a predetermined straight line in the x-axis direction in the image of 2 (f1)
Data θ _unwrapRepresents the change (profile). This
The difference is that the phase data θ varies from −π to π.
2 (e1), the phase data θ
There is an indefiniteness that is an integral multiple of 2π, and a sudden phase change (ja
This is because there is a point at which like this
The jump is not limited to the stripe scanning method, and any of the solutions described above can be used.
It also occurs when the interference fringe intensity data is analyzed by the analysis method. There
Then, this indeterminacy is resolved and the original phase data θ_unwrapTo
It is necessary to ask, and this work is unwrapping. here
And θ and θ_unwrapHas the relationship of the following expression (2).     θ_unwrap= Θ + 2πn (2) Here, n is an integer, and will be referred to as order below,
θ_unwrapWill be called unwrap data. Anla
Up is to obtain this order n.

As a conventional unwrapping method, for example, one point (pixel) of the phase data θ obtained by the equation (1) is selected and its order n is appropriately set (eg 0), and the phase data is smoothed. The difference between the phase data of adjacent points is within a predetermined range (for example, -π to + π)
Order n of the phase data of the adjacent points so that
There is a method of determining the degree n of all the points by deciding, and repeating this work for the points adjacent to each other. At this time, points (areas) where the interference fringe intensity data is smaller than a predetermined value due to the presence of holes in the subject are excluded from the processing targets in advance and the remaining effective areas are processed. As a method of avoiding this invalid area and sequentially determining adjacent points, a filling algorithm or the like is applied. Details are described in paragraphs 0005 to 0014 of Japanese Patent Application Laid-Open No. 10-90112 (publication 2). However, this method is known to be erroneously calculated due to Fresnel diffraction, noise, and the like that occur at the edge of the subject.

For this reason, the following method has been proposed in the above publication 2. That is, 2 obtained by the interferometer
The effective area in the dimensional phase data θ is divided into small areas that are a group of points where the phase difference between adjacent points is sufficiently smaller than π, and for each small area, the phase of 2π is used for unwrapping. A variable (corresponding to the order) indicating whether or not to shift by a factor of 2 is assigned, and the phase difference between adjacent points is divided by 2π and rounded to an integer along the boundary between the adjacent small areas. Create a first equation that is the difference between the variables of, and find the variable by solving a second equation for each boundary of adjacent small regions by adding the first equation for that boundary to each other. (Hereinafter, this is referred to as conventional technology).

[0007]

However, in the above-mentioned conventional technique, it is necessary to divide the region into small regions having a sufficiently small phase difference, and the device is installed with an inclination with respect to the subject or the incident light having local unevenness. When the object is measured, the number of divisions of the small area is large where the interference fringes are very dense. In this case, as shown in paragraph 0055 of the above-mentioned publication 2, the size of the matrix for solving the equation becomes large, so that the calculation load becomes large, which is not practical. In addition, even in the case of an object having few local unevenness, when the measurement is performed by fine adjustment so that the object is not tilted with respect to the incident light, the adjustment takes time, and thus the throughput of the entire measurement is increased. There was also a problem that it decreased. Therefore, the present invention has been made in view of the above circumstances, and an object thereof is to accurately perform measurement even when measuring an object having noise or local unevenness, or an object having an inclination with respect to incident light. An object of the present invention is to provide a method and apparatus for unwrapping phase data that can be unwrapped.

