WO2018174392A1

WO2018174392A1 - Method and device for measuring reflection surface profile

Info

Publication number: WO2018174392A1
Application number: PCT/KR2018/000494
Authority: WO
Inventors: 김종안; 엄태봉; 김재완; 진종한; 이재용
Original assignee: 한국표준과학연구원
Priority date: 2017-03-21
Filing date: 2018-01-10
Publication date: 2018-09-27
Also published as: KR101968916B1; KR20180106575A

Abstract

The present invention provides a device and method for measuring a reflection surface profile. The device for measuring a reflection surface profile comprises: a Twyman-Green interferometer (120); a scanning stage (110) for moving a reflecting optical element (12) disposed in a measurement path of the Twyman-Green interferometer; a stage mirror (112) mounted to the scanning stage (110) and moved; a linear/angular interferometer (150) for measuring the location and a rotary motion error of the scanning stage (110) by using a beam reflected from the stage mirror; and a signal processing unit (130).

Description

Reflective profile measurement method and apparatus

The present invention relates to a method for measuring a flat mirror profile, and more particularly, a method for measuring the total reflection surface profile of a flat mirror by measuring interference images of a flat mirror mounted on a scanning stage and continuously conveyed at regular scanning step intervals. It is about.

In many precision systems, precision reflecting surfaces are used as reference planes for measurement systems. The precision reflecting surface corresponds to a reference mirror of a laser interferometer for precision stage position control, an X-ray optical system reflective mirror, and a large diameter interferometer reference mirror. Therefore, in order to increase the accuracy of the entire precision system, it is essential to accurately evaluate and machine / correct the reflection profile.

In general, reflective optical elements are secured to precision systems using screwing or adhesives. However, the profile of the precision reflecting surface may be deformed by an external force applied to fix the reflective optical element having the precision reflecting surface. Thus, the evaluation results and correction data obtained during machining or in a separate reflecting surface profile measuring system may differ from the actual profile of the precision reflecting surface fixed in the precision system. This reduces the accuracy of the overall precision system. In order to solve this problem, on-site measurement can be applied to evaluate the profile of the precision reflecting surface and fix the profile error with the reflective optical device fixed at the position to be finally used. In order to apply on-site measurement, the precision reflector profile measuring system must be applicable to a narrow installation space and high measuring speed is required to reduce external influences during the measurement.

Precision reflective profile measurement methods are divided into contact and non-contact methods. In general, non-contact measurement methods can avoid damage to the precision reflecting surface and achieve relatively high measurement accuracy. The laser interferometer is a representative non-contact profile measuring method, and may measure an accurate reflection surface profile by analyzing an interference signal formed between a reference mirror plane and a beam reflected from a measurement target reflection plane. Precision reflector profile measurement using laser interferometer is divided into full aperture interferometry (FAI) and sub-aperture interferometry (or stitching interferometry, SI).

Fizeau interferometry, a representative example of full aperture interferometry, requires a reference mirror of the same size as the reflecting surface to be measured. Therefore, the size of the measurement target is limited and on-site application is difficult. However, because the entire measuring area can be measured at once, high measuring speeds can be achieved, reducing the environmental impact. In addition, very high accuracy can be achieved depending on the quality of interferometer components such as reference mirrors and collimators. The cost is greatly increased in proportion to the quality of the optical system or the measuring range.

Sub-aperture interferometry can be used to obtain the total reflecting surface profile by continuously connecting the measured profile in a small measurement area as the object is moved. Therefore, it is a measuring method which can extend the measuring range without limitation. Therefore, although a relatively small installation space is required and the measurement range is easy to extend, the measurement time is increased to measure a large area, and thus the measurement accuracy is likely to decrease due to environmental influences.

Reflective profile measurement research using the SI method includes a measurement method using a three-axis laser interferometer. (Multi-probe scanning system comprising three laser interferometers and one autocollimator for measuring flat bar mirror profile with nanometer accuracy, Precision Engineering 35 (2011), 686-692). In this study, an autocollimator was used to measure the rotational motion of the scanning stage to reduce stitching errors. Since each axis interferometer is constructed as a separate optical system, the number and beam size of the interferometer axes are limited. This makes it difficult to achieve high spatial resolution when measuring profiles. The complexity of the signal processor for converting each axis interferometer signal into a displacement value increases.

An SI study using a profile measuring interferometer constructed using a camera was also performed. (Exact reconstruction method for on-machine measurement of profile, Precision Engineering 38 (2014), 969-978), a profile measurement interferometer constructed using a camera can measure the profile of the precision reflecting surface for each pixel of the camera. Spatial resolution can be provided. However, a phase-shifting interferometer (PSI) method is used to measure the profile of the precision reflecting surface. Thus, the scanning stage must be stopped at each measurement position, which makes it difficult to measure high-speed reflective surface profiles insensitive to the external environment.

