Patent Publication Number: US-11664401-B2

Title: Image sensor and electronic device including the same

Description:
CROSS-REFERENCE TO RELATED APPLICATION 
     This application claims priority to Korean Patent Application No. 10-2020-0016627, filed on Feb. 11, 2020, and Korean Patent Application No. 10-2020-0120027, filed on Sep. 17, 2020, in the Korean Intellectual Property Office, the disclosures of which are incorporated by reference herein in their entireties. 
     BACKGROUND 
     1. Field 
     Example embodiments consistent with the present disclosure relate to image sensors and electronic devices including the image sensors. 
     2. Description of Related Art 
     In general, image sensors use color filters to display images having various colors or detect the colors of incident light. However, color filters absorb all colors of light except for a corresponding color of each color filter, and thus, the optical efficiency of color filters may be low. For example, because RGB (red, green, and blue) color filters only transmit about ⅓ of incident light and absorb about ⅔ of the incident light, RGB color filters have an optical efficiency of only about 33% and result in large optical loss. 
     Recently, attempts to use color separation devices instead of color filters have been made to improve the optical efficiency of image sensors. Color separation devices are capable of separating the colors of incident light by using the diffraction or refraction of light which varies depending on the wavelength of light, and it is possible to adjust the directivity of light by using the refractive index and shape of color separation devices. Colors separated by color separation devices may be transmitted to corresponding pixels. However, the purity of colors separated by color separation devices of the related art is poor, and thus, improvements in color purity are needed. 
     SUMMARY 
     Example embodiments provide image sensors and electronic devices including the image sensors. 
     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 the presented embodiments of the disclosure. 
     According to an aspect of an example embodiment, there is provided an image sensor including: a light detector including a plurality of photosensitive cells configured to sense light; a color separation lens array provided above the light detector and including a plurality of pattern structures, the color separation lens array being configured to collect light having different wavelength spectra respectively on at least two photosensitive cells of the plurality of photosensitive cells; and a variable interlayer element configured to adjust an optical distance between the light detector and the color separation lens array. 
     The variable interlayer element may be further configured to adjust a physical distance between the light detector and the color separation lens array. 
     The variable interlayer element may include a microelectromechanical system actuator configured to drive a position of the color separation lens array. 
     The variable interlayer element may include: a variable shape structure including a variable shape material that is variable in shape according to an electrical signal applied thereto; and a signal application unit configured to apply the electrical signal to the variable shape structure. 
     The variable shape material may include a shape memory alloy or an electro-active polymer. 
     The variable interlayer element may include: a frame structure including a variable height region, provided with a stretchable membrane, and a reservoir region in which an optical fluid to be introduced into the variable height region is stored; and a signal application unit configured to apply a signal to move the optical fluid between the reservoir region and the variable height region for stretching or shrinking the stretchable membrane. 
     The variable interlayer element may include: a variable refractive index layer having a refractive index that is variable according to an electrical signal applied thereto; and a signal application unit configured to apply the electrical signal to the variable refractive index layer. 
     The variable refractive index layer may include LiNbO3, LiTaO3, potassium tantalate niobite (KTN), lead zirconate titanate (PZT), VO2, VO2O3, EuO, MnO, CoO, CoO2, LiCoO2, Ca2RuO4, or liquid crystal. 
     The image sensor may further include a processor configured to: control the variable interlayer element to form a plurality of optical distances that are different from each other, and obtain image data by processing signals sensed by the light detector respectively at the plurality of optical distances. 
     The processor may be configured to perform computations on the image data by using spectrum data set according to the optical distances for the color separation lens array. 
     The color separation lens array may include a plurality of regions respectively facing the plurality of photosensitive cells of the light detector and including at least one pattern structure, and the plurality of regions may be configured to collect light having different wavelength spectra respectively on adjacent photosensitive cells of the plurality of photosensitive cells. 
     The plurality of regions may include a first region, a second region, a third region, and a fourth region which each include at least one of the plurality of pattern structures, and the plurality of photosensitive cells may include first photosensitive cell, second photosensitive cell, third photosensitive cell, and fourth photosensitive cell which face the first region, the second region, the third region, and the fourth region, respectively. 
     The image sensor may have a pixel arrangement structure in which a plurality of unit pixels are arranged in a Bayer pattern according to the optical distance and the plurality of unit pixels include red, green, and blue pixels. 
     Shapes, arrangements, and sizes of pattern structures respectively provided in the first region, the second region, the third region, and the fourth region may be determined such that immediately after passing through the color separation lens array, light having a first wavelength has a phase difference of 2Nπ at positions corresponding to a center portion of the first photosensitive cell and a center portion of the fourth photosensitive cell and a phase difference of (2N−1)π at positions corresponding to center portion of the second photosensitive cell and a center portion of the third photosensitive cell, where N is an integer greater than 0. 
     Shapes, arrangements, and sizes of pattern structures respectively provided in the first region, the second region, the third region, and the fourth region may be determined such that immediately after passing through the color separation lens array, light having a second wavelength has a phase difference of 2Mπ at a position corresponding to a center portion of the second photosensitive cell, a phase difference of (2M−1)π at positions corresponding to a center portion of the first photosensitive cell and a center portion of the fourth photosensitive cell, and a phase difference of greater than (2M−2)π and less than (2M−1)π at a position corresponding to a center portion of the third photosensitive cell, where M is an integer greater than 0. 
     Shapes, arrangements, and sizes of pattern structures respectively provided in the first region, the second region, the third region, and the fourth region may be determined such that immediately after passing through the color separation lens array, light having a third wavelength has a phase difference of 2Lπ at a position corresponding to a center portion of the third photosensitive cell, a phase difference of (2L−1)π at positions corresponding to a center portions of the first photosensitive cell and a center portion of the fourth photosensitive cell, and a phase difference of greater than (2L−2)π and less than (2L−1)π at a position corresponding to a center portion of the second photosensitive cell, where L is an integer greater than 0. 
     The plurality of pattern structures may include a plurality of nano-posts, and nano-posts provided in the first region, nano-posts provided in the second region, nano-posts provided in the third region, and nano-posts provided in the fourth region may be different from each other in at least one of shape, size, and arrangement. 
     Nano-posts, which are provided in regions corresponding to green pixel among the first region, the second region, the third region, and the fourth region, may be arranged according to distribution rules that are different in a first direction and a second direction perpendicular to the first direction. 
     Nano-posts, which are provided in regions corresponding to blue and red pixels among the first region, the second region, the third region, and the fourth region, may be arranged according to symmetrical distribution rules in the first direction and the second direction. 
     The plurality of pattern structures may include a first pattern structure, a second pattern structure, a third pattern structure, and a fourth pattern structure formed in the first region, the second region, the third region, and the fourth region, respectively. 
     The first pattern structure may include a first dielectric having a first refractive index and provided in a first form, and a second dielectric having a second refractive index less than the first refractive index and filled in gaps of the first dielectric provided in the first form, and the first dielectric may be present in any vertical cross-section of the first pattern structure. 
     The first region and the fourth region may correspond to green pixel, the second region corresponds to blue pixel, and the third region corresponds to red pixel, and the first pattern structure and the fourth pattern structure may have a 2-fold symmetrical form, the second pattern structure and the third pattern structure may have a 4-fold symmetrical form, and the fourth pattern structure may have a form rotated 90 degrees with respect to the first pattern structure. 
     According to an aspect of an example embodiment, there is provided an photographing device including: an imaging unit configured to form an optical image by condensing light reflected from an object; and an image sensor configured to convert the optical image formed by the imaging unit into an electrical signal, wherein the image sensor includes: a light detector including a plurality of photosensitive cells configured to sense light; a color separation lens array provided above the light detector and including a plurality of pattern structures, the color separation lens array being configured to collect light having different wavelength spectra respectively on at least two photosensitive cells of the plurality of photosensitive cells; and a variable interlayer element configured to adjust an optical distance between the light detector and the color separation lens array. 
     According to an aspect of an example embodiment, there is provided an electronic device including a photographing device, the photographing device including: an imaging unit configured to form an optical image by condensing light reflected from an object; and an image sensor configured to convert the optical image formed by the imaging unit into an electrical signal, wherein the image sensor includes: a light detector including a plurality of photosensitive cells configured to sense light; a color separation lens array provided above the light detector and including a plurality of pattern structures, the color separation lens array being configured to collect light having different wavelength spectra respectively on at least two photosensitive cells of the plurality of photosensitive cells; and a variable interlayer element configured to adjust an optical distance between the light detector and the color separation lens array. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       The above and other aspects, features, and advantages of certain example embodiments of the disclosure will be more apparent from the following description taken in conjunction with the accompanying drawings, in which: 
         FIG.  1    is a block diagram illustrating an image sensor according to an example embodiment; 
         FIG.  2    is a conceptual view schematically illustrating a pixel array configuration of an image sensor according to an example embodiment; 
         FIGS.  3 A and  3 B  are different cross-sectional views schematically illustrating the pixel array configuration of the image sensor of example embodiments; 
         FIGS.  4 A and  4 B  are example plan views illustrating an arrangement of pixels of the image sensor and an arrangement of photosensitive cells of the image sensor which correspond to pixel regions according to example embodiments; 
         FIGS.  4 C and  4 D  are an example plan view illustrating fine structures arranged in a plurality of regions of a color separation lens array according to an example embodiment, and an enlarged plan view illustrating a region of  FIG.  4 C , 
         FIG.  5    is a conceptual view illustrating that incident light has different spectra according to the distance from the color separation lens array in the image sensor according to an example embodiment; 
         FIGS.  6 A to  6 D  are graphs illustrating spectra of light which are separately incident on a plurality of photosensitive cells for different optical distances between the color separation lens array and a light detector in the image sensor according to example embodiments; 
         FIG.  7    is a flow chart schematically illustrating image acquisition processes of the image sensor according to an example embodiment; 
         FIG.  8    is a cross-sectional view schematically illustrating a pixel array configuration of an image sensor according to another example embodiment; 
         FIG.  9    is a cross-sectional view schematically illustrating a pixel array configuration of an image sensor according to another example embodiment; 
         FIG.  10    is a cross-sectional view schematically illustrating a pixel array configuration of an image sensor according to another example embodiment; 
         FIG.  11    is a cross-sectional view schematically illustrating a pixel array configuration of an image sensor according to another example embodiment; 
         FIG.  12    is an example plan view illustrating a unit pattern array of a color separation lens array provided in an image sensor according to another example embodiment; 
         FIG.  13    is an example plan view illustrating a unit pattern array of a color separation lens array provided in an image sensor according to another example embodiment; 
         FIG.  14    is an example plan view schematically illustrating a unit pattern array of a color separation lens array provided in an image sensor according to another example embodiment; 
         FIGS.  15 A to  15 D  are plan views respectively illustrating first to fourth regions of the unit pattern array shown in  FIG.  14   ; 
         FIG.  16    is an example plan view illustrating a unit pattern array of a color separation lens array according to another example embodiment; 
         FIG.  17    is an example plan view illustrating a unit pattern array of a color separation lens array according to another example embodiment; 
         FIG.  18    is a block diagram schematically illustrating an electronic device including an image sensor according to an example embodiment; and 
         FIGS.  19  to  29    are views illustrating various multimedia devices as examples of electronic devices to which images sensors are applied according to example embodiments. 
     
    
    
     DETAILED DESCRIPTION 
     Hereinafter, embodiments will be described with reference to the accompanying drawings. The embodiments described herein are for illustrative purposes only, and various modifications may be made therein. In this regard, the present 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. 
     In the drawings, like reference numerals refer to like elements, and the sizes of elements may be exaggerated for clarity of illustration. 
     In the following description, when an element is referred to as being “above” or “on” another element, it may be directly on the other element while making contact with the other element or may be above the other element without making contact with the other element. 
     Although the terms “first” and “second” are used to describe various elements, these terms are only used to distinguish one element from another element. These terms do not limit elements to having different materials or structures. 
     The terms of a singular form may include plural forms unless otherwise mentioned. It will be further understood that the terms “comprises” and/or “comprising” used herein specify the presence of stated features or elements, but do not preclude the presence or addition of one or more other features or elements. 
     In the present disclosure, terms such as “unit” or “module” may be used to denote a unit that has at least one function or operation and is implemented with hardware, software, or a combination of hardware and software. 
     An element referred to with the definite article or a demonstrative pronoun may be construed as the element or the elements even though it has a singular form. 
     Operations of a method may be performed in appropriate order unless explicitly described in terms of order or described to the contrary. In addition, examples or exemplary terms (for example, “such as” and “etc.”) are used for the purpose of description and are not intended to limit the scope of the disclosure unless defined by the claims. 
       FIG.  1    is a block diagram schematically illustrating an image sensor  1000  according to an example embodiment, and  FIG.  2    is a conceptual view illustrating a pixel array configuration of the image sensor  1000  according to an example embodiment. 
     Referring to  FIG.  1   , according to an example embodiment, the image sensor  1000  may include an pixel array  1100 , a timing controller (T/C)  1010 , a row decoder  1020 , an output circuit  1030 , and a processor  1040  which is configured to control the pixel array  1100 , the timing controller  1010 , and the output circuit  1030 , and process image signals output through the output circuit  1030 . The image sensor  1000  of the example embodiment may include a charge coupled device (CCD) image sensor or a complementary metal oxide semiconductor (CMOS) image sensor. 
     The pixel array  1100  includes a plurality of pixels which are two-dimensionally arranged in a plurality of rows and a plurality of columns. The row decoder  1020  selects one of the rows of the pixel array  1100  in response to a row address signal which is output from the timing controller  1010 . The output circuit  1030  outputs, on a column basis, light detection signals received from a plurality of pixels arranged in the selected row. To this end, the output circuit  1030  may include a column decoder and an analog-to-digital converter (ADC). For example, the output circuit  1030  may include a plurality of ADCs which are arranged between the column decoder and the pixel array  1100  respectively for the columns. Alternatively, the output circuit  1030  may include an ADC which is arranged at an output end of the column decoder. According to example embodiments, the timing controller  1010 , the row decoder  1020 , the output circuit  1030 , and the processor  1040  may be implemented as a single chip, or may be implemented as separate chips. 
     As shown in  FIG.  2   , the pixel array  1100  includes a light detector  100  including a plurality of photosensitive cells for sensing light, a color separation lens array  700  arranged above the light detector  100  and including a plurality of pattern structures PS, and a variable interlayer element  500  configured to adjust an optical distance OL between the light detector  100  and the color separation lens array  700 . 
     The color separation lens array  700  is configured to split incident light such that light having different wavelength spectra may be incident on at least two different cells of the light detector  100 . For this, factors such as the sizes, positions, or arrangement of the pattern structures PS of the color separation lens array  700  may be set. The color separation lens array  700  may include a plurality of regions respectively facing the photosensitive cells of the light detector  100 , and immediately after incident light passes through the color separation lens array  700 , the light may have a predetermined phase distribution according to the arrangement of the regions and the pattern structures PS of the color separation lens array  700 . 
     When the light having the predetermined phase distribution is incident on the light detector  100  after proceeding a predetermined distance from the color separation lens array  700 , the wavelength spectrum of the light incident on the photosensitive cells of the light detector  100  is determined according to the predetermined distance. The predetermined distance is an optical length OL, which is determined by the refractive index (n) of a medium ME between the color separation lens array  700  and the light detector  100  and the physical distance S between the color separation lens array  700  and the light detector  100 , as OL=n*S. 
     According to an example embodiment, the pixel array  1100  of the image sensor  1000  includes the variable interlayer element  500  configured to vary the optical distance OL. The variable interlayer element  500  includes the medium ME and a variable driving provider VS configured to variably drive the medium ME. The variable driving provider VS may include a structure and/or a variable signal application unit which are connected in various forms to the medium ME to adjust the optical distance OL. The variable driving provider VS may be controlled by the processor  1040 . For example, the processor  1040  may control the variable interlayer element  500  to form a predetermined optical distance OL, or a plurality of optical distances OL which are different from each other. The optical distance OL or optical distances OL which are set as described above may be used when the processor  1040  processes signals output from the optical detection unit  100 . This will be described with reference to  FIGS.  5  to  7   . The variable interlayer element  500  may vary the physical distance S between the light detector  100  and the color separation lens array  700 , or the refractive index of the medium ME between the light detector  100  and the color separation lens array  700 . In the medium ME and the structure connected in various forms to the medium ME, elements positioned between the color separation lens array  700  and the light detector  100  may include a light-transmitting material. The light detector  100  may be positioned at a plurality of positions depending on the optical distance OL determined by the variable interlayer element  500 , and optical information may be obtained at the positions based on different spectra. 
     Each element of the pixel array  1100  will now be described. 
       FIGS.  3 A and  3 B  are different cross-sectional views schematically illustrating the pixel array  1100  of the image sensor  1000  according to example embodiments, and  FIGS.  4 A and  4 B  are plan views illustrating an arrangement of pixels of the image sensor  1000  and an arrangement of photosensitive cells of the image sensor  1000  which correspond to pixel regions according to example embodiments.  FIG.  4 C  is an example plan view illustrating a plurality of pattern structures PS arranged in a plurality of regions of the color separation lens array  700  according to an example embodiment, and  FIG.  4 D  is an enlarged plan view illustrating a region of  FIG.  4 C . The pixel array  1100  includes the light detector  100  including the photosensitive cells such as first photosensitive cells  110 , second photosensitive cells  120 , third photosensitive cells  130 , and fourth photosensitive cells  140  which are configured to sense light; and the color separation lens array  700  arranged above the light detector  100  at a distance from the light detector  100 . 
