Patent Publication Number: US-9903984-B1

Title: Achromatic optical-dispersion corrected refractive-gradient index optical-element for imaging applications

Description:
REFERENCE TO RELATED PATENTS 
     This application is a continuation-in-part of U.S. patent application Ser. No. 14/599,731 filed Jan. 19, 2015, which is a continuation-in-part of U.S. patent application Ser. No. 14/293,574 filed Jun. 2, 2014 and also claims benefit of U.S. Provisional Patent Application No. 62/013,500 filed Jun. 17, 2014. 
    
    
     TECHNICAL FIELD OF THE DISCLOSURE 
     The present disclosure relates in general to correcting optical chromatic aberration caused by optical-dispersion in media. The disclosure relates in particular to optical-dispersion corrected refractive-gradient index (GRIN) optic for imaging onto pixelated imagers or focal plane arrays (FPA). 
     DISCUSSION OF BACKGROUND ART 
     Optical-dispersion is a well-known optical phenomenon which refers to wavelength dependency of refractive index in media. For applications such as spectroscopy, optical-dispersion can be desirable to cause wavelength separation. For imaging optics, optical-dispersion causes undesirable wavelength dependent focal shift, called chromatic aberration. A variety of solutions to reduce chromatic aberration are known in the art. 
     An achromatic lens provides chromatic aberration compensation by utilizing different glass types with different optical-dispersion, often crown glass and flint glass. One example of an achromatic lens is a doublet-lens. A doublet-lens consists of a positive-lens and a negative-lens, with different optical-dispersion, sandwiched together, forming a single optic. In the doublet-lens, the different optical-dispersion and lens shape reduce chromatic aberration, generally limited for focal shift correction of two wavelengths. Increased wavelength correction can be accomplished with additional lenses, air-space between lenses, and aspheric lens shape. Another correction solution utilizes gradient refractive index (GRIN) films. 
     One method to correct chromatic aberration with GRIN optics is by forming a lens out of a continuous GRIN material. One such method is described in U.S. Patent Publication No. US 20130003186 A1, where wavelength separation, caused by initial dispersion of light entering into a single-lens, is partially corrected by the optical-dispersion of a continuous GRIN material that form the lens. 
     This application relates to another approach. 
     SUMMARY OF THE DISCLOSURE 
     The present disclosure is directed to dispersion n optical-dispersion corrected optical-element with a first and a second surface for imaging equal angle quadrilateral image plane array (FPA). The optical-dispersion element comprises a first nanocomposite-ink with a first nanofiller dispersed in a cured organic-matrix and a second nanocomposite-ink with a second nanofiller dispersed in the cured organic-matrix. Optical-dispersion of the second nanocomposite-ink is different than optical-dispersion of the first nanocomposite-ink. The distribution of the first nanocomposite-ink and second nanocomposite-ink corrects chromatic aberration and creates a refractive gradient that is non-radially symmetric to correct for an image plane array. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       The accompanying drawings, which are incorporated in and constitute a part of the specification, schematically illustrate preferred embodiments of the present disclosure, and together with the general description given above and the detailed description of preferred methods and embodiment given below, serve to explain principles of the present disclosure. 
         FIG. 1A  is a perspective view schematically illustrating a two printer-head optical printing apparatus for manufacture of optical-elements in accordance with the present disclosure. 
         FIG. 1B  is a perspective view schematically illustrating a four-head optical printing apparatus for manufacture of an optical-element in accordance with the present disclosure. 
         FIG. 2A  is a cross-section view, schematically illustrating deposition of a first nanocomposite-ink at a voxel on a substrate in accordance with the present disclosure. 
         FIG. 2B  is a cross-section view, schematically illustrating that shown in  FIG. 2A , further including a second nanocomposite-ink deposit. 
