JP3483139B2 - Method and apparatus for unwrapping two-dimensional phase data in an interferometer - Google Patents

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 an interferometer, and in particular, it is convoluted in the range of phase 0 to 2π without being affected by noise. 2 in an interferometer that can obtain the original continuous phase distribution from the measured phase distribution.
The present invention relates to a method and apparatus for unwrapping dimensional phase data.

[0002]

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

In this procedure, in general, when the intensity is converted into phase information in the procedure of (2), the calculation of the arc tangent is included, and therefore, the phase data includes the right side of FIG. 1 and the upper stage of FIG. As illustrated in, the range of tan ⁻¹ is −π
To π corresponding to 0 to 2π.

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

[0005]

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

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

[0007]

[Equation 2]

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

[0009]

[Equation 3]

Jumps close to 2π appear on the right side of FIG. 1 and the upper part of FIG. 2 in the phase data area obtained as a result of the 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 the point where unwrapping starts as a reference point, the phase of that point and the adjacent point are compared. (2) If there is a phase jump, an offset of an integral multiple (see the middle part of FIG. 2) is added to the phase at the adjacent point so that the jump is eliminated. (3) After completing the procedure of (2), the procedure returns to the procedure of (1) with the adjacent point as a new reference point.

[0013]

However, in this method, as shown in FIG. 3 (exemplified in one dimension) and FIG. 4 (A) (exemplified in two dimensions), unwrapping is correctly performed when the boundary noise is large. However, the difference between the boundary portions of area 1 and area 2 (in the case of FIG. 3), which are originally different areas, becomes smaller than 2π due to the noise of the boundary portion.
And as shown in FIG. 4 (C), another area originally is
As shown in (B), it was sometimes integrated into one area. Moreover, in order to perform unwrapping locally,
There was also a problem that global errors are likely to occur.

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

[0015]

SUMMARY OF THE INVENTION The present invention is a method for unwrapping two-dimensional phase data obtained by an interferometer, wherein after phase calculation, pixels near the boundary (boundary pixels) are extracted, and further extracted. Pixels (neighboring pixels) in the vicinity of the border pixels are extracted, the border pixels and the pixels excluding the neighboring pixels are integrated into each region, and then the border pixels and the neighboring pixels are The above-mentioned problems are solved by integrating them in corresponding areas.

Further, when integrating into each area, a small area in which the number of elements of the area is less than or equal to a threshold value is regarded as noise and is regarded as an invalid area, thereby eliminating an error due to the small area. is there.

Further, regarding the pixels in the invalid area, data is interpolated after the areas are integrated so that valid data can be obtained also in the invalid area.

For each area, the amount of movement of each area is calculated by solving the minimization problem that minimizes the sum of the amount of phase jump between all areas, and the accurate amount of movement is calculated. Is required.

The present invention is also provided by an interferometer.
In a device for unwrapping three-dimensional phase data, a boundary pixel extracting unit that extracts pixels near a boundary (boundary pixels) after phase calculation, and a neighborhood that extracts pixels (neighboring pixels) near the extracted boundary pixels. Pixel extraction means, area boundary integration means for integrating the boundary pixels and their neighboring pixels into corresponding areas after performing integration into each area for pixels excluding both of the boundary pixels and its neighboring pixels By solving the optimization problem of minimizing the sum of the phase jump amounts between all the regions, the calculation means for calculating the movement amount of each region is provided to solve the above problem.

[0020]

DETAILED DESCRIPTION OF THE INVENTION Embodiments of the present invention will be described in detail below with reference to the drawings.

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

This 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. Is equipped with.

The interferometer 10 includes a light source 12 which emits a laser beam of parallel light flux, and a beam splitter which receives the laser beam from the light source 12, reflects a part of the incident light, and transmits the remaining part. 14, a reference mirror 16 that reflects the light emitted from the light source 12 and transmitted through the beam splitter 14 to generate a reference surface, a drive 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, and the imaging lens 2
And a camera 22 for capturing an image formed by 0.

On the optical path of the light emitted from the light source 12 and reflected by the beam splitter 14, the measured surface 8 of the object is arranged, and the return light from the measured surface 8 is directed onto the beam splitter 14. It is supposed to be incident.

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

The output of the camera 22 is input to the signal processing circuit 30, where signal processing such as amplification and analog-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 unwrap device of the present invention. During the fringe scanning operation, the computer 32 controls the drive 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), and at each position, The interference fringe intensity data from the signal processing circuit 30 is fetched and phase data is generated 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 and characteristic diagrams on the monitor 34 as necessary.

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

Next, in step 104, noise is removed 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, the edges shown in the right side of FIG. 1 and the upper stage of FIG. 2 occur.

Next, in step 106, pixels having a small phase difference in the vicinity are integrated with respect to the phase information to perform area integration. At this time, when there is a lot of noise, as described with reference to FIG. 3 and FIG. 4, areas that originally have a difference of 2π may be regarded as the same area and integrated.
Therefore, in the present invention, according to the procedure as shown in FIG.
Perform area integration. Although the actual processing is two-dimensional,
For the sake of explanation, reference will be made to a one-dimensional drawing.

That is, after calculating the phase region, step 302
, The phase of the pixel is close to 0 corresponding to one boundary (determined by a threshold value), and there is a pixel in the vicinity, which belongs to another region and has a phase close to 2π, or The condition that the phase of the pixel is close to 2π corresponding to the boundary of the other (determined by the threshold value) and that there is a pixel near the phase that is close to 0 and should belong to another region of the other Pixels (referred to as boundary pixels) are extracted. The boundary pixels extracted by this processing are shown in FIG. The boundary pixels extracted in step 302 are shown in FIG.
As shown in (3), not all boundaries are extracted.

