Patent Publication Number: US-2023142328-A1

Title: Apparatus and method of measuring uniformity based on pupil image and method of manufacturing mask by using the method

Description:
CROSS-REFERENCE TO RELATED APPLICATION 
     This application is a Divisional application of U.S. patent application Ser. No. 17/189,893, filed Mar. 2, 2021, which claims priority under 35 U. S.C. §119 to Korean Patent Application No. 10-2020-0083673, filed on Jul. 07, 2020, in the Korean Intellectual Property Office, the disclosure of each of which is incorporated by reference herein in its entirety. 
    
    
     BACKGROUND 
     Aspects of the inventive concept relate to a measurement apparatus and a measurement method, and particularly, a measurement apparatus and a measurement method based on a pupil image. 
     Recently, in semiconductor manufacturing processes, design rules are being continuously shrunk, and thus, sizes of patterns are being progressively reduced. Also, in terms of a measurement apparatus for measuring a pattern of a wafer or a mask, a resolution issue caused by a reduced pattern size may occur, and the accuracy of measurement may be reduced. In order to address such problems, methods of enhancing optical resolution are being continuously researched and developed. The methods of enhancing the optical resolution include a method of implementing a short wavelength and a method of implementing a high numerical aperture (NA). The method of implementing a short wavelength may have a limitation because the amount of light may be insufficient. Also, the method of implementing a high NA may have a physical limitation in increasing a size of an objective lens. 
     SUMMARY 
     Aspects of the inventive concept provide an apparatus and method of measuring pattern uniformity, which may accurately measure the uniformity of patterns in an array area of a measurement target, and a method of manufacturing a mask by using the measurement method. 
     According to an aspect of the inventive concept, there is provided an apparatus for measuring pattern uniformity on the basis of a pupil image, the apparatus including a light source configured to generate and output light, a stage configured to support a measurement target, an optical system configured to transfer the light, output from the light source, to the measurement target supported on the stage, and a first detector configured to detect light reflected and diffracted by the measurement target, or to detect light diffracted by passing through the measurement target, wherein the first detector is configured to detect a pupil image of a pupil plane and to measure pattern uniformity of an array area of the measurement target on the basis of intensity of at least one of zero-order light and 1 st -order light of the pupil image. 
     According to another aspect of the inventive concept, there is provided an apparatus for measuring pattern uniformity on the basis of a pupil image, the apparatus including a light source configured to generate and output light, a stage configured to support a mask, an optical system including a beam splitter configured to split the light into first light and second light, the optical system being configured to transfer the first light to the mask, and a first detector configured to detect the first light after the first light is reflected and diffracted by the mask, or to detect the first light after the first light is diffracted by passing through the mask, and a second detector configured to detect the second light, wherein each of the first detector and the second detector is configured to detect a pupil image of a pupil plane, and the first detector is configured to measure pattern uniformity of an array area of the mask on the basis of intensity of at least one of zero-order light and 1 st -order light of the pupil image. 
     According to another aspect of the inventive concept, there is provided a method of measuring pattern uniformity on the basis of a pupil image, the method including generating and outputting light by using a light source, transferring, by using an optical system, the light from the light source to a measurement target disposed on a stage, detecting, by using a first detector, light reflected and diffracted by the measurement target or light diffracted by passing through the measurement target, and measuring pattern uniformity of an array area of the measurement target on the basis of the light detected by the first detector, wherein the detecting of the light includes detecting a pupil image of a pupil plane by using the first detector, and the measuring of the pattern uniformity includes measuring the pattern uniformity on the basis of intensity of at least one of zero-order light and 1 st -order light of the pupil image. 
     According to another aspect of the inventive concept, there is provided a method of manufacturing a mask, the method including preparing a mask having an array area, generating and outputting light by using a light source, transferring, by using an optical system, the light from the light source to the mask disposed on a stage, detecting, by using a first detector, light reflected and diffracted by the mask or light diffracted by passing through the mask, and measuring pattern uniformity of the array area on the basis of the light detected by the first detector, wherein the detecting of the light includes detecting a pupil image of a pupil plane by using the first detector, and the measuring of the pattern uniformity is performed on the basis of intensity of at least one of zero-order light and 1 st -order light of the pupil image. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       Embodiments of the inventive concept will be more clearly understood from the following detailed description taken in conjunction with the accompanying drawings in which: 
         FIG.  1    is a block diagram of a measurement apparatus for measuring pattern uniformity on the basis of a pupil image, according to an embodiment; 
         FIG.  2    is a block diagram illustrating in more detail an illumination formation system (IFS) in the measurement apparatus of  FIG.  1   ; 
         FIGS.  3 A and  3 B  are conceptual diagrams for describing a relationship between a pitch of a pattern and a diffraction angle of diffracted light in the pattern; 
         FIGS.  4 A and  4 B  are conceptual diagrams illustrating a shape of an array area included in one shot of a first detector; 
         FIG.  5 A  is a photograph showing an image (i.e., a pupil image) of a pupil plane corresponding to a shape of an array area of  FIG.  4 A , and  FIG.  5 B  is a photograph showing an image (i.e., a pupil image) of a pupil plane corresponding to a shape of an array area of  FIG.  4 B ; 
         FIGS.  6 A and  6 B  are graphs respectively showing intensities of pupil images of  FIGS.  5 A and  5 B ; 
         FIG.  7    is a graph for describing a method of determining uniformity of a pattern by using the measurement apparatus of  FIG.  1   ; 
         FIGS.  8 A and  8 B  are photographs for describing a method of correcting/compensating fluctuation of light by using a second detector of the measurement apparatus of  FIG.  1   ; 
         FIGS.  9  and  10    are block diagrams of a measurement apparatus for measuring pattern uniformity on the basis of a pupil image, according to embodiments; 
         FIGS.  11 A to  11 D  are flowcharts simply illustrating a measurement method of measuring pattern uniformity on the basis of a pupil image, according to an embodiment; and 
         FIG.  12    is a flowchart simply illustrating a method of manufacturing a mask by using the measurement method of  FIG.  11 A , according to an embodiment. 
     
    
    
     DETAILED DESCRIPTION OF THE EMBODIMENTS 
     Hereinafter, embodiments will be described in detail with reference to the accompanying drawings. Like numeral references refer to like elements, and their repetitive descriptions are omitted. 
       FIG.  1    is a block diagram of an apparatus  1000  for measuring pattern uniformity on the basis of a pupil image, according to an embodiment. 
     Referring to  FIG.  1   , the apparatus  1000  for measuring pattern uniformity (hereinafter referred to as a measurement apparatus) on the basis of a pupil image according to an embodiment may be an apparatus for measuring the uniformity of a pattern in an array area of a measurement target  2000 . The measurement apparatus  1000  according to an embodiment may include a light source  100 , an optical system  200 , a stage  300 , a detection unit  400 , and an advanced illumination unit (AIU)  500 . The pupil image in this disclosure may be an image representing a diffracted light including an information of a zero-order light and a 1 st -order light of the diffracted light. The pupil image may refer to an image formed based on light passing through an aperture, without later passing through a condenser lens (e.g., a focusing lens or collimator). 