[0008]

To achieve the above object, the present invention provides a phase data unwrapping method for unwrapping two-dimensional phase data obtained by an interferometer, wherein a predetermined one of the phase data is selected. Local phase data which is one of the reference phase data and at least three or more phase data in the vicinity thereof are corrected by an integral multiple of 2π so that the difference between the reference phase data and the reference phase data falls within a predetermined phase difference range. A local unwrap procedure for obtaining unwrap data, a fitting equation calculation procedure for obtaining a fitting equation of two variables that approximates the reference phase data and the local unwrap data, and fitting of the fitting equation with the reference phase data and the local unwrap data A fitting error calculation procedure for obtaining an error, and the fitting The local unwrap data, the reference phase data is determined to be invalid data if the error exceeds a predetermined allowable error, and the reference phase data is determined to be valid data otherwise. One of the two is used as the reference phase data to execute the local unwrap procedure, the fitting equation calculation procedure, the fitting error calculation procedure, and the valid / invalid determination procedure,
This is a method of unwrapping the phase data in which after validating or invalidating all the phase data by sequentially repeating this, unwrapping is performed only on the valid data. As described above, since the validity or invalidity of the data is determined by the fitting error with respect to the fitting formula that reflects the tilt of the subject with respect to the incident light, the phase difference between the neighboring data caused by the tilt of the subject is subtracted, and noise or noise is reduced. Only the data having a large phase difference between neighboring data generated by the unevenness of the surface of the subject, that is, only the data that should be invalidated are determined to be invalidated. As a result, data that should be invalid (large error) is judged to be valid,
It is possible to prevent the error from being sequentially propagated to the unwrap of the neighboring data, resulting in an incorrect unwrap as a whole. In the opposite case, the steep slope of the object causes a large phase difference between neighboring data,
It is also possible to prevent a large amount of data that should be valid originally from being determined to be invalid, which prevents sufficient unwrapping.

Further, with respect to quasi-neighborhood effective data which is the effective data in the vicinity of the effective data in the vicinity of the reference effective data which is a predetermined one of the effective data, the reference effective data is the reference phase data. By extrapolation based on the fitting formula obtained when
An extrapolation value of the phase of the quasi-neighborhood effective data is calculated, and extrapolation is performed using data obtained by correcting the quasi-neighborhood effective data by an integer multiple of 2π so that the difference from the extrapolated value falls within a predetermined range. An unwrap procedure, the extrapolation unwrap procedure is executed by using one of the valid data in the vicinity of the reference valid data as the new reference valid data, and the unwrap procedure is performed for all the valid data by sequentially repeating the procedure. A method of obtaining data is also possible. As a result, since the unwrapping is performed by the relative evaluation with the extrapolated value based on the fitting formula that reflects the tilt of the subject, the unwrapping can be correctly performed even if the subject is tilted.

Further, in the case where the valid data for which the unwrap data is obtained exists in the vicinity of the invalid data, an outside based on the fitting formula obtained when the valid data is used as the reference phase data. An extrapolation value of the phase of the invalid data is obtained by insertion, and the invalid data unwrap is data obtained by correcting the invalid data by an integer multiple of 2π so that the difference from the extrapolation value falls within a predetermined range. It is also possible to have a procedure. This is effective when an incorrect order is determined at the time of the local unwrap due to the inclination of the subject, and as a result, many points determined to be invalid data occur.

By using a linear two-variable equation as the fitting equation, the fitting equation can be obtained with a relatively small amount of calculation when the surface of the subject is a substantially flat surface.

Further, it may be regarded as a phase data unwrapping device having means for executing the process in the phase data unwrapping method.

[0013]

BEST MODE FOR CARRYING OUT THE INVENTION Embodiments and examples of the present invention will be described below with reference to the accompanying drawings to provide an understanding of the present invention. It should be noted that the following embodiments and examples are merely examples embodying the present invention and are not of the nature to limit the technical scope of the present invention. 1 is a diagram showing a schematic configuration of a surface shape measuring apparatus X to which the phase data unwrapping method according to the embodiment of the present invention is applied, and FIG. 2 is a phase data unwrapping method according to the embodiment of the present invention. FIG. 3 is a diagram showing the interference fringe intensity data and its phase data obtained by the surface shape measuring apparatus X to which is applied. FIG. 3 is extracted by the surface shape measuring apparatus X to which the phase data unwrapping method according to the embodiment of the present invention is applied. Figure showing an example of the effective area,
FIG. 4 is a flowchart showing a processing procedure of the surface profile measuring apparatus X to which the phase data unwrapping method according to the embodiment of the present invention is applied, and FIGS. 5 and 6 are phase data unwrapping methods according to the embodiment of the present invention. FIG. 7 is a diagram showing an example of phase data, and FIG. 7 is a diagram showing an example of neighboring points of the phase data in the phase data unwrapping method according to the embodiment of the present invention.