One technical problem to be solved by the present invention is to provide a reflection surface measuring method for acquiring an interference image at regular scanning step intervals and extracting an entire reflection surface profile using the interference images without stopping the scanning stage.

According to an aspect of the present invention, there is provided a method of measuring a reflection surface profile, comprising: providing a scanning stage, a reflective optical element having a precision reflective surface mounted on the scanning stage and moving, and a stage mirror mounted and moving on the scanning stage ; Measuring the position of the scanning stage and the rotational motion error (e ₂ ) of the scanning stage using the stage mirror and a linear / angular interferometer; Reflected from the precision reflecting surface and the reference mirror from a Twyman-Green interferometer providing a spatial modulation frequency f ₀ using a reference mirror tilted for each position at each scanning step interval s as the scanning stage moves Obtaining a local reflective surface interference profile by the beam; After the FFT of each of the local reflection surface interference profiles g _n (x) measured at each position, a component is extracted from each of the positive spatial modulation frequencies using a filter in the spatial frequency domain, and the positive spatial modulation frequency IFFT the components and perform phase unwrap to extract the local phase profiles Ψ _n (x), respectively; Multiplying each of the local phase profiles Ψ _n (x) by a predetermined coefficient and converting each into a local reflecting surface profile M _n (x); Converting each of the local reflecting surface profiles M _n (x) into a selected local reflecting surface profile _mi (x); And extracting the entire reflective surface profile f (x) using the selected local reflective surface profiles _mi (n) and the rotational motion error e ₂ of the scanning stage.

In one embodiment of the present invention, the total reflection surface profile f (x) is extracted using the selected local reflection surface profiles m _i (n) and the rotational motion error e ₂ of the scanning stage. The step of extracting the total reflection surface profile f (x) using the determinant Y = AX, and selecting from the selected cells and the first cell to select the selected local reflection surface profile m _i (x) The distance (D _i = d _i xs) is given as the product of the prime number and the scanning step spacing (s), Y is the selected local reflector profile (m _i (n)) and the rotational motion error (e ₂ ) A is a measurement vector composed of X, X is an objective vector composed of the total reflection surface profile and errors, and A represents a linear relation of the measurement vector (Y) and the objective vector (X) in the form of a matrix.

n: scanning step index (i = 1, ..., N _s )

N _s : Total number of scanning steps

i: Selected pixel index (i = 1, ..., N _p ) selected in the local reflector profile (M _n (x))

N _p : Total number of all selected pixels

m _i (n): The value of the i th selected pixel of the selected local reflection surface profile m _i (x) in the n th scanning step

m _a (n): Rotation angle (pitch) measurement of the scanning stage in the nth scanning step

x _n : the measurement position of the precision reflective surface of the reflective optical element corresponding to the first pixel of the local reflective surface interference profile g _n (x) in the _nth scanning step

D _i : Distance between the first selection pixel and the i th selection pixel of the local reflection interference profile g _n (x) (D ₁ = 0)

d _i : Normalized distance between the first and i selection pixels

s: Scanning step interval set to a multiple of the pixel spacing of the camera acquiring the local reflectance interference profile

e ₁ (n): Straightness motion error of the scanning stage in the nth scanning step

e ₂ (n): Rotational motion error of the scanning stage in the nth scanning step

c _i : Offset of the i-th selection pixel measurement relative to the first selection pixel (c ₁ = 0)

N: number of sampling points on the precision reflective surface

f (x _n ): The overall reflection surface profile corresponding to the first selection pixel in the nth scanning step.

Reflective surface profile measuring apparatus according to an embodiment of the present invention, Twyman-Green interferometer; A scanning stage for moving a reflective optical element disposed in the measurement path of the Twyman-Green interferometer; A stage mirror mounted on the scanning stage and moving; A linear / angular interferometer for measuring the position and rotational motion error of the scanning stage using the beam reflected from the stage mirror; And a signal processor. The Twyman-Green interferometer may include a laser light source; A beam splitter separating the output beam of the laser light source into a reference path and a measurement path; A reference mirror tilted on the reference path to provide a spatial modulation frequency; A reflective optical element disposed on the measurement path and having a precision reflective surface; And a camera for obtaining a local reflection surface interference profile formed by combining the measurement beam reflected from the precision reflective surface and the beam reflected from the reference mirror by the beam splitter. The signal processor reads the position of the scanning stage to provide a trigger signal to the camera at a constant scanning step interval, and provides a control signal to the scanning stage to continuously move the scanning stage, and is synchronized with the trigger signal. The local reflection surface interference profile and the rotational motion error of the linear / angle interferometer are processed to provide full coverage for the entire scanning area. The reflective surface profile f (x) is extracted.

