Patent Publication Number: US-11035790-B2

Title: Inspection apparatus and inspection method

Description:
CROSS-REFERENCE TO RELATED APPLICATION 
     This U.S. nonprovisional application claims priority under 35 U.S.C § 119 to Korean Patent Application Nos. 10-2018-0173269 filed on Dec. 31, 2018 and 10-2019-0121610 filed on Oct. 1, 2019 in the Korean Intellectual Property Office, the entire contents of which are hereby incorporated by reference. 
     BACKGROUND 
     The present inventive concepts relate to an inspection apparatus and an inspection method, and more particularly, to an inspection apparatus and an inspection method that measure an image of a measured object. 
     Imaging technology has been widely used to investigate and study physical phenomena changed in real-time, and may be applied to various diagnosis and inspection tools. Polarization-based imaging technology is one of high resolution and high precision measurement techniques applicable to diverse fields. 
     Most of polarization measurement techniques require either mechanically rotational polarizer mechanism or electronic polarization modulation device. However, the polarization measurement technique which employs mechanical mechanism or electronic polarization modulation has a disadvantage of complex hardware configuration and long measurement time. 
     SUMMARY 
     Some example embodiments of the present inventive concepts provide an inspection apparatus and an inspection method that are capable of measuring an image at high speed. 
     According to some example embodiments of the present inventive concepts, an inspection apparatus may comprise: a light generator that generates light; a first linear polarizer that linearly polarizes the light; a polarization interferometer that splits the linearly polarized light into a first light and a second light and that modulates the first light and the second light to have phase difference information; a line converter that converts an output wave light to have a linear line-shape in a first direction and that provides a measured object with the line-shaped output wave light, the output wave light coming out of the polarization interferometer; a scanner that loads the measured object, the scanner being configured such that the measured object is scanned in a second direction intersecting the first direction or is scanned rotationally about an axis in a third direction perpendicular to the first and second directions; a second linear polarizer that receives a measurement light and linearly polarizes the first light and the second light of the measurement light to generate an interference light, the measurement light coming from the output wave light that passes through or reflects from the measured object; and an imaging spectrograph that receives the interference light to obtain an image of the measured object. 
     In certain embodiments, the line converter may be a cylindrical lens elongated in the first direction. 
     In certain embodiments, the inspection apparatus may further comprise an imaging lens that converts the interference light to have a linear line-shape in the first direction and that provides the imaging spectrograph with the line-shaped interference light. 
     In certain embodiments, the first direction and the second direction may be perpendicular to each other. 
     In certain embodiments, the polarization interferometer may include: a polarizing splitter that splits the linearly polarized light into the first light and the second light, the polarizing splitter including an incident surface on which the linearly polarized light is incident, a first reflective surface on which the first light is incident, and a second reflective surface on which the second light is incident, wherein the first reflective surface faces the incident surface, and wherein the first and second reflective surfaces are adjacent to each other; a first mirror on the first reflective surface; and a second mirror on the second reflective surface. 
     In certain embodiments, a length of an optical path along which the first light reciprocally travels between the first reflective surface and the first mirror may be different from a length of an optical path along which the second light reciprocally travels between the second reflective surface and the second mirror. A difference in the optical path between the first light and the second light may be 10 μm to 100 μm. 
     In certain embodiments, the first mirror and the second mirror may have an angle deviated from perpendicular. The deviation angle may range from 0.02° to 0.1°. 
     In certain embodiments, the output wave light may be irradiated at a measurement angle deviated from a direction perpendicular to the measured object, and the measurement light may be reflected at the measurement angle deviated from the direction perpendicular to the measured object. A propagation direction of the output wave light, a propagation direction of the measurement light, and the second direction may be provided on the same plane. 
     In certain embodiments, the polarizing splitter may be a non-polarizing beam splitter, and the polarization interferometer may further include: a first sub-linear polarizer between the first reflective surface and the first mirror of the polarizing splitter; and a second sub-linear polarizer between the second reflective surface and the second mirror of the polarizing splitter, wherein the first sub-linear polarizer and the second sub-linear polarizer have a polarization difference of as much as 90°. The line converter may be disposed between the polarization interferometer and the measured object. 
     In certain embodiments, the polarizing splitter may be a polarizing beam splitter, and the inspection apparatus may further comprise a non-polarizing beam splitter between the first linear polarizer and the polarization interferometer, the non-polarizing beam splitter providing the polarization interferometer with the linearly polarized light and providing the measured object with the output wave light. The line converter may be disposed between the non-polarizing beam splitter and the measured object. 
     In certain embodiments, the output wave light may be vertically incident on the measured object, and the measurement light may be vertically reflected from the measured object. 
     In certain embodiments, the inspection apparatus may further comprise a non-polarizing beam splitter that is adjacent to the polarization interferometer and provides the measured object with the output wave light. The line converter may be disposed between the polarization interferometer and the non-polarizing beam splitter. The output wave light may be provided through the line converter and the non-polarizing beam splitter to the measured object, and the measurement light may be provided through the non-polarizing beam splitter to the second linear polarizer. 
     In certain embodiments, the interference light may be vertically incident on the imaging spectrograph. 
     In certain embodiments, the light generated from the light generator may be a white light. 
     In certain embodiments, the first light and the second light may be a P-polarization wave and an S-polarization wave, respectively. 
     According to some example embodiments of the present inventive concepts, an inspection method may comprise: linearly polarizing light; splitting the linearly polarized light into a first light and a second light; modulating the first light and the second light to have a phase difference to produce an output wave light; converting the output wave light to have a linear line-shape in a first direction to radiate the converted output wave light to a measured object; receiving a measurement light coming out of the measured object and linearly polarizing the first light and the second light of the measurement light to generate an interference light; and obtaining an image of the measured object from the interference light. The measured object may be scanned in a second direction intersecting the first direction or scanned rotationally about an axis in a third direction perpendicular to the first and second directions. 
     In certain embodiments, the inspection method may further comprise converting the interference light to have a linear line-shape in the first direction. 
     In certain embodiments, the light may be a monochromatic light, and a wavelength of the light may be variable. 
     In certain embodiments, the light may be a white light. 
     In certain embodiments, the inspection method may further comprise obtaining, from the interference light, spatio-spectral ellipsometric information on an axis of the first direction, an axis of the second direction, and a wavelength axis of the light. The image of the measured object may be extracted from the spatio-spectral ellipsometric information. 
     In certain embodiments, the first light and the second light may be a P-polarization wave and an S-polarization wave, respectively. 
     In certain embodiments, the first direction and the second direction are perpendicular to each other. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         FIG. 1  illustrates a simplified schematic diagram showing an inspection apparatus according to an example of a first embodiment of the present inventive concepts. 
         FIG. 2A  illustrates an example of an interference fringe image measured in an imaging spectrograph according an example of the first embodiment of the present inventive concepts. 
         FIG. 2B  illustrates a spectral interference signal with wavelength at one position on a spatial axis depicted in  FIG. 2A . 
         FIG. 3  illustrates an example of a spatio-spectral frequency image created by the Fourier transform on the interference fringe image depicted in  FIG. 2A . 
         FIG. 4  illustrates an example of information about spectral ellipsometric phase differences on the one-dimensional space obtained by the inverse Fourier transform on the spatio-spectral frequency image depicted in  FIG. 3 . 
         FIG. 5  illustrates a graph showing a comparison between spectral ellipsometric phase difference information for various wavelengths at x=8.353 measured by an inspection apparatus according to the present inventive concepts and those measured by a commercial apparatus. 
         FIG. 6  illustrates spectral ellipsometric information measured in the form of cubic cells on the two-dimensional space according to the present inventive concepts. 
         FIG. 7  illustrates a simplified schematic diagram showing an example of the inspection apparatus according to the first embodiment of the present inventive concepts. 
         FIG. 8  illustrates a simplified schematic diagram showing an example of the inspection apparatus according to the first embodiment of the present inventive concepts. 
         FIG. 9  illustrates a simplified schematic diagram showing an example of an inspection apparatus according to a second embodiment of the present inventive concepts. 
         FIG. 10  illustrates an example of an interference fringe image measured in an imaging spectrograph according an example of the second embodiment of the present inventive concepts. 
         FIG. 11  illustrates an example of information about spectral ellipsometric phase differences on the one-dimensional space that are obtained from the interference fringe image of  FIG. 10 . 
         FIG. 12  illustrates a simplified schematic diagram showing an example of the inspection apparatus according to the second embodiment of the present inventive concepts. 
         FIG. 13  illustrates a simplified schematic diagram showing an example of the inspection apparatus according to the second embodiment of the present inventive concepts. 
     
    
    
