KR102076601B1 - Electronic device and operating method thereof - Google Patents

Abstract

An electronic device according to one embodiment of the present invention comprises: a wrapped phase acquisition unit which acquires a wrapped phase from an interference fringe of a measurement target; a coordinate system conversion unit for mapping the wrapped phase to a three-dimensional cylinder coordinate system to convert the wrapped phase into a curve on the cylinder curved surface; an absolute phase calculation unit for calculating an absolute phase based on azimuth differences of each of a plurality of curve elements included in the curve; and a measurement target restoration unit restoring a shape for the measurement target based on the absolute phase.

Description

ELECTRICAL DEVICE AND OPERATING METHOD THEREOF

The present invention relates to an electronic device, and more particularly, to an electronic device for restoring a shape of a measurement object from a phase information image of a measurement object and a method of operating the same.

An interferometer is a precision measuring device that uses an interference phenomenon of light, and may have a resolution of several nm or less with respect to a measurement target. The interferometer can precisely measure the surface or the inside of the measurement object by analyzing the interference fringes generated by the reflected light and collimated light passing through the measurement object. In order to restore the shape of the measurement object from the interference fringe, the interferometer may perform phase unwrapping to restore phase information of the measurement object by using a folded phase. The interferometer may obtain an absolute phase from the folded phase through phase spreading. When the absolute phase is obtained, it is possible to restore the shape of the measurement object from the absolute phase.

Various methods have been developed as phase spreading methods for obtaining an absolute phase. Representative examples thereof include the Itoh algorithm and the Goldstein algorithm. However, these algorithms may be difficult or complicated to apply to measurement objects having various shapes. As a result, the accuracy of the restored shape may be reduced, and a calculation speed for restoring the shape may be slow.

SUMMARY OF THE INVENTION The present invention has been made to solve the above-described technical problem, and an object of the present invention is to provide an electronic device and an operation method thereof for improving the accuracy of shape restoration and the calculation speed of shape restoration for an object to be measured in an interferometer. .

According to an embodiment of the present disclosure, an electronic device includes a folded phase obtaining unit configured to obtain a folded phase from an interference fringe of a measurement target, and mapping the folded phase to a three-dimensional cylinder coordinate system to convert the folded phase into a cylinder. A coordinate system converting unit converting a curve on a curved surface, an absolute phase calculating unit calculating an absolute phase based on azimuth differences of each of the plurality of curve elements included in the curve, and based on the absolute phase It includes a measurement object recovery unit for restoring the shape for the measurement object.

According to an embodiment, the coordinate system transform unit may convert the folded phase into the curve using a mapping function P 'that performs local isometry transformation.

이고, 상기 n은 상기 간섭 무늬의 픽셀 인덱스이고, 상기

는 상기 n에 대응하는 접힌 위상 값일 수 있다.In one embodiment, the mapping function P 'is

N is the pixel index of the interference fringe,

May be a folded phase value corresponding to n.

According to an embodiment, the absolute phase calculator may calculate the absolute phase based on a cumulative result of the azimuth differences of each of the plurality of curve elements.

이고, 상기 r은 상기 실린더의 반지름이고, 상기

는 상기 커브의 방위각이고, 상기 z는 상기 간섭 무늬의 픽셀 인덱스이고, 상기

는 상기 z에 대응하는 커브 엘리먼트의 방위각 차이이고, 상기 r은 1이고, 상기

는 상기 z+1에 대응하는 제1 커브 값의 제1 방위각과 z에 대응하는 제2 커브 값의 제2 방위각의 차이일 수 있다.In an embodiment, the absolute phase calculator calculates the absolute phase using a mapping function U, and the mapping function U is

R is the radius of the cylinder,

Is the azimuth of the curve, z is the pixel index of the interference fringe,

Is the azimuth difference of the curve elements corresponding to z, r is 1, and

May be a difference between a first azimuth angle of the first curve value corresponding to z + 1 and a second azimuth angle of the second curve value corresponding to z.