In the method of measuring a reflection surface profile according to an embodiment of the present invention, if the reflection surface is continuously moved without stopping, the entire reflection surface profile may be measured.

1 is a conceptual diagram illustrating a reflective surface profile measuring apparatus according to an embodiment of the present invention.

FIG. 2 is a conceptual diagram illustrating a Twyman-Green interferometer of the reflective surface profile measuring apparatus of FIG. 1.

3 is a flowchart illustrating a method of measuring a reflection surface profile according to an embodiment of the present invention.

4 is an intensity profile in the x-axis direction among interference images acquired by a camera of the reflective surface profile measuring apparatus.

5 is a spectrum shown in the spatial frequency domain of the intensity profile of an interference image.

6 shows the phase component φ (x).

FIG. 7 shows the phase unfolded phase Ψ (x) of the phase component φ (x) of FIG.

FIG. 8 is a diagram illustrating a selected local reflection surface profile _mi (x) and a measurement vector when the scanning step interval s is 1 pixel.

9 is a diagram illustrating a selected local reflection surface profile _mi (x) and a measurement vector according to an embodiment of the present invention when the scanning step interval s is 2 pixels.

10 is a diagram illustrating a restoration profile average error according to the number of selected pixels Np.

11 shows the reflection surface profile measurement result (a) measured three times and the measurement repeatability (b) at each sampling position.

12 shows the rotational movement e ₂ (a) of the scanning stage and the straightness error e ₁ (b) of the scanning stage.

13 is a result of a two-dimensional total reflection surface profile according to an embodiment of the present invention.

The present invention proposes a new reflection surface profile measuring method to solve the problems of the conventional measuring method. First, we propose a method to reduce the environmental impact by improving the measurement speed. To increase the measurement speed, the measurement speed can be improved by increasing the sub-aperture size or by reducing the overlapping area of successive sub-apertures. It may be difficult to miniaturize the stitching interferometry method and increase the stitching error. In order to overcome this problem, instead of the phase-shifting interferometer method, which requires acquiring multiple interference images in the stationary state, the interference image analysis method using Fourier transform that can measure the profile with one interference image is applied. The profile can be measured with a single interference image, allowing continuous measurement without stopping the scanning stage, greatly improving the measurement speed.

The main source of error in the stitching interferometry method is the accumulation of local profile measurement errors during the stitching process. This cumulative error appears as a quadratic function in the overall profile. To reduce this stitching error, very precise optical aberration correction and environmental control of the profile interferometer is required. This solution requires high cost and time.

Therefore, in the present invention, the rotational motion error of the scanning stage is further measured so that the profile measurement error does not accumulate. Automatic collimators are commonly used to measure rotational motion errors. However, the autocollimator is limited in measurement speed and is difficult to apply when continuously measuring the scanning stage. Therefore, the present invention measures the rotational motion error of the scanning stage and eliminates the stitching error by using an angle laser interferometer capable of high-speed measurement.

According to the present invention, the linear / angular laser interferometer is used to measure the linear / angular displacement of the scanning stage, and generate a trigger signal TRG whenever the linear displacement coincides with the set scanning step interval, thereby generating the linear / angular displacement and profile. Synchronize and record the interference image of the interferometer. The interference profile in the x-axis direction in the interference image is obtained by using a spatial filter. By processing the phase profile Calculate the profile of the entire reflecting surface.

Hereinafter, exemplary embodiments of the present invention will be described in detail with reference to the accompanying drawings. Advantages and features of the present invention, and methods for achieving them will be apparent with reference to the embodiments described below in detail with the accompanying drawings. However, the present invention is not limited to the embodiments described herein but may be embodied in different forms. Rather, the embodiments introduced herein are provided so that the disclosure may be made thorough and complete, and to fully convey the spirit of the invention to those skilled in the art, and the invention is defined only by the scope of the claims.

Like reference numerals refer to like elements throughout the specification. Accordingly, the same or similar reference numerals may be described with reference to other drawings, even if not mentioned or described in the corresponding drawings. Also, although reference numerals are not indicated, they may be described with reference to other drawings.