     DETAILED DESCRIPTION OF EMBODIMENTS 
     The following will now describe preferable embodiments of the present inventive concepts with reference to the accompanying drawings. 
     In the embodiments that follow, a reflection-based inspection is explained, but the embodiments may also be similarly applied to a transmission-based inspection. 
       FIG. 1  illustrates a simplified schematic diagram showing an inspection apparatus according to an example of a first embodiment of the present inventive concepts. Referring to  FIG. 1 , an inspection apparatus may include a light generator  10 , a collimating lens  20 , a first linear polarizer  30 , a polarization interferometer  40 , a line converter  61 , a scanner  70 , a second linear polarizer  80 , an imaging lens  62 , and an imaging spectrograph  90 . 
     The light generator  10  may generate a white light. The light generator  10  may be a white-light source which has a uniform spectral distribution over a wide range of wavelength λ. The light generator  10  may be, for example, a deuterium lamp or a tungsten-halogen lamp. It is preferable that the white light has a wavelength range of, for example, at least 200 nm wide. The wavelength range of the white light may include one or more of a near-ultraviolet range (e.g., 200 nm to 400 nm), a visible light range (e.g., 400 nm to 700 nm), and a near-infrared range (e.g., 700 nm to 1,700 nm). 
     The white light may be illuminated to the collimating lens  20 . The collimating lens  20  may convert the white light, which travels away from the light generator  10 , into a collimated light. 
     The first linear polarizer  30  may be illuminated with an input wave light Ern from the collimating lens  20 . The first linear polarizer  30  may linearly polarize the white light (e.g., with a rotation angle of 45°). 
     The polarization interferometer  40  may be a one-piece polarization interferometer by which the white light undergoes polarization modulation. The polarization interferometer  40  may include a polarizing splitter  41 , a first mirror MR 1 , and a second mirror MR 2 , which first and second mirrors MR 1  and MR 2  are integrally disposed on the polarizing splitter  41 . 
     The polarizing splitter  41  may be a non-polarizing beam splitter and may split the linearly polarized white light into a first light and a second light. The polarizing splitter  41  may have an incident surface  41   c  on which linearly polarized light is incident, a first reflective surface  41   a , and a second reflective surface  41   b  perpendicularly adjacent to the first reflective surface  41   a . A distance between the incident surface  41   c  and the first reflective surface  41   a  may be the same as that between the incident surface  41   c  and the second reflective surface  41   b . The first mirror MR 1  may be disposed on the first reflective surface  41   a , and the second mirror MR 2  may be disposed on the second reflective surface  41   b.    
     A first sub-linear polarizer P 1  may be disposed between the first reflective surface  41   a  and the first mirror MR 1 , and a second sub-linear polarizer P 2  may be disposed between the second reflective surface  41   b  and the second mirror MR 2 . For example, the first sub-linear polarizer P 1  may be a linear polarizer oriented at 0°, and the second sub-linear polarizer P 2  may be a linear polarizer oriented at 90°. Therefore, the first light may be linearly polarized into a P-polarization wave, and then the P-polarization wave may be incident on and reflected from the first mirror MR 1 . The second light may be linearly polarized into an S-polarization wave, and then the S-polarization wave may be incident on and reflected from the second mirror MR 2 . Alternatively, the first and second sub-linear polarizers P 1  and P 2  may be differently arranged, and thus the first light and the second light may be an S-polarization wave and a P-polarization wave, respectively. For convenience of description, the first light and the second light are respectively explained below as the P-polarization wave and the S-polarization wave. 
     A gap z 1 /2 between the first reflective surface  41   a  and the first mirror MR 1  may be different from a gap z 2 /2 between the second reflective surface  41   b  and the second mirror MR 2 . To achieve this configuration, air may be interposed between the first reflective surface  41   a  and the first mirror MR 1  and between the second reflective surface  41   b  and the second mirror MR 2 . The first and second sub-linear polarizers P 1  and P 2  may have the same thickness. Therefore, the first light and the second light may be different in optical path length. An optical path difference OPD, z 0 =|z 1 −z 2 |, may be created between the first light and the second light. The optical path difference OPD, z 0 =|z 1 −z 2 |, may be about 30 μm to about 50 μm for the visible light range. The optical path difference OPD may be appropriately changed for other wavelength ranges. The optical path difference OPD may be about 10 μm to about 100 μm at a range including the near-ultraviolet, visible light, and near-infrared ranges. The polarizing splitter  41 , or a non-polarizing beam splitter, may have no optical path difference. 
     In such cases, the polarization interferometer  40  may split the linearly polarized white light into a P-polarization wave and an S-polarization wave, and may modulate the P-polarization and S-polarization waves to have a phase difference, which may result in the generation of an output wave light E out . For example, the polarization interferometer  40  may produce a spectral carrier frequency. 
     The line converter  61  may be disposed between the polarization interferometer  40  and a measured object OBJ, and may convert the output wave light E out  to have a linear line-shape in a first direction D 1  and provide the measured object OBJ with the line-shaped output wave light E out . The line converter  61  may be, for example, a cylindrical lens elongated in the first direction D 1 . Alternatively, the line converter  61  may be a slit elongated in the first direction D 1 . 
     The output wave light E out  coming out of the polarization interferometer  40  may be irradiated at a measurement angle θ deviated from a direction perpendicular to the measured object OBJ on the scanner  70 . For example, the angle θ corresponds to an incident angle of the output wave light E out . A measurement light E mea  may be reflected at the measurement angle θ deviated from the direction perpendicular to the measured object OBJ. 
     The measured object OBJ may be loaded on the scanner  70 , and the scanner  70  may be configured such that the measured object OBJ is transferred (scanned) in a second direction D 2  intersecting the first direction D 1 . Preferably, the second direction D 2  may be perpendicular to the first direction D 1 . Alternatively, the scanner  70  may be configured such that the measured object OBJ is scanned rotationally about an axis in a third direction D 3  perpendicular to the first and second directions D 1  and D 2 . For example, the third direction D 3  may be perpendicular to the scanner  70 . 
     The measured object OBJ may be, for example, a thin layer deposited on a silicon substrate. In this case, the phrase “the object OBJ is absent” may indicate a silicon substrate on which no thin layer is deposited. 
     The measured object OBJ may have polarization anisotropy. The polarization anisotropy of the measured object OBJ may provide amplitude modulation and phase modulation to the measurement light E mea  coming out of the measured object OBJ. The second linear polarizer  80  may be provided with the measurement light E mea  reflected from the measured object OBJ. 
     The second linear polarizer  80  may receive P- and S-polarization waves of the measurement light E mea , and may linearly polarize the P- and S-polarization waves (e.g., with a rotation angle of 45°). Therefore, the P- and S-polarization waves interfere with each other to generate an interference light E SP  that is polarization-modulated. 
     The imaging lens  62  may be disposed between the second linear polarizer  80  and the imaging spectrograph  90 . The imaging lens  62  may be, for example, a cylindrical lens elongated in the first direction D 1 . The imaging lens  62  may thus convert the interference light E SP  to a linear line-shape in the first direction D 1 . Alternatively, the imaging lens  62  may be an ordinary imaging lens. 
     The interference light E SP  may be provided to the imaging spectrograph  90 . The interference light E SP  may vertically enter an incident surface of the imaging spectrograph  90 . The interference light E SP  imaged by the imaging lens  62  may have spectral information on the one-dimensional space along the first direction D 1 . The scanner  70  may drive the measured object OBJ to move in the second direction D 2 , and thus it may be possible to obtain spectral ellipsometric information (e.g., spectral ellipsometric cubic information) on two-dimensional spatial axes (e.g., the first and second directions D 1  and D 2 ) (see  FIG. 6 ). The imaging spectrograph  90  may generate from the interference light E SP  a spatio-spectral interference fringe that includes spatio-spectral ellipsometric information of the measured object OBJ. Even when the scanner  70  drives the measured object OBJ to rotate about an axis in the third direction D 3 , a similar result may be obtained. 
     In the present embodiment, a propagation direction of the output wave light E out , a propagation direction of the measurement light E mea , and the first direction D 1  may be provided on the same plane. 
     In the embodiment mentioned above, the polarizing splitter  41  is a non-polarizing beam splitter, but the present inventive concepts are not limited thereto. The polarizing splitter  41  may be, for example, a polarizing beam splitter. In this case, the first sub-linear polarizer P 1  and the second sub-linear polarizer P 2  of  FIG. 1  may be omitted. The polarizing splitter  41  may split the linearly polarized white light into a first light and a second light. The first light and the second light may be directed toward and reflected from the first mirror MR 1  and the second mirror MR 2 , without passing through the first and second sub-linear polarizers P 1  and P 2 . 
     The following will describe an extraction method in which the inspection apparatus of  FIG. 1  is utilized to extract, from a spatio-spectral interference fringe, spatio-spectral ellipsometric information (spatio-spectral ellipsometric phase difference Δ(x,k) and spatio-spectral ellipsometric amplitude ratio Ψ(x,k)) of the measured object OBJ. 
     The input wave light E in  incident on the polarization interferometer  40  may be expressed as follows. 
     
       
         
           
             
               
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     Here, k is a wavenumber represented by 2π/λ. The symbol λ refers to the wavelength of a light source. In the equation above, j is an operator which follows the rule j 2 =−1. The symbols u and v represent amplitudes of the input wave light for P-polarization and S-polarization, respectively. The symbols ξ and η denote phases of the input wave light for P-polarization and S-polarization, respectively. An x-direction indicates the first direction D 1 , or an extending direction of the line converter  61 . A component in a moving direction of the scanner  70 , or in a y-direction related to the second direction D 2 , is uniform and thus may be neglected. 
     The output wave light E out  coming out of the polarization interferometer  40  is expressed as follows.
 
 E   out ( x,k )= E   1 ( x,k )+ E   2 ( x,k )
 
     In the equation above, E 1 (x, k) and E 2 (x, k) are respectively related to a P-polarization-modulated path and an S-polarization-modulated path. The terms E 1 (x, k) and E 2 (x, k) meet at an exit of the polarization interferometer  40 , and may be represented as follows. 
     
       
         
           
             
               
                 
                   
                     
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     Here, J pol(45)  denotes a Jones matrix of the first linear polarizer  30  oriented at a rotation angle of 45°. The term J BS  is a Jones matrix of a non-polarizing beam splitter used as the polarizing splitter  41 , and the terms J pol(0)  and J pol(90)  are Jones matrices of the first sub-linear polarizer P 1  and the second sub-linear polarizer P 2 , respectively. The terms J M1  and J M2  represent Jones matrices of the first mirror MR 1  and the second mirror MR 2 , respectively. The terms z 1  and z 2  denote optical path lengths along which the P- and S-polarization waves reciprocally travel between corresponding mirrors and corresponding reflective surfaces. It is assumed that the optical path difference OPD is absent in the polarizing splitter  41 , or the non-polarizing beam splitter. Any other components of the one-piece polarization interferometer  40  are stably fixed and thus presumed to have the same optical path. The symbols u′ and v′ indicate newly defined unknown amplitude terms of E 1 (x, k) and E 2 (x, k), respectively. The symbols ξ′ and η′ indicate newly defined unknown amplitude terms of E 1 (x, k) and E 2 (x, k), respectively. 
     The output wave light E out  is reflected from the anisotropic measured object OBJ shown in  FIG. 1 , and then changed into the measurement light E mea . The polarization anisotropy of the measured object OBJ may provide amplitude modulation and phase modulation to the measurement light E mea . The second linear polarizer  80  may be provided with the measurement light E mea  reflected from the measured object OBJ. The second linear polarizer  80  may receive P- and S-polarization waves of the measurement light E mea , and may linearly polarize the P- and S-polarization waves (e.g., with a rotation angle of 45°). Therefore, the P- and S-polarization waves interfere with each other to generate the interference light E SP  that is polarization-modulated. The interference light E SP   obj  from the measured object OBJ may be expressed as follows.
 
 E   SP   obj ( x,k )= E   SP   1,obj ( z,k )+ E   SP   2,obj ( x,k )
 
     Where,
 
 E   SP   1,obj ( x,k )= u ′( x,k )| r   P ( x,k )|exp[ j (2 kz   1 +ξ′( x,k )+δ P ( x,k )]
 
 E   SP   2,obj ( x,k )= v ′( x,k )| r   S ( x,k )|exp[ j (2 kz   2 +η′( x,k )+δ s ( x,k )]
 
     Here, E SP   1,obj  and E SP   2,obj  indicate interference light waves related to P-polarization and S-polarization, respectively. The symbols |r P | and |r S | represent amplitudes of complex Fresnel transmission coefficients for P-polarization and S-polarization, respectively, in a case of reflection from the measured object. The symbols δ P  and δ S  represent spatial phase changes for P-polarization and S-polarization, respectively, in a case of reflection from the measured object. 
     The optical path difference OPD at the one-piece polarization interferometer  40  according to the present inventive concepts generates a spectral carrier frequency required for extracting spatio-spectral ellipsometric information (e.g., spatio-spectral ellipsometric phase difference Δ(x, k) and spatio-spectral ellipsometric amplitude ratio Ψ(x, k)). 
     A spatio-spectrally interfered spectrum I(x, k) produced from the interference light E SP  may be expressed as follows.
 