FIG. 1 shows a structure of a surface shape measuring apparatus X for a wafer or the like to which an unwrap method according to an embodiment of the present invention is applied. The hardware configuration of the surface profile measuring apparatus X is the same as that of the conventional surface profile measuring apparatus Z described above, and therefore the description thereof is omitted here. Further, in the surface profile measuring apparatus X, the drive unit 5 is controlled so that the set position of the reference reflecting mirror 4 is set in four stages (0, λ / 8) in the optical axis direction by λ / 8 (λ is the wavelength of light). , 2λ / 8, 3λ / 8), and at each set position, the interference fringe intensity data I ₀ , I ₉₀ , I ₁₈₀ , I ₂₇₀ of each pixel (point) from the signal processing circuit 11 is transferred to the computer. It is as described above that the phase data θ is obtained by taking the data into 12 and using the equation (1). The phase data unwrapping method according to the present invention is characterized by a method of unwrapping the phase data θ, and is embodied by the computer 12 executing a predetermined program registered in advance.

Next, the unwrap processing procedure will be described with reference to FIG. Hereinafter, S1, S2, ... represent the numbers of procedures (steps) processed by the computer 12. It is assumed that the interference fringe intensity data has already been captured before the processing of FIG. 4 is started.
First, in S1, by the method described below, the entire area of the measured two-dimensional coordinates is removed by removing the area of the outer edge of the measured surface 8a and the area of the hole portion on the surface of the measured surface 8a. Extract a region. Since interference light cannot be obtained at the outer edge of the surface to be measured 8a or in the region of the hole in the surface to be measured 8a, the interference intensity data at each of the four setting positions of the reference reflecting mirror 4 is obtained. I ₀ , I ₉₀ , I ₁₈₀ , I
_{The value} of the combined intensity data (amplitude value of interference light) _obtained by combining _270- becomes smaller. Therefore, only the points where the combined intensity data is equal to or more than a predetermined value are extracted as the effective area, and the phase data θ is extracted by using the equation (1) only for the effective area.
Is calculated, and the subsequent unwrap processing is performed on the phase data θ. As a result, it is possible to prevent an erroneous calculation from being performed by using the data of the hole and the outer edge area of the measured surface 8a. This processing is conventionally performed generally. The composite intensity data I
_kyodo is expressed by the following equation (3). _{I kyodo = √ ((I 0} -I 180) 2 + (I 90 -I 270) 2) ... (3) shows an example of the effective region extracted this way in FIG. In FIG. 3, the right direction is the x-axis direction and the downward direction is the y-axis direction. Further, the inside of the broken line represents all the two-dimensional areas in which the interference intensity data is obtained, of which the blank portion 31
The shaded area except 1 represents the effective area 312.