     The light source  100  may be a device which generates and outputs light L. The light L of the light source  100  may include or may be a laser. The laser output from the light source  100  may include or may be a pulse laser, and for example, may include or may be a laser having a pulse width of about 500 Hz to about 1 kHz. The light L of the light source  100  is not limited to the pulse laser. Also, a pulse width of the pulse laser is not limited to the numerical value. For example, according to an embodiment, the light L of the light source  100  may include or may be a continuous wave laser. 
     Terms such as “about” or “approximately” may reflect amounts, sizes, orientations, or layouts that vary only in a small relative manner, and/or in a way that does not significantly alter the operation, functionality, or structure of certain elements. For example, a range from “about 0.1 to about 1” may encompass a range such as a 0%-5% deviation around 0.1 and a 0% to 5% deviation around 1, especially if such deviation maintains the same effect as the listed range. 
     The light source  100  may generate and output light having various wavelengths. For example, the light source  100  may generate and output light having a wavelength of about 200 nm such as 248 nm (KrF), 193 nm (ArF), or 157 nm (F2). For example, the laser beam may have a wavelength between 150 nm and 250 nm. A wavelength of the light L of the light source  100  is not limited to the wavelengths. For example, the light source  100  may generate and output extreme ultraviolet (EUV) light corresponding to tens of nanometers. 
     The optical system  200  may transfer the light L, output from the light source  100 , to the measurement target  2000 . The optical system  200  may include an illumination formation system (IFS)  210 , a beam splitter  220 , a polarization control module (PCM)  230 , and a high numerical aperture (NA) (HNA) condenser  240 . 
     The IFS  210  may include various elements, and the IFS  210  may shape the light L, output from the light source  100 , into an appropriate shape and may transfer the shaped light L to the beam splitter  220 . For example, based on a size or a shape of a pattern in an array area of the measurement target  2000 , the IFS  210  may shape light into a shape which enables the uniformity of the pattern to be optimally measured and may transfer the shaped light to the beam splitter  220 . The elements of the IFS  210  will be described in more detail with reference to  FIG.  2   . 
     The beam splitter  220  may split the light L, output from the IFS  210 , into two pieces of light. For example, the beam splitter  220  may split the light L, output from the IFS  210 , into first light L 1  and second light L 2 . As illustrated in  FIG.  1   , the beam splitter  220  may reflect a portion of the light L from the IFS  210  to allow the first light L 1  to be irradiated onto the measurement target  2000  and may transmit the other portion of the light L to allow the second light L 2  to be irradiated onto a second detector  400 - 2 . 
     The PCM  230  may control a polarization state of the first light L 1  by using a polarizing filter. For example, the PCM  230  may perform polarization, such as linear polarization, circular polarization, or elliptical polarization, on the first light L 1  by using the polarizing filter to polarize the first light L 1 . For example, the PCM  230  may polarize the first light L 1  to have a polarization direction. In some embodiments, the PCM  230  may be disposed between the IFS  210  and the beam splitter  220 . In certain embodiments, the PCM  230  may be omitted. 
     The HNA condenser  240  may include an objective lens which focuses light and may have a high NA of 1 or more. For example, the HNA condenser  240  may condense the first light L 1  and may irradiate the condensed first light L 1  onto the measurement target  2000 . According to an embodiment, a medium NA (MNA) condenser having an NA of less than 1 may be provided. For example, in some embodiments, the measurement apparatus  1000  may include an MNA instead of the HNA of  FIG.  1   . In certain embodiments, the HNA condenser  240  and the MNA condenser may be provided together, e.g., in a serial arrangement along a light path of the first light L 1 . 
     The measurement target  2000  may be disposed on the stage  300 . The stage  300  may support and fix the measurement target  2000 . The measurement apparatus  1000  according to an embodiment may include or may be, for example, a transmissive measurement apparatus which measures light diffracted by passing through the measurement target  2000 . Therefore, the stage  300  may support and fix a side surface and/or edge portions of the measurement target  2000 . The stage  300  may include or may be a three-dimensional (3D) movement stage which may three-dimensionally move. As the stage  300  moves, the measurement target  2000  may move together therewith. For example, based on the movement of the stage  300 , focusing with respect to a Z axis or scanning with respect to an X-Y plane may be performed on the measurement target  2000 . For example, the measurement target  2000  may be detected through a full scanning of the entire surface of the measurement target  2000 . Here, the Z axis may correspond to a light axis of the first light L 1 , and the X-Y plane may correspond to a plane perpendicular to the light axis of the first light L 1 . 
     The measurement target  2000  may include a device where a plurality of repetition patterns are included in an array area like a mask or a wafer. For example, the array area may include an array of repeating patterns. For example, in the measurement apparatus  1000  according to an embodiment, the measurement target  2000  may include or may be a mask where a plurality of repetition patterns are included in an array area. Therefore, the measurement apparatus  1000  according to an embodiment may include or may be an apparatus which measures the uniformity of a pattern in an array area of a mask. 
     The detection unit  400  may include a first detector (DT1)  400 - 1  and a second detector (DT2)  400 - 2 . According to an embodiment, the detection unit  400  may include only the first detector  400 - 1 . 
     The first detector  400 - 1  may detect light which is generated when the first light L 1  is diffracted by passing through the measurement target  2000 . For example, the first light L 1  may be diffracted after passing through the measurement target  2000 , and the detector  400 - 1  may detect the diffracted light. In the measurement apparatus  1000  according to an embodiment, the first detector  400 - 1  may detect an image (i.e., a pupil image) at a pupil plane PP 1  corresponding to diffracted light. In  FIG.  1   , the pupil plane PP 1  corresponding to the diffracted light is illustrated by a dashed line. In the measurement apparatus  1000  according to an embodiment, the first detector  400 - 1  may directly detect a pupil image, and thus, may not need a separate condensing lens for condensing diffracted light. The first detector  400 - 1  may include or may be, for example, a charge-coupled device (CCD) or a photo-multiplier tube (PMT). The first detector  400 - 1  is not limited to the above-described devices. Pupil planes in this disclosure may be planes corresponding to incident surfaces of light detectors on which light intensities are detected as shown in  FIGS.  9  and  10   . The pupil plane may refer to a plane at which a pupil image is received. For example, a pupil image may be created after light passes through HNA condenser  240 , which image may be diffracted by passing through the measurement target  2000 . An image received at a pupil plane such as PP 1  (e.g., at a detector arranged on that plane), may be described as a pupil image. 
     As illustrated in  FIG.  1   , light passing through the measurement target  2000  may be diffracted based on a pattern of the measurement target  2000 . Light (i.e., diffracted light DL) diffracted through the measurement target  2000  may include pieces of high-order light at a periphery as well as zero-order light at a center. In  FIG.  1   , for convenience, only zero-order light and 1 st -order light are illustrated. In pieces of higher-order light (for example, 1 st -order light), an angle (i.e., a diffraction angle) diffracted based on a size or a pitch of a pattern of the measurement target  2000  may vary (see θd 1  of  FIG.  3 A ). An example, where a diffraction angle of 1 st -order light varies based on a size or a pitch of a pattern, will be described below in more detail with reference to  FIGS.  3 A and  3 B . 
     In the measurement apparatus  1000  according to an embodiment, the first detector  400 - 1  may move on a horizontal plane perpendicular to an optical axis of the diffraction light DL. The first detector  400 - 1  may move, and thus, when a diffraction angle of each of pieces of 1 st -order or a higher light is large, the first detector  400 - 1  may move to sufficiently detect a pupil image of an array area of the measurement target  2000 . 
