JP2002195806A - Method and device for unwrapping two-dimensional phase data in interferometer - Google Patents

Abstract

PROBLEM TO BE SOLVED: To perform a precise unwrapping even in a state having a large noise. SOLUTION: A phase calculation is performed by extracting a pixel (boundary pixel) near a boundary, extracting a pixel (vicinity pixel) in the vicinity of the extracted boundary pixel, performing an integration to each region for pixels except the boundary pixel and the vicinity pixel, and integrating the boundary pixel and the vicinity pixel to each corresponding region.

Description

DETAILED DESCRIPTION OF THE INVENTION

[0001]

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to a method and an apparatus for unwrapping two-dimensional phase data obtained by an interferometer, and more particularly, to a method of convolving a phase of 0 to 2π without being affected by noise. The interferometer is capable of obtaining the original continuous phase distribution from the
The present invention relates to a method and an apparatus for unwrapping dimensional phase data.

[0002]

2. Description of the Related Art An interferometer that causes an interference between an object and a reference surface to form an interference fringe, obtains two-dimensional phase data from intensity data of the interference fringe, and calculates a shape difference between the reference surface and the object is known. Are known. This interferometer generally comprises (1) obtaining an interference fringe intensity distribution, (2) converting the intensity into phase information, and (3)
Determination of effective area, (4) unwrapping of phase, (5)
The shape is calculated by the procedure of converting the phase information into the shape.

In this procedure, when the intensity is converted into phase information in the procedure (2), the calculation of the arc tangent is generally included. For this reason, the phase data is stored on the right side of FIG. -Π which is the range of tan ^-1
Are convolved in the range of 0 to 2π corresponding to.

For example, in the Hariharan algorithm for calculating height information from five phase-shifted images, assuming that the amount of phase shift is α, the luminance of each image at a certain point is expressed by the following equation. You.

[0005]

(Equation 1) Here, I _{1 to} I ₅ (x, y) are image intensities and I ′ (x, y
y) is a DC component, I ″ (x, y) is an AC component, and φ (x,
y) is height information (phase information).

From the five equations, the following equation for φ (x, y) is obtained.

[0007]

(Equation 2)

Accordingly, the phase information φ (x, y) can be calculated by the following equation.

[0009]

(Equation 3)

As shown in the right side of FIG. 1 and the upper part of FIG. 2, jumps close to 2π appear in various parts of the phase data area obtained as a result of such phase data calculation. Eliminating this jump and obtaining continuously changing phase data as shown on the left side of FIG. 1 and the lower part of FIG. 2 is called unwrapping.

A general unwrapping algorithm is performed in the following procedure.

(1) Using a point starting unwrapping as a reference point, the phase of the point and the adjacent point are compared. (2) If there is a jump in phase, an integer multiple offset (see the middle part of FIG. 2) is added to the phase at the adjacent point so that the jump is eliminated. (3) When the procedure of (2) is completed, the procedure returns to the procedure of (1) using the next point as a new reference point.

[0013]

However, according to this method, as shown in FIG. 3 (exemplified in one dimension) and FIG. 4A (exemplified in two dimensions), when the noise at the boundary is large, unwrapping is performed correctly. 3 and the difference between the boundary portions becomes smaller than 2π due to the influence of noise at the boundary portions between the region 1 and the region 2 (in the case of FIG. 3).
As shown in FIG. 4C and FIG.
As shown in (B), there is a case where they are integrated into one area. Also, in order to perform unwrapping locally,
There is also a problem that a global error is likely to occur.

The present invention has been made to solve the above-mentioned conventional problems, and has as its object to enable accurate unwrapping without being affected by noise.

[0015]

The present invention is a method for unwrapping two-dimensional phase data obtained by an interferometer. After calculating a phase, a pixel near a boundary (boundary pixel) is extracted. A pixel (neighboring pixel) in the vicinity of the boundary pixel thus extracted is extracted, and after integrating the boundary pixel and the pixel excluding the neighboring pixel into each region, the boundary pixel and the neighboring pixel are extracted. The above-mentioned problem is solved by integrating the above-mentioned areas.

In the integration into each of the above-mentioned regions, a small region in which the number of elements of the region is equal to or less than the threshold value is regarded as noise and is regarded as an invalid region, thereby eliminating errors due to the small region. is there.

Further, for the pixels in the invalid area, the data is interpolated after the area integration, so that effective data can be obtained also for the invalid area.