Next, in S2, a normal unwrap (hereinafter referred to as local unwrap) is performed at a certain point of the effective area 312 by comparison with eight points in the vicinity thereof (corresponding to the local unwrap procedure). The local unwrap means the phase data of the reference point P (hereinafter referred to as reference phase data θp) with respect to a point Q near a certain reference point P in the effective area 312 (for example, a point near the center of gravity of the effective area). ) Is corrected by an integral multiple of 2π so that the difference (phase difference) with) falls within the range of −π to + π, that is, (2) above.
To find the order n in the equation. When this is expressed by an equation, the degree n at the reference point P that satisfies the following equation (4)
It means to ask for q. −π ≦ θq + 2πnq−θp <+ π (4) where θp is the phase data at the point P, θq and nq
Are the phase data and the order of the neighboring point Q.
Further, in the present embodiment, the neighboring points Q refer to eight surrounding points (hereinafter referred to as neighboring points) adjacent to the reference point P, as shown in FIG. 7A. Using the equation (4), the order nq is calculated for each of the eight neighboring points Q. Obtaining the degree nq of the neighboring point Q by the equation (4) means that the phase data will be smoothly changed between the reference point P and its neighboring point Q. If the difference in the phase data between the reference point P and the neighboring point Q is extremely large, it is assumed that a so-called jump has occurred, and the indeterminacy is corrected (that is, unwrapped). . For example, in the data shown in FIG. 5A, when each of the coordinates (i, j) and (i + 1, j) is the reference point P and the neighboring point Q, the reference phase data θp = 5.
5, since the phase data θq = 0.22 at the point Q,
The degree nq of the Q point that satisfies the equation (4) is nq = 1 (the number in parentheses in FIG. 5B). A value obtained by correcting the phase data at the point Q by the order nq, that is, θq _LU obtained by the following equation (5) is hereinafter referred to as local unwrap data at the point Q. In the example of FIG. 5B, θq _LU = 6.5. .theta.q the _{LU = θq + 2πnq ... (5} ) such the local unwrapping (Calculation of nq), performed on eight of the respective neighboring point Q, and stores the local unwrap data .theta.q _LU in the storage unit of the computer 12.

Next, in S3, a fitting formula which is an approximate formula of the reference phase data θp and the local unwrap data θq _LU is obtained by least-squares approximation. The fitting equation is a primary two-variable equation, that is, the following equation (6) which is a primary plane equation. z = a * x + b * y + c (6) where a, b, and c are coefficients obtained by least-squares approximation. The coefficients a to c of the fitting equation obtained in this way are replaced with the coefficients a to c of the fitting equation at the point P.
Is stored in the storage unit of the computer 12 (corresponding to the fitting formula calculation procedure). Here, of the 9 points, when the number of points within the effective area 312 extracted in S1 is 3 or less, a plane equation cannot be obtained by least square approximation, and thus the reference point at that time P is
It is stored as invalid data. For example, FIG. 5 (b)
In the above example, if i = j = 0 and the fitting equation is obtained by least-squares approximation, the following equation (7) is obtained. z = 1x + 0.55y + 5.533 (7)

Next, in S4, a fitting error of the reference phase data θp and the local unwrap data θq _{LU at} the neighboring point Q with respect to the fitting formula is obtained (corresponding to the fitting error calculation procedure). Here, for each of θp and θq _LU , S
The difference from the value (z) obtained by substituting the coordinates of each point in the fitting equation (that is, the equation (7)) at the reference point P obtained in 3 above, and the absolute value of the phase difference Is stored in the storage unit of the computer 12 as the fitting error at the reference point P. For example, in the example of FIG. 5B, the local unwrap data θq _{LU of} the point (i, j + 1) adjacent to the lower side of the reference point P and the fitting expression at the reference point P (7) When the difference from the value of z obtained by substituting (i, j + 1) into the expression is obtained, i = j = 0, so 6.3- (0 + 0.55 × 1 + 5.53)
3) = 0.217. Similarly, for the remaining 8 points, the difference from the value of z obtained by the equation (7) is obtained, and the one having the maximum absolute value is taken as the fitting error. In addition to the above, the fitting error is, for example, the average value of the absolute values of the differences between the values obtained by the fitting formula at the nine points P and Q, and the error between the fitting formula and each point. Any other method may be used as long as it can be used as an index representing.