     In the measurement apparatus  1000  according to an embodiment, the first detector  400 - 1  may have a size of one shot, which is relatively small. For example, the first detector  400 - 1  may have a size of one shot of about 40 μm*40 μm. However, a size of one shot of the first detector  400 - 1  is not limited to 40 μm*40 μm. For example, the size of one shot of the first detector  400 - 1  may be between 1000 μm 2  and 2000 μm 2 . As described above, in the measurement apparatus  1000  according to an embodiment, a size of one shot of the first detector  400 - 1  may be reduced to be small, and thus, an accuracy of measuring pattern uniformity may be enhanced. 
     To provide description for reducing a size of one shot of the first detector  400 - 1 , in measuring pattern uniformity, whether only a signal of an array area is included in a shot or a signal of an array area and a signal of a non-array area are included in the shot has to be determined before measuring pattern uniformity on the basis of the analysis of an image of the shot. Here, the array area may denote an area including the same repeating pattern, and the non-array area may denote an area including no pattern or an area including a pattern differing from a pattern of the array area and may be a concept opposite to the array area. For example, the array area may be an area including an array of repeating patterns, and the non-array area may be an area including irregular patterns and/or a blank without any pattern. 
     A method mainly used for determining whether the signal of the non-array area is included in a shot may include a method of filtering whether there is a portion where intensity varies largely (e.g., greater than a predetermined value/difference), e.g., by positions, after imaging of a corresponding shot. For example, when only the signal of the array area is included in one shot, intensity does not largely vary (e.g., it only varies less than the predetermined value/difference) in an image corresponding to the one shot, but when the signal of the non-array area is included in one shot, there may be a portion where intensity varies largely (e.g., it varies greater than the predetermined value/difference) in an image corresponding to the one shot. However, recently, as sizes of patterns are progressively miniaturized, a pattern may be finely changed between the array area and the non-array area, and thus, an intensity difference may not be large enough to be distinguished in an image. As a result, in measuring pattern uniformity, the signal of the non-array may not be removed and may act as noise. For example, accuracy of measurements may deteriorate because of reduced pattern sizes. 
     In a measurement apparatus of the related art, a size of one shot is about 180 μm*90 μm and may be too large to measure pattern uniformity, and thus, a possibility of including noise in measuring pattern uniformity is high. For example, because a size of one shot is large, there is high possibility that the signal of the non-array area is included in the one shot, and as described above, as a pattern is progressively miniaturized, an image of a shot including the non-array area may not be removed and may be used to measure pattern uniformity, whereby the signal of the non-array may act as noise, e.g., leading to a wrong result of the uniformity measurement of the array pattern. As a result, in the measurement apparatus of the related art, an accuracy of measuring pattern uniformity may be low due to a size of one shot which is relatively large. 
     On the other hand, in the measurement apparatus  1000  according to the present embodiment, a size of one shot of the first detector  400 - 1  may be about 40 μm*40 μm and may be 10 or more times less than a size of one shot of the measurement apparatus of the related art. Therefore, the possibility of including noise in measuring pattern uniformity may be relatively lowered. As a result, in the measurement apparatus  1000  according to the present embodiment, an accuracy of measuring pattern uniformity may be relatively high due to a small size of one shot. 
     However, as a size of one shot of the first detector  400 - 1  is reduced, a time for detecting pupil images of all of an array area of the measurement target  2000  by using the first detector  400 - 1  may increase. Accordingly, the following methods for reducing a time may be applied to the measurement apparatus  1000  according to the present embodiment. A first method may be a method of constructing a focus map. For example, a focus map may be constructed, and a pupil image may be detected by automatically adjusting a focus on the basis of the focus map, thereby considerably decreasing a time for detecting the pupil image. For example, the focus map may be a map including information of focusing distances from the first detector  400 - 1  at respective positions of the measurement target  2000 . A process of constructing a focus map will be described below in more detail with reference to  FIG.  11 D . A second method may be a method of detecting a pupil image corresponding to only predetermined positions of the array area of the measurement target  2000  through sampling, instead of detecting a pupil image corresponding to all of the array area of the measurement target  2000 . Considering that photographing is performed tens of thousands to hundreds of thousands times, for obtaining pupil images corresponding to all of the array area of the measurement target  2000 , a position for obtaining a pupil image may be limited to only positions which are set through sampling, and thus, a time for detecting a pupil image may be considerably reduced. 
     The measurement apparatus  1000  according to the present embodiment may detect a pupil image by using the first detector  400 - 1 , select a pupil image including only an array area by using an on-off selection method, and use the selected pupil image in measuring pattern uniformity, thereby more enhancing an accuracy of measuring pattern uniformity. For example, the on-off selection method may be a method setting a reference boundary of a category and one side of the boundary is to be in the category (on) and the other side of the boundary is to be out of the category (off). An operation of detecting a pupil image and the on-off selection method will be described below in more detail with reference to  FIGS.  4 A to  6 B . 
     The second detector  400 - 2  may detect second light L 2  coming from the beam splitter  220 . The second detector  400 - 2  may detect an image (i.e., a pupil image) of a pupil plane PP 2  corresponding to the second light L 2 . In  FIG.  1   , the pupil plane PP 2  corresponding to the second light L 2  is illustrated by a dashed line. For example, the second detector  400 - 2  may include a CCD or a PMT. However, the second detector  400 - 2  is not limited to the CCD or the PMT. The second detector  400 - 2  may directly detect the second light L 2  from the beam splitter  220  to sense fluctuation of the second light L 2  in real time. For example, the second detector  400 - 2  may sense a variation of laser power in real time. Fluctuation information about light (e.g., emitting from the light source  100 ) obtained through the second detector  400 - 2  may be used to correct/compensate pattern uniformity and/or a pupil image obtained by the first detector  400 - 1 . An operation of detecting fluctuation of light by using the second detector  400 - 2  and an operation of correcting/compensating pattern uniformity and/or a pupil image by using fluctuation information about light will be described below in more detail with reference to  FIGS.  8 A and  8 B . When light emitting from the light source  100  is uniform and thus hardly fluctuates, the second detector  400 - 2  may be omitted according to some embodiments. 
     The AIU  500  may be disposed between the light source  100  and the IFS  210 . The AIU  500  may delay a pulse laser to increase energy of light incident on the IFS  210 . As a result, the AIU  500  may increase energy of light irradiated onto the measurement target  2000 , thereby enabling high-magnification measurement. According to certain embodiments, the AIU  500  may be omitted. 
     The measurement apparatus  1000  according to the present embodiment may detect a pupil image of a pattern of the array area of the measurement apparatus  2000  by using the first detector  400 - 1  where a size of one shot thereof is small (e.g., having a size mentioned above), and may determine pattern uniformity on the basis of the intensity of the pupil image, thereby measuring the pattern uniformity of the array area of the measurement target  2000  at a high accuracy. Also, based on the on-off selection method, the measurement apparatus  1000  according to the present embodiment may select a pupil image including only an array area and may use the selected pupil image in measuring pattern uniformity or extracting data, thereby enhancing an accuracy of measuring pattern uniformity. Furthermore, the measurement apparatus  1000  according to the present embodiment may obtain information about fluctuation of light by using the second detector  400 - 2  and may correct/compensate pattern uniformity and/or a pupil image obtained through the first detector  400 - 1 , thereby enhancing an accuracy of measuring pattern uniformity. For example, the on-off selection method may be carried out by hardware/software, e.g., by a computer including a processor, etc. 