Further, by solving the minimization problem for minimizing the sum of the phase jump amounts between all the regions for each of the regions, the movement amount of each region is calculated, so that the accurate movement amount is obtained. Is required.

The present invention also relates to the two-phase detector provided by the interferometer.
In an apparatus for unwrapping dimensional phase data, a boundary pixel extracting means for extracting a pixel near a boundary (boundary pixel) after calculating a phase, and a neighborhood for extracting a pixel (neighboring pixel) near the extracted boundary pixel Pixel extraction means, and, after performing integration on each area for the pixels excluding both the boundary pixels and the neighboring pixels, the boundary pixels and the area integration means for integrating the neighboring pixels into the corresponding area. Solving the optimization problem for minimizing the sum of the phase jump amounts between all the regions, and calculating means for calculating the movement amount of each region, thereby solving the above problem.

[0020]

Embodiments of the present invention will be described below in detail with reference to the drawings.

FIG. 5 is an explanatory diagram showing the configuration of a component evaluation system including an unwrapping device according to one embodiment of the present invention.

The evaluation system includes an interferometer 10, a signal processing circuit 30 connected to the interferometer 10, a computer 32 connected to the signal processing circuit 30, and a monitor 34 connected to the computer 32. It has.

The interferometer 10 includes a light source 12 that emits a parallel beam of laser light, and a beam splitter that receives the laser light from the light source 12, reflects a part of the incident light, and transmits the remaining part. 14, a reference mirror 16 that reflects light emitted from the light source 12 and transmitted through the beam splitter 14 to generate a reference surface, and a driving unit 18 for moving the reference mirror 16 in the optical axis direction. An imaging lens 20 disposed on the optical path of the light reflected by the reference mirror 16 and further reflected by the beam splitter 14;
A camera 22 for picking up an image formed by the zero.

On the optical path of the light emitted from the light source 12 and reflected by the beam splitter 14, a measured surface 8 of the subject is arranged, and the return light from the measured surface 8 is reflected on the beam splitter 14. It is designed to be incident.

In this interferometer 10, a laser beam of a parallel light beam emitted from the light source 12 is incident on the beam splitter 14, part of which is reflected, and part of which is transmitted. The light reflected by the beam splitter 14 is incident on the surface 8 to be measured, and the light returned from the surface 8 to be measured is again reflected by the beam splitter 1.
4, a part of the light is transmitted, and enters the camera 22 via the imaging lens 20. On the other hand, emitted from the light source 12,
The light transmitted through the beam splitter 14 is transmitted to a reference mirror 16.
The light is again incident on the beam splitter 14, is partially reflected, and is incident on the camera 22 via the imaging lens 20. As a result, interference fringes are formed on the camera 22 due to interference between the surface to be measured by the light from the surface 8 to be measured and the reference surface by the light from the reference mirror 16, and the interference fringes are imaged by the camera 22.

The output of the camera 22 is input to a signal processing circuit 30, where signal processing such as amplification and analog-to-digital conversion is performed to generate interference fringe intensity data for each two-dimensional position (pixel). Then, the interference fringe intensity data is input to the computer 32 corresponding to the unwrapping device of the present invention. At the time of the fringe scanning operation, the computer 32 controls the driving unit 18 to move the reference mirror 16 in four steps in the optical axis direction by, for example, λ / 4 (where λ is the wavelength of light). It takes in the interference fringe intensity data from the signal processing circuit 30 and generates phase data from the interference fringe intensity data based on the fringe scanning method. The computer 32 performs arithmetic processing such as phase unwrapping, and displays data, a characteristic diagram, and the like on the monitor 34 as necessary.

FIG. 6 shows the processing procedure of this embodiment performed by the computer 32. First, in step 100, the phase of each pixel is calculated.

Then, the process proceeds to a step 104, wherein noise removal is performed using the assumption that the phase information is continuous in the vicinity of each pixel. However, since the phase information is convolved in the range of 0 to 2π, an edge as shown in the right side of FIG. 1 and the upper part of FIG. 2 is generated.

Next, the routine proceeds to step 106, where pixels having a small phase difference in the vicinity are integrated with respect to the phase information to perform area integration. At this time, if there is a lot of noise, as described with reference to FIGS. 3 and 4, a region having a difference of 2π may be regarded as the same region and integrated.
Therefore, in the present invention, according to a procedure as shown in FIG.
Perform area integration. Although the actual processing is two-dimensional,
For the purpose of explanation, a description will be given with reference to a one-dimensional figure.