Next, in S5, it is determined whether the reference phase data θp is valid data or invalid data based on the fitting error obtained in S4. That is, when the fitting error exceeds a predetermined allowable error range (for example, −π / 5 to + π / 5, etc.),
The reference phase data θp is stored in the storage unit of the computer 12 as invalid data, and otherwise stored as valid data (corresponding to the valid / invalid determination procedure). The tolerance is the computer 12
It can be set by an input unit such as a keyboard. The effects of performing such processing are as follows. The phase data may include noise due to, for example, adhesion of dust to the surface of the subject, protrusions on the surface of the subject, or Fresnel diffraction at the end of the subject. Then, since the unwrapping (determination of the order n) of each of the phase data is performed by relative evaluation with the phase data of a nearby (adjacent) point or a point in the vicinity thereof, the noise including such noise is If the phase data is not excluded from the target of unwrapping, this noise will propagate to the next unwrapping, resulting in a totally incorrect unwrapping. However, for example, when the subject is tilted in the direction of canceling the noise, if the presence or absence of the noise is determined only by the phase difference from the neighboring point, the valid data should be the invalid data. I will erroneously judge that. The opposite is also true. Therefore, even if the subject is tilted, the tilt is reflected in the fitting formula by determining the validity / invalidity based on the fitting error with the fitting formula that approximates the nearby points. The erroneous determination as described above can be prevented. As a result, it is possible to prevent the propagation of noise to the entire unwrap.

Next, in S6, the effective area 312 is
If it is determined whether or not the valid / invalid determination has been performed for all the phase data in the above, and if it is determined that the valid / invalid determination is not performed for all of the phase data, Is set as the new reference point P (that is, the local unwrap data at that point is set as the new reference data θp) (S7), and the new reference point P and its neighboring points. About S2-S5
Process. The processes of S2 to S7 are sequentially performed while further setting the neighboring point of the neighboring point as the new reference point P, and the valid / invalid determination is performed for all the phase data in the valid area 312. Up to (No side of S6). Here, as a method of sequentially determining the new reference point P, a filling algorithm or the like is applied.

On the other hand, if it is determined in S6 that the validity / invalidity is determined for all the phase data in the valid area 312, the process proceeds to S8, and a certain point is determined as the valid data. In step 1, unwrapping by extrapolation based on the fitting equation (hereinafter referred to as extrapolation unwrap) is performed (corresponding to the extrapolation unwrap procedure). The extrapolation unwrap refers to one of the points determined as the valid data as a reference valid point A (the phase data θa at the point A corresponds to the reference valid data), and the neighboring points of the reference valid point A. For a point C (hereinafter referred to as a quasi-neighbor point) nearer to B, the fitting equation at the reference effective point A (that is, the fitting equation obtained when the reference effective point A is set to the reference point P).
The extrapolated value of the quasi-neighboring point C is obtained by
Is to be corrected by an integer multiple of 2π, that is, the order at the quasi-neighboring point C is recalculated. This means to obtain the order nc that satisfies the following equation (8). −π ≦ θc + 2πnc−θc ′ <πθc ′ = θa + 2πna + a (ic−ia) + b (jc−ja) (8) where θa and θc are the phase data at points A and C,
ia and ic are the x coordinates of the points A and C, and ja and jc are the points A and C.
Of the fitting equation at the point A, and a and b are coefficients representing the inclinations in the x direction and the y direction, respectively, and n.
a and nc represent the orders at the points A and C, and θc ′ represents the extrapolated value at the point C, respectively. In this way, for the point C on which the extrapolation unwrapping has been performed, information indicating that the extrapolation unwrapping has been performed is stored in the storage unit of the computer 12 together with the degree nc.