According to an embodiment of the present disclosure, a method of operating an electronic device may include obtaining a folded phase from an interference fringe for a measurement object, mapping the folded phase to a three-dimensional cylinder coordinate system, and converting the folded phase into a cylinder. Converting to a curve on a curved surface, calculating an absolute phase based on azimuth differences of each of the plurality of curve elements included in the curve, and calculating the absolute phase based on the absolute phase. Restoring the shape.

In one embodiment, the folded phase can be transformed into the curve by a mapping function P 'that performs local isometry transformation.

이고, 상기 n은 상기 간섭 무늬의 픽셀 인덱스이고, 상기

는 상기 n에 대응하는 접힌 위상 값일 수 있다.In one embodiment, the mapping function P 'is

N is the pixel index of the interference fringe,

May be a folded phase value corresponding to n.

In an embodiment, the calculating of the absolute phase may include calculating the azimuth differences of each of the plurality of curve elements, and calculating the absolute phase based on a cumulative sum result of the azimuth differences. can do.

이고, 상기 r은 상기 실린더의 반지름이고, 상기

는 상기 커브의 방위각이고, 상기 z는 상기 간섭 무늬의 픽셀 인덱스이고, 상기

는 상기 z에 대응하는 커브 엘리먼트의 방위각 차이이고, 상기 r은 1이고, 상기

는 상기 z+1에 대응하는 제1 커브 값의 제1 방위각과 z에 대응하는 제2 커브 값의 제2 방위각의 차이일 수 있다.In one embodiment, the absolute phase is calculated using a mapping function U, the mapping function U is

R is the radius of the cylinder,

Is the azimuth of the curve, z is the pixel index of the interference fringe,

Is the azimuth difference of the curve elements corresponding to z, r is 1, and

May be a difference between a first azimuth angle of the first curve value corresponding to z + 1 and a second azimuth angle of the second curve value corresponding to z.

When the electronic device restores a shape based on the folded phase, the electronic device according to an embodiment of the present disclosure may improve the accuracy and calculation speed of shape recovery.

In addition, the electronic device according to an embodiment of the present disclosure may have a high resistance to noise when restoring a shape of a measurement target.

1 is a block diagram illustrating an electronic device according to an exemplary embodiment.
FIG. 2 illustrates a change in a domain of a folded phase according to the operation of the electronic device of FIG. 1.
3A illustrates an example of a folded phase in accordance with an embodiment of the present invention.
3B shows an example of a curve according to an embodiment of the present invention.
3C illustrates an example of an absolute phase in accordance with an embodiment of the present invention.
4 is a diagram illustrating an example for describing a curve element according to an exemplary embodiment of the present invention.
5 is a view showing an example for explaining the difference in azimuth angle of the curve element according to an embodiment of the present invention.
6 is a flowchart illustrating an operation of the electronic device of FIG. 1.
7 is a diagram illustrating an example of an experiment to which a phase spreading algorithm is applied according to an exemplary embodiment of the present invention.
8 is a diagram illustrating resistance to noise of a phase spreading algorithm according to an exemplary embodiment of the present invention.

Hereinafter, exemplary embodiments of the present invention will be described in detail with reference to the accompanying drawings. In the following description, details such as detailed configurations and structures are provided merely to assist the overall understanding of the embodiments of the present invention. Therefore, modifications of the embodiments described in the present disclosure may be performed by those skilled in the art without departing from the spirit and scope of the present invention. Moreover, descriptions of well-known functions and structures are omitted for clarity and conciseness. Terms used in the present specification are terms defined in consideration of the functions of the present invention, and are not limited to the specific functions. Definitions of terms may be determined based on matters described in the detailed description.

Modules in the following figures or detailed description can be connected to other than components shown in the drawings or described in the detailed description. Connections between modules or components can be direct or non-direct, respectively. The connections between the modules or components may each be a communication connection or a physical connection.