     The light detector  100  may include the first photosensitive cells  110 , the second photosensitive cells  120 , the third photosensitive cells  130 , and the fourth photosensitive cells  140  that are configured to convert light into electrical signals. The first photosensitive cells  110 , the second photosensitive cells  120 , the third photosensitive cells  130 , and the fourth photosensitive cells  140  may be alternately arranged. As shown in the cross-sectional view of  FIG.  3 A , the first photosensitive cells  110  and the second photosensitive cells  120  may be alternately arranged in a first direction (X direction), and as shown in another cross-sectional view of  FIG.  3 B  taken at a different position in a Y direction, the third photosensitive cells  130  and the fourth photosensitive cells  140  may be alternately arranged. This cell arrangement is for sensing incident light on a pixel basis, and for example, the first photosensitive cells  110  and the fourth photosensitive cells  140  may sense light having a first spectrum corresponding to first pixels P 1 , the second photosensitive cells  120  may sense light having a second spectrum corresponding to second pixels P 2 , and the third photosensitive cells  130  may sense light having a third spectrum corresponding to third pixels P 3 . Light having the first spectrum may be green light, light having the second spectrum may be blue light, and light having the third spectrum may be red light. However, this is a non-limiting example. In an example embodiment, because the optical distance OL between the light detector  100  and the color separation lens array  700  of the image sensor  1000  is variable, the first spectrum, the second spectrum, and the third spectrum may have different ratios of green light, red light, and blue light, and the ratios may vary depending on the optical distance OL. A separation film may be further formed at cell boundaries to separate cells. 
     The color separation lens array  700  includes the pattern structures PS, which are arranged according to a predetermined rule. Here, the rule is applied to parameters such as the shapes, sizes (width, height), spacing, and arrangement of the pattern structures PS, and the parameters may be determined depending on a target phase distribution for light incident on the color separation lens array  700 . The target phase distribution refers to a phase distribution that incident light has at a position immediately after passing through the color separation lens array  700 . 
     The pattern structures PS may include at least one selected from the group consisting of c-Si, p-Si, a-Si, a Group III-V compound semiconductor (GaP, GaN, GaAs, or the like), SiC, TiO 2 , and SiN. 
     The pattern structures PS may have a sub-wavelength shape dimension. The term “sub-wavelength” refers to a value less than the wavelength of incident light that is to have an intended phase distribution. At least one of the dimensions defining the shapes of the pattern structures PS may be a sub-wavelength dimension. 
     The pattern structures PS may be supported by a material of the medium ME arranged between the pattern structures PS and the light detector  100 . However, this is merely an example. In another example, the material of the medium ME may be air, and an additional support layer may be provided. In this case, the support layer may include any one selected from the group consisting of glass (fused silica, BK7, or the like), quartz, polymers (PMMA, SU-8, or the like), and plastics. The material of the medium ME or the support layer may have a refractive index lower than the refractive index of a material of the pattern structures PS. In addition, a protective layer for protecting the pattern structures PS may be further provided. The protective layer may include a dielectric material having a refractive index lower than the refractive index of the material of the pattern structures PS. 
     The pattern structures PS having a refractive index different from the refractive index of surrounding materials may change the phase of light passing through the pattern structures PS. This is due to a phase delay caused by the sub-wavelength shape dimension of the pattern structures PS, and the amount of phase delay is determined by factors such as the shape dimensions and arrangement of the pattern structures PS. The amount of phase delay occurring at each of the pattern structures PS of the color separation lens array  700  may be set such that incident light may have an intended phase distribution. 
     The pattern structures PS may be shaped, sized, and arranged to form a phase distribution for collecting light of different spectra onto the first photosensitive cells  110  and the second photosensitive cells  120  that are adjacent to each other. In addition, the pattern structures PS may be shaped, sized, and arranged to form a phase distribution for collecting light of different spectra onto the third photosensitive cells  130  and the fourth photosensitive cells  140  that are adjacent to each other. 
     The color separation lens array  700  is divided into a plurality of regions such as first regions  710 , second regions  720 , third regions  730 , and fourth regions  740 , which correspond to the first, second, third, and fourth photosensitive cells  110 ,  120 ,  130 , and  140  in a one-to-one manner. At least one pattern structure PS may be arranged in each of the first, second, third, and fourth regions  710 ,  720 ,  730 , and  740 , and at least one of the shapes, sizes, and arrangement of the pattern structures PS may vary depending on the first, second, third, and fourth regions  710 ,  720 ,  730 , and  740 . 
     As shown in  FIGS.  3 A and  3 B , the color separation lens array  700  may be divided into regions such that the first regions  710  and the first photosensitive cells  110  may correspond to each other, the second regions  720  and the second photosensitive cells  120  may correspond to each other, the third regions  730  and the third photosensitive cells  130  may correspond to each other, and the fourth regions  740  and the fourth photosensitive cells  140  may correspond to each other. The color separation lens array  700  includes a plurality of unit pattern arrays which are two-dimensionally arranged, and each of the unit pattern arrays includes four regions arranged in 2×2 form: that is, the first regions  710 , the second region  720 , the third region  730 , and the fourth region  740 . 
       FIGS.  3 A and  3 B  illustrate that the first, second, third, and fourth regions  710 ,  720 ,  730 , and  740 , and the first, second, third, and fourth photosensitive cells  110 ,  120 ,  130 , and  140  have the same size and face each other in a vertical direction, but this is a non-limiting example. A plurality of regions defined in a different form may correspond to a plurality of photosensitive cells. This also applies to other example embodiments described below. 
     The color separation lens array  700  may be divided into regions to split light and collect the split light on the first, second, third, and fourth photosensitive cells  110 ,  120 ,  130 , and  140  in such a manner that light having the first spectrum is collected on the first photosensitive cells  110  and the fourth photosensitive cells  140 , light having the second spectrum is collected on the second photosensitive cells  120 , and light having the third spectrum is collected on the third photosensitive cells  130 , and the sizes, shapes, and arrangement of the pattern structures PS may be determined according to the regions of the color separation lens array  700 . As illustrated in  FIG.  4 A , the arrangement of pixels in the pixel array  1100  may be similar to a Bayer pattern. Each unit pixel includes four quadrant regions to which two first pixels P 1 , one second pixel P 2 , and one third pixel P 3  are allocated. The unit pixels are repeatedly two-dimensionally arranged in the first direction (X direction) and a second direction (Y direction). Two first pixels P 1  are arranged in a diagonal direction in each unit pixel having a 2×2 array form, and one second pixel P 2  and one third pixel P 3  are arranged in the other diagonal direction in the unit pixel. As a whole, first and second rows are repeatedly arranged, wherein a plurality of first pixels P 1  and a plurality of second pixels P 2  are alternately arranged in the first direction in each of the first rows, and a plurality of third pixels P 3  and a plurality of first pixels P 1  are alternately arranged in the first direction in each of the second rows. The colors of the first pixels P 1 , the second pixels P 2 , and the third pixels P 3  are not fixed, but may be varied depending on the optical distance OL between the light detector  100  and the color separation lens array  700 . The colors or wavelength distributions of the first pixels P 1 , the second pixels P 2 , and the third pixels P 3  may be expressed by the first spectrum, the second spectrum, and the third spectrum, respectively. In addition, specific wavelength distribution forms of the first spectrum, the second spectrum, and the third spectrum may vary depending on the optical distance OL. 
     Referring to  FIG.  4 B , the first photosensitive cells  110 , the second photosensitive cells  120 , the third photosensitive cells  130 , and the fourth photosensitive cells  140  are two-dimensionally arranged in the first direction (X direction) and the second direction (Y direction) such that rows, in which the first photosensitive cells  110  and the second photosensitive cells  120  are alternately arranged, and rows, in which the third photosensitive cells  130  and the fourth photosensitive cells  140  are alternately arranged, may be alternately repeated. Therefore, the first photosensitive cells  110  or the fourth photosensitive cells  140  correspond to the first pixels P 1 , the second photosensitive cells  120  correspond to the second pixels P 2 , and the third photosensitive cells  130  correspond to the third pixels P 3 . 
     Referring to  FIGS.  4 B and  4 C , the first photosensitive cells  110  and the first regions  710  may correspond to some of the first pixels P 1 , the fourth photosensitive cells  140  and the fourth regions  740  may correspond to the rest of the first pixels P 1 , the second photosensitive cells  120  and the second regions  720  may correspond to the second pixels P 2 , and the third photosensitive cells  130  and the third regions  730  may correspond to the third pixels P 3 . 
     As illustrated in  FIG.  4 C , pattern structures PS having different cross-sectional areas may be arranged on center portions of the first pixels P 1 , the second pixels P 2 , and the third pixels P 3 , and pattern structures PS may be arranged on centers and intersections of boundaries between the first pixels P 1 , the second pixels P 2 , and the third pixels P 3 . The cross-sectional areas of the pattern structures PS arranged on the boundaries of the first pixels P 1 , the second pixels P 2 , and the third pixels P 3  may be less than the cross-sectional areas of the pattern structures PS arranged on the center portions of the first pixels P 1 , the second pixels P 2 , and the third pixels P 3 . 
