Patent Publication Number: US-11640645-B2

Title: Apparatus and method of acquiring image by employing color separation lens array

Description:
CROSS-REFERENCE TO RELATED APPLICATION 
     This application claims priority to Korean Patent Application No. 10-2019-0134112, filed on Oct. 25, 2019, and Korean Patent Application No. 10-2020-0126374, filed on Sep. 28, 2020, in the Korean Intellectual Property Office, the disclosures of which are incorporated by reference herein in their entireties. 
     BACKGROUND 
     1. Field 
     Example embodiments of the present disclosure relate to an apparatus and method of acquiring images, which employ a color separation lens array. 
     2. Description of Related Art 
     In image sensors, in order to capture color images, a color filter of red, green, and blue color is arranged with a certain pattern, on light sensing pixels and considering human visual characteristics sensitive to green color, a Bayer pattern structure in which 50% of green color filter elements, 25% of red color filter elements, and 25% of blue color filter elements are arranged to cross each other may be used. 
     In order to compose a color image by using captured green, red, and blue raw images, a method of interpolating color values of empty pixels of each color by using color values of surrounding pixels may be used. Interpolating a color for each pixel from a raw image is called demosaicing. 
     The existing methods of demosaicing Bayer raw images are optimized for a case where only a light component corresponding to the color of a corresponding pixel, in incident light of the unit pixel, is incident on a light sensing surface by using a microlens and an absorption-type color filter. 
     The number of pixels of the image sensor has gradually increased, and accordingly, miniaturization of pixels is required, and increasing of light quantity and noise removal are important issues for pixel miniaturization. Recently, in order to improve light utilization efficiency of the image sensor, in addition to an incident light component having a certain color, light component having the same color as the certain color from surrounding pixels may also be incident on a pixel to improve light efficiency, and thus, a new image processing method is required to compose a color image by using captured green, red, and blue raw images. 
     SUMMARY 
     One or more example embodiments provide apparatuses and methods of acquiring images, in which light utilization efficiency is improved by using a color separation lens array capable of separating and condensing incident light according to wavelengths. 
     Additional aspects will be set forth in part in the description which follows and, in part, will be apparent from the description, or may be learned by practice of example embodiments of the disclosure. 
     According to an aspect of an example embodiment, there is provided an apparatus for acquiring images, the apparatus including an image sensor including a sensor substrate including a plurality of photo-sensing cells configured to sense light, and a color separation lens array provided above the sensor substrate, the color separation lens array including a fine structure in each of a plurality of regions respectively facing the plurality of photo-sensing cells and configured to separate incident light based on color, the fine structure forming a phase distribution to condense light having different wavelengths on adjacent photo-sensing cells, a signal processor configured to perform, based on a point spread function (PSF) corresponding to each color pixel by the color separation lens array, deconvolution on sensing signals of the plurality of photo-sensing cells to process an image signal for each color obtained by the image sensor, and an image processor configured to form a color image from the image signal for each color processed by the signal processor. 
     The color separation lens array may be configured to condense a light component corresponding to a certain pixel and further the light component from at least one of surrounding pixels of the certain pixel onto the certain pixel. 
     The deconvolution may be performed by the signal processor to erase convoluted information from at least one surrounding pixel. 
     The signal processor may be a logic circuit of the image sensor or a companion chip. 
     The signal processor may be included in the image processor. 
     The image sensor may include a Bayer pattern array, wherein the signal processor is further configured to obtain an image signal for each color of the Bayer pattern array, and wherein the image processor is further configured to form a color image based on the image signal for each color obtained by the signal processor. 
     To form a color image based on the image signal for each color obtained by the signal processor, the image processor may be further configured to form the color image by interpolating a color value of an empty pixel of each color based on a color value of at least one surrounding pixel. 
     The sensor substrate may include a plurality of first photo-sensing cells and a plurality of second photo-sensing cells, wherein the color separation lens array includes a plurality of first regions respectively corresponding to the plurality of first photo-sensing cells and having a first fine structure, and a plurality of second regions respectively corresponding to the plurality of second photo-sensing cells and having a second fine structure, wherein the first fine structure and the second fine structure are configured to form, at a position after the incident light passing through the first regions and the second regions, a phase distribution in which light of a first wavelength and light of a second wavelength that are different from each other from among incident lights incident on the color separation lens array are branched in different directions and are respectively condensed in the first photo-sensing cells and the second photo-sensing cells. 
     The first fine structure and the second fine structure may be configured such that the light of the first wavelength forms, at a position immediately after passing through the color separation lens array, a phase distribution of 2Nπ at central portions of the first photo-sensing cells and forms a phase distribution of (2N−1)π at central portions of the second photo-sensing cells, wherein N is an integer greater than 0, and the light of the second wavelength forms, at a position immediately after passing through the color separation lens array, a phase distribution of (2M−1)π at the central portions of the first photo-sensing cells and forms a phase distribution of 2Mπ at the central portions of the second photo-sensing cells, wherein M is an integer greater than 0. 
     The sensor substrate further may include a plurality of third photo-sensing cells and a plurality of fourth photo-sensing cells, wherein the color separation lens array includes a plurality of third regions respectively corresponding to the plurality of third photo-sensing cells and having a third fine structure, and a plurality of fourth regions respectively corresponding to the plurality of fourth photo-sensing cells and having a fourth fine structure, and wherein the sensor substrate includes an array of unit pixels including the first photo-sensing cells, the second photo-sensing cells, the third photo-sensing cells, and the fourth photo-sensing cells. 
     The first fine structure to the fourth fine structure may be configured to form, at a position after the incident light passing through the first regions to the fourth regions, a phase distribution in which light of a first wavelength, light of a second wavelength, and light of a third wavelength that are different from one another from among incident lights incident on the color separation lens array are branched in different directions, and the light of the first wavelength is condensed in the first photo-sensing cells and the fourth photo-sensing cells, the light of the second wavelength is condensed in the second photo-sensing cells, and the light of the third wavelength is condensed in the third photo-sensing cells. 
     The first fine structure, the second fine structure, the third fine structure, and the fourth fine structure may be configured such that, at a position immediately after passing through the color separation lens array, the light of the first wavelength forms a phase distribution of 2Nπ at central portions of the first photo-sensing cells and central portions of the fourth photo-sensing cells and forms a phase distribution of (2N−1)π at central portions of the second photo-sensing cells and central portions of the third photo-sensing cells, the light of the second wavelength forms a phase distribution of (2M−1)π at the central portions of the first photo-sensing cells and the central portions of the fourth photo-sensing cells, forms a phase distribution of 2Mπ at the central portions of the second photo-sensing cells, and forms a phase distribution that is greater than (2M−2)π and less than (2M−1)π at the central portions of the third photo-sensing cells, and the light of the third wavelength forms a phase distribution of (2L−1)π at the central portions of the first photo-sensing cells and the central portions of the fourth photo-sensing cells, forms a phase distribution of 2Lπ at the central portions of the third photo-sensing cells, and forms a phase distribution that is greater than (2L−2)π and less than (2L−1)π at the central portions of the second photo-sensing cells, wherein N, M, and L are integers greater than 0. 
     The first fine structure, the second fine structure, the third fine structure, and the fourth fine structure of the first regions, the second regions, the third regions, and the fourth regions may include a plurality of nanoposts, and at least one of a shape, size, and arrangement of the nanoposts may be different from each other. 
     The image sensor may have a pixel array structure in which unit pixels including at least one red pixel, at least one green pixel, and at least one blue pixel are repeatedly provided, wherein nanoposts provided in a region corresponding to a green pixel from among the first regions, the second regions, the third regions, and the fourth regions have different distribution rules in a first direction and a second direction perpendicular to the first direction, and wherein nanoposts provided in regions corresponding to a blue pixel and a red pixel from among the first regions, the second regions, the third regions, and the fourth regions have symmetrical distribution rules in the first direction and the second direction. 
     The image sensor may have a Bayer pattern structure in which unit pixels, each having four quadrant regions including a blue pixel, a green pixel, a red pixel, and a green pixel, respectively, are repeatedly provided two-dimensionally in a first direction and a second direction. 
     The fine structure of the plurality of regions may include a plurality of nanoposts, and wherein, among the plurality of nanoposts, nanoposts provided in a region corresponding to a green pixel from among the plurality of regions includes a nanopost provided in a central portion, which has a larger cross-sectional area than a nanopost provided in a region corresponding to a pixel of a color other than green, and a nanopost provided in a peripheral portion, which has a smaller cross-sectional area than the nanopost provided in the central portion. 
     The fine structure of the plurality of regions may include a plurality of nanoposts, wherein nanoposts provided in a region corresponding to a green pixel from among the plurality of regions have different distribution rules in the first direction and the second direction, and wherein nanoposts provided in regions corresponding to a blue pixel and a red pixel from among the plurality of regions have symmetrical distribution rules in the first direction and the second direction. 
     According to another aspect of an example embodiment, there is provided a method of acquiring images, the method including obtaining a raw image for each color by the image sensor of the image acquisition apparatus, performing deconvolution on the raw image for each color by using a point spread function (PSF) corresponding to each color pixel by a color separation lens array of the image sensor to thereby obtain an image for each color and processing the image for each color to thereby form a color image. 
     The deconvolution may be performed on the raw image for each color to erase convoluted information from a surrounding pixel. 
     The raw image for each color may have a Bayer pattern arrangement. 
     A color image may be formed by interpolating a color value of an empty pixel of each color with respect to the raw image for each color, which has the Bayer pattern arrangement, based on a color value of a surrounding pixel. 
     According to another aspect of an example embodiment, there is provided an electronic apparatus including the image acquisition apparatus configured to obtain image information with respect to an object, the image acquisition apparatus including an image sensor including a sensor substrate including a plurality of photo-sensing cells configured to sense light, and a color separation lens array provided above the sensor substrate, the color separation lens array including a fine structure in each of a plurality of regions respectively facing the plurality of photo-sensing cells and configured to separate incident light based on color, the fine structure forming a phase distribution to condense light having different wavelengths on adjacent photo-sensing cells, a signal processor configured to perform, based on a point spread function (PSF) corresponding to each color pixel by the color separation lens array, deconvolution on sensing signals of the plurality of photo-sensing cells to process an image signal for each color obtained by the image sensor, and an image processor configured to form a color image from the image signal for each color processed by the signal processor, and a processor configured to perform image processing on the image information provided from the image acquisition apparatus. 
     The electronic apparatus may be one of a smart phone, a mobile phone, a personal digital assistant, a laptop, a tablet, or a personal computer. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       The above and/or other aspects, features, and advantages of example embodiments of the disclosure will be more apparent from the following description taken in conjunction with the accompanying drawings, in which: 
         FIG.  1    illustrates a configuration of an apparatus for acquiring images (hereinafter, referred to as an image acquisition apparatus), according to an example embodiment; 
         FIG.  2    is a schematic block diagram of an image sensor according to an example embodiment; 
         FIGS.  3 A,  3 B, and  3 C  illustrate various pixel arrangements of a pixel array of an image sensor; 
         FIGS.  4 A and  4 B  illustrate an image sensor according to an example embodiment; 
         FIGS.  5 A and  5 B  are schematic cross-sectional views of a pixel array of an image sensor according to an example embodiment; 
         FIG.  6    is a schematic plan view illustrating an arrangement of photo-sensing cells in a pixel array of an image sensor; 
         FIG.  7 A  is a plan view illustrating an arrangement of a plurality of nanoposts in a plurality of regions of a color separation lens array, the arrangement corresponding to an arrangement of photo-sensing cells of a sensor substrate of an image sensor, and  FIG.  7 B  is an enlarged and detailed plan view of a portion of  FIG.  7 A ; 
         FIGS.  8 A and  8 B  are diagrams illustrating a transfer simulation of a phase distribution of blue light passing through a color separation lens array and a focusing distribution of blue light in the corresponding photo-sensing cells,  FIG.  8 C  is a diagram illustrating a direction of blue light incident on and around a second region of the color separation lens array corresponding to a blue pixel, and  FIG.  8 D  is a diagram illustrating a microlens array that acts equivalently to the color separation lens array with respect to blue light; 
         FIGS.  9 A and  9 B  are illustrating a transfer simulation of a phase distribution of green light passing through a color separation lens array and a focusing distribution of green light in the corresponding photo-sensing cells,  FIG.  9 C  is a diagram illustrating a direction of green light incident on and around a first region of the color separation lens array corresponding to a green pixel, and  FIG.  9 D  is a diagram illustrating a microlens array that acts equivalently to the color separation lens array for green light; 
         FIGS.  10 A and  10 B  are illustrating a transfer simulation of a phase distribution of red light passing through a color separation lens array and a focusing distribution of red light in the corresponding photo-sensing cells,  FIG.  100    is a diagram illustrating a direction of red light incident on and around a third region of the color separation lens array corresponding to a red pixel, and  FIG.  10 D  is a diagram illustrating a microlens array that acts equivalently to the color separation lens array for red light; 
         FIG.  11    is a perspective view illustrating a form of nanopost that may be employed in a color separation lens array of an image sensor according to an example embodiment; 
         FIGS.  12 A,  12 B,  12 C,  12 D,  12 E,  12 F,  12 G, and  12 H  are plan views illustrating shapes of nanoposts that may be employed in a color separation lens array of an image sensor according another example embodiment; 
         FIG.  13    is a plan view illustrating an arrangement of a plurality of nanoposts constituting a color separation lens array that may be employed in the image sensor according to another example embodiment; 
         FIG.  14    is a plan view illustrating an arrangement of a plurality of nanoposts constituting a color separation lens array of an image sensor according to another example embodiment; 
         FIG.  15    is a plan view illustrating an arrangement of a plurality of nanoposts constituting a color separation lens array of an image sensor according to another example embodiment; 
         FIG.  16    is a plan view illustrating an arrangement of a plurality of nanopost constituting a color separation lens array according to another example embodiment; 
         FIGS.  17 A,  17 B, and  17 C  are schematic plan views illustrating changes in the arrangement shape of nanoposts of a color separation lens array according to positions on an image sensor; 
         FIG.  18 A  is a cross-sectional view illustrating a schematic structure of a pixel array according to another example embodiment; 
         FIG.  18 B  is a perspective view illustrating a shape of a nanopost employed in a color separation lens array of an image sensor of  FIG.  18 A , 
         FIG.  19    is a cross-sectional view illustrating a schematic structure of a pixel array according to another example embodiment; 
         FIG.  20    is a conceptual diagram illustrating a schematic structure and operation of a color separation lens array according to another example embodiment; 
         FIG.  21    is a plan view illustrating a color separation lens array according to another example embodiment; 
         FIG.  22    is a cross-sectional view illustrating a schematic structure of a pixel array of an image sensor including the color separation lens array shown in  FIG.  21   ; 
         FIG.  23    illustrates a principle of improving light efficiency by a color separation lens array in an image sensor according to an example embodiment; 
         FIGS.  24 A,  24 B, and  24 C  illustrate an increase in the amount of light incident on a unit pixel of a Bayer pattern array of an image sensor which a color separation lens array is applied; 
         FIG.  25    illustrates point spread function (PSF) characteristics by a color separation lens array of an image sensor according to an example embodiment; 
         FIG.  26    is a comparative example, which illustrates PSF characteristics by an absorption-type color filter when the absorption-type color filter is applied to an image sensor; 
         FIGS.  27 A,  27 B,  27 C, and  27 D  illustrate a local color patch to which deconvolution kernel is defined considering light branching characteristics of a color separation lens array; 
         FIG.  28    illustrates a process of configuring a color image in an image acquisition apparatus according to an example embodiment; 
         FIG.  29    illustrates a schematic configuration of a signal processor of an image acquisition apparatus according to an example embodiment; 
         FIG.  30    illustrates a bilinear demosaicing scheme; 
         FIG.  31    illustrates an image acquisition process using an image acquisition apparatus according to an example embodiment; 
         FIG.  32    is a schematic block diagram of an electronic apparatus including an image acquisition apparatus according to an example embodiment; and 
         FIGS.  33 ,  34 ,  35 ,  36 ,  37 ,  38 ,  39 ,  40 ,  41 ,  42 , and  43    illustrate various examples of an electronic apparatus to which an image acquisition apparatus according to an example embodiment is applied. 
     