       FIG.  2    is a block diagram illustrating in more detail an IFS  210  in the measurement apparatus  1000  of  FIG.  1   . Hereinafter, the IFS  210  will be described with reference to  FIGS.  1  and  2   , and description given above with reference to  FIG.  1    will be briefly given or will be omitted. 
     Referring to  FIG.  2   , the IFS  210  may include a beam steering module (BSM)  211 , an attenuation wheel (AW)  212 , a speckle reduction module (SRM)  213 , a beam homogenizer module (BHM)  214 , an NA &amp; σ wheel  215 , and a zoom adaptor (ZA)  216 . The BSM  211  may perform a function of adjusting a focus of light. The AW  212  may perform a function of adjusting attenuation of light. The SRM  213  may perform a function of removing a speckle, such as interference dots, of light (for example, a laser). The BHM  214  may perform a filtering function to maintain only light having the same wavelength. The NA &amp; σ wheel  215  may perform a function of adjusting a shape and a size of an aperture. The ZA  216  may adjust a focus of light. 
     In the measurement apparatus  1000  according to the present embodiment, the IFS  210  may include all of the elements described above. However, according to some embodiments, the IFS  210  may not include some of the elements described above. According to certain embodiments, the IFS  210  may further include elements other than the elements described above. 
       FIGS.  3 A and  3 B  are conceptual diagrams for describing a relationship between a pitch of a pattern and a diffraction angle of diffracted light by the pattern and each show a pattern of a measurement target, incident light, and a shape of after-transmission diffracted light. 
     Referring to  FIGS.  3 A and  3 B , incident light Li may be incident on a measurement target  2000  and may be diffracted by passing through the measurement target  2000 . Light (i.e., diffracted light) diffracted through the measurement target  2000  may include zero-order light at a center and 1 st -order light (−1, +1) at both sides with respect to the zero-order light. The diffracted light may include 2 nd  or higher-order light. However, in the measurement apparatus  1000  according to the present embodiment, 2 nd  and higher-order light may not be used to measure pattern uniformity, and thus, are omitted and not illustrated in  FIGS.  3 A and  3 B . Hereinafter, an operation of measuring the uniformity of a pattern by using zero-order light and 1 st -order light (−1, +1) will be described for example. 
     A pattern of the measurement target  2000  of  FIG.  3 A  may have a first pitch P 1 , and a pattern of a measurement target  2000   a  of  FIG.  3 B  may have a second pitch P 2 . The first pitch P 1  may be greater than the second pitch P 2 . In  FIG.  3 A , a diffraction angle of 1 st -order light (−1, +1) may have a first diffraction angle θd 1 , and in  FIG.  3 B , a diffraction angle of 1 st -order light (−1, +1) may have a second diffraction angle θd 2 . Here, a diffraction angle of 1 st -order light (−1, +1) may be defined as an angle between a proceeding direction of the 1 st -order light (−1, +1) and an optical axis. 
     Generally, in light diffracted by a pattern having a certain shape (for example, a pattern having a line &amp; space shape, e.g., a stripe pattern), as a pitch of a pattern is reduced, a diffraction angle of 1 st -order light (−1, +1) may increase. Therefore, as seen in  FIGS.  3 A and  3 B , the first diffraction angle θd 1  of the 1 st -order light (−1, +1) in the measurement target  2000  including a pattern of the first pitch P 1  may be less than the second diffraction angle θd 2  of the 1 st -order light (−1, +1) in the measurement target  2000   a  in that the second pitch P 2  is smaller than the first pitch P 1 . 
     Therefore, whether only a signal of an array area is included in one shot or a signal of the array area and a signal of an area (i.e., a non-array area) other than the array area are included in the one shot may be determined based on that a diffraction angle of diffracted light (for example, 1 st -order light) varies according to a size or a pitch of a pattern. For example, in an array area where uniform patterns are included in one shot, diffracted light (for example, 1 st -order light) may include only a certain diffraction angle. On the other hand, when an array area and a non-array area are included in one shot, 1 st -order light outside a certain diffraction angle range may be generated. 
     An on-off selection method, which selects a pupil image including only an array area by determining whether only an array area is included in one shot or an array area and a non-array area are included in the one shot, will be described in more detail with reference to  FIGS.  4 A to  6 B . 
       FIGS.  4 A and  4 B  are conceptual diagrams illustrating a shape of an array area included in one shot of a first detector.  FIG.  4 A  shows an example where only an array area is included in one shot, and  FIG.  4 B  shows an example where an array area and a non-array area are included in one shot. 
     Referring to  FIGS.  4 A and  4 B , in  FIG.  4 A , only an array area Aarr may be included in one shot, and for example, a uniform pattern having a line &amp; space shape may be included in the array area Aarr. In  FIG.  4 B , an array area Aarr and a non-array area (for example, an external area Aout) may be included in one shot. Like the array area Aarr of  FIG.  4 A , a uniform pattern having a line &amp; space shape may be included in the array area Aarr. However, as shown in  FIG.  4 B , there is no pattern included in the external area Aout. 
       FIG.  5 A  is a photograph showing an image (i.e., a pupil image) of a pupil plane corresponding to a shape of an array area of  FIG.  4 A , and  FIG.  5 B  is a photograph showing an image (i.e., a pupil image) of a pupil plane corresponding to a shape of an array area of  FIG.  4 B . In  FIGS.  5 A and  5 B , an X axis and a Y axis represent positions and units of the X axis and the Y axis are arbitrary units. 
     Referring to  FIG.  5 A ,  FIG.  5 A  is a pupil image corresponding to a shape of the array area of  FIG.  4 A  and shows that zero-order light (a circle at a center) and two pieces of 1 st -order light (circles at both outer portions) are in clear circular shapes. This may be because one shot corresponding to  FIG.  4 A  includes only an array area Aarr, and thus, diffracted light (i.e., 1 st -order light) has only a certain diffraction angle. 
     Referring to  FIG.  5 B ,  FIG.  5 B  is a pupil image corresponding to a shape of the array area of  FIG.  4 B  and shows that zero-order light (a circle of a center thereof) and two pieces of1 st -order light (circles of both outer portions) are in blurred shapes which spread in an X-axis direction. This may be because one shot corresponding to  FIG.  4 B  includes an array area Aarr and an external area Aout, and thus, diffracted light (i.e., 1 st -order light) further has a diffraction angle other than a certain diffraction angle. For example, the 1 st -order diffracted light may have multiple diffraction angles and/or may have a blurred boundary when irregular patterns are included in a shot. 
       FIGS.  6 A and  6 B  are graphs respectively showing intensities of pupil images of  FIGS.  5 A and  5 B . In  FIGS.  6 A and  6 B , an X axis represents a position, a Y axis represents intensity, and units of the X axis and the Y axis are arbitrary units. 
     Referring to  FIG.  6 A , the intensity of zero-order light at a center may be the highest, and intensities of pieces of 1 st -order light at both sides may be lower than that of the zero-order light. Also, the intensities of the pieces of 1 st -order light at both sides may be substantially the same. As shown in  FIG.  6 A , the zero-order light may be clearly differentiated from the pieces of 1 st -order light. For example, the boundaries of the zero-order light and the 1 st -order light of the diffracted light may be clear. 