       FIG.  4 D  illustrates a region of  FIG.  4 C , that is, an arrangement of pattern structures PS in first, second, third, and fourth regions  710 ,  720 ,  730 , and  740  which form a unit pattern array. In  FIG.  4 D , the pattern structures PS are denoted with p 1  to p 9  according to the positions of the pattern structures PS in the unit pattern array. Referring to  FIG.  4 D  illustrating the pattern structures PS, the cross-sectional area of a pattern structure p 1  arranged in a center portion of the first region  710  and the cross-sectional area of a pattern structure p 4  arranged in a center portion of the fourth region  740  are greater than the cross-sectional area of a pattern structure p 2  arranged on a center portion of the second region  720  and the cross-sectional area of a pattern structure p 3  arranged in a center portion of the third region  730 , and the cross-sectional area of a pattern structure p 2  arranged in a center portion of the second region  720  is greater than the cross-sectional area of a pattern structure p 3  arranged in a center portion of the third region  730 . However, this is only an example, and the pattern structures PS may be variously shaped, sized, and arranged. Here, the cross-sectional area of each pattern structure PS refers to the area of a cross-section of the pattern structure PS perpendicular to the height direction (Z direction) of the pattern structure PS. 
     The pattern structures PS provided in the first and fourth regions  710  and  740  corresponding to the first pixels P 1  may be distributed according to different distribution rules in the first direction (X direction) and the second direction (Y direction). For example, the pattern structures PS provided in the first and fourth regions  710  and  740  corresponding to the first pixels P 1  may be arranged with different sizes in the first direction (X direction) and the second direction (Y direction). Referring to  FIG.  4 D  illustrating the pattern structures PS, the cross-sectional area of a pattern structure p 5  positioned at the boundary of the first region  710  adjacent to the second region  720  in the first direction (X direction) is different from the cross-sectional area of a pattern structure p 6  positioned at the boundary of the first region  710  adjacent to the third region  730  in the second direction (Y direction). Similarly, the cross-sectional area of a pattern structure p 7  positioned at the boundary of the fourth region  740  adjacent to the third region  730  in the first direction (X direction) is different from the cross-sectional area of a pattern structure p 8  positioned at the boundary of the fourth region  730  adjacent to the second region  720  in the second direction (Y direction). 
     The pattern structures PS provided in the second region  720  corresponding to the second pixel P 2  and the third region  730  corresponding to the third pixel P 3  may be arranged according to symmetrical distribution rules in the first direction (X direction) and the second direction (Y direction). As shown in  FIG.  4 D , among the pattern structures PS, the cross-sectional area of pattern structures p 5  arranged at the boundaries between the second region  720  and regions adjacent to the second region  720  in the first direction (X direction) is equal to the cross-sectional area of pattern structures p 8  arranged at the boundaries between the second region  720  and regions adjacent to the second region  720  in the second direction (Y direction), and the cross-sectional area of pattern structures p 7  arranged at the boundaries between the third region  730  and regions adjacent to the third region  730  in the first direction (X direction) is equal to the cross-sectional area of pattern structures p 6  arranged at the boundaries between the third region  730  and regions adjacent to the third region  730  in the second direction (Y direction). 
     In addition, pattern structures p 9 , which are arranged at four corners of each of the first, second, third, and fourth regions  710 ,  720 ,  730 , and  740 , that is, at each position at which four regions meet each other, have the same cross-sectional area. 
     This distribution is due to the arrangement of pixels similar to the Bayer pattern. Both the second pixel P 2  and the third pixel P 3  have the first pixels P 1  as pixels adjacent thereto in the first direction (X direction) and the second direction (Y direction), whereas the first pixel P 1  corresponding to the first region  710  has different pixels as pixels adjacent thereto: the second pixel P 2  in the first direction (X direction) and the third pixel P 3  in the second direction (Y direction), and the first pixel P 1  corresponding to the fourth region  740  has different pixels as pixels adjacent thereto: the third pixel P 3  in the first direction (X direction) and the second pixel P 2  in the second direction (Y direction). In addition, each of the first pixels P 1  corresponding to the first region  710  and the fourth region  740  has first pixels P 1  as pixels adjacent thereto in four diagonal directions, the second pixel P 2  corresponding to the second region  720  has third pixels P 3  as pixels adjacent thereto in four diagonal directions, and the third pixel P 3  corresponding to the third region  730  has second pixels P 2  as pixels adjacent thereto in four diagonal directions. Therefore, pattern structures PS may be arranged in 4-fold symmetry in the second region  720  and the third region  730  which respectively correspond to the second pixel P 2  and the third pixel P 3 , and pattern structures PS may be arranged with 2-fold symmetry in the first and fourth regions  710  and  740  which correspond to the first pixels P 1 . In particular, the first region  710  and the fourth region  740  are rotated 90 degrees with respect to each other. 
     The pattern structures PS are all illustrated as having a symmetrical circular cross-sectional shape, but are not limited thereto. Some of the pattern structures may have an asymmetrical cross-sectional shape. For example, pattern structures PS having an asymmetrical cross-sectional shape with different widths in the first direction (X direction) and the second direction (Y direction) may be arranged in the first region  710  and the fourth region  740  corresponding to the first pixels P 1 , and pattern structures PS having a symmetrical cross-sectional shape with the same width in the first direction (X direction) and the second direction (Y direction) may be arranged in the second regions  720  and the third regions  730  respectively corresponding to the second pixels P 2  and the third pixels P 3 . 
     The arrangement rules of the color separation lens array  700  are an example in which, immediately after passing through the color separation lens array  700 , light has a target phase distribution for being split and collected in such a manner that light having a first spectrum is collected on the first and fourth photosensitive cells  110  and  140 , light having a second spectrum is collected on the second photosensitive cells  120 , and light having a third spectrum is collected on the third photosensitive cells  130 . However, the arrangement rules of the color separation lens array  700  are not limited to the illustrated patterns. 
     The shapes, sizes, and arrangement of the pattern structures PS provided in each region of the color separation lens array  700  may be determined such that after passing through the color separation lens array  700 , light having the first spectrum may have a phase distribution for being collected on the first and fourth photosensitive cells  110  and  140  while not proceeding to the second and third photosensitive cells  120  and  130  adjacent to the first and fourth photosensitive cells  110  and  140 . 
     Likewise, the shapes, sizes, and arrangement of the pattern structures PS provided in each region of the color separation lens array  700  may be determined such that after passing through the color separation lens array  700 , light having the second spectrum may have a phase distribution for being collected on the second photosensitive cells  120  while not proceeding to the first, third, and fourth photosensitive cells  110 ,  130 , and  140  adjacent to the second photosensitive cells  120 . 
     Likewise, the shapes, sizes, and arrangement of the pattern structures PS provided in each region of the color separation lens array  700  may be determined such that after passing through the color separation lens array  700 , light having the third spectrum may have a phase distribution for being collected on the third photosensitive cells  120  while not proceeding to the first, second, and fourth photosensitive cells  110 ,  120 , and  140  adjacent to the third photosensitive cells  130 . 
     According to example embodiments, the pixel array  1100  of the image sensor  1000  may have a variable optical distance between the light detection unit  100  and the color separation lens array  700 , and thus, wavelength-dependent light separation according to the shapes, sizes, and arrangement of the pattern structures PS is described by assuming a particular optical distance. 
     The shapes, sizes, and/or arrangement of the pattern structures PS may be determined to satisfy all of such conditions, and light may have the following target phase distribution immediately after passing through the color separation lens array  700 . At a position immediately after the color separation lens array  700 , that is, on the lower surface of the color separation lens array  700  or the upper surface of the variable interlayer element  500 , light having a first wavelength may have a phase difference of 2Nπ in center portions of the first regions  710  corresponding to the first photosensitive cells  110  and in center portions of the fourth regions  740  corresponding to the fourth photosensitive cells  140 , and a phase difference of (2N−1)π in center portions of the second regions  720  corresponding to the second photosensitive cells  120  and in center portions of the third regions  730  corresponding to the third photosensitive cells  130 . Here, N is an integer greater than 0. In other words, at a position immediately after the color separation lens array  700 , light having a first wavelength may have a phase distribution which peaks in center portions of the first regions  710  and center portions of the fourth regions  740  and gradually decreases therefrom in a concentric circle shape to have valleys in center portions of the second regions  720  and center portions of the third regions  730 . For example, when N=1, at a position after the color separation lens array  700 , the phase of light having a first wavelength may be 2π in the center portions of the first regions  710  and center portions of the fourth regions  740  and π in the center portions of the second regions  720  and the center portions of the third regions  730 . Here, the phase of light may refer to a phase relative to the phase of the light before passing through the color separation lens array  700 . 