A specific example of the extrapolation unwrap will be described below with reference to the data shown in FIG. In the data shown in FIG. 6, among the points determined to be valid, the coordinates are (i-
1, j), (i, j), (i + 1, j), which are the phase data at three points A, B, and C. These data are obtained as a result of the subject being installed with a relatively large inclination,
The phase data has a gradient of 2 rad in the x-axis direction, and noise of 1.5 rad is added only to the point C. In the case of such a measurement target, the image obtained by the camera 11 has dense interference fringes. Therefore, if the conventional technique is applied to this, the number of the small regions to be divided becomes large. Not practical. Therefore, the extrapolation unwrapping is applied to the data in FIG. Where point A,
The orders na and nb at the point B have already been calculated (na =
nb = 3), and the coefficient a (inclination in the x-axis direction) of the fitting equation at the point A is also obtained (a =
2) It shall be. Then, the data of FIG. 6, that is, a =
2, i = j = 0, na = 3, θa = 3.160, θc =
Substituting 2.477 into the equation (8), the order of the quasi-neighboring point C is nc = 4, and the phase data after unwrapping (that is, unwrapping data) is θc + 2πnc = 27.
It becomes 597. On the other hand, in the general unwrap, the unwrap data (θc + 2πnc) at the point C and the unwrap data (θb + 2πnb) at the point B adjacent thereto.
= 24.000), the order nc of the point C is determined such that the difference is within the range of -π to π. According to this general unwrapping, nc = 3. This result is incorrect because the phase data has a gradient of 2 rad in the x-axis direction. As described above, according to the present invention, since the inclination of the phase data caused by the inclination of the subject is taken into consideration, the unwrapping can be correctly performed even when the subject is tilted. As a result, it is not necessary to finely adjust the positioning of the subject so that the subject is not tilted, and the measurement throughput is improved. Also, in the example of FIG. 6, even when the present invention is applied to the data obtained by removing 1.5 rad of noise added to the phase data θc at the point C, the order of the point C is nc = 4.
This indicates that the present invention also has a feature that it is resistant to noise.

Next, in S9, it is determined whether or not the extrapolation unwrapping has been completed (whether the order has been recalculated) for all the data determined to be the valid data, and the extrapolation unwrapping has been performed for all of them. If it is determined that it has not been completed, one of the neighboring points (adjacent points) of the reference valid data A is set as the new reference valid point A (S10), and the points in the neighborhood of the neighboring points are set. The extrapolation unwrapping of S8 is performed on the data (that is, the new quasi-neighborhood effective data C). By repeating this in sequence, the extrapolation unwrapping is performed on all the data determined to be the valid data, and then the processing ends.
Here, as a method of sequentially determining the new reference valid data, a filling algorithm or the like is applied.

[0024]

EXAMPLES Next, application examples of the above-described embodiment will be described. In the above-described embodiment, as shown in FIG. 7A, the surrounding eight points near the reference point (the reference point P, the reference effective point A) are used as the neighboring points, and the local unwrap and The calculation of the fitting formula, the extrapolation unwrap, and the like are performed, but the present invention is not limited to this, and FIG.
As shown in Fig. 4, 4 adjacent to the top, bottom, left and right of the reference point
A point may be similarly processed as the neighboring point. This is because, if the fitting formula is two variables of the first order, the fitting formula can be obtained by least-squares approximation if there are four points or more in total. 7 (c) and 7 (d)
As shown in FIG. 5, it is also possible to perform similar processing using the neighborhood used in the filter processing in so-called image processing, for example, a reference point and its neighborhood 24 points, or neighborhood 20 points as the neighborhood points.

In the above-described embodiment, a Michelson interferometer is used as the interferometer 1.
Other interferometers such as the Fizeau interferometer or the Twyman-Green interferometer may be used.

Further, in the above-described embodiment, as the fitting equation, the linear two-variable equation (primary planar equation) shown in the equation (6) is used. In addition, a quadratic two-variable equation such as the following equations (9) and (10) may be used. z = ax ² + by ² + cx + dy + e (9) z = ax ² + by ² + cxy + dx + ey + f (10) where a to f are coefficients obtained by least-squares approximation.
In this case, it is necessary to consider the number of neighboring points so that each coefficient can be obtained. For example, when there are five coefficients to be obtained, at least 6 points are required for the reference point and the neighboring points. Also, similarly,
It is also possible to use a bivariate expression of third or higher order, taking into consideration the number of the neighboring points.

