KR101968916B1 - Flat Mirror Profile Measuring Apparatus and Method Of The Same - Google Patents

Flat Mirror Profile Measuring Apparatus and Method Of The Same Download PDF

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KR101968916B1
KR101968916B1 KR1020170035111A KR20170035111A KR101968916B1 KR 101968916 B1 KR101968916 B1 KR 101968916B1 KR 1020170035111 A KR1020170035111 A KR 1020170035111A KR 20170035111 A KR20170035111 A KR 20170035111A KR 101968916 B1 KR101968916 B1 KR 101968916B1
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reflection surface
scanning
profile
stage
scanning stage
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KR20180106575A (en
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김종안
엄태봉
김재완
진종한
이재용
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한국표준과학연구원
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    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01N—INVESTIGATING OR ANALYSING MATERIALS BY DETERMINING THEIR CHEMICAL OR PHYSICAL PROPERTIES
    • G01N21/00—Investigating or analysing materials by the use of optical means, i.e. using sub-millimetre waves, infrared, visible or ultraviolet light
    • G01N21/17—Systems in which incident light is modified in accordance with the properties of the material investigated
    • G01N21/41—Refractivity; Phase-affecting properties, e.g. optical path length
    • G01N21/45—Refractivity; Phase-affecting properties, e.g. optical path length using interferometric methods; using Schlieren methods
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01N—INVESTIGATING OR ANALYSING MATERIALS BY DETERMINING THEIR CHEMICAL OR PHYSICAL PROPERTIES
    • G01N21/00—Investigating or analysing materials by the use of optical means, i.e. using sub-millimetre waves, infrared, visible or ultraviolet light
    • G01N21/17—Systems in which incident light is modified in accordance with the properties of the material investigated
    • G01N21/55—Specular reflectivity
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01N—INVESTIGATING OR ANALYSING MATERIALS BY DETERMINING THEIR CHEMICAL OR PHYSICAL PROPERTIES
    • G01N21/00—Investigating or analysing materials by the use of optical means, i.e. using sub-millimetre waves, infrared, visible or ultraviolet light
    • G01N21/17—Systems in which incident light is modified in accordance with the properties of the material investigated
    • G01N21/55—Specular reflectivity
    • G01N2021/557—Detecting specular reflective parts on sample

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Abstract

The present invention provides an apparatus and method for measuring a reflection surface profile. The reflection surface profile measuring apparatus 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 and moved to the scanning stage 110; A linear / angular interferometer 150 for measuring a position and a rotational motion error of the scanning stage 110 using a beam reflected from the stage mirror; And a signal processing unit 130.

Description

FIELD OF THE INVENTION [0001] The present invention relates to a flat mirror profile measuring method and apparatus,

The present invention relates to a method of measuring a flat mirror profile, and more particularly, to a method of measuring an entire reflection surface profile of a flat mirror by measuring an interference image of a continuously transmitted flat mirror mounted on a scanning stage at a predetermined scanning step interval .

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

Generally, the reflective optical element is fixed to a precision system using a screw fastening or an adhesive. However, the profile of the precision reflecting surface can be deformed by the external force applied for fixing the reflective optical element having the precision reflecting surface. Thus, the evaluation results and correction data obtained in machining or in separate reflective surface profile measurement systems may differ from the actual profiles of precision reflective surfaces fixed in the precision system. As a result, the accuracy of the entire precision system is reduced. In order to solve such a problem, the on-site measurement which can evaluate the profile of the precision reflecting surface and correct the profile error should be applied in a state where the reflecting optical element is fixed at the position where it is finally used. In order to apply on-site measurements, a precision surface profile measurement system must be able to be applied to a small footprint and a high measurement speed is required to reduce the external influence during the measurement.

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

Fizeau interferometry, which is a typical example of full aperture interferometry, requires a reference mirror of the same size as the reflective surface to be measured. Therefore, the size of the object to be measured is limited and on-site application is difficult. However, since the whole measurement area can be measured at one time, high measurement speed can be obtained and the environmental impact is reduced. Also, very high accuracy can be obtained depending on the quality of the interferometer components such as the reference mirror and the collimator. The cost is greatly increased in proportion to the quality or the measuring range of the optical system.

