Patent Publication Number: US-2023148437-A9

Title: Imaging apparatus and image sensor including the same

Description:
CROSS-REFERENCE TO RELATED APPLICATION 
     This application is a continuation-in-part of U.S. application Ser. No. 15/923,554, filed on Mar. 16, 2018, which is a continuation of U.S. application Ser. No. 15/134,885, filed on Apr. 21, 2016, which issued as U.S. Pat. No. 9,946,051 and claims priority from U.S. Provisional Application No. 62/151,108, filed on Apr. 22, 2015 in the U.S. Patent and Trademark Office, and Korean Patent Application No. 10-2016-0003672, filed on Jan. 12, 2016 in the Korean Intellectual Property Office, the disclosures of which are incorporated herein in their entireties by reference. 
    
    
     This invention was made with government support under Grant No. W911NF-14-1-0345 awarded by the ARO-US Army. The government has certain rights in the invention. 
    
    
     BACKGROUND 
     1. Field 
     Apparatuses and systems consistent with exemplary embodiments relate to imaging apparatuses and image systems including the same. 
     2. Description of the Related Art 
     Optical sensors including semiconductor sensor arrays are frequently used in mobile devices, wearable devices, and the Internet of Things. Although such devices are ideally small, it is difficult to reduce the thicknesses of imaging apparatuses included in such sensor arrays. 
     Conventional imaging apparatuses using optical lenses include many optical lenses in order to remove chromatic aberration and geometric aberration and ensure a desired f-number. Since the optical lenses must have predetermined shapes in order to perform their respective functions, there is a limitation in reducing the thicknesses of such conventional imaging apparatuses. 
     SUMMARY 
     One or more exemplary embodiments provide imaging apparatuses that may be designed to be small and image systems including such imaging apparatuses. 
     Additional exemplary aspects and advantages 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 
     According to an aspect of an example embodiment, there is provided an imaging apparatus including a first optical device, a second optical device disposed such that light transmitted through the first optical device is incident on the second optical device, and a third optical device disposed such that light transmitted through the second optical device is incident on the third optical device, wherein at least one of the first optical device, the second optical device, and the third optical device includes a plurality of nanostructures, and heights of at least two nanostructures of the plurality of nanostructures are different from each other. 
     A difference in the heights of the at least two nanostructures may be equal to or less than 2λ, where λ is a wavelength of the light. 
     The heights of the at least two nanostructures may be equal to or greater than λ/2 and equal to or less than 3λ, where λ is a wavelength of the light. 
     The plurality of nanostructures may be disposed in a multilayer structure. 
     The multilayer structure may include a first layer and a second layer, and the plurality of nanostructures may include a plurality of lower nanostructures included in the first layer and a plurality of upper nanostructures included in the second layer. 
     The plurality of lower nanostructures and the plurality of upper nanostructures may be disposed to face each other, and a central axis of at least one of the plurality of lower nanostructures and a central axis of at least one of the plurality of upper nanostructures are offset. 
     A distance between the plurality of lower nanostructures and the plurality of upper nanostructures in a height direction may be greater than λ/2, where λ is a wavelength of the light. 
     A shape distribution of the plurality of lower nanostructures and a shape distribution of the plurality of upper nanostructures may be determined such that a performance index for each location of the imaging apparatus is different from performance indices of other locations of the imaging apparatus, and the shape distribution may include a shape, a width, a height, and an arrangement of each of the plurality of nanostructures. 
     The shape distribution of the plurality of lower nanostructures and the shape distribution of the plurality of upper nanostructures may be determined such that non-uniformity of focusing performances for locations of the imaging apparatus compensate each other. 
     At least two nanostructures of the plurality of nanostructures may have widths that are different from each other. 
     The first optical device may be a refractive optical lens, and each of the second optical device and the third optical device may be a thin lens including the plurality of nanostructures. 
     The plurality of nanostructures of the second optical device and the plurality of nanostructures of the third optical device may be configured to offset a chromatic aberration of the second optical device and a chromatic aberration of the third optical device with each other. 
     The first optical device may be configured to offset at least one of a geometric aberration and a chromatic aberration of at least one of the second optical device and the third optical device. 
     Each of the plurality of nanostructures may include at least one material selected from a group consisting of crystalline silicon (c-Si), polycrystalline silicon (p-Si), amorphous silicon (a-Si), III-V compound semiconductors, SiC, TiO 2 , and SiN. 
     According to an aspect of an example embodiment, there is provided an image system including at least one imaging apparatus, and at least one light measurer corresponding, respectively, to each imaging apparatus of the at least one imaging apparatus, each light measurer of the at least one light measurer being configured to measure light incident on an image plane of a corresponding imaging apparatus of the at least one imaging apparatus, wherein the at least one imaging apparatus includes a first optical device, a second optical device disposed such that light transmitted through the first optical device is incident on the second optical device, and a third optical device disposed such that light transmitted through the second optical device is incident on the third optical device, and wherein at least one of the first optical device, the second optical device, and the third optical device includes a plurality of nanostructures, and at least two nanostructures of the plurality of nanostructures have heights that are different from each other. 
     A difference in the heights of the at least two nanostructures may be less than or equal to 2λ, where λ is a wavelength of the light. 
     A height of each of the at least two nanostructures may be equal to or great than λ/2 and equal to or less than 3λ, where λ is a wavelength of the light. 
     The plurality of nanostructures may be disposed in a multilayer structure. 
     The multilayer structure may include a first layer and a second layer, and the plurality of nanostructures may include a plurality of lower nanostructures included in the first layer and a plurality of upper nanostructures included in the second layer. 
     The plurality of lower nanostructures and the plurality of upper nanostructures may be disposed to face each other, and a central axis of at least one of the plurality of lower nanostructures and a central axis of at least one of the plurality of upper nanostructures may be offset. 
     The plurality of lower nanostructures and the plurality of upper nanostructures in a height direction may be greater than λ/2, where λ is a wavelength of the light. 
     A shape distribution of the plurality of lower nanostructures and a shape distribution of the plurality of upper nanostructures may be determined such that a performance index for each location of the imaging apparatus is different from performance indices of other locations of the imaging apparatus, and the shape distribution includes a shape, a width, a height, and an arrangement of each of the plurality of nanostructures. 
     The shape distribution of the plurality of lower nanostructures and the shape distribution of the plurality of upper nanostructures may be determined such that non-uniformity of focusing performances for locations of the at least one imaging apparatus compensate each other. 