1 to 2, the reflection surface profile measuring apparatus 100 includes: a Twyman-Green interferometer 120; A scanning stage (110) for moving the reflective optical element (12) disposed in the measurement path of the Twyman-Green interferometer; A stage mirror 112 mounted on the scanning stage 110 and moving; A linear / angular interferometer 150 for measuring the position and rotational motion error of the scanning stage 110 using the beam reflected from the stage mirror; And a signal processor 130.

The Twyman-Green interferometer 120, the laser light source 121; A beam separator (122) for separating the output beam of the laser light source into a reference path and a measurement path; A reference mirror 125 tilted on the reference path to provide a spatial modulation frequency f ₀ ; A reflective optical element (12) disposed on the measurement path and having a precision reflective surface (11); And a camera for obtaining a local reflection surface interference profile g _n (x) formed by combining the measurement beam reflected by the precision reflecting surface 11 and the reference beam reflected by the reference mirror 125 by the beam splitter. 129;

The signal processor 130 reads the position of the scanning stage 110, provides a trigger signal TRG to the camera 129 at a constant scanning step interval s, and continuously supplies the scanning stage 110 to the camera 129. The local reflective surface interference profile g _n (x) and the linear / angle interferometer 150 to provide a control signal CTRL to the scanning stage 110 to be moved and synchronized to the trigger signal TRG. The rotational motion error (e ₂ ) of the The reflective surface profile f (x) is extracted.

The Twyman-Green interferometer 120 measures the local reflecting surface profile g _n (x), respectively, in synchronization with the trigger signal TRG. Local reflective surface interference profile g _n (x), stage at equal intervals at scanning step interval s while continuously conveying reflective optical element 12 with precision reflective surface 11 to scanning stage 110 It is obtained by synchronizing the rotational motion error (e ₂ ) of.

According to the present invention, the scanning stage 110 may continuously transfer the reflective optical element 12 without stopping. The camera 129 acquires a single interference image (or local reflection surface profile) for each constant scanning step interval s of the scanning stage 110. The local reflection surface profiles obtained for each scanning step interval s are analyzed by using a Fourier transform to calculate the overall reflection surface profile f (x). To this end, the tilt of the reference mirror 125 of the Twyman-Green interferometer 120 is adjusted so that the spatial modulation frequency (f) is sufficiently high compared to the spatial frequency of the reflective surface profile of the reflective optical element in the interference image (or local reflective interference profile). Generate an interference fringe with ₀ ).

The laser light source 121 is a laser having sufficient coherence and may be a laser diode of 635 nm. The output of the laser light source 121 may be transmitted to the first parallel light lens 123 through the single mode optical fiber 121a. The single mode optical fiber 121a may generate a stable interference image by suppressing speckle.

The first parallel light lens 123 may convert the light emitted from the single mode optical fiber 121a into parallel light and provide it to the first mirror 124. The first mirror 124 may be provided to the beam splitter 122 by bending the parallel light provided by the first parallel light lens 123 by 90 degrees.

The beam splitter 122 may be a cube beam splitter consisting of two prisms. The beam splitter 122 may perform a beam splitting function and a beam combining function. The beam splitter 122 may provide a reference path that passes through the beam splitter and a measurement path that is bent by 90 degrees by reflecting by the beam splitter. The reference mirror 125 is disposed in the reference path.

The reference mirror 125 may be disposed to be tilted at an angle of 1 degree or less instead of being perpendicular to the reference path. Accordingly, the reference mirror 125 may provide a spatial modulation frequency component f ₀ to the interference fringe. The reference beam reflected by the reference mirror 125 may be reflected by the beam splitter and bent 90 degrees to travel toward the camera.

The precision reflecting surface 11 may be disposed in the measurement path. The precision reflecting surface may be disposed on the scanning stage 110 to continuously move in the x-axis direction. The measurement beam reflected by the precision reflecting surface may pass through the beam splitter 122 and travel toward the camera.

The camera 129 may measure an interference fringe or a local reflecting surface profile g _n (x) by the existing beam reflected by the reference mirror 125 and the measuring beam reflected by the precision reflecting surface 11. have. The camera may be a CCD camera or a CIS camera. The camera 129 may acquire an image in synchronization with a specific position of the scanning stage 110.

A relay optical system may be disposed in front of the camera 129. The relay optical system may include a first lens 128 disposed in front of the camera 129, an opening 127, and a second lens 126 disposed to face the beam splitter. The opening 127 may be disposed at the confocal point of the first lens 128 and the second lens 126. The relay optical system may operate as a beam expander. The opening 127 may remove stray light.