The sub-aperture interferometry can obtain the total reflection surface profile by continuously connecting the measured profiles in a small measurement area while moving the position of the measurement object. Therefore, it is a measurement method capable of enlarging the measurement range without limitation. Therefore, a relatively small installation space is required and the measurement range can be easily expanded. However, in order to measure a large area, the measurement time is increased and the measurement accuracy is likely to be reduced due to the environmental influence.

The measurement method of the reflection surface profile using the SI method is a measurement method using a three-axis laser interferometer. (Multi-probe scanning system comprising three laser interferometers and one autocollimator for measuring flat mirror profile with nanometer accuracy, Precision Engineering 35 (2011), 686-692). In this study, the rotational motion of the scanning stage was measured using an autocollimator to reduce the stitching error. Since each axis interferometer is constructed by a separate optical system, the number of interferometer axes and the beam size are limited. This makes it difficult to obtain high spatial resolution in profile measurement. The complexity of the signal processing unit for converting each axis interferometer signal to the displacement value is increased.

An SI study using a profile measuring interferometer constructed using a camera was also performed. The profile measuring interferometer constructed using a camera can measure the profile of a precision reflecting surface for each pixel of a camera and can measure a high (high) Spatial resolution can be provided. However, the profile of the precision reflecting surface is measured by the phase-shifting interferometer (PSI) method. Therefore, the scanning stage must be stopped at each measurement position, which makes it difficult to measure the high-speed reflection surface profile insensitive to the external environment.

SUMMARY OF THE INVENTION It is an object of the present invention to provide a method of measuring a reflection surface that acquires an interference image at a constant scanning step interval without stopping the scanning stage and extracts an entire reflection surface profile using the interference images.

A method of measuring a reflection surface profile according to an embodiment of the present invention includes the steps of providing a scanning stage, a reflective optical element having a precision reflecting surface mounted on the scanning stage and moving and a stage mirror mounted on the scanning stage, ; Measuring a position of the scanning stage and a rotational motion error e 2 of the scanning stage using the stage mirror and the linear / angular interferometer; And a reference mirror that reflects the fine reflection surface and the reference mirror from a Twyman-Green interferometer that provides a spatial modulation frequency f 0 using a reference mirror tilted at each position every scanning step interval s as the scanning stage moves. Obtaining a local reflection surface interference profile by the beam; Each of the local reflection surface interference profiles g n (x) measured for each position is subjected to an FFT and then a component is extracted as a positive spatial modulation frequency using a filter in the spatial frequency domain, IFFTing the component and performing a phase unwrap to extract a local phase profile (x n (x)), respectively; Multiplying each of the local phase profiles (x n (x)) by a predetermined coefficient and transforming them into a local reflection surface profile (M n (x)); Respectively, into a selected local reflection surface profile m i (x) consisting of selected cells in each of said local reflection surface profiles M n (x); And extracting the entire reflection surface profile f (x) using the selected local reflection surface profiles m i (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 (X (x)) using the determinant Y = AX and selecting the selected local reflection surface profile m i (x) from the selected cells and the first cell The distance D i = d i xs is given by the prime number and the scanning step interval s, Y is the local reflection surface profile m i (n) and the rotational motion error e 2 , X is a target vector composed of the total reflection surface profile and errors, and A is a linear relation of the measurement vector Y and the target vector X in the form of a determinant.

Figure 112017027749584-pat00001

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

N s : Total number of scanning steps

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

N p : total number of all selected pixels

m i (n): the value of the ith 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 value of the scanning stage in the nth scanning step

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

D i : the distance between the first selected pixel and the ith selected pixel of the local reflection surface interference profile (g n (x)) (D 1 = 0)

d i : normalized distance between the first selected pixel and the ith selected pixel

s: the scanning step interval set to a multiple of the pixel spacing of the camera obtaining the local reflection surface 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 selected pixel measurement value for the first selected pixel (c 1 = 0)

N: Number of sampling points of precision reflecting surface

f (x n ): the total reflecting surface profile corresponding to the first selected pixel in the nth scanning step.

An apparatus for measuring a reflection surface profile according to an embodiment of the present invention includes: a Twyman-Green interferometer; A scanning stage for moving the 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 a position and a rotational motion error of the scanning stage using a beam reflected from the stage mirror; And a signal processing unit. The Twyman-Green interferometer includes 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 reflection surface and the beam reflected from the reference mirror by the beam splitter. Wherein the signal processing unit reads a position of the scanning stage and provides a trigger signal to the camera at a predetermined scanning step interval and provides a control signal to the scanning stage to continuously move the scanning stage, And processing the rotational reflection error of the linear / angular interferometer to calculate the total reflection area for the scanning full- The reflection surface profile f (x) is extracted.