     At least two nanostructures of the plurality of nanostructures may have widths that are different from each other. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       These and/or other exemplary aspects and advantages will become apparent and more readily appreciated from the following description of exemplary embodiments, taken in conjunction with the accompanying drawings in which: 
         FIG.  1    is a view of a related art imaging apparatus including refractive optical lenses; 
         FIG.  2    is a view of an imaging apparatus according to an exemplary embodiment; 
         FIG.  3    is a view illustrating a state in which incident light passes through a first optical device according to an exemplary embodiment; 
         FIG.  4    is a view illustrating a state in which light passes through a second optical device according to an exemplary embodiment; 
         FIG.  5    is a view illustrating a state in which light passes through a third optical device according to an exemplary embodiment; 
         FIG.  6    is a view illustrating an entire optical path of the imaging apparatus of  FIGS.  2  through  5    according to an exemplary embodiment; 
         FIG.  7    is a view of an imaging apparatus according to an exemplary embodiment; 
         FIG.  8    is a view of an imaging apparatus according to an exemplary embodiment; 
         FIG.  9    is a view of an imaging apparatus according to an exemplary embodiment; 
         FIG.  10    is a view of a thin-lens according to an exemplary embodiment; 
         FIG.  11    is a view illustrating a part of a surface of the first optical device of  FIG.  10    according to an exemplary embodiment; 
         FIG.  12    is a view illustrating a surface of the first optical device of  FIG.  10    according to another exemplary embodiment; 
         FIG.  13    is a view of the imaging apparatus according to an exemplary embodiment; 
         FIG.  14    is a plan view showing that an optical device according to an embodiment is divided into a plurality of regions; 
         FIG.  15    is a cross-sectional view taken along line AA′ of  FIG.  14   ; 
         FIG.  16    is a cross-sectional view of a schematic structure of an optical device according to another exemplary embodiment; 
         FIG.  17    is a graph illustrating a target phase for each wavelength to be satisfied by nanostructures included in respective regions of the optical device of  FIG.  16   ; 
         FIG.  18    is a cross-sectional view of a schematic structure of an optical device according to another exemplary embodiment. 
         FIG.  19    is a cross-sectional view of a schematic structure of an optical device according to another exemplary embodiment; 
         FIG.  20    shows example design data of a width and a pitch of positions of lower nanostructures arranged in a first layer in the optical device of  FIG.  19   ; 
         FIG.  21    is a graph showing comparison between a target phase value and phase values by nanostructures designed as shown in  FIG.  20   ; 
         FIG.  22    is a graph showing a performance index obtained by quantifying a difference between the target value and the design value shown in  FIG.  21   ; 
         FIG.  23    is a cross-sectional view of a schematic structure of an optical device according to another exemplary embodiment; 
         FIG.  24    is a view of an image system according to an exemplary embodiment; and 
         FIG.  25    is a view of the image system according to an exemplary embodiment. 
     
    
    
     DETAILED DESCRIPTION 
     The inventive concept will now be described more fully with reference to the accompanying drawings, in which exemplary embodiments of the invention are shown. In the drawings, the same reference numerals denote the same elements and sizes of components may be exaggerated for clarity. The inventive concept may have different forms and should not be construed as limited to the exemplary embodiments set forth herein. For example, it will also be understood that when a layer is referred to as being “over” another layer or a substrate, it can be directly on the other layer or the substrate, or intervening layers may also be present therebetween. 
     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. 
       FIG.  1    is a view of a related art imaging apparatus including optical lenses  10 ,  20 ,  30 , and  40 . The optical lenses  10 ,  20 ,  30 , and  40  are refractive lenses. 
     Each of the optical lenses  10 ,  20 ,  30 , and  40  may include a material having a refractive index different from that of a medium outside the optical lens. A path of light passing through each of the optical lenses  10 ,  20 ,  30 , and  40  may be changed by changing at least one of a refractive index of the lens, and the shape of the lens, for example, the curvature of a surface of the lens. Also, a light-converging point on an image plane S 1 , as formed by light transmitted through the imaging apparatus, may be changed by appropriately changing the shapes of the optical lenses  10 ,  20 ,  30 , and  40  and/or intervals between the optical lenses  10 ,  20 ,  30 , and  40 . 
     However, since a refractive index of a refractive optical lens is different for different wavelengths of light, chromatic aberration may occur. Also, the light-converging points formed by light transmitted through an optical lens may have geometric aberration in which a focus is distorted. For example, geometric aberration in which a plane on which a focus is formed is not flat but curved, may lead to field curvature. 
     In order to control chromatic aberration and geometric aberration, an imaging apparatus may be designed by combining lenses having various shapes. However, in this case, since a number of optical lenses having various shapes are included in the imaging apparatus, the thickness of the imaging apparatus may be increased. Alternately, when the thickness of the imaging apparatus is reduced, that is, an f-number of the lenses is reduced, the ratio of a thickness to a diameter of each of the lenses may be increased. The f-number of a lens is a number obtained by dividing a focal length of the lens by a diameter of the lens, and the luminance of an image projected by the lens is dependent, in part, on the f-number. Clearly, if the thickness of each lens in an imaging apparatus is increased, there is limit in the degree to which the total thickness of the imaging apparatus may be reduced. 
     In order to reduce the size of an imaging apparatus, the thickness of the imaging apparatus has to be reduced and the f-number of each of the lenses included in the imaging apparatus has to be reduced to a predetermined value or less. Since there is a limit by using refractive index-based lenses, a new thin-lens may be used to achieve these objectives. 
       FIG.  2    is a view of an imaging apparatus  100  according to an exemplary embodiment. 
     Referring to  FIG.  2   , the imaging apparatus  100  according to an exemplary embodiment may include a first optical device  110  configured to focus incident light so that the location of a focal point of the incident light is dependent on the incident angle of the light, a second optical device  120  configured to focus light having been transmitted through the first optical device  110  so that the light transmitted through the second optical device  120  has a focal length that is dependent on the location of the focal point of the light transmitted through the first optical device  110 , and a third optical device  130  configured so that light transmitted through the second optical device  120  is focused onto focal points on the image plane S 1 . 
     At least one of the first through third optical devices  110 ,  120 , and  130  may be a thin-lens including a substrate on which plurality of nanostructures are provided. The term ‘thin-lens’ refers to an optical device that alters a path of light transmitted therethrough by adjusting a phase delay and a phase delay distribution of the transmitted light according to nanostructures disposed on a surface of a substrate. In contrast, as discussed above, an optical lens determines a path of light transmitted therethrough according to the shape and refractive index of the optical lens. Accordingly, a degree to which the thickness of a thin-lens array can be reduced is not limited in the way that the thickness of an optical lens array is limited, and a thin-lens array may be quite thin. 
     The nanostructures may have a sufficiently greater refractive index than that of a medium outside the nanostructures and may have a transmittance and a transmission phase dependent on a shape and a material of the nanostructures. Light incident on nanostructures is coupled in one or more waveguide modes of the nanostructures and resonates within the nanostructures. Amplitudes and phases of light transmitted through or reflected from the nanostructures may be determined by such resonance characteristics. In order to form a desired optical device (e. g. a thin-lens), nanostructures may be arranged, and the shapes of the nanostructures may be determined in accordance with a transmission phase and amplitude distribution (e.g., a converging or diverging wave front) of the desired optical device. 
     Although nanostructures  112 ,  122 , and  132  are respectively illustrated on surfaces of substrates of the first through third optical devices  110 ,  120 , and  130  facing the image plane S 1  in  FIG.  2   , the present exemplary embodiment is not limited thereto. For example, the nanostructures  112 ,  122 , and  132  may be provided on surfaces of substrates of the first through third optical devices  110 ,  120 , and  130  on which light is incident. Alternatively, the nanostructures  112 ,  122 , and  132  may be provided on both surfaces of substrates of the first through third optical devices  110 ,  120 , and  130 . 