That is, after calculating the phase area, step 302
Then, the phase of the pixel is close to 0 (determined by the threshold value) corresponding to one of the boundaries, and there is a pixel in the vicinity that belongs to another region and has a phase close to 2π, or It satisfies the condition that the phase of the pixel is close to 2π corresponding to the other boundary (determined by the threshold value), and there is a pixel having a phase close to 0 that belongs to another area in the vicinity. Pixels (referred to as boundary pixels) are extracted. FIG. 6 shows the boundary pixels extracted by this processing. The boundary pixels extracted in step 302 are shown in FIG.
, And not all the boundaries have been extracted.

Next, proceeding to step 304, step 3
Pixels in the vicinity (for example, 8 neighborhoods) of the boundary pixel extracted in 02 are extracted (neighboring pixels). This step 30
FIG. 10 shows an example of the neighboring pixels extracted by No. 4. The neighboring pixels extracted in this step 304 are
When added to the boundary pixels extracted in 2, the plane is as shown in FIG. 11, and all the boundaries are extracted.

Next, the process proceeds to step 306, and as shown in FIG. 12, region integration is performed on pixels excluding the boundary pixels and neighboring pixels extracted in steps 302 and 304.
FIG. 13 shows the pixels excluding the boundary pixels and the neighboring pixels in a plan view, and performs the area integration processing only on the white areas.

After the area integration, the process proceeds to step 308,
When the number of elements in each area is equal to or less than a threshold value, for example, 4 to 16 pixels, this is regarded as noise and is regarded as an invalid area.
The remaining area is left as an effective area. This prevents a small area caused by noise from being mistakenly set as an effective area.

Next, the routine proceeds to step 310, where step 3
By integrating the boundary pixels extracted in step 02 and the neighboring pixels extracted in step 304 into corresponding areas as shown in FIG. 14, they are correctly integrated into different areas as shown in FIG. 4C. be able to.

After the area integration is completed, the process proceeds to step 108 in FIG.
If the number of pixels is six or less, this is regarded as noise and is set as an invalid area, and the remaining area is left as an effective area. This allows
A small area caused by noise is not mistakenly set as an effective area. The threshold value in step 108 can be set to a value different from the threshold value in step 308 in FIG.

Next, the routine proceeds to step 110, where a best fit is performed for each region to solve an optimization problem that minimizes the sum of the phase jump amounts between the respective regions. Now, consider the simultaneous best fit of a plurality of areas as shown in FIG. 15, as shown in FIG. 16, 'a boundary corresponding points ^{_{r i (S), r i}} (S' region S and S ^and).

At this time, the rotation and parallel movement of the surfaces S and S 'after the best fit are represented by R ^(S) , R ^(S') and T ^(S) , respectively.
Assuming that T ^{(S ′)} , the distance f _i ^{(s, s ′)} between the corresponding points at this time is
It is expressed by the following equation.

[0038]

(Equation 4)

At this time, by rounding f _i ^{(s, s ′)} by an integral multiple of 2π, an effect of reducing an error may be obtained.

Next, the following constraints are considered.

[0041]

(Equation 5) Here, tx, ty, and tz represent translation components in the x, y, and z directions, and φ, ψ, and θ represent roll, yaw, and pitch.

Here, since the vertical movement is almost the same, tx ^(sys) , ty ^(sys) , φ ^{(sys )} , ψ ^(sys) , θ
The constraint condition of ^(sys) is a value very close to 0.

When the rotation R is expressed by φ, ψ, θ,
It becomes the following formula.

[0044]

(Equation 6)

If this constraint is considered by the penalty method, the penalty function p of the surface s is defined as follows.

[0046]

(Equation 7) Here, γ _tx , γ _ty , γ _tz , γ φ, γ θ, and γ で are weights of each penalty, and are positive constants given in advance as reciprocals of allowable values of the constraint conditions.

From the above, the evaluation function vector F in which the constraints are incorporated as a penalty function is as follows.

[0048]

(Equation 8) However, the peterty term whose value is 0 is excluded.

Therefore, the evaluation amount Φ corresponding to the shift distance between the boundaries is given by the following equation.

[0050]

(Equation 9)

The unknown parameter X that minimizes the evaluation amount Φ is obtained by, for example, iterative calculation of the nonlinear least squares method. Here, Ns is the number of faces to be subjected to simultaneous best fitting, N (s, s ') is the number of corresponding points between the faces s and s', and the unknown parameter X is given by the following equation. Can be

[0052]

(Equation 10)

Based on the best fit solution obtained as described above, in step 112 of FIG. 6, the phase calculation is performed for the mutual pixels in each region, and the phase calculation is performed for each region as shown in the middle part of FIG. By adding different phases to each other, the whole is integrated as shown in the lower part of FIG. 2 to obtain the whole figure as shown on the left side of FIG.