The method of measuring a reflection surface profile according to an embodiment of the present invention can measure the entire reflection surface profile by continuously moving the reflection surface without stopping the reflection surface.

1 is a conceptual diagram illustrating a reflection surface profile measuring apparatus according to an embodiment of the present invention.
2 is a conceptual diagram illustrating a Twyman-Green interferometer of the reflection surface profile measuring apparatus of FIG.
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 the interference images acquired by the camera of the reflection surface profile measuring apparatus.
5 is a spectrum displayed in the spatial frequency domain of the intensity profile of the interference image.
6 shows the phase component? (X).
Figure 7 shows the phase spread phase (x (x)) of the phase component phi (x) of Figure 6.
8 is a diagram showing a selected local reflection surface profile m i (x) and a measurement vector according to an embodiment of the present invention when the scanning step interval s is 1 pixel.
9 is a diagram showing a selected local reflection surface profile m i (x) and a measurement vector according to an embodiment of the present invention when the scanning step interval s is 2 pixels.
FIG. 10 is a diagram showing a restoration profile average error according to the number Np of selected pixels.
11 shows the result (a) of the reflection surface profile measured repeatedly three times and the measurement repetition diagram (b) of each sampling position.
Fig. 12 shows the rotational motion 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 full reflection surface profile according to an embodiment of the present invention.

In the present invention, a new reflection surface profile measurement method is proposed to solve the problems of the conventional measurement method. First, we propose a method to reduce environmental impact by improving measurement speed. To improve the measurement speed, the measurement speed can be improved by increasing the sub-aperture size or decreasing the overlap area of successive sub-apertures. It is difficult to miniaturize the stitching interferometry method and the stitching error may be increased. In order to overcome this problem, an interference image analysis method using a Fourier transform which can measure a profile with a single interference image is applied instead of a phase-shifting interferometer method in which a plurality of interference images must be obtained in a stationary state. Because the profile measurement is possible with a single interference image, it is possible to continuously measure without stopping the scanning stage, which greatly improves the measurement speed.

The main error factor of the stitching interferometry method is the accumulation of local profile measurement errors in 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 are required. This solution requires high cost and time.

 Accordingly, in the present invention, the rotational motion error of the scanning stage is further measured to prevent accumulation of profile measurement errors. The automatic collimator is often used to measure rotational motion error. However, the automatic collimator is difficult to apply when the measuring speed is limited and the scanning stage is continuously transported and measured. Accordingly, in the present invention, a rotational motion error of a scanning stage is measured using an angular laser interferometer capable of high-speed measurement, and a stitching error is eliminated.

According to the present invention, linear / angular displacement of a scanning stage is measured using a linear / angular laser interferometer, a trigger signal (TRG) is generated whenever a linear displacement is matched with a set scanning step interval, The interference image of the interferometer is synchronously recorded. 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 reflective surface.

Hereinafter, preferred embodiments of the present invention will be described in detail with reference to the accompanying drawings. BRIEF DESCRIPTION OF THE DRAWINGS The advantages and features of the present invention and the manner of achieving them will become apparent with reference to the embodiments described in detail below with reference to 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 disclosed herein are provided so that the disclosure can be thorough and complete, and will fully convey the concept of the invention to those skilled in the art, and the invention is only defined by the scope of the claims.

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

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

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

Referring to FIGS. 1 and 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 and moved to the scanning stage 110; A linear / angular interferometer 150 for measuring a position and a rotational motion error of the scanning stage 110 using a beam reflected from the stage mirror; And a signal processing unit 130.

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

The signal processing unit 130 reads the position of the scanning stage 110 and provides the trigger signal TRG to the camera 129 at a predetermined scanning step interval s and sequentially transmits the scanning stage 110 And provides the control signal CTRL to the scanning stage 110 so as to move the linear / angular interferometer 150 and the local reflection surface interference profile g n (x) synchronized to the trigger signal TRG. processes the turning error (e 2) of the whole of the scanning area Film The reflection surface profile f (x) is extracted.

The Twyman-Green interferometer 120 measures the local reflection surface profile g n (x) in synchronization with the trigger signal TRG. The reflection optical element 12 having the precision reflecting surface 11 is successively transferred to the scanning stage 110 and the local reflection surface interference profile g n (x) is scanned at equal intervals by the scanning step interval s, the rotary motion error (e 2) to obtain sikieo synchronization.