     Also, although the first through third optical devices  110 ,  120 , and  130  of  FIG.  2    are all thin-lenses, the present exemplary embodiment is not limited thereto. For example, one or two of the first through third optical devices  110 ,  120 , and  130  may be designed as thin-lenses, and the remaining one or more lenses may be optical lens(es). 
     Light reflected from an object (not shown) may be incident on the first optical device  110 .  FIG.  3    is a view illustrating a state in which incident light is transmitted through the first optical device  110  according to an exemplary embodiment. 
     Referring to  FIG.  3   , the first optical device  110  may focus incident light so that the focal point of the incident light is dependent on the incident angle of the incident light. For example, second incident light L 21  is incident in a direction parallel to an arrangement direction in which the first through third optical devices  110 ,  120 , and  130  are arranged (e.g. a direction normal to planes of each of the first through third optical devices  110 ,  120 , and  130 —i.e. a left-to-right direction as illustrated in  FIG.  3   ), and the second incident light L 21  may therefore be directed to a focal point along a line parallel to the arrangement direction which passes through the center of the second optical device  120 , as shown in  FIG.  3   . In contrast, first incident light L 11 , which is incident on the first optical device  110  in a direction oblique to the arrangement direction may be directed to a focal point spaced away from a line which passes through the center of the second optical device  120 . The first optical device  110  may include the plurality of nanostructures  112  provided on a surface of a substrate thereof, such that the path of light incident thereon is re-directed. 
     The nanostructures  112  may be provided on a surface of a substrate of the first optical device  110  facing the image plane S 1 . However, the present exemplary embodiment is not limited thereto. Alternatively, the nanostructures  112  may be provided on a surface of a substrate on which incident light is incident. Alternatively, the nanostructures  112  may be provided on both surfaces of a substrate of the first optical device  110 . 
     The nanostructures  112  provided on a surface of a substrate of the first optical device  110  may be designed so that the first optical device  110  functions as a lens having positive refractive power. By selecting the shapes and heights of and the intervals between the nanostructures  112 , the first optical device  110  may be made to change a path of light incident thereon in the same way that a lens having positive refractive power changes a path of light incident thereon. Thus, since the first optical device  110  has positive refractive power and is arranged substantially parallel to the second and third optical devices  120  and  130 , the first incident light L 11 , incident in a direction oblique to the arrangement direction of the first through third optical devices  110 ,  120 , and  130 —i.e. incident at a non-normal angle with respect to a plane of the first optical device  110 , may be directed to a focal point at off a principal axis of the first optical device  110 . The principal axis of the first optical device is illustrated by the long- and short-dashed line of  FIG.  3   . Also, the second incident light L 21 , incident in a direction normal to the plane of the first optical device  110 , may be directed to a focal point along the principal axis of the first optical device  110 . 
     Light transmitted through the first optical device  110  may be incident on the second optical device  120 . The second optical device  120  may focus light incident thereon so that the light transmitted through the second optical device  120  has a focal length dependent on the position on the second optical device  120  on which the light is incident. 
       FIG.  4    is a view illustrating a state in which light passes through the second optical device  120  according to an exemplary embodiment. 
     Referring to  FIG.  4   , the second optical device  120  may focus light so that the focal lengths of the light depend on the position on the second optical device on which the light is incident. For example, second light L 22  is incident on a center of the second optical device  120  and is focused to have a relatively short focal length. In contrast, first light L 12  is incident on an edge of the second optical device  120  and is focused to have a relatively long focal length. Since the second optical device  120  focuses incident light so that light incident on an edge has a longer focal length, an optical path difference according to an incident angle may be compensated for. The second optical device  120  may include the plurality of nanostructures  122  provided on a surface of a substrate thereof in order to refract incident light. 
     The nanostructures  122  may be provided on a surface of a substrate the second optical device  120  facing the image plane S 1 . However, the present exemplary embodiment is not limited thereto. Alternatively, the nanostructures  122  may be provided on a surface a substrate of the second optical device  120  on which light is incident. Alternatively, the nanostructures  122  may be provided on both surfaces of a substrate of the second optical device  120 . 
     The nanostructures  122  provided on a surface of the substrate of the second optical device  120  may be designed so that the second optical device  120  functions as a lens having negative refractive power. By selecting the shapes and heights of and the intervals between the nanostructures  122 , the second optical device  120  may be made to change a path of light incident thereon, like a lens having negative refractive power. Thus, since the second optical device  120  has negative refractive power and is arranged substantially parallel to the first and third optical devices  110  and  130 , the first incident light L 12 , incident in a direction oblique to the arrangement direction of the first through third optical devices  110 ,  120 , and  130  (incident at a non-normal angle with respect to a plane of the first optical device  120 ) may be focused to have a relatively long focal length. Also, the second incident light L 22 , incident in a direction normal to the plane of the second optical device  120 , may be focused to have a relatively short focal length. 
     Light having been transmitted through the second optical device  120  may be incident on the third optical device  130 . The third optical device  130  may change a path of light having passed through the second optical device  120  to form a focal point on the image plane S 1 . In this case, the image plane S 1  may be an arbitrary plane spaced apart by a predetermined interval from the third optical device  130 . The image plane S 1  may be flat. However, the present exemplary embodiment is not limited thereto, and the image plane S 1  may be curved. 
       FIG.  5    is a view illustrating a state in which light passes through the third optical device  130  according to an exemplary embodiment. 
     Referring to  FIG.  5   , the third optical device  130  may be configured so that light incident on the third optical device  130  form focal points on the image plane S 1 . In this case, the third optical device  120  may change paths of light having passed through the third optical device  130  so that the light having passed through the third optical device  130  is incident on the image plane S 1  at an angle normal to the image plane. However, the present exemplary embodiment is not limited thereto. Alternatively, light having passed through different positions on the third optical device  130  may be incident at different angles on the image plane S 1 . 
     For example, the third optical device  130  may be configured so that light incident toward an edge of the third optical device  130  has a transmission phase distribution having a short focal length. That is, first light L 13  incident on an edge of the third optical device  130  may be focused to have a transmission phase distribution having a relatively short focal length. In contrast, second light L 23  incident on a center of the third optical device  130  may be focused to have a transmission phase distribution having a relatively long focal length. Since the third optical device  130  focuses light so that the light has different focal lengths of the third optical device dependent on the position on the third optical device  130  on which the light is incident. The light having passed through the third optical device  130  may form imaging focal points on the image plane S 1 . The third optical device  130  may include the plurality of nanostructures  132  provided on a surface of a substrate thereof in order to change a travel direction of incident light. 
     The nanostructures  132  may be provided on a surface of a substrate of the third optical device  130  facing the image plane S 1 . However, the present exemplary embodiment is not limited thereto. Alternatively, the nanostructures  132  may be provided on a surface of a substrate of the third optical device  130  on which light is incident. Alternatively, the nanostructures  132  may be provided on both surfaces of a substrate of the third optical device  130 . 