    
    
     DETAILED DESCRIPTION 
     Reference will now be made in detail to example embodiments of which are illustrated in the accompanying drawings, wherein like reference numerals refer to like elements throughout. In this regard, the example embodiments may have different forms and should not be construed as being limited to the descriptions set forth herein. Accordingly, the example embodiments are merely described below, by referring to the figures, to explain aspects. As used herein, the term “and/or” includes any and all combinations of one or more of the associated listed items. Expressions such as “at least one of,” when preceding a list of elements, modify the entire list of elements and do not modify the individual elements of the list. For example, the expression, “at least one of a, b, and c,” should be understood as including only a, only b, only c, both a and b, both a and c, both b and c, or all of a, b, and c. 
     Hereinafter, example embodiments will be described in detail with reference to the accompanying drawings. In the following drawings, like reference numerals refer to like elements, and the size of each element in the drawings may be exaggerated for clarity and convenience of explanation. Meanwhile, the example embodiments described below are merely illustrative, and various other modifications can be made from these example embodiments. 
     Hereinafter, when a first element is described as being “above” or “on” a second element, example embodiments using these expressions may include the case in which the first element may be directly on the second element and the case in which the first element is located above the second element while the first and second elements do not contact each other. As used herein, the singular forms “a”, “an”, and “the” are intended to include the plural forms as well, unless the context clearly indicates otherwise. When a portion “includes” an element, unless otherwise described, another element may be further included, rather than the presence of other elements being excluded. The use of the terms “a” and “an” and “the” and similar referents in the context of describing the disclosure (especially in the context of the following claims) are to be construed to cover both the singular and the plural. 
       FIG.  1    illustrates a configuration of an apparatus  100  for acquiring images (hereinafter, referred to as an image acquisition apparatus  100 ), according to an example embodiment. 
     Referring to  FIG.  1   , the image acquisition apparatus  100  includes an image sensor  200  that acquires an image signal (hereinafter, referred to as a color image signal) for each color by converting an optical image formed by an imaging lens unit  120 , which focuses light reflected from an object OBJ to form the optical image, into an electrical signal, a signal processor  250  that processes the color image signal acquired by the image sensor  200 , and an image processor  160  that forms a color image from the color image signal processed by the signal processor  250 . The image acquisition apparatus  100  may further include a display unit  170  displaying an image formed by the image processor  160 , a memory  180  storing the image formed by the image processor  160  and the like. An additional optical element, for example, an infrared cutoff filter may be further arranged between the image sensor  200  and the imaging lens unit  120 . 
       FIG.  2    is a schematic block diagram of an image sensor  200  according to an example embodiment. 
     Referring to  FIG.  2   , the image sensor  200  may include a pixel array  210 , a timing controller  240 , a row decoder  220 , and an output circuit  230 . The image sensor  200  may include a charge-coupled device (CCD) image sensor or a complementary metal oxide semiconductor (CMOS) image sensor. 
     The pixel array  210  includes pixels arranged two-dimensionally along a plurality of rows and columns. The row decoder  220  selects one of the rows of the pixel array  210  in response to a row address signal output from the timing controller  240 . The output circuit  230  outputs a light sensing signal in column units from a plurality of pixels arranged along the selected row. To this end, the output circuit  230  may include a column decoder and an analog to digital converter (ADC). For example, the output circuit  230  may include a plurality of ADCs arranged for each column between the column decoder and the pixel array  210 , or one ADC arranged at an output terminal of the column decoder. The timing controller  240 , the row decoder  220 , and the output circuit  230  may be implemented as a single chip or as separate chips. The signal processor  250  and the image processor  160  (see  FIG.  1   ) for processing an image signal output through the output circuit  230  may be implemented as a single chip together with the timing controller  240 , the row decoder  220 , and the output circuit  230 . 
     The pixel array  210  may include a plurality of pixels sensing light of different wavelengths. The pixels may be arranged in various types. For example,  FIGS.  3 A,  3 B, and  3 C  illustrate various arrangements of the pixel array  210  in  FIG.  2   . 
     First,  FIG.  3 A  shows a Bayer pattern that may be adopted in the image sensor  200 . Referring to  FIG.  3 A , one unit pixel includes four quadrant regions, and first quadrant, the second quadrant, the third quadrant, and the fourth quadrants may be a blue pixel B, a green pixel G, a red pixel R, and a green pixel G, respectively. These unit pixels are repeatedly arranged two-dimensionally in a first direction (X-direction) and a second direction (Y-direction). In other words, two green pixels G are arranged in one diagonal direction within a 2×2 array-type unit pixel, and one blue pixel B and one red pixel R are arranged in the other diagonal direction. In an overall pixel arrangement, a first row in which a plurality of green pixels G and a plurality of blue pixels B are alternately arranged in the first direction, and a second row in which a plurality of red pixels R and a plurality of green pixels G are alternately arranged in the first direction are repeatedly arranged in the second direction. 
     However, the arrangement type of the pixel array  210  is not limited to the Bayer pattern, and there may be various arrangement types other than the Bayer pattern. For example, as in  FIG.  3 B , the arrangement type of the pixel array may include a CYGM type in which a magenta pixel M, a cyan pixel C, a yellow pixel Y, and a green pixel G constitute one unit pixel. In addition, as in  FIG.  3 C , arrangement of an RGBW type in which a green pixel G, a red pixel R, a blue pixel B, and a white pixel W constitute one unit pixel is also possible. The unit pixel may have a 3×2 array form. In addition, the pixels of the pixel array  210  may be arranged in various types according to color characteristics of the image sensor  200 . Hereinafter, for convenience, the pixel array  210  of the image sensor  200  is described as having a Bayer pattern, but the principles of example embodiments described below may be applied to a pixel arrangement other than a Bayer pattern. As shown in  FIGS.  4 A and  4 B , the pixel array of the image sensor  200  includes a sensor substrate  500  including an array of a plurality of photo-sensing cells that sense light, and a color separation lens array  300  arranged in front of the sensor substrate  500  and separating the light according to color to make the separated light enter the plurality of photo-sensing cells. 
       FIGS.  4 A and  4 B  illustrate an image sensor  200  according to an example embodiment.  FIG.  4 B  illustrates a conceptual diagram showing a schematic structure and operation of a color separation lens array  300 . 
     Referring to  FIGS.  4 A and  4 B , a sensor substrate  500  of the image sensor  200  may include a first photo-sensing cell  511 , a second photo-sensing cell  512 , a third photo-sensing cell  513 , and a fourth photo-sensing cell  514 , which convert light into an electrical signal. The unit pixels of the first photo-sensing cell  511 , the second photo-sensing cell  512 , the third photo-sensing cell  513 , and the fourth photo-sensing cell  514  may be repeatedly arranged in two dimensions. When the pixel array  210  of the image sensor  200  has a Bayer pattern, the first photo-sensing cell  511  and the fourth photo-sensing cell  514  may correspond to a green pixel G, and one of the second photo-sensing cell  512  and the third photo-sensing cell  513  may correspond to a red pixel R and the other may correspond to a blue pixel B. 
     The color separation lens array  300  may include a fine structure in each of a plurality of regions  311 ,  312 ,  313 , and  314  facing a plurality of photo-sensing cells, for example, the first to fourth photo-sensing cells  511 ,  512 ,  513 , and  514 , respectively. The color separation lens array  300  may be provided to form a phase distribution for condensing light having different wavelengths on adjacent photo-sensing cells to separate incident light according to color. As illustrated in  FIG.  4 B , the fine structure of the color separation lens array  300  may include a plurality of nanoposts arranged such that one or more nanoposts NP are distributed to form a phase distribution for condensing light of different wavelengths to adjacent photo-sensing cells. As another example, the fine structure of the color separation lens array  300  may be made of a pattern to form a phase distribution for condensing light of different wavelengths to adjacent photo-sensing cells. Hereinafter, a case where the fine structure is made of nanoposts will be described as an example. 
     The signal processor  250  performs, by using a point spread function (PSF) corresponding to each color pixel by the color separation lens array  300  of the image sensor  200 , deconvolution on sensing signals of the plurality of photo-sensing cells  511 ,  512 ,  513 , and  514  of the sensor substrate  500  to process the color image signal acquired by the image sensor  200 . An image signal for each color processed by the signal processor  250  is constructed into a color image by the image processor  160 . Referring to  FIG.  4 B , the color separation lens array  300  may include a plurality of regions  311 ,  312 ,  313 , and  314  that correspond to and face a plurality of photo-sensing cells  511 ,  512 ,  513 ,  514  of the sensor substrate  500  in a one-to-one manner. For example, the color separation lens array  300  may include first to fourth regions  311 ,  312 ,  313 , and  314  that correspond to and face the first to fourth photo-sensing cells  511 ,  512 ,  513 , and  514  of the sensor substrate  500  in a one-to-one manner, and the first to fourth regions  311 ,  312 ,  313 , and  314  may include first to fourth fine structures to form a phase distribution for condensing light of different wavelengths to adjacent photo-sensing cells. 
     When the first to fourth fine structures each include one or more nanoposts as illustrated in  FIG.  4 B , the first region  311  may include one or more first nanoposts, the second region  312  may include one or more second nanoposts, the third region  313  may include one or more third nanoposts, and the fourth region  314  may include one or more fourth nanoposts. The shapes, sizes, and arrangements of the first to fourth nanoposts may be determined to form a phase at which light having a certain wavelength, which has passed through the color separation lens array  300 , is travels and is condensed to one of the first to fourth photo-sensing cells  511 ,  512 ,  513 , and  514  and does not travel to the remaining photo-sensing cells. In addition, each of the plurality of regions  311 ,  312 ,  313 , and  314  included in the color separation lens array  300  may include a plurality of sub-regions, and the plurality of nanoposts may be respectively arranged one-to-one in the plurality of sub-regions. In addition, each of the plurality of regions  311 ,  312 ,  313 , and  314  included in the color separation lens array  300  may include a plurality of sub-regions, and the plurality of nanoposts may be arranged one-to-one at intersections between the plurality of sub-regions. 
     The image sensor  200  may have a pixel array structure in which unit pixels are repeatedly arranged. For example, the image sensor  200  may have a Bayer pattern structure in which unit pixels, each having four quadrant regions including a blue pixel, a green pixel, a red pixel, and a green pixel, respectively, are repeatedly arranged two-dimensionally in a first direction and a second direction. In this case, among the plurality of nanoposts of the color separation lens array  300 , a nanopost provided in a region corresponding to the green pixel from among the plurality of regions may have a larger cross-sectional area than nanoposts provided in regions corresponding to pixels of colors other than the green. In addition, among the plurality of nanoposts, nanoposts provided in a region corresponding to the green pixel from among the plurality of regions may include a nanopost arranged in a central portion and a nanopost arranged in a peripheral portion, which may have a smaller cross-sectional area than the nanopost arranged in the central portion. In addition, nanoposts provided in a region corresponding to the green pixel from among the plurality of regions may have different distribution rules in the first direction and the second direction, and nanoposts provided in regions corresponding to the blue pixel and the red pixel from among the plurality of regions may have symmetrical distribution rules in the first direction and the second direction. 
     For example, the first photo-sensing cell  511  may sense light having a first wavelength which corresponds to a first pixel, the second photo-sensing cell  512  may sense light having a second wavelength which corresponds to a second pixel, the third photo-sensing cell  513  may sense light having a third wavelength which corresponds to a third pixel, and the fourth photo-sensing cell  514  may sense light having a fourth wavelength which corresponds to a fourth pixel. However, embodiments are not limited thereto. A partition wall for cell separation may be further formed at the boundary between the photo-sensing cells. 
     In the image sensor  200 , when the first pixel, the second pixel, the third pixel, and the fourth pixel are the green pixel G, the blue pixel B, the red pixel R, and the green pixel G, respectively, and form a Bayer pattern array, the first photo-sensing cell  511 , the second photo-sensing cell  512 , the third photo-sensing cell  513 , and the fourth photo-sensing cell  514  of the sensor substrate  500  may be arranged to correspond to a Bayer pattern array. 
     The color separation lens array  300  separates incident light according to color and makes the separated light travel to the plurality of photo-sensing cells, for example, the first to fourth photo-sensing cells  511 ,  512 ,  513 , and  514 . As shown in  FIG.  4 B , the color separation lens array  300  may include a plurality of nanoposts NP. 
     For example, the color separation lens array  300  may separate incident light according to color, and thus, light having a first wavelength may be incident on the first photo-sensing cell  511  to form the green pixel G, light having a second wavelength may be incident on the second photo-sensing cell  512  to form the blue pixel B, light having a third wavelength may be incident on the third photo-sensing cell  513  to form the red pixel R, and light having the first wavelength may be incident on the fourth photo-sensing cell  514  to form the green pixel G. 
     The color separation lens array  300  may include a nanopost array in which a plurality of nanoposts NP are arranged according to a certain rule. The nanopost array may be supported by a spacer layer. The spacer layer may maintain a constant gap between the sensor substrate  500  and the color separation lens array  300 . The spacer layer may include a material transparent to visible light. For example, the spacer layer may include a dielectric material, such as silicon oxide (SiO 2 ) or siloxane-based spin on glass (SOG), having a refractive index lower than that of the nanopost NP of the color separation lens array  300  and having a low absorption rate in a visible band. In  FIG.  4 B , the illustration of the spacer layer is omitted for convenience to more clearly express separation according to the color of incident light in the color separation lens array  300 . The color separation lens array  300  may be further provided with a protective layer for protecting the plurality of nanoposts NP. The protective layer may include a dielectric material having a refractive index lower than that of a material forming the nanoposts NP. 
     In this case, the rule is applied to parameters such as the shape, size (width and height), interval, and arrangement of the nanoposts NP and may be determined according to a target phase distribution to be implemented by the color separation lens array  300  with respect to incident light. The target phase distribution may be determined in consideration of a target region to condense light on by separating the wavelength of the incident light. The target phase distribution is indicated between the color separation lens array  300  and the target region, but this is merely for convenience of illustration. An actual target phase distribution refers to a phase distribution at a position immediately after incident light passes through the color separation lens array  300 , for example, on the lower surface of the color separation lens array  300  or the upper surface of the spacer layer. 
     The nanoposts NP of the color separation lens array  300  may form a phase distribution in which light of different wavelengths included in the incident light is branched in different directions and condensed. For example, the shape, size, and arrangement of nanoposts NP distributed in first to fourth regions  311 ,  312 ,  313 , and  314  of the color separation lens array  300  may be determined to form a target phase distribution in which light (e.g., green light) of a first wavelength included in incident light has a first phase distribution, light (e.g., blue light) of a second wavelength included in the incident light has a second phase distribution, and light (e.g., red light) of a third wavelength included in the incident light has a third phase. According to the target phase distribution, specific color light may be condensed at a target position at a certain distance from the array of nanoposts NP. 
     The nanopost NP may have a shape dimension of a sub-wavelength smaller than a wavelength band in which light is branched. The nanopost NP may have a shape dimension smaller than the shortest wavelength among the first to third wavelengths, and may have a dimension smaller than 400 nm, 300 nm, or 200 nm when incident light is visible light. 
     The nanopost NP may include a material having a refractive index higher than that of a surrounding material. For example, the nanopost NP may include c-Si, p-Si, a-Si, III-V group compound semiconductor (gallium phosphide (GaP), gallium nitride (GaN), gallium arsenide (GaAs_, etc.), silicon carbide (SiC), titanium oxide (TiO 2 ), silicon nitride (SiN), and/or a combination thereof. The nanopost NP having a difference in refractive index from the surrounding material may change the phase of passing light. This is due to a phase delay caused by the shape dimension of the sub-wavelength, and the degree of the phase delay is determined by the detailed shape dimension and arrangement shape of the nanopost NP. The surrounding material may include a dielectric material (e.g., SiO 2  or air) having a refractive index lower than that of the nanopost NP. 
     The first to third wavelengths may be in the range of visible light wavelength bands, but are not limited thereto. Various wavelength bands may be implemented according to the rules of the arranged nanoposts NP. 
     Hereinafter, an example in which the color separation lens array  300  described above is applied to the pixel array  210  of the image sensor  200  will be described in more detail. 
       FIGS.  5 A and  5 B  are schematic cross-sectional views of a pixel array of an image sensor according to an example embodiment. 
     Referring to  FIGS.  5 A and  5 B , the pixel array  210  includes a sensor substrate  500  including a plurality of photo-sensing cells  311 ,  312 ,  313 , and  314  for sensing light, a spacer layer  520  that is transparent and arranged on the sensor substrate  500 , and a color separation lens array  300  arranged on the spacer layer  520 . 
     The sensor substrate  500  may include a first photo-sensing cell  511 , a second photo-sensing cell  512 , a third photo-sensing cell  513 , and a fourth photo-sensing cell  514 , which convert light into an electrical signal. As shown in  FIG.  5 A , the first photo-sensing cell  511  and the second photo-sensing cell  512  may be alternately arranged in the first direction (X direction). In a cross-section with a different position in the second direction (Y direction), the third photo-sensing cell  513  and the fourth photo-sensing cell  514  may be alternately arranged as shown in  FIG.  5 B . The area division is for sensing incident light by dividing the incident light in pixel units. For example, the first photo-sensing cell  511  and the fourth photo-sensing cell  514  may sense light of a first wavelength corresponding to a first pixel, the second photo-sensing cell  512  may sense light of a second wavelength corresponding to a second pixel, and the third photo-sensing cell  513  may sense light of a third wavelength corresponding to a third pixel. Hereinafter, the light of the first wavelength, the light of the second wavelength and the light of the third wavelength may be green light, blue light and red light, respectively, and the first pixel, the second pixel and the third pixel may be the green pixel G, the blue pixel B and the red pixel R, respectively, but embodiments are not limited thereto. A partition wall for cell separation may be further formed at the boundary between the photo-sensing cells. 
     The spacer layer  520  serves to support the color separation lens array  300  and maintain a constant interval between the sensor substrate  500  and the color separation lens array  300 . The spacer layer  520  may include a material transparent to visible light. For example, the spacer layer  520  may include a dielectric material, such as SiO 2  and siloxane-based spin on glass (SOG), having a refractive index lower than that of the nanopost NP of the color separation lens array  300  and having a low absorption rate in the visible light band. 
     The pixel array  210  of the image sensor  200  may have a two-dimensional arrangement. That is, as shown in  FIG.  6   , in the sensor substrate  500 , a plurality of first photo-sensing cells  511 , a plurality of second photo-sensing cells  512 , a plurality of third photo-sensing cells  513 , and a plurality of fourth photo-sensing cells  514  may be two-dimensionally arranged in the first direction (X direction) and the second direction (Y direction), and thus, a first row, in which the first photo-sensing cells  511  and the second photo-sensing cells  512  are alternately arranged, and a second row, in which the third photo-sensing cells  513  and the fourth photo-sensing cells  514  are alternately arranged, may be alternately repeated. In this case, when the pixel array  210  of the image sensor  200  is a Bayer pattern array as shown in  FIG.  3 A , the first photo-sensing cell  511  and the fourth photo-sensing cell  514  correspond to the green pixel G, the second photo-sensing cell  512  corresponds to the blue pixel B, and the third photo-sensing cell  513  corresponds to the red pixel R. The nanopost array of the color separation lens array  300  may be divided into a plurality of regions, for example, first to fourth regions  311 ,  312 ,  313 , and  314 , corresponding one-to-one to the first to fourth photo-sensing cells  511 ,  512 ,  513 , and  514  of the sensor substrate  500 , as shown in  FIGS.  7 A and  7 B .  FIG.  6    is a schematic plan view illustrating an arrangement of photo-sensing cells in a pixel array of an image sensor.  FIG.  7 A  is a plan view illustrating an arrangement of a plurality of nanoposts in a plurality of regions of a color separation lens array, the arrangement corresponding to an arrangement of photo-sensing cells of a sensor substrate of an image sensor, and  FIG.  7 B  is an enlarged and detailed plan view of a portion of  FIG.  7 A . 
     For example, when the pixel array of the image sensor  200  is a Bayer pattern array, one unit pixel includes four quadrant regions and first to fourth quadrants may be a blue pixel B, a green pixel G, a red pixel R, and a green pixel G, respectively. Unit pixels are repeatedly arranged two-dimensionally in the first direction (X direction) and the second direction (Y direction). 
     Referring to  FIGS.  6 ,  7 A, and  7 B , in the unit cells, the first photo-sensing cell  511  and the first region  311  of the color separation lens array  300  corresponding thereto may correspond to the green pixel G, and the second photo-sensing cell  512  and the second region  312  of the color separation lens array  300  corresponding thereto may correspond to the blue pixel B. The third photo-sensing cell  513  and the third region  313  of the color separation lens array  300  corresponding thereto may correspond to the red pixel R, and the fourth photo-sensing cell  514  and the fourth region  314  of the color separation lens array  300  corresponding thereto may correspond to the green pixel G. 
     Referring to  FIGS.  6  and  7 A , the nanopost array of the color separation lens array  300  is divided into the first to fourth regions  311 ,  312 ,  313 , and  314  corresponding to and facing the first to fourth photo-sensing cells  511 ,  512 ,  513 , and  514 , respectively. One or more nanoposts NP may be arranged in each of the first to fourth regions  311 ,  312 ,  313 , and  314 , and at least one of the shape, size, and arrangement of each of the nanoposts NP may vary depending on regions. 
     The shapes, sizes, and arrangement of the plurality of nanoposts NP of the color separation lens array  300  may be determined to form a phase distribution for condensing light having different wavelengths on the first photo-sensing cell  511  and the second photo-sensing cell  512  of the sensor substrate  500 , which are adjacent to each other. In addition, the shapes, sizes, and arrangement of the plurality of nanoposts NP of the color separation lens array  300  may be determined to form a phase distribution for condensing light having different wavelengths on the third photo-sensing cell  513  and the fourth photo-sensing cell  514  of the sensor substrate  500 , which are adjacent to each other. 
     For example, when the pixel array  210  of the image sensor  200  is a Bayer pattern array, since, as shown in  FIG.  7 A , the first region  311  of the color separation lens array  300  corresponds to the green pixel G, the second region  312  of the color separation lens array  300  corresponds to the blue pixel B, the third region  313  of the color separation lens array  300  corresponds to the red pixel R, and the fourth region  314  of the color separation lens array  300  corresponds to the green pixel G, nanoposts NP having different cross-sectional areas may be arranged in the central portions of regions of the color separation lens array  300  corresponding to the green pixel G, the blue pixel B, and the red pixel R, and nanoposts NP may be arranged at the center of each of the boundaries between pixels and at the intersection between the boundaries. The nanoposts NP arranged at the boundaries between the pixels may have smaller cross-sectional areas than the nanoposts NP arranged at the central portions of the pixels. 
       FIG.  7 B  illustrates the arrangement of nanoposts NP in some regions of  FIG.  7 A , that is, the regions  311 ,  312 ,  313 , and  314  constituting a unit pattern array. In  FIG.  7 B , the nanoposts NP are indicated as p 1  to p 9  according to detailed positions in the unit pattern array. Referring to  FIG.  7 B , the cross-sectional areas of the nanopost p 1  arranged in the central portion of the region  311  and the nanopost p 4  arranged in the central portion of the region  314  are greater than the cross-sectional area of the nanopost p 2  arranged in the central portion of the region  312  or the nanopost p 3  arranged in the central portion of the region  313 , and the cross-sectional area of the nanopost p 2  arranged in the central portion of the region  312  is greater than the cross-sectional area of the nanopost p 3  arranged in the central portion of the region  313 . However, this is only an example, and nanoposts NP having various shapes, sizes, and arrangements may be used as needed. 
     For example, the cross-sectional areas of nanoposts NP arranged in the central portions of the regions  311  and  314  corresponding to the green pixel G are greater than the cross-sectional area of a nanopost NP arranged in the central portion of the region  312  corresponding to the blue pixel B or the region  313  corresponding to the red pixel R, and the cross-sectional area of the nanopost NP arranged in the central portion of the region  312  corresponding to the blue pixel B is greater than the cross-sectional area of the nanopost NP arranged in the central portion of the region  313  corresponding to the red pixel R. However, this is only an example, and nanoposts NP having various shapes, sizes, and arrangements may be used as needed. In this case, the cross-sectional area denotes the area of a cross-section perpendicular to the height direction (Z direction) of the nanopost NP. 
     The nanoposts NP provided in the regions  311  and  314  corresponding to the green pixel G may have different distribution rules in the first direction (X direction) and the second direction (Y direction). That is, the nanoposts NP provided in the regions  311  and  314  corresponding to the green pixel G may have an asymmetric size arrangement in the first direction (X direction) and the second direction (Y direction). As shown in  FIG.  7 B , the cross-sectional area of a nanopost p 5  positioned at the boundary between the region  311  and the region  312  adjacent to the region  311  in the first direction (X direction) may be different from the cross-sectional area of a nanopost p 6  positioned at the boundary between the region  311  and the region  313  adjacent to the region  311  in the second direction (Y direction). Likewise, the cross-sectional area of a nanopost p 7  positioned at the boundary between the region  314  and the region  313  adjacent to the region  314  in the first direction (X direction) may be different from the cross-sectional area of a nanopost p 8  positioned at the boundary between the region  314  and the region  312  adjacent to the region  314  in the second direction (Y direction). 
     On the other hand, the nanoposts NP provided in the regions  312  and  313  corresponding to the blue pixel B and the red pixel R may have a symmetrical distribution rule in the first direction (X direction) and the second direction (Y direction). As shown in  FIG.  7 B , in the region  312  corresponding to the blue pixel B, the cross-sectional area of the nanopost p 5  placed at the boundary between adjacent pixels in the first direction (X direction) may be equal to the cross-sectional area of the nanopost p 8  placed at the boundary between adjacent pixels in the second direction (Y direction). In addition, also in the region  313  corresponding to the red pixel R, the cross-sectional area of the nanopost p 7  placed at the boundary between adjacent pixels in the first direction (X direction) may be equal to the cross-sectional area of the nanopost p 6  placed at the boundary between adjacent pixels in the second direction (Y direction). 
     The nanoposts p 9  arranged at four corners of each of the region  311 , the region  312 , the region  313 , and the region  314 , that is, at positions where the four regions intersect one another have the same cross-sectional area. This distribution is caused because, in the Bayer pattern array, pixels adjacent to the blue pixel B and the red pixel R in the first direction (X direction) and the second direction (Y direction) are of the same type, that is, are green pixels G, whereas a pixel adjacent to the green pixel G in the first direction (X direction) is the blue pixel B and a pixel adjacent to the green pixel G in the second direction (Y direction) is the red pixel R different from the blue pixel B. Therefore, in the second region  312  and the third region  313  respectively corresponding to the blue pixel B and the red pixel R, the nanoposts NP may be arranged in a form of 4-fold symmetry. In addition, in the first and fourth regions  311  and  314  corresponding to the green pixel G, the nanoposts NP may be arranged in a form of 2-fold symmetry. In particular, the region  311  and the region  314  are rotated 90 degrees with respect to each other. 
     In  FIGS.  4 B,  7 A, and  7 B , the plurality of nanoposts NP are illustrated as having symmetrical circular cross-sectional shapes, but embodiments are not limited thereto. Some nanoposts may have asymmetrical cross-sectional shapes. For example, a nanopost having an asymmetric cross-sectional shape having different widths in the first direction (X direction) and the second direction (Y direction) may be employed in the regions  311  and  314  corresponding to the green pixel G. A nanopost having a symmetric cross-sectional shape having the same width in the first direction (X direction) and the second direction (Y direction) may be employed in the region  312  corresponding to the blue pixel B and the region  313  corresponding to the red pixel R. 
     The arrangement rule of the nanopost array shown is only an example for realizing a target phase distribution to separate and condense light having a first wavelength onto the first photo-sensing cell  511  and the fourth photo-sensing cell  514 , to separate and condense light having a second wavelength onto the second photo-sensing cell  512 , and to separate and condense light having a third wavelength onto the third photo-sensing cell  513 , but embodiments are not limited thereto. 
     The shapes, sizes, and arrangements of the nanoposts NP provided in the first to fourth regions  311 ,  312 ,  313 , and  314  of the color separation lens array  300  may be determined to form a phase at which light (e.g., green (G) light) of a first wavelength at a position after passing through the color separation lens array  300  is condensed to the first and fourth photo-sensing cells  511  and  514  and does not travel to the second and third photo-sensing cells  512  and  513  adjacent to the first and fourth photo-sensing cells  511  and  514 . The shapes, sizes, and arrangements of the nanoposts NP provided in the first to fourth regions  311 ,  312 ,  313 , and  314  of the color separation lens array  300  may be determined to form a phase at which light (e.g., blue (B) light) having a second wavelength at a position after passing through the color separation lens array  300  is condensed to the second photo-sensing cell  512  and does not travel to the first, third, and fourth photo-sensing cells  511 ,  513 , and  514  adjacent to the second photo-sensing cell  512 . In addition, the shapes, sizes, and arrangements of the nanoposts NP provided in the first to fourth regions  311 ,  312 ,  313 , and  314  of the color separation lens array  300  may be determined to form a phase at which light (e.g., red (R) light) having a third wavelength at a positon after passing through the color separation lens array  300  is condensed to the third photo-sensing cell  513  and does not travel to the first, second, and fourth photo-sensing cells  511 ,  512 , and  514  adjacent to the third photo-sensing cell  513 . 