According to the present invention, the scanning stage 110 can transfer the reflective optical element 12 continuously without stopping. The camera 129 acquires a single interference image (or a local reflection surface profile) for a predetermined scanning step interval s of the scanning stage 110. The total reflection surface profile (f (x)) is calculated by analyzing the local reflection surface profiles obtained for each scanning step interval (s) using the Fourier transform. To this end, the slope of the reference mirror 125 of the Twyman-Green interferometer 120 is adjusted to adjust the tilt of the reference mirror 125 to a spatial modulation frequency f (i. E., A local reflection surface interference profile) 0 ) < / RTI >

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

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

The beam splitter 122 may be a cubic beam splitter formed 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 passing through the beam splitter and a measurement path reflected by the beam splitter and proceeding by 90 degrees. A reference mirror 125 is disposed in the reference path.

The reference mirror 125 may be disposed tilted at an angle of 1 degree or less without being disposed perpendicular to the reference path. Thus, the reference mirror 125 may provide a spatial modulated frequency component f o to the interferogram. The reference beam reflected by the reference mirror 125 is reflected by the beam splitter and can be deflected by 90 degrees and travel in the camera direction.

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

The camera 129 can measure an interference fringe or a local reflection surface profile g n (x) by the existing beam reflected by the reference mirror 125 and the measurement beam reflected by the precision reflection surface 11 have. The camera may be a CCD camera or a CIS camera. The camera 129 may acquire an image by being synchronized with a specific position of the scanning stage 110.

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

The signal processing unit 130 provides the trigger signal TRG to the camera 129. The camera 129 may be synchronized with the trigger signal TRG to measure an interference image or a local reflection surface interference profile g n (x). The trigger signal TRG may be generated when the position of the stage mirror 112 is determined and an integer multiple of the predetermined scanning step interval s is reached. The camera 130 can capture an interference fringe every time the scanning stage 110 moves continuously and corresponds to a predetermined scanning step interval s. The signal processor 130 may perform FFT on the local reflection surface interference profile g n (x) to transform the spectrum into a spectrum in the spatial frequency domain, and extract only a positive spatial modulation frequency component using the filter. The signal processor 130 may perform an operation of calculating a total 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 to an integral multiple of the pixel interval of the camera 129. [ The scanning stage 110 moves in the x-axis direction, and the arrangement plane of the scanning stage 110 may be an xy plane defined by an x-axis direction and a y-axis direction. As the scanning stage 110 transmits the reflective optical element 12, a pitch due to the fine rotation in the y-axis direction can be generated. The linear / angular interferometer can measure the distance and the pitch (rotational motion error) in the x-axis direction using the stage reference mirror 112.

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

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

The camera 129 is synchronized with the trigger signal TRG to obtain a two-dimensional intensity distribution of the interference fringes. For the sake of explanation, the camera 129 uses the one-dimensional intensity distribution in the x- (x)) is calculated.

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 the interference images acquired by the camera of the reflection surface profile measuring apparatus.

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

3 to 5, a method of measuring a reflection surface profile according to an embodiment of the present invention includes a scanning stage, a reflective optical element having a precision reflecting surface mounted on the scanning stage and mounted on the scanning stage, (S110) of providing a moving stage mirror; (S120) measuring the position of the scanning stage and the rotational motion error e 2 of the scanning stage using the stage mirror and the linear / angular interferometer; And a reference mirror that reflects the fine reflection surface and the reference mirror from a Twyman-Green interferometer that provides a spatial modulation frequency f 0 using a reference mirror tilted at each position every scanning step interval s as the scanning stage moves. Obtaining a local reflection surface interference profile by the beam (S130); Each of the local reflection surface interference profiles g n (x) measured for each position is subjected to an FFT to extract a component of a positive spatial modulation frequency using a filter in the spatial frequency domain, (S140) of IFFTing the frequency components and performing phase unwrapping to extract a local phase profile? N (x), respectively; (S150) multiplying each of the local phase profiles (x n (x)) by predetermined coefficients and transforming them into local reflection surface profiles (M n (x)); Into a selected local reflection surface profile m i (x) consisting of selected cells in each of the local reflection surface profiles M n (x); And extracting an entire reflection surface profile f (x) using the selected local reflection surface profiles m i (n) and the rotational motion error e 2 of the scanning stage (S170) .

A reflective optical element 12 having a precision reflecting surface mounted on the scanning stage, and a stage mirror 112 mounted on the scanning stage and moving are prepared. The scanning stage successively conveys 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 S120. The position of the scanning stage is used to generate a trigger signal (TRG) for operating the camera for each scanning step interval (s). The rotational motion error is used to calculate the total reflection surface profile.

The camera 129 acquires a two-dimensional image of the placement plane of the reflective optical element at each 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. With the exception of the step index, the local reflection surface interference profile g (x) is given by:

[Equation 1]

Figure 112017027749584-pat00002

&Quot; (2) "

Figure 112017027749584-pat00003

Here, a (x) is the background intensity distribution, b (x) is the amplitude distribution of the interference pattern, f 0 is a space modulation frequency of the interference pattern, φ (x) is a phase component of the measuring position x, c * (x) Represents a complex conjugate of c (x), respectively.

If a Fourier transform is applied to Equation (1), it is given as follows (S140).

&Quot; (3) "

Figure 112017027749584-pat00004

Here, G (f x) is a one-dimensional intensity distribution of the Fourier spectrum, and x f is the spatial frequency along the x axis, A (f x) is the Fourier spectrum in the background, the amount of the spatial frequency component of the intensity distribution 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) shifted by ± f 0 by the spatial modulation frequency, respectively.

6 shows the phase component? (X).

Figure 7 shows the phase spread phase (x (x)) of the phase component phi (x) of Figure 6.

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

&Quot; (4) "

Figure 112017027749584-pat00005

In the above equation, mod represents the modulo function, the remainder value obtained by dividing the input value by π is obtained, and the output value of the modulo function has a value within the range of ππ. A phase unwrap operation is applied by sensing the phase discontinuity position in the phase value obtained in equation (4) to calculate a continuous phase value.

In the phase unwrap operation, it is determined that phase discontinuity occurs when the difference in phase values of two adjacent pixels (data) deviates from the range of ± π. When the difference in phase value is larger than?, 2? Is subtracted from the second pixel phase value. When the difference in phase value 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 the pixels.

(The local reflection surface profile M n (x) of the precision reflection surface 11 inclusive of the reference mirror 125 at each pixel position x using the phase-spread local phase profile (x (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.

&Quot; (5) "

Figure 112017027749584-pat00006

Here,? Is the wavelength of the laser light source.

[Restoration of the reflection surface profile]

8 is a diagram showing a selected local reflection surface profile m i (x) and a measurement vector according to an embodiment of the present invention when the scanning step interval s is 1 pixel.

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

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). The entire pixel data of the local reflection surface profile M n (x) is not used in the calculation, but only the profile values of some pixel positions (hereinafter, selected pixels) are selected and applied (S160). The selected local reflecting surface profile m i (x) is transformed to be composed of the selected cells in the local reflecting surface profile M n (x) in the n th scanning step.

d i represents a normalized inter-pixel distance value obtained by dividing the distance (D i ) between the first selected pixel and the ith selected pixel by the scanning step interval (s) in the local reflection plane profile (M n (x)). A distance value between the normalized pixel (i d) to have the constant value to be determined and the value D i s value. Np represents the total number of all selected pixels. d 2 ~ d Np The greatest common divisor of 1 is 1. Between the normalized pixel value distances (d i) is a set of sequential decimal (prime number) is selected. For this purpose, the s value corresponding to the spatial resolution of the total reflection surface profile (f (x)) to be obtained in the final stage is determined as a multiple of the pixel interval of the camera. In the next step, the normalized inter-pixel distance value (d i ) to be used in the calculation is determined, and the value of D i is determined by multiplying the two values (d i , s).

Referring to FIG. 8, a scanning example is shown when the scanning step interval s is one pixel of the camera. Set of the first scanning step on the (n = 1), the local reflecting surface profile (M 1 (x)) is composed of 10 pixels, the pixel distance between the normalized value (d i) is {0, 1, 2, 3, 4, 7}. In this case, the distance between the first set of selected pixels and the i-th selected pixels (D i) is given by {0,1s, 2s, 3s, 4s , 7s}. Thus, the selected pixels are {1,2,3,4,6,8}. Np = 6. The selected local reflection surface profile m i (x) is reordered sequentially with the selected pixels ({1,2,3,4,6,8}).

Referring to Fig. 9, a scanning example is shown 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 is reduced. The second scanning in the step (n = 2), the local reflecting surface profile (M 1 (x)) is composed of 10 pixels, the set of pixels between the normalized distance value (d i) is {0, 1, 2, 3}. In this case, the distance between the first set of selected pixels and the i-th selected pixels (D i) is given by {0,2s, 4s, 6s}. Thus, the selected pixels are {1,3,5,7}. The selected local reflection surface profile m i (x) is reordered sequentially with the selected pixels ({1, 3, 5, 7}).

The relationship between the data value of the selected local reflection surface profile (m i (x)) and the rotational motion error (e 2 ) can be expressed as:

&Quot; (6) "

Figure 112017027749584-pat00007

A description of each variable used in the above equation is as follows.

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

N s : Total number of scanning steps

i: selected pixel index (i = 1, ..., N p )

N p : total number of all selected pixels

m i (n): measurement value of the ith selected pixel of the local reflection surface profile obtained by the profile measuring interferometer in the nth scanning step

m a (n): the scanning stage rotation angle measurement value in the nth scanning step

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

D i : the distance between the first selected pixel and the ith selected pixel in the local reflection surface profile (D 1 = 0)

d i : normalized distance between the first selected pixel and the ith selected pixel in the local reflection surface profile

s: Scanning step interval set to multiples of camera's pixel spacing

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 (c 1 = 0) of the i-th selected pixel measurement value for the first selected pixel in the local reflection plane profile,

f (x n ): total reflection surface profile corresponding to the first selected pixel in the n-th scanning step

Equation (6) can be expressed as a matrix form as follows (S170).

&Quot; (7) "

Figure 112017027749584-pat00008

&Quot; (8) "

Figure 112017027749584-pat00009

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

In the equation (8), only the profile value at the N-2 position among the data of the total reflection surface profile f (x) can be independently determined. N is the number of sampling positions of the total reflection surface profile (f (x)). The constraint set so that the offset and slope of the calculated total reflection surface profile are 0 is as follows.

&Quot; (9) "

Figure 112017027749584-pat00010

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

&Quot; (10) "

Figure 112017027749584-pat00011

The following two conditions must be satisfied in order to obtain the solution in equation (7)

Condition 1: Linear relation matrix A PQ The number of rows P of each row must be greater than or less than the number of columns Q. (P > Q)

Condition 2: linear relation matrix A PQ Should be equal to the number of columns (Q).

In order to satisfy Condition 1, the total number of scanning steps Ns must satisfy the following condition.

&Quot; (11) "

Figure 112017027749584-pat00012

Where d Np (= D Np / s) represents the normalized inter-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 divisor of the normalized distance values (d 2 ~d Np ) between the first selected pixel and each pixel should be 1. Therefore, the selected pixel should be determined so that the normalized distance value d i among the data of the local reflection surface profile (M n (x)) in the profile interferometer satisfies this condition. When such a condition is satisfied, the solution of the equation (7) can be given as follows (S170).

&Quot; (12) "

Figure 112017027749584-pat00013

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

The error of the straightness profile restored by this calculation method is affected by the scanning step interval (s), the number of selected pixels (Np), and the distribution of the selected pixels. In the proposed method, it is possible to freely select the measurement conditions affecting the restoration error, so that the optimized measurement conditions can be applied.

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

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

[Reflectometer Profile Measurement Apparatus and Measurement Results]

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

An example of measuring the entire reflective surface profile of a flat mirror surface in the range of 260 mm is presented. The camera has 640 x-axis pixels. 12 selection pixels are used in the process of converting the local reflection surface profile m i (x) into the selected local reflection surface profile m i (x) composed of the cells selected in each of the local reflection surface profiles M n (x) Was set to 0.3 mm (corresponding to 12 pixels of the camera).

11 shows the result (a) of the reflection surface profile measured repeatedly three times and the measurement repetition diagram (b) of each sampling position.

Referring to Fig. 11, it exhibits a low and high profile at both sides in the central region of about 130 mm in the 260 mm range. The measurement repeatability is a standard deviation, about several nm.

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

Referring to FIG. 12, even when the straightness error (b) and the rotational motion error (a) of the scanning stage used in the measurement were changed, a repetition rate of the reflection surface profile measurement of 10 nm was obtained.