     The nanostructures  132  provided on a surface of a substrate of the third optical device  130  may be designed so that the third optical device  120  functions as a lens having positive refractive power. By adjusting the shapes and heights of and the intervals between the nanostructures  132 , the third optical device  130  may be made to deflect light at each location, like a lens having positive refractive power. Since the third optical device  130  has a positive refractive power, the first incident light L 13  incident in a direction oblique to the arrangement direction of the first through third optical devices  110 ,  120 , and  130  may be focused by a relatively short focal length of the third optical device in the location where L 13  is incident. Also, the second incident light L 23  incident in a direction parallel to the arrangement direction of the first through third optical devices  110 ,  120 , and  130  may be focused by a relatively long focal length of the third optical device in the location where L 13  is incident. 
       FIG.  6    is a view illustrating an entire optical path of the imaging apparatus  100  of  FIGS.  2  through  5    according to an exemplary embodiment. 
     Referring to  FIG.  6   , irrespective of an incident angle of incident light, as light passes through the first through third optical devices  110 ,  120 , and  130 , focal points may be formed on the image plane S 1 . Also, a position at which a focal point is formed on the image plane S 1  may vary according to the incident angle of incident light. Accordingly, when a plurality of light-receiving units having different coordinates are provided on the image plane S 1 , each of the light-receiving units may correspond to a pixel. 
     The first through third optical devices  110 ,  120 , and  130  may be designed to offset chromatic aberration and geometric aberration which may alter a path of light. To this end, the shapes, cross-sectional areas, heights, material compositions, and intervals of the nanostructures  112 ,  122 , and  132  respectively included in the first through third optical devices  110 ,  120 , and  130  may be appropriately determined. 
     The first through third optical devices  110 ,  120 , and  130  are thin-lenses respectively including the nanostructures  112 ,  122 , and  132  in  FIGS.  2  through  6   . However, the present exemplary embodiment is not limited thereto. For example, any two of the first through third optical devices  110 ,  120 , and  130  may be thin-lenses and the remaining one may be an optical lens using a refractive index-based method. Alternatively, any one of the first through third optical devices  110 ,  120 , and  130  may be a thin-lens and the remaining two may be optical lenses using a refractive index-based method. 
       FIG.  7    is a view of the imaging apparatus  100  according to an exemplary embodiment. 
     Referring to  FIG.  7   , the first optical device  110  may be an optical device using a refractive index-based method, and the second and third optical devices  120  and  130  may be thin-lenses respectively including the nanostructures  122  and  132 . The nanostructures  122  and  132  of the second and third optical devices  120  and  130  may be designed to minimize chromatic aberration that occurs in the second and third optical devices  120  and  130 . To this end, shapes, cross-sectional areas, heights, material compositions, and intervals of the nanostructures  122  and  132  respectively included in the second and third optical devices  120  and  130  may be appropriately determined. 
     The first optical device  110  may be designed to correct at least one of chromatic aberration and geometric aberration not corrected by the second and third optical devices  120  and  130 . To this end, a refractive index of the first optical device  110  may be determined by appropriately selecting a material included in the first optical device  110 . Also, lens characteristics of the first optical device  110  may be adjusted by changing a surface shape and a thickness of the first optical device  110 . 
       FIG.  8    is a view of the imaging apparatus  100  according to an exemplary embodiment. 
     Referring to  FIG.  8   , the first optical device  110  may be a thin-lens including the nanostructures  112 , and the second and third optical devices  120  and  130  may be optical lenses using a refractive index-based method. The nanostructures  112  of the first optical device  110  may be designed to offset at least one of chromatic aberration and geometric aberration that occur in the second and third optical devices  120  and  130 . To this end, shapes, cross-sectional areas, heights, material compositions, and intervals of the nanostructures  112  included in the first optical device  110  may be appropriately determined. 
     The first optical device  110  is separate from the second optical device  120  in  FIG.  8   . However, since the first optical device  110  is a thin-lens and there is no limitation in a surface shape, the first optical device  110  may be integrally formed with the second optical device  120 . 
       FIG.  9    is a view of the imaging apparatus  100  according to an exemplary embodiment. 
     Referring to  FIG.  9   , the first optical device  110  that is a thin-lens may be provided on a surface of the second optical device  120 . Although the first optical device  110  is provided on a surface of the second optical device  120  on which light is incident in  FIG.  9   , the present exemplary embodiment is not limited thereto. For example, the first optical device  110  may be provided on a surface of the second optical device  120  facing the image plane S 1 . 
     When the first optical device  110  is provided on a surface of the second optical device  120  as shown in  FIG.  9   , since there is no interval between the first optical device  110  and the second optical device  120 , a size of the imaging apparatus  100  may be reduced. 
       FIG.  10    is a view of a thin-lens described in the above according to an exemplary embodiment. 
     With reference to  FIG.  10   , exemplary embodiments of the first optical device  110  of  FIGS.  2  through  6    will be explained. 
     Referring to  FIG.  10   , the first optical device  110  that is a thin-lens may include the plurality of nanostructures  112  and a substrate  114  on which the nanostructures  112  are arranged. The substrate  114  may be a support for forming the nanostructures  112 . Also, a material layer (not shown) that surrounds the nanostructures  112  may be added.  FIG.  10    is a conceptual view of the nanostructures  112 , and actual sizes and numbers of the nanostructures  112  may be different from those shown in  FIG.  10   . 
     Referring to an alternate view of a surface S 2  in  FIG.  10   , shapes, materials, and arrangements of the nanostructures  112  may vary according to positions on the first optical device  110 . Since shapes, materials, and arrangements of the nanostructures  112  vary according to positions on the first optical device  110 , travel directions of transmitted light may be changed by determining a transmission phase distribution of light according to positions on the first optical device  110 . 
       FIG.  11    is a view illustrating a part of a surface of the first optical device  110  of  FIG.  10    according to an exemplary embodiment. 
     Referring to  FIG.  11   , the nanostructures  112  having circular cylindrical shapes may be arranged on the substrate  114 . Although the nanostructures  112  have circular cylindrical shapes in  FIG.  11   , the present exemplary embodiment is not limited thereto. For example, the nanostructures  112  may have any of various shapes such as polygonal prism shapes, circular cylindrical shapes, or elliptic cylindrical shapes. Alternatively, cross-sections of the nanostructures  112  may have “L”-like prism shapes. 
     Shapes of the nanostructures  112  may not be symmetric in a specific direction. For example, cross-sections of the nanostructures  112  may not be symmetric in a horizontal direction, to have, for example, elliptic shapes. Also, since cross-sections of the nanostructures  112  vary according to heights, shapes of the nanostructures  112  may not be symmetric in a vertical direction. 
     A refractive index of a material included in the nanostructures  112  may be greater (for example, by 1.5 or more) than a refractive index of materials composing the substrate  114 , a material layer (not shown), which may surround the nanostructures  112  and a peripheral portion. Accordingly, the substrate  114  may include a material with a relatively low refractive index and the nanostructures  112  may include a material with a relatively high refractive index. 