 I ( x,k )=( E   SP   1 ( x,k )+ E   SP   2 ( x,k ))( E   SP   1 ( x,k )+ E   SP   2 ( x,k ))
 
     To perform calibration before obtaining spatio-spectral ellipsometric information of the measured object OBJ, an interfered reference spectrum I ref (x, k) is extracted from a silicon substrate, or a state in which the measured object OBJ is absent. 
     
       
         
           
             
               
                 
                   
                     
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                          
                         
                           E 
                           SP 
                           
                             2 
                             , 
                             ref 
                           
                         
                          
                       
                       2 
                     
                     + 
                     
                       2 
                       ⁢ 
                       
                         γ 
                         ⁡ 
                         
                           ( 
                           
                             x 
                             , 
                             k 
                           
                           ) 
                         
                       
                       ⁢ 
                       
                          
                         
                           E 
                           SP 
                           
                             1 
                             , 
                             ref 
                           
                         
                          
                       
                       ⁢ 
                       
                          
                         
                           E 
                           SP 
                           
                             2 
                             , 
                             ref 
                           
                         
                          
                       
                       × 
                     
                   
                 
               
             
             
               
                   
               
               
                 
                     
                   ⁢ 
                   
                     cos 
                     ⁡ 
                     
                       [ 
                       
                         
                           Φ 
                           ref 
                         
                         ⁡ 
                         
                           ( 
                           
                             x 
                             , 
                             k 
                           
                           ) 
                         
                       
                       ] 
                     
                   
                 
               
             
             
               
                 
                     
                   = 
                 
               
               
                 
                     
                   ⁢ 
                   
                     
                       α 
                       2 
                     
                     + 
                     
                       β 
                       2 
                     
                     + 
                     
                       2 
                       ⁢ 
                       
                         γ 
                         ⁡ 
                         
                           ( 
                           
                             x 
                             , 
                             k 
                           
                           ) 
                         
                       
                       ⁢ 
                       αβ 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       
                         cos 
                         ⁡ 
                         
                           [ 
                           
                             
                               Φ 
                               ref 
                             
                             ⁡ 
                             
                               ( 
                               
                                 x 
                                 , 
                                 k 
                               
                               ) 
                             
                           
                           ] 
                         
                       
                     
                   
                 
               
             
           
         
       
       
         
           
             where 
             , 
             
               
                 
                   Φ 
                   ref 
                 
                 ⁡ 
                 
                   ( 
                   
                     x 
                     , 
                     k 
                   
                   ) 
                 
               
               = 
               
                 
                   2 
                   ⁢ 
                   
                     kz 
                     o 
                   
                 
                 + 
                 
                   [ 
                   
                     
                       
                         ξ 
                         ′ 
                       
                       ⁡ 
                       
                         ( 
                         
                           x 
                           , 
                           k 
                         
                         ) 
                       
                     
                     - 
                     
                       
                         η 
                         ′ 
                       
                       ⁡ 
                       
                         ( 
                         
                           x 
                           , 
                           k 
                         
                         ) 
                       
                     
                   
                   ] 
                 
               
             
           
         
       
     
     In the equation above, γ(x, k) represents a spatio-spectral coherence function of the entire optical measurement system, and does not change regardless of the presence of the measured object. The term Φref(x, k) denotes a reference spatio-spectral phase function. The symbols α(x, k) and β(x, k) relate to absolute values of DC components of waves that travel along P- and S-polarization paths, respectively. That is, α(x, k)=|E SP   1,ref |, β(x,k)=|E SP   2,ref |. 
     The spatio-spectral coherence function γ(x, k) and the reference spatio-spectral phase function Φref(x, k) may be obtained from the spatio-spectrally interfered reference spectrum I ref (x, k). To do this, it may be needed to change the interfered reference spectrum I ref (x, k) into I mod   ref (x, k). 
     
       
         
           
             
               
                 
                   
                     
                       I 
                       mod 
                       ref 
                     
                     ⁡ 
                     
                       ( 
                       
                         x 
                         , 
                         k 
                       
                       ) 
                     
                   
                   = 
                   
                     
                       
                         
                           I 
                           ref 
                         
                         ⁡ 
                         
                           ( 
                           
                             x 
                             , 
                             k 
                           
                           ) 
                         
                       
                       - 
                       
                         ( 
                         
                           
                             α 
                             2 
                           
                           + 
                           
                             β 
                             2 
                           
                         
                         ) 
                       
                     
                     
                       2 
                       ⁢ 
                       αβ 
                     
                   
                 
               
             
             
               
                 
                   = 
                   
                     
                       γ 
                       ⁡ 
                       
                         ( 
                         
                           x 
                           , 
                           k 
                         
                         ) 
                       
                     
                     ⁢ 
                     cos 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     
                       
                         Φ 
                         ref 
                       
                       ⁡ 
                       
                         ( 
                         
                           x 
                           , 
                           k 
                         
                         ) 
                       
                     
                   
                 
               
             
           
         
       
     
     The term I mod   ref (x, k) may undergo the Fourier transform in a spatio-spectral frequency domain, so that unwanted DC and AC components may be filtered out. The spatio-spectral coherence function γ(x, k) and the reference spatio-spectral phase function Φ ref (x, k) are extracted from a result of the inverse Fourier transform on data where the DC and AC components are filtered out. The calibration step for obtaining Φ ref (x, k) and γ(x, k) is required only once, and because Φ ref (x, k) and γ(x, k) are fixed values inherent to an optical measurement system, Φ ref (x, k) and γ(x, k) may be applied to Δ(x, k) and Ψ(x, k) of any measured object after the calibration step. 
     When the output wave light E out  is reflected from the measured object and then changed into the measurement light E mea , an interfered spectrum I obj (x, k) is expressed as follows. 
     
       
         
           
             
               
                 
                   
                     
                       I 
                       obj 
                     
                     ⁡ 
                     
                       ( 
                       
                         x 
                         , 
                         k 
                       
                       ) 
                     
                   
                   ⁢ 
                     
                   = 
                 
               
               
                 
                     
                   ⁢ 
                   
                     
                       
                         ( 
                         
                           
                              
                             
                               E 
                               SP 
                               
                                 1 
                                 , 
                                 obj 
                               
                             
                              
                           
                           ⁢ 
                           
                              
                             
                               
                                 r 
                                 P 
                               
                               ⁡ 
                               
                                 ( 
                                 
                                   x 
                                   , 
                                   k 
                                 
                                 ) 
                               
                             
                              
                           
                         
                         ) 
                       
                       2 
                     
                     + 
                     
                       
                         ( 
                         
                           
                              
                             
                               E 
                               SP 
                               
                                 2 
                                 , 
                                 obj 
                               
                             
                              
                           
                           ⁢ 
                           
                              
                             
                               
                                 r 
                                 S 
                               
                               ⁡ 
                               
                                 ( 
                                 
                                   x 
                                   , 
                                   k 
                                 
                                 ) 
                               
                             
                              
                           
                         
                         ) 
                       
                       2 
                     
                     + 
                   
                 
               
             
             
               
                   
               
               
                 
                     
                   ⁢ 
                   
                     2 
                     ⁢ 
                     γ 
                     ⁢ 
                     
                        
                       
                         E 
                         SP 
                         
                           1 
                           , 
                           obj 
                         
                       
                        
                     
                     ⁢ 
                     
                        
                       
                         E 
                         SP 
                         
                           2 
                           , 
                           obj 
                         
                       
                        
                     
                     × 
                     
                        
                       
                         r 
                         P 
                       
                        
                     
                     ⁢ 
                     
                        
                       
                         
                           r 
                           S 
                         
                         ⁡ 
                         
                           ( 
                           
                             x 
                             , 
                             k 
                           
                           ) 
                         
                       
                        
                     
                     ⁢ 
                     
                       cos 
                       ⁡ 
                       
                         [ 
                         
                           
                             Φ 
                             obj 
                           
                           ⁡ 
                           
                             ( 
                             
                               x 
                               , 
                               k 
                             
                             ) 
                           
                         
                         ] 
                       
                     
                   
                 
               
             
             
               
                 
                     
                   = 
                 
               
               
                 
                     
                   ⁢ 
                   
                     
                       
                         ( 
                         
                           α 
                           ⁢ 
                           
                              
                             
                               
                                 r 
                                 P 
                               
                               ⁡ 
                               
                                 ( 
                                 
                                   x 
                                   , 
                                   k 
                                 
                                 ) 
                               
                             
                              
                           
                         
                         ) 
                       
                       2 
                     
                     + 
                     
                       
                         ( 
                         
                           β 
                           ⁢ 
                           
                              
                             
                               
                                 r 
                                 S 
                               
                               ⁡ 
                               
                                 ( 
                                 
                                   x 
                                   , 
                                   k 
                                 
                                 ) 
                               
                             
                              
                           
                         
                         ) 
                       
                       2 
                     
                     + 
                   
                 
               
             
             
               
                   
               
               
                 
                     
                   ⁢ 
                   
                     2 
                     ⁢ 
                     γαβ 
                     ⁢ 
                     
                        
                       
                         
                           r 
                           P 
                         
                         ⁡ 
                         
                           ( 
                           
                             x 
                             , 
                             k 
                           
                           ) 
                         
                       
                        
                     
                     ⁢ 
                     
                        
                       
                         
                           r 
                           S 
                         
                         ⁡ 
                         
                           ( 
                           
                             x 
                             , 
                             k 
                           
                           ) 
                         
                       
                        
                     
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     
                       cos 
                       ⁡ 
                       
                         [ 
                         
                           
                             Φ 
                             obj 
                           
                           ⁡ 
                           
                             ( 
                             
                               x 
                               , 
                               k 
                             
                             ) 
                           
                         
                         ] 
                       
                     
                   
                 
               
             
           
         
       
       
         
           
             where 
             , 
             
               
                 
                   Φ 
                   obj 
                 
                 ⁡ 
                 
                   ( 
                   
                     x 
                     , 
                     k 
                   
                   ) 
                 
               
               = 
               
                 
                   2 
                   ⁢ 
                   
                     kz 
                     o 
                   
                 
                 + 
                 
                   [ 
                   
                     
                       
                         ξ 
                         ′ 
                       
                       ⁡ 
                       
                         ( 
                         
                           x 
                           , 
                           k 
                         
                         ) 
                       