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

Referring to FIG. 13, the calculation process of the one-dimensional profile is described as an example of calculation of the reflection surface profile described above. By connecting the calculation results of the one-dimensional profile as described above two-dimensionally, a two-dimensional profile can be obtained and the flatness of the reflecting surface can be evaluated.

While the present invention has been described in connection with what is presently considered to be practical exemplary embodiments, it is to be understood that the invention is not limited to the disclosed embodiments, but, on the contrary, It will be understood. It is therefore to be understood that the above-described embodiments are illustrative and non-restrictive in every respect.

11: Precise reflective surface
12: reflective optical element
110: scanning stage
120: Twyman-Green interferometer
130: Signal processor
150: linear / angular interferometer

Claims (3)

Providing a scanning optical system including a scanning stage, a reflective optical element having a precision reflecting surface mounted on the scanning stage, and a stage mirror movably mounted on the scanning stage;
Measuring a position of the scanning stage and a rotational motion error e 2 of the scanning stage using the stage mirror and the linear / angular interferometer;
And a reference mirror that reflects the fine reflection surface and the reference mirror from a Twyman-Green interferometer that provides a spatial modulation frequency f 0 using a reference mirror tilted at each position every scanning step interval s as the scanning stage moves. Obtaining a local reflection surface interference profile by the beam;
Each of the local reflection surface interference profiles g n (x) measured for each position is subjected to an FFT and then a component is extracted as a positive spatial modulation frequency using a filter in the spatial frequency domain, IFFTing the component and performing a phase unwrap to extract a local phase profile (x n (x)), respectively;
Multiplying each of the local phase profiles (x n (x)) by a predetermined coefficient and transforming them into a local reflection surface profile (M n (x));
Respectively, into a selected local reflection surface profile m i (x) consisting of selected cells in each of said local reflection surface profiles M n (x); And
And extracting the entire reflection surface profile f (x) using the selected local reflection surface profiles m i (n) and the rotational motion error e 2 of the scanning stage Method of measuring a reflective surface profile. The method according to claim 1,
The step of extracting the total reflection surface profile f (x) using the selected local reflection surface profiles m i (n) and the rotational motion error e 2 of the scanning stage
The total reflection surface profile f (x) is extracted using the determinant Y = AX,
The distance (D i = d i x s) between the selected cells and the first cell to select the selected local reflection surface profile m i (x) is multiplied by a prime number and a scanning step interval s Given,
Y is a measurement vector composed of a selected local reflection surface profile (m i (n)) and a rotational motion error (e 2 )
X is a target vector composed of the total reflection surface profile and errors,
A is a linear relational matrix showing a linear relationship between the measurement vector Y and the target vector X,

Figure 112017027749584-pat00014




n: scanning step index (i = 1, ..., N s )
N s : Total number of scanning steps
i: the selected pixel index (i = 1, ..., N p ) selected in the local reflection surface profile (M n (x)
N p : total number of all selected pixels
m i (n): the value of the ith 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 value of the scanning stage in the nth scanning step
x n is the measurement position of the precision reflecting surface of the reflective optical element corresponding to the first pixel of the local reflection surface interference profile g n (x) in the nth scanning step
D i : the distance between the first selected pixel and the ith selected pixel of the local reflection surface interference profile (g n (x)) (D 1 = 0)
d i : normalized distance between the first selected pixel and the ith selected pixel
s: the scanning step interval set to a multiple of the pixel spacing of the camera obtaining the local reflection surface 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 selected pixel measurement value for the first selected pixel (c 1 = 0)
N: Number of sampling points of precision reflecting surface
f (x n ) is a total reflection surface profile corresponding to the first selected pixel in the n-th scanning step. Twyman-Green interferometer;
A scanning stage for moving the reflective optical element disposed in the measurement path of the Twyman-Green interferometer;
A stage mirror spaced from the reflective optical element and mounted on the scanning stage and moving;
A linear / angular interferometer for measuring a position and a rotational motion error of the scanning stage using a beam reflected from the stage mirror; And
And a signal processing unit,
The Twyman-Green interferometer comprises:
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
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,
Wherein the signal processing unit reads a position of the scanning stage and provides a trigger signal to the camera at a predetermined scanning step interval and provides a control signal to the scanning stage to continuously move the scanning stage, And processing the rotational reflection error of the linear / angular interferometer to calculate the total reflection area for the scanning full- And the reflection surface profile (f (x)) is extracted.
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