Components described with reference to terms such as units or units, modules, layers, logic, and the like used in the detailed description may be implemented in the form of software, hardware, or a combination thereof. Can be. By way of example, the software may be machine code, firmware, embedded code, and application software. For example, the hardware may include electrical circuits, electronic circuits, processors, computers, integrated circuits, integrated circuit cores, pressure sensors, inertial sensors, Micro Electro Mechanical System (MEMS), passive components, or combinations thereof. Can be.

Unless defined otherwise, all terms including technical or scientific meanings used in the text have a meaning that can be understood by those skilled in the art. Generally, the terms defined in the dictionary are interpreted to have the same meaning as the contextual meaning in the related technical field, and are not interpreted to have the ideal or excessively formal meaning unless clearly defined in the text.

1 is a block diagram illustrating an electronic device according to an exemplary embodiment. Referring to FIG. 1, the electronic device 100 includes a folded phase obtaining unit 110, a coordinate system converting unit 120, an absolute phase calculating unit 130, and a measurement object reconstructing unit 140. The electronic device 100 may collimate light to the measurement object, and restore the shape of the measurement object from interference fringes generated by the light that is transmitted through the measurement object or reflected and collimated light. For example, the electronic device 100 may be an interferometer.

The folded phase acquirer 110 may acquire the folded phase from the interference fringe of the measurement object. The folded phase is a set of discontinuous phase information, indicating that phase information corresponding to each of the pixels representing the interference fringe is discontinuous. For example, the folded phase acquirer 110 may obtain the folded phase from the brightness information of the interference fringe.

The folded phase acquirer 110 may acquire a folded phase having a curved shape belonging to a plane. The folded phase includes phase values corresponding to the pixel, and each phase value may form a curve. In this case, the folded phase may include discrete points. For example, the range of phase values of the folded phase may be between -π and π. Accordingly, discontinuous points may appear at points where the phase value of the folded phase becomes smaller than -π or larger than π. Details relating to the folded phase of the present invention will be described in detail with reference to FIG. 3A.

The coordinate system converter 120 may map the folded phase to the cylinder coordinate system. The coordinate system converter 120 may convert the folded phase into a curve on the curved surface of the cylinder by mapping the folded phase to the cylinder coordinate system. In this case, the folded phase can be mapped to a three-dimensional cylinder coordinate system. Accordingly, the folded phase in the shape of a curve can be converted into a shape of a curve on a curved cylinder surface.

The coordinate system converter 120 may use a mapping function that performs local isometry transformation to map the folded phase to the cylinder coordinate system. The conversion of the folded phase into a curved shape on the curved surface of the cylinder by using a mapping function for performing a local appearance transformation will be described in detail with reference to FIGS. 2 and 3B.

The absolute phase calculator 130 may calculate an absolute phase based on azimuth differences of each of the curve elements constituting the curve on the curved cylinder surface. The absolute phase is a set of continuous phase information and may include actual phase information corresponding to each of the pixels. The range of the phase value of the absolute phase may not be limited, and the phase difference between the absolute phase and the folded phase may be an integer multiple of 2π. Thus, the calculated absolute phase may differ from the folded phase.

The curve may include a plurality of curve elements. The curve values constituting the curve may have different azimuth angles depending on their position on the cylinder surface. The curve element may include two different curve values, and the azimuth of the two different curve values may be different. Therefore, the azimuth difference of the curve elements may represent the difference between the azimuth angles of the two curve values included in the curve element. The content of calculating the curve element and the azimuth angle of the curve element will be described in detail with reference to FIGS. 4 and 5.

For example, the absolute phase calculator 130 may calculate azimuth differences of each of the curve elements and calculate an absolute phase based on a cumulative sum result of the azimuth differences. The calculated absolute phase may be in the form of a curve belonging to a two-dimensional plane. For example, the absolute phase includes phase values corresponding to the pixel, and each phase value may form a curve.