     In addition, at a position immediately after the color separation lens array  700 , the phase of light having a second wavelength may be 2Mπ in the center portions of the second regions  720  corresponding to the second photosensitive cells  120 , (2M−1)π in the center portions of the first regions  710  corresponding to the first photosensitive cells  110  and in the center portions of the fourth regions  740  corresponding to the fourth photosensitive cells  140 , and a value greater than (2M−2)π but less than (2M−1)π in the center portions of the third regions  730  corresponding to the third photosensitive cells  130 . Here, M is an integer greater than 0. In other words, at a position immediately after the color separation lens array  700 , light having the second wavelength may have a phase distribution which peaks in the center portions of the second regions  720  and gradually decreases therefrom in a concentric circle shape to have local minimums in the center portions of the first, fourth, and third regions  710 ,  740 , and  730 . For example, when M=1, at a position after the color separation lens array  700 , the phase of light having the second wavelength may be 2π in the center portions of the second regions  720  and π in the center portions of the first regions  710  and the center portions of the fourth regions  740 , and a value of about 0.2π to about 0.7π in the center portions of the third regions  730 . 
     In addition, similarly, at a position immediately after the color separation lens array  700 , the phase of light having a third wavelength may be 2Lπ in the center portions of the third regions  730  corresponding to the third photosensitive cells  130 , (2L−1)π in the center portions of the first regions  710  corresponding to the first photosensitive cells  110  and in the center portions of the fourth regions  740  corresponding to the fourth photosensitive cells  140 , and a value greater than (2L−2)π but less than (2L−1)π in the center portions of the second regions  720  corresponding to the second photosensitive cells  120 . Here, L is an integer greater than 0. In other words, at a position immediately after the color separation lens array  700 , light having the third wavelength may have a phase distribution which peaks in the center portions of the third regions  730  and gradually decreases therefrom in a concentric circle shape to have local minimums in the center portions of the first, fourth, and second regions  710 ,  740 , and  720 . For example, when L=1, at a position after the color separation lens array  700 , the phase of light having the third wavelength may be 2π in the center portions of the third regions  730  and π in the center portions of the first regions  710  and the center portions of the fourth regions  740 , and a value of about 0.27 to about 0.77 in the center portions of the second regions  720 . 
     Light having the first wavelength, light having the second wavelength, and light having the third wavelength may be green light, blue light, and red light, respectively. However, this is a non-limiting example. 
     As described above, the target phase distribution refers to a phase distribution at a position immediately after the color separation lens array  700 , and when light having the target phase distribution proceeds toward the first, second, third, and fourth photosensitive cells  110 ,  120 ,  130 , and  140 , the light may have different spectra depending on the distance the light has traveled. That is, light having different spectra may be collected on the first, second, third, and fourth photosensitive cells  110 ,  120 ,  130 , and  140  by adjusting the optical distance OL to the light detector  100 . 
       FIG.  5    is a conceptual view illustrating that incident light Li has different spectra according to the distance from the color separation lens array  700  in the image sensor  1000  of the example embodiment, and  FIGS.  6 A to  6 D  are graphs illustrating spectra of incident light separated by the first, second, and third photosensitive cells  110 ,  120 , and  130  for different optical distances OL between the color separation lens array  700  and the light detector  100  in the image sensor  1000  of the example embodiment. 
     Referring to  FIG.  5   , the incident light Li has a predetermined target phase distribution immediately after passing through the color separation lens array  700 . Different spectrum patterns are separated from the light Li in different regions according to the distance that the light Li has traveled. Different colors (or wavelength distributions) are presented on unit pixels, which have a pattern similar to a Bayer pattern and are formed at optical distances Z 1 , Z 2 , Z 3 , and Z 4 . In  FIG.  4   , the unit pixels are denoted with PU 1  at the distance Z 1 , PU 2  at the distance Z 2 , PU 3  at the distance Z 3 , and PU 4  at the distance Z 4 . The color of each unit pixel is a mixture of red, green, and blue in different proportions. This is merely an example, and in another example, a unit pixel expressed by green, blue, green, and blue may be formed at a certain position. In  FIG.  5   , the pattern structures PS are illustrated as having a circular post shape, but the pattern structures PS are not limited thereto. The pattern structures PS may be nano-posts having various cross-sectional shapes such as a polygon shape, an ellipse shape, a circular ring shape, a polygonal ring shape, and a cross shape. 
     In  FIGS.  6 A to  6 D,  51    refers to the spectrum of light incident on the first photosensitive cells  110  and fourth photosensitive cells  140 , S 2  refers to the spectrum of light incident on the second photosensitive cells  120 , and S 3  refers to the spectrum of light incident on the third photosensitive cells  130 . Colors (or wavelength distributions) sensed by the first photosensitive cells  110 , the second photosensitive cells  120 , the third photosensitive cells  130 , and the fourth photosensitive cells  140  according to the incident spectra are denoted with C 1k , C 2k , and C 3k . k is an index for denoting the distances Z 1 , Z 2 , Z 3 , and Z 4  with 1, 2, 3, and 4. 
     Colors (or wavelength distributions) C ik  (i=1, 2, and 3 and k=1, 2, 3, and 4) may all be different from each other, some of the colors Cik may be very similar to each other, or some of the colors Cik may be red, green, and blue. 
     When the color of an object is restored using a plurality of optical signal sets sensed at different distances as described above, reproduction may be possible with high spectroscopic sensitivity compared to the case of using only three colors: red, green, and blue. 
     RGB-based graphic technology of the related art has limitations in that colors are expressed by the simple sums of RGB spectral weights, and thus, it is difficult to apply the RGB-based graphic technology to various lighting environments or media. In addition, when a global multi-spectrum is obtained to increase color reproducibility, a large number of channels may be required, and thus, spatial resolution may decrease. 
     Because the image sensor  1000  of the example embodiment obtains images from a plurality of optical signal sets obtained by varying the optical distance OL, the color reproducibility of the image sensor  1000  may be improved without decreasing the spatial resolution of the image sensor  1000 . 
       FIG.  7    is a flowchart schematically illustrating image acquisition processes of the image sensor  1000  according to an example embodiment. 
     The processor  1040  controls the variable interlayer element  500  to form a plurality of different optical distances (S 810 ). The optical distances may be determined by considering a light collection pattern according to the propagation distance of light having a phase distribution immediately after passing through the color separation lens array  700 . The light collection pattern according to the propagation distance may depend on the wavelength A of incident light and the pixel size (p) of the light detector  100 . The variable range of the optical distances may be determined by considering the light collection pattern according to the propagation distance. The minimum optical distance may be, for example, about 1λ or more. The pixel size (p) may be expressed as the distance between adjacent photosensitive cell centers. For example, the minimum optical distance may be within the range of about 1λ or more, or within the range of about 1 p to about 3 p. For example, the variable optical distance may be within the range of about 500 nm to about 5 μm. 
     The processor  1040  may vary the physical distance between the light detector  100  and the color separation lens array  700  according to the type of the variable interlayer element  500 , or may apply a signal to the variable interlayer element  500  to vary the refractive index of a medium between the light detector  100  and the color separation lens array  700 . When an optical distance is set by the operation of the variable interlayer element  500 , the light detector  100  senses an optical signal at the optical distance (S 830 ). In this manner, a plurality of optical signal sets may be obtained for a plurality of optical distances. The processor  1040  may perform computations to obtain image data by using such optical signals (S 850 ), and in the processing, spectrum data previously acquired according to optical distances for the color separation lens array  700  and the light detector  100  may be used. That is, as illustrated in  FIGS.  6 A to  6 D , the arrangement of colors (wavelength distributions) of unit pixels may vary depending on optical distances, and unit pixel data may be previously prepared according to each of a plurality of optical distances to be set by the operation of the variable interlayer element  500 . Artificial intelligence (AI)-based computational techniques may be used for computation thereof. Because image information included in incident light is acquired by using a plurality of optical signal sets which are proportional to the number of set optical distances, when the light detector  100  includes an Q×Q cell array, data corresponding to an m(Q×Q) array may be obtained, wherein m refers to the number of optical distances. 
     Example configurations of variable interlayer elements and image sensors including the variable interlayer elements will be described according to example embodiments with reference to  FIGS.  8  to  11   . 
       FIG.  8    is a cross-sectional view schematically illustrating a pixel array configuration of an image sensor  1001  according to another example embodiment. 
     A pixel array  1101  includes a color separation lens array  700 , a light detector  100 , and a variable interlayer element. 
     The variable interlayer element may include a microelectromechanical system (MEMS) actuator  501  configured to vary a physical distance S between the color separation lens array  700  and the light detector  100 . A medium between the color separation lens array  700  and the light detector  100  may be air, and thus, a support layer  710  for supporting the pattern structures PS may be provided. 
     The support layer  710  and the light detector  100  are electromechanically connected to the MEMS actuator  501  such that the position of the support layer  710  may be varied with respect to the light detector  100  according to the operation of the MEMS actuator  501 . Therefore, the physical distance S between the color separation lens array  700  and the light detector  100  may be adjusted. 
       FIG.  9    is a cross-sectional view schematically illustrating a pixel array configuration of an image sensor  1002  according to another example embodiment. 