         FIG. 2C  is a cross-section view, schematically illustrating a resultant nanocomposite from the diffusion or convective mixing of nanofillers from the first and the second nanocomposite-ink as shown in  FIG. 2B . 
         FIG. 2D  is a cross-section view, schematically illustrating a resultant refractive-gradient between the first nanocomposite-ink and second nanocomposite-ink from diffusion of nanofillers of the first and second nanocomposite-inks, where the first nanocomposite was partially cured before deposition of the second nanocomposite. 
         FIG. 2E  is a cross-section view, schematically illustrating deposition of the nanocomposite-ink side-by-side. 
         FIG. 2F  is a cross-section view, schematically illustrating that shown in  FIG. 2E , where nanocomposite-ink mixing resulted in a slow transition in the refractive-gradient profile. 
         FIG. 2G  is a cross-section view, schematically illustrating that shown in  FIG. 2E , where nanocomposite-ink mixing resulted in a fast transition in the refractive-gradient profile. 
         FIG. 2H  is a cross-section view, schematically illustrating an mixing of nanocomposite-inks in air. 
         FIG. 3A  is a cross-section view, schematically illustrating the refractive gradient of an optical-element of one preferred embodiment in accordance with the present disclosure, including a first nanocomposite-ink, the first nanocomposite-ink comprising of nanofillers dispersed in a cured organic-matrix, and second nanocomposite-ink, the second nanocomposite-ink comprising nanofillers dispersed in a cured organic-matrix, optical-dispersion of the second nanocomposite-ink different than dispersion of the first nanocomposite-ink, wherein the distribution of the first nanocomposite-ink and second nanocomposite-ink result in dispersion gradients, the dispersion gradients compensating chromatic aberration. 
         FIG. 3B  is a cross-section view, schematically illustrating that shown in  FIG. 3A  further including exemplary rays. 
         FIG. 3C  is a cross-section view, schematically illustrating that shown in  FIG. 3B , where the exemplary rays approach the optical-element at angle. 
         FIG. 4A  is a perspective view, schematically illustrating that shown in  FIG. 3A , wherein the gradient-index (GRIN) Abbe-number varies radially from an optical-axis. 
         FIG. 4B  is a cross-section view, schematically illustrating further detail of that shown in  FIG. 4A . 
         FIG. 5A  is a partially-transparent perspective view, schematically illustrating that shown in  FIG. 3A , wherein the GRIN Abbe-number varies radially and varies along an optical axis. 
         FIG. 5B  is a perspective view, partly in cross-section, schematically illustrating further detail of that shown in  FIG. 5A . 
         FIG. 6A  is a cross-section view, schematically illustrating another embodiment of the present disclosure, where the optical-element is has negative power. 
         FIG. 6B  is a cross-section view, schematically illustrating another embodiment of the present disclosure, where the optical-element is an imaging optic. 
         FIG. 6C  is a cross-section view, schematically illustrating another embodiment of the present disclosure where the optical element is a beam-expander. 
         FIG. 6D  is a cross-section view, schematically illustrating another beam expanding optical-element in accordance with the present disclosure. 
         FIG. 7A  is a cross-section view, schematically illustrating an optical system with chromatic aberration. 
         FIG. 7B  is a cross-section view, schematically illustrating that shown in  FIG. 7A  with the addition of another embodiment in accordance with the present disclosure, where the optical-element corrects chromatic aberration of the optical system. 
         FIG. 8A  is a cross section view, schematically illustrating another embodiment in accordance with the present disclosure wherein the substrate is an optic. 
         FIG. 8B  is a cross-section view, schematically illustrating another embodiment in accordance with the present disclosure, wherein the optical-element is shaped after deposition. 
         FIG. 8C  is a cross-section view, schematically illustrating another embodiment in accordance with the present disclosure, wherein the optical-element is printed in a mold. 
         FIG. 9A  is a cross-section view illustrating an chromatic corrected optical-element with a field-of-view matching an image sensor aspect ratio. 
     
    
    
     DETAILED DESCRIPTION 
     Referring now to the drawings, wherein like components are designated by like reference numerals. Drawings are characterized by cartesian (mutually perpendicular) axes x, y, and, z, although anyone skilled in the art can transform the axis to other coordinates or topologies. When referring to an optical-element, the z-axis refers generally to the direction of light propagation, and x and y being transverse axes. Methods of manufacture and optical-elements are described further herein below. 
       FIG. 1A  schematically illustrates an ink-jet printing apparatus  10  for manufacture of optical-elements in accordance with the present disclosure. Printing apparatus  10  is simplified for explanatory purposes. Printing apparatus  10  of  FIG. 1A  has a reservoir  12 A and a reservoir  12 B that hold a nanocomposite-ink  22 A and  22 B, respectively. Reservoirs  12 A and  12 B provide a printing-head  16 A and  16 B with nanocomposite-ink  22 A and  22 B via a feed-line  14 A and  14 B, respectively. Printing-heads  16 A and  16 B deposit nanocomposite-ink  22 A and  22 B, on a substrate  18  at particular voxels, thereby forming an optical-element in-process  20 . Voxels refer to positions in three-dimensional space. A Stage  17  positions substrate  18 , with respect to the printing-heads, for deposition of the nanocomposite-inks at particular voxels. 
     Substrate  18  can be made from a variety of materials which include glasses, metals, ceramics, and organic resins. Substrate  18  can become part of the optical-element or alternatively the optical-element may be removed from the substrate. For applications in which the substrate becomes part of the optical-element, the substrate may be optically transmissive, reflective, or absorptive. For example, in applications where the optical-element is optically transmissive and the substrate becomes a part of the optical-element, it is desirable for the substrate to be optically transparent. 
     After deposition of the nanocomposite-ink from one of the printing-heads, substrate  18  can be positioned with respect to a radiation source  19 A for selective-curing of the nanocomposite-ink, at voxels. Selective-curing refers to localized radiation about voxels, activating the organic-host matrix. Activation of the organic-host matrix solidifies the nanocomposite-ink. Selective-curing means zero-curing, partial-curing, or fully-curing, which respectively means not solidifying, partially solidifying, or fully solidifying the nanocomposite-ink. Another radiation source  19 B flood cures the substrate the nanocomposite-ink on the substrate. Flood curing is desirable when the all the nanocomposite-ink needs to be partially or fully cured. 
       FIG. 1B  illustrate printing apparatus  10  shown in  FIG. 1B  with an additional reservoir  12 C and  12 D, holding a nanocomposite-ink  22 C and  22 D, a feed-line  14 C and  14 D, and a printing head  16 C and  16 D. The additional printing heads provide additional nanocomposite-ink different from the nanocomposite-ink in other printing heads. 
       FIG. 2A  schematically illustrate further detail of the optical-element in-process  20  shown in  FIG. 1A . Nanocomposite-ink  22 A, deposited on substrate  18  is bounded by a nanocomposite-air interface  26 A. The nanocomposite-ink consists of an organic-matrix with a dispersed nanofiller  24 A throughout the organic-matrix. The organic matrix is inkjet printable, optically clear, photo-curable resin. Four non-limiting examples of suitable organic-matrix material are polyacrylate, hexanediol diacrylate (HDODA), polymethyl methacrylate (PMMA), diethylene glycol diacrylate (DEGDA) and SU-8. The nanofillers are ceramic nanoparticles sufficiently small with respect to light wavelengths, for those wavelengths the optical element is intended for use, not to scatter the light. The nanocomposite-ink can be different by the nanofiller type, the organic-host matrix type, or concentration of nanofillers and combinations thereof. Non-limiting examples of nanofillers include beryllium oxide (BeO), aluminum nitride (AlO), silicon carbide (SiC), zinc oxide (ZnO), zinc sulfide (ZnS), zirconium oxide (ZrO), yttrium orthovanadate (YVO 4 ), titanium oxide (TiO 2 ), copper sulfide (CuS 2 ), cadmium selenide (CdSe), lead sulfide (PbS), molybdenum disulfide (MoS 2 ) and silicon dioxide (SiO 2 ), including those with core, core-shell, and core-shell-ligand architectures. Optical-dispersion of the nanocomposite-ink depends on the organic-matrix and the nanofillers. 
     Optical-dispersion is characterized by an Abbe-number (V d ). The Abbe-number indicates the degree of optical-dispersion, described by equation: 
                 V   d     =         n   yellow     -   1         n   blue     -     n   red           ,         
where n yellow  is the refractive index at 587.56 nanometers (nm), n blue  is the refractive index at 486.13 nm, and n red  is the refractive index at 656.27 nm. A high Abbe-number indicates low optical dispersion. When referring to GRIN optics a GRIN Abbe-number (V GRIN ) is useful for describing change in the optical-dispersion within the optical-element. The GRIN Abbe-number is described by equation:
 
                 V   GRIN     =       Δ   ⁢           ⁢     n   yellow           Δ   ⁢           ⁢     n   blue       -     Δ   ⁢           ⁢     n   red             ,         
where Δ in indicates change in refractive index at the aforementioned wavelength dependent index reference points. A high GRIN Abbe-number indicates low optical dispersion through the GRIN material. The optical-dispersion of nanocomposite-ink can be tailored by combination of the organic-matrix and the nanofillers. Positive and negative values of the GRIN Abbe-number may be obtained as demonstrated by following examples herein. Combining the nanofillers BeO, and organic host Polyacrylate results in the GRIN Abbe-number of about 2244.
 