                     
                     - 
                     
                       
                         η 
                         ′ 
                       
                       ⁡ 
                       
                         ( 
                         
                           x 
                           , 
                           k 
                         
                         ) 
                       
                     
                   
                   ] 
                 
                 + 
                 
                   [ 
                   
                     
                       
                         δ 
                         P 
                       
                       ⁡ 
                       
                         ( 
                         
                           x 
                           , 
                           k 
                         
                         ) 
                       
                     
                     - 
                     
                       
                         δ 
                         S 
                       
                       ⁡ 
                       
                         ( 
                         
                           x 
                           , 
                           k 
                         
                         ) 
                       
                     
                   
                   ] 
                 
               
             
           
         
       
     
       FIG. 2A  illustrates an example of the spatio-spectrally interfered spectrum I obj (x, k) of the measured object OBJ, which I obj (x, k) is measured in the imaging spectrograph  90  according to the first embodiment of the present inventive concept. The measured object OBJ was a silicon oxide layer (SiO 2 ) whose nominal thickness is 1.5 μm deposited on a silicon substrate. In  FIG. 2A , the horizontal axis represents a spectral axis (λ), the vertical axis denotes a spatial axis (x) in the first direction D 1 , and brightness indicates spatio-spectral polarization-sensitive interference information. An interference fringe image is seen along the spectral axis (λ) and the spatial axis (x).  FIG. 2B  illustrates a spectral interference signal at wavelength λ at one position (e.g., x=2.79 mm) on the spatial axis of  FIG. 2A . 
     The inspection apparatus according to the first embodiment of the present inventive concepts may use a spectral carrier frequency to obtain spectral ellipsometric information on the one-dimensional space (i.e., the first direction D 1 ) of the measured object OBJ. 
       FIG. 3  illustrates an example of a spatio-spectral frequency image created when the interference fringe image of  FIG. 2A  is Fourier-transformed in the spatio-spectral frequency domain. In  FIG. 3 , the horizontal axis is a spectral frequency axis (f λ ), and the vertical axis a spatial frequency axis (f x ). The Fourier transform is performed in the spatio-spectral frequency domain, and thereafter, unwanted DC and AC components may be filtered out. 
     Afterwards, a spatio-spectral phase function Φ obj (x, k) of the measured object may be extracted by performing a similar Fourier transform to that used for extracting the reference spatio-spectral phase function Φ ref (x, k). 
     A spatio-spectral ellipsometric phase difference Δ(x, k) may be obtained as follows. 
     
       
         
           
             
               
                 
                   
                     Δ 
                     ⁡ 
                     
                       ( 
                       
                         x 
                         , 
                         k 
                       
                       ) 
                     
                   
                   = 
                   
                     
                       
                         Φ 
                         obj 
                       
                       ⁡ 
                       
                         ( 
                         
                           x 
                           , 
                           k 
                         
                         ) 
                       
                     
                     - 
                     
                       
                         Φ 
                         ref 
                       
                       ⁡ 
                       
                         ( 
                         
                           x 
                           , 
                           k 
                         
                         ) 
                       
                     
                   
                 
               
             
             
               
                 
                   = 
                   
                     
                       
                         δ 
                         P 
                       
                       ⁡ 
                       
                         ( 
                         
                           x 
                           , 
                           k 
                         
                         ) 
                       
                     
                     - 
                     
                       
                         δ 
                         S 
                       
                       ⁡ 
                       
                         ( 
                         
                           x 
                           , 
                           k 
                         
                         ) 
                       
                     
                   
                 
               
             
           
         
       
     
       FIG. 4  illustrates the spatio-spectral ellipsometric phase difference Δ(x, k) of the measured object. In  FIG. 4 , the horizontal axis represents a spectral axis λ, the vertical axis denotes a spatial axis x in the first direction D 1 , and brightness indicates the spatio-spectral ellipsometric phase difference Δ(x, k). The measured object OBJ was a silicon oxide layer (SiO 2 ) whose nominal thickness is 1.5 μm deposited on a silicon substrate. 
       FIG. 5  illustrates a comparison between the spatio-spectral ellipsometric phase difference Δ(x, k) measured with the inspection apparatus according to the present inventive concepts and Δ(k) for a specific point measured with a commercial tool (e.g., an spectroscopic ellipsometer available from J. A. Woollam Co.), which comparison shows almost the same result. The spectral ellipsometric phase difference Δ(k) shown in  FIG. 5  is a result at the position of x=8.352 mm depicted in  FIG. 4 . 
     The spatio-spectral ellipsometric amplitude ratio Ψ(x, k) may be obtained in a similar way to that used to acquire the spatio-spectral ellipsometric phase difference Δ(x, k). 
     In a case of reflection from the anisotropic measured object, the interfered spectrum I obj (x, k) may be expressed as follows.
 
 I   obj ( x,k )= A   obj   DC +2γ( x,k ) A   obj   AC cosΦ obj ( x,k )
 
     Here, A obj   DC =(α′|r P |) 2 +(β′|r S |) 2 , A obj   AC =α′β′|r P ||r S |, α′=|E SP   1,obj |, β′=|E SP   2,obj | 
     Finally, 
     
       
         
           
             
               
                 α 
                 ′ 
               
               ⁢ 
               
                  
                 
                   t 
                   P 
                 
                  
               
             
             = 
             
               
                 
                   
                     
                       A 
                       obj 
                       DC 
                     
                     + 
                     
                       2 
                       ⁢ 
                       
                         A 
                         obj 
                         AC 
                       
                     
                   
                 
                 + 
                 
                   
                     
                       A 
                       obj 
                       DC 
                     
                     - 
                     
                       2 
                       ⁢ 
                       
                         A 
                         obj 
                         AC 
                       
                     
                   
                 
               
               2 
             
           
         
       
       
         
           
             
               
                 β 
                 ′ 
               
               ⁢ 
               
                  
                 
                   t 
                   S 
                 
                  
               
             
             = 
             
               
                 
                   
                     
                       A 
                       obj 
                       DC 
                     
                     + 
                     
                       2 
                       ⁢ 
                       
                         A 
                         obj 
                         AC 
                       
                     
                   
                 
                 - 
                 
                   
                     
                       A 
                       obj 
                       DC 
                     
                     - 
                     
                       2 
                       ⁢ 
                       
                         A 
                         obj 
                         AC 
                       
                     
                   
                 
               
               2 
             
           
         
       
     
     And, these terms α′|t p | and β′|t s | may be used to obtain the spatio-spectral ellipsometric amplitude ratio Ψ(x, k) expressed below. 
     
       
         
           
             
               
                 
                   
                     Ψ 
                     ⁡ 
                     
                       ( 
                       
                         x 
                         , 
                         k 
                       
                       ) 
                     
                   
                   = 
                   
                     
                       tan 
                       
                         - 
                         1 
                       
                     
                     ⁡ 
                     
                       [ 
                       
                         
                            
                           
                             t 
                             P 
                           
                            
                         
                         
                            
                           
                             t 
                             S 
                           
                            
                         
                       
                       ] 
                     
                   
                 
               
             
             
               
                 
                   = 
                   
                     
                       tan 
                       
                         - 
                         1 
                       
                     
                     ⁡ 
                     
                       [ 
                       
                         
                           
                             β 
                             ′ 
                           
                           
                             α 
                             ′ 
                           
                         
                         · 
                         
                           
                             
                               
                                 
                                   A 
                                   obj 
                                   DC 
                                 
                                 + 
                                 
                                   2 
                                   ⁢ 
                                   
                                     A 
                                     obj 
                                     AC 
                                   
                                 
                               
                             
                             + 
                             
                               
                                 
                                   A 
                                   obj 
                                   DC 
                                 
                                 - 
                                 
                                   2 
                                   ⁢ 
                                   
                                     A 
                                     obj 
                                     AC 
                                   
                                 
                               
                             
                           
                           
                             
                               
                                 
                                   A 
                                   obj 
                                   DC 
                                 
                                 + 
                                 
                                   2 
                                   ⁢ 
                                   
                                     A 
                                     obj 
                                     AC 
                                   
                                 
                               
                             
                             - 
                             
                               
                                 
                                   A 
                                   obj 
                                   DC 
                                 
                                 - 
                                 
                                   2 
                                   ⁢ 
                                   
                                     a 
                                     obj 
                                     AC 
                                   
                                 
                               
                             
                           
                         
                       
                       ] 
                     
                   
                 
               
             
           
         
       
     