     A pixel array  1102  includes a color separation lens array  700 , a light detector  100 , and a variable interlayer element  502 . 
     The variable interlayer element  502  includes: a variable shape structure  522  including a variable shape material which is variable in shape in response to an electrical signal to change a physical distance S between the color separation lens array  700  and the light detector  100 ; and a signal application unit  525  configured to apply an electrical signal to the variable shape structure  522 . 
     The variable shape material included in the variable shape structure  522  may be, for example, a shape memory alloy (SMA) or an electro-active polymer. The variable shape structure  522  may be embodied in various forms, and the specific shape of the variable shape structure  522  is not shown. The variable shape structure  522  may have various shapes combined with a member having a predetermined shape and fixing the variable shape material. However, the variable shape structure  522  is not limited thereto, and in another example, the variable shape structure  522  may be entirely formed of the variable shape material. The shape of the variable shape material may be varied in response to a signal applied from the signal application unit  525 , and thus, the physical distance S between the light detector  100  and the color separation lens array  700  may be varied. 
       FIG.  10    is a cross-sectional view schematically illustrating a pixel array configuration of an image sensor  1003  according to another example embodiment. 
     A pixel array  1103  includes a color separation lens array  700 , a light detector  100 , and a variable interlayer element  503 . 
     The variable interlayer element  503  includes: a frame structure  533  including a reservoir region RA and a variable height region VA; and a signal application unit  535  configured to move an optical fluid FL from the reservoir region RA to the variable height region VA. 
     The variable height region VA is a region between the color separation lens array  700  and the light detector  100 , and may include a stretchable membrane  532  and a fixing member  531  configured to support the stretch deformation of the stretchable membrane  532 . The stretchable membrane  532 , the fixing member  531 , the reservoir region RA, and the variable height region VA may form the frame structure  533 . 
     The signal application unit  535  may apply hydraulic pressure to the reservoir region RA to move the optical fluid FL to the variable height region VA. Alternatively, additional elements such as electrodes for moving a fluid may be provided in the reservoir region RA or the variable height region VA such that the optical fluid FL may be moved as the signal application unit  545  applies an electrical signal to the additional elements. 
     When the optical fluid FL flows between the reservoir region RA and the height variable region VA, the stretchable membrane  532  of the height variable region VA may be stretched or shrunk according to the amount of the optical fluid FL, and thus, the height of the variable height region VA may be adjusted. As the height of the variable height region VA is adjusted, the physical distance S between the color separation lens array  700  and the light detector  100  may be adjusted. 
     Although  FIG.  10    illustrates a support layer  710  configured to support pattern structures PS, the image sensor  1003  is not limited thereto. For example, the support layer  710  may be omitted, and the pattern structures PS may be supported by the stretchable membrane  532 . 
       FIG.  11    is a cross-sectional view schematically illustrating a pixel array configuration of an image sensor  1004  according to another example embodiment. 
     A pixel array  1104  includes a color separation lens array  700 , a light detector  100 , and a variable interlayer element  504 . 
     The variable interlayer element  504  includes a variable refractive index layer  543  having a refractive index variable in response to a signal input from the outside; and a signal application unit  545  configured to apply an electrical signal to the variable refractive index layer  543 . Transparent electrodes  541  and  542  may be arranged on upper and lower surfaces of the variable refractive index layer  543 . 
     The variable refractive index layer  543  may include a material of which optical characteristics are variable in response to an external signal. The external signal may be an electrical signal. The variable refractive index layer  543  may include, for example, an electro-optic material having an effective dielectric constant variable in response to an electrical signal. Examples of a material that may be included in the variable refractive index layer  543  may include LiNbO 3 , LiTaO 3 , potassium tantalate niobate (KTN), lead zirconate titanate (PZT), and liquid crystal, and may also include various polymer materials having electro-optic characteristics. The external signal is not limited to an electrical signal, and for example, the variable refractive index layer  543  may include VO 2 , VO 2 O 3 , EuO, MnO, CoO, CoO 2 , LiCoO 2 , Ca 2 RuO 4 , or the like which undergoes a phase transition and thus varies in refractive index at a certain temperature or higher in response to heat applied thereto. 
     When the refractive index of the variable refractive index layer  543  is varied in response to a signal applied from the signal application unit  545 , an optical distance expressed by the product of the refractive index and a physical distance S is also varied. 
       FIG.  12    is an example plan view illustrating a unit pattern array of a color separation lens array  701  provided in an image sensor according to another example embodiment. 
     The color separation lens array  701  may have a pixel array corresponding to the Bayer pattern-like pixel arrangement illustrated in  FIG.  4 A  and may include quadrant regions including a first region  711  corresponding to a first pixel P 1 , a second region  721  corresponding to a second pixel P 2 , a third region  731  corresponding to a third pixel P 3 , and a fourth region  741  corresponding to a first pixel P 1 . Such unit pattern arrays may be repeatedly arranged in a first direction (X direction) and a second direction (Y direction). Each region may be divided into a plurality of sub-regions, and pattern structures PS may be arranged at intersections of the boundaries of the sub-regions.  FIG.  12    shows an example in which: the number of sub-regions is nine for each region; pattern structures PS are arranged at grid points defining the nine sub-regions; no pattern structure PS is arranged at the center of each of the first, second, third, and fourth regions  711 ,  721 ,  731 , and  741 ; and four pattern structures PS having the same size form a center portion of each of the first, second, third, and fourth regions  711 ,  721 ,  731 , and  741 . Pattern structures PS in a peripheral portion are arranged on the boundaries between regions. The pattern structures PS are denoted with r 1  to r 9  according to the positions of the pattern structures PS in the unit pattern array. 
     Referring to  FIG.  12   , pattern structures r 1  arranged in the center portion of the first region  711  corresponding to the first pixel P 1  have a larger cross-sectional area than peripheral pattern structures r 5 , r 6 , and r 9 , and pattern structures r 4  arranged in the central portion of the fourth region  741  corresponding to the first pixel P 1  also have a larger cross-sectional area than peripheral pattern structures r 7 , r 8 , and r 9 . The cross-sectional sizes of the pattern structures r 1  and r 4  arranged in the center portions of the first and fourth regions  711  and  741  corresponding to the first pixels P 1  may be greater than the cross-sectional size of pattern structures r 2  arranged in the center portion of the second region  721  corresponding to the second pixel P 2  and the cross-sectional size of pattern structures r 3  arranged in the center portion of the third region  731  corresponding to the third pixel P 3 . The cross-sectional area of the pattern structures r 2  arranged in the center portion of the second region  721  corresponding to the second pixel P 2  may be greater than the cross-sectional area of the pattern structure r 3  arranged in the center portion of the third region  731  corresponding to the third pixel P 3 . 
     The pattern structures PS of the second region  721  and the third region  731  may be symmetrically arranged in the first direction (X direction) and the second direction (Y direction), and the pattern structures PS of the first region  711  and the fourth region  741  may be asymmetrically arranged in the first direction (X direction) and the second direction (Y direction). In other words, the pattern structures PS of the second region  721  and the third region  731  respectively corresponding to the second pixel P 2  and the third pixel P 3  may arranged according to the distribution rules in the first direction (X direction) and the second direction (Y direction), and the pattern structures PS of the first region  711  and the fourth region  741  corresponding to the first pixels P 1  may be arranged according to different distribution rules in the first direction (X direction) and the second direction (Y direction). 
     The cross-sectional area of the pattern structures r 5  positioned at a boundary of the first region  711  adjacent to the second region  721  in the first direction (X direction) is different from the cross-sectional area of the pattern structures r 6  positioned at a boundary of the first region  711  adjacent to the third region  731  in the second direction (Y direction). In addition, the cross-sectional area of the pattern structures r 7  positioned at a boundary of the fourth region  741  adjacent to the third region  731  in the first direction (X direction) is different from the cross-sectional area of the pattern structures r 8  positioned at a boundary of the fourth region  741  adjacent to the second region  721  in the second direction (Y direction). 
     However, the cross-sectional area of the pattern structures r 5  positioned at the boundary of the first region  711  adjacent to the second region  721  in the first direction (X direction) is equal to the cross-sectional area of the pattern structures r 8  positioned at the boundary of the fourth region  741  adjacent to the second direction (Y direction), and the cross-sectional area of the pattern structures r 6  positioned at a boundary of the first region  711  adjacent to the third region  731  in the second direction (Y direction) is equal to the cross-sectional area of the pattern structures r 7  positioned at the boundary of the fourth region  741  adjacent to the third region  731  in the first direction (X direction). 
     In addition, the pattern structures r 9 , which are arranged at the four corners of each of the first region  711 , the second region  721 , the third region  731 , and the fourth region  741 , that is, at positions at which the four regions meet each other, have the same cross-sectional area. 