     For example, the nanostructures  112  may include at least one of crystalline silicon (c-Si), polycrystalline silicon (poly-Si), amorphous silicon (a-Si), Si 3 N 4 , GaP, TiO0 2 , AlSb, AlAs, AlGaAs, AlGaInP, BP, and ZnGeP2. Also, the substrate  114  may include any one of a polymer (e.g., poly(methyl methacrylate) (PMMA)), plastic, and SiO 2  (e.g., glass or quartz). 
     The first through third optical devices  110 ,  120 , and  130  may change a direction of incident light according to a wavelength of the incident light. Accordingly, the imaging apparatus  100  may be configured so that only incident light of a predetermined wavelength range forms a focal point on the image plane S 1 . A wavelength that is allowed by the imaging apparatus  100  to form a focal point on the image plane S 1  in a wavelength range of incident light is referred to as an operating wavelength. The operating wavelength may include, for example, a wavelength (about 650 nm) of red light, a wavelength (about 475 nm) of blue light, and a wavelength (about 510 nm) of green light. Also, the operating wavelength may include a wavelength (about 800 nm to 900 nm) of infrared light. The values are exemplary, and the operating wavelength of the imaging apparatus  100  may be set in other ways. For example, a band of wavelengths can be set as an operating wavelength range. 
     Once the operating wavelength is determined, the first through third optical devices  110 ,  120 , and  130  may also be designed to correspond to the operating wavelength. For example, detailed shapes (e.g., intervals, cross-sectional shapes, or heights) and materials of the nanostructures  122 ,  122 , and  132  respectively included in the first through third optical devices  110 ,  120 , and  130  may be determined to correspond to the operating wavelength. 
     Referring back to  FIG.  11   , an interval T between adjacent nanostructures of the nanostructures  112  may be less than the operating wavelength of the imaging apparatus  100 . For example, the interval T between the nanostructures  112  may be equal to or less than ¾ or ⅔ of the operating wavelength of the imaging apparatus  100  or may be equal to or less than ½ of the operating wavelength. A height h of each of the nanostructures  112  may be equal to or less than ⅔ of the operating wavelength. The interval T, height h and shape of the nanostructures may vary depending on the location of the nanostructures in the thin-lens. 
       FIG.  12    is a view illustrating a surface of the first optical device  110  of  FIG.  10    according to another exemplary embodiment. 
     Referring to  FIG.  12   , the nanostructures  112  having rectangular parallelepiped shapes may be arranged on the substrate  114 . Although the nanostructures  112  have rectangular parallelepiped shapes in  FIG.  12   , the present exemplary embodiment is not limited thereto. For example, the nanostructures  112  may have any of various shapes such as polygonal prism shapes, circular cylindrical shapes, or elliptic cylindrical shapes. Alternatively, cross-sections of the nanostructures  112  may have prism shapes. 
     Heights and intervals of the nanostructures  112  may be determined according to an operating wavelength of the imaging apparatus  100 . An interval T between adjacent nanostructures of the nanostructures  112  may be less than the operating wavelength of the imaging apparatus  100 . For example, the interval T between the nanostructures  112  may be equal to or less than ¾ or ⅔ of the operating wavelength of the imaging apparatus  100 , or may be equal to or less than ½ of the operating wavelength. Also, a height h of each of the nanostructures  112  may be less than the operating wavelength. For example, the height h of each of the nanostructures  112  may be equal to or less than ⅔ of the operating wavelength. The interval T, height h and shape of the nanostructures may vary depending on the location of the nanostructures in the thin-lens. 
     The description of the substrate  114  and the nanostructures  112  made with reference to  FIGS.  11  and  12    may apply to the second and third optical devices  120  and  130 . That is, when the second and third optical devices  120  and  130  are thin-lenses, the description of the nanostructures  112  made with reference to  FIGS.  11  and  12    may apply to the nanostructures  122  and  132  respectively included in the second and third optical devices  120  and  130 . 
       FIG.  13    is a view of the imaging apparatus  100  according to an exemplary embodiment. 
     In  FIG.  13   , a repeated explanation of the same elements or operations as those in  FIGS.  1  through  12    will not be given. 
     Referring to  FIG.  13   , the imaging apparatus  100  according to an exemplary embodiment may further include an optical filter  140  configured to prevent light having a wavelength other than operating wavelength range from being incident on the image plane S 1 . Although the optical filter  140  is provided between the third optical device  130  and the image plane S 1  in  FIG.  13   , a position of the optical filter  140  is not limited thereto. The optical filter  140  may be provided between the second optical device  120  and the third optical device  130  or may be provided between the first optical device  110  and the second optical device  120 . Alternatively, the optical filter  140  may be provided in front of an incident surface of the optical filter  110  and may enable only light having the operating wavelength from among incident light to be incident on the first optical device  110 . 
     The optical filter  140  may absorb or reflect light having wavelengths other than the operating wavelength range of the imaging apparatus  100  from among light incident on the optical filter  140 . The optical filter  140  may prevent light having wavelengths other than the operating wavelength range from being incident as noise on the image plane S 1 . 
     Hereinafter, optical elements included in the image pickup device according to the exemplary embodiment will be described. 
       FIG.  14    is a plan view showing that a region of an optical device  200  according to an embodiment is divided into a plurality of regions.  FIG.  15    is a cross-sectional view taken along line AA′ of  FIG.  14   . 
     Referring to  FIGS.  14  and  15   , the optical device  200  may include a first region  220 _ 1 , a second region  220 _ 2 , . . . and an N-th region  220 _N. The first region  220 _ 1  may be a central region and have a circular shape, and the second region  220 _ 2  to the N-th region  220 _N may have a ring shape concentrically surrounding the first region  220 _ 1 . N may be a natural number that is equal to or greater than three. The plurality of regions are provided such that the shape, spacing, arrangement rules, etc. of the nanostructures NS 1  to NS N  disposed in each region may be distinguished and controlled for each region. Further, the number of regions, the size of each of the regions, etc. may be determined based on optical functions and performances to be implemented by the optical device  200 . 
     Referring to  FIG.  15   , the first region  220 _ 1  includes a plurality of first nanostructures NS 1  two-dimensionally arranged in a radial direction and a circumferential direction. The plurality of first nanostructures NS 1  may be distributed according to a first rule. Here, a rule may be applied to parameters such as shape, size (width, height), spacing, array shape, etc. of the k-th nanostructure NS k  (1≤k≤N), and these parameters may be constant within the same area, or may be expressed as a function of position. 
     The second region  220 _ 2  includes a plurality of second nanostructures NS 2  that are two-dimensionally arranged in the radial direction and the circumferential direction. The plurality of second nanostructures NS 2  may be distributed according to a second rule. 
     The N-th region  220 _N includes a plurality of N-th nanostructures NS N  two-dimensionally arranged in the radial direction and the circumferential direction. The plurality of N-th nanostructures NS N  may be distributed according to an N-th rule. 
     Shapes, widths, heights, and spacing of the nanostructures NS k  (1≤k≤N) included in each of the plurality of regions are shown as constant, and a k-th nanostructure NS k  provided in the k-th region  120 _ k  may be set according to a k-th rule. Not all of the first to N-th rules may be different from each other. For example, some or all of the first to N-th rules may be identical to each other. 
     The substrate  210  and the nanostructure NS k  may include materials having different refractive indices. A refractive index difference between the refractive index of the substrate  210  and a refractive indices of the nanostructure NS k  may be greater than or equal to 0.5. The refractive index of the nanostructure NS k  may be greater than that the refractive index of the substrate  210 , but embodiments are not limited thereto. For example, the refractive index of the nanostructure NS k  may be less than the refractive index of the substrate  210 . 
     The protective layer  230  is a layer covering and protecting the plurality of nanostructures NS k  as a whole, and may include a material having a refractive index different from refractive indices of the nanostructures NS k . A difference between the refractive index of the protective layer  230  and the refractive index of the nanostructure NS k  may be greater than or equal to 0.5. The protective layer  230  may include a material having a refractive index less than refractive indices of the nanostructure NS k . In this case, the protective layer  230  may be omitted. However, embodiments are not limited thereto, and the refractive index of the protective layer  230  may be greater than refractive indices of the nanostructure NS k . 
     The substrate  210  may include any one of glass (fused silica, BK7, etc.), quartz, polymer (PMMA, SU-8, etc.), and plastic, or may include a semiconductor substrate. The nanostructure NS k  may include at least one of c-Si, p-Si, a-Si, and a Group III-V compound semiconductor (GaP, GaN, GaAs, etc.), SiC, TiO 2 , and SiN. The protective layer  230  may include a polymer material, such as SU-8, PMMA, or a low refractive index material, such as SiO 2 . 
     In this way, the nanostructure NS k  having a refractive index difference from a surrounding material may change the phase of light passing through the nanostructure NS k  based on the phase delay caused by geometric dimensions of sub-wavelengths of the nanostructures NS k . The degree of the phase delay may be determined by a detailed shape dimension, an arrangement form, etc. of the nanostructure NS k . Various optical functions may be achieved by appropriately setting the degree of phase delay occurring in each of the plurality of nanostructures NS k . 
     The number of the plurality of regions and a rule applied thereto may be arranged such that the optical element  200  shows refractive power with respect to light of a predetermined wavelength band. For example, the predetermined wavelength band may be a visible light wavelength band. The refractive power may be a positive refractive power, such as a convex lens or a negative refractive power, such as a concave lens. An absolute value of the refractive power may be increased by increasing the number of regions. A sign of refractive power is determined according to the size distribution trend in each region, and the trend may be opposite to each other based on the optical element  200  having a positive refractive power or a negative refractive power. For example, the optical element  200  may have a positive refractive power when the size of the nanostructure NS k  decreases in a radial direction in each region, and the optical element  200  may have a negative refractive power when the size of the nanostructure NS k  increases in the radial direction. 
     The number of the plurality of regions and a rule applied thereto may be set such that the optical element  200  has a negative Abbe number. Since a general refractive lens, for example, a refractive lens having a curved shape on an entrance or exit surface of light to exhibit refractive power has a positive Abbe number, there is a limit in controlling dispersion to a desired degree. 
     Abbe&#39;s number is related to the dispersion shown by the optical element  200 . Chromatic dispersion is due to the property that a general medium exhibits different refractive indices for different wavelengths, and Abbe&#39;s number V d  is defined as follows in Equation 1. 
         V   d =( n   d −1)/( n   F   −n   C )  [Equation 1]
 
     In Equation 1, nd, nF, and nC respectively represent the refractive index with respect to light of d line (587.5618 nm), C line (656.2816 nm), and F line (486.1327 nm). 
     If the color dispersion due to the refractive index difference according to a wavelength is large, the refractive power acting on incident light varies according to a color of the incident light, and thus chromatic aberration occurs. In order to compensate for such chromatic aberration, when composing an imaging lens, a method of using two lenses having a large difference in Abbe&#39;s number together is generally used. Since the optical element  200  according to an exemplary embodiment may have a negative Abbe number, it may more effectively compensate for chromatic aberration generated in another lens by being employed in an imaging lens. Here, the negative Abbe&#39;s number is an example, but embodiments are not limited thereto. The number of the plurality of regions and a rule applied thereto may be set such that the optical element  200  has an Abbe number of a desired value for appropriate chromatic aberration compensation. 
     Widths of the plurality of regions may be different from each other. For example, a radius of the first region  220 _ 1  having a circular shape may be greater than a radial width of the ring-shaped second region  220 _ 2 . Also, the width of the ring shape may gradually decrease from the third region  220 _ 3  to the N-th region  220 _N. However, this is an example and embodiments are not limited thereto. 
     A plurality of first nanostructures NS 1 , a plurality of second nanostructures NS 2 , . . . a plurality of N-th nanostructure NS N  may be arranged as a whole to have polar symmetry. For example, the plurality of nanostructures NS k  (1≤k≤N) may be arranged to have rotational symmetry of a predetermined angle with a Z axis as a rotation axis. In this case, the shape of the nanostructure NS k  at each position or a distance between the nanostructures NS k  adjacent to each other may be expressed as a function of r irrespective of φ. Here, r is a radius in polar coordinates, and φ is an angle between a reference line in the polar coordinates. 
     According to an example embodiment, the plurality of first nanostructure NS 1 , the plurality of second nanostructures NS 2 , . . . the plurality of N-th nanostructures NS N  may be arranged to have polar symmetry in the k-th region  120 _ k  to which each nanostructure NS k  belongs. For example, the first nanostructures NS 1  disposed in the first region  120 _ 1  may be arranged to have rotational symmetry of a predetermined angle Δφ 1 , and the second nanostructures NS 2  disposed in the second region  120 _ 2  may have rotational symmetry of an angle Δφ 2  different from the predetermined angle. An angle Δφ k  of rotational symmetry may become smaller as k becomes larger, for example, a region farther from the center of the optical element  200 . However, this is an example. The angle of rotational symmetry may not be different in all regions, but may be different in at least two regions. 
       FIG.  16    is a cross-sectional view of a schematic structure of an optical device  201  according to an exemplary embodiment.  FIG.  17    is a graph conceptually showing a target phase for each wavelength to be satisfied by the nanostructures included in each region of  FIG.  16   . 
       FIG.  16    is a view corresponding to a cross-sectional view taken along line AA′ in the plan view of  FIG.  14   . The optical device  201  may include a first region  221 _ 1 , a second region  221 _ 2 , . . . and an N-th region  221 _N. The optical element  201  may define an arrangement rule of nanostructures NS k  in each of the k-th regions  221 _ k  (1≤k≤N) to exhibit refractive power with respect to light of a predetermined wavelength band. The optical element  201  according to the exemplary embodiment is different from the above-described optical element  200  in that heights H different from each other are applied to at least two nanostructures NS k  included in the same region among the first region  221 _ 1  and the second region  221 _ 2 , . . . to the N-th region  221 _N. In  FIG.  16   , nanostructures NS k  having different heights are provided in all regions, however, embodiments are not limited thereto. For example, in some regions, the heights of the nanostructures NS k  may be the same. 