     The shapes, sizes, and arrangements of the nanoposts NP satisfying all of these conditions may be determined, and the color separation lens array  300  may allow light immediately after passing through the color separation lens array  300  to have the following target phase distribution. At a position immediately after passing through the color separation lens array  300 , that is, on the lower surface of the color separation lens array  300  or the upper surface of the spacer layer, the target phase distribution to be implemented by the color separation lens array  300  may be a distribution in which the phase of light of a first wavelength is 2Nπ in the central portions of the first and fourth regions  311  and  314  corresponding to the first and fourth photo-sensing cells  511  and  514  and is (2N−1)π in the central portion of the second region  312  corresponding to the second photo-sensing cell  512  and in the central portion of the third region  313  corresponding to the third photo-sensing cell  513 . Here, N is an integer greater than 0. For example, the phase of light of a first wavelength at a position immediately after passing through the color separation lens array  300  may be maximum in the central portion of the first region  311  and the central portion of the fourth region  314 , may gradually decrease in a concentric circle shape as the distance from the central portion of the first region  311  and the central portion of the fourth region  314  increases, and may be minimized in the central portion of the second region  312  and the central portion of the third region  313 . For example, in the case of N=1, the phase of the light of the first wavelength at a position after passing through the color separation lens array  300  may be 27 in the central portion of the first region  311  and the central portion of the fourth region  314  and may be π in the central portion of the second region  312  and the central portion of the third region  313 . In this case, the phase may refer to a phase value relative to a phase immediately before light passes through the nanopost NP. 
     In addition, in the target phase distribution, the phase of light of a second wavelength at a position immediately after passing through the color separation lens array  300  may be 2Mπ in the central portion of the second region  312  corresponding to the second photo-sensing cell  512 , may be (2M−1)π in the central portion of the first region  311  corresponding to the first photo-sensing cell  511  and in the central portion of the fourth region  314  corresponding to the fourth photo-sensing cell  514 , and may be greater than (2M−2)π and less than (2M−1)π in the central portion of the third region  313  corresponding to the third photo-sensing cell  513 . Here, M is an integer greater than 0. For example, the phase of light of a second wavelength at a position immediately after passing through the color separation lens array  300  may be maximum in the central portion of the second region  312 , may gradually decrease in a concentric circle shape as the distance from the central portion of the second region  312  increases, and may be locally minimized in the central portion of the third region  313 . For example, in the case of M=1, the phase of the light of the second wavelength at a position after passing through the color separation lens array  300  may be 27 in the central portion of the second region  312 , may be π in the central portion of the first region  311  and the central portion of the fourth region  314 , and may be 0.77 in the central portion of the third region  313 . 
     In addition, in the target phase distribution, the phase of light of a third wavelength at a position immediately after passing through the color separation lens array  300  may be 2Lπ in the central portion of the third region  313  corresponding to the third photo-sensing cell  513 , may be (2L−1)π in the central portion of the first region  311  corresponding to the first photo-sensing cell  511  and in the central portion of the fourth region  314  corresponding to the fourth photo-sensing cell  514 , and may be greater than (2L−2)π and less than (2L−1)π in the central portion of the second region  312  corresponding to the second photo-sensing cell  512 . Here, L is an integer greater than 0. For example, the phase of light of a third wavelength at a position immediately after passing through the color separation lens array  300  may be maximum in the central portion of the third region  313 , may gradually decrease in a concentric circle shape as the distance from the central portion of the third region  313  increases, and may be locally minimized in the central portion of the second region  312 . For example, in the case of L=1, the phase of the light of the third wavelength at a position after passing through the color separation lens array  300  may be 27 in the central portion of the third region  313 , may be π in the central portion of the first region  311  and the central portion of the fourth region  314 , and may be about 0.27 to about 0.77 in the central portion of the second region  313 . 
     The target phase distribution refers to the phase distribution of light at the position immediately after passing through the color separation lens array  300 , that is, on the lower surface of the color separation lens array  300  or the upper surface of the spacer layer. When light passing through the color separation lens array  300  has such a phase distribution, lights of the first to third wavelengths are collected in the first to fourth photo-sensing cells  511 ,  512 ,  513 , and  514  of the sensor substrate  500 , respectively. It is possible to obtain an optical effect that light transmitted through the color separation lens array  300  is branched according to wavelength and travels in different directions to be condensed. 
     In this way, a certain propagation distance requirement may be determined in order to condense light of a corresponding wavelength to a photo-sensing cell corresponding thereto, and accordingly, a thickness of the spacer layer may be determined. The thickness of the spacer layer may vary depending on a wavelength λ of the light to be branched, a pixel size, and an arrangement period p of the photo-sensing cells. The thickness of the spacer layer may be greater than a center wavelength λ of a visible light wavelength band to be branched. Compared with the arrangement period p of the photo-sensing cells, which is the distance between the centers of adjacent photo-sensing cells, the thickness of the spacer layer may be within a range of about 1p to about 3p. Specifically, the thickness of the spacer layer may be within a range of about 500 nm to about 5 μm. 
       FIGS.  8 A and  8 B  are illustrating a transfer simulation of a phase distribution of blue light passing through the color separation lens array and a focusing distribution of blue light in the corresponding photo-sensing cells,  FIG.  8 C  is a diagram illustrating a direction of blue light incident on and around the second region  312  of the color separation lens array  300  corresponding to a blue pixel B, and  FIG.  8 D  is a diagram illustrating a microlens array that acts equivalently to the color separation lens array  300  with respect to blue light. 
     According to the phase distribution of the blue light illustrated in  FIG.  8 A , a phase at the central portion of a region corresponding to blue pixel B may be approximately 2π, a phase at the central portion of a region corresponding to adjacent green pixel G may be approximately π, and a phase in the central portion of a region corresponding to the red pixel R in the diagonal direction may represent a value approximately smaller than π (e.g., about 0.2π to about 0.77). The phase distribution may represent a focusing distribution of the blue light as shown in  FIG.  8 B . Due to the phase distribution, the blue light is mostly focused on the second photo-sensing cell  512  of the sensor substrate  500  corresponding to the blue pixel B, and rarely reaches the first, third, and fourth photo-sensing cells  511 ,  513 , and  514  corresponding to the other pixels. 
     As a result, the blue light incident on and around the second region  312  corresponding to the blue pixel B passes through the color separation lens array  300  and then travels as shown in  FIG.  8 C . For example, among incident lights incident on the second region  312  of the color separation lens array  300  and some of the other regions surrounding the second region  312 , the blue light is condensed on the second photo-sensing cell  512  directly under the second region  312 . For example, blue light from the second region  312  corresponding to the blue pixel B, blue light from two first regions  311  adjacent to the second region  312  in a horizontal direction, blue light from two fourth regions  314  adjacent to the second region  312  in a longitudinal direction, and blue light from four third regions  313  adjacent to the second region  312  in a diagonal direction are incident on one blue pixel B. 
     Accordingly, as illustrated in  FIG.  8 D , the color separation lens array  300  may function equivalent to an array of a plurality of microlens ML 1  arranged around the second photo-sensing cell  512  for blue light. Because each equivalent microlens ML 1  is larger than the corresponding second photo-sensing cell  512 , the blue light incident on a region of the second photo-sensing cell  512  as well as blue light incident on another region surrounding the second photo-sensing cell  512  may be condensed onto the second photo-sensing cell  512 . For example, each microlens ML 1  may be about 4 times larger than the corresponding second photo-sensing cell  512 , and the four sides of each microlens ML 1  may be parallel to the four sides of the second photo-sensing cell  512 . 
       FIGS.  9 A and  9 B  are diagrams illustrating a transfer simulation of a phase distribution of green light passing through the color separation lens array  300  and a focusing distribution of green light in the corresponding photo-sensing cells,  FIG.  9 C  is a diagram illustrating a direction of green light incident on and around the first region  311  of the color separation lens array  300  corresponding to a green pixel, and  FIG.  9 D  is a diagram illustrating a microlens array that acts equivalently to the color separation lens array  300  for green light. 
     According to the phase distribution of green light exemplarily shown in  FIG.  9 A , the phase at the central portion of the region corresponding to the green pixel G may be about 2π, and the phase at the central portions of the regions corresponding to the blue pixel B and the red pixel R adjacent to the green pixel G may represent a value of about π. The above phase distribution may represent a focusing distribution of the green light as shown in  FIG.  9 B . Due to the phase distribution, the green light is branched to be condensed on the first and fourth photo-sensing cells  511  and  514  corresponding to two green pixels G, and rarely reaches the second and third photo-sensing cells  512  and  513  corresponding to the other pixels. 
     As a result, the green light incident on and around the first and fourth regions  311  and  314  corresponding to the green pixel G passes through the color separation lens array  300  and then travels as shown in  FIG.  9 C . For example, among incident lights incident on the first region  311  of the color separation lens array  300  and some of the other regions surrounding the first region  311 , the green light is condensed on the first photo-sensing cell  511  directly under the first region  311 . For example, green light from the first region  311  or fourth region  314  corresponding to the green pixel G and green light from two second region  312  and two third region  313  adjacent to the first region  311  or fourth region  314  in the horizontal direction and longitudinal direction are incident one green pixel G. 
     Accordingly, as illustrated in  FIG.  9 D , the color separation lens array  300  may function equivalent to an array of a plurality of microlens ML 2  arranged around the first photo-sensing cell  511  and the fourth photo-sensing cell  514  for green light. Because each equivalent microlens ML 2  is larger than the corresponding first photo-sensing cell  511  or fourth photo-sensing cell  514 , the green light incident on regions of the first photo-sensing cell  511  and fourth photo-sensing cell  514  as well as green light incident on another region surrounding the first photo-sensing cell  511  and the fourth photo-sensing cell  514  may be condensed onto the first photo-sensing cell  511  and the fourth photo-sensing cell  514 . For example, each microlens ML 2  may be about twice as large as the corresponding first photo-sensing cell  511  or fourth photo-sensing cell  514 , and may be arranged to contact with respect to the corresponding first photo-sensing cell  511  and fourth photo-sensing cell  514  in a diagonal direction. 
       FIGS.  10 A and  10 B  are diagrams illustrating a transfer simulation of a phase distribution of red light passing through the color separation lens array  300  and a focusing distribution of red light in the corresponding photo-sensing cells,  FIG.  100    is a diagram illustrating a direction of red light incident on and around the third region  313  of the color separation lens array  300  corresponding to a red pixel, and  FIG.  10 D  is a diagram illustrating a microlens array that acts equivalently to the color separation lens array  300  for red light. According to the phase distribution of red light illustrated in  FIG.  10 A , a phase at the central portion of a region corresponding to red pixel R may be approximately 2π, a phase at the central portion of a region corresponding to adjacent green pixel G may be approximately π and a phase in the central portion of a region corresponding to the blue pixel B in the diagonal direction may represent a value approximately smaller than π (e.g., about 0.2π to about 0.7π). The above phase distribution may represent a focusing distribution of the red light as shown in  FIG.  10 B . Due to the phase distribution, the red light is condensed on the third photo-sensing cell  513  of the sensor substrate  500  corresponding to the red pixel R and rarely reaches the first, second, and fourth photo-sensing cells  511 ,  512 , and  514  corresponding to the other pixels. 
     As a result, the light incident on and around the third region  313  corresponding to the red pixel R passes through the color separation lens array  300  and then travels as shown in  FIG.  10 C . For example, among incident lights incident on the third region  313  of the color separation lens array  300  and some of the other regions surrounding the third region  313 , the red light is condensed on the third photo-sensing cell  513  directly under the third region  313 . For example, red light from the third region  313  corresponding to the red pixel R, red light from two fourth regions  314  adjacent to the third region  313  in a horizontal direction, red light from two first regions  311  adjacent to the third region  313  in a longitudinal direction, and red light from four second regions  312  adjacent to the third region  313  in a diagonal direction are incident on one red pixel R. 
     Accordingly, as illustrated in  FIG.  10 D , the color separation lens array  300  may function equivalent to a plurality of microlens ML 3  arrays arranged around the third photo-sensing cell  513  for red light. Because each equivalent microlens ML 3  is larger than the corresponding third photo-sensing cell  513 , the red light incident on a region of the third photo-sensing cell  513  as well as red light incident on another region surrounding the third photo-sensing cell  513  may be condensed onto the third photo-sensing cell  513 . For example, each microlens ML 3  may be about 4 times larger than the corresponding third photo-sensing cell  513 , and the four sides of each microlens ML 3  may be parallel to the four sides of the third photo-sensing cell  513 . 
     When the results shown in  FIGS.  8 C,  8 D,  9 C,  9 D,  10 C, and  10 D  are expressed differently, among the incident lights incident on the first region  311  of the color separation lens array  300 , the green light travels toward the central portion of the first photo-sensing cell  511  corresponding to the first region  311 , the blue light travels toward the central portion of the second photo-sensing cell  512  around the first photo-sensing cell  511  corresponding to the first region  311 , and the red light travels toward the central portion of the third photo-sensing cell  513  around the first photo-sensing cell  511  corresponding to the first region  311 . In addition, among the incident lights incident on the second region  312  of the color separation lens array  300 , the blue light travels toward the central portion of the second photo-sensing cell  512  corresponding to the second region  312 , the green light travels toward the central portions of the first photo-sensing cell  511  and the fourth photo-sensing cell  514  around the second photo-sensing cell  512  corresponding to the second region  312 , and the red light travels toward the central portion of the third photo-sensing cell  513  around the second photo-sensing cell  512  corresponding to the second region  312 . Similarly, among the incident light incident on the third region  313  of the color separation lens array  300 , the red light travels toward the central portion of the third photo-sensing cell  513  corresponding to the third region  313 , the green light travels toward the central portion of the first photo-sensing cell  511  and the fourth photo-sensing cell  514  around the third photo-sensing cell  513  corresponding to the third region  313 , and the blue light travels toward the central portion of the second photo-sensing cell  512  around the third photo-sensing cell  513  corresponding to the third region  313 . Finally, among the incident light incident on the fourth region  314  of the color separation lens array  300 , the green light travels toward the central portion of the fourth photo-sensing cell  514  corresponding to the fourth region  314 , the blue light travels toward the central portion of the second photo-sensing cell  512  around the fourth photo-sensing cell  514  corresponding to the fourth region  314 , and the red light travels toward the central portion of the third photo-sensing cell  513  around the fourth photo-sensing cell  514  corresponding to the fourth region  314 . 
     This color separation and condensing of light may be achieved more effectively by properly setting the thickness of the spacer layer. For example, when a theoretical thickness of the spacer layer is h t  and a refractive index of the spacer layer with respect to a wavelength of λ 0  is n, and a pitch of the photo-sensing cells is p, the following equation 1 may be satisfied. 
     