For example, when the folded phase is two-dimensional, the absolute phase calculator 130 may calculate an absolute phase by averaging the absolute phase calculated in the row direction and the absolute phase calculated in the column direction.

In order to calculate the two-dimensional absolute phase from the curve on the three-dimensional cylinder curved surface, the absolute phase calculator 130 may use a mapping function. The calculation of the absolute phase using the mapping function will be described in detail with reference to FIGS. 2 and 3C.

The measurement object restorer 140 may restore the shape of the measurement object based on the calculated absolute phase.

As described above, the electronic device 100 according to an embodiment of the present disclosure may calculate the absolute phase by performing a phase unfolding operation from the folded phase, and restore the shape of the measurement target based on the calculated absolute phase. have. According to an embodiment of the present disclosure, the electronic device 100 may map a folded phase into a three-dimensional cylinder coordinate system to convert the folded phase into a curve, and calculate a two-dimensional absolute phase using a mapping function from the converted curve. have. Accordingly, in the electronic device 100 according to an embodiment of the present disclosure, an optimization process performed by a conventional phase unfolding algorithm may be omitted, thereby improving computation speed and accuracy of shape restoration.

FIG. 2 illustrates a change in a domain of a folded phase according to the operation of the electronic device of FIG. 1. 3A shows an example of a folded phase according to an embodiment of the present invention, FIG. 3B shows an example of a curve according to an embodiment of the present invention, and FIG. 3C shows an example of an absolute phase according to an embodiment of the present invention. 1 to 3C, the folded phase obtaining unit 110 may obtain a folded phase from an interference fringe of a measurement target. In this case, the folded phase may be a curve belonging to the two-dimensional domain. Hereinafter, the two-dimensional domain to which the folded phase belongs is referred to as D '. For example, the folded phase acquirer 110 may obtain the folded phase as shown in FIG. 3A from the interference fringe of the measurement target.

Referring to FIG. 3A, the horizontal axis n represents a pixel index of an interference fringe, and the vertical axis Ψ represents a phase value of a folded phase. As shown in FIG. 3A, the pixel index may be a value between '1' and '500', and the phase value may be a value between −π and π. The folded phase may be a set of phase values Ψ (n) corresponding to the pixel index n.

The folded phase acquirer 110 may calculate phase values Ψ (n) corresponding to the pixel index n and obtain a folded phase therefrom. Assuming that a function equation exists between the pixel index n and the corresponding phase value Ψ (n), and the function equation is β, β indicates the folded phase and may be represented by Equation 1 below.

After the folded phase is obtained, the coordinate system converter 120 may map the folded phase on the D 'domain to the cylinder coordinate system S' using the mapping function P '. In this case, the folded phase on the domain D 'may be mapped to the three-dimensional cylinder coordinate system S' and converted into curves on the cylinder curved surface. The mapping function P 'may be represented by Equation 2 below.

Referring to Equation 2, the coordinate system converter 120 may convert a phase value Ψ (n) corresponding to the pixel index n on the D 'domain into x, y, and z values on the 3D S' domain. Can be. The x and y values may be obtained using trigonometric functions for the phase value Ψ (n), respectively, and the z value may be equal to the pixel index n value on the D 'domain. Accordingly, the x and y values may be values between '-1' and '1', and the z value may be a value between '1' and '500' which is equal to the range of pixel index n on the D 'domain. That is, the z value may represent a pixel index of the interference fringe.

P 'may be a local isotonic transformation. The range of phase values of the folded phase on the D 'domain is limited between -π and π, which may be the same as the range of the cylinder surface. Thus, the D 'domain and the S' domain can be a one-to-one mapping, and the mapping function P 'can be a local isotonic transformation.

Referring to FIG. 3B, the z axis represents the length of the cylinder, the x axis represents the width of the cylinder, and the y axis represents the height of the cylinder. Since x, y, and z values can be obtained from Equation 2, the length of the cylinder may be '500', the width of the cylinder may be '2', and the height of the cylinder may be '2'.