     Terms such as “same,” “equal,” “planar,” or “coplanar,” as used herein when referring to orientation, layout, location, shapes, sizes, compositions, amounts, or other measures do not necessarily mean an exactly identical orientation, layout, location, shape, size, composition, amount, or other measure, but are intended to encompass nearly identical orientation, layout, location, shapes, sizes, compositions, amounts, or other measures within acceptable variations that may occur, for example, due to manufacturing processes. The term “substantially” may be used herein to emphasize this meaning, unless the context or other statements indicate otherwise. For example, items described as “substantially the same,” “substantially equal,” or “substantially planar,” may be exactly the same, equal, or planar, or may be the same, equal, or planar within acceptable variations that may occur, for example, due to manufacturing processes. 
     Referring to  FIG.  6 B , similarly to  FIG.  6 A , the intensity of zero-order light at a center may be the highest, and intensities of pieces of 1 st -order light at both sides may be lower than that of the zero-order light. As shown in  FIG.  6 B , it may be seen that the zero-order light is not clearly differentiated from the pieces of 1 st -order light, and moreover, a portion having an intensity of a small magnitude is between the zero-order light and the pieces of 1 st -order light. The portion having the intensity of the small magnitude may correspond to a portion where the pieces of 1 st -order light spread in  FIG.  5 B . For example, the portion having the intensity of the small magnitude may be based on 1 st -order light having a different diffraction angle. 
     The measurement apparatus  1000  according to the present embodiment may use an on-off selection method which selects a pupil image including only an array area, uses the selected pupil image in measuring pattern uniformity, and removes a pupil image including a non-array area, e.g., in addition to the array area. For example, the measurement apparatus  1000  according to the present embodiment may select a pupil image where zero-order light is clearly differentiated from 1 st -order light as shown in  FIG.  5 A  and may remove a pupil image where zero-order light is not clearly differentiated from 1 st -order light as shown in  FIG.  5 B . As described above, the measurement apparatus  1000  according to the present embodiment may measure pattern uniformity by using a pupil image including only an array area, thereby considerably enhancing an accuracy of measuring pattern uniformity. 
     The on-off selection method is not limited to that zero-order light is clearly differentiated from 1 st -order light. For example, a pupil image may be selected based on only zero-order light or 1 st -order light. For example, in a pupil image including only an array area, each of zero-order light and 1 st -order light may be shown in a clear circular shape, and in a pupil image including an array area and a non-array area, each of zero-order light and 1 st -order light may be shown in a blurred shape which spreads to both sides, e.g., in an X direction as shown in  FIGS.  5 B and  6 B . Therefore, a pupil image may be selected based on clearness of one of zero-order light and 1 st -order light. 
     Also, the on-off selection method of selecting a pupil image based on a distance between zero-order light and 1 st -order light may be used. For example, in a pupil image including only an array area, a distance between zero-order light and 1 st -order light may be clearly defined and may be constant. On the other hand, in a pupil image including an array area and a non-array area, a distance between zero-order light and 1 st -order light may not be clearly defined or may not be constant, e.g., because of blurred boundaries of the zero-order light and the 1 st -order light. This may be seen in the graphs of  FIGS.  6 A and  6 B . For example, in the graph of  FIG.  6 A , zero-order light and 1 st -order light may be clearly differentiated from each other, and thus, a distance therebetween may be defined and may be constant regardless of a magnitude of intensity. On the other hand, in the graph of  FIG.  6 B , it may be seen that zero-order light and 1 st -order light are not clearly differentiated from each other and are shown in a combined shape, and thus, a distance therebetween is difficult to define and varies based on a magnitude of intensity. 
       FIG.  7    is a graph for describing a method of determining uniformity of a pattern by using the measurement apparatus of  FIG.  1   . X axis of  FIG.  7    represents positions, the unit of the X axis is an arbitrary unit, and Y axis of  FIG.  7    represents a gray scale. 
     Referring to  FIG.  7   , intensity of a pupil image may be represented by a gray scale. For example, the intensity of zero-order light in the intensity graph of  FIG.  6 A  may be converted into a gray scale as shown in  FIG.  7   , and thus, an intensity graph of zero-order light may be represented by a certain grayscale value. Here, a grayscale value may be in a range of 0 to 255. 
     Pupil images, corresponding to various pitches and various patterns determined to be normal (e.g., in an acceptable range) may be obtained, calculation of intensity and conversion to a gray scale may be performed on each of the pupil images, and the calculated intensity may be stored as a reference grayscale value Rg, e.g., in a storage (not shown) of the measurement apparatus  1000 . In the graph of  FIG.  7   , an example of the reference grayscale value Rg is illustrated by a solid line. For example, the reference grayscale value Rg may be used as a reference to determine uniformity of patterns in an array area. 
     Therefore, the measurement apparatus  1000  according to the present embodiment may measure the uniformity of a pattern in an array area of the measurement target  2000  through the following process. First, pupil images corresponding to the array area of the measurement target  2000  may be obtained, only a pupil image (including no noise—e.g., non-array area noise) having the same patterns may be extracted by determining the on/off of the pupil images, the intensity of each of the pupil images may be calculated, and the calculated intensity may be converted into a measurement grayscale value. Subsequently, uniformity may be calculated by comparing the measurement grayscale value with a corresponding reference grayscale value Rg. Here, the reference gray value Rg may be an average of measurement grayscale values, and a deviation (a) value may be calculated based on the reference gray value Rg. For example, the deviation value may be calculated by dividing the measurement grayscale values by the reference grayscale value Rg. The deviation value may be represented by a % value, and the % value may be referred to as pattern uniformity. Whether the calculated uniformity is within an allowable range may be determined. When the calculated uniformity is within the allowable range, pattern uniformity may be determined to be normal/acceptable, and when the calculated uniformity is outside the allowable range, the pattern uniformity may be determined to be abnormal/unacceptable. Here, the allowable range may denote a certain range with respect to reference uniformity, and the reference uniformity may correspond to, for example, 100%. For example, these processes may be carried out by hardware/software, e.g., by a computer including a processor, etc. 
     As is traditional in the field of the disclosed technology, features and embodiments are described, and illustrated in the specification and drawings, in terms of units or modules, and/or in terms of performing, calculations, determinations, measurements, comparisons, and other functions. Those skilled in the art will appreciate that these units, modules, and functions are physically implemented by the physical components described in the various figures, combined with electronic (or optical) circuits such as logic circuits, discrete components, microprocessors, image processors, CPUs, hard-wired circuits. memory elements, wiring connections, and the like, which may be formed using semiconductor-based fabrication techniques or other manufacturing technologies. In the case of the units, modules, or functions being implemented by microprocessors or similar, they may be programmed using software (e.g., microcode) and may optionally be driven by firmware and/or software. Alternatively, certain units, modules, or functions may be implemented by dedicated hardware, or as a combination of dedicated hardware to perform some functions and a processor (e.g., one or more programmed microprocessors and associated circuitry) to perform other functions. 
     According to certain embodiments, a separate process of converting intensity into a gray scale may be omitted, and pattern uniformity may be measured based on a method of comparing intensity with pre-stored reference intensity. 