     As described above, pattern structures PS are arranged in 4-fold symmetry in the second region  721  and the third region  731  which respectively correspond to the second pixel P 2  and the third pixel P 3 , and pattern structures PS are arranged with 2-fold symmetry in the first and fourth regions  711  and  741  which correspond to the first pixels P 1  such that the pattern structures PS of the first and fourth regions  711  and  741  may be rotated 90 degrees from each other. This form also applies to example embodiments shown in  FIGS.  13  and  14   . 
       FIG.  13    is a plan view schematically illustrating a color separation lens array  702  provided in a pixel array of an image sensor according to another example embodiment. 
     In the present example embodiment, each of a first region  712 , a second region  722 , a third region  732 , and a fourth region  742  included in the color separation lens array  702  may be divided into a plurality of sub-regions, and at least a portion of one pattern structure PS may be positioned in each of the sub-regions. Pattern structures PS may not be arranged on center portions of some of the sub-regions, but may be arranged only on boundaries of the sub-regions. Although it is illustrated that the number of sub-regions of each region is four, this is a non-limiting example. 
     Also in the present example embodiment, pattern structures PS of the second region  722  and the third region  732  may be arranged according to the same arrangement rules in a first direction (X direction) and a second direction (Y direction), and pattern structures PS of the first region  712  and the fourth region  742  may be arranged according to different arrangement rules in the first direction (X direction) and the second direction (Y direction). The arrangement of the pattern structures PS in the first region  712  and the arrangement of the pattern structures PS in the fourth region  742  may be rotated 90 degrees with respect to each other. 
     In the above description, color separation lens arrays which include pattern structures having a post shape and arranged in definable forms have been described. However, color separation pattern arrays having non-definable free patterns may also be implemented. Hereinafter, examples of various free forms that may be employed in color separation lens arrays will be described. 
       FIG.  14    is a plan view schematically illustrating a color separation lens array  703  provided in a pixel array of an image sensor according to another example embodiment. 
     The color separation lens array  703  shown in  FIG.  14    may be applied to an image sensor in which pixels are arranged in the form of a Bayer pattern, and  FIG.  14    shows four regions of a unit pattern array. The color separation lens array  703  includes a first pattern structure PS 1  formed in a first region  713 , a second pattern structure PS 2  formed in a second region  723  and having a shape different from the shape of the first pattern structure PS 1 , a third pattern structure PS 3  formed in a third region  733  and having a shape different from the shapes of the first pattern structure PS 1  and the second pattern structure PS 2 , and a fourth pattern structure PS 4  formed in a fourth region  743 . 
     The first pattern structure PS 1  includes: a first dielectric D 1  having a first refractive index and provided in a first form; and a second dielectric D 2  having a second refractive index less than the first refractive index and filled in gaps of the first dielectric D 1  having the first form. The first form is a free form defined without limitations except that the first dielectric D 1  is present in any vertical cross-section of the first pattern structure PS 1 . Here, the term “vertical cross-section” refers to a cross-section taken along a straight line on an XY plane. 
     Similarly, the second pattern structure PS 2  includes: a third dielectric D 3  having a third refractive index and provided in a second form; and a fourth dielectric D 4  having a fourth refractive index less than the third refractive index and filled in gaps of the third dielectric D 3  having the second form. The second form may be determined such that the third dielectric D 3  may be present in any vertical cross-section of the second pattern structure PS 2 . 
     Similarly, the third pattern structure PS 3  includes: a fifth dielectric D 5  having a fifth refractive index and provided in a third form; and a sixth dielectric D 6  having a sixth refractive index less than the fifth refractive index and filled in gaps of the fifth dielectric D 5  having the third form. The third form may be determined such that the fifth dielectric D 5  may be present in any vertical cross-section of the third pattern structure PS 3 . 
     Similarly, the fourth pattern structure PS 4  includes: a seventh dielectric D 7  having a seventh refractive index and provided in a fourth form; and an eighth dielectric D 8  having an eighth refractive index less than the seventh refractive index and filled in gaps of the seventh dielectric D 7  having the fourth form. The fourth form may be determined such that the seventh dielectric D 7  may be present in any vertical cross-section of the fourth pattern structure PS 4 . The fourth pattern structure PS 4  may be in a form rotated 90 degrees from the first pattern structure PS 1 . 
     All the first dielectric D 1 , the third dielectric D 3 , the fifth dielectric D 5 , and the seventh dielectric D 7  may include the same material, and all the second dielectric D 2 , the fourth dielectric D 4 , the sixth dielectric D 6 , and the eighth dielectric D 8  may include the same material. For example, the first dielectric D 1 , the third dielectric D 3 , the fifth dielectric D 5 , and the seventh dielectric D 7  may include a dielectric material having a high refractive index and a low absorptivity in a visual light band, such as TiO 2 , GaN, SiN 3 , ZnS, ZnSe, or Si 3 N 4 . In addition, the second dielectric D 2 , the fourth dielectric D 4 , the sixth dielectric D 6 , and the eighth dielectric D 8  may include a dielectric material having a low refractive index and a low absorptivity in a visual light band, such as air, SiO 2 , or silanol-based glass (for example, siloxane-based spin on glass (SOG)). For example, when the second dielectric D 2 , the fourth dielectric D 4 , the sixth dielectric D 6 , and the eighth dielectric D 8  are air, the color separation lens array  703  may easily be formed by etching the first dielectric D 1 , the third dielectric D 3 , the fifth dielectric D 5 , and the seventh dielectric D 7  in the form shown in  FIG.  14   . 
       FIGS.  15 A,  15 B,  15 C, and  15 D  respectively illustrate the first region  713 , the second region  723 , the third region  733 , and the fourth region  743  of the color separation lens array  703  of  FIG.  14   . 
     As shown in  FIG.  15 A , the first pattern structure PS 1  of the first region  713  may have a 2-fold symmetrical form. For example, the first pattern structure PS 1  of the first region  713  may be symmetrical with respect to a first axis (I) defined in a Y direction and may also be symmetrical with respect to a second axis II defined in an X direction. 
     As shown in  FIG.  15 B , the second pattern structure PS 2  of the second region  723  may have a 4-fold symmetrical form. For example, the second pattern structure PS 2  of the second region  723  may be symmetrical with respect to a first axis (I) defined in the Y direction, a second axis II defined in the X direction, a third axis III defined in a diagonal direction, and a fourth axis IV defined in a diagonal direction. 
     As shown in  FIG.  15 C , the third pattern structure PS 3  of the third region  733  may have a 4-fold symmetrical form. For example, the third pattern structure PS 3  of the third region  733  may be symmetrical with respect to a first axis (I) defined in the Y direction, a second axis II defined in the X direction, a third axis III defined in a diagonal direction, and a fourth axis IV defined in a diagonal direction. 
     As shown in  FIG.  15 D , the fourth pattern structure PS 4  of the third region  743  may be symmetrical with respect to a first axis (I) defined in the Y direction and a second axis II defined in the X direction. The fourth pattern structure PS 4  of the fourth region  743  may have the same form as that obtained by rotating the first pattern structure PS 1  of the first region  713  by 90 degrees. 
     The symmetry of each of the first pattern structure PS 1 , the second pattern structure PS 2 , the third pattern PS 3 , and the fourth pattern structure PS 4  respectively provided in the first region  713 , the second region  723 , the third region  733 , and the fourth region  743  are determined by considering the arrangement of a pixel corresponding thereto and pixels adjacent thereto. 
     The four regions of the unit pattern array, that is, the first region  713 , the second region  723 , the third region  733 , and the fourth region  743 , respectively correspond to the first pixel P 1 , the second pixel P 2 , the third pixel P 3 , and the first pixel P 1  of the pixel arrangement shown in  FIG.  4 A . In this arrangement, pixels adjacent to the second pixel P 2  and the third pixel P 3  in the first direction (X direction) and the second direction (Y direction) are the first pixels P 1 , and the first pixel P 1  has the second pixel P 2  as a pixel adjacent thereto in the first direction (X direction) and the third pixel P 3  as a pixel adjacent thereto in the second direction (Y direction). By considering the symmetry of the pixel arrangement, the symmetry of each of the first pattern structure PS 1 , the second pattern PS 2 , the third pattern structure PS 3 , and the pattern structure PS 4  respectively provided in the first region  713 , the second region  723 , the third region  733 , and the fourth region  743  may be determined. 
     The shape of the color separation lens array  703  shown in  FIG.  14    is an example, and the color separation lens array  703  may have any other shape as long as light has a target phase distribution immediately after passing through the color separation lens array  703 . 
     The shape of the color separation lens array  703  that satisfies a target phase distribution may be automatically designed through various computer simulations. For example, the shape of the pattern structure of each region may be designed using a nature-inspired algorithm such as a genetic algorithm, a particle swarm optimization algorithm, and an ant colony optimization algorithm, or using a reverse engineering method based on an adjoint optimization algorithm. 