                                                         n red     n yellow     n blue                            Polyacrylate   1.4995   1.4942   1.4917           BeO   1.7239   1.7186   1.7162           Δ   0.2244   0.2244   0.2245                             GRIN Abbe-   2244                                     number                                    
Combining the nanofillers wurtzite w-AlN with the organic-host Polyacrylate results in the GRIN Abbe-number of about 959.
 
                                                         n red     n yellow     n blue                            Polyacrylate   1.4995   1.4942   1.4917           wurtzite w-AlN   2.1730   2.1658   2.1659           Δ   0.6735   0.6716   0.6742                             GRIN Abbe-   959                                     number                                    
Combining the nanofillers AlN and the organic-host SU8 results in the GRIN Abbe-number of about −356.
 
                                                         n red     n yellow     n blue                            SU8   1.5994   1.5849   1.5782           AlN   2.1704   2.1543   2.1476           Δ   0.5710   0.5694   0.5694                             GRIN Abbe-   −356                                     number                                    
Combining the nanofillers ZrO 2  and the organic-host SU8 results in the GRIN Abbe-number of about −242.
 
                                                         n red     n yellow     n blue                            SU8   1.5994   1.5849   1.5782           ZrO 2     2.2272   2.2148   2.2034           Δ   0.6278   0.6299   0.6252                             GRIN Abbe-   −242                                     number                                    
Those skilled in the art will recognize that the exact GRIN Abbe-number will vary dependent on the material and variability in the material manufacture processes. The aforementioned Abbe-number and the GRIN Abbe-number use three wavelength reference points in the visible spectrum, but other wavelength reference points may be chosen for applications in other spectrum, those wavelength reference points being in the correct order from short-wavelength to long-wavelength. For instance, in near-IR applications 800 nm, 900 nm and 1000 nm could replace wavelength references n blue , n yellow , and n red , respectively. Additionally partial dispersion of materials will affect the choice the organic-matrix and nanoparticles. The partial dispersion of a material is characterized by a rate of change of the refractive-index as a function of wavelength.
 