The signal processor 130 provides a trigger signal TRG to the camera 129. The camera 129 may measure an interference image or a local reflecting surface interference profile g _n (x) in synchronization with the trigger signal TRG. The trigger signal TRG may be generated when the position of the stage mirror 112 is determined to reach an integer multiple of a predetermined scanning step interval s. The camera 130 may image an interference fringe whenever the scanning stage 110 continuously moves and corresponds to a constant scanning step interval s. The signal processor 130 may FFT the local reflection surface interference profile g _n (x) to convert the spectrum into a spectrum of a spatial frequency domain, and extract only a positive spatial modulation frequency component using a filter. The signal processor 130 may calculate an overall reflection surface profile.

The scanning stage 110 may be a linear air bearing stage. The scanning step interval s may be several hundred micrometers to several millimeters. The scanning step interval s may be set as an integer multiple of the pixel interval of the camera 129. The scanning stage 110 may move in the x-axis direction, and the placement plane of the scanning stage 110 may be an xy plane defined by the x-axis direction and the y-axis direction. As the scanning stage 110 transfers the reflective optical element 12, a pitch may be generated due to the minute rotation in the y-axis direction. The linear / angle interferometer may measure the distance and pitch (rotational motion error) in the x-axis direction using the stage reference mirror 112.

Reflective optical element 12 may be a flat bar mirror. The precision reflecting surface 11 may have a length of several centimeters to several tens of centimeters. The reflective surface 11 of the reflective optical element 12 may be precisely processed and deformed while being mounted on a plane or the scanning stage 110.

The linear / angle interferometer 150 may measure the position (x _n ) and the rotational motion error (e ₂ (n)) of the scanning stage. The linear / angle interferometer may provide the signal processor 130 with the position (x _n ) and the rotational motion error (e ₂ (n)) of the scanning stage.

The camera 129 acquires the two-dimensional intensity distribution of the interference fringe in synchronization with the trigger signal TRG, but for the sake of explanation, the entire reflection surface profile f is obtained by using the one-dimensional intensity distribution in the x-axis direction parallel to the scanning direction. Explain how to calculate (x)).

3 to 5, the method for measuring a reflection surface profile according to an embodiment of the present invention includes a scanning stage, a reflective optical element having a precision reflective surface mounted and moving on the scanning stage, and mounted on the scanning stage. Providing a moving stage mirror (S110); Measuring the position of the scanning stage and the rotational motion error (e ₂ ) of the scanning stage by using the stage mirror and a linear / angular interferometer (S120), respectively; Reflected from the precision reflecting surface and the reference mirror from a Twyman-Green interferometer providing a spatial modulation frequency f ₀ using a reference mirror tilted for each position at each scanning step interval s as the scanning stage moves Acquiring a local reflection surface interference profile by the beam (S130); After FFT of each of the local reflectance interference profiles g _n (x) measured at each position, a component is extracted from each of the positive spatial modulation frequencies using a filter in the spatial frequency domain, and the positive spatial modulation is performed. IFFT the frequency components and perform phase unwrap to extract local phase profiles Ψ _n (x), respectively (S140); Multiplying each of the local phase profiles Ψ _n (x) by a predetermined coefficient and converting them into local reflecting surface profiles M _n (x) (S150); Converting each of the local reflecting surface profiles M _n (x) to a selected local reflecting surface profile m _i (x) composed of selected cells (S160); And extracting an entire reflection surface profile f (x) using the selected local reflection surface profiles _mi (n) and the rotational motion error e ₂ of the scanning stage (S170). .

The scanning stage 110, the reflective optical element 12 having the precision reflective surface mounted on the scanning stage and moving, and the stage mirror 112 mounted and moving on the scanning stage are prepared. The scanning stage continuously transfers the reflective optical element (S110).

The stage mirror 112 and the linear / angular interferometer 150 measure the position x _{n of} the scanning stage and the rotational motion error e ₂ of the scanning stage, respectively (S120). The position of the scanning stage is used to generate a trigger signal TRG for operating the camera at each scanning step interval s. The rotational motion error is used to calculate the overall reflection surface profile.

The camera 129 acquires a two-dimensional image of the placement plane of the reflective optical element at every scanning step interval s (S130). In the following description, the interference profile in the x-axis direction, which is the extending direction of the reflective optical element, will be described. Except for the step index, the local reflectance interference profile g (x) is given by

[Equation 1]

[Equation 2]

Where a (x) is the background intensity distribution, b (x) is the amplitude distribution of the interference fringe, f ₀ is the spatial modulation frequency of the interference fringe, φ (x) is the phase component at the measurement position x, c ^* (x) Denotes a complex conjugate of c (x), respectively.

Applying a Fourier transform to Equation 1 is given as follows (S140).