Then, the process proceeds to a step 114, wherein a step 1
If interpolation is possible for the small invalid area excluded in step 08, interpolation is performed to supplement the data. If the interpolation cannot be performed because there are few neighboring pixels, it can be left as it is.

In this way, a particularly excellent effect can be obtained by combining the area integration processing shown in FIG. 7 and the best-fit method for solving the optimization problem. Note that the method of obtaining the movement amount of each region is not limited to the best-fit method, and is described in, for example, Japanese Patent Application Laid-Open No. 10-901.
A method using an equation, such as that proposed in No. 12, may be used.

[0056]

According to the present invention, correct unwrapping can be performed even in a situation where noise is large.

[Brief description of the drawings]

FIG. 1 is a perspective view for explaining unwrapping.

FIG. 2 is also a one-dimensional diagram.

FIG. 3 is a one-dimensional diagram for explaining a problem in the conventional unwrapping.

FIG. 4 is a plan view of the same.

FIG. 5 is an explanatory diagram showing a configuration of a component evaluation system including an unwrap device according to an embodiment of the present invention.

FIG. 6 is a flowchart showing an unwrap processing procedure in the embodiment.

FIG. 7 is a flowchart showing an area integration processing procedure.

FIG. 8 is a one-dimensional diagram showing an example of boundary pixels extracted by the area integration processing procedure.

FIG. 9 is a plan view of the same.

FIG. 10 is a one-dimensional diagram showing an example of neighboring pixels extracted by the area integration processing procedure.

FIG. 11 is a plan view showing boundary pixels and neighboring pixels extracted by the area integration processing procedure;

FIG. 12 is a one-dimensional diagram showing a state in which region integration is performed on pixels excluding the boundary pixels and neighboring pixels.

FIG. 13 is a plan view of the same.

FIG. 14 is a one-dimensional view showing how the boundary pixels and neighboring pixels are integrated into each region.

FIG. 15 is a perspective view showing an example of a best fit target.

FIG. 16 is an explanatory diagram of symbols used in the best fit.

[Explanation of symbols]

 8 Surface to be measured 10 Interferometer 12 Light source 14 Beam splitter 16 Reference mirror 18 Drive unit 20 Imaging lens 22 Camera 30 Signal processing device 32 Computer (unwrapping device) 34 Monitor

 ──────────────────────────────────────────────────続 き Continued on the front page F term (reference) 2F064 AA09 CC01 FF01 GG12 GG22 GG52 HH03 HH08 JJ01

Claims (5)

[Claims] In a method for unwrapping two-dimensional phase data obtained by an interferometer, a pixel near a boundary (boundary pixel) is extracted after calculating a phase, and a pixel (neighboring pixel) near the extracted boundary pixel is extracted. (Pixel), and after integrating the boundary pixel and its neighboring pixels together with each region, the boundary pixel and its neighboring pixels are integrated into the corresponding region. Unwrapping method of two-dimensional phase data in the interferometer. 2. The interference according to claim 1, wherein, at the time of integration into each area, a small area in which the number of elements of each area is equal to or smaller than a threshold value is regarded as noise and regarded as an invalid area. Unwrapping method of two-dimensional phase data in the meter. 3. The method of unwrapping two-dimensional phase data in an interferometer according to claim 2, wherein data is interpolated after pixel integration of the invalid area. 4. The moving amount of each region is calculated by solving an optimization problem for minimizing the sum of the amount of phase jump between all the regions for each region. 4. The method of unwrapping two-dimensional phase data in the interferometer according to any one of claims 1 to 3. 5. An apparatus for unwrapping two-dimensional phase data obtained by an interferometer, comprising: a boundary pixel extracting means for extracting a pixel (boundary pixel) near a boundary after calculating a phase; A neighboring pixel extracting means for extracting neighboring pixels (neighboring pixels); integrating the boundary pixels and the pixels excluding the neighboring pixels into each region; , A region integrating means for integrating into a corresponding region, and a calculating means for calculating a moving amount of each region by solving an optimization problem that minimizes a sum of phase jump amounts between all the regions. A device for unwrapping two-dimensional phase data in an interferometer, characterized in that: