Patent Publication Number: US-11378797-B2

Title: Focusing device comprising a plurality of scatterers and beam scanner and scope device

Description:
CROSS-REFERENCE TO RELATED APPLICATIONS 
     This application is a continuation in part application of U.S. patent application Ser. No. 15/987,090, filed on May 23, 2018, which is a continuation of application Ser. No. 15/093,987, filed on Apr. 8, 2016, now U.S. Pat. No. 995,930, issued on Jun. 12, 2018, which claims the benefit of U.S. Provisional Patent Application 62/144,750, filed on Apr. 8, 2015, in the U.S. Patent and Trademark Office, and Korean Patent Application No. 10-2016-0014992, filed on Feb. 5, 2016, in the Korean Intellectual Property Office, the disclosures of which are incorporated herein in their entireties by reference. 
    
    
     STATEMENT REGARDING FEDERALLY SPONSORED RESEARCH OR DEVELOPMENT 
     This invention was made with government support under Grant No. W911NF-14-1-0345 awarded by the U.S. Army. The government has certain rights in the invention. 
    
    
     BACKGROUND 
     1. Field 
     Apparatuses and methods consistent with the present disclosure relate to a focusing device, and a beam scanner and a scope device that use the focusing device as an optical path modifier. 
     2. Description of the Related Art 
     Optical sensors using semiconductor-based sensor arrays are widely used in mobile devices, wearable devices, and the Internet of Things (IoT). Although size reduction of the aforementioned devices is desired, it is difficult to reduce the thickness of focusing devices in the aforementioned devices. 
     Also, due to the increased use of 3-dimensional (3D) image sensors in the IoT, gaming devices, and other mobile devices, focusing devices for adjusting a path of light incident on the 3D image sensors are required. However, the fields of view of the focusing devices may be limited by coma aberration of the focusing devices. Thus, research has been conducted to combine a plurality of optical lenses and thus remove coma aberration. However, since a substantial amount of space is necessary to combine a plurality of optical lenses, it is difficult to reduce the size of the focusing devices. 
     SUMMARY 
     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 exemplary embodiments. 
     According to an aspect of an exemplary embodiment, a focusing device includes a substrate; a first thin lens provided at a first surface of the substrate and comprising a plurality of first scatterers; and a second thin lens provided at a second surface of the substrate and comprising a plurality of second scatterers. The first scatterers of the first thin lens are configured to correct geometric aberration (field curvature, coma aberration, astigmatism, etc.) of the second thin lens. 
     The first and second thin lenses may be configured to allow light to form a focusing point on a focal plane regardless of an angle at which light is incident on the first surface. 
     A phase shift of light that passes through the second scatterers may decrease from a central area of the second thin lens to a peripheral area of the second thin lens. 
     A phase shift of light that passes through the first scatterers may decrease from a peripheral area of the first thin lens to a middle area of the first thin lens and increases again from the middle area of the first thin lens to a central area of the first thin lens. 
     The first and second thin lenses may be configured to change a location at which light is focused on the focal plane according to the angle at which the light is incident on the first surface. 
     The first and second thin lenses area configured to determine the location at which the light may be focused on the focal plane according to Equation 1:
 
 h=f *tan θ
 
     wherein ‘h’ is a distance between the location of the focusing point and an optical axis of the focusing device, ‘f’ is an effective focal length of the focusing device, and ‘θ’ is the incident angle of light. 
     Respective refractive indexes of the first and second scatterers may be greater than a refractive index of the substrate. 
     The substrate may include at least one selected from glass (fused silica, BK7, etc.), quartz, polymer (PMMA, SU-8, etc.) and plastic, and the first and second scatterers comprise at least one selected from crystalline silicon (c-Si), polycrystalline silicon (poly Si), amorphous silicon (a-Si), and group III-V compound semiconductors (GaP, GAN, GaAs, etc.), SiC, TiO 2 , and SiN. 
     The first and second scatterers may be configured to allow incident light within a wavelength band to form a focusing point on a focal plane. 
     Distances between the first scatterers and distances between the second scatterers may be less than wavelengths in the wavelength band. 
     Respective heights of the first scatterers and respective heights of the second scatterers may be less than wavelengths in the wavelength band. 
     The focusing device may further include an optical filter configured to block the incident light of wavelengths of outside the wavelength band. 
     At least one of respective shapes of the first and second scatterers and respective sizes of the first and second scatterers may change according to a thickness of the substrate. 
     Each of the first and second scatterers may have at least one of a cylindrical shape, a cylindroid shape, and a polyhedral pillar shape. 
     According to another aspect of an exemplary embodiment, a beam scanner includes an optical path modifier comprising a substrate, a first thin lens provided at a first surface of the substrate and comprising a plurality of first scatterers, and a second thin lens provided at a second surface of the substrate and comprising a plurality of second scatterers; and a light source array spaced apart from the second surface of the substrate and comprising a plurality of light sources. The first scatterers of the first thin lens are configured to correct coma aberration of the second thin lens. 
     The optical path modifier may change path of light emitted from the light sources according to respective locations of the light sources. 
     The optical path modifier may modify light emitted from one of the light sources into parallel rays. 
     According to another aspect of an exemplary embodiment, a scope device includes an object lens unit comprising a substrate; a first thin lens provided at a first surface of the substrate and comprising a plurality of first scatterers, and a second thin lens provided at a second surface of the substrate and comprising a plurality of second scatterers; and a light source facing the second surface of the substrate and configured to emit light on a target object. The first scatterers of the first thin lens are configured to correct coma aberration of the second thin lens. 
     Light emitted by the light source may have at least two wavelengths with different transmission rates with respect to the target object. 
     The light emitted by the light source may be scattered at different locations by the target object according to wavelengths of the light emitted by the light source. The object lens unit may be configured to change a path of the light according to the locations at which the light is scattered by the target object. 
     According to another aspect of an exemplary embodiment, a focusing device with respect to light of predetermined wavelength band includes: a substrate; a first thin lens provided at a first surface of the substrate and comprising a plurality of first scatterers; and a second thin lens provided at a second surface of the substrate and comprising a plurality of second scatterers, wherein the plurality of first scatterers of the first thin lens are configured to correct geometric aberration of the second thin lens, and wherein at least two of the plurality of second scatterers have different height to each other. 
     A height difference of the at least two second scatterer may be equal to or less than 2λ, with respect to the wavelength λ within the predetermined wavelength band. 
     A height H of the plurality of second scatterers may be in a range that λ/2≤H≤3λ, with respect to the wavelength A within the predetermined wavelength band. 
     The second thin lens may further include a low refractive index material layer covering the plurality of second scatterers and including a material having a refractive index lower than a refractive index of plurality of the second scatterers; and a plurality of third scatterer arranged on the low refractive index material layer and including a material having a refractive index higher than a refractive index of the low refractive index material layer. 
     The plurality of second scatterers and the plurality of third scatterers may face each other to be misaligned with each other. 
     A separation distance in a height direction between adjacent second and third scatterers among the plurality of second scatterers and the plurality of third scatterers may be greater than λ/2, with respect to the wavelength λ within the predetermined wavelength band 
     A shape distribution of the plurality of second scatterers and a shape distribution of the plurality of third scatterers may be determined to have different distributions of performance indexes by locations from each other. 