     The inspection apparatus according to the present inventive concepts may be configured such that spatio-spectral ellipsometric information of the measured object OBJ that moves in the second direction D 2  are successively measured to obtain spatio-spectral ellipsometric information (e.g., spectral ellipsometric cubic information) along two-dimensional spatial axes (e.g., the first and second directions D 1  and D 2 ) (see  FIG. 6 ). 
     Referring to  FIG. 6 , the bottom surface represents a spatial axis (i.e., x-axis) in the first direction D 1  and a spectral axis (i.e., λ-axis), and the vertical axis denotes a spatial axis (i.e., y-axis) in the second direction D 2 . Brightness of each cubic cell expresses spatio-spectral ellipsometric information. 
     The inspection apparatus according to the present inventive concepts may provide an apparatus, without mechanically rotational mechanism or electronic signal modulation, which processes signals of three-dimensional spectral ellipsometric cubic data to detect microscopic defects on the two-dimensional space or to measure uniformity of nano-patterns or nano-films on the two-dimensional space. 
       FIG. 7  illustrates a simplified schematic diagram showing another example of the inspection apparatus according to the first embodiment of the present inventive concepts. Omission will be made to avoid duplicate explanation of components and functions discussed with reference to  FIG. 1 . 
     Referring to  FIG. 7 , a non-polarizing beam splitter  50  may further be included in an inspection apparatus according to an example of the first embodiment of the present inventive concepts. The non-polarizing beam splitter  50  may be disposed between the first linear polarizer  30  and the polarization interferometer  40 . For example, the input wave light Ern linearly polarized (e.g., with a rotation angle of 45°) in the first linear polarizer  30  may be provided through the non-polarizing beam splitter  50  to the polarization interferometer  40 . 
     The polarizing splitter  41  of the polarization interferometer  40  may be a polarizing beam splitter. Moreover, neither the first sub-linear polarizer P 1  nor the second sub-linear polarizer P 2  of  FIG. 1  may be disposed. The polarizing splitter  41  may split the linearly polarized white light into a first light and a second light. The first light and the second light may be directed toward and reflected from the first mirror MR 1  and the second mirror MR 2 , without passing through the first and second sub-linear polarizers P 1  and P 2 . 
     The output wave light E out  it that is polarization-modulated in the polarization interferometer  40  may be provided through the non-polarizing beam splitter  50  and the line converter  61  to the measured object OBJ on the scanner  70 . The output wave light E out  coming out of the polarization interferometer  40  may be irradiated at a measurement angle θ deviated from a direction perpendicular to the measured object OBJ on the scanner  70 . For example, the angle θ corresponds to an incident angle of the output wave light E out . The measurement light E mea  may be reflected at the measurement angle θ deviated from the direction perpendicular to the measured object OBJ. 
     The polarization anisotropy of the measured object OBJ may provide amplitude modulation and phase modulation to the measurement light E mea  coming out of the measured object OBJ. The second linear polarizer  80  may be provided with the measurement light E mea  reflected from the measured object OBJ, which may result in the creation of the interference light E SP . The interference light E SP  may be provided through the imaging lens  62  to the imaging spectrograph  90 . The interference light E SP  may vertically enter an incident surface of the imaging spectrograph  90 . The imaging spectrograph  90  may generate, from the interference light E SP , a spatio-spectral interference fringe that includes spatio-spectral ellipsometric information of the measured object OBJ. 
       FIG. 8  illustrates a simplified schematic diagram showing an example of the inspection apparatus according to the first embodiment of the present inventive concepts. Omission will be made to avoid duplicate explanation of components and functions discussed with reference to  FIG. 1 . Components in the present example may be spatially arranged differently from those shown in  FIG. 1 . 
     Referring to  FIG. 8 , a non-polarizing beam splitter  50  may further be included in an inspection apparatus according to an example of the first embodiment of the present inventive concepts. The non-polarizing beam splitter  50  may be disposed on one side of the polarization interferometer  40 , and the line converter  61  may be placed between the polarization interferometer  40  and the non-polarizing beam splitter  50 . The non-polarizing beam splitter  50  may provide the measured object OBJ with the output wave light E out  coming out of the line converter  61 . 
     The output wave light E out  may be vertically irradiated to the measured object OBJ on the scanner  70 , and the measurement light E mea  may be vertically reflected from the measured object OBJ. 
     The measurement light E mea  reflected from the measured object OBJ may reenter the non-polarizing beam splitter  50  and travel to the second linear polarizer  80 . 
       FIG. 9  illustrates a simplified schematic diagram showing an example of an inspection apparatus according to a second embodiment of the present inventive concepts. Omission will be made to avoid duplicate components and functions discussed with reference to  FIG. 1 . In an inspection apparatus according to the present embodiment, the polarization interferometer  40  may be different from that discussed with reference to  FIG. 1 . 
     Referring to  FIG. 9 , the first and second mirrors MR 1  and MR 2  of the polarization interferometer  40  are not perpendicular to each other. For example, the first mirror MR 1  and the second mirror MR 2  may have an off-axis angle ε deviated from perpendicular. The off-axis angle ε may be about 0.01° to about 1°, preferably 0.02° to 0.1°. Because the first mirror MR 1  is tilted at the off-axis angle ε, the polarization interferometer  40  may generate a high spatial carrier frequency to spatially modulate a polarization signal that is spatio-spectroscopically separated. 
     Therefore, the polarization interferometer  40  may split the linearly polarized white light into P- and S-polarization waves, and may allow the P- and S-polarization waves to have a spatial phase difference. For example, the polarization interferometer  40  may create a high spatial carrier frequency having a spatial phase shift. 
     Further, it may be possible to neglect the optical path difference OPD between the first light and the second light shown in  FIG. 1 . 
     The first light and the second light that are output from the polarization interferometer  40  may be provided through the line converter  61  to the measured object OBJ. The measured object OBJ may have polarization anisotropy. The polarization anisotropy may provide amplitude modulation and phase modulation to light coming out of the measured object OBJ. The second linear polarizer  80  may be provided with the measurement light E mea  reflected from the measured object OBJ. 
     The second linear polarizer  80  may receive P- and S-polarization waves of the measurement light E mea , and may linearly polarize the P- and S-polarization waves (e.g., with a rotation angle of 45°). Therefore, the P- and S-polarization waves interfere with each other to generate the interference light E SP  that is polarization-modulated. The imaging spectrograph  90  may generate, from the interference light E SP , a spatio-spectral interference fringe that includes spatio-spectral ellipsometric information of the measured object OBJ. 
     The interference light E SP  may be provided through the imaging lens  62  to the imaging spectrograph  90 . The imaging spectrograph  90  may produce a spatio-spectral interference fringe from the interference light E SP . 
     In the embodiment mentioned previously, the polarizing splitter  41  is a non-polarizing beam splitter, but the present inventive concepts are not limited thereto. The polarizing splitter  41  may be, for example, a polarizing beam splitter. In this case, neither the first sub-linear polarizer P 1  nor the second sub-linear polarizer P 2  of  FIG. 9  may be used. In this case, the polarizing splitter  41  may split a linearly polarized laser beam into a first light and a second light. The first light and the second light may be directed toward and reflected from the first mirror MR 1  and the second mirror MR 2 , without passing through the first and second sub-linear polarizers P 1  and P 2 . 
     The following will describe an extraction method in which the inspection apparatus of  FIG. 9  is utilized to extract, from an interference fringe, spatio-spectral ellipsometric information (spatio-spectral ellipsometric phase difference Δ(x, k) and spatio-spectral ellipsometric amplitude ratio Ψ(x, k)) of the measured object OBJ. 
     The input wave light E in  incident on the polarization interferometer  40  may be expressed as follows. 
     
       
         
           
             
               
                 
                   
                     
                       E 
                       in 
                     
                     ⁡ 
                     
                       ( 
                       
                         
                           x 
                           ′ 
                         
                         , 
                         
                           y 
                           ′ 
                         
                         , 
                         k 
                       
                       ) 
                     
                   
                   = 
                   
                     ( 
                     
                       
                         
                           
                             
                               E 
                               x 
                             
                             ⁡ 
                             
                               ( 
                               
                                 
                                   x 
                                   ′ 
                                 
                                 , 
                                 
                                   y 
                                   ′ 
                                 
                                 , 
                                 k 
                               
                               ) 
                             
                           
                         
                       
                       
                         
                           
                             
                               E 
                               y 
                             
                             ⁡ 
                             
                               ( 
                               
                                 
                                   x 
                                   ′ 
                                 
                                 , 
                                 
                                   y 
                                   ′ 
                                 
                                 , 
                                 k 
                               
                               ) 
                             
                           
                         
                       
                     
                     ) 
                   
                 
               
             
             
               
                 
                   = 
                   
                     ( 
                     
                       
                         
                           
                             
                               u 
                               ⁡ 
                               
                                 ( 
                                 
                                   
                                     x 
                                     ′ 
                                   
                                   , 
                                   
                                     y 
                                     ′ 
                                   
                                   , 
                                   k 
                                 
                                 ) 
                               
                             
                             ⁢ 
                             
                               exp 
                               ⁡ 
                               
                                 [ 
                                 
                                   j 
                                   ⁢ 
                                   
                                       
                                   
                                   ⁢ 
                                   
                                     ξ 
                                     ⁡ 
                                     
                                       ( 
                                       
                                         
                                           x 
                                           ′ 
                                         
                                         , 
                                         
                                           y 
                                           ′ 
                                         
                                         , 
                                         k 
                                       
                                       ) 
                                     
                                   
                                 
                                 ] 
                               
                             
                           
                         
                       
                       
                         
                           
                             
                               v 
                               ⁡ 
                               
                                 ( 
                                 
                                   
                                     x 
                                     ′ 
                                   
                                   , 
                                   
                                     y 
                                     ′ 
                                   
                                   , 
                                   k 
                                 
                                 ) 
                               
                             
                             ⁢ 
                             exp 
                             ⁢ 
                             
                               { 
                               
                                 j 
                                 ⁢ 
                                 
                                     
                                 
                                 ⁢ 
                                 
                                   η 
                                   ⁡ 
                                   
                                     ( 
                                     
                                       
                                         x 
                                         ′ 
                                       
                                       , 
                                       
                                         y 
                                         ′ 
                                       
                                       , 
                                       k 
                                     
                                     ) 
                                   
                                 
                               
                               ] 
                             
                           
                         
                       
                     
                     ) 
                   
                 
               
             
           
         
       
     
     Here, k is a wavenumber represented by 2π/λ. The symbol λ refers to the wavelength of a light source. The symbol j is an operator which follows the rule j 2 =−1. The symbols x′- and y′-axes represent axes on the polarization interferometer  40 . The symbols u and v represent amplitudes of the incident wave light along the x′-axis and y′-axis, respectively. The symbols ξ and η denote phases of the incident wave light along the x′-axis and y′-axis, respectively. The P-polarization wave and S-polarization wave are oriented toward the x′-axis and the y′-axis, respectively. 
     The output wave light E out  coming out of the polarization interferometer  40  is expressed as follows.
 
 E   out ( x′,y′,k )= E   1 ( x′,y′,k )+ E   2 ( x′,y′,k )
 
     Here, E 1 (x′, y′) and E 2 (x′, y′) are respectively related to a P-polarization path and an S-polarization path. The terms E 1 (x′, y′) and E 2 (x′, y′) meet at an exit of the polarization interferometer  40 , and may be represented as follows. 
     