       
         
           
             
               
                 
                   
                     h 
                     t 
                   
                   = 
                   
                     
                       
                         np 
                         2 
                       
                       
                         λ 
                         0 
                       
                     
                     - 
                     
                       
                         λ 
                         0 
                       
                       
                         4 
                         ⁢ 
                         n 
                       
                     
                   
                 
               
               
                 
                   [ 
                   
                     Equation 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     1 
                   
                   ] 
                 
               
             
           
         
       
     
     Here, the theoretical thickness h t  of the spacer layer may be the focal length at which light having a wavelength of λ 0  is condensed on the upper surface of the photo-sensing cell  511 ,  512 ,  513 , or  514  by the color separation lens array  300 . For example, the light having the wavelength of λ 0  may be focused at a distance h t  from a lower surface of the color separation lens array  300  while passing through the color separation lens array  300 . 
     As described in Equation 1, the theoretical thickness h t  of the spacer layer may vary according to the pitch p of the photo-sensing cells  511 ,  512 ,  513 , and  514  and the refractive index n of the spacer layer. For example, when the center wavelength λ 0  of the visible light band is about 540 nm, the pitch p of the photo-sensing cells  511 ,  512 ,  513 , and  514  is about 0.8 μm, and the refractive index n of the spacer layer at a wavelength of about 540 nm is about 1.46, the theoretical thickness h t  of the spacer layer, that is, the distance between the lower surface of the color separation lens array  300  and the upper surface of the sensor substrate  500  may be about 1.64 μm. However, the actual thickness of the spacer layer need not be limited only to the theoretical thickness h t  described in Equation 1. For example, the actual thickness of the spacer layer  120  may be selected within a certain range based on the theoretical thickness h t  considering the efficiency of the color separation lens array  300 . For example, the actual thickness h of the spacer layer may be selected within a range of h t −p≤h≤h t +p. 
     Because the color separation lens array  300  described above may branch the incident light by wavelength without absorbing or blocking the incident light and condense the branched light on a specific region, the light utilization efficiency of the image sensor may be improved. Also, since the color separation lens array  300  has an improved color separation performance, the image sensor adopting the color separation lens array  300  may have a good color purity. In addition, the image sensor adopting the color separation lens array  300  may implement the Bayer pattern type that is generally adopted in the image sensor. Moreover, since the color separation lens array  300  may function as a lens for condensing the incident light, the image sensor employing the color separation lens array  300  may not require a separate microlens for condensing the light on each pixel. 
       FIG.  11    is a perspective view illustrating a form of nanopost that may be employed in a color separation lens array of an image sensor according to an example embodiment. 
     Referring to  FIG.  11   , the nanopost may have a cylindrical shape having a diameter D and a height H. At least one of the diameter D and the height H may be a sub-wavelength. The diameter D may vary depending on where the nanopost is placed. 
     The nanopost may include a pillar having various cross-sectional shapes, for example, a square shape, a square ring shape, or a cross shape.  FIGS.  12 A to  12 H  are plan views illustrating shapes of nanoposts that may be used in a color separation lens array of an image sensor. 
     As shown in  FIG.  12 A , the cross-section of a nanopost may have the shape of a circular ring having an outer diameter D and an inner diameter Di. A width w of the circular ring may correspond to a sub-wavelength. 
     As shown in  FIG.  12 B , the cross-section of a nanopost may have an elliptical shape in which a major axis length Dx in the first direction (X direction) is different from a minor axis length Dy in the second direction (Y direction). The elliptical shape may be employed, for example, in the first region  311  and the fourth region  314  corresponding to the green pixel, as described above with reference to  FIG.  7 A . 
     As shown in  FIGS.  12 C,  12 D, and  12 F , the cross-section of a nanopost may have a square shape, a square ring shape, or a cross shape. 
     As shown in  FIGS.  12 E and  12 G , the cross-section of a nanopost may have a rectangular shape or a cross shape, in which a length Dx in the first direction (X direction) is different from a length Dy in the second direction (Y direction). The rectangular shape or the cross shape may be employed in the first region  311  and the fourth region  314  corresponding to the green pixel, as described above with reference to  FIG.  7 A . 
     In addition, as shown in  FIG.  12 H , the cross-section of a nanopost may have a shape having a plurality of concave arcs. 
     Although  FIGS.  4 B and  7 A  illustrate a case in which one nanopost NP is arranged in the central portion of each of the regions  311 ,  312 ,  313 , and  314  of the color separation lens array  300 , embodiments are not limited thereto. For example, as shown in  FIG.  13   , a plurality of nanoposts may be arranged in the central portion. 
       FIG.  13    is a plan view illustrating an arrangement of a plurality of nanoposts constituting a color separation lens array  400  that may be employed in the image sensor  200 , according to another example embodiment. 
     A nanopost array region of the color separation lens array  400  may have a form corresponding to the pixel arrangement of the Bayer pattern illustrated in  FIG.  3 A , and may include a region divided into four regions, that is, a first region  411  corresponding to a green pixel G, a second region  412  corresponding to a blue pixel B, a third region  413  corresponding to a red pixel R, and a fourth region  414  corresponding to a green pixel G. These unit regions may be repeatedly arranged in the first direction (X direction) and the second direction (Y direction). 
     Each of the four regions may be divided into a plurality of sub-regions, and nanoposts NP may be arranged at the intersections between the boundaries of the sub-regions. In  FIG.  13   , the number of sub-regions is illustrated as nine. 
     As shown in  FIG.  13   , in each of the first region  411 , the second region  412 , the third region  413 , and the fourth region  414 , a nanopost NP located at a relatively central portion may have a larger cross-sectional area than a nanopost NP located at a peripheral portion, and the cross-sectional areas of nanoposts arranged in the first and fourth regions  411  and  414  corresponding to the green pixels G may be greater than those of nanoposts NP arranged in a central portion of the second region  412  and a central region of the third region  413 . The cross-sectional area of the nanopost NP arranged in the central portion of the second region  412  may be greater than that of the nanopost NP arranged in the central portion of the third region  413 . 
     Nanoposts NP are arranged on grid points of 9 sub-regions, and thus, a nanopost NP is not arranged in the center of each of the regions  411 ,  412 ,  413 , and  414  and four nanoposts NP having a same size form a central portion. Nanoposts NP in a peripheral portion other than the central portion are arranged on boundary lines with other regions. However, this arrangement is only an example and embodiments are not limited thereto. Nanoposts NP are indicated by r 1  to r 9  according to their detailed positions in the unit pattern array. 
     Referring to  FIG.  13   , a nanopost r 1  arranged in the central portion of the first region  411  corresponding to a green pixel has a larger cross-sectional area than nanoposts r 5 , r 6 , and r 9  arranged in the peripheral portion, and a nanopost r 4  arranged in the central portion of the fourth region  414  corresponding to a green pixel has a larger cross-sectional area than nanoposts r 7 , r 8 , and r 9  arranged in the peripheral portion. The cross-sectional areas of the nanoposts r 1  and r 4  respectively arranged in the central portions of the first region  411  and the fourth region  414  corresponding to the green pixels may be greater than that of the nanopost r 2  arranged in the central portion of the second region  412  corresponding to the blue pixel and that of the nanopost r 3  arranged in the central portion of the third region  413  corresponding to the red pixel. In addition, the cross-sectional area of the nanopost r 2  arranged in the central portion of the second region  412  corresponding to the blue pixel may be greater than that of the nanopost r 3  arranged in the central portion of the third region  413  corresponding to the red pixel. 
     The arrangement of nanoposts NP in the second region  412  and the arrangement of nanoposts NP in the third region  413  may be symmetrical in the first direction (X direction) and the second direction (Y direction), and the arrangement of nanoposts NP in the first region  411  and the arrangement of nanoposts NP in the fourth region  414  may be asymmetrical in the first direction (X direction) and the second direction (Y direction). For example, the nanoposts NP in the second region  412  corresponding to the blue pixel and the nanoposts NP in the third region  413  corresponding to the red pixel may have the same distribution rule in the first direction (X direction) and the second direction (Y direction). The nanoposts NP in the first region  411  corresponding to the green pixel and the nanoposts NP in the fourth region  414  corresponding to the green pixel may have different distribution rules in the first direction (X direction) and the second direction (Y direction). 
     The cross-sectional area of the nanopost r 5  located at the boundary between the first region  411  and the second region  412  adjacent thereto in the first direction (X direction) is different from that of the nanopost r 6  located at the boundary between the first region  411  and the third region  413  adjacent thereto in the second direction (Y direction). In addition, the cross-sectional area of the nanopost r 7  located at the boundary between the fourth region  414  and the third region  413  adjacent thereto in the first direction (X direction) is different from that of the nanopost r 8  located at the boundary between the forth region  414  and the second region  412  adjacent thereto in the second direction (Y direction). 
     On the other hand, the cross-sectional area of the nanopost r 5  located at the boundary between the first region  411  and the second region  412  adjacent thereto in the first direction (X direction) is equal to that of the nanopost r 8  located at the boundary between the forth region  414  and the second region  412  adjacent thereto in the second direction (Y direction). The cross-sectional area of the nanopost r 6  located at the boundary between the first region  411  and the third region  413  adjacent thereto in the second direction (Y direction) is equal to that of the nanopost r 7  located at the boundary between the forth region  414  and the third region  413  adjacent thereto in the first direction (X direction). 
     Nanoposts r 9  arranged at four corners of each of the first region  411 , the second region  412 , the third region  413 , and the fourth region  414 , that is, at the intersections between the four regions, have the same cross-sectional area. 
     In this way, in the second region  412  and the third region  413  corresponding to the blue pixel and the red pixel, respectively, nanoposts NP are arranged in a form of 4-fold symmetry, and in the first and fourth regions  411  and  414  corresponding to the green pixels, nanoposts NP are arranged in a form of 2-fold symmetry. In addition, the first region  411  and the fourth region  414  are rotated 90 degrees with respect to each other. This form corresponds to the example embodiments of  FIGS.  15  and  16    to be described later. 
     Although  FIG.  13    illustrates a case where the number of sub-regions is 9 and a nanopost NP is not arranged in the center of each of the regions  411 ,  412 ,  413 , and  414 , the number of sub-regions may be set to 16 and a nanopost NP may be arranged in the center of each of the regions  411 ,  412 ,  413 , and  414 . 
       FIG.  14    is a plan view illustrating an arrangement of a plurality of nanoposts constituting a color separation lens array  450  of an image sensor according to another example embodiment. 
     The color separation lens array  450  may have a form corresponding to the pixel arrangement of the Bayer pattern, and may include a region divided into four regions, that is, a first region  451  corresponding to a green pixel, a second region  452  corresponding to a blue pixel, a third region  453  corresponding to a red pixel, and a fourth region  454  corresponding to a green pixel. Each of the four regions may be divided into a plurality of sub-regions, and nanoposts NP may be arranged at the intersections between the boundaries of the sub-regions.  FIG.  14    illustrates an example in which the number of sub-regions is 16, unlike  FIG.  13   , and in  FIG.  14   , nanoposts NP are arranged on grid points of 16 sub-regions and thus a nanopost NP is arranged in the center of each of the regions  451 ,  452 ,  453 , and  454 . Nanoposts NP are indicated by s 1  to s 11  according to their detailed positions in the unit pattern array. 
     In the example embodiment of  FIG.  14   , a nanopost s 1  located at the center of the first region  451  corresponding to a green pixel and a nanopost s 4  located at the center of the fourth region  454  corresponding to a green pixel may have cross-sectional areas greater than those of nanoposts NP located in a peripheral portion, and may have cross-sectional areas greater than those of nanoposts NP located in the second region  452  corresponding to a blue pixel and the third region  453  corresponding to a red pixel. 
     In the example embodiment of  FIG.  14    as in the example embodiment of  FIG.  13   , nanoposts NP in the second region  452  and nanoposts NP in the third region  453  may be symmetrically arranged in the first direction (X direction) and the second direction (Y direction), and nanoposts NP in the first region  451  and nanoposts NP in the fourth region  454  may be asymmetrically arranged in the first direction (X direction) and the second direction (Y direction). In addition, nanoposts s 9  arranged at four corners of each of the first region  451 , the second region  452 , the third region  453 , and the fourth region  454 , that is, at the intersections between the four regions, have the same cross-sectional area. 
       FIG.  15    is a plan view illustrating an arrangement of a plurality of nanoposts constituting a color separation lens array  460  of an image sensor according to another example embodiment. 
     The color separation lens array  460  may have a form corresponding to the pixel arrangement of the Bayer pattern, and may include a region divided into four regions, that is, a first region  461  corresponding to a green pixel, a second region  462  corresponding to a blue pixel, a third region  463  corresponding to a red pixel, and a fourth region  464  corresponding to a green pixel. 
     Each of the four regions may be divided into a plurality of sub-regions, and nanoposts NP may be arranged in the sub-regions. As in  FIG.  13   , each region of the color separation lens array  460  may be divided into 9 sub-regions. However, the example embodiment of  FIG.  15    is different from the example embodiment of  FIG.  13    in that nanoposts NP are arranged inside the sub-regions, not at the intersections between the sub-regions. The nanoposts NP are indicated by t 1  to t 16  according to their detailed positions in the unit pattern array. 
     In the example embodiment of  FIG.  15   , a nanopost t 1  located in a central portion of the first region  461  and a nanopost t 4  located in a central portion of the fourth region  464  may have cross-sectional areas greater than those of nanoposts NP arranged in the second region  462  and the third region  463  as well as nanoposts NP located in a peripheral portion. 
     The cross-sectional area of a nanopost t 2  arranged in a central portion of the second region  462  may be greater than that of a nanopost t 3  arranged in a central portion of the third region  463 . In the second region  462 , the cross-sectional areas of nanoposts t 6  and t 10  located in a peripheral portion spaced apart from the central portion of the second region  462  in the first direction (X direction) and the second direction (Y direction) are greater than that of the nanopost t 2  arranged in the central portion of the second region  462 . Unlike this, the cross-sectional areas of nanoposts t 14  located in a peripheral portion spaced apart from the central portion in a diagonal direction are less than that of the nanopost t 2  arranged in the central portion of the second region  462 . 
     In the third region  463 , the cross-sectional area of the nanopost t 3  arranged in the central portion of the third region  463  is the smallest, and all of the nanoposts t 7 , t 11 , and t 15  in the peripheral portion have larger cross-sectional areas than the nanopost t 3  arranged in the central portion of the third region  463 . 
     Nanoposts NP in the second region  462  and nanoposts NP in the third region  463  may be symmetrically arranged in the first direction (X direction) and the second direction (Y direction), and nanoposts NP in the first region  461  and nanoposts NP in the fourth region  464  may be asymmetrically arranged in the first direction (X direction) and the second direction (Y direction). For example, the nanoposts NP in the second region  462  corresponding to the blue pixel and the nanoposts NP in the third region  463  corresponding to the red pixel have the same distribution rule in the first direction (X direction) and the second direction (Y direction). The nanoposts NP in the first region  461  corresponding to the green pixel and the nanoposts NP in the fourth region  464  corresponding to the green pixel have different distribution rules in the first direction (X direction) and the second direction (Y direction). 
     In the first region  461 , a nanopost t 1  in a central portion of the first region  461 , a nanopost t 5  adjacent to the nanopost t 1  in the first direction (X direction), and a nanopost t 9  adjacent to the nanopost t 1  in the second direction (Y direction) have different cross-sectional areas. Also in the fourth region  464 , a nanopost t 4  in a central portion of the fourth region  464 , a nanopost t 8  adjacent to the nanopost t 4  in the first direction (X direction), and a nanopost t 12  adjacent to the nanopost t 4  in the second direction (Y direction) have different cross-sectional areas. In addition, the nanopost t 1  in the central portion of the first region  461  and the nanopost t 5  adjacent to the nanopost t 1  in the first direction (X direction) have the same cross-sectional areas as the nanopost t 4  in the central portion of the fourth region  464  and the nanopost t 12  adjacent to the nanopost t 4  in the second direction (Y direction), respectively. The nanopost t 1  in the central portion of the first region  461  and the nanopost t 9  adjacent to the nanopost t 1  in the second direction (Y direction) have the same cross-sectional areas as the nanopost t 4  in the central portion of the fourth region  464  and the nanopost t 8  adjacent to the nanopost t 4  in the first direction (X direction), respectively. Nanoposts t 13  at positions adjacent to four corners of the first region  461  and nanoposts t 16  at positions adjacent to four corners of the fourth region  464  have the same cross-sectional area. In this way, the first region  461  and the fourth region  464  are rotated 90 degrees with respect to each other. 
     In the second region  462 , a nanopost t 2  in a central portion of the second region  462 , a nanopost t 6  adjacent to the nanopost t 2  in the first direction (X direction), and a nanopost t 10  adjacent to the nanopost t 2  in the second direction (Y direction) have the same cross-sectional area. Nanoposts t 14  at positions adjacent to four corners of the second region  462  have the same cross-sectional area. 
     Also in the third region  463 , a nanopost t 3  in a central portion of the third region  463 , a nanopost t 7  adjacent to the nanopost t 3  in the first direction (X direction), and a nanopost t 11  adjacent to the nanopost t 3  in the second direction (Y direction) have the same cross-sectional area. Nanoposts t 15  at positions adjacent to four corners of the third region  463  have the same cross-sectional area. 
       FIG.  16    is a plan view illustrating an arrangement of a plurality of nanopost constituting a color separation lens array  470  according to another example embodiment. 
     The color separation lens array  470  of the image sensor according to the example embodiment may be an embodiment of the simplest structure. One nanopost NP is arranged in each of a first region  471  corresponding to a green pixel, a second region  472  corresponding to a blue pixel, a third region  473  corresponding to a red pixel, and a fourth region  474  corresponding to a green pixel. The cross-sectional area of a nanopost NP provided in the first region  471  and the fourth region  474  is the largest, the cross-sectional area of a nanopost NP provided in the second region  472  is less than that of the nanopost NP provided in the first region  471 , and the cross-sectional area of a nanopost NP provided in the third region  473  is the smallest. 
     In this way, depending on sub-region partitioning, a nanopost may or may not be arranged in the center. 
     In the pixel array  210  of the image sensor  200 , a color filter may be further arranged between the sensor substrate  500  and the color separation lens array  300 ,  400 ,  450 ,  460 , or  470 . In particular, a color filter may be arranged between the sensor substrate  500  and the spacer layer. Also, the pixel array  210  may further include a transparent dielectric layer covering the nanoposts NP to protect the color separation lens arrays  300 ,  400 ,  450 ,  460 , or  470 . The dielectric layer may be arranged to completely cover spaces between adjacent nanoposts NP and upper surfaces of the nanoposts NP. The dielectric layer may include a material having a refractive index lower than those of the nanoposts NP. For example, the dielectric layer may include the same material as the spacer layer. 
     Since the color separation lens arrays  300 ,  400 ,  450 ,  460 , and  470  branch light of different wavelengths and condense the light of different wavelengths onto a plurality of photo-sensing cells  511 ,  512 ,  513 , and  514 , the color filter may not be included. However, by providing an additional color filter in this way, color purity may be more supplemented, and since light that is color-separated to a considerable extent is incident on the color filter, light loss may not be significant. 
     The color separation lens arrays  300 ,  400 ,  450 ,  460 , and  470  applied to the image sensor  200  may have a nanopost arrangement as shown in  FIG.  7 A , a nanopost arrangement as shown in  FIGS.  13  to  16   , and various nanopost arrangements. 
     In this way, the color separation lens arrays  300 ,  400 ,  450  and  460 , which are arranged on the sensor substrate  500  in the image sensor  200  to separate light according to color and make the separated light incident on the plurality of photo-sensing cells  511 ,  512 ,  513 , and  514 , may include a plurality of nanopost arrays, and the arrangement of nanoposts, the cross-sectional shapes of the nanoposts, and the cross-sectional size distribution of the nanoposts may be variously modified. 
     The image sensor  200  including the color separation lens array  300 ,  400 ,  450 ,  460 , or  470  according to the above-described example embodiments may be applied to various optical devices such as a camera. The camera may be mounted in mobile electronic apparatuses such as cellular phones, smart phones, notebook computers, and tablet PCs. 
     From the perspective of the image sensor  200 , the main ray angle of light incident on a central portion of the image sensor  200  is 0 degrees, and the closer to the edge of the image sensor  200 , the larger the main ray angle of the incident light. However, the color separation lens arrays  300 ,  400 ,  450 ,  460 , and  470  described above may generally have directionality. For example, the color separation lens arrays  300 ,  400 ,  450 ,  460 , and  470  operates more efficiently with respect to light incident in a certain angle range, but when the incident angle of the light is further away from the certain angle range, the color separation performance of the color separation lens array  300 ,  400 ,  450 ,  460 , and  470  may be deteriorated. Therefore, when the nanoposts of the color separation lens arrays  300 ,  400 ,  450 ,  460 , and  470  all have the same arrangement shape in the entire area of the image sensor  200 , the color separation efficiency may be not uniform in the entire area of the image sensor  200  and may vary depending on regions of the image sensor  200 . Due to this, the quality of images provided by the camera may be deteriorated. 
     Therefore, taking into account the main ray angle of the incident light that varies depending on positions on the image sensor  200 , the arrangement of the nanoposts of the color separation lens arrays  300 ,  400 ,  450 ,  460 , and  470  may be designed differently as illustrated in  FIGS.  17 A to  17 C . 
       FIGS.  17 A to  17 C  are schematic plan views illustrating changes in the arrangement shape of nanoposts of a color separation lens array according to positions on the image sensor  200 . In particular,  FIG.  17 A  illustrates the position of a nanopost NP arranged in a central portion of the image sensor  200 ,  FIG.  17 B  illustrates the position of a nanopost NP arranged between the central portion and the edge of the image sensor  200 , and  FIG.  17 C  illustrates the position of a nanopost NP arranged on the edge of the image sensor  200 .  FIGS.  17 A to  17 C  are not intended to limit a certain arrangement of nanoposts NP, but are merely for conceptually explaining the relative position change of the nanoposts NP according to positions on the image sensor  200 . 
     As shown in  FIGS.  17 A to  17 C , the closer to the edge from the central portion of the image sensor  200 , the further a first region, a second region, a third region, and a fourth region of the color separation lens array may be shifted away from pixels or photo-sensing cells corresponding to the first region, the second region, the third region, and the fourth region, respectively. For example, in the central portion of the image sensor  200 , the central portion of the color separation lens array, or the central portion of the sensor substrate, the positions of the first region, the second region, the third region, and the fourth region of the color separation lens array may coincide with the positions of a green pixel, a blue pixel, a red pixel, and a green pixel (or the positions of photo-sensing cells) corresponding to the first region, the second region, the third region, and the fourth region, respectively. In addition, the further away from the central portion of the image sensor  200 , the central portion of the color separation lens array, or the central portion of the sensor substrate, the further the first region, the second region, the third region, and the fourth region of the color separation lens array may be shifted away from the positions of the green pixel, the blue pixel, the red pixel, and the green pixel (or the positions of the photo-sensing cells) corresponding to the first region, the second region, the third region, and the fourth region, respectively. The degree to which the first region, the second region, the third region, and the fourth region of the color separation lens array are shifted may be determined by the main ray angle of light incident on the color separation lens array. In particular, in a peripheral portion of the image sensor  200 , a peripheral portion of the color separation lens array, or a peripheral portion of the sensor substrate, the first region, the second region, the third region, and the fourth region of the color separation lens array are shifted toward the central portion of the image sensor  200  with respect to a first photo-sensing cell, a second photo-sensing cell, a third photo-sensing cell, and a fourth photo-sensing cell corresponding to the first region, the second region, the third region, and the fourth region, respectively. 
     Hereinafter, although expressed as the central portion of the image sensor  200 , the central portion of the image sensor  200  may also refer to the central portion of the color separation lens array or the central portion of the sensor substrate because the image sensor  200 , the color separation lens array, and the sensor substrate are arranged to face one another. Similarly, hereinafter, the peripheral portion/edge of the image sensor  200  may refer to the peripheral portion/edge of the color separation lens array or the peripheral portion/edge of the sensor substrate. 
       FIG.  18 A  is a cross-sectional view illustrating a schematic structure of a pixel array  210   a  according to another example embodiment. 
     Referring to  FIG.  18 A , the pixel array  210   a  of an image sensor according to the example embodiment differs from those of the above-described example embodiments in that the pixel array  210   a  includes a color separation lens array  320  having nanoposts NP stacked in two layers. Each of the nanoposts NP may include a first nanopost NP 1  arranged on a spacer layer  520 , and a second nanopost NP 2  arranged on the first nanopost NP 1 . The second nanopost NP 2  may be shifted in an inclination direction of light with respect to the first nanopost NP 1 . For example, when light incident on the color separation lens array  320  is inclined from right to left, the second nanopost NP 2  may be shifted to the right with respect to the first nanopost NP 1 . Conversely, when the light incident on the color separation lens array  320  is inclined from left to right, the second nanopost NP 2  may be shifted to the left with respect to the first nanopost NP 1 . 
     In addition, the second nanopost NP 2  may be shifted toward the central portion of the image sensor  200  with respect to the first nanopost NP 1 . For example, the closer to the left edge from the central portion of the image sensor  200 , the further the second nanopost NP 2  may be shifted to the right with respect to the first nanopost NP 1 . The closer to the right edge from the central portion of the image sensor  200 , the further the second nanopost NP 2  may be shifted to the left with respect to the first nanopost NP 1 . 
     Similarly, a third region  323  and a fourth region  324  of the color separation lens array  320  may be shifted toward the central portion of the image sensor  200  with respect to a red pixel (or third photo-sensing cell) and a green pixel (or fourth photo-sensing cell) corresponding to the third region  323  and the fourth region  324 , respectively. For example, the closer to the left edge from the central portion of the image sensor  200 , the further the third region  323  and the fourth region  324  of the color separation lens array  320  may be shifted to the right with respect to the red pixel and the green pixel corresponding to the third region  323  and the fourth region  324 , respectively. A first region and a second region arranged in another cross-section of the color separation lens array  320  may be also shifted toward the central portion of the image sensor  200  with respect to a green pixel (or first photo-sensing cell) and a blue pixel (or second photo-sensing cell) corresponding to the first region and the second region, respectively. 
     In particular, the third region  323  and the fourth region  324  of the color separation lens array  320  may be shifted to respectively condense red light and green light in a central portion of a third photo-sensing cell  513  corresponding to the third region  323  and a central portion of a fourth photo-sensing cell  514  corresponding to the fourth region  324 . A distance s at which the third region  323  and the fourth region  324  of the color separation lens array  320  are shifted may be determined by, for example, Equation 2 below.
 