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

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

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

Then, the process proceeds to step 310 and step 3
The boundary pixel extracted in 02 and the neighboring pixel extracted in step 304 are integrated into corresponding areas as shown in FIG. 14 so that they are correctly integrated into different areas as shown in FIG. 4C. be able to.

After the region integration is completed, the process proceeds to step 108 in FIG. 6 and the number of elements in each region is a threshold value, for example, 4 to 1.
In the case of 6 pixels 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 will not be mistaken as an effective area. The threshold in step 108 can be set to a value different from the threshold in step 308 of FIG.

Next, in step 110, the best fit for solving the optimization problem that minimizes the sum of the phase jump amounts between the respective regions is performed for each region. Now, considering simultaneous best-fitting of a plurality of regions as shown in FIG. 15, assume that the boundary corresponding points of the regions S and S ′ are r _i ^(S) and r _i ^{(S ′)} as shown in FIG.

At this time, the rotations and the parallel movements of the surfaces S and S'after the best fit are respectively changed by R ^(S) , R ^{(S ')} and T ^(S) ,
If T ^{(S ')} , the distance f _i ^{(s, s')} between corresponding points at this time is
It is expressed by the following equation.

[0038]

[Equation 4]

At this time, it is possible to obtain the effect of reducing the error by rounding f _i ^{(s, s')} by an integral multiple of 2π.

Next, consider the following constraints.

[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.

Since most of the vertical translation is performed here, 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 represented by φ, ψ, and θ,
It becomes the following formula.

[0044]

[Equation 6]

Considering this constraint condition 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 ψ are weights of the respective penalties, and are positive constants given in advance as the reciprocals of the allowable values of the constraint conditions.

From the above, the evaluation function vector F incorporating the constraint condition as a penalty function is as follows.

[0048]

[Equation 8] However, the peterty term with a value of 0 is excluded.

Therefore, the evaluation amount Φ corresponding to the displacement 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 iterative calculation of the nonlinear least squares method, for example. Here, Ns is the number of surfaces to be subjected to simultaneous best fitting, N (s, s ′) is the number of corresponding points between the surfaces s and s ′, and the unknown parameter X is given by the following equation. To be

[0052]

[Equation 10]

Based on the solution obtained by the best fit obtained as described above, in step 112 of FIG. 6, the phase calculation is performed for the mutual pixels in each region, and the regions are calculated as shown in the middle part of FIG. By adding different phases to, the whole is integrated as shown in the lower part of FIG. 2 and the whole figure as shown on the left side of FIG. 1 is obtained.

Then, the process proceeds to step 114 and step 1
If interpolation is possible with respect to the small invalid area excluded in 08, interpolation is performed and data is replenished. If interpolation cannot be performed due to a small number of neighboring pixels, it can be left as it is.

In this way, a particularly excellent effect can be obtained by combining the region integration processing shown in FIG. 7 and the best fit method for solving the optimization problem. The method of obtaining the movement amount of each area is not limited to the best-fit method, and is, for example, JP-A-10-901.
A method using equations, such as that proposed in 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 drawings]

FIG. 1 is a perspective view for explaining unwrapping.

[Figure 2] Similarly, a one-dimensional diagram

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

FIG. 4 is a plan view of the same.

FIG. 5 is an explanatory diagram showing a configuration of a parts evaluation system including an unwrapping 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 flow chart showing a region integration processing procedure.

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

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

FIG. 12 is a one-dimensional diagram showing how regions are integrated with pixels excluding the boundary pixels and neighboring pixels.

FIG. 13 is a plan view of the same.

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

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

FIG. 16 is an explanatory diagram of codes used in 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

Continuation of front page (56) Reference JP 2000-155051 (JP, A) JP 2001-241930 (JP, A) JP 2001-153797 (JP, A) JP 2002-131027 (JP, A) ( 58) Fields surveyed (Int.Cl. ⁷ , DB name) G01B 9/02 G01J 9/02

Claims (5)

(57) [Claims] 1. A method for unwrapping two-dimensional phase data obtained by an interferometer, wherein after calculating a phase, pixels near a boundary (boundary pixels) are extracted, and pixels near the extracted boundary pixel (neighborhood) are extracted. Pixel) is extracted, and the boundary pixel and its neighboring pixels are removed, and after the pixels are integrated into each area, the boundary pixel and its neighboring pixels are integrated into a corresponding area. Method for unwrapping two-dimensional phase data in an interferometer. 2. The interference according to claim 1, wherein, in the integration into each of the areas, a small area in which the number of elements of the area is equal to or less than a threshold value is regarded as noise and is regarded as an invalid area. Method for unwrapping two-dimensional phase data in a meter. 3. The method of unwrapping two-dimensional phase data in an interferometer according to claim 2, wherein data is interpolated for pixels in the invalid area after area integration. 4. The amount of movement of each region is calculated by solving an optimization problem for each region that minimizes the sum of the amount of phase jump between all regions. 4. An unwrapping method for two-dimensional phase data in the interferometer according to any one of 3 to 3. 5. An apparatus for unwrapping two-dimensional phase data obtained by an interferometer, comprising boundary pixel extraction means for extracting pixels near a boundary (boundary pixels) after phase calculation, and further for extracting the extracted boundary pixels. A neighboring pixel extraction unit that extracts neighboring pixels (neighboring pixels), the boundary pixels, and the pixels excluding the neighboring pixels are integrated into each area, and then the boundary pixels and the neighboring pixels are combined. , Area integration means for integrating the areas into corresponding areas, and calculation means for calculating the movement amount of each area by solving an optimization problem that minimizes the sum of phase jump amounts between all areas. A two-dimensional phase data unwrapping device for an interferometer.