[Equation 3]

Where G (f _x ) is the Fourier spectrum of the one-dimensional intensity distribution, f _x is the spatial frequency in the x-axis direction, A (f _x ) is the Fourier spectrum of the background intensity distribution, and the positive spatial frequency component C (f _x -f ₀ ) and the negative spatial frequency component C (f _x + f ₀ ) represent the Fourier spectra of c (x) and c ^* (x), respectively, shifted by ± f ₀ by the spatial modulation frequency.

6 shows the phase component φ (x).

6 and 7, only the C (f _x -f ₀ ) component is separated through appropriate filtering in the spatial frequency domain of the three components to calculate the phase component φ (x). After applying the inverse Fourier transform (IFFT) to the filtered Fourier spectrum, the local phase profile Ψ (x) can be calculated as follows.

[Equation 4]

In the above formula, mod represents the modulo function, the input value divided by π is obtained, and the output value of the modulo function has a value in the range ㅁ π. In order to calculate the continuous phase value, a phase unwrap operation is applied by detecting a phase discontinuity position in the phase value obtained in Equation (4).

In a phase unwrap operation, it is determined that a phase discontinuity has occurred when a phase difference between two adjacent pixels (data) is out of a ± π range. If the phase difference is greater than π, subtract 2π from the second pixel phase value. When the phase value difference is smaller than -π, 2π is added to the phase value to obtain a continuous phase value. This discontinuous phase value removal process is sequentially applied to all pixels.

The local reflecting surface profile M _n (x of the precision reflecting surface 11 containing the inclination of the reference mirror 125 at each pixel position x using the unfolded local phase profile Ψ (x)). ) May be calculated for the n th scanning step (S150) The number of pixels of the local reflection surface profile M _n (x) may be equal to the number of pixels of the camera.

[Equation 5]

Is the wavelength of the laser light source.

Restore Mirror Profile

8 and 9, the total reflection surface profile f (x) is calculated using the local reflection surface profile M _n (x) obtained as shown in Equation 5. In operation S160, the entire pixel data of the local reflecting surface profile M _n (x) is not used, but only a profile value of some pixel positions (hereinafter, selected pixels) is selected and applied. The selected local reflecting surface profile _mi (x) is transformed to consist of the cells selected from the local reflecting surface profile M _n (x) in the nth scanning step.

d _i represents a normalized interpixel distance value obtained by dividing the distance D _i between the first selection pixel and the i th selection pixel in the local reflection surface profile M _n (x) by the scanning step interval s. The s value and D _i value should be determined such that the normalized inter pixel distance value d _i has an integer value. Np represents the total number of all selected pixels. d ₂ to d _Np The greatest common divisor of must be chosen to be 1. The normalized interpixel distance value d _i is a set of sequentially selected prime numbers. To this end, first, an s value corresponding to the spatial resolution of the total reflection surface profile f (x) to be obtained in the final step is determined as a multiple of the pixel spacing of the camera. In the next step, the normalized pixel-to-pixel value d _i to be used in the calculation is determined, and the value D _i is determined by the product of these two values d _i and s.

Referring to FIG. 8, a scanning example is shown when the scanning step interval s is 1 pixel of the camera. In the first scanning step n = 1, the local reflecting surface profile M ₁ (x) consists of 10 pixels, and the set of normalized interpixel distance values d _i is equal to {0,1,2, 3,4,7}. In this case, the set of distances D _i between the first selection pixel and the i-th selection pixel is given by {0,1s, 2s, 3s, 4s, 7s}. Thus, the selected pixels are {1,2,3,4,6,8}. Np = 6. The selective local reflection surface profile _mi (x) is sequentially rearranged into the selected pixels {1,2,3,4,6,8}.

9 shows an example of scanning when the scanning step interval s is 2 pixels of the camera. As the size of the scanning step interval s increases, the number of selectable pixels decreases. In the second scanning step n = 2, the local reflecting surface profile M ₁ (x) consists of 10 pixels, and the set of normalized interpixel distance values d _i is equal to {0,1,2, 3}. In this case, the set of distances D _i between the first selection pixel and the i-th selection pixel is given by {0, 2s, 4s, 6s}. Thus, the selected pixels are {1,3,5,7}. Selecting local reflecting surface profiles (m _i (x)) is sequentially rearranged into the selected pixels ({1,3,5,7}).

The relation between the data value of the selected local reflecting surface profile m _i (x) and the rotational motion error e ₂ can be expressed as follows.