 s=d ×tan( CRA ′)   Equation 2 
 
     In Equation 2, d is the shortest straight line distance or interval between the lower surface of the color separation lens array  320  and the upper surface of a sensor substrate  500 , and CRA′ is the incident angle of light incident on the sensor substrate  500 . In addition, CRA′ may be determined by Equation 3 below.
 
 CRA ′=sin −1 (sin  CRA×n )   Equation 3 
 
     In Equation 3, CRA is the incident angle of light incident on the color separation lens array  320 , and n is the refractive index of a material arranged between the color separation lens array  320  and the sensor substrate  500 . Accordingly, the distance s at which the third region  323  and the fourth region  324  of the color separation lens array  320  are shifted from pixels corresponding to the third region  323  and the fourth region  324  may be determined by the incident angle of light incident on the color separation lens array  320  and the refractive index of a material arranged between the color separation lens array  320  and the sensor substrate  500 . When the spacer layer  520  and a color filter  505  are arranged between the color separation lens array  320  and the sensor substrate  500 , CRA′ may be determined considering the incident angle of light incident on the spacer layer  520  and the refractive index of the spacer layer  520 , and the incident angle of light incident on the color filter  505  and the refractive index of the color filter  105 . 
     Even when a pixel array includes the color separation lens array  320  having nanoposts NP stacked in two layers, like the pixel array  210   a  of the image sensor according to the example embodiment, the first to fourth regions of the color separation lens array  320  may not be shifted, with respect to pixels (or photo-sensing cells) corresponding to the first to fourth regions, in the central portion of the image sensor  200 . In addition, in the central portion of the image sensor  200 , the second nanopost NP 2  may not be shifted with respect to the first nanopost NP 1 . In addition, in the peripheral portion of the image sensor  200 , the first to fourth regions of the color separation lens array  320  may be shifted toward the central portion of the image sensor  200 , and the second nanopost NP 2  may also be shifted toward the central portion of the image sensor  200  with respect to the first nanopost NP 1 . In consideration of this, in the case of the image sensor  200  employed in a camera, the total area of the color separation lens array  320  may be less than the total area of the pixel array  210   a  of the image sensor  200  or the total area of the sensor substrate  500 . 
     In the example embodiment of  FIG.  18 A , the color filter  505  is arranged on the sensor substrate  500 . However, when the color separation lens array  320  has sufficient performance in the peripheral portion of the image sensor  200 , the color filter  505  may be omitted. 
       FIG.  18 B  is a perspective view illustrating a shape of a nanopost employed in the color separation lens array of the image sensor of  FIG.  18 A . As shown in  FIG.  18 B , a first nanopost NP 1  and a second nanopost NP 2  arranged on the first nanopost NP 1  may be stacked to be shifted from each other. The degree of being shifted from each other is indicated by b in  FIG.  18 B , and the size of the degree may increase from the central portion of the image sensor  200  to the peripheral portion thereof, that is, in a radial direction. A direction in which the second nanopost NP 2  is shifted from the first nanopost NP 1  may be a direction from the peripheral portion toward the central portion. In particular, the degree b of being shifted may be determined such that light is incident on a central portion of the upper surface of the second nanopost NP 2  and is incident on a central portion of the upper surface of the first nanopost NP 1 . 
     The first nanopost NP 1  and the second nanopost NP 2  of the two-layered structure may be covered with a dielectric layer having a refractive index lower than that of the material of the first and second nanoposts NP 1  and NP 2 . 
       FIGS.  18 A and  18 B  illustrate a structure in which nanoposts NP are stacked in two layers, but the structure is not limited thereto and may have a structure of three or more layers as in  FIG.  19   . 
       FIG.  19    is a cross-sectional view illustrating a schematic structure of a pixel array  210   b  according to another example embodiment. 
     Referring to  FIG.  19   , the pixel array  210   b  of an image sensor includes a color separation lens array  330  having nanoposts NP stacked in three layers. Each of the nanoposts NP may include a first nanopost NP 1  arranged on a spacer layer  520 , a second nanopost NP 2  arranged on the first nanopost NP 1 , and a third nanopost NP 3  arranged on the second nanopost NP 2 . The second nanopost NP 2  may be shifted toward a central portion of the image sensor with respect to the first nanopost NP 1 , and the third nanopost NP 3  may be shifted toward the central portion of the image sensor with respect to the second nanopost NP 2 . 
     In addition, a fourth region  334  of the color separation lens array  330  may be shifted toward the central portion of the image sensor with respect to a green pixel or a fourth photo-sensing cell  514  corresponding to the fourth region  334 , and a third region  333  of the color separation lens array  330  may be shifted toward the central portion of the image sensor with respect to a red pixel or a third photo-sensing cell  514  corresponding to the third region  333 . 
     Even when nanoposts NP are stacked in two layers shifted from each other, or have a structure in which three or more layers are stacked, nanoposts having various shapes may be used. 
     For example, nanoposts having rectangular shapes having different sizes and stacked in two layers may be shifted with respect to each other. In addition, ring-type nanoposts stacked in two layers, circular nanoposts stacked in two layers, and rectangular nanoposts stacked in two layers may be shifted with respect to each other in respective regions of the color separation lens array. 
     In addition, an inclined surface may be formed on the side of each of the nanoposts stacked in two layers. For example, an inclined surface may be formed on the side of the nanopost in a way that the cross-sectional area of the nanopost increases from the bottom to the top, and thus, the nanopost may have a trapezoidal cross-section in which an upper side is larger than a lower side. In addition, an inclined surface may be formed on the side of the nanopost in a way that the cross-sectional area of the nanopost decreases from the bottom to the top, and thus, the nanopost may have a trapezoidal cross-section in which a lower side is larger than an upper side. In this case, the inclination degrees of the inclined surfaces of nanoposts arranged in the first region, the second region, the third region, and the fourth region of the color separation lens array may be different from one another. In addition, the inclination degree of the inclined surfaces of nanoposts positioned corresponding to the central portion of the image sensor may be different from the inclination degree of the inclined surfaces of nanoposts positioned corresponding to the peripheral portion of the image sensor. As described above, the color separation efficiency may be increased by a color separation lens array in which sub-wavelength nanoposts are arranged in a certain rule, and the performance of an image sensor using the color separation lens array may be improved. The specific forms described above are only examples, and various modifications and combinations thereof are possible. For example, although the wavelength band of visible light has been described as an example, embodiments are not limited thereto, and color separation by wavelength bands other than the wavelength band of visible light is possible according to nanopost arrangement rules. In addition, the number of nanoposts provided in each of the plurality of regions of a nanopost array may be variously changed. The pixel arrangement of the image sensor has been described as including a Bayer pattern, but is not limited thereto. For example, an arrangement in which red, green, and blue pixels are repeated in one direction in this order may be applied to the pixel arrangement of the image sensor. Alternatively, an arrangement by the CYGM method shown in  FIG.  3 B  or an arrangement by the RGBW method shown in  FIG.  3 C  may be applied to the pixel arrangement of the image sensor. In addition, it may be applied to a pixel arrangement pattern in which a plurality of unit pixels including pixels of two or more colors are repeatedly arranged. The color separation lens array may adopt a region division suitable for this pixel arrangement, and a nanopost arrangement rule may be selected for each region. 
     According to example embodiments, the color separation lens array may be composed of an array of nanoposts formed in a definable shape, but embodiments are not limited thereto. For example, the color separation lens array may also be composed of various types of free patterns that may not be defined, as illustrated in  FIG.  20   . 
       FIG.  20    is a conceptual diagram illustrating a schematic structure and operation of a color separation lens array  330  according to another example embodiment. 
     Referring to  FIG.  20   , a unit pattern array of the color separation lens array  330  may include first to fourth regions  331 ,  332 ,  333 , and  334  respectively having first to fourth fine structures separated from one another. For example, the first region  331  may have a first pattern, the second region  332  may have a second pattern patterned in a different form from the first pattern, the third region  333  may have a third pattern patterned in a form different from the first pattern and the second pattern, and the fourth region  334  may have a fourth pattern patterned in a form different from the first to third patterns. 
     The first to fourth regions  331 ,  332 ,  333 , and  334  may be arranged on the same plane in the form of, for example, 2×2. Accordingly, the first region  331  and the second region  332  may be arranged adjacent to each other in a first direction, and the third region  333  and the fourth region  334  may be arranged adjacent to each other in the first direction. In addition, the first region  331  and the third region  333  may be arranged adjacent to each other in a second direction perpendicular to the first direction, and the second region  332  and the fourth region  334  may be arranged adjacent to each other in the second direction. The first region  331  and the fourth region  334  may be arranged in a diagonal direction, and the second region  332  and the third region  333  are arranged in a different diagonal direction. 
     According to an example embodiment, the first to fourth patterns may be determined so that, among incident lights incident on the color separation lens array  330 , first wavelength light λ 1  is condensed in a first photo-sensing cell  511  facing the first region  331  in the vertical direction, second wavelength light λ 2  is condensed in a second photo-sensing cell  512  facing the second region  332  in the vertical direction, third wavelength light λ 3  is condensed in a third photo-sensing cell  513  facing the third region  333  in the vertical direction, and fourth wavelength light λ 4  is condensed in a fourth photo-sensing cell  514  facing the fourth region  334  in the vertical direction. 
     The first to fourth patterns of the first to fourth regions  331 ,  332 ,  333  and  334  may be variously designed according to the pixel arrangement and color characteristics of the image sensor to which the color separation lens array  330  is applied. 
     For example, when the color separation lens array  330  is applied to the Bayer pattern type image sensor shown in  FIG.  3 A , the first region  331  and the fourth region  334  may be arranged to face the green pixel G, the second region  332  may be arranged to face the blue pixel B, and the third region  333  may be arranged to face the red pixel R. In addition, the first wavelength light λ 1  and the fourth wavelength light λ 4  may be green light, the second wavelength light λ 2  may be blue light, and the third wavelength light λ 3  may be red light. 
     In the color separation lens array  330  applied to the Bayer pattern type image sensor, as another rule of the first to fourth patterns of the first to fourth regions  331 ,  332 ,  333 , and  334 , the first to fourth patterns of the first to fourth regions  331 ,  332 ,  333 , and  334  may be designed so that the blue light, green light, and red light transmitted through the color separation lens array  330  have a certain target phase distribution. For example, the first to fourth patterns of the first to fourth regions  331 ,  332 ,  333  and  334  may be determined to form a phase at which the blue light transmitted through the color separation lens array  330  is condensed to a position of the blue pixel B corresponding to the second region  332  and does not travel to positions corresponding to the first region  331  and the fourth region  334  adjacent to the second region  332 . 
     In addition, the first to fourth patterns of the first to fourth regions  331 ,  332 ,  333  and  334  may be determined to form a phase at which the green light transmitted through the color separation lens array  330  is condensed to positions of the green pixel G corresponding to the first region  331  and the fourth region  334  and does not travel to positions corresponding to the second region  332  and third region  333  adjacent to the first region  331  and the fourth region  334 . 
     In addition, the first to fourth patterns of the first to fourth regions  331 ,  332 ,  333  and  334  may be determined to form a phase at which the red light transmitted through the color separation lens array  330  is condensed to a position of the red pixel R corresponding to the third region  333  and does not travel to positions corresponding to the first region  331  and the fourth region  334  adjacent to the third region  333 . 
     Since the target phase distribution to be implemented by the color separation lens array  330  is the same as described above, a detailed description will be omitted. According to the shapes of the first to fourth patterns of the first to fourth regions  331 ,  332 ,  333 , and  334 , the color separation lens array  330  may perform the same operation as described with reference to  FIGS.  8 A to  8 D,  9 A to  9 D, and  10 A to  10 D . 
     The pattern of the color separation lens array  300  that satisfies the phase distribution described above may be automatically designed through various computer simulations. For example, the patterns of the first to fourth regions  331 ,  332 ,  333 , and  334  may be optimized through a nature-inspired algorithm such as a genetic algorithm, a particle swarm optimization algorithm, an ant colony optimization algorithm, etc., or a reverse design based on an adjoint optimization algorithm. 
     For the design of the color separation lens array  300 , the first to fourth patterns of the first to fourth regions  331 ,  332 ,  333 , and  334  may be optimized by evaluating the performance of a candidate color separation lens arrays by using evaluation factors such as color separating spectrum, luminance efficiency, and signal-to-noise ratio. For example, the first to fourth patterns of the first to fourth regions  331 ,  332 ,  333 , and  334  may be optimized in a manner that a target numerical value of each evaluation element is determined in advance and then the sum of the differences between the actual values and the target numerical values of a plurality of evaluation elements may be minimized. Alternatively, the performance may be indexed for each evaluation element, and the first to fourth patterns of the first to fourth regions  331 ,  332 ,  333 , and  334  may be optimized so that a value representing the performance may be maximized. 
     Various types of color separation lens array  330  may be obtained through the above-described optimized design according to the size and thickness of the first to fourth regions  331 ,  332 ,  333 , and  334  of the color separation lens array  330 , the color characteristics and the pixel pitch of an image sensor to which the color separation lens array  300  is applied, the distance between the color separation lens array  330  and the sensor substrate  500 , and the incident angle of incident light. 
     The above-described specific patterns of the color separation lens array  330  are merely examples and may be variously modified. For example, according to the different pattern types of the first to fourth regions  331 ,  332 ,  333 , and  334  of the color separation lens array  330 , it is possible to separate light of wavelength bands other than visible light. Also, the number of color separation patterns constituting one unit pattern array in the color separation lens array  330  may vary depending on the application examples of the color separation lens array  330 . The pixel arrangement of the image sensor has been described by exemplifying the Bayer pattern, but is not limited thereto, and may also be applied to the pixel arrangement shown in  FIGS.  3 B and  3 C . A pattern suitable for this pixel arrangement may be determined by adopting regions of the color separation lens array  330  and using the above-described optimization method for each region. 
       FIG.  21    is a plan view illustrating a color separation lens array  340  according to another example embodiment. Referring to  FIG.  21   , the color separation lens array  340  may include a plurality of unit pattern arrays indicated by bold lines and arranged two-dimensionally. Each unit pattern array may be arranged in the form of 2×2 including a first region  341 , a second region  342 , a third region  343 , and a fourth region  344 . In the entire structure of the color separation lens array  340 , the first region  341  and the second region  342  are alternately arranged in the horizontal direction within one row, and the third region  343  and the fourth region  344  are alternately arranged in the horizontal direction within another row. In addition, the first region  341  and the third region  343  are alternately arranged in the longitudinal direction within one column, and the second region  342  and the fourth region  344  are alternately arranged in the longitudinal direction within another column. 
     In addition, the color separation lens array  340  may further include a plurality of first to fourth regions  341 ,  342 ,  343 , and  344  that are not included in any of the unit pattern arrays. The first to fourth regions  341 ,  342 ,  343 , and  344  that are not included in any of the unit pattern arrays may be arranged along the edge of the color separation lens array  340 . For example, a plurality of second regions  342  and a plurality of fourth regions  344  constituting one column are additionally arranged at the left edge of the color separation lens array  340 , a plurality of first regions  341  and a plurality of third regions  343  constituting one column are additionally arranged at the right edge, a plurality of third regions  343  and a plurality of fourth regions  344  constituting one row are additionally arranged at the upper edge, and a plurality of first regions  341  and a plurality of second regions  342  constituting one row may be additionally arranged at the lower edge. 