       FIGS.  8 A and  8 B  are photographs for describing a method of correcting/compensating fluctuation of light by using a second detector of the measurement apparatus of  FIG.  1   .  FIG.  8 A  is a photograph of a bare intensity map obtained through the second detector, and  FIG.  8 B  is a photograph of a pattern intensity map obtained through a first detector. For example, the bare intensity map may be a map of light source intensity. For example, the bare intensity map may be an intensity map of a light distribution without an obstacle between a light source and a sensing area of the light intensity. For example, the pattern intensity map may be a map of diffracted light by a measurement target. In the map/graph of  FIG.  8 A , an X axis represents a shot number, and a Y axis represents a shot number. For example, shots are arranged in a matrix-like arrangement. In the map/graph of  FIG.  8 B , an X axis represents a position (e.g., in an X direction), a Y axis represents a position (e.g., in a Y direction), and units of the X axis and the Y axis are arbitrary units. Hereinafter, the graphs of  FIGS.  8 A and  8 B  will be described with reference to  FIG.  1   , and descriptions given above with reference to  FIG.  1    will be briefly given or will be omitted. 
     Referring to  FIG.  8 A , the second detector  400 - 2  may directly detect the light L 2  coming from the beam splitter  220  without/regardless of the measurement target  2000 . Therefore, a bare intensity map (e.g., a map of intensity of light coming from the light source) may be represented by intensity based on a shot number regardless of the measurement target  2000 . As seen in  FIG.  8 A , fluctuation of light based on shots (e.g., by shots) may be checked/detected. For example, a tetragonal portion illustrated by a dashed line may correspond to a portion where fluctuation of light occurs largely. When a pattern uniformity is measured without compensating fluctuation of source light, a distorted/inaccurate value of uniformity may be obtained. 
     Referring to  FIG.  8 B , the first detector  400 - 1  may detect light which is generated when the first light L 1  from the beam splitter  220  is diffracted by passing through the measurement target  2000 . For example, the first detector  400 - 1  may detect a diffracted light by the measurement target  2000 . A pattern intensity map may be associated with a pattern of the measurement target  2000 , and thus, may be represented by intensity based on positions of the measurement target  2000 . For reference, the first light L 1  and the second light L 2  may be pieces of light which are split from the light L output from the same light source  100 , and thus, may have substantially the same fluctuation of light. Therefore, fluctuation of light in the bare intensity map may be substantially the same as fluctuation of light in the pattern intensity map. The bare intensity map may not be affected by the pattern of the measurement target  2000 , and thus, fluctuation of light may be readily/immediately extracted. However, in the pattern intensity map, the pattern of the measurement target  2000  may influence the pattern intensity map, and thus, it may be unable to clearly determine and extract fluctuation of light. Therefore, the pattern intensity map may be corrected/compensated by reflecting light fluctuation information obtained from the bare intensity map, and thus, a more accurate pattern intensity map may be obtained by removing fluctuation of light therefrom. 
     The measurement apparatus  1000  according to the present embodiment, by using the second detector  400 - 2 , may directly detect the second light L 2  which does not pass through the measurement target  2000  (i.e., which is not diffracted), and thus, may obtain information about fluctuation of light in real time. Here, real time may denote a time which is substantially the same as a time for detecting a pupil image of the measurement target  2000  by using the first detector  400 - 1 . As a result, the measurement apparatus  1000  according to the present embodiment may obtain in real time information about fluctuation of light by using the second detector  400 - 2  and may correct/compensate uniformity of a pattern and/or a pupil image obtained by the first detector  400 - 1  on the basis of the information about the fluctuation of the source light, thereby considerably enhancing an accuracy of measuring uniformity of a pattern. 
       FIGS.  9  and  10    are block diagrams of a measurement apparatus for measuring pattern uniformity on the basis of a pupil image, according to example embodiments. Hereinafter, a measurement apparatus according to the example embodiments will be described with reference to  FIGS.  9  and  10    in conjunction with  FIG.  1   , and descriptions given above with reference to  FIGS.  2  to  8 B  will be briefly given or will be omitted. 
     Referring to  FIG.  9   , a function and a configuration of a beam splitter  220   a  of an optical system  200   a  of a measurement apparatus  1000   a  according to the present embodiment may differ from those of the measurement apparatus  1000  of  FIG.  1   . More specifically, the measurement apparatus  1000   a  according to the present embodiment may include a light source  100 , the optical system  200   a,  a stage  300 , a detection unit  400 , and an AIU  500 . The light source  100 , the stage  300 , the detection unit  400 , and the AIU  500  may be the same as the ones described with respect to the measurement apparatus  1000  of  FIG.  1   . 
     An IFS  210 , a PCM  230 , and an HNA  240  of the optical system  200   a  may be the same as the ones described with respect to the optical system  200  of the measurement apparatus  1000  illustrated in  FIG.  1   . The beam splitter  220   a  may split the light L, output from the IFS  210 , into two pieces of light (for example, first light L 1  and second light L 2 ). As illustrated in  FIG.  9   , the beam splitter  220   a  may transmit a portion of the light L coming from the IFS  210  to allow the first light L 1  to travel to the measurement target  2000  and may reflect the other portion of the light L to allow the second light L 2  to travel to the second detector  400 - 2 . 
     In the measurement apparatus  1000   a  according to the present embodiment, the beam splitter  220   a  may have a modified function (e.g., different functions from the previous ones). For example, the arrangement positions of optical elements and detectors may be different from the previously described embodiments with respect to the beam splitter  220   a.  For example, the second detector  400 - 2  may be disposed in a direction and/or a position in which a light coming from the light source  100  is reflected by the beam splitter  220   a,  and the PCM  230 , the HNA condenser  240 , the stage  300 , and the first detector  400 - 1  may be disposed in a direction and/or positions that the light coming from the light source  100  passing through the beam splitter  220   a.    
     According to an embodiment, an additional beam splitter may be further disposed between the beam splitter  220   a  and the PCM  230 , a third detector may detect light passing through the additional beam splitter, and the first detector  400 - 1  may detect light reflected by the additional beam splitter. Similarly, in the measurement apparatus  1000  of  FIG.  1   , an additional beam splitter may be further disposed between the IFS  210  and the beam splitter  220 , a third detector may detect light reflected by the additional beam splitter, and light passing through the additional beam splitter may be incident on the beam splitter  220 . 
     Referring to  FIG.  10   , a measurement apparatus  1000   b  according to the present embodiment may be a reflective measurement apparatus, and thus, may differ from the measurement apparatus  1000  of  FIG.  1   . More specifically, the measurement apparatus  1000   b  according to the present embodiment may include a light source  100 , an optical system  200   b,  a stage  300   a,  a detection unit  400 , and an AIU  500 . The light source  100 , the detection unit  400 , and the AIU  500  may be the same as the ones described with respect to the measurement apparatus  1000  of  FIG.  1   . 