The coordinate system converter 120 may convert the folded phase of FIG. 3A into a curve on the curved surface of FIG. 3B using the mapping function P '. Since the folded phase of FIG. 3A may be represented by β, the curve of FIG. 3B may be represented by P ′ (β). P ′ (β) representing the curve may be represented by Equation 3 below.

Referring to Equation 3, the curve can be represented by using r, Ф, z. r is the radius of the cylinder, Ф is the azimuth angle of the curve, and z is the index of the pixel. That is, the curves belonging to the cylinder coordinate system S 'may be represented by x, y, z values or r, Ф, z values.

The absolute phase calculator 130 may calculate an absolute phase from the curve on the S ′ domain. The absolute phase calculator 130 may calculate the absolute phase directly from the curve on the S ′ domain by using the mapping function U. Alternatively, the absolute phase calculator 130 may map the curve on the S 'domain to the curve on the S domain using the mapping function F, and then calculate the absolute phase from the curve on the S domain using the mapping function U.

When the absolute phase calculator 130 maps a curve on the S 'domain to a curve on the S domain, the mapping function F may be identity mapping. Therefore, the absolute phase calculator 130 may convert the curve values on the S 'domain to the same value by using the mapping function F, and the converted values may appear in the cylinder coordinate system in the S domain. Thus, the curve on the S domain may be the same as the curve on the S 'domain, as shown in FIG. 3B.

When the absolute phase calculator 130 calculates the absolute phase from the curve on the S 'domain or the curve on the S domain using the mapping function U, the calculated absolute phase may belong to the D domain. The D domain may be a two-dimensional domain like the D 'domain. For example, the absolute phase calculator 130 may calculate the absolute phase of FIG. 3C from a curve on the curved surface of the cylinder of FIG. 3B.

The mapping function U used by the absolute phase calculator 130 to calculate the absolute phase may be represented by Equation 4 below.

이 되며,

는 z에 대응하는 커브 엘리먼트의 방위각 차이이다. 즉, D 도메인 상의 절대 위상은 픽셀의 인덱스와 커브 엘리먼트들의 방위각 차이들의 누적합으로 나타낼 수 있다.

는 아래의 수학식 5로 나타낼 수 있다.Referring to Equation 4, the mapping function U may convert a curve on the 3D to a curve on the 2D. Where r is the radius of the cylinder, Ф is the azimuth of the curve, and z is the index of the pixel. As shown in FIG. 3B, since the radius of the cylinder is '1', r may be '1'. When r is '1', the two-dimensional curve can be expressed as a function of only Ф and z. The absolute phase produced by the mapping function U is

Becomes

Is the azimuth difference of the curve elements corresponding to z. That is, the absolute phase on the D domain may be represented by the cumulative sum of the azimuth differences between the indexes of the pixels and the curve elements.

May be represented by Equation 5 below.

Referring to Equation 5, the azimuth angle difference of the curve element corresponding to z is the difference between the first azimuth angle of the first curve value corresponding to z + 1 and the second azimuth angle of the second curve value corresponding to z. Details of the azimuth difference and the cumulative sum of the azimuth differences of the curve elements are described in detail with reference to FIGS. 4 and 5.

Assuming that the absolute phase calculated by the mapping function U is α, α may be in a curved form on a two-dimensional domain as shown in FIG. 3C, and α may be represented by Equation 6 below.

는 픽셀의 인덱스에 대응하는 위상 값이다. 수학식 4 및 수학식 6을 비교하면, n은 z이고,

는

일 수 있다. 여기서,

는 절대 위상의 위상 값을 나타내고, Ф는 실린더 곡면 상의 커브의 방위각을 나타낸다.Where n is the index of the pixel of the interference fringe,

Is the phase value corresponding to the index of the pixel. Comparing Equations 4 and 6, n is z,

Is

Can be. here,

Denotes the phase value of the absolute phase, and denote the azimuth angle of the curve on the curved surface of the cylinder.