       
         
           
             
               
                 
                   
                     
                       E 
                       1 
                     
                     ⁡ 
                     
                       ( 
                       
                         
                           x 
                           ′ 
                         
                         , 
                         
                           y 
                           ′ 
                         
                         , 
                         k 
                       
                       ) 
                     
                   
                   = 
                   
                     
                       J 
                       BS 
                     
                     ⁢ 
                     
                       J 
                       
                         pol 
                         ⁡ 
                         
                           ( 
                           0 
                           ) 
                         
                       
                     
                     ⁢ 
                     
                       J 
                       
                         M 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         1 
                       
                     
                     ⁢ 
                     
                       J 
                       
                         pol 
                         ⁡ 
                         
                           ( 
                           0 
                           ) 
                         
                       
                     
                     ⁢ 
                     
                       J 
                       BS 
                     
                     ⁢ 
                     
                       J 
                       
                         pol 
                         ⁡ 
                         
                           ( 
                           45 
                           ) 
                         
                       
                     
                     ⁢ 
                     
                       
                         E 
                         in 
                       
                       ⁡ 
                       
                         ( 
                         
                           
                             x 
                             ′ 
                           
                           , 
                           
                             y 
                             ′ 
                           
                           , 
                           k 
                         
                         ) 
                       
                     
                   
                 
               
             
             
               
                 
                   = 
                   
                     ( 
                     
                       
                         
                           
                             
                               
                                 u 
                                 ′ 
                               
                               ⁡ 
                               
                                 ( 
                                 
                                   
                                     x 
                                     ′ 
                                   
                                   , 
                                   
                                     y 
                                     ′ 
                                   
                                   , 
                                   k 
                                 
                                 ) 
                               
                             
                             ⁢ 
                             
                               exp 
                               ⁡ 
                               
                                 [ 
                                 
                                   j 
                                   ⁡ 
                                   
                                     ( 
                                     
                                       
                                         2 
                                         ⁢ 
                                         
                                           k 
                                           ⁡ 
                                           
                                             ( 
                                             
                                               
                                                 
                                                   k 
                                                   
                                                     x 
                                                     ⁢ 
                                                     
                                                         
                                                     
                                                     ⁢ 
                                                     1 
                                                   
                                                 
                                                 ⁢ 
                                                 
                                                   x 
                                                   ′ 
                                                 
                                               
                                               + 
                                               
                                                 
                                                   k 
                                                   
                                                     y 
                                                     ⁢ 
                                                     
                                                         
                                                     
                                                     ⁢ 
                                                     1 
                                                   
                                                 
                                                 ⁢ 
                                                 
                                                   y 
                                                   ′ 
                                                 
                                               
                                             
                                             ) 
                                           
                                         
                                       
                                       + 
                                       
                                         
                                           ξ 
                                           ′ 
                                         
                                         ⁡ 
                                         
                                           ( 
                                           
                                             
                                               x 
                                               ′ 
                                             
                                             , 
                                             
                                               y 
                                               ′ 
                                             
                                             , 
                                             k 
                                           
                                           ) 
                                         
                                       
                                     
                                     ) 
                                   
                                 
                                 ] 
                               
                             
                           
                         
                       
                       
                         
                           0 
                         
                       
                     
                     ) 
                   
                 
               
             
           
         
       
       
         
           
             And 
             , 
             
               
 
             
             ⁢ 
             
               
                 
                   
                     
                       
                         E 
                         2 
                       
                       ⁡ 
                       
                         ( 
                         
                           
                             x 
                             ′ 
                           
                           , 
                           
                             y 
                             ′ 
                           
                           , 
                           k 
                         
                         ) 
                       
                     
                     = 
                     
                       
                         J 
                         BS 
                       
                       ⁢ 
                       
                         J 
                         
                           pol 
                           ⁡ 
                           
                             ( 
                             90 
                             ) 
                           
                         
                       
                       ⁢ 
                       
                         J 
                         
                           M 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           2 
                         
                       
                       ⁢ 
                       
                         J 
                         
                           pol 
                           ⁡ 
                           
                             ( 
                             90 
                             ) 
                           
                         
                       
                       ⁢ 
                       
                         J 
                         BS 
                       
                       ⁢ 
                       
                         J 
                         
                           pol 
                           ⁡ 
                           
                             ( 
                             45 
                             ) 
                           
                         
                       
                       ⁢ 
                       
                         
                           E 
                           in 
                         
                         ⁡ 
                         
                           ( 
                           
                             
                               x 
                               ′ 
                             
                             , 
                             
                               y 
                               ′ 
                             
                             , 
                             k 
                           
                           ) 
                         
                       
                     
                   
                 
               
               
                 
                   
                     = 
                     
                       ( 
                       
                         
                           
                             0 
                           
                         
                         
                           
                             
                               
                                 
                                   v 
                                   ′ 
                                 
                                 ⁡ 
                                 
                                   ( 
                                   
                                     
                                       x 
                                       ′ 
                                     
                                     , 
                                     
                                       y 
                                       ′ 
                                     
                                     , 
                                     k 
                                   
                                   ) 
                                 
                               
                               ⁢ 
                               
                                 exp 
                                 ⁡ 
                                 
                                   [ 
                                   
                                     j 
                                     ⁡ 
                                     
                                       ( 
                                       
                                         
                                           2 
                                           ⁢ 
                                           
                                             k 
                                             ⁡ 
                                             
                                               ( 
                                               
                                                 
                                                   
                                                     k 
                                                     
                                                       x 
                                                       ⁢ 
                                                       
                                                           
                                                       
                                                       ⁢ 
                                                       2 
                                                     
                                                   
                                                   ⁢ 
                                                   
                                                     x 
                                                     ′ 
                                                   
                                                 
                                                 + 
                                                 
                                                   
                                                     k 
                                                     
                                                       y 
                                                       ⁢ 
                                                       
                                                           
                                                       
                                                       ⁢ 
                                                       2 
                                                     
                                                   
                                                   ⁢ 
                                                   
                                                     y 
                                                     ′ 
                                                   
                                                 
                                               
                                               ) 
                                             
                                           
                                         
                                         + 
                                         
                                           
                                             η 
                                             ′ 
                                           
                                           ⁡ 
                                           
                                             ( 
                                             
                                               
                                                 x 
                                                 ′ 
                                               
                                               , 
                                               
                                                 y 
                                                 ′ 
                                               
                                               , 
                                               k 
                                             
                                             ) 
                                           
                                         
                                       
                                       ) 
                                     
                                   
                                   ] 
                                 
                               
                             
                           
                         
                       
                       ) 
                     
                   
                 
               
             
           
         
       
     
     Here, J pol(45)  denotes a Jones matrix of the first linear polarizer  30  oriented at an rotation angle of 45°. The term J BS  is a Jones matrix of a non-polarizing beam splitter used as the polarizing splitter  41 , and the terms J pol(0)  and J pol(90)  are Jones matrices of the first sub-linear polarizer P 1  and the second sub-linear polarizer P 2 , respectively. The terms J M1  and J M2  represent Jones matrices of the first mirror MR 1  and the second mirror MR 2 , respectively. The symbols k x1 , k y1 , k x2 , and k y2  are related to the off-axis angle ε of  FIG. 9 , the symbols k x1  and k y1  represent components of the wave vector traveled along the P-polarization paths of the polarization interferometer  40 , and the symbols k x2  and k y2  denote components of the wave vector traveled along the S-polarization paths of the polarization interferometer  40 . 
     The symbols u′ and v′ indicate newly defined unknown amplitude terms of E 1 (x′, y′) and E 2 (x′, y′), respectively. The symbols ξ′ and η′ indicate newly defined unknown amplitude terms of E 1 (x′, y′) and E 2 (x′, y′), respectively. 
     A spatial optical path difference in the polarization interferometer  40  may become a condition to generate spatial interference fringes. The line converter  61  may irradiate the output wave light E out  having a linear line-shape in the first direction D 1 . Because the spatial interference fringe is significant only in the first direction D 1  or an x-direction, the symbols E 1 (x′, y′, k) and E 2 (x′, y′, k) may be expressed as follows. 
     
       
         
           
             
               
                 
                   
                     
                       E 
                       1 
                     
                     ⁡ 
                     
                       ( 
                       
                         
                           x 
                           ′ 
                         
                         , 
                         k 
                       
                       ) 
                     
                   
                   = 
                   
                     
                       J 
                       BS 
                     
                     ⁢ 
                     
                       J 
                       
                         pol 
                         ⁡ 
                         
                           ( 
                           0 
                           ) 
                         
                       
                     
                     ⁢ 
                     
                       J 
                       
                         M 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         1 
                       
                     
                     ⁢ 
                     
                       J 
                       
                         pol 
                         ⁡ 
                         
                           ( 
                           0 
                           ) 
                         
                       
                     
                     ⁢ 
                     
                       J 
                       BS 
                     
                     ⁢ 
                     
                       J 
                       
                         pol 
                         ⁡ 
                         
                           ( 
                           45 
                           ) 
                         
                       
                     
                     ⁢ 
                     
                       
                         E 
                         in 
                       
                       ⁡ 
                       
                         ( 
                         
                           
                             x 
                             ′ 
                           
                           , 
                           k 
                         
                         ) 
                       
                     
                   
                 
               
             
             
               
                 
                   = 
                   
                     ( 
                     
                       
                         
                           
                             
                               
                                 u 
                                 ′ 
                               
                               ⁡ 
                               
                                 ( 
                                 
                                   
                                     x 
                                     ′ 
                                   
                                   , 
                                   k 
                                 
                                 ) 
                               
                             
                             ⁢ 
                             
                               exp 
                               ⁡ 
                               
                                 [ 
                                 
                                   j 
                                   ⁡ 
                                   
                                     ( 
                                     
                                       
                                         2 
                                         ⁢ 
                                         
                                           k 
                                           ⁡ 
                                           
                                             ( 
                                             
                                               
                                                 k 
                                                 
                                                   x 
                                                   ⁢ 
                                                   
                                                       
                                                   
                                                   ⁢ 
                                                   1 
                                                 
                                               
                                               ⁢ 
                                               
                                                 x 
                                                 ′ 
                                               
                                             
                                             ) 
                                           
                                         
                                       
                                       + 
                                       
                                         
                                           ξ 
                                           ′ 
                                         
                                         ⁡ 
                                         
                                           ( 
                                           
                                             
                                               x 
                                               ′ 
                                             
                                             , 
                                             k 
                                           
                                           ) 
                                         
                                       
                                     
                                     ) 
                                   
                                 
                                 ] 
                               
                             
                           
                         
                       
                       
                         
                           0 
                         
                       
                     
                     ) 
                   
                 
               
             
           
         
       
       
         
           
             And 
             , 
             
               
 
             
             ⁢ 
             
               
                 
                   
                     
                       
                         E 
                         2 
                       
                       ⁡ 
                       
                         ( 
                         
                           
                             x 
                             ′ 
                           
                           , 
                           k 
                         
                         ) 
                       
                     
                     = 
                     
                       
                         J 
                         BS 
                       
                       ⁢ 
                       
                         J 
                         
                           pol 
                           ⁡ 
                           
                             ( 
                             90 
                             ) 
                           
                         
                       
                       ⁢ 
                       
                         J 
                         
                           M 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           2 
                         
                       
                       ⁢ 
                       
                         J 
                         
                           pol 
                           ⁡ 
                           
                             ( 
                             90 
                             ) 
                           
                         
                       
                       ⁢ 
                       
                         J 
                         BS 
                       
                       ⁢ 
                       
                         J 
                         
                           pol 
                           ⁡ 
                           
                             ( 
                             45 
                             ) 
                           
                         
                       
                       ⁢ 
                       
                         
                           E 
                           in 
                         
                         ⁡ 
                         
                           ( 
                           
                             
                               x 
                               ′ 
                             
                             , 
                             k 
                           
                           ) 
                         
                       
                     
                   
                 
               
               
                 
                   
                     = 
                     
                       ( 
                       
                         
                           
                             0 
                           
                         
                         
                           
                             
                               
                                 
                                   v 
                                   ′ 
                                 
                                 ⁡ 
                                 
                                   ( 
                                   
                                     
                                       x 
                                       ′ 
                                     
                                     , 
                                     k 
                                   
                                   ) 
                                 
                               
                               ⁢ 
                               
                                 exp 
                                 ⁡ 
                                 
                                   [ 
                                   
                                     j 
                                     ⁡ 
                                     
                                       ( 
                                       
                                         
                                           2 
                                           ⁢ 
                                           
                                             k 
                                             ⁡ 
                                             
                                               ( 
                                               
                                                 
                                                   k 
                                                   
                                                     x 
                                                     ⁢ 
                                                     
                                                         
                                                     
                                                     ⁢ 
                                                     2 
                                                   
                                                 
                                                 ⁢ 
                                                 
                                                   x 
                                                   ′ 
                                                 
                                               
                                               ) 
                                             
                                           
                                         
                                         + 
                                         
                                           
                                             η 
                                             ′ 
                                           
                                           ⁡ 
                                           
                                             ( 
                                             
                                               
                                                 x 
                                                 ′ 
                                               
                                               , 
                                               k 
                                             
                                             ) 
                                           
                                         
                                       
                                       ) 
                                     
                                   
                                   ] 
                                 
                               
                             
                           
                         
                       
                       ) 
                     
                   
                 
               
             
           
         
       
     
     The output wave light E out  is reflected from the anisotropic measured object OBJ shown in  FIG. 9 , and then changed into the measurement light E mea . The polarization anisotropy of the measured object OBJ may provide amplitude modulation and phase modulation to the measurement light E mea . The measurement light E mea  may be expressed as follows.
 