[Equation 6]

The description of each variable used in the above expression is as follows.

n: scanning step index (i = 1, ..., N _s )

N _s : Total number of scanning steps

i: Selection pixel index (i = 1, ..., N _p )

N _p : Total number of all selected pixels

m _i (n): measured value of the i th selected pixel of the local reflector profile obtained with the profile measurement interferometer in the n th scanning step

m _a (n): Scanning stage rotation angle measurement in the nth scanning step

x _n : measurement position on the reflective surface corresponding to the first selection pixel in the nth scanning step

D _i : Distance between the first and i selection pixels in the local reflection profile (D ₁ = 0)

d _i : Normalized distance between the first and i selection pixels in the local reflection profile

s: Scanning step interval set to a multiple of the camera's pixel interval

c _i : Offset of the i-th selection pixel measurement relative to the first selection pixel in the local reflector profile (c ₁ = 0)

f (x _n ): Total reflection surface profile corresponding to the first selection pixel in nth scanning step

If Equation (6) is arranged in the form of a determinant, it can be expressed as follows (S170).

[Equation 7]

[Equation 8]

Y is a measurement vector consisting of the data of the selected local reflecting profile and the rotational motion error e ₂ of the scanning stage. X is the objective vector consisting of the overall reflection surface profile f (x) and errors. A represents a linear relationship between the measurement vector (Y) and the target vector (X) in the form of a determinant.

In Equation (8), among the data of the total reflection surface profile f (x), only the profile value at the N-2 position can be determined independently. N is the number of sampling positions of the total reflection surface profile f (x). The constraint set to zero offset and slope of the calculated total reflection surface profile is as follows.

[Equation 9]

Applying the constraint of Equation 9, the profile value at two positions can be determined as follows.

[Equation 10]

In order to solve the solution in Equation (7), the following two conditions must be satisfied.

Condition 1: The number of rows P of the linear relation matrix A _PQ must be greater than or less than the number of columns Q. (P ≥ Q)

Condition 2: The rank of the linear relation matrix A _PQ must match the number of columns (Q).

In order to satisfy condition 1, the total scanning step number Ns must satisfy the following condition.

[Equation 11]

Here, d _Np (= D _Np / s) represents a normalized pixel-to-pixel distance value obtained by dividing the distance between the first selected pixel and the last pixel by the scanning step interval s. In order to satisfy condition 2, the greatest common factor of the normalized distance values d ₂ to d _Np between the first selection pixel and each pixel must be 1. Therefore, in the profile interferometer, the selection pixel must be determined such that the normalized distance value d _i of the data of the local reflection surface profile M _n (x) satisfies this condition. When such a condition is satisfied, the solution of Equation (7) can be given as follows (S170).

[Equation 12]

Using equation (12), the object vector X is calculated from the measurement vector Y and the linear relation matrix A. Accordingly. The objective vector X provides the overall reflection surface profile f (x), the straightness motion error of the scanning stage (e ₁ ), the rotational motion error of the scanning stage (e ₂ ), and the selected pixel measurement error (c _i ). can do.

The error of the straightness profile reconstructed by this calculation method is influenced by the scanning step interval s, the number of selected pixels Np, the selection pixel distribution, and the like. In the proposed method, it is possible to freely select the measurement conditions affecting the restoration error and to apply the optimized measurement conditions.

Referring to FIG. 10, as the number of selected pixels increases, the reconstruction profile average error decreases. Preferably, the number of selected pixels may be 12 or more to have an average error of 1 nm or less.

[Reflection Profile Profile Device and Measurement Results]

According to one embodiment of the invention, the measuring method of the present invention can measure the profile of the reflective surface without stopping the scanning stage for each scanning step. Therefore, the measurement speed can be greatly improved and the influence of disturbance can be reduced.

An example of measuring the total reflecting surface profile of the planar mirror surface in the 260 mm range is presented. The camera's x-axis pixels are 640 pixels. In the process of converting each of the local reflecting surface profiles M _n (x) into selected local reflecting surface profiles m _i (x), 12 selection pixels were used, and the scanning step spacing (s) Was set to 0.3 mm (corresponding to 12 pixels of the camera).

Referring to FIG. 11, it shows a low profile on both sides and a high profile on both sides in the 260 mm range. Measurement repeatability is standard deviation and is on the order of several nm.

Referring to FIG. 12, even if the straightness error (b) and the rotational motion error (a) of the scanning stage used for the measurement were changed, a repeatability profile measurement repeatability of 10 nm level was obtained.

Referring to FIG. 13, the reflection surface profile calculation process described above has been described taking the one-dimensional profile calculation process as an example. By connecting the above two-dimensional profile calculation results two-dimensionally, a two-dimensional profile can be obtained and the plan view of the reflective surface can be evaluated.