는 접힌 위상의 위상 값의 범위를 넘어선 위상 값을 가질 수 있다. 예를 들어, 절대 위상의 위상 값은 π보다 더 큰 값일 수 있고, -π보다 더 작은 값일 수 있다.As shown in FIG. 3B, the range of z is from '1' to '500' and n and z are the same, so as shown in FIG. 3C, the range of n is from '1' to '500'. . Unlike the range of phase values of the folded phase, the range of phase values of the absolute phase is not limited,

May have a phase value over a range of phase values of the folded phase. For example, the phase value of the absolute phase can be a value greater than π and a value smaller than -π.

As shown in FIGS. 3A and 3C, the phase value of the absolute phase α calculated from the folded phase β may be different from the phase value of the folded phase.

The measurement object restorer 140 may restore the shape of the measurement object based on the calculated absolute phase. For example, the measurement object reconstructor 140 may reconstruct the pixel value of the corresponding pixel based on the phase value corresponding to the pixel index of FIG. 3C.

The folded phases, curves, and absolute phases shown in FIGS. 3A to 3C are only examples according to embodiments of the present invention, and the present invention is not limited thereto.

4 is a diagram illustrating an example for describing a curve element according to an exemplary embodiment of the present invention. The three-dimensional curve of FIG. 3B may be represented by the two-dimensional curve of FIG. 4 when the x axis is not considered. The horizontal axis z in FIG. 4 represents an index of a pixel.

The curve may include a plurality of curve elements. As shown in FIG. 4, the curve may include first to third curve elements. The first curve element includes a first curve value c1 corresponding to the index z1 of the first pixel and a second curve value c2 corresponding to the index z2 of the second pixel, and the first curve value It may be formed by connecting (c1) and the second curve value (c2). The second curve element includes a second curve value c2 corresponding to the index z2 of the second pixel and a third curve value c3 corresponding to the index z3 of the third pixel, and the second curve value It may be formed by connecting (c2) and the third curve value (c3). The third curve element includes a third curve value c3 corresponding to the index z3 of the third pixel and a fourth curve value c4 corresponding to the index z4 of the fourth pixel, and the third curve value It may be formed by connecting (c3) and the fourth curve value c4.

For example, as shown in FIG. 3B, when the pixel index z is an integer value from '1' to '500', the curve of FIG. 3B may include first to fourth curve elements.

5 is a view showing an example for explaining the difference in azimuth angle of the curve element according to an embodiment of the present invention. 3B and 5, the three-dimensional curve of FIG. 3B may be represented by the two-dimensional curve of FIG. 5 when the z axis is not considered. As shown in FIG. 5, the cylinder plane viewed based on the x and y axes may have a circular shape having a radius of '1'. In this case, the curve is located on the cylinder plane and may comprise a first curve element and a second curve element. The first curve element may include a first curve value c1 and a second curve value c2, and the second curve element may include a second curve value c2 and a third curve value c3.

The azimuth angle of the curve value may be an angle formed by a straight line connecting the origin of the x and y planes and the curve value with the x axis. In this case, the difference in the azimuth angle of the first curve element is the difference in the azimuth angle Ф2 of the first curve value c1 and the azimuth angle Ф2 of the second curve value c2, and the difference in the azimuth angle of the second curve element is the second curve. It may be a difference between the azimuth angle φ2 of the value c2 and the azimuth angle φ3 of the third curve value c3.

The absolute phase calculator 130 may calculate the cumulative sum of the azimuth differences of the curve elements, as shown in Equation 4, to calculate the absolute phase. For example, in order to calculate the phase value of the absolute phase corresponding to the pixel index '3', the absolute phase calculator 130 may sum the azimuth difference of the first curve element and the azimuth difference of the second curve element. As shown in FIG. 5, the phase value of the absolute phase corresponding to the pixel index '3' may be an azimuth angle Фa obtained by adding the azimuth difference of the first curve element and the azimuth difference of the second curve element.