     When designing the color separation lens array  703 , it is possible to optimize the pattern shape of each region of each unit pattern array while evaluating the performance of color separation lens array candidates according to evaluation factors such as color separation spectrum, optical efficiency, and signal-to-noise ratio. For example, the pattern shape of each region may be optimized by previously determining a target value for each evaluation factor and minimizing the sum of differences with the target values of the evaluation factors. Alternatively, performance indexes may be prepared for evaluation factors, and the pattern shape of each region may be optimized to result in maximum performance indexes. 
       FIG.  16    is an example plan view illustrating a unit pattern array of a color separation lens array which is applicable to a Bayer-pattern image sensor according to another example embodiment, and  FIG.  17    is an example plan view illustrating a unit pattern array of a color separation lens array which is applicable to a Bayer-pattern image sensor according to another example embodiment. 
     Each of the regions of the unit pattern array shown in  FIG.  14    is optimized in a digitized binary form of a 14×14 rectangular array, and each region of the unit pattern array shown in  FIG.  16    is optimized in a digitized binary form of a 16×16 rectangular array. Therefore, the unit pattern array of the color separation lens array  703  illustrated in  FIG.  14    has a 28×28 rectangular array form, and the unit pattern array of the color separation lens array illustrated in  FIG.  16    has a 32×32 rectangular array form. In this case, the vertical cross-sectional shape of each of the regions shown in  FIGS.  14  and  16    may discontinuously vary as line A-A′ moves in the Y direction or line B-B′ moves in the X direction. 
     In addition, as shown in  FIG.  17   , each region of the unit pattern array may be optimized in a non-digitized continuous curve form. In this case, the vertical cross-sectional shape of each region continuously varies as line A-A′ moves in the Y direction or line B-B′ moves in the X direction as shown in  FIG.  14   . 
     The shapes and arrangements of the pattern structures PS of the color separation lens arrays illustrated in  FIGS.  12  to  17    are examples, and various modifications may be made therein according to intended target phase distributions. In addition, the color separation lens arrays may be combined with various variable interlayer elements such as those illustrated in  FIGS.  8  to  11   . 
     The image sensors described above may be employed in various electronic devices. Because the image sensors described above provide object information having high spectroscopic sensitivity, the image sensors may be used in spectroscopic devices, inspection devices, photographing devices, and the like. Non-limiting examples of such electronic devices may include smartphones, cellular phones, mobile phones, personal digital assistants (PDAs), laptop computers, personal computers (PCs), various portable devices, and other mobile or non-mobile computing devices. 
     For example,  FIG.  18    is a schematic block diagram illustrating an electronic device including an image sensor according to an example embodiment. The electronic device includes an image sensor  1000 , a processor  2200 , a memory  2300 , a display  2400 , and a bus  2500 . The image sensor  1000  acquires image information on an external object under the control of the processor  2200  and provides the image information to the processor  2200 . The processor  2200  may store the image information received from the image sensor  1000  in the memory  2300  through the bus  2500 . The processor  2200  may output the image information stored in the memory  2300  to the display  2400  for showing the image information to a user. In addition, as described above, the processor  2200  may variously process the image information received from the image sensor  1000 . 
       FIGS.  19  to  29    illustrate various examples of multimedia devices as electronic devices to which image sensors are applied according to example embodiments. 
     The image sensors of the example embodiments may be applied to various multimedia devices having an image capturing function. For example, an image sensor may be applied to a camera  2000  as shown in  FIG.  19   . The camera  2000  may be a digital camera or a digital camcorder. 
     Referring to  FIG.  20   , the camera  2000  may include an imaging unit  2100 , an image sensor  1000 , and a processor  2200 . 
     The imaging unit  2100  forms an optical image by condensing light reflected from an object OBJ. The imaging unit  2100  may include an objective lens  2010 , a lens driving unit  2120 , a aperture  2130 , and a aperture driving unit  2140 . Although only one lens element is shown in  FIG.  20    for ease of illustration, the objective lens  2010  may include a plurality of lens elements having different sizes and shapes. The lens driving unit  2120  may communicate with the processor  2200  for information about focus detection and may adjust the position of the objective lens  2010  according to a control signal received from the processor  2200 . The lens driving unit  2120  may move the objective lens  2010  to adjust the distance between the objective lens  2010  and the object OBJ, or may adjust the positions of the lens elements of the objective lens  2010 . Focusing on the object OBJ may be adjusted as the lens driving unit  2120  drives the objective lens  2010 . The camera  2000  may have an auto focus (AF) function. 
     In addition, the aperture driving unit  2140  may communicate with the processor  2200  for information on the amount of light and may adjust the aperture  2130  according to a control signal received from the processor  2200 . For example, the aperture driving unit  2140  may increase or decrease the aperture of the aperture  2130  to adjust the amount of light entering the camera  2000  through the objective lens  2010 , and may adjust the aperture opening time of the aperture  2130 . 
     The image sensor  1000  may generate an electrical image signal based on the intensity of incident light. The image sensor  1000  may include a pixel array  1100 , a timing controller  1010 , and an output circuit  1030 . The image sensor  1000  may further include a row decoder as shown in  FIG.  1   . Light passing through the objective lens  2010  and the aperture  2130  may form an image of the object OBJ on a light-receiving surface of the pixel array  1100 . The pixel array  1100  may be a CCD or CMOS configured to convert optical signals into electrical signals. The pixel array  1100  may include additional pixels for performing an AF function or a distance measurement function. In addition, the pixel array  1100  may include one, a combination, or a modification of the color separation lens arrays  700 ,  701 ,  702 , and  703  described with reference to  FIGS.  12  to  17   , and may also include any one of the variable interlayer elements  501 ,  502 ,  503 , and  504  described with reference to  FIGS.  8  to  11   . 
     The processor  2200  may control the overall operation of the camera  2000  and may have an image processing function. For example, the processor  2200  may provide control signals for operations of devices such as the lens driving unit  2120 , the aperture driving unit  2140 , and the timing controller  1010 . 
     As described above, the pixel array  1100  of the image sensor  1000  has a structure in which an optical distance between a light detector and a color separation lens array is adjustable such that the image sensor  1000  may form an image using a plurality of optical signal sets obtained at a plurality of optical distances, and thus, the camera  2000  including the image sensor  1000  may provide high-quality images having high color purity with high reproducibility. 
     In addition, according to example embodiments, an image sensor may be applied to a mobile phone or smart phone  3000  as shown in  FIG.  21   , a tablet or smart tablet  3100  as shown in  FIG.  22   , a laptop computer  3200  as shown in  FIG.  23   , or a television or smart television  3300  as shown in  FIG.  24   . 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. The high-resolution cameras may be used to extract information about the depths of objects in an image, adjust out-of-focus images, or automatically detect objects in an image. 
     In addition, the image sensor may be applied to a smart refrigerator  3400  as shown in  FIG.  25   , a security camera  3500  as shown in  FIG.  26   , a robot  3600  as shown in  FIG.  27   , a medical camera  3700  as shown in  FIG.  28   , or the like. For example, the smart refrigerator  3400  may automatically recognize foods stored in the smart refrigerator  3400  by using the image sensor and may provide information about the foods stored in the smart refrigerator  3400  and information about foods put into or taken out of the smart refrigerator  3400  to a user through a smartphone of the user. The security camera  3500  may provide ultra-high resolution images and may be highly sensitive to enable the detection of objects or people even in images captured in dark environments. The robot  3600  may be sent to disaster or industrial sites that humans cannot directly access and may provide high-resolution images of the sites. The medical camera  3700  may provide high-resolution images for diagnosis or surgery and may have a function of dynamically adjusting a field of view. 
     In addition, the image sensor may be applied to a vehicle  3800  as shown in  FIG.  29   . For example, the vehicle  3800  may include a plurality of vehicle cameras  3810 ,  3820 ,  3830 , and  3840  arranged at various positions. Each of the vehicle cameras  3810 ,  3820 ,  3830 , and  3840  may include an image sensor according to an example embodiment. The vehicle  3800  may provide various information about the interior or surroundings of the vehicle  3800  to a driver by using the vehicle cameras  3810 ,  3820 ,  3830 , and  3840 , and may provide information for autonomous driving by automatically recognizing objects or people in images. 
     While image sensors including color separation lens arrays, and electronic devices including the image sensors have been described according to example embodiments with reference to the accompanying drawings, the image sensors and the electronic devices are merely examples, and it will be understood by those of ordinary skill in the art that various changes and equivalent other embodiments may be made therefrom. Therefore, the example embodiments described herein should be considered in a descriptive sense only and not for purposes of limitation. The scope of the present disclosure is defined not by the above description but by the following claims, and all differences within equivalent ranges of the scope of the present disclosure should be considered as being included in the scope of the present disclosure. 
     As described above, according to the one or more of the above example embodiments, the image sensor is capable of adjusting the optical distance between the light detector and the color separation lens array configured to split incident light according to the wavelength of the incident light. 
     Because the image sensor acquires optical information from different spectra formed according to a plurality of optical distances, the image sensor may have reproducibility with high spectroscopic sensitivity compared to the case of using only three colors: red, green, and blue. 
     The photographing device employing the image sensor may provide high-quality images. 
     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 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.