JPH05340843A - Method for connecting phase of wave front by fringe scanning interference measurement system - Google Patents

Abstract

PURPOSE:To obtain a method for connecting phase which can obtain a continuous phase distribution even if dust or defects exist within an interference fringe pattern and a partial phase data is lost. CONSTITUTION:In a method for obtaining the phase at each phase where a measurement light and a reference light are interfered on an area sensor by a fringe scanning interference measurement system, the phase of the reference light is changed stepwise. the intensity value of interference fringes at each step is read, and then an operation processing is performed based on the data, the obtained phase data region is scanned in one direction, a continuous phase region where the phase data exists continuously for each scanning line is detected, and then phase is connected within the region. The phases of the continuous phase regions are connected, thus obtaining a continuous phase distribution.

Description

Detailed Description of the Invention

[0001]

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to a method for connecting wavefront phases in a fringe scanning interferometry system.

[0002]

2. Description of the Related Art The fringe scanning interferometry method is
The phase difference between the object light and the reference light is N by the phase change of the reference light.
The number of steps (however, N is an integer) is changed, the interference fringe pattern at each step is read by a two-dimensional area sensor, photoelectrically converted, digitized,

[0003]

[Equation 1]

It is known as a method for obtaining the phase W (X, Y) by the above-mentioned equation 1. However, in Equation 1, I
_j (X, Y) is the light intensity at the (X, Y) position of the interference fringe pattern in the j-th phase change, and k is the wave number 2π / λ when λ is the wavelength of the light. Also, l _j
= (Λ / 2π) j, which is the phase change amount at the j-th stage. Number 1
However, the tan ^-1 calculation is limited to the main value (-π / 2 to π / 2), and in reality, the continuous phase distribution has a phase discontinuity of π. Occurs. Therefore, the direction of phase jump (-π / 2 to π / 2,
Alternatively, it is necessary to two-dimensionally determine (π / 2 to −π / 2) and correct it to obtain a continuous phase distribution.

As a conventionally known method for obtaining the phase distribution, there is a technique disclosed in Japanese Patent Laid-Open No. 3-218431. This is because, as shown in the flowchart of FIG. 8, the correction value δ at each pixel (X _i , Y _i ) is obtained by scanning the phase data obtained by the equation 1 in the X direction.
_x (X _i , Y _i ) is _calculated with reference to the value on the line of X = X _c . Next, on the line of X = X _c , the correction value δ _y (X _i , Y _i ) in the Y direction is obtained with the value at Y = Y _c as a reference. Finally, the correction value δ obtained as described above
_x (X _i , Y _i ) and δ _y (X _i , Y _i ) are added to the phase data at each pixel (X _i , Y _i ) to obtain a continuous phase distribution.

[0006]

However, in the above-mentioned conventional technique, since the phase jump is determined only from the phase between two points before and after on the scanning line in one direction, the phase data of the previous pixel is If it is missing, the phase jump cannot be determined and the phase connection becomes discontinuous.

The present invention has been made in view of the above problems, and it is possible to obtain a continuous phase distribution even if a part of phase data is lost due to dust or defects existing in the interference fringe pattern. The purpose is to provide a phase connecting method.

[0008]

In order to achieve the above object, in the phase joining method of the present invention, the measurement light and the reference light are caused to interfere with each other on the area sensor by the fringe scanning interferometry, and the phase of the reference light is changed. Change in stages,
Reading the intensity value of the interference fringes at each stage, in the method of calculating the phase at each point by performing arithmetic processing based on the data, scan the phase data area obtained in one direction,
The first step of connecting the phases in the continuous phase region where the phase data continuously exists for each scanning line,
A continuous phase distribution is obtained by a second step of connecting the phases of the continuous phase regions in a direction orthogonal to the direction.

[0009]

Next, the operation of the phase connecting method of the present invention will be described with reference to the flowchart of FIG. First, in step S1, the continuous phase region L _jk in the X direction is detected. That is, as shown in FIG. 2, the phase data obtained by the equation 1 is sequentially scanned in the X direction to detect a region where the phase data continuously exists on each scanning line. Here, the k-th continuous phase area on the j-th scanning line is L _jk .

Next, in step S2, the continuous phase region L
Perform phase connection in _jk . That is, as shown in FIG. 3, the phase distribution in the region L _jk takes a value from −π / 2 to π / 2, and there is a portion where a phase jump of π occurs. As a means for correcting this, two adjacent points (X _i-1 , Y _j ) and (X
There is a phase difference ΔW between _i , Y _j ), that is, ΔW = W (X _i , Y _j ) −W (X _i-1 , Y _j ) ... (2) absolute value | ΔW | If it is larger than the threshold value θ, it is determined that there is a phase jump, and if not, it is determined to be continuous. When a phase jump occurs, the following correction value δ (X _i , Y _j ) (where (X _i , Y _j ) εL _jk ) is given according to the positive or negative of ΔW. When | ΔW |> θ and ΔW <0 δ (X _i , Y _j ) = δ (X _i-1 , Y _j ) + π | ΔW |> θ and ΔW> 0 δ (X _i , Y _j ) = Δ (X _i-1 , Y _j ) -π In other cases, δ (X _i , Y _j ) = δ (X _i-1 , Y _j ). However, the correction value at the start point of each area L _jk is set to 0. The correction value δ (X _i , Y _j ) obtained as described above is added to all the phase data W (X _i , Y _j ) in each region L _jk , and W ′ (X _i , Y _j ) is added. And That is, W '(X _i , Y _j ) = W (X _i , Y _j ) + δ (X _i , Y _j ) ... (3).