 E   mea   obj ( x,k )= J   obj ( x,k ) E   out ( x′,k )
 
     Here, the x-direction indicates the first direction D 1 , or an extending direction of the line converter  61 . The equation above neglects a component in a moving direction of the scanner  70 , or in a y-direction related to the second direction D 2 . 
     Here, J obj (x, k) represents a Jones matrix of the measured object OBJ. 
     
       
         
           
             
               
                 J 
                 obj 
               
               ⁡ 
               
                 ( 
                 
                   x 
                   , 
                   k 
                 
                 ) 
               
             
             = 
             
               ( 
               
                 
                   
                     
                       
                          
                         
                           
                             r 
                             P 
                           
                           ⁡ 
                           
                             ( 
                             
                               x 
                               , 
                               k 
                             
                             ) 
                           
                         
                          
                       
                       ⁢ 
                       
                         exp 
                         ⁡ 
                         
                           [ 
                           
                             j 
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             
                               
                                 δ 
                                 P 
                               
                               ⁡ 
                               
                                 ( 
                                 
                                   x 
                                   , 
                                   k 
                                 
                                 ) 
                               
                             
                           
                           ] 
                         
                       
                     
                   
                   
                     0 
                   
                 
                 
                   
                     0 
                   
                   
                     
                       
                          
                         
                           
                             r 
                             S 
                           
                           ⁡ 
                           
                             ( 
                             
                               x 
                               , 
                               k 
                             
                             ) 
                           
                         
                          
                       
                       ⁢ 
                       
                         exp 
                         ⁡ 
                         
                           [ 
                           
                             j 
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             
                               
                                 δ 
                                 S 
                               
                               ⁡ 
                               
                                 ( 
                                 
                                   x 
                                   , 
                                   k 
                                 
                                 ) 
                               
                             
                           
                           ] 
                         
                       
                     
                   
                 
               
               ) 
             
           
         
       
     
     The symbols |r p | and |r s | represent amplitudes of complex Fresnel reflection coefficients for P-polarization and S-polarization, respectively, in a case of reflection from the measured object OBJ. The symbols δ p  and δ s  represent spatio-spectral phase changes for P-polarization and S-polarization, respectively, in a case of reflection from the measured object. 
     The second linear polarizer  80  may be provided with the measurement light E mea  reflected from the measured object OBJ. The second linear polarizer  80  receives P- and S-polarization waves of the measurement light E mea , and linearly polarizes the P- and S-polarization waves (e.g., with a rotation angle of 45°). Therefore, the P- and S-polarization waves may interfere with each other to generate the interference light E SP  that is polarization-modulated. The interference light E SP   obj  may be expressed as follows.
 
 E   SP   obj ( x,k )= E   SP   1,obj ( x,k )+ E   SP   2,obj ( x,k )
 
     Where,
 
 E   SP   1,obj ( x,k )= u ′( x,k )| r   P ( x,k )|exp[ j (2 k ( k   x1   x )+ξ′( x,k )+δ P ( x,k )]
 
 E   SP   2,obj ( x,k )= v ′( x,k )| r   S ( x,k )|exp[ j (2 k ( k   x2   x )+′( x,k )+δ S ( x,k )]
 
     Here, E SP   1,obj  and E SP   2,obj  indicate output light waves related to P-polarization and S-polarization, respectively. 
     An spatio-spectrally interfered spectrum I(x,k) resulting from the interference between the P-polarization wave and the S-polarization wave may be expressed as follows.
 
 I ( x,k )=( E   SP   1,obj ( x,k )+ E   SP   2,obj ( x,k ))( E   SP   1,obj ( x,k )+ E   SP   2,obj ( x,k ))*
 
     When the output wave light E out  is reflected from an anisotropic measured object and is change into the measurement light E mea , an interfered spectrum is I obj (x, k) expressed as follows. 
     
       
         
           
             
               
                 
                   
                     
                       I 
                       obj 
                     
                     ⁡ 
                     
                       ( 
                       
                         x 
                         , 
                         k 
                       
                       ) 
                     
                   
                   ⁢ 
                     
                   = 
                 
               
               
                 
                     
                   ⁢ 
                   
                     
                       
                         ( 
                         
                           
                              
                             
                               E 
                               SP 
                               
                                 1 
                                 , 
                                 obj 
                               
                             
                              
                           
                           ⁢ 
                           
                              
                             
                               r 
                               P 
                             
                              
                           
                         
                         ) 
                       
                       2 
                     
                     + 
                     
                       
                         ( 
                         
                           
                              
                             
                               E 
                               SP 
                               
                                 2 
                                 , 
                                 obj 
                               
                             
                              
                           
                           ⁢ 
                           
                              
                             
                               r 
                               S 
                             
                              
                           
                         
                         ) 
                       
                       2 
                     
                     + 
                   
                 
               
             
             
               
                   
               
               
                 
                     
                   ⁢ 
                   
                     2 
                     ⁢ 
                     γ 
                     ⁢ 
                     
                        
                       
                         E 
                         SP 
                         
                           1 
                           , 
                           obj 
                         
                       
                        
                     
                     ⁢ 
                     
                        
                       
                         E 
                         SP 
                         
                           2 
                           , 
                           obj 
                         
                       
                        
                     
                     × 
                     
                        
                       
                         r 
                         P 
                       
                        
                     
                     ⁢ 
                     
                        
                       
                         r 
                         S 
                       
                        
                     
                     ⁢ 
                     
                       cos 
                       ⁡ 
                       
                         [ 
                         
                           
                             Φ 
                             obj 
                           
                           ⁡ 
                           
                             ( 
                             
                               x 
                               , 
                               k 
                             
                             ) 
                           
                         
                         ] 
                       
                     
                   
                 
               
             
             
               
                 
                     
                   = 
                 
               
               
                 
                     
                   ⁢ 
                   
                     
                       
                         ( 
                         
                           α 
                           ⁢ 
                           
                              
                             
                               
                                 r 
                                 P 
                               
                               ⁡ 
                               
                                 ( 
                                 
                                   x 
                                   , 
                                   k 
                                 
                                 ) 
                               
                             
                              
                           
                         
                         ) 
                       
                       2 
                     
                     + 
                     
                       
                         ( 
                         
                           β 
                           ⁢ 
                           
                              
                             
                               
                                 r 
                                 S 
                               
                               ⁡ 
                               
                                 ( 
                                 
                                   x 
                                   , 
                                   k 
                                 
                                 ) 
                               
                             
                              
                           
                         
                         ) 
                       
                       2 
                     
                     + 
                   
                 
               
             
             
               
                   
               
               
                 
                     
                   ⁢ 
                   
                     2 
                     ⁢ 
                     γαβ 
                     ⁢ 
                     
                        
                       
                         
                           r 
                           P 
                         
                         ⁡ 
                         
                           ( 
                           
                             x 
                             , 
                             k 
                           
                           ) 
                         
                       
                        
                     
                     ⁢ 
                     
                        
                       
                         
                           r 
                           S 
                         
                         ⁡ 
                         
                           ( 
                           
                             x 
                             , 
                             k 
                           
                           ) 
                         
                       
                        
                     
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     
                       cos 
                       ⁡ 
                       
                         [ 
                         
                           
                             Φ 
                             obj 
                           
                           ⁡ 
                           
                             ( 
                             
                               x 
                               , 
                               k 
                             
                             ) 
                           
                         
                         ] 
                       
                     
                   
                 
               
             
           
         
       
     
     Here, the terms α and β relate to absolute values of DC components of waves that travel along the P- and S-polarization paths, respectively. That is, α=|E SP   1,obj |, β=|E SP   2,obj |. In the equation above, γ represents a spatio-spectral coherence function. 
       FIG. 10  illustrates an example of a spatio-spectral interfered spectrum I obj (x, k) on the one-dimensional space of the measured object OBJ, which I obj (x, k) is measured in the imaging spectrograph  90  according to the second embodiment of the present inventive concepts. The measured object OBJ was a silicon oxide layer (SiO 2 ) whose nominal thickness is 1.5 μm deposited on a silicon substrate. In  FIG. 10 , the horizontal axis represents a spectral axis (λ), the vertical axis denotes a spatial axis (x) in the first direction D 1 , and brightness indicates spatio-spectral interference information. An interference fringe image is seen along the spectral axis (λ) and the spatial axis (x). The interference fringe image is created along a direction of the spectral axis (λ) in  FIG. 2A  according to the first embodiment, whereas the interference fringe image is produced along a direction of the spatial axis (x) in  FIG. 10  according to the second embodiment. 
     A spatio-spectral phase function Φ obj (x, k) may be expressed as follows.
 
Φ obj ( x,k )=2 kx ( k   x1   −k   x2 )+[ξ′( x,k )−η′( x,k )]+[δ P ( x,k )−δ S ( x,k )]
 
     To obtain the spatio-spectral phase function Φ obj (x, k), a similar way to that of the first embodiment may be applied to perform the 2D Fourier transform in a spatio-spectral frequency domain. After the Fourier transform in the spatio-spectral frequency domain, unwanted DC and AC components may be filtered out. Afterwards, the spatio-spectral phase function Φ obj (x, k) is extracted from a result of the inverse Fourier transform. 
     To measure a calibrated spatio-spectral ellipsometric phase difference Δ(x, k), it may be required to obtain a reference spatio-spectral phase function Φ ref (x, k) when no measured object is present. The reference spatio-spectral phase function Φ ref (x, k) may be acquired in a similar way to that of the first embodiment. 
     