As described above, the absolute phase calculator 130 may calculate azimuth differences from the plurality of curve elements constituting the curve on the curved cylinder surface, and may calculate an absolute phase based on a cumulative sum result of the azimuth differences. .

4 and 5 are only examples according to an embodiment of the present invention, but the present invention is not limited thereto. For example, the curve of the present invention may include various numbers of curve elements corresponding to various numbers of pixel indices depending on the pixels of the interference fringe.

6 is a flowchart illustrating an operation of the electronic device of FIG. 1. 1 and 6, in step S101, the electronic device 100 may obtain a folded phase from an interference fringe of a measurement target. In operation S102, the electronic device 100 may convert the folded phase into a curve on a curved cylinder by mapping the folded phase to a three-dimensional cylinder coordinate system. The folded phase can be transformed into a curve by a mapping function that performs a local isotonic transformation.

In operation S103, the electronic device 100 may calculate an absolute phase based on azimuth differences of each of the plurality of curve elements. For example, the electronic device 100 may calculate azimuth differences of each of the plurality of curve elements in order to calculate an absolute phase. The electronic device 100 may calculate an absolute phase based on the cumulative sum of the azimuth differences. When the folded phase is two-dimensional, the electronic device 100 may calculate an absolute phase by averaging the absolute phase calculated in the row direction and the absolute phase calculated in the column direction.

In operation S104, the electronic device 100 may restore the shape of the measurement target based on the calculated absolute phase.

7 is a diagram illustrating an example of an experiment using a phase spreading algorithm according to an exemplary embodiment of the present invention. Specifically, FIG. 7 shows an experimental example of restoring the shape from the folded phases of (i) to (iv) using various phase spreading algorithms. The measured data represents a shape restored from a commercially available interferometer, and the more similar the measured data and the restored shape are, the higher the accuracy of shape restoration may be.

Goldstein algorithm, Costantini algorithm and Itoh algorithm are conventional phase spreading algorithms. As shown in Figure 7, it can be seen that the shape reconstructed by the proposed algorithm according to the embodiment of the present invention is more similar to the measured data than the shape reconstructed by other conventional algorithms. Therefore, the interferometer to which the phase spreading algorithm according to the embodiment of the present invention is applied can improve the accuracy of shape recovery as compared to the interferometer to which the conventional algorithms are applied.

Table 1 below shows the accuracy and computing time of the algorithm according to the embodiment of the present invention and other conventional algorithms.

Measurement target
(Pixel size) algorithm Residual RMS (Root Mean Square) Computing time (s) A (457 * 458) The present invention 3.82e-4 0.15 Gold stain 2.41e-3 19.3 Costantini 8.43e-2 11.21 Ito 2.85e-1 0.3 B (995 * 1003) The present invention 1.95e-3 0.56 Gold stain 1.08e-1 70.32 Costantini 2.18e-1 42.73 Ito 3.08e-1 0.91 C (475 * 463) The present invention 1.95e-4 0.28 Gold stain 1.81e-1 19.06 Costantini 7.59e-2 9.37 Ito 2.41e-1 0.31 D (999 * 1000) The present invention 2.93e-2 0.51 Gold stain 4.00e-2 94.49 Costantini 1.46e-1 43.22 Ito 1.08e-1 0.91

Referring to Table 1, the residual RMS refers to a difference between a shape obtained from a commercially available interferometer (ie, measured data of FIG. 7) and a reconstructed shape, thereby indicating the accuracy of the reconstructed shape. Therefore, it may be determined that the smaller the residual RMS value, the higher the accuracy of the restored shape. Since the residual RMS of the reconstructed shape according to the algorithm of the present invention shows a small value compared to the residual RMS of the reconstructed shape according to other conventional algorithms, the interferometer to which the algorithm of the present invention is applied improves the accuracy of the shape reconstruction. Computing time may refer to the time taken to restore the shape. Since the computing time according to the algorithm of the present invention has a small value compared with the computing time according to other conventional algorithms, the interferometer to which the algorithm of the present invention is applied can improve the computation speed of shape recovery.