Further, in the above-mentioned embodiment, the extrapolation unwrapping is not performed for the points determined to be the invalid data, but the degree is obtained in the vicinity of the points determined to be the invalid data. If the valid data is present (ie, the unwrap data was determined), then
Also using the fitting formula for the neighboring points, the degree is determined (unwrapped) so that the difference between the point determined to be the invalid data and the extrapolated value falls within a predetermined range (-π to + π). It may be one. This is effective when, for example, an incorrect order is determined at the time of the local unwrap due to the inclination of the subject, and as a result, a large number of points determined to be the invalid data are generated.

[0028]

As described above, according to the present invention,
Since it is unlikely to be affected by noise included in the measurement data or local unevenness on the surface of the subject, it is possible to prevent erroneous unwrapping due to propagation of an error due to this. Further, even when measuring an object having an inclination with respect to the incident light, the inclination of the object is reflected in the fitting equation, so that the measurement can be correctly unwrapped and the throughput of the entire measurement including the installation of the object can be improved.

[Brief description of drawings]

FIG. 1 is a diagram showing a schematic configuration of a surface shape measuring apparatus X to which a phase data unwrapping method according to an embodiment of the present invention is applied.

FIG. 2 is a diagram showing interference fringe intensity data and its phase data obtained by the surface profile measuring apparatus X to which the phase data unwrapping method according to the embodiment of the present invention is applied.

FIG. 3 is a diagram showing an example of an effective region extracted by a surface shape measuring apparatus X to which a phase data unwrapping method according to an embodiment of the present invention is applied.

FIG. 4 is a flowchart showing a processing procedure of the surface profile measuring apparatus X to which the phase data unwrapping method according to the exemplary embodiment of the present invention is applied.

FIG. 5 is a diagram (1) showing an example of phase data for explaining an unwrapping method of phase data according to the embodiment of the present invention.

FIG. 6 is a diagram (2) showing an example of phase data for explaining the phase data unwrapping method according to the embodiment of the present invention.

FIG. 7 is a diagram showing an example of neighboring points of phase data in the phase data unwrapping method according to the embodiment of the present invention.

[Explanation of symbols]

1 ... Interferometer 2 ... Light source device 3 ... Beam splitter 4 ... Reference reflector 4a ... Reference surface 5 ... Drive unit 6 ... Imaging lens 7 ... Camera 8 ... Subject 8a ... Surface to be measured 11 ... Signal processing circuit 12 ... Computer 13 ... Monitor P ... Reference point (reference phase data) S1, S2, ... Processing procedure (step)

   ─────────────────────────────────────────────────── ─── Continued front page    F term (reference) 2F064 AA09 CC03 EE01 FF01 GG12                       GG23 GG52 HH03 HH08 JJ01                 2F065 AA53 BB03 CC19 DD04 DD11                       FF04 FF52 FF61 FF67 GG04                       HH03 HH13 JJ03 JJ26 LL12                       LL37 MM03 PP12 QQ17 QQ25                       QQ28 QQ31

Claims (8)