     The optical system  200   b  may include two beam splitters (for example, first and second beam splitters)  220 - 1  and  220 - 2 , and thus, may differ from the optical system  200  of the measurement apparatus  1000  of  FIG.  1   . An IFS  210 , a PCM  230 , and an HNA  240  may be also included in the optical system  200   b  and may be the same as the ones described with respect to the optical system  200  of the measurement apparatus  1000  illustrated in  FIG.  1   . The first beam splitter  200 - 1  of the two beam splitters (the first and second beam splitters  220 - 1  and  220 - 2 ) may be substantially the same as the beam splitter  220  of the measurement apparatus  1000  of  FIG.  1   . Therefore, the first beam splitter  220 - 1  may split light L, output from the light source  100 , into two pieces of light. For example, the first beam splitter  220 - 1  may split light L, output from the light source  100 , into first light L 1  and second light L 2 . The first light L 1  may be irradiated onto the measurement target  2000 , and the second light L 2  may be irradiated onto the second detector  400 - 2 . 
     The second beam splitter  220 - 2  of the two beam splitters (the first and second beam splitters  220 - 1  and  220 - 2 ) may be disposed between the PCM  230  and the HNA condenser  240 . The second beam splitter  220 - 2  may transmit the first light L 1  to allow the first light L 1  to be irradiated onto the measurement target  2000  and may reflect light reflected from the measurement target  2000  to allow the reflected light to be irradiated onto the first detector  400 - 1 . According to an embodiment, the second beam splitter  220 - 2  may reflect the first light L 1  to allow the reflected first light L 1  to be irradiated onto the measurement target  2000  and may transmit light reflected from the measurement target  2000  to allow the reflected light to be irradiated onto the first detector  400 - 1 , e.g., differently from the illustration of  FIG.  10   . 
     The measurement target  2000  may be disposed on the stage  300   a,  and the stage  300   a  may support and fix the measurement target  2000 . Because the measurement apparatus  1000   b  according to the present embodiment is a reflective measurement apparatus, the stage  300   a  may support and fix a bottom surface of the measurement target  2000 . The stage  300   a  may be a 3D movable stage which is three-dimensionally movable, and as the stage  300   a  moves, the measurement target  2000  may move together therewith. 
     The first light L 1  may be condensed through the HNA condenser and may be irradiated onto and reflected by the measurement target  2000 . Light reflected by the measurement target  2000  may be diffracted based on a pattern included in the measurement target  2000 . For example, the first light L 1  may be reflected and diffracted by the measurement target  2000 , and thus, may be converted into diffracted light DL. The diffracted light DL based on reflection may include 2 nd  or higher-order pieces of light. However, for convenience, the diffracted light DL is illustrated as including zero-order light and 1 st -order light in  FIG.  10   . For example, second and higher order of light diffractions are omitted in  FIG.  10    for a simpler illustration. Also, the diffracted light DL may be incident on the first detector  400 - 1  via the HNA condenser  240  and the second beam splitter  220 - 2 , but for convenience, in elements next to the HNA condenser  240 , the diffracted light DL is not illustrated as being split into zero-order light and 1 st -order light and is illustrated as only one light (e.g., illustrated as one line of a beam). 
     In the measurement apparatus  1000   b  according to the present embodiment, the first detector  400 - 1  may detect a pupil image of a pupil plane PP 1  with respect to the diffracted light DL by a reflection. Also, the second detector  400 - 2  may detect a pupil image of a pupil plane PP 2  with respect to the second light L 2  from the first beam splitter  220 - 1 . 
       FIGS.  11 A to  11 D  are flowcharts simply illustrating a measurement method of measuring pattern uniformity on the basis of a pupil image, according to an embodiment. Hereinafter, a measurement method according to embodiments will be described with reference to  FIGS.  11 A to  11 D  in conjunction with  FIG.  1   , and descriptions given above with reference to  FIGS.  1  to  10    will be briefly given or will be omitted. 
     Referring to  FIG.  11 A , in a method (hereinafter referred to as a measurement method) of measuring pattern uniformity on the basis of a pupil image according to the present embodiment, first, the light source  100  may generate and output light in operation S 110 . The light of the light source  100  may include, for example, a pulse laser, and may have a pulse width of about 500 Hz to about 1 kHz and may have a wavelength of about 200 nm. For example, the pulse laser may have a 50% duty cycle. The light of the light source  100  is not limited to the pulse laser. Also, a pulse width or a wavelength of the pulse laser is not limited to the above numerical value. 
     Subsequently, in operation S 130 , the light may be transferred to the measurement target  2000  by using the optical system  200 . For example, the light from the light source  100  may be shaped by the IFS  210  and may be reflected or transmitted by the beam splitter  220 , the PCM  230  may control a polarization state, and the HNA condenser  240  may condense the light and may irradiate the condensed light onto the measurement target  2000 . For example, in a case where light is reflected by the beam splitter  220  and is irradiated onto the measurement target  2000 , the measurement apparatus  1000  of  FIG.  1    may be used, and in a case where light passes through the beam splitter  220  and is irradiated onto the measurement target  2000 , the measurement apparatus  1000   a  of  FIG.  9    may be used. 
     Subsequently, in operation S 150 , light diffracted by the measurement target  2000  may be detected from a pupil plane by using the first detector  400 - 1 . The first detector  400 - 1  may include a CCD or a PMT and may detect an image (i.e., a pupil image) of the pupil plane corresponding to the diffracted light. The diffracted light may be light which is transmitted through and diffracted by the measurement target  2000 , or may be light which is reflected and diffracted by the measurement target  2000 . In a case where the diffracted light is light which is transmitted through and diffracted by the measurement target  2000 , the measurement apparatus  1000  of  FIG.  1    or the measurement apparatus  1000   a  of  FIG.  9    may be used, and in a case where the diffracted light is reflected and diffracted by the measurement target  2000 , the measurement apparatus  1000   b  of  FIG.  10    may be used. 
     After the pupil image is detected, the pattern uniformity of an array area of the measurement target  200  may be measured in operation S 170 . In measuring the pattern uniformity of the array area, as described above, the intensity of the pupil image may be calculated and converted into a measurement grayscale value, and the measurement grayscale value may be compared with the reference grayscale value Rg. By measuring pattern uniformity like the above-described method, the measurement method according to the present embodiment may accurately measure the pattern uniformity of the array area of the measurement target  2000 , and thus, may accurately determine whether the pattern uniformity of the array area of the measurement target  2000  is normal/acceptable. 
     Referring to  FIG.  11 B , a measurement method according to the present embodiment may further include operation S 160  of selecting a pupil image, and thus, may differ from the measurement method of  FIG.  11 A . For example, the measurement method according to the present embodiment may sequentially perform operation S 110  of generating and outputting light, operation S 130  of transferring the light to the measurement target  2000 , and operation S 150  of detecting the light from a pupil plane, and the operations may be the same as the ones described above with respect to the measurement method of  FIG.  11 A . 
     Subsequently, in operation  5160 , a pupil image including only the array area of the measurement target  2000  may be selected from among a plurality of pupil images. For example, as described above with reference to  FIGS.  4 A to  6 B , by using the on-off selection method, a pupil image including only an array area may be selected, and a pupil image including a non-array area and an array area may be removed. For example, a plurality of pupil images of a plurality of shots may be examined to choose which pupil images are used to determine a pattern uniformity of a mask. 
     After the pupil image is selected, operation S 170  of measuring pattern uniformity may be performed. Operation S 170  of measuring pattern uniformity may be the same as the operation S 170  described with respect to the measurement method of  FIG.  11 A . However, in operation S 170  of measuring pattern uniformity, a pupil image including only an array area selected by the on-off selection method may be used to measure pattern uniformity. 