Next, in step S3, the continuous phase region L _{(j-1) 1} or L _{(j + 1) m} adjacent to the phase data in the continuous phase region L _jk obtained in the above process in the Y direction. The following processing is performed so that the phase data in 1 is continuously connected. That is,
As shown in FIG. 4, the j-th row k-th continuous phase region L _jk
Among arbitrary phase data among them, data having phase data Wp ′ (L _{(j−1) k} ) in the pixel on the same column and one row above in the Y direction is _defined as Wp ′ (L _jk ). Wp '(L _jk ) and Wp'
(L _{(j-1) k} ) Phase difference ΔWp ', that is, ΔWp' = Wp '(L _jk ) -Wp' (L _{(j-1) k} ) ... (4) Absolute value | ΔWp If '| is smaller than a certain threshold value θ, π is added to or subtracted from Wp' (L _jk ), and ΔWp '= (Wp' (L _jk ) ± nπ) -Wp '(L _{(j-1) k} ) (N: integer) (5), the addition and subtraction of π is repeated n times until | ΔWp ′ | becomes smaller than θ. Then, when | ΔWp ′ | <θ, for all the phase data W ′ (X _i , Y _j ) in the region L _jk , W ″ (X _i , Y _j ) = W ′ (X _i , Y _j ) ± nπ (where (X _i , Y _j ) εL _jk ) ... (6) is calculated, where all the phase data Wp ′ in L _jk are calculated.
When Wp '(L _{(j-1) k} ) does not exist for (L _jk ), after processing of all the phase regions is completed, 1 in the same column in the phase data in the region L _jk in the Y direction. If the phase data Wq ″ (L _{(j + 1) k} ) exists in the pixel just below the row, Wq ′
(L _jk ), Wq ′ (L _jk ) and W ″ (L _{(j + 1) k} ).
ΔWq ', that is, ΔWq' = Wq '(L _jk ) -W "(L _{(j + 1) k} ) ... (7) absolute value | ΔWq' | Π is added to or subtracted from Wq ′ (L _jk ) so as to be small, and ΔWq ′ = (Wq ′ (L _jk ) ± nπ) −Wq ″ (L _{(j-1) k} ) (n: integer) ... By (8), the adjustment of π is repeated n times until | ΔWq ′ | becomes smaller than θ. When | ΔWq '| <θ, (6)
Compute W ″ (X _i , Y _j ) according to the formula. W ″
(X _i , Y _j ) is the continuous phase distribution to be obtained.

If processing is performed according to the procedure described above,
A continuous phase distribution as shown in FIG. 5 (B) can be obtained from the phase distribution with the phase jump as shown in FIG. 5 (A).

[0013]

[Embodiment 1] An embodiment of a phase connecting method according to the present invention will be described below with reference to the accompanying drawings. First, a first embodiment of the present invention will be described. FIG. 6 is a diagram for explaining the first embodiment of the present invention. In the first embodiment, the procedure corresponding to step S1 in FIG. 1, that is, when the area L _jk is detected in the X direction, the coordinates of the start point and the end point of each area L _jk are stored, and the coordinates are calculated from the coordinates. The midpoint M _{jk of} each area is calculated, and the phase data at that point is used to connect the phases of the areas L _{jk in the} Y direction (corresponding to step S3 in FIG. 1).

The phase data near the end point of each region L _jk is susceptible to noise and may include an error. However, since the phase data at the midpoint is used in this embodiment, the measurement accuracy is higher. improves.

[0015]

Second Embodiment Next, a second embodiment of the present invention will be described. Figure 7
FIG. 8 is a diagram illustrating a second embodiment of the present invention. In the second embodiment, the procedure corresponding to step S1 in FIG. 1, that is, when detecting the region L _{jk in the} X direction, the regions at the upper and lower ends in the Y direction and the phases at the start and end points of the other regions After the data is cut, the processing of step S2 and thereafter in FIG. 1 is performed.

The phase data in the vicinity of the aperture of the interference fringes and in the vicinity of the missing area of the phase data due to dust or defects are likely to be affected by noise and may contain an error. Since the included data is excluded, the measurement accuracy is further improved.

[0017]

As described above, according to the phase connecting method of the present invention, it is possible to apply it to the interference fringes having dust or defects, or the interference fringes of a test object having a hole in shape. In addition, the measurement accuracy can be improved.

[Brief description of drawings]

FIG. 1 is a flowchart showing a phase connecting method according to the present invention.

FIG. 2 is a diagram illustrating a process of step S1 of FIG.

FIG. 3 is a diagram illustrating a process of step S2 of FIG.

FIG. 4 is a diagram illustrating a process of step S3 of FIG.

FIG. 5 is a diagram illustrating a continuous phase distribution obtained by the present invention.

FIG. 6 is a diagram illustrating a first embodiment of the present invention.

FIG. 7 is a diagram illustrating a second embodiment of the present invention.

FIG. 8 is a flowchart showing a conventional phase connecting method.

Claims (1)

[Claims] 1. A fringe scanning interferometry method causes measurement light and reference light to interfere on an area sensor, the phase of the reference light is changed stepwise, and the intensity value of interference fringes at each step is read, In the method of calculating the phase at each point by performing arithmetic processing based on that data, scan the calculated phase data area in one direction, and phase in the continuous phase area where the phase data continuously exists for each scanning line. A phase connecting method, wherein a continuous phase distribution is obtained by a first step of connecting and a second step of connecting phases of the continuous phase regions in a direction orthogonal to the direction.