     A height difference ΔH of the at least two nanostructures NS k  may be 2λ or less with respect to a wavelength λ within a predetermined wavelength band. The height H of the second nanostructure NS 2  may be in a range of λ/2≤H≤3λ with respect to the wavelength λ, within a predetermined wavelength band. 
     Based on the plurality of nanostructures NS k  being formed to have different heights from each other, chromatic aberration, dispersion according to a wavelength in applying refractive power to light of a wider wavelength band, may be more easily controlled. 
     In order to express refractive power with respect to incident light, a predetermined arrangement rule may be applied to the nanostructure NS k  disposed in each of the plurality of regions  221 _ k . The nanostructure NS k  having a refractive index difference from a surrounding material may change the phase of light passing through the nanostructure NS k . Here, the phase change to be implemented by the nanostructure NS k  may be a target phase. For each region, a target phase φ target  as shown in  FIG.  17    may be set. The target phase φ target  is set to represent a phase change range of 2π based on the center wavelength λ m  in a given region in the form as shown in  FIG.  14   , and in this regard, the plurality of regions  221 _ k  may be a 2π zone. 
     As shown in  FIG.  17   , the target phase φ target  is slightly different for light having different wavelengths λ 1 , λ m , and λ s . The different wavelengths λ 1 , λ m , and λ s  may be, for example, red, green, and blue wavelength bands. In order to implement desired target phases for light having a predetermined wavelength, a rule defining the shape, size, and arrangement of the nanostructures NS k  disposed in the plurality of 2π zones may be determined. Hereinafter, a shape distribution may include shape, size, arrangement, etc. together. The degree of changing the target phase φ target  is related to the dispersion Δφ, and the wavelength range including λ 1 , λ m , and λ s  described above is related to a bandwidth BW. The shape condition of each of the nanostructures NS k  that may implement a dispersion Δφ within a desired range for a desired bandwidth BW may be set from a pre-prepared phase-dispersion map. The phase-dispersion map may be created by a method in which the nanostructures are set to a constant height and the shape conditions by various combinations of a width and a pitch are displayed at a position corresponding to a phase-dispersion at the center wavelength. Design dimensions that may exhibit a desired performance at the desired location may be selected within the map. In the case of introducing a height variation, a plurality of phase-dispersion maps having different height conditions may be set and overlapped, for example, a range for selecting the shape of the nanostructure NS k  may be increased. In this way, the shape and arrangement of the nanostructures NS k  may be determined to freely control chromatic aberration while widening the focusing wavelength band. 
     In  FIG.  16   , heights H, widths w, and pitches p of the plurality of nanostructures NS k  are randomly illustrated, but embodiments are not limited thereto. For each of the plurality of regions  221 _ k , a predetermined rule may be set and applied to the height H, the width w, and the pitch p. 
       FIG.  18    is a cross-sectional view showing a schematic structure of an optical device  202  according to another exemplary embodiment. 
     Similar to  FIG.  16   ,  FIG.  18    is a view corresponding to a cross-sectional view taken along line AA in the plan view of  FIG.  14   . The optical device  202  may include a first region  222 _ 1 , a second region  222 _ 2 , . . . and an N-th region  222 _N. The optical device  202  may define an arrangement rule of nanostructures NS k  in each of the first region  222 _ 1  and the second region  222 _ 2  to the N-th region  222 _N to exhibit refractive power with respect to light of a predetermined wavelength band. 
     In the optical device  202  according to the exemplary embodiment, the plurality of nanostructures NS k  included in the first region  222 _ 1 , the second region  222 _ 2 , . . . and the N-th region  222 _N are arranged in a multi-layer structure. The multi-layer structure may include, for example, a first layer LA 1  and a second layer LA 2 . The plurality of nanostructures NS k  may include a plurality of lower nanostructures constituting the first layer LA 1  and a plurality of upper nanostructures constituting the second layer LA 2 . 
     The first layer LA 1  and the second layer LA 2  may be separated in a height direction (Z direction). In order to form the first layer LA 1  and the second layer LA 2 , a low refractive index material layer  231  including a material having a refractive index that is lower than the refractive index of the lower nanostructures and covering the plurality of lower nanostructures may be formed, and a plurality of upper nanostructures may be arranged on the low refractive index material layer  231 . In order to cover and protect the plurality of upper nanostructures, a protective layer  233  including a material having a refractive index that is lower than the refractive index of the upper nanostructures may further be provided. The low refractive index protective layer  233  may be omitted. 
       FIG.  19    is a cross-sectional view of a schematic structure of an optical device  203  according to another exemplary embodiment. 
     Similar to  FIG.  16   ,  FIG.  19    is also a view corresponding to a cross-sectional view taken along line AA in the plan view of  FIG.  14   . The optical device  203  may include a first region  223 _ 1 , a second region  223 _ 2 , and an N-th region  223 _N. The optical device  203  may define an arrangement rule of nanostructures NS k  in each of the first region  223 _ 1 , the second region  223 _ 2 , . . . and the N-th region  223 _N to exhibit refractive power with respect to light of a predetermined wavelength band. 
     The optical device  203  according to the exemplary embodiment is different from the optical devices  200  and  201  in that a plurality of nanostructures NS k  included in the first region  223 _ 1 , the second region  223 _ 2 , . . . and the N-th region  223 _N are arranged in a plurality of layers. The plurality of nanostructures NS k  may be classified into a plurality of lower nanostructures constituting a first layer LA 1  and a plurality of upper nanostructures constituting a second layer LA 2 . 
     The first layer LA 1  and the second layer LA 2  are separated in a height direction (Z direction). In order to form the first layer LA 1  and the second layer LA 2 , a low refractive index material layer  231  including a material having a refractive index that is lower than a refractive index of the lower nanostructures and covering the plurality of lower nanostructures may be formed, and a plurality of upper nanostructures may be arranged on the low refractive index material layer  231 . In order to cover and protect the plurality of upper nanostructures, a protective layer  233  including a material having a refractive index that is lower than a refractive index of the upper nanostructures may further be provided. The low refractive index protective layer  233  may be omitted. 
     The lower nanostructures constituting the first layer LA 1  and the upper nanostructures constituting the second layer LA 2  may be arranged to face each other in an offset manner. For example, central axes of at least some of the upper nanostructures and the lower nanostructures facing each other may not match with each other, however, not all of the lower nanostructures and the upper nanostructures that are facing each other may be arranged in an offset manner from each other. 
     A distance d between the lower nanostructures and the upper nanostructures of the plurality of lower nanostructures and the plurality of upper nanostructures, for example, a separation distance in the height direction (Z direction) may be greater than λ/2 with respect to the wavelength λ, within the predetermined wavelength band. 
     Based on the nanostructures NS k  being arranged in a plurality of layers may reduce the possibility of performance degradation that may occur at some locations even if the shape of each of the nanostructures NS k  is set to match with the desired target phase. This will be described with reference to  FIGS.  17 ,  20 , and  21   . 