       FIG.  22    is a cross-sectional view illustrating a schematic structure of a pixel array of an image sensor including the color separation lens array  340  shown in  FIG.  21   . The cross-section in  FIG.  22    is a cross-section of the color separation lens array  340  of  FIG.  21    taken along line C-C′. Referring to  FIG.  22   , the color separation lens array  340  may include a plurality of first regions  341  and a plurality of second regions  342  that are arranged to protrude in a horizontal direction with respect to an edge of the sensor substrate  500  and do not face any photo-sensing cell of the sensor substrate  500  in the vertical direction. The plurality of first to fourth regions  341 ,  342 ,  343 , and  344  that are not included in any unit pattern array in  FIG.  21    are all arranged to protrude in the horizontal direction and the longitudinal direction with respect to the corresponding edges of the sensor substrate  500  and do not face any photo-sensing cell in the vertical direction. 
     As described with reference to  FIGS.  8 A to  8 D,  9 A to  9 D, and  10 A to  10 D , a photo-sensing cell receives light not only from a corresponding region of the color separation lens array  340  in the vertical direction, but also from a plurality of other regions around the region. Therefore, when the first to fourth regions  341 ,  342 ,  343 , and  344  are not added along the edges of the color separation lens array  340 , the amount of light incident on the photo-sensing cells arranged along the edges of the sensor substrate  500  may decrease, and color purity may also decrease. 
     When the first to fourth regions  341 ,  342 ,  343 , and  344  are additionally arranged along the edges of the color separation lens array  340 , light may be provided to photo-sensing cells arranged along the edges of the sensor substrate  500  in the same manner as photo-sensing cells arranged inside the sensor substrate  500 . The example embodiments shown in  FIGS.  21  and  22    may also be applied to a color separation lens array including an arrangement of a plurality of nanoposts described above. 
       FIG.  23    illustrates a principle of improving light efficiency by a color separation lens array in the image sensor  200  according to the example embodiment. Hereinafter, for convenience, a reference numeral of the color separation lens array is indicated as  300 , but the color separation lens arrays  300 ,  330 ,  400 ,  450 , and  460  of various example embodiments described above may be applied thereto. 
     Referring to  FIG.  23   , as the image sensor  200  includes the color separation lens array  300  that separates light according to color to make the separated light enter the plurality of photo-sensing cells  511 ,  512 , and  513  of the sensor substrate  500 , a light component incident through a region of the color separation lens array  300  corresponding to a pixel of the image sensor  200  is incident on the pixel, and in addition, light incident on regions corresponding to a plurality of surrounding pixels surrounding the pixel, for example, four or eight surrounding pixels, is also incident on the pixel by the color separation lens array  300 . 
     As illustrated in  FIG.  23   , a light component incident on a pixel R 33  may be the sum of a red light component, which is incident through a region of the color separation lens array  300  corresponding to the pixel R 33 , and red light components, which are branched by the color separation lens array  300  from light incident on regions corresponding to pixels G 23 , G 32 , G 34 , and G 43  and pixels B 22 , B 24 , B 42 , and B 44  and are incident on the pixel R 33 . 
     By applying the color separation lens array  300  for separating light according to color to the image sensor  200 , as described above, in addition to a light component incident on a unit pixel, incident light corresponding to the light component from surrounding pixels may be condensed, and thus, light efficiency may be improved. 
       FIGS.  24 A to  24 C  illustrate an increase in the amount of light incident on a unit pixel of the Bayer pattern array of the image sensor  200  to which the color separation lens array  300  is applied.  FIG.  24 A  illustrates an increase in the amount of light incident on a red pixel of the unit pixel,  FIG.  24 B  illustrates an increase in the amount of light incident on two green pixels of the unit pixel, and  FIG.  24 C  illustrates an increase in the amount of light incident on a blue pixel of the unit pixel. In the Bayer pattern array, the unit pixel includes a red pixel R, two green pixels G, and a blue pixel B. The red pixel R and the blue pixel B may be arranged in a diagonal direction with each other, and the two green pixels G may be arranged in other diagonal direction crossing the arrangement of the red pixel R and the blue pixel B in the diagonal direction. The Bayer pattern array corresponds to a plurality of two-dimensional arrays of such unit pixels. With reference to  FIGS.  24 A to  24 C , an example of a unit pixel including a red pixel R 33 , two green pixels G 34  and G 43 , and a blue pixel B 44  will be described. 
     Referring to  FIG.  24 A , a light component incident on a red pixel R 33  may include a red light component, which is incident through a region of the color separation lens array  300  corresponding to the red pixel R 33 , and red light components, which are branched by the color separation lens array  300  from light incident on regions corresponding to green pixels G 23 , G 32 , G 34 , and G 43  positioned in horizontal and vertical directions and blue pixels B 22 , B 24 , B 42 , and B 44  positioned in a diagonal direction and are incident on the red pixel R 33 . 
     Referring to  FIG.  24 B , a light component incident on a green pixel G 34  may include a green light component, which is incident through a region of the color separation lens array  300  corresponding to the green pixel G 34 , and green light components, which are branched by the color separation lens array  300  from light incident on regions corresponding to red pixels R 33  and R 35  and blue pixels B 24  and B 44  positioned in the horizontal and vertical directions and are incident on the green pixel G 34 . In addition, the light component incident on the green pixel G 34  may include green light components, which are branched by the color separation lens array  300  from light incident on regions corresponding to green pixels G 23 , G 25 , G 43 , and G 45  positioned in the diagonal direction and are incident on the green pixel G 34 . 
     A light component incident on a green pixel G 43  may include a green light component, which is incident through a region of the color separation lens array  300  corresponding to the green pixel G 43 , and green light components, which are branched by the color separation lens array  300  from light incident on regions corresponding to blue pixels B 42  and B 44  and red pixels R 33  and R 53  positioned in the horizontal and vertical directions and are incident on the green pixel G 43 . In addition, the light component incident on a green pixel G 43  may include green light components, which are branched by the color separation lens array  300  from light incident on regions corresponding to green pixels G 32 , G 34 , G 52 , and G 54  positioned in the diagonal directions and are incident on the green pixel G 43 . 
     Referring to  FIG.  24 C , a light component incident on a blue pixel B 44  may include a blue light component, which is incident through a region of the color separation lens array  300  corresponding to the blue pixel B 44 , and blue light components, which are branched by the color separation lens array  300  from light incident on regions corresponding to green pixels G 34 , G 43 , G 45 , and G 54  positioned in horizontal and vertical directions and red pixels R 33 , R 35 , R 53 , and R 55  positioned in the diagonal directions and are incident on the blue pixel B 44 . 
     As such, by applying the color separation lens array  300  for separating light according to color to the image sensor  200 , the amount of light for a color corresponding to a certain pixel may be additionally secured from four or eight surrounding pixels surrounding the certain pixel, and thus, light efficiency may be improved. 
       FIG.  25    illustrates point spread function (PSF) characteristics by the color separation lens array  300  of the image sensor  200  according to an example embodiment. The sizes of PSF bar graphs at upper left, upper right, lower left, and lower right of  FIG.  25    represents normalized values.  FIG.  25    illustrates color separation characteristics by regions of the color separation lens array  300  corresponding to a red pixel R, two green pixels G, and a blue pixel B, which are in a unit pixel of a Bayer pattern array, when red light is incident on the color separation lens array  300 . 
     As can be seen from the PSF bar graph shown at the upper left of  FIG.  25   , when red light is incident on a region of the color separation lens array  300  corresponding to the red pixel R, a red light component reaches only the red pixel R. As can be seen from the PSF bar graph at the upper right of  FIG.  25   , when red light is incident on a region of the color separation lens array  300  corresponding to the green pixel G, a larger amount of red light components reaches red pixels R positioned at both sides of the green pixel G in the vertical direction. As can be seen from the PSF bar graph at lower left of  FIG.  25   , when red light is incident on a region of the color separation lens array  300  corresponding to the green pixel G, a larger amount of red light components reaches red pixels R positioned at both sides of the green pixel G in the horizontal direction. As can be seen from the PSF bar graph at the lower right of  FIG.  35   , when red light is incident on a region of the color separation lens array  300  corresponding to the blue pixel B, a larger amount of red light components reaches red pixels R positioned at both sides of the blue pixel B in the diagonal directions. 
       FIG.  26    is a related example, which illustrates PSF characteristics by an absorption-type color filter when the absorption-type color filter is applied to an image sensor. The sizes of PSF bar graphs at the upper left, upper right, lower left, and lower right of  FIG.  26    represents normalized values.  FIG.  26    illustrates PSF bar graphs for a red filter region R, two green filter regions G, and a blue filter region B of the absorption-type color filter, which correspond to a unit pixel of a Bayer pattern array, when red light is incident on the absorption-type color filter having the Bayer pattern array. 
     As can be seen from the PSF bar graph shown at the upper left of  FIG.  26   , when red light is incident on the red filter region R, a red light component reaches only a red pixel R. As can be seen from the PSF bar graph at the upper right of  FIG.  26   , when red light is incident on the green filter region G, a smaller amount of red light components reaches red pixels R, which are positioned at both sides of a green pixel G, than the green pixel G in the vertical direction. As can be seen from the PSF bar graph at the lower left of  FIG.  26   , when red light is incident on the green filter region G, a smaller amount of red light components reaches red pixels R, which are positioned at both sides of a green pixel G, than the green pixel G in the horizontal direction. As can be seen from the PSF bar graph at the lower right of  FIG.  26   , when red light is incident on the blue filter region B, a smaller amount of red light components reaches red pixels R, which are positioned at both sides of a blue pixel B, than the blue pixel B in the diagonal direction. As can be seen from the comparison of PSF bar graph distributions of  FIGS.  25  and  26   , by applying the color separation lens array  300  for separating light according to color to the image sensor  200 , the amount of light for a color corresponding to a certain pixel may be additionally secured from four or eight surrounding pixels surrounding the certain pixel, and thus, light efficiency may be improved. On the other hand, in the related image sensor to which the absorption-type color filter is applied, it is difficult to additionally secure the amount of light for a color corresponding to a certain pixel from surrounding pixels, and thus, light efficiency is significantly lower than that of a case in which the color separation lens array  300  according to an example embodiment is employed. 
     By applying the color separation lens array  300  for separating light according to color to the image sensor  200 , the amount of light for a color corresponding to a certain pixel is additionally secured from four or eight surrounding pixels surrounding the certain pixel, and information of the surrounding pixels is convoluted into the certain pixel. According to the image acquisition apparatus  100  according to the example embodiment, a deconvolution kernel may be defined with respect to a local color patch as shown in  FIGS.  27 A to  27 D  considering the light branching characteristics of the color separation lens array  300 . 
     When the pixel arrangement of the image sensor  200  forms a Bayer pattern arrangement, a unit pixel includes two green pixels G, a red pixel R, and a blue pixel B, and as shown in  FIG.  27 A , blue pixels B may be positioned on both sides of a green pixel G in a horizontal direction, red pixels R are positioned on both sides of the green pixel in a vertical direction, and green pixels G are positioned on both sides of the green pixel G in two diagonal directions. As shown in  FIG.  27 B , green pixels G are positioned on both sides of a red pixel R in the horizontal and vertical directions, and blue pixels B are positioned on both sides of the red pixel R in the two diagonal directions. As shown in  FIG.  27 C , green pixels G are positioned on both sides of a blue pixel B in the horizontal and vertical directions, and red pixels R are positioned on both sides of the blue pixel B in the two diagonal directions. As shown in  FIG.  27 D , red pixels R are positioned on both sides of a green pixel G in the horizontal direction, blue pixels B are positioned on both sides of the green pixel G in the vertical direction, and green pixels G are positioned on both sides of the green pixel G in the two diagonal directions. 
     Therefore, according to the image acquisition apparatus  100  according to the example embodiment, an image for each color may be composed using a deconvolution kernel branched by the color separation lens array  300 , as shown in  FIG.  28   , and with respect to the image for each color, a color image may be composed by interpolating color values of pixels having empty colors by using color values of surrounding pixels. To this end, the image acquisition apparatus  100  may include the signal processing unit  250  to configure a deconvolution kernel for each color pixel branched by the color separation lens array  300 . 
       FIG.  29    illustrates a schematic configuration of the signal processor  250  of the image acquisition apparatus  100  according to the example embodiment. 
     Referring to  FIG.  29   , the signal processor  250  performs, by using a PSF Red, Green, and Blue corresponding to each color pixel by the color separation lens array  300 , deconvolution on sensing signals RAW image of the plurality of photo-sensing cells  511 ,  512 , and  513  of the sensor substrate  500  to process a color image signal acquired by the image sensor  200 . As a result, a color image signal in which information of surrounding pixels convoluted by the color separation lens array  300  that is erased may be obtained by the signal processor  250 . The color image signal obtained by the signal processor  250  may include a Bayer-equivalent raw image similar to an image of a Bayer pattern array obtained when an absorption-type color filter, which is hardly influenced by surrounding pixels is applied. 
     The signal processor  250  may be provided in a logic circuit of the image sensor  200  or may be provided in a companion chip. In addition, the signal processor  250  may be provided in the image processor  160 . 
     The color image signal acquired by the signal processor  250  is input to the image processor  160 . The image processor  160  processes the color image signal obtained by the signal processor  250  to form a color image. 
     The image processor  160  uses images for color (Green, Red, and Blue RAW images) obtained by the signal processor  250  to compose a color image, and forms the color image by performing demosaicing, which interpolates color values of empty pixels of each color by using color values of surrounding pixels. Demosaicing for forming a color image may be applied in various ways. For example, a bilinear demosaicing method as shown in  FIG.  30    may be used to form a color image, and in addition, various demosaicing schemes may be used. 
       FIG.  30    illustrates a bilinear demosaicing scheme. 
     Referring to  FIG.  30   , considering pixels R 33 , B 44 , G 43 , and G 34  constituting a unit pixel, in the case of the pixel R 33 , a red value may be R 33 , a green value may be interpolated using the average of color values of surrounding green pixels, that is, (G 23 +G 34 +G 32 +G 43 )/4, and a blue value may be interpolated using the average of color values of surrounding blue pixels, that is, (B 22 +B 24 +B 42 +B 44 )/4. In the case of the pixel B 44 , a blue value may be B 44 , a green value may be interpolated using the average of color values of surrounding green pixels, that is, (G 34 +G 43 +G 45 +G 54 )/4, and a red value may be interpolated using the average of color values of surrounding red pixels, that is, (R 33 +R 35 +R 53 +R 55 )/4. In the case of the pixel G 43 , a green value may be G 43 , a blue value may be interpolated using the average of color values of surrounding blue pixels, that is, (B 42 +B 44 )/2, and a red value may be interpolated using the average of color values of surrounding red pixels, that is, (R 33 +R 53 )/2. In the case of the pixel G 34 , a green value may be G 34 , a blue value may be interpolated using the average of color values of surrounding blue pixels, that is, (B 24 +B 44 )/2, and a red value may be interpolated using the average of color values of surrounding red pixels, that is, (R 33 +R 35 )/2. 
     As such, a color image formed by the image processor  160  may be displayed through the display  170  or may be stored in the memory  180  or the like. 
       FIG.  31    illustrates an image acquisition process using the image acquisition apparatus  100  according to an example embodiment. 
     Referring to  FIG.  31   , when an input image is x, a PSF of the color separation lens array  300  is c, and a measured image is b, the measured image b sensed by the image sensor  200  corresponds to a convolution of the input image x and the PSF c of the color separation lens array  300 , as in Equation 4 below.
 