8 is a diagram illustrating resistance to noise of a phase spreading algorithm according to an exemplary embodiment of the present invention. Referring to FIG. 8, higher levels of noise are added to each pixel to be measured as going to (i) to (iv). As shown in FIG. 8, the algorithm of the present invention may have a smaller degree of change in the reconstructed shape according to noise compared to other conventional algorithms. Therefore, the algorithm according to the embodiment of the present invention may be more resistant to noise than other conventional algorithms.

The foregoing is specific embodiments for practicing the present invention. The present invention will include not only the above-described embodiments but also embodiments that can be simply changed in design or easily changed. In addition, the present invention will also include techniques that can be easily modified and practiced using the embodiments. Therefore, the scope of the present invention should not be limited to the above-described embodiments, but should be defined by the equivalents of the claims of the present invention as well as the following claims.

100: electronic device
110: folded phase acquisition unit
120: coordinate system conversion unit
130: absolute phase calculator
140: measurement object recovery unit

Claims (10)

A folded phase obtaining unit obtaining a folded phase from an interference fringe of a measurement object;
A coordinate system converting unit converting the folded phase into a three-dimensional cylinder coordinate system and converting the folded phase into a curve on a curved surface of the cylinder;
An absolute phase calculator configured to calculate an absolute phase based on azimuth differences of each of a plurality of curve elements included in the curve; And
A measurement object restoration unit for restoring a shape of the measurement object based on the absolute phase;
The coordinate system transform unit converts the folded phase into the curve using a mapping function P 'that performs local isometry transformation,
The mapping function P 'is based on a pixel index of the interference fringe and a folded phase value corresponding to the pixel index. delete The method of claim 1,
The mapping function P 'is

N is the pixel index of the interference fringe,

Is the folded phase value corresponding to n. The method of claim 1,
And the absolute phase calculator calculates the absolute phase based on a cumulative result of the azimuth differences of each of the plurality of curve elements. The method of claim 4, wherein
The absolute phase calculator calculates the absolute phase using a mapping function U,
The mapping function U is

ego,
R is the radius of the cylinder,

Is the azimuth of the curve, z is the pixel index of the interference fringe,

Is the azimuth difference of the curve elements corresponding to z, r is 1,
remind

Is a difference between a first azimuth angle of the first curve value corresponding to z + 1 and a second azimuth angle of the second curve value corresponding to z. In the operating method of the electronic device,
Obtaining a folded phase from an interference fringe for the measurement object;
Mapping the folded phase to a three-dimensional cylinder coordinate system to convert the folded phase into a curve on a cylinder surface;
Calculating an absolute phase based on azimuth differences of each of a plurality of curve elements included in the curve; And
Restoring a shape for the measurement object based on the absolute phase;
The folded phase is transformed into the curve by the mapping function P 'which performs local isometry transformation,
And the mapping function P 'is based on a pixel index of the interference fringe and a folded phase value corresponding to the pixel index. delete The method of claim 6,
The mapping function P 'is

N is the pixel index of the interference fringe,

Is the folded phase value corresponding to n. The method of claim 6,
The step of calculating the absolute phase,
Calculating the azimuth differences of each of the plurality of curve elements;
Calculating the absolute phase based on a cumulative sum result of the azimuth differences. The method of claim 9,
The absolute phase is calculated using the mapping function U,
The mapping function U is

ego,
R is the radius of the cylinder,

Is the azimuth of the curve, z is the pixel index of the interference fringe,

Is the azimuth difference of the curve elements corresponding to z, r is 1,
remind

Is a difference between a first azimuth angle of the first curve value corresponding to z + 1 and a second azimuth angle of the second curve value corresponding to z.

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