     Referring to  FIG.  11 C , a measurement method according to the present embodiment may correct/compensate pattern uniformity (e.g., a measured pattern uniformity by the first detector  400 - 1 ) by using the second detector  400 - 2 , and thus, may differ from the measurement method of  FIG.  11 B . For example, the measurement method according to the present embodiment may perform operation S 110  of generating and outputting light, and then, may split the light into first light L 1  and second light L 2  by using the beam splitter  220  in operation  5120 . Subsequently, in operation S 130   a,  the first light L 1  may be transferred to the measurement target  200  by using the optical system  200 , and the second light L 2  may be transferred to the second detector  400 - 2 . 
     Subsequently, based on the first light L 1 , light diffracted by the measurement target  2000  may be detected from a pupil plane by the first detector  400 - 1  in operation S 150   a,  and a pupil image may be selected by using the on-off selection method in operation S 160 . Operation S 150   a  of detecting the light from the pupil plane and operation S 160  of selecting the pupil image may be the same as corresponding operations described above with reference to  FIGS.  11 A and  11 B . 
     Based on the second light L 2 , by using the second detector  400 - 2 , the second light L 2  may be detected from the pupil plane and fluctuation of the second light L 2  may be sensed in operation S 155 , and fluctuation information about the second light L 2  may be obtained in operation S 157 . 
     Subsequently, in operation S 170   a,  the pattern uniformity of the array area of the measurement target  2000  may be measured and corrected/compensated. An operation of measuring pattern uniformity may be the same as the operation described with respect to the measurement method of  FIG.  11 A . An operation of correcting pattern uniformity may be performed based on the following two methods. A first method may be a method which corrects/compensates a pupil image on the basis of the fluctuation information about the second light L 2  and measures the pattern uniformity of the array area of the measurement target  2000  by using the corrected/compensated pupil image. A second method may be a method which measures the pattern uniformity of the array area of the measurement target  2000  by using a pupil image stored in advance, e.g., in a database including a correlation between fluctuation of light and the pattern uniformity, and corrects/compensates the pattern uniformity on the basis of the stored data by using fluctuation information about light. 
     Referring to  FIG.  11 D , a measurement method according to the present embodiment may construct a focus map corresponding to the measurement target  2000  in operation S 101 , and thus, may differ from the measurement method of  FIG.  11 C . For example, before generating and outputting light, the measurement method according to the present embodiment may construct a focus map corresponding to the measurement target  2000  in operation S 101 . Generally, an operation of capturing an image by using a detector may be performed after focusing each of corresponding areas. However, in a case where photographing (capturing images) is performed tens of thousands to hundreds of thousands times because a measurement area (i.e., an array area) of the measurement target  2000  is wide, performing an operation of individually adjusting focus each time may take a long time to finish to capture throughout the wide measurement area of the measurement target  2000 . Therefore, in the measurement method according to the present embodiment, a focus map corresponding to the measurement target  2000  may be previously constructed, and then, in a case which detects a pupil image by using the first detector  400 - 1 , focusing may be automatically performed based on the focus map, whereby an individual focus adjustment process may be omitted. Accordingly, a time for detecting a pupil image by using the first detector  400 - 1  may be considerably reduced. According to an embodiment, the focus map may be reflected/used in operation S 170   a  of measuring and correcting pattern uniformity. 
     In order to decrease a time for detecting a pupil image by using the first detector  400 - 1 , in operation S 150   a  of detecting the light from the pupil plane, the first detector  400 - 1  may detect a pupil image at only positions of the measurement target  2000  which are set through sampling. For example, before operation S 101  of constructing the focus map, a sampling operation of selecting positions, from which a pupil image is to be detected/obtained, in the measurement target  2000  may be performed. Subsequently, in operation S 101  of constructing the focus map, the focus map may be constructed at only positions selected through the sampling operation. 
     After operation S 101  of constructing the focus map, operations from operation S 110  of generating and outputting the light to operation S 170   a  of measuring and correcting the pattern uniformity may be the same as the operations described with respect to the measurement method of  FIG.  11 C . 
       FIG.  12    is a flowchart simply illustrating a method of manufacturing a mask by using the measurement method of  FIG.  11 A , according to an embodiment. Hereinafter, a method of manufacturing a mask according to an embodiment will be described with reference to  FIG.  12    in conjunction with  FIG.  1   , and descriptions given above with reference to  FIGS.  11 A to  11 D  will be briefly given or will be omitted. 
     Referring to  FIG.  12   , first, in the method of manufacturing a mask according to the present embodiment, a mask may be prepared in operation S 201 . The mask may be the measurement target  2000  and may include an array area, and a plurality of repetition patterns may be disposed in the array area. Operation S 201  of preparing the mask may include a process of forming a pattern in the array area of the mask. For example, in operation S 201  of preparing the mask, the pattern may be formed in the array area of the mask through a process such as a process of designing a pattern, an optical proximity correction (OPC) process, a process of preparing mask data, and an exposure process. 
     Subsequently, operations from operation S 210  of generating and outputting light to operation S 270  of measuring pattern uniformity may be sequentially performed. The operations from operation S 210  of generating and outputting the light to operation S 270  of measuring the pattern uniformity may be the same as the operations described with respect to the measurement method of  FIG.  11 A . For example, the operations from operation S 210  of generating and outputting the light to operation S 270  of measuring the pattern uniformity may be applied to the mask. 
     After operation S 270  of measuring the pattern uniformity, whether the pattern uniformity of the array area of the mask is normal/acceptable may be determined in operation S 280 . As described above, when the calculated uniformity is within an allowable range, the uniformity of the pattern may be determined to be normal/pass, and when the calculated uniformity is outside the allowable range, the uniformity of the pattern may be determined to be abnormal/fail. 
     When the uniformity of the pattern is normal/pass (Yes), a subsequent process may be performed on the mask in operation S 290 . The subsequent process performed on the mask may include a process of coating a pellicle on the mask and a finishing process performed on the mask. The finishing process performed on the mask may include, for example, a process of loading and keeping mask or a document processing process of recording a finished date. The mask may be finished through the subsequent process performed on the mask. 
     When the uniformity of the pattern is abnormal/fail (No), the cause thereof may be analyzed and the process condition may be changed in operation S 285 . Here, the process condition may denote a process condition for the process of forming the pattern in the array area of the mask. After the process condition is changed, operation S 201  of preparing the mask may be performed. In operation S 201  of preparing the mask, the changed process condition may be applied to the process of forming the pattern in the array area of the mask. 
     A method of manufacturing a mask on the basis of the measurement method of  FIG.  11 A  has been described above, but is not limited thereto and may be performed based on one of the measurement methods of  FIGS.  11 B to  11 D . Also, the method of manufacturing a mask according to the present embodiment may be applied to all kinds of devices based on the measurement methods of  FIGS.  11 A to  11 D . For example, the measurement methods of  FIGS.  11 A to  11 D  may be applied to a method of measuring uniformity of a pattern of an array area of a wafer, and thus, the method of manufacturing a mask according to the present embodiment may be applied to a semiconductor device included in a wafer. 
     While the inventive concept has been particularly shown and described with reference to embodiments thereof, it will be understood that various changes in form and details may be made therein without departing from the spirit and scope of the following claims.