 b=x*c   [Equation 4]
 
     In order to reconstruct an input image from a signal sensed by the image sensor  200 , deconvolution may be performed. When an image reconstructed through a deconvolution process using an inverse kernel c −1  of the PSF of the color separation lens array  300  is {tilde over (x)}, the reconstructed image may be ideally expressed as Equation 5 below. 
     
       
         
           
             
               
                 
                   
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                     Equation 
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     According to the image acquisition apparatus  100  according to the example embodiment, a correction term may be further included to prevent divergence when the high frequency component of F(c) is close to zero. When a Wiener filtering method including a signal to noise ratio (SNR) of an image is used, a reconstructed image may be expressed as in Equation 6 below. 
     
       
         
           
             
               
                 
                   
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     In Equation 6, SNR may correspond to the standard deviation of an intermediate signal/image noise of an image. When the correction term is applied as in Equation 6, less amplification is performed when there is a high frequency component. 
     Equation 6 shows a case in which the Wiener filtering method including the SNR of the image is used as a method of performing deconvolution while reducing noise amplification. This is only an example, and in order to reduce the noise amplification in the deconvolution, various methods may be used. 
     The image acquisition apparatus  100 , to which the image sensor  200  according to the example embodiments described above is applied, may be implemented as various optical devices such as a camera or electronic apparatuses. For example, these electronic apparatuses are, for example, smart phones, mobile phones, personal digital assistants (PDAs), laptop computers, tablets, personal computers (PCs), various portable devices, home appliances, security cameras, medical cameras, and automobiles, Internet of Things (IoT), mobile computing device, or non-mobile computing device, but are not limited thereto. 
       FIG.  32    is a schematic block diagram of an electronic apparatus including the image acquisition apparatus  100  according to an example embodiment. The electronic apparatus includes the image acquisition apparatus  100 , a processor  190 , a memory  180 , a display  170 , and a bus  110 . The image acquisition apparatus  100  acquires image information about an external object under the control of the processor  190  and provides the image information to the processor  190 . The processor  190  may store the image information provided from the image acquisition apparatus  100  in the memory  180  through the bus  110 , and output the image information stored in the memory  180  to the display  170  to be displayed to the user. Also, the processor  190  may perform various image processing on image information provided from the image acquisition apparatus  100 . 
       FIGS.  33  to  43    illustrate various examples of an electronic apparatus to which an image acquisition apparatus according to an example embodiment may be applied. 
     The image acquisition apparatus according to the example embodiment may be applied to various multimedia apparatuses having an image capturing function. For example, the image acquisition apparatus according to the example embodiment may be applied to a camera  1000  as shown in  FIG.  33   . The camera  1000  may be a digital camera or a digital camcorder. 
     Referring to  FIG.  34   , the camera  1000  may include an imaging lens unit  120 , an image sensor  200 , a processor  190 , and the like.  FIG.  34    illustrates configurations of the imaging lens assembly  120  and the image sensor  200 , which are controlled according to control signals provided from the processor  190 , from among the components of the image acquisition apparatus  100  applied to the camera  1000 . The main configuration of the image acquisition apparatus  100  is illustrated in  FIG.  1   , and the main configuration of the image sensor  200  is illustrated in  FIG.  2   . 
     The imaging lens assembly  120  forms an optical image by focusing light reflected from an object OBJ. The imaging lens unit  120  may include an objective lens  121 , a lens driver  122 , a diaphragm  123 , and a diaphragm driver  124 . In  FIG.  34   , only one lens is representatively shown for convenience, but in fact, the objective lens  121  may include a plurality of lenses having different sizes and shapes. The lens driver  122  may communicate information about focus detection with the processor  190 , and may adjust the position of the objective lens  121  according to a control signal provided from the processor  190 . The lens driver  122  may move the objective lens  121  to adjust the distance between the objective lens  121  and the object OBJ, or may adjust the positions of individual lenses in the objective lens  121 . As the objective lens  121  is driven by the lens driver  122 , the focus to the object OBJ may be adjusted. The camera  1000  may have an auto focus function. 
     The diaphragm driver  124  may communicate information about the amount of light with the processor  190 , and may adjust the diaphragm  123  according to a control signal provided from the processor  190 . For example, the diaphragm driver  124  may increase or decrease an aperture of the diaphragm  123  according to the amount of light entering the camera  1000  through the objective lens  121 , and may adjust the opening time of the diaphragm  123 . 
     The image sensor  200  may generate an electrical image signal based on the intensity of incident light. The image sensor  200  may include a pixel array  210 , a timing controller  240 , and an output circuit  230 . The image sensor  200  may further include the row decoder  220  shown in  FIG.  2   . The light passed through the objective lens  121  and diaphragm  123  may form an image of the object OBJ on a light receiving surface of the pixel array  210 . The pixel array  210  may be a charge coupled device (CCD) or a complementary metal oxide semiconductor (CMOS) that converts an optical signal into an electrical signal. 
     The pixel array  210  of the image sensor  200  may include additional pixels for performing an auto focus (AF) function or a distance measurement function. In addition, the pixel array  210  may include the above-described color separation lens array. The pixel array  210  of the image sensor  200  may acquire an image signal for each color by converting an optical image formed by the imaging lens assembly  120  into an electrical signal, In this case, the color separation lens array forms a phase distribution for condensing light having different wavelengths on adjacent photo-sensing cells of a sensor substrate to separate incident light according to color, and thus, in addition to a light component incident on a unit pixel, incident light corresponding to the light component from surrounding pixels may be condensed and thus light efficiency may be improved The acquired image signal for each color is processed by the signal processor  250 , and the image processor  160  forms a color image from the image signal for each color processed by the signal processor  250 . In this case, the signal processor  250  performs, by using a PSF corresponding to each color pixel by the color separation lens array, deconvolution on sensing signals of a plurality of photo-sensing cell to thereby process the acquired image signal for each color, and thus, higher light efficiency and clearer images may be acquired. The images formed by the image processor  160  may be stored in the memory  180  and may also be displayed on the display  170 . 
     The processor  190  may control the overall operation of the camera  1000  and may have an image processing function. For example, the processor  190  may provide a control signal for operation of each component, such as the lens driver  122 , the diaphragm driver  124 , and the timing controller  240 . 
     The image acquisition apparatus  100  according to the example embodiment may be applied to a mobile phone or a smart phone  3000  shown in  FIG.  35   , a tablet or a smart tablet  3100  shown in  FIG.  36   , a notebook computer  3200  shown in  FIG.  37   , a television or a smart television  3300  shown in  FIG.  38   , in addition to the camera  1000 . For example, the smart phone  3000  or the smart tablet  3100  may include a plurality of high resolution cameras each equipped with a high resolution image sensor. High resolution cameras may be used to extract depth information of objects in an image, adjust the out-of-focusing of an image, or automatically identify objects in an image. 
     In addition, the image acquisition apparatus  100  may be applied to a smart refrigerator  3400  shown in  FIG.  39   , a security camera  3500  shown in  FIG.  40   , a robot  3600  shown in  FIG.  41   , a medical camera  3700  shown in  FIG.  42   , and the like. For example, the smart refrigerator  3400  may automatically recognize food in a refrigerator using an image sensor and inform the user of the existence of a specific food, the type of food that has been put in or released, and the like through the smart phone. The security camera  3500  may provide an ultra-high resolution image and may have a high sensitivity to allow objects or people in the image to be recognized even in a dark environment. The robot  3600  may enter a disaster or industrial site where humans cannot directly access to provide high resolution images. The medical camera  3700  may provide high resolution images for diagnosis or surgery and may dynamically adjust the field of view. 
     Furthermore, the image acquisition apparatus  100  may be applied to a vehicle  3800  as shown in  FIG.  43   . The vehicle  3800  may include a plurality of vehicle cameras  3810 ,  3820 ,  3830 , and  3840  arranged in various positions of the vehicle  3800 . Each of the vehicle cameras  3810 ,  3820 ,  3830 , and  3840  may include the image acquisition apparatus  100  according to the example embodiment. The vehicle  3800  may provide a variety of information about the interior or surroundings of the vehicle  3800  to a driver using a plurality of vehicle cameras  3810 ,  3820 ,  3830 , and  3840 , and may automatically recognize objects or people in the image to provide information necessary for autonomous driving. 
     According to an apparatus and method of acquiring images, according to an example embodiment, an image sensor uses a color separation lens array that includes a fine structure, which forms a phase distribution for condensing light having different wavelengths on adjacent photo-sensing cells, in each of a plurality of regions respectively facing a plurality of photo-sensing cells in a sensor substrate, and separates incident light according to color. Therefore, in addition to a light component incident on a unit pixel, incident light corresponding to the light component from surrounding pixels may be condensed, and thus, light efficiency may be improved. 
     In addition, a signal processor may perform, by using a PSF corresponding to each color pixel by the color separation lens array, deconvolution on sensing signals of a plurality of photo-sensing cell to process an image signal for each color acquired by the image sensor, and thus, higher light efficiency and clearer images may be obtained. 
     It should be understood that example embodiments described herein should be considered in a descriptive sense only and not for purposes of limitation. Descriptions of features or aspects within each example embodiment should typically be considered as available for other similar features or aspects in other embodiments. While example embodiments have been described with reference to the figures, it will be understood by those of ordinary skill in the art that various changes in form and details may be made therein without departing from the spirit and scope as defined by the following claims.