     The shape distribution of the plurality of second scatterers and the shape distribution of the plurality of third scatterers may be determined to mutually compensate for non-uniformity in focusing performance by locations. 
     At least two of the plurality of third scatterers may have different heights from each other. 
     A height difference between at least two of the plurality of third scatterers may be equal to or less than 2λ, with respect to the wavelength λ within the predetermined wavelength band. 
     A height H of a plurality of fourth scatterers may be in a range that λ/2≤H≤3λ, with respect to the wavelength λ within the predetermined wavelength band. 
     At least two of the plurality of first scatterers may have different heights from each other. 
     The first thin lens may further include: a low refractive index material layer covering the plurality of first scatterers and including a material having a refractive index lower than a refractive index of the first scatterer; and a plurality of fourth scatterers arranged on the low refractive index material layer and including a material having a refractive index higher than a refractive index of the low refractive index material layer. 
     The plurality of first scatterers and the plurality of fourth scatterers may face each other to be misaligned with each other. 
     A separation distance in a height direction between adjacent first and fourth scatterers among the plurality of first scatterers and the plurality of fourth scatterers may be equal to or less than λ/2, with respect to the wavelength λ within the predetermined wavelength band. 
     According to another aspect of the exemplary embodiment, a focusing device with respect to light of predetermined wavelength band includes: a substrate; a first thin lens provided at a first surface of the substrate and comprising a plurality of first scatterers; and a second thin lens provided at a second surface of the substrate and comprising a plurality of scatterers, wherein the plurality of first scatterers of the first thin lens are configured to correct geometric aberration of the second thin lens, and wherein the plurality of scatterers of the second thin lens are arranged in multi-layered structure. 
     The second thin lens may include: a plurality of second scatterers arranged on the second surface; a low refractive index material layer covering the plurality of second scatterers and including a material having a refractive index lower than a refractive index of the plurality of second scatterers; and a plurality of third scatterers arranged on the low refractive index material layer and including a material having a refractive index higher than a refractive index of the low refractive index material layer. 
     The plurality of second scatterers and the plurality of third scatterers may face each other to be misaligned with each other. 
     A shape distribution of the plurality of second scatterers and a shape distribution of the plurality of third scatterers may be determined to mutually compensate for non-uniformity in focusing performance by locations. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       These and/or other aspects will become apparent and more readily appreciated from the following description of the exemplary embodiments, taken in conjunction with the accompanying drawings in which: 
         FIG. 1  is a diagram of a focusing device according to a comparative example; 
         FIG. 2  is a diagram of an example in which light is obliquely incident with respect to an optical axis of the focusing device of  FIG. 1 ; 
         FIGS. 3A to 3C  are diagrams of light intensity distribution of a focal plane; 
         FIGS. 4A and 4B  are diagrams of light intensity distribution on the focal plane according to incident angles of light; 
         FIG. 5  is a focusing device according to an exemplary embodiment; 
         FIG. 6  is an exemplary diagram of a surface of a second thin lens; 
         FIGS. 7A to 7C  are perspective views of various shapes of first and second scatterers; 
         FIG. 8A  is a phase profile of a second thin lens; 
         FIG. 8B  is a diagram of a phase profile of a first thin lens; 
         FIG. 9  is an exemplary diagram of a path of light incident on the focusing device of  FIG. 5 ; 
         FIGS. 10A and 10B  are diagrams of light intensity distribution in a substrate in the focusing device of  FIG. 5 ; 
         FIGS. 11A to 11F  are diagrams of light intensity distribution of an image formed on a focal plane by the focusing device of  FIG. 5 ; 
         FIG. 12  is a graph of light intensity distribution of an image formed on a focal plane by the focusing device of  FIG. 5 ; 
         FIG. 13  is an exemplary diagram of forming an image of an object by a focusing device; 
         FIG. 14  is a graph of a relationship between locations of focusing points and incident angles of light; 
         FIG. 15  is an exemplary diagram of an arrangement of first and second scatterers; 
         FIGS. 16A to 16C  are diagrams for describing changes in paths of incident light according to wavelengths of the incident light; 
         FIGS. 17A to 17C  are diagrams of light intensity distribution of an image formed on a focal plane by light incident in parallel to an optical axis of a focusing device; 
         FIG. 18  is a diagram of changes in light intensity distribution of an image according to wavelengths and incident angles of incident light; 
         FIG. 19  is a diagram of a focusing device according to another exemplary embodiment; 
         FIG. 20  is an imaging device according to another exemplary embodiment; 
         FIG. 21  is a diagram of a beam scanner according to an exemplary embodiment; 
         FIG. 22  is a diagram of a scope device according to another exemplary embodiment; and 
         FIG. 23  is an exemplary diagram of observing a target object by using a scope device. 
         FIG. 24  is a diagram of a focusing device according to another exemplary embodiment. 
         FIG. 25  is an exemplary diagram of classification of regions related to the arrangement of second scatterers provided in a second thin lens of the focusing device of  FIG. 24 . 
         FIG. 26  is a graph conceptually showing a target phase for each wavelength to be satisfied by scatterers in each region of  FIG. 25 . 
         FIG. 27  is a diagram of a focusing device according to another exemplary embodiment. 
         FIG. 28  is an exemplary diagram of the second scatterers arranged in one region of a first layer of the second thin lens in the focusing device of  FIG. 27 . 
         FIG. 29  is an exemplary diagram of design data of a pitch and a width by locations of the second scatterers arranged in the first layer of the second thin lens of the focusing device of  FIG. 27 . 
         FIG. 30  is a graph of a comparison between a target phase value and a phase value by the scatterers designed as in  FIG. 28 . 
         FIG. 31  is a graph of a performance index obtained by quantifying a difference between a target value and a design value in  FIG. 30 . 
         FIG. 32  is a diagram of a focusing device according to another exemplary embodiment. 
         FIG. 33  is a diagram of a focusing device according to another exemplary embodiment. 
         FIG. 34  is a diagram of a focusing device according to another exemplary embodiment. 
     
    
    
     DETAILED DESCRIPTION 
     Reference will now be made in detail to exemplary embodiments, examples of which are illustrated in the accompanying drawings, wherein like reference numerals refer to like elements throughout. In this regard, the present exemplary embodiments may have different forms and should not be construed as being limited to the descriptions set forth herein. Accordingly, the exemplary embodiments are merely described below, by referring to the figures, to explain aspects. 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. 
     Reference will now be made in detail to exemplary embodiments, examples of which are illustrated in the accompanying drawings. 
     The terms used in the exemplary embodiments are selected as general terms used currently as widely as possible considering the functions in the present disclosure, but they may depend on the intentions of one of ordinary skill in the art, practice, the appearance of new technologies, etc. In specific cases, terms arbitrarily selected by the applicant are also used, and in such cases, their meaning will be described in detail. Thus, it should be noted that the terms used in the specification should be understood not based on their literal names but by their given definitions and descriptions through the specification. 
     Throughout the specification, it will also be understood that when an element is referred to as being “connected to” another element, it can be directly connected to the other element, or electrically connected to the other element while intervening elements may also be present. Also, when a part “includes” or “comprises” an element, unless there is a particular description contrary thereto, the part can further include other elements, not excluding the other elements. In addition, the terms such as “unit,” “-er (-or),” and “module” described in the specification refer to an element for performing at least one function or operation, and may be implemented in hardware, software, or the combination of hardware and software. 
     The terms “configured of” or “includes” should not be construed as necessarily including all elements or operations described in the specification. It will be understood that some elements and some operations may not be included, or additional elements or operations may be further included. 
     While such terms as “first,” “second,” “A,” “B,” etc., may be used to describe various components, such components must not be limited to the above terms. The above terms are used only to distinguish one component from another. 
     The present exemplary embodiments may have different forms and should not be construed as being limited to the descriptions set forth herein. Elements and features that may be easily derived by one of ordinary skill in the art to which the present disclosure pertains are within the spirit and scope of the present disclosure as defined by the appended claims. Hereinafter, the present exemplary embodiments will be described with reference to the accompanying drawings. 
       FIG. 1  is a diagram of a focusing device according to a comparative example. 
     Referring to  FIG. 1 , the focusing device according to the comparative example may include a substrate  10  and a plurality of scatterers  20  provided at a side of the substrate  10 . In the focusing device of  FIG. 1 , a path of light exiting the substrate  10  may change as light passes through the plurality of scatterers  20 . Shapes and materials of the plurality of scatterers  20  may vary according to functions performed by the plurality of scatterers  20 . For example, the plurality of scatterers  20  of the focusing device of  FIG. 1  may have a shape and a size appropriate for performing a function of a lens with positive refractive power. Also, as shown in  FIG. 1 , the plurality of scatterers  20  may allow light that is perpendicularly incident on the substrate  10  to form a focusing point at a focal plane S 0 . 
       FIG. 2  is a diagram of an example in which light is obliquely incident with respect to an optical axis (z-axis) of the focusing device of  FIG. 1 ; 
     Referring to  FIG. 2 , light incident in a direction that is not parallel to the optical axis of the focusing device may pass through the plurality of scatterers  20  but not focus on a single focusing point. Such phenomenon is referred to as geometric aberration. The geometric aberration may include coma aberration and field of curvature aberration. The aforementioned geometric aberration may decrease sharpness of images formed by the focusing device. Also, the geometric aberration limits a field of view (FOV) of the focusing device. 
       FIGS. 3A to 3C  are diagrams of light intensity distribution of a focal plane. 
       FIG. 3A  shows light intensity distribution of an image formed by light that is parallel to the optical axis (z-axis) of the focusing device.  FIG. 3B  shows light intensity distribution of an image formed by light incident at an incident angle of 1° with respect to the optical axis.  FIG. 3C  shows light intensity distribution of an image formed by light incident at an incident angle of 3° with respect to the optical axis. Bars at a right hand side of  FIGS. 3A to 3B  indicates relative intensity of light. 
     Referring to  FIG. 3A , when an incident angle of light is 0° (i.e., when light is parallel to the optical axis of the focusing device), an area with high light intensity distribution may be narrow. That is, a focusing effect of the focusing device may be relatively excellent. Referring to  FIG. 3B , when the incident angle of light is 1°, an area with high intensity of light is wide. As the incident angle of light increases, the focusing effect of the focusing device may decrease. Referring to  FIG. 3C , when the incident angle of light is 3°, intensity of light may decrease in a central area of the image. However, peripheral areas of the image may have greater intensity of light as the incident angle increases. That is, even when the incident angle of light increases by a small amount, the focusing effect of the focusing device may substantially decrease. 
       FIGS. 4A and 4B  are diagrams of light intensity distribution on the focal plane S 0  according to incident angles of light. 
     Referring to  FIG. 4A , as the incident angle of light increases, peaks may be differently located in a graph of light intensity distribution. Also, as the incident angle increases, the graph of light intensity distribution may be widened and peak values may decrease. Referring to  FIG. 4B , when the incident angle is 3° or higher, peak values of the light intensity distribution may decrease below more than half of peak values of when the incident angle is 0°. Also, a range of light intensity distribution may substantially increase. When the incident angle of light exceeds about 1°, image distortion due to coma aberration may increase. 
       FIG. 5  is a focusing device  100  according to an exemplary embodiment. 
     Referring to  FIG. 5 , the focusing device  100  according to an exemplary embodiment may include a substrate  110 , a first thin lens  120  including a plurality of first scatterers  122  provided on a first surface S 1  of the substrate  110 , and a second thin lens  130  including a plurality of second scatterers  132  provided on a second surface S 2  of the substrate  110 . 
     The substrate  110  may be shaped as a plate. The first and second surfaces S 1  and S 2  of the substrate  110  may be substantially parallel to each other. However, the first and second surfaces S 1  and S 2  do not have to be completely parallel to each other but may be oblique with respect to each other. The substrate  110  may include a transparent material. The transparent material indicates a material with a high light transmission rate. For example, the substrate  110  may include at least one selected from glass (fused silica, BK7, etc.), quartz, polymer (PMMA, SU-8, etc.), and plastic. 
     The first thin lens  120  may include the plurality of first scatterers  122  that are arranged on the first surface S 1  of the substrate  110 . Also, the second thin lens  130  may include the plurality of second scatterers  132  that are arranged on the second surface S 2  of the substrate  110 . Unlike optical lenses of the related art, the first and second thin lenses  120  and  130  may change a path of light by using the plurality of first and the plurality of second scatterers  122  and  132 . The plurality of first and the plurality of second scatterers  122  and  132  may capture light incident near one another and resonate light inside the plurality of first and the plurality of second scatterers  122  and  132 . The plurality of first and the plurality of second scatterers  122  and  132  may adjust transmission and reflection properties of the light incident on the plurality of first and the plurality of second scatterers  122  and  132 . For example, the plurality of first and the plurality of second scatterers  122  and  132  may modulate at least one of an amplitude, phase, and polarization of transmitted light according to structures and included materials of the plurality of first and the plurality of second scatterers  122  and  132 . The plurality of first and the plurality of second scatterers  122  and  132  may be arranged such that distribution of at least one of an amplitude, phase, and polarization of the transmitted light is modulated and thus a wavefront of the transmitted light changes with respect to a wavefront of the incident light. Therefore, the plurality of first and the plurality of second scatterers  122  and  132  may change a proceeding direction of the transmitted light with respect to that of the incident light. 
     The second thin lens  130  may function as a lens with positive refractive power. Shapes, sizes, materials, and an arrangement pattern of the plurality of second scatterers  132  may be modified so that the second thin lens  130  has positive refractive power. Also, the plurality of second scatterers  132  may be designed such that the second thin lens  130  does not cause spherical aberration. To do so, the shapes, the sizes, the materials, and the arrangement of the plurality of second scatterers  132  may vary according to a location on a surface of the substrate  110  where the plurality of second scatterers  132  are arranged. 
       FIG. 6  is an exemplary diagram of a surface of the second thin lens  130 . 
     Referring to  FIG. 6 , the plurality of second scatterers  132  may be arranged on the surface of the second thin lens  130 . Waveform of light that passed through the second thin lens  130  may vary according to shapes, arrangement intervals, and an arrangement pattern of the plurality of second scatterers  132 . When the plurality of second scatterers  132  are arranged on the surface of the second thin lens  130  as shown in  FIG. 6 , the second thin lens  130  may function as a lens with positive refractive power. 
     The plurality of first scatterers  122  of the first thin lens  120  may be designed to correct coma aberration of the second thin lens  130 . Shapes, materials, and arrangement pattern of the plurality of first scatterers  122  may vary depending on a thickness of the substrate  110  and the shapes, the materials, and the arrangement pattern of the plurality of second scatterers  132 . In a general optical system, a plurality of optical lenses are combined to correct coma aberration of lenses. Therefore, the general optical system may be difficult to design and size reduction may be difficult. However, the focusing device  100  according to an exemplary embodiment may have the first and second thin lenses  120  and  130  on both surfaces of the substrate  110  by arranging the plurality of first and plurality of second scatterers  122  and  132  on the both surfaces of the substrate  110 . Accordingly, size reduction of the focusing device  100  may become convenient. Also, since the first thin lens  120  may correct coma aberration of the second thin lens  130 , the focusing device  100  may have a wide FOV. 
       FIGS. 7A to 7C  are perspective views of various shapes of the individual scatterers of plurality of first and plurality of second scatterers  122  and  132 . 
     Referring to  FIGS. 7A to 7C , the individual scatterers of the plurality of first and the individual scatterers of the plurality of second scatterers  122  and  132  in the first and second thin lenses  120  and  130  may have a pillar structure. Such pillar structure may have any one of circular, oval, rectangular, and square cross-sections.  FIG. 7A  shows a scatterer shaped as a pillar with a circular cross-section.  FIG. 7B  shows a scatterer shaped as a pillar with an oval cross-section.  FIG. 7C  shows a scatterer shaped as a pillar with a quadrilateral cross-section. The pillar structure may be inclined at an angle in a height direction. 
     Although exemplary shapes of the plurality of first and the plurality of second scatterers  122  and  132  are shown in  FIGS. 7A to 7C , exemplary embodiments are not limited thereto. For example, the plurality of first and plurality of second scatterers  122  and  132  may be shaped as polyhedral pillars or pillars with an L-shaped cross-section. The shapes of the plurality of first and plurality of second scatterers  122  and  132  may be asymmetrical in a direction. For example, respective cross-sections of the plurality of first and the plurality of second scatterers  122  and  132  may be asymmetrical in a horizontal direction. Also, since the respective cross-sections of the plurality of first and the plurality of second scatterers  122  and  132  may vary according to respective heights of the plurality of first and the plurality of second scatterers  122  and  132 , respective shapes of the plurality of first and the plurality of second scatterers  122  and  132  may be asymmetrical with respect to the respective heights thereof. 
     Respective refractive indexes of the plurality of first and the plurality of second scatterers  122  and  132  may be higher than a refractive index of the substrate  110 . For example, the respective refractive indexes of the plurality of first and the plurality of second scatterers  122  and  132  may be greater than the refractive index of the substrate  110  by approximately 1 or more. Therefore, the substrate  110  may include a material with a relatively low refractive index, and the plurality of first and the plurality of second scatterers  122  and  132  may include a material with a relatively high refractive index. For example, the plurality of first and the plurality of second scatterers  122  and  132  may include at least one selected from crystalline silicon (c-Si), polycrystalline silicon (poly Si), amorphous silicon, Si 3 N 4 , GaP, GaAs, TiO 2 , AlSb, AIAs, AlGaAs, AlGaInP, BP, and ZnGeP 2 . The plurality of first and the plurality of second scatterers  122  and  132  may be additionally surrounded by materials with a low refractive index (SiO 2 , polymer (PMMA, SU-8, etc.)) in upper and horizontal directions. 
       FIG. 8A  is a phase profile of the second thin lens  130 . 
     Referring to  FIG. 8A , a phase shift of light incident on the second thin lens  130  may decrease from a central area of the second thin lens  130  to a peripheral area of the second thin lens  130 . When the second thin lens  130  is configured such that the phase profile shown in  FIG. 8A  is satisfied, the second thin lens  130  may function as a lens with positive refractive power. Also, spherical aberration that occurs in general optical lenses may be decreased. The phase profile of the second thin lens  130  shown in  FIG. 8A  is merely exemplary, and exemplary embodiments are not limited thereto. For example, a shape of the phase profile may be changed according to a diameter, a focal length, etc. of the second thin lens  130  changes. 
     Design conditions of the plurality of second scatterers  132  in the second thin lens  130  may be modified according to the phase profile of the second thin lens  130 . For example, at least one of the shapes, the sizes, the materials, and the arrangement pattern of the plurality of second scatterers  132  may be modified according to an arranged location of the plurality of second scatterers  132  on the surface of the substrate  110 . The shapes, the sizes, the materials, and the arrangement pattern of the plurality of second scatterers  132  may be determined according to an amount of unwrapped phase shift of light that passes through the plurality of second scatterers  132 . The amount of unwrapped phase shift indicates a phase component corresponding to a phase shift value between 0 and 2π remaining after subtracting an integer multiple of 2π from an amount of phase shift. Respective structures and materials of the plurality of first and the plurality of second scatterers  122  and  132  may vary according to the amount of unwrapped phase shift of light that passes through the plurality of first and the plurality of second scatterers  122  and  132 . 
       FIG. 8B  is a diagram of a phase profile of the first thin lens  120 . 
     Referring to  FIG. 8B , a phase shift of light incident on the first thin lens  120  may decrease from a peripheral area of the first thin lens  120  to a middle area of the first thin lens  120  and then increase again from the middle area of the first thin lens  120  to a central area of the first thin lens  120 . For example, as shown in  FIG. 8B , the first thin lens  120  may have a phase profile in which the phase shift of the incident light decreases from the central area to a middle area having a diameter of approximately 150 μm and increases from the middle area to the peripheral area. When the first thin lens  120  is configured such that the phase profile shown in  FIG. 8B  is satisfied, the first thin lens  120  may change a path of the incident light and thus correct coma aberration of the second thin lens  130 . The phase profile of the first thin lens  120  shown in  FIG. 8B  is merely exemplary, and exemplary embodiments are not limited thereto. For example, a specific shape of the phase profile of the first thin lens  120  may be changed according to a diameter, a focal length, etc. of the first thin lens  120 . Also, the specific shape of the phase profile of the first thin lens  120  may be changed according to the phase profile of the second thin lens  130  and the thickness of the substrate  110 . 
       FIG. 9  is an exemplary diagram of a path of light incident on the focusing device  100  of  FIG. 5 . 
     Referring to  FIG. 9 , light may be incident on the focusing device  100  in a direction that is not parallel to the optical axis (z-axis) of the focusing device  100 . A path of light incident on the first thin lens  120  may be changed by the plurality of first scatterers  122 . After the path is changed by the plurality of first scatterers  122 , the light may pass through the substrate  110 , and the path of the light may be changed again by the plurality of second scatterers  132 . The first and second thin lenses  120  and  130  may correct coma aberration of one another. Also, the first and second thin lenses  120  and  130  may allow the light to form a focusing point on the focal plane S 0  regardless of angles at which light is incident on the first surface S 1  of the substrate  110 . 
       FIGS. 10A and 10B  are diagrams of light intensity distribution inside the substrate  110  in the focusing device  100  of  FIG. 5 . 
       FIG. 10A  shows an example in which light is incident in a direction parallel to an optical axis of the focusing device  100 , and  FIG. 10B  shows an example in which light is obliquely incident (at an incident angle of 12°) with respect to the optical axis of the focusing device  100 . Referring to  FIGS. 10A and 10B , light intensity distribution in the substrate  110  may vary according to an incident angle of light because the plurality of first scatterers  122  change a path of light that proceeds into the substrate  110 . Also, coma aberration of the focusing device  100  may be corrected by changing the light intensity distribution in the substrate  110 . 
       FIGS. 11A to 11F  are diagrams of light intensity distribution of an image formed on the focal plane S 0  by the focusing device  100  of  FIG. 5 . 
       FIG. 11A  shows light intensity distribution of an image formed by light incident in parallel to an optical axis of the focusing device  100 .  FIG. 11B  shows light intensity distribution of an image formed by light incident at an incident angle of 3°.  FIG. 11C  shows light intensity distribution of an image formed by light incident at an incident angle of 6°.  FIG. 11D  shows light intensity distribution of an image formed by light incident at an incident angle of 9°.  FIG. 11E  shows light intensity distribution of an image formed by light incident at an incident angle of 12°.  FIG. 11F  shows light intensity distribution of an image formed by light incident at an incident angle of 15°. Bars at a right hand side of  FIGS. 11A to 11F  indicates intensity of light. 
     Referring to  FIGS. 11A to 11F , a location of a focusing point may change as an incident angle of light changes from 0° to 15°. However, a shape of light intensity distribution may nearly not change at the location of the focusing point. By using the focusing device  100  of  FIG. 5 , intensity of light at the focusing point may be almost maintained at a steady rate even when the incident angle of light changes. Also, unlike  FIGS. 3A to 3C , the focusing device  100  of  FIG. 5  may prevent defocusing even when the incident angle of light increases. 
       FIG. 12  is a graph of light intensity distribution of an image formed on the focal plane S 0  by the focusing device  100  of  FIG. 5 . 
     Referring to  FIG. 12 , a location of a focusing point may change as an incident angle changes from 0° to 15°. However, a shape and a peak of light intensity distribution graph may almost not change at the location of the focusing point. Also, unlike  FIGS. 4A and 4B , the graph may show only one peak instead of a plurality of peaks even when the incident angle of light increases. As shown in  FIG. 12 , coma aberration of the focusing device  100  may be corrected. Therefore, even when the incident angle of light changes, the shape of the light intensity distribution may almost not change at the focusing point. Also, the focusing device  100  may have a wide FOV. 
       FIG. 13  is an exemplary diagram of forming an image of an object by the focusing device  100 . 
     For convenience, the focusing device  100  and an image are enlarged in  FIG. 13  and are not drawn to scale. However, an actual distance between an object and the focusing device  100  and a size of the object may be substantially different from a height of the focusing device  100 . Therefore, when light reflected from a point of the object is incident on the focusing device  100 , the light may be substantially parallel rays. Referring to  FIG. 13 , a distance h between a location of a focusing point and an optical axis of the focusing device  100  may vary according to an angle θ at which light is incident. For example, when the focusing device  100  is designed such that image distortion is not created, the distance h between the location of the focusing point and the optical axis of the focusing device  100  may satisfy Equation 1.
 
 h=f *tan θ  [Equation 1]
 
     In Equation 1, ‘h’ is the distance between the location of the focusing point and the optical axis of the focusing device  100 , T is an effective focal length of the focusing device  100 , and ‘θ’ is an incident angle of light. 
     As another example, when the focusing device  100  is provided as an orthographic fisheye lens to enlarge the FOV of the focusing device  100 , the distance h between the location of the focusing point and the optical axis of the focusing device  100  may satisfy Equation 2
 
 h=f *sin θ  [Equation 2]
 
     In Equation 2, ‘h’ is the distance h between the location of the focusing point and the optical axis of the focusing device  100 , ‘f’ is an effective focal length of the focusing device  100 , and ‘θ’ is an incident angle of light. 
       FIG. 14  is a graph of a relationship between locations of focusing points and incident angles of light. 
     In  FIG. 14 , a solid line indicates the focusing device  100  forming a distortion free image, and a dashed line indicates the focusing device  100  provided as an orthographic fisheye lens. A location at which an image is formed according to incident angles of light may be changed by modifying designs of the plurality of first and the plurality of second scatterers  122  and  132 . Accordingly, an image distortion degree and the FOV of the focusing device  100  may be adjusted. For example, when image accuracy is required, an image formed by light that passed through the focusing device  100  may be determined according to the solid line of  FIG. 14 . As another example, a wide FOV is required, an image formed by light that passed through the focusing device  100  may be determined according to the dashed line of  FIG. 14 . 
     The focusing device  100  of  FIG. 5  may focus incident light according to wavelengths of incident light. 
     The first and second thin lenses  120  and  130  may differently change a direction of incident light according to wavelengths of the incident light. Therefore, the focusing device  100  according to an exemplary embodiment may only allow incident light within a certain wavelength band to form a focusing point on the focal plane S 0 . Also, the first and second thin lenses  120  and  130  may differently correct coma aberration according to the wavelengths of the incident light. A wavelength of light that is allowed by the focusing device  100  to form the focusing point on the focal plane S 0  is a design wavelength of the focusing device  100 . Design conditions of the plurality of first and the plurality of second scatterers  122  and  132  may vary according to the wavelength of light that is to be focused by the focusing device  100 , i.e., the design wavelength of the focusing device  100 . 
       FIG. 15  is an exemplary diagram of an arrangement of the plurality of first and the plurality of second scatterers  122  and  132 . 
     Referring to  FIG. 15 , intervals T between the plurality of first and the plurality of second scatterers  122  and  132 , respective heights h of the plurality of first and the plurality of second scatterers  122  and  132 , and an arrangement pattern of the plurality of first and the plurality of second scatterers  122  and  132  may be determined according to the design wavelength of the focusing device  100 . The intervals T between the plurality of first and the plurality of second scatterers  122  and  132  may be less than the design wavelength. For example, the intervals between the plurality of first and the plurality of second scatterers  122  and  132  may be equal to or less than ¾ or ⅔ of the design wavelength. Also, the respective heights h of the plurality of first and the plurality of second scatterers  122  and  132  may be less than the design wavelength. For example, the respective heights h of the plurality of first and the plurality of second scatterers  122  and  132  may be equal to or less than ⅔ of the design wavelength. 
       FIGS. 16A to 16C  are diagrams for describing changes in path of incident light according to wavelengths of the incident light. The focusing device  100  of  FIGS. 16A to 16C  are designed to be appropriate for focusing about light having a wavelength of 850 nm. 
     Referring to  FIG. 16A , when light having a wavelength that corresponds to the design wavelength of the focusing device  100  is incident, a focusing point of the light may be formed on the focal plane S 0  regardless of an incident angle of the light. However, referring to  FIG. 16B , when light having a wavelength (830 nm) that is less than the design wavelength is incident, the light may reach the focal plane S 0  before a focusing point of the light is formed. Also, referring to  FIG. 16C , when light having a wavelength (870 nm) that is greater than the design wavelength is incident, a focusing point may be formed before the light reaches the focal plane S 0 . 
       FIGS. 17A to 17C  are diagrams of light intensity distribution of an image formed on the focal plane S 0  by light incident in parallel to an optical axis of the focusing device  100 . 
     Referring to  FIG. 17B , an image formed by light having a wavelength (850 nm) corresponding to the design wavelength of the focusing device  100  may have narrow light intensity distribution. However, referring to  FIGS. 17A and 17C , an image formed by light having a wavelength (830 nm or 870 nm) different from the design wavelength of the focusing device  100  may have wide light intensity distribution. That is, when the wavelength of incident light is different from the design wavelength of the focusing device  100 , a focusing effect of the light incident in parallel to the optical axis of the focusing device  100  may decrease. 
       FIG. 18  is a diagram of changes in light intensity distribution of an image according to wavelengths and incident angles of incident light. 
     Referring to  FIG. 18 , when a wavelength of incident light corresponds to a design wavelength (850 nm), a focusing effect may not decrease until an incident angle reaches 20°. Also, when the incident angle is equal to 40°, light intensity distribution may change by a minor degree. However, when light has a wavelength of 810 nm, there may be a significant change in light intensity distribution as an incident angle changes to 20°. Also, when light has a wavelength of 870 nm, there may be a significant change in light intensity distribution as an incident angle changes to 40°. That is, when the wavelength of incident light is different from the design wavelength of the focusing device  100 , the focusing device  100  may be less effective in correcting coma aberration. 
       FIG. 19  is a diagram of a focusing device  100  according to another exemplary embodiment. 
     Referring to  FIG. 19 , the focusing device  100  may include an optical filter  160  that blocks wavelengths of the incident light which are different from the design wavelength of the focusing device  100 . The optical filter  160  may transmit light having a wavelength equal or similar to the design wavelength of the focusing device  100  from the incident light. Also, the optical filter  160  may reflect or absorb light having a wavelength that is not similar to the design wavelength. The optical filter  160  may filter the wavelength of incident light and thus prevent a light component with a weak focusing effect from reaching a focal plane S 0 . 
       FIG. 20  is an imaging device according to another exemplary embodiment. 
     Referring to  FIG. 20 , the imaging device may include the focusing device  100  of  FIG. 5 , and an optical detector  140  that detects light that passed through the focusing device  100 . The optical detector  140  may include an optical detection layer  144  provided at the focal plane S 0  of the focusing device  100  and a cover glass  142  that protects the optical detection layer  144  and the optical detection layer  144 . The optical detection layer  144  may include a plurality of charge-coupled devices (CCDs), complementary metal-oxide semiconductor (CMOS) sensors, photo diodes, etc. The optical detection layer  144  may convert optical signals incident on the optical detection layer  144  into electric signals. 
       FIG. 21  is a diagram of a beam scanner  200  according to an exemplary embodiment. 
     Referring to  FIG. 21 , the beam scanner  200  may include the focusing device  100  of  FIG. 5 . Also, the beam scanner  200  may include a light source array  220  that includes a plurality of light sources  222 . The light source array  220  may be provided at a location of the focal plane S 0  of the focusing device  100  of  FIG. 5 . Therefore, a distance between the light source array  220  and the focusing device  100  may vary according to an effective focal length of the focusing device  100 . 
     The focusing device  100  may focus incident light to another location according to an incident angle of the light incident on the first surface S 1  of the substrate  110 . Similarly, a path of light that passed through the focusing device  100  may change depending on respective locations of the plurality of light sources  222  emitting light from the light source array  220  facing the second surface S 2  of the substrate  110 . For example, as shown in  FIG. 21 , paths of light rays L 1  and light rays L 2  that passed through the focusing device  100  may change according to the respective locations of the plurality of light sources  222  emitting light. Also, the light rays L 1  and L 2  that passed through the focusing device  100  may be parallel rays. Therefore, the focusing device  100  may function as an optical path modifier of the beam scanner  200 . 
     Since the first and second thin lenses  120  and  130  are designed to correct coma aberration of each other, the focusing device  100  may have a wide FOV. Accordingly, an area of the light source array  220  may be less limited. Also, the light source array  220  may adjust the respective locations of the plurality of light sources  222  and thus easily adjust direction of light emitted by the beam scanner  200 . 
       FIG. 22  is a diagram of a scope device  300  according to another exemplary embodiment. Referring to  FIG. 22 , the scope device  300  may include a focusing device  100 , and a light source  310  arranged to face a second surface S 2  of a substrate  110  of the focusing device  100  and emitting light on a target object  10 . Light emitted from the light source  310  may pass through the target object  10  and be incident on the focusing device  100 . Also, since the focusing device  100  may function as a focusing lens, the focusing device  100  may be used as an object lens of the scope device  300 . In this case, the scope device  300  refers to a device for observing objects that are small or far away, such as a microscope or a telescope. Since the focusing device  100  has a wide FOV, the scope device  300  may observe a large area of the target object  10  without coma aberration. 
       FIG. 23  is an exemplary diagram of 3-dimensional (3D) volumetric imaging a target object  20  by using the scope device  300 . 
     Referring to  FIG. 23 , when the light source  310  emits light having various wavelengths on the target object  20 , the focusing device  100  of the scope device  300  may function as an object lens that has different focal lengths with respect to the target object  20  according to the wavelengths of the light emitted from the light source  310 . The light source  310  may emit light having different wavelengths on the target object  20  according to time variation. Alternatively, the light source  310  may simultaneously emit light having different wavelengths on the target object  20 . The scope device  300  may divide light that passed through the target object  20  according to its wavelengths and record images of the target object  20 . Also, the scope device  300  may analyze the images according to the wavelengths of light, and thus extract a 3D image including depth information of the target object  20 . 
     Examples of focusing devices according to various embodiments are described below. The below-described focusing devices may be applied to various optical devices, for example, the above-described imaging devices, scope devices, or beam scanners. 
       FIG. 24  is a diagram of a focusing device  1000  according to another exemplary embodiment.  FIG. 25  is an exemplary diagram of classification of regions related to the arrangement of second scatterers provided in a second thin lens  1300  of the focusing device  1000  of  FIG. 24 .  FIG. 26  is a graph conceptually showing a target phase for each wavelength to be satisfied by the scatterers in each region of  FIG. 25 . 
     Referring to  FIG. 24 , the focusing device  1000  for focusing light of a predetermined wavelength band on a predetermined focal plane S 0  may include the substrate  110 , a first thin lens  1200  including a plurality of first scatterers NS 1  formed on a first surface S 1  of the substrate  110 , and the second thin lens  1300  including a plurality of second scatterers NS 2  formed on a second surface S 2  of the substrate  110 . 
     Like the above-described embodiments, the first scatterers NS 1  of the first thin lens  1200  may be configured to correct geometric aberration of the second thin lens  1300 , and the second scatterers NS 2  may be configured so that the second thin lens  1300  may function as a lens with positive refractive power. 
     Furthermore, a low refractive index material layer  190  including a material with a refractive index lower than that of the first scatterers NS 1  and covering the first scatterers NS 1  may be further provided to protect the first scatterers NS 1 , and a low refractive index material layer  180  including a material with a refractive index lower than that of the second scatterers NS 2  and covering the second scatterers NS 2  may be further provided to protect the second scatterers NS 2 . The low refractive index material layers  180  or  190  may be omitted. 
     In the present embodiment, at least two of the second scatterers NS 2  provided in the second thin lens  1300  may have different heights H from each other. A height difference ΔH between at least two second scatterers NS 2  may be equal to or less than 2λ with respect to a wavelength λ within the predetermined wavelength band. The respective heights H of the second scatterers NS 2  may be in a range that λ/2≤H≤3λ with respect to the wavelength λ within the predetermined wavelength band. 
     The second scatterers NS 2  have different heights from each other to further freely adjust chromatic aberration, that is, dispersion according to wavelengths, when focusing light of a relatively wide wavelength band on the focal plane S 0 . 
     In order to have refractive power to incident light, the classification of regions of  FIG. 25  may be used for determining the shapes of the second scatterers NS 2  and arranging the second scatterers NS 2 . A predetermined rule regarding the sizes and arrangement of the second scatterers NS 2  is applied to each of a plurality of regions R 1 , R 2 , . . . R k , . . . R N . A target phase φ target  as illustrated in  FIG. 26  may be set to each region. The target phase φ target  may be set to indicate a phase change range of 2π with respect to a central wavelength λ m  in the region given in  FIG. 25 , and thus the regions R 1 , R 2 , . . . R k , . . . R N  may be referred to as the “2π zone”. In the vertical axis of the graph of  FIG. 26 , the negative (−) sign is shown as an example of being a phase for indicating positive refractive power. 
     The target phase φ target  target may slightly vary according to light of different wavelengths λ l , λ m , and λ s , as illustrated in  FIG. 26 . In order to implement a desired target phase to each light of a determined wavelength, a rule regarding the shape, size, and arrangement of the second scatterers NS 2  arranged in a plurality of 2π zones may be determined. In the following description, an expression “shape distribution” may be used together as an expression meaning the “shape, size, and arrangement”. A degree that the target phase φ target  varies according to light of a different wavelength is related to a dispersion Δφ, and a wavelength range including presented examples λ l , λ m , and λ s  is related to a bandwidth BW. A shape condition of each of the second scatterers NS 2  which may implement a dispersion Δφ within a desired range with respect to desired bandwidth BW may be set from a phase-dispersion map prepared in advance. A phase-dispersion map may be generally created by a method of setting the second scatterers NS 2  to a certain height and marking a shape condition at a position corresponding to (phase, dispersion) at the central wavelength by various combinations of a width and a pitch. A design dimension that may produce desired performance at a desired position may be selected from the map. When a height variation is introduced, a plurality of phase-dispersion maps having different height conditions from each other may be set to overlap each other, that is, a range of selecting the shape of the second scatterers NS 2  may extend. As such, the shape and arrangement of the second scatterers NS 2  may be determined so as to freely correct chromatic aberration while increasing a focusing wavelength band. 
     Although  FIG. 24  randomly illustrates the height H, width w, and pitch p of each of the second scatterers NS 2 , this is merely for convenience of explanation, and the present disclosure is not limited thereto. For example, a predetermined rule may be set and applied not only to the width and pitch but also to the height in the region as illustrated in  FIG. 25 . 
       FIG. 27  is a diagram of a focusing device  1001  according to another exemplary embodiment. 
     Referring to  FIG. 27 , the focusing device  1001  may include the substrate  110 , the first thin lens  1200  including the first scatterers NS 1  formed on the first surface S 1  of the substrate  110 , and a second thin lens  1301  including a plurality of scatterers formed on the second surface S 2  of the substrate  110 . 
     As in the above-described embodiments, the first thin lens  1200  may be configured to correct geometric aberration of the second thin lens  1301 , and the second thin lens  1301  may be configured to function as a lens with positive refractive power. 
     In the present embodiment, the second thin lens  1301  may have a scatterer arrangement of a plurality of layers. The second thin lens  1301  may include the second scatterers NS 2  formed on the second surface S 2  of the substrate  110 , the low refractive index material layer  180  covering the second scatterers NS 2  and including a material having a refractive index lower than the refractive index of the second scatterers NS 2 , and a plurality of third scatterers NS 3  formed on the low refractive index material layer  180  and including a material having a refractive index higher than the refractive index of the low refractive index material layer  180 . The second scatterers NS 2  form a first layer LA 1 , and the third scatterers NS 3  form a second layer LA 2 . A low refractive index material layer  185  that covers the third scatterers NS 3  and including a material having a refractive index lower than the refractive index of the third scatterers NS 3  may be further provided. The low refractive index material layer  185  may protect the third scatterers NS 3  and may planarize an upper surface of the second thin lens  1301 . The low refractive index material layer  185  may be omitted. 
     The second scatterers NS 2  and the third scatterers NS 3  may face each other to be misaligned with each other. This means that the center axes of at least some of the second scatterers NS 2  and the third scatterers NS 3  vertically facing each other may be misaligned with each other. Also, it is not limited to that all of the second scatterers NS 2  and the third scatterers NS 3  face each other to be misaligned with each other. 
     An interval d between the second scatterer NS 2  and the third scatterer NS 3 , which are adjacent to each other, among the second scatterers NS 2  and the third scatterers NS 3 , that is, a separation distance in a height direction (Z direction), may be greater than λ/2 with respect to the wavelength λ within the predetermined wavelength band. 
     The arrangement of the second and third scatterers NS 2  and NS 3  in a multilayer is to reduce deterioration of performance that may occur at some positions even when the shape of each scatter is set to a desired target phase. In this regard, a description is presented with reference to  FIGS. 25, 26, and 28 to 31 . 
     The classification of regions in  FIG. 25  and the target phases of the respective regions in  FIG. 26  may be applied to the second thin lens  1301  of  FIG. 27 . In other words, the sizes and arrangements of the second scatterers NS 2  and the third scatterers NS 3  arranged in the first layer LA 1  and the second layer LA 2  of the second thin lens  1301  may be set to satisfy the target phase of  FIG. 26  for each region.  FIG. 28  is an exemplary diagram of the second scatterers NS 2  arranged in one region of the first layer LA 1  of the second thin lens  1301  of  FIG. 27 . The arrangement rule of the width w and the pitch p may be repeated in a plurality of regions.  FIG. 29  is an exemplary diagram of design data of the width w and the pitch p by locations of the second scatterers NS 2  arranged in the first layer LA 1  of the second thin lens  1301  of the focusing device  1001  of  FIG. 27 . 
       FIG. 30  is a graph of a comparison between a target phase value and a phase value by the scatterers designed as in  FIG. 28 . In the graph, a target phase value graph is indicated by “target”, and a phase value graph by the scatterers designed to implement the target phase is indicated by “designed”. In the graph, the two graphs are not completely congruous with each other and have an error. Furthermore, a degree of mismatch appears to vary according to the position. 
       FIG. 31  is a graph of a performance index obtained by quantifying a difference between a target value and a design value in  FIG. 30 . The performance index is obtained such that correlation degree between a target transmissivity (transmission intensity and transmission phase) and an actual transmissivity in an entire wavelength band to be considered is integrated and quantified by locations in a radial direction. The graph may be referred to as the “merit function”. The correlation degree is good as a value on the vertical axis of the graph is close to 1, and a position where the correlation degree is the lowest may be known from points Q indicating the lower extreme points. 
       FIGS. 29 to 31  illustrate the design data of the first layer LA 1 , and as multiple layers are introduced, correlation properties that are non-uniformly low may be compensated. For example, the rule regarding the size and arrangement of the third scatterers NS 3  forming the second layer LA 2  may be determined such that, as illustrated in  FIG. 31 , a position where correlation is low in the first layer LA 1 , for example, the extreme point Q, may be moved to another position. By making the position where correlation is low appear to be different in the first layer LA 1  and the second layer LA 2  and overlapping dispersion and phase features of each layer, when desired light of a predetermined wavelength band is to be focused while maintaining dispersion in an appropriate range, performance deterioration that may occur at some particular positions may be reduced. 
     The shape distribution of the second scatterers NS 2  provided in the first layer LA 1  and the shape distribution of the third scatterers NS 3  provided in the second layer LA 2  may be determined to have different distributions of performance index by locations from each other. The shape distribution of the second scatterers NS 2  provided in the first layer LA 1  and the shape distribution of the third scatterers NS 3  provided in the second layer LA 2  may be determined such that degree of non-uniformity of focusing performance by the respective shape distributions are different from each other. The shape distribution of the second scatterers NS 2  provided in the first layer LA 1  and the shape distribution of the third scatterers NS 3  provided in the second layer LA 2  may be determined such that degree of non-uniformity of focusing performance by locations in each layer may be compensated by each other. Any one of the first layer LA 1  and the second layer LA 2  may be set to alleviate the non-uniformity of focusing performance by the other layer. 
     As in the embodiment, when the scatterers are arranged in multiple layers in the second thin lens  1301 , the number of “27 zones” to which a rule of a predetermined unit is applied may be reduced. The number of 2π zones R 1 , R 2 , . . . , R k , . . . , R N  as illustrated in  FIG. 25  may be set to a level appropriate to achieve a desired refractive power, and the number of the regions increases for high refractive power. By using the multilayer arrangement, the number of regions formed in a radial direction may be reduced. 
     Although the number of multiple layers is set to, for example, two, the present disclosure is not limited thereto. For example, three or more layers may be selected. When the number of multiple layers is LN, the number of 2π zones formed in the radial direction may be reduced to 1/LN. Furthermore, the dispersion range may be reduced to 1/LN. 
       FIG. 32  is a diagram of a focusing device  1002  according to another exemplary embodiment. 
     The focusing device  1002  may include the substrate  110 , the first thin lens  1200  including the first scatterers NS 1  formed on the first surface S 1  of the substrate  110 , and a second thin lens  1302  including a plurality of scatterers formed on the second surface S 2  of the substrate  110  and arranged in a two layer structure. 
     In the present embodiment, at least two of the second scatterers NS 2  forming the first layer LA 1  of the second thin lens  1302  may have different heights from each other. Furthermore, at least two of the third scatterers NS 3  forming the second layer LA 2  of the second thin lens  1302  may have different heights from each other. As described in the embodiment of  FIG. 24 , by applying height variation to each layer, a design value to implement appropriate phase and dispersion at each position may be easy. In particular, when the multilayer scatterer arrangement is introduced to compensate for the deterioration of performance of each layer, the selection of a design value of a scatterer to mutually compensate for the deterioration of performance of one layer in another layer corresponding to a low correlation position may be easier. Furthermore, effective compensation of the phase and the dispersion performance between layers may be possible. 
     Although the drawing illustrates that the second and third scatterers NS 2  and NS 3  having various heights are applied to both of the first layer LA 1  and the second layer LA 2 , this is merely exemplary and the present disclosure is not limited thereto. For example, the scatterers may be arranged with a constant height in one of the first layer LA 1  and the second layer LA 2 , and the scatterers having a different height may be selected in the other layer at an appropriately position as necessary. 
       FIG. 33  is a diagram of a focusing device  1003  according to another exemplary embodiment. 
     Referring to  FIG. 33 , the focusing device  1003  may include the substrate  110 , a first thin lens  1201  including the first scatterers NS 1  formed on the first surface S 1  of the substrate  110 , and a second thin lens  1303  including the second scatterers NS 2  formed on the second surface S 2  of the substrate  110 . 
     The first scatterers NS 1  of the first thin lens  1201  may be configured to correct geometric aberration of the second thin lens  1303 , and the second scatterers NS 2  may be configured such that in the second thin lens  1303  may function as a lens with positive refractive power. 
     In the present embodiment, at least two of the first scatterers NS 1  of the first thin lens  1201  may have different heights H from each other. The height difference ΔH of at least two first scatterers NS 1  may be equal to or less than 2λ with respect to wavelength λ in the focusing wavelength band. The height H of the first scatterers NS 1  may be in a range that λ/2≤H≤3λ, with respect to the wavelength λ of the focusing wavelength band. 
     As described above, the geometric aberration signifies a phenomenon that light incident in a direction that is not parallel to the optical axis of the focusing device  1003  is not focused on one focusing point. The geometric aberration of the second thin lens  1303  may be corrected by setting the shape distribution of the first scatterers NS 1  in the first thin lens  1201 . A target phase to be implemented by locations may be set for the correction of geometric aberration. To achieve the target phase, the effect of correcting geometric aberration may be increased by selecting various heights of the first scatterers NS 1 . 
       FIG. 34  is a diagram of a focusing device  1004  according to another exemplary embodiment. 
     Referring to  FIG. 34 , the focusing device  1004  may include the substrate  110 , a first thin lens  1204  including a plurality of scatterers arranged in a double layer structure on the first surface S 1  of the substrate  110 , and the second thin lens  1302  including a plurality of scatterers arranged in a double layer structure on the second surface S 2  of the substrate  110 . 
     The first thin lens  1204  may include the first scatterers NS 1  arranged on the first surface S 1  of the substrate  110 , the low refractive index material layer  190  covering the first scatterers NS 1  and including a material having a refractive index lower than the refractive index of the first scatterers NS 1 , and a plurality of fourth scatterers NS 4  arranged on the low refractive index material layer  190  and including a material having a refractive index higher than the refractive index of the low refractive index material layer  190 . Furthermore, a low refractive index material layer  195  having a refractive index lower than the refractive index of the fourth scatterers NS 4  may be further provided to cover and protect the fourth scatterers NS 4 . 
     The second thin lens  1302  may include the second scatterers NS 2  arranged on the second surface S 2  of the substrate  110 , the low refractive index material layer  180  covering the second scatterers NS 2 , and the third scatterers NS 3  arranged on the low refractive index material layer  180 . Furthermore, the low refractive index material layer  185  having a refractive index lower than the refractive index of the third scatterers NS 3  may be further provided to cover and protect the third scatterers NS 3 . 
     In the present embodiment, the scatterers are arranged in a double layer structure on each of the first thin lens  1204  for correcting geometric aberration and the second thin lens  1302  for focusing light of a predetermined wavelength band with less color dispersion. Different heights may be applied to the first scatterers NS 1 , the fourth scatterers NS 4 , the second scatterers NS 2 , and the third scatterers NS 3 , which form the respective layers. 
     Although, in the drawing, the scatterer arrangement of a multi-layered structure is applied to both of the first thin lens  1204  and the second thin lens  1302  and height variation is applied to all layers, this is merely exemplary and the present disclosure is not limited thereto. For the aberration correction and focusing effect suitable for each lens, an appropriate combination of multilayer arrangement and height variation may be selected to mutually compensate for the performance deterioration of each layer and extend the phase-dispersion map including design data to be selected therefor. 
     Although the two thin lenses included in each of the above-described embodiments are formed on both sides of the substrate  110 , this is merely exemplary. For example, the two thin lenses may be formed on different substrates and fixed such that an appropriate interval therebetween may be maintained by a predetermined support member. 
     It should be understood that exemplary embodiments described herein should be considered in a descriptive sense only and not for purposes of limitation. Descriptions of features or aspects within each exemplary embodiment should typically be considered as available for other similar features or aspects in other exemplary embodiments. 
     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.