     As illustrated in  FIG.  17   , the target phase in each region may also be applied to the optical device  203  of  FIG.  19   . For example, the size and arrangement of the nanostructures NS k  arranged in a two-layer structure in the plurality of regions  223 _ k  of the optical device  203  may be set to satisfy the target phase as shown in  FIG.  17    for each of the plurality of regions.  FIG.  20    shows example design data of a width w and a pitch p of positions of the nanostructures NS k  arranged in the first layer LA 1  in the optical device  203  of  FIG.  19   . 
       FIG.  21    is a graph showing comparison between a target phase value and phase values by nanostructures NS k  designed as shown in  FIG.  20   . In the graph, a graph of a target phase value is indicated as ‘target’, and a graph of a phase value by the nanostructures NS k  designed to implement the target phase value is indicated as ‘designed’. As illustrated in  FIG.  21   , the two graphs do not completely match but have errors, and also, the degree of inconsistency is different depending on positions. 
       FIG.  22    is a graph showing a performance index representing a difference between a target value and a designed value shown in  FIG.  21   . The performance index is numerically calculated for each position in a radial direction by integrating the degree of correlation between a target transmittance, transmission intensity and transmission phase, and an actual transmittance in an entire wavelength band under consideration. The graphs may be merit functions. The closer to 1 a number appearing on the vertical axis of the graph is the better the correlation, and a position where the degree of correlation is the lowest may be seen from points Q downwardly indicating polar point. 
       FIG.  23    is a cross-sectional view of a schematic structure of an optical device  204  according to another exemplary embodiment. 
     The optical device  204  may include a first region  224 _ 1 , a second region  224 _ 2 , . . . and an N-th region  224 _N. The optical device  204  may define an arrangement rule of nanostructures NS k  in each of the first region  224 _ 1 , the second region  224 _ 2 , . . . and the N-th region  224 _N to exhibit refractive power with respect to light of a predetermined wavelength band. 
     In the exemplary embodiment, among the plurality of nanostructures NS k  constituting the first layer LA 1  of the optical element  204 , at least two of the nanostructures NS k  included in the same region may have different heights from each other. Also, among the plurality of nanostructures NS k  constituting the second layer LA 2  of the optical device  204 , at least two nanostructures NS k  included in the same region may have different heights from each other. As described in the embodiment described with reference to  FIG.  16   , it is more easy to set a design value that may implement an appropriate phase dispersion at each position by applying a height variation. In particular, when it is needed to mutually compensate for performance degradation of each layer by introducing a plurality of nanostructure NS k  arrays, it may be easier to select a design value of the nanostructures NS k  that compensate for the performance degradation of the nanostructure NS k  located at the position of another layer corresponding to the position of low correlation in a layer. Also, a more effective mutual compensation for phase and dispersion performance between layers may be possible. 
     In  FIG.  23   , it is depicted that nanostructures NS k  of various heights are applied to both the first layer LA 1  and the second layer LA 2 , but embodiments are not limited thereto. For example, in one of the first layer LA 1  and the second layer LA 2 , the nanostructures NS k  may be arranged at a constant height, and in another layer, nanostructures NS k  having different heights may be selected at appropriate positions as needed. Also, although a plurality of layers are illustrated in all regions  224 _ k , embodiments are not limited thereto. A parameter for determining a rule to be applied to each region  224 _ k  may include a plurality of layers or a height variation. 
       FIG.  24    is a view of an image system  1000  according to an exemplary embodiment. 
     Referring to  FIG.  24   , the image system  1000  according to an exemplary embodiment may include the imaging apparatus  1100  and a light measurer  1200  provided to correspond to the imaging apparatus  1100 . 
     The description of the imaging apparatus  100  made with reference to  FIGS.  2  through  23    may apply to the imaging apparatus  100  of  FIG.  24   . The light measurer  1200  may be provided on the image plane S 1  of the imaging apparatus  100 . The light measurer  1200  may measure light focused by the imaging apparatus  100 . The light measurer  1200  may include a plurality of light systems. As the number of the light systems included in the light measurer  1200  increases, a resolution of an image output from the light measurer  1200  may increase. The light system may be a pixel array of a complementary metal-oxide-semiconductor (CMOS) image sensor (CIS) using a charge-coupled device (CCD) or a CMOS. Alternatively, the light sensor may be a photodiode sensor. 
       FIG.  25    is a view of the image system  1000 A according to an exemplary embodiment. 
     Referring to  FIG.  25   , the image system  1000 A according to an exemplary embodiment may include a plurality of imaging apparatuses, for example, first through third imaging apparatuses  1100   a ,  1100   b , and  1100   c . At least two of the first through third imaging apparatuses  1100   a ,  1100   b , and  1100   c  may have different operating wavelengths. That is, at least two of the first through third imaging apparatuses  1100   a ,  1100   b , and  1100   c  may concentrate light having different wavelengths so that the light having different wavelengths are directed to the image plane S 1 . Also, each of the first through third imaging apparatuses  1100   a ,  1100   b , and  1100   c  may include an optical filter for filtering light having wavelengths other than an operating wavelength range from among incident light. 
     For example, the first imaging apparatus  1100   a  may focus red light, the second imaging apparatus  1100   b  may focus blue light, and the third imaging apparatus  1100   c  may focus green light. However, the present exemplary embodiment is not limited thereto, and operating wavelengths of the imaging apparatuses  1100   a ,  1100   b , and  1100   c  may be set in other ways. Also, all of the first through third imaging apparatuses  1100   a ,  1100   b , and  1100   c  may have different operating wavelengths, or some of the first through third imaging apparatuses  1100   a ,  1100   b , and  1100   c  may have the same operating wavelength. 
     The image system  1000 A may include a plurality of light measurers  1200   a ,  1200   b , and  1200   c  provided to respectively correspond to the first through third imaging apparatuses  1100   a ,  1100   b , and  1100   c . The light measurers  1200   a ,  1200   b , and  1200   c  may be provided on the image planes Si of the first through third imaging apparatuses  1100   a ,  1100   b , and  1100   c  and may generate images of an object OBJ by measuring light focused by the imaging apparatuses  1100   a ,  1100   b , and  1100   c.    
     The imaging apparatus  1100  and the image system  1000  including the imaging apparatus  1100  according to the one or more exemplary embodiments have been described with reference to  FIGS.  1  through  23    As described above, since at least one of the first through third optical devices  110 ,  120 , and  130  of the imaging apparatus  100  is a thin-lens including nanostructures, a thickness of the imaging apparatus  100  may be reduced. Also, chromatic aberration and geometric aberration of the imaging apparatus  100  may be reduced. 
     Since the imaging apparatus  1100  and the image system  1000  according to the one or more embodiments may be easily made compact, the imaging apparatus  1100  and the image system  1000  may be applied to a camera requiring a small pixel and a high resolution. Also, the imaging apparatus  100  and the image system  1000  may be applied to a pixel array of a color image system for a light field 3D camera requiring a lot of pixel information. Also, the imaging apparatus  100  and the image system  1000  may be applied to a system array for hyperspectral imaging. In addition, the imaging apparatus  1100  and the image system  1000  may be included in an optical bio-system such as a blood pressure system or a heart rate system using a spectrometer. 
     While one or more exemplary 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.