       
         
           
             
               
                 
                   
                     
                       I 
                       ref 
                     
                     ⁡ 
                     
                       ( 
                       
                         x 
                         , 
                         k 
                       
                       ) 
                     
                   
                   ⁢ 
                     
                   = 
                 
               
               
                 
                     
                   ⁢ 
                   
                     
                       
                          
                         
                           E 
                           SP 
                           
                             1 
                             , 
                             ref 
                           
                         
                          
                       
                       2 
                     
                     + 
                     
                       
                          
                         
                           E 
                           SP 
                           
                             2 
                             , 
                             ref 
                           
                         
                          
                       
                       2 
                     
                     + 
                     
                       2 
                       ⁢ 
                       γ 
                       ⁢ 
                       
                          
                         
                           E 
                           SP 
                           
                             1 
                             , 
                             ref 
                           
                         
                          
                       
                       ⁢ 
                       
                          
                         
                           E 
                           SP 
                           
                             2 
                             , 
                             ref 
                           
                         
                          
                       
                       × 
                     
                   
                 
               
             
             
               
                   
               
               
                 
                     
                   ⁢ 
                   
                     cos 
                     ⁡ 
                     
                       [ 
                       
                         
                           Φ 
                           ref 
                         
                         ⁡ 
                         
                           ( 
                           
                             x 
                             , 
                             k 
                           
                           ) 
                         
                       
                       ] 
                     
                   
                 
               
             
             
               
                 
                     
                   = 
                 
               
               
                 
                     
                   ⁢ 
                   
                     
                       α 
                       2 
                     
                     + 
                     
                       β 
                       2 
                     
                     + 
                     
                       2 
                       ⁢ 
                       
                         γ 
                         ⁡ 
                         
                           ( 
                           
                             x 
                             , 
                             k 
                           
                           ) 
                         
                       
                       ⁢ 
                       αβ 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       
                         cos 
                         ⁡ 
                         
                           [ 
                           
                             
                               Φ 
                               obj 
                             
                             ⁡ 
                             
                               ( 
                               
                                 x 
                                 , 
                                 k 
                               
                               ) 
                             
                           
                           ] 
                         
                       
                     
                   
                 
               
             
           
         
       
       
         
           
             Where 
             , 
             
               
 
             
             ⁢ 
             
               
                 
                   Φ 
                   ref 
                 
                 ⁡ 
                 
                   ( 
                   
                     x 
                     , 
                     k 
                   
                   ) 
                 
               
               = 
               
                 
                   2 
                   ⁢ 
                   
                     kx 
                     ⁡ 
                     
                       ( 
                       
                         
                           k 
                           
                             x 
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             1 
                           
                         
                         - 
                         
                           k 
                           
                             x 
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             2 
                           
                         
                       
                       ) 
                     
                   
                 
                 + 
                 
                   [ 
                   
                     
                       
                         ξ 
                         ′ 
                       
                       ⁡ 
                       
                         ( 
                         
                           x 
                           , 
                           k 
                         
                         ) 
                       
                     
                     - 
                     
                       
                         η 
                         ′ 
                       
                       ⁡ 
                       
                         ( 
                         
                           x 
                           , 
                           k 
                         
                         ) 
                       
                     
                   
                   ] 
                 
               
             
           
         
       
     
     In a similar way to that of the first embodiment, the 2D Fourier transform may be used to extract the reference spatio-spectral phase function Φ ref (x, k). 
     It may be possible as described below to measure the spatio-spectral ellipsometric phase difference Δ(x, k) between P-polarization and S-polarization that are created by the anisotropic measured object. 
     
       
         
           
             
               
                 
                   
                     Δ 
                     ⁡ 
                     
                       ( 
                       
                         x 
                         , 
                         k 
                       
                       ) 
                     
                   
                   = 
                   
                     
                       
                         Φ 
                         obj 
                       
                       ⁡ 
                       
                         ( 
                         
                           x 
                           , 
                           k 
                         
                         ) 
                       
                     
                     - 
                     
                       
                         Φ 
                         ref 
                       
                       ⁡ 
                       
                         ( 
                         
                           x 
                           , 
                           k 
                         
                         ) 
                       
                     
                   
                 
               
             
             
               
                 
                   = 
                   
                     
                       
                         δ 
                         P 
                       
                       ⁡ 
                       
                         ( 
                         
                           x 
                           , 
                           k 
                         
                         ) 
                       
                     
                     - 
                     
                       
                         δ 
                         S 
                       
                       ⁡ 
                       
                         ( 
                         
                           x 
                           , 
                           k 
                         
                         ) 
                       
                     
                   
                 
               
             
           
         
       
     
       FIG. 11  illustrates the spatio-spectral ellipsometric phase difference Δ(x, k) of the measured object. In  FIG. 11 , the horizontal axis represents a spectral axis λ, the vertical axis denotes a spatial axis x in the first direction D 1 , and brightness indicates the spatio-spectral ellipsometric phase difference Δ(x, k). The measured object OBJ was a silicon oxide layer (SiO 2 ) whose nominal thickness is 1.5 μm deposited on a silicon substrate. 
     A similar way to that of the first embodiment may obtain a spatio-spectral ellipsometric amplitude ratio Ψ(x, k) between P-polarization and S-polarization. 
     As discussed above, the inspection apparatus according to an example of the second embodiment of the present inventive concepts may be configured similarly to the first embodiment, such that spatio-spectral ellipsometric information on the one-dimensional space of the measured object OBJ that moves in the second direction D 2  are successively measured to obtain spatio-spectral ellipsometric information (e.g., spectral ellipsometric cubic information) along two-dimensional spatial axes (e.g., the first and second directions D 1  and D 2 ) (see  FIG. 6 ). 
       FIG. 12  illustrates a simplified schematic diagram showing an example of the inspection apparatus according to the second embodiment of the present inventive concepts. Omission will be made to avoid duplicate explanation of components and functions discussed with reference to  FIG. 9 . 
     Referring to  FIG. 12 , a non-polarizing beam splitter  50  may further be included in an inspection apparatus according to an example of the second embodiment of the present inventive concepts. The non-polarizing beam splitter  50  may be disposed between the first linear polarizer  30  and the polarization interferometer  40 . For example, the input wave light E in  linearly polarized (e.g., with a rotation angle of 45°) in the first linear polarizer  30  may be provided through the non-polarizing beam splitter  50  to the polarization interferometer  40 . 
     As shown in  FIG. 12 , the polarizing splitter  41 , the first mirror MR 1 , and the second mirror MR 2  of the polarization interferometer  40  may be configured similarly to those illustrated in  FIG. 9 . For example, the first mirror MR 1  and the second mirror MR 2  may have an off-axis angle ε deviated from perpendicular. The polarization interferometer  40  may split the linearly polarized white light into P- and S-polarization waves, and may allow the P- and S-polarization waves to have a spatial phase difference. For example, the polarization interferometer  40  may create a high spatial carrier frequency having a spatial phase shift. 
     The polarizing splitter  41  of the polarization interferometer  40  may be a polarizing beam splitter. Moreover, the first sub-linear polarizer P 1  and the second sub-linear polarizer P 2  of  FIG. 9  may be omitted. The polarizing splitter  41  may split the linearly polarized white light into a first light and a second light. The first light and the second light may be directed toward and reflected from the first mirror MR 1  and the second mirror MR 2 , without passing through the first and second sub-linear polarizers P 1  and P 2  of  FIG. 9 . 
     The output wave light E out  that is polarization-modulated in the polarization interferometer  40  may be provided through the non-polarizing beam splitter  50  to the measured object OBJ on the scanner  70 . The output wave light E out  that is polarization-modulated in the polarization interferometer  40  may be provided through the non-polarizing beam splitter  50  and the line converter  61  to the measured object OBJ on the scanner  70 . The output wave light E out  coming out of the polarization interferometer  40  may be irradiated at a measurement angle θ deviated from a direction perpendicular to the measured object OBJ on the scanner  70 , and the measurement light E mea  may be reflected at the measurement angle θ deviated from the direction perpendicular to the measured object OBJ. 
     The polarization anisotropy of the measured object OBJ may provide amplitude modulation and phase modulation to the measurement light E mea  coming out of the measured object OBJ. The second linear polarizer  80  may be provided with the measurement light E mea  reflected from the measured object OBJ. The interference light E SP  may be provided through the imaging lens  62  to the imaging spectrograph  90 . The interference light E SP  may vertically enter an incident surface of the imaging spectrograph  90 . The imaging spectrograph  90  may generate from the interference light E SP  a spatio-spectral interference fringe that includes spatio-spectral ellipsometric information of the measured object OBJ. 
       FIG. 13  illustrates a simplified schematic diagram showing a still another example of the inspection apparatus according to the second embodiment of the present inventive concepts. Omission will be made to avoid duplicate explanation of components and functions discussed with reference to  FIG. 9 . Components in the present example may be spatially arranged differently from those shown in  FIG. 9 . 
     Referring to  FIG. 13 , a non-polarizing beam splitter  50  may further be included in an inspection apparatus according to still another example of the second embodiment of the present inventive concepts. The non-polarizing beam splitter  50  may be disposed on one side of the polarization interferometer  40 , and the line converter  61  may be placed between the polarization interferometer  40  and the non-polarizing beam splitter  50 . The non-polarizing beam splitter  50  may provide the measured object OBJ with the output wave light E out  coming out of the line converter  61 . 
     The output wave light E out  may be vertically irradiated to the measured object OBJ on the scanner  70 , and the measurement light E mea  may be vertically reflected from the measured object OBJ. 
     The measurement light E mea  reflected from the measured object OBJ may reenter the non-polarizing beam splitter  50  and travel to the second linear polarizer  80 . 
     According to the present inventive concepts, without mechanically rotational mechanism and electronic signal modulation, spatio-spectral ellipsometric information on the one-dimensional space of a measured object may be successively measured to obtain spatio-spectral ellipsometric information (e.g., spectral ellipsometric cubic information) along two-dimensional spatial axes. The spectral ellipsometric information may be used to measure uniformity of nano-patterns or nano-films on the two-dimensional space or to detect microscopic defects at high speed (several hundred times compared to the prior art) on the two-dimensional space. 
     Although the embodiments have been described with reference to a number of illustrative examples thereof, it will be understood by those of ordinary skill in the art that various changes in form and details may be made without departing from the spirit and scope of the present inventive concepts as set forth in the following claims. Thus, the technical scope of the present inventive concepts is not limited by the embodiments and examples described above, but by the following claims.