[Claims] 1. A phase data unwrapping method for unwrapping two-dimensional phase data obtained by an interferometer, comprising: reference phase data, which is a predetermined one of the phase data, and at least three or more in the vicinity thereof. A local unwrap procedure for obtaining local unwrap data, which is data obtained by correcting the phase data by an integer multiple of 2π so that the difference from the reference phase data falls within a predetermined phase difference range, the reference phase data and the local unwrap procedure. A fitting equation calculation procedure for obtaining a fitting equation of two variables that approximates the local unwrap data, a fitting error calculation procedure for obtaining a fitting error between the fitting equation and the reference phase data and the local unwrap data, and the fitting error is predetermined. If the tolerance is exceeded, the standard position A valid / invalid determination procedure for determining data as invalid data and otherwise determining the reference phase data as valid data, wherein the local unwrap procedure is used as one of the local unwrap data as the reference phase data, The fitting equation calculation procedure, the fitting error calculation procedure, and the validity / invalidity determination procedure are executed, and the validity or invalidity is determined for all the phase data by sequentially repeating the procedure, and then the unwrapping is performed only for the valid data. How to unwrap the phase data. 2. For the quasi-neighbor effective data which is the effective data in the vicinity of the effective data in the vicinity of the effective reference data which is a predetermined one of the effective data, the reference effective data is set to the reference phase data. The extrapolation value of the phase of the quasi-neighborhood effective data is obtained by extrapolation based on the fitting equation obtained when, and the quasi-neighborhood effective data is calculated so that the difference from the extrapolated value falls within a predetermined range. Two
The method has an extrapolation unwrap procedure in which data corrected by an integer multiple of π is used as unwrap data, and the extrapolation unwrap procedure is executed by using one of the valid data in the vicinity of the reference valid data as the new reference valid data. The method of unwrapping phase data according to claim 1, wherein the unwrap data is obtained for all the valid data by sequentially repeating this. 3. For the invalid data, if the valid data for which the unwrap data is obtained is present in the vicinity of the invalid data, an extrapolation based on the fitting equation obtained when the valid data is used as the reference phase data. By extrapolation, the extrapolated value of the phase of the invalid data is obtained, and the invalid data is set to 2π so that the difference from the extrapolated value falls within a predetermined range.
3. The unwrapping method of phase data according to claim 2, further comprising an invalid data unwrapping procedure in which data corrected by an integer multiple of is used as unwrapped data. 4. The unwrapping method of phase data according to claim 1, wherein the fitting formula is a linear two-variable formula. 5. A phase data unwrapping device for unwrapping two-dimensional phase data obtained by an interferometer, wherein said phase data in the vicinity of reference phase data, which is a predetermined one of said phase data, Local unwrap means for obtaining local unwrap data, which is data corrected by an integral multiple of 2π so that the difference from the reference phase data falls within a predetermined phase difference range, and is approximated to the reference phase data and the local unwrap data. Fitting equation calculating means for obtaining a fitting equation of two variables, fitting error calculating means for obtaining a fitting error between the fitting equation and the reference phase data and the local unwrap data, and the fitting error calculating means for determining if the fitting error exceeds a predetermined tolerance. The reference phase data is judged as invalid data, If the reference phase data is not valid, the valid / invalid determination means is provided for determining the reference phase data as valid data, and one of the local unwrap data is used as the reference phase data, the local unwrap means, the fitting formula calculation means, and the fitting error calculation. Means and the validity / invalidity determining means to determine validity or invalidity, and by sequentially repeating this, all the phase data are validated or invalidated, and then only the valid data is unwrapped. A phase data unwrapping device. 6. The reference phase data is the reference phase data for quasi-neighborhood effective data which is the effective data in the vicinity of the effective data in the vicinity of the effective reference data which is a predetermined one of the effective data. The extrapolation value of the phase of the quasi-neighborhood effective data is obtained by extrapolation based on the fitting equation obtained when, and the quasi-neighborhood effective data is calculated so that the difference from the extrapolated value falls within a predetermined range. Two
an extrapolation unwrap means for making data corrected by an integer multiple of π as unwrap data, wherein one of the valid data in the vicinity of the reference valid data is used as the new reference valid data by using the extrapolation unwrap means. 6. The phase data unwrapping device according to claim 5, wherein the unwrapping data is calculated for all the valid data by calculating the unwrapping data and sequentially repeating the calculation. 7. In the case where the valid data for which the unwrap data is obtained exists in the vicinity of the invalid data, an exterior value based on the fitting formula obtained when the valid data is used as the reference phase data. By extrapolation, the extrapolated value of the phase of the invalid data is obtained, and the invalid data is set to 2π so that the difference from the extrapolated value falls within a predetermined range.
7. The phase data unwrapping device according to claim 6, further comprising invalid data unwrapping means for making data corrected by an integral multiple of 1 as unwrapped data. 8. The phase data unwrapping device according to claim 5, wherein the fitting equation is a linear two-variable equation.