Although the embodiments of the present invention have been described above with reference to the accompanying drawings, those skilled in the art may implement the present invention in other specific forms without changing the technical spirit or essential features thereof. You will understand that. Therefore, it should be understood that the embodiments described above are exemplary in all respects and not restrictive.

Claims

Providing a scanning stage, a reflective optical element having a precision reflective surface mounted and moving on the scanning stage, and a stage mirror mounted and moving on the scanning stage;

Measuring the position of the scanning stage and the rotational motion error (e 2 ) of the scanning stage using the stage mirror and a linear / angular interferometer;

Reflected from the precision reflecting surface and the reference mirror from a Twyman-Green interferometer providing a spatial modulation frequency f 0 using a reference mirror tilted for each position at each scanning step interval s as the scanning stage moves Obtaining a local reflective surface interference profile by the beam;

After the FFT of each of the local reflection surface interference profiles g n (x) measured at each position, a component is extracted from each of the positive spatial modulation frequencies using a filter in the spatial frequency domain, and the positive spatial modulation frequency IFFT the components and perform phase unwrap to extract the local phase profiles Ψ n (x), respectively;

Multiplying each of the local phase profiles Ψ n (x) by a predetermined coefficient and converting each into a local reflecting surface profile M n (x);

Converting each of the local reflecting surface profiles M n (x) into a selected local reflecting surface profile mi (x); And

Extracting the entire reflecting surface profile f (x) using the selected local reflecting surface profiles mi (n) and the rotational motion error e 2 of the scanning stage. Method for measuring reflective surface profile.
According to claim 1,

Extracting the total reflection surface profile f (x) by using the selected local reflection surface profiles mi (n) and the rotational motion error e 2 of the scanning stage

Extract the total reflection profile (f (x)) using the determinant Y = AX,

The distance (D i = d i × s) between the selected cells and the first cell to select the selected local reflecting profile (m i (x)) is multiplied by the prime number and the scanning step spacing (s). Given,

Y is the measurement vector consisting of the selected local reflector profile (m i (n)) and the rotational motion error (e 2 ),

X is an objective vector composed of the overall reflection surface profile and errors,

A is a linear relation matrix showing a linear relation between the measurement vector (Y) and the objective vector (X),

n: scanning step index (i = 1, ..., N s )

N s : Total number of scanning steps

i: Selected pixel index (i = 1, ..., N p ) selected in the local reflector profile (M n (x))

N p : Total number of all selected pixels

m i (n): The value of the i th selected pixel of the selected local reflection surface profile m i (x) in the n th scanning step

m a (n): Rotation angle (pitch) measurement of the scanning stage in the nth scanning step

x n : the measurement position of the precision reflective surface of the reflective optical element corresponding to the first pixel of the local reflective surface interference profile g n (x) in the nth scanning step

D i : Distance between the first selection pixel and the i th selection pixel of the local reflection interference profile g n (x) (D 1 = 0)

d i : Normalized distance between the first and i selection pixels

s: Scanning step interval set to a multiple of the pixel spacing of the camera acquiring the local reflectance interference profile

e 1 (n): Straightness motion error of the scanning stage in the nth scanning step

e 2 (n): Rotational motion error of the scanning stage in the nth scanning step

c i : Offset of the i-th selection pixel measurement relative to the first selection pixel (c 1 = 0)

N: number of sampling points on the precision reflective surface

f (x n ): a reflection surface profile measuring method characterized in that the total reflection surface profile corresponding to the first selection pixel in the nth scanning step.
Twyman-Green interferometer;

A scanning stage for moving a reflective optical element disposed in the measurement path of the Twyman-Green interferometer;

A stage mirror mounted on the scanning stage and moving;

A linear / angular interferometer for measuring the position and rotational motion error of the scanning stage using the beam reflected from the stage mirror; And

A signal processor,

The Twyman-Green interferometer is:

Laser light source;

A beam splitter separating the output beam of the laser light source into a reference path and a measurement path;

A reference mirror tilted on the reference path to provide a spatial modulation frequency;

A reflective optical element disposed on the measurement path and having a precision reflective surface; And

And a camera for obtaining a local reflection surface interference profile formed by combining the measurement beam reflected from the precision reflection surface and the beam reflected from the reference mirror by the beam splitter.

The signal processor reads the position of the scanning stage to provide a trigger signal to the camera at a constant scanning step interval, and provides a control signal to the scanning stage to continuously move the scanning stage, and is synchronized with the trigger signal. The local reflection surface interference profile and the rotational motion error of the linear / angle interferometer are processed to provide full coverage for the entire scanning area. A reflection surface profile measuring device characterized by extracting a reflection surface profile (f (x)).