       FIG. 2B  schematically illustrate further detail of optical-element in-process  20  shown in  FIG. 2A  with additional deposit of nanocomposite-ink  22 B at a voxel above the voxel of nanocomposite-ink  22 A. Here, nanocomposite-ink  22 B is shown after deposition, characterized by a dispersed nanofillers  24 B, an ink-ink interface  28 A (where mixing between nanoparticle-inks has not yet occurred), and an air-ink interface  26 B. 
       FIG. 2C  schematically illustrates the optical-element in-process  20  as that shown in  FIG. 2B , wherein the selective-curing of nanocomposite-ink  22 A before deposition of nanocomposite-ink  22 B was zero-curing. A nanocomposite-ink  30  is the resultant mixture of uncured nanocomposite  22 A and  22 B. Nanocomposite-ink  30  is characterized by air-ink interface  32  and nanofillers  24 A and  24 B dispersed within. A refractive-gradient between the top and bottom of nanocomposite-ink  30  depends on convective mixing resulting from relative size, velocities, and nanofiller concentrations between the nanocomposite-inks, any partial-curing of nanocomposite-ink  22 A drop before deposition of nanocomposite-ink  22 B, the temperature of the substrate, and time allowed for diffusion of nanofillers from nanocomposite-inks  22 A and  22 B, before additional partial-curing of the nanocomposite-inks. 
       FIG. 2D  schematically illustrates optical-element in-process  20  as that shown in  FIG. 2B  wherein nanocomposite  22 A was partially cured. Here, partial-cure of nanocomposite  22 A results in gradient-area  28 B between nanocomposite  22 A and  22 B. The extent of gradient-area  28 B depends on the selective-cure of nanocomposite-ink  22 A. Zero-curing allows mixture of the nanocomposite-inks as exemplified in  FIG. 2C . Partial-curing allows diffusion in a limited gradient area  28 A as exemplified in  FIG. 2D . Fully-curing allows little diffusion and results in a substantially ink-ink interface  28 A as exemplified in  FIG. 2B . In addition to controlling gradient-areas, partial-curing before subsequent deposition reduces stress and strain in the resultant optical-element. 
       FIG. 2E  schematically illustrates optical-element in-process  20  shown in  FIG. 1A  where the nanocomposite-ink is deposited side-by-side. Here, nanocomposite-ink  22 B with nanofillers  24 B and ink-air interface  26 B is deposited along the side of a nanocomposite-ink  22 C. Nanocomposite-ink  22 C has no nanofillers bound by an air-interface  26 C. 
       FIG. 2F  schematically illustrates optical-element in-process  20  as shown in  FIG. 2E , where nanocomposite-ink  22 B has mixed with nanocomposite  22 C resulting in a gradient nanocomposite  22 D. Here, nanocomposite  22 D, bound by an ink-air interface  26 D, has a nanofiller  24 D, the same nanofillers as nanocomposite-ink  22 B distributed in a refractive-gradient profile  29 B. The gradient is a result of mixture of the nanocomposites where the partial-curing of nanocomposite  22 B was minimal and aforementioned convective mixing and time was allowed before further partial-curing. Refractive-gradient profile  29 B is characterized by high refractive-index n B , the high refractive-index due to higher concentration of nanoparticles  24 D, the refractive-gradient&#39;s refractive-index slowly and smoothly transitioning in the y-direction to low refractive-index n C , the low refractive-index due to the low concentration of nanoparticles  24 D. 
       FIG. 2G  schematically illustrates optical-element in-process  20  as shown in  FIG. 2E , where nanocomposite-ink  22 B has been partially-cured before deposition of nanocomposite-ink  22 C. Here partial-cure of nanocomposite-ink  22 B, results in limited mixing of nanocomposite-ink  22 C at an interface  24 AB, resulting in a refractive-gradient  29 C. Refractive-gradient profile  29 C is characterized by high refractive-index n B , the high refractive-index due to higher concentration of nanoparticles  24 D, the refractive-gradient&#39;s refractive-index unchanging in the y-direction until quickly transitioning to low refractive index n B  at former interface  24 AB. Alternatively, refractive-gradient profile  29 C could be obtained without partial-curing of nanocomposite-ink  22 B before deposition of nanocomposite  22 C, by limiting the aforementioned mixing factors, such as controlling nanocomposite-ink deposition velocities, and limiting diffusion temperature control of the substrate, and curing the deposited nanocomposite-inks within a controlled time. 
       FIG. 2H  schematically illustrates another nanocomposite-ink mixing method. Nanocomposite-ink  26 B and nanocomposite-ink  26 C are deposited such that the respective printing heads are aligned to cause the nanocomposite-ink to mix in air creating a nanocomposite-ink  22 E. Nanocomposite-ink  22 E, then deposits, mixed, onto substrate  18  with nanofillers  24 E bounded by ink-air interface  26 B. 
       FIG. 3A  schematically illustrates an optical-dispersion corrected optical-element  40  manufactured with the printing apparatus. Optical-element  40  is a positive gradient index lens (GRIN) characterized by an optical axis  41 , an air-element interface  42 A and an element-air interface  42 B. Optical-element  40  has a higher nanofillers concentration  44 A along the optical axis and a lower concentration  44 B forming a refractive-gradient. Here, the refractive gradient is characterized by a hyperparabolic index profile  45 , highest concentration of the nanofillers being along optical axis  41 . Those skilled in the art will recognize the general design as the “wood lens.” Deposition of the nanocomposite-ink forming the optical-element allows other refractive-gradient profiles including spherical, parabolic, axial, tapered, asymmetric, or otherwise graded profiles in one, two, or three axis, including profiles generated in other coordinate transforms, such as angular. Further, the refractive-gradient profile may change from those profiles aforementioned to other profiles aforementioned along any axis. 
       FIG. 3B  schematically illustrates the optical-element  40  of that shown in  FIG. 3A  with additional exemplary light-rays  51 ,  52 , and  53 . Light-rays  51  consists of at least two different wavelengths and enters optical-element  40  at air-element interface  42 A along optical-axis  41  at zero degree angle-of-incidence, the optical-element having a symmetric refractive gradient about the optical-axis, whereby a light-ray  51 , consisting of at least two different wavelengths, refracts into the nanocomposite-ink according to snell&#39;s, law,
 
 n   1 (λ)sin(θ 1 )= n   2 (λ)sin(θ 2 ),
 
where, n 1 (λ) is the wavelength dependent refractive-index of a first medium, θ 1  is the incoming angle-of-incidence normal to a second medium, n 2 (λ) is the wavelength dependent refractive-index of the second medium, and θ 2  is the angle entering the second medium. Here, the first medium is air, the incoming angle-of-incidence is zero, the second medium is nanocomposite-ink and the angle entering the second medium is zero, resulting in no optical-dispersion of light-ray  51 .
 
     A light ray  52 , consisting of at least two different wavelengths enters optical-element  40  at air-element interface  42 A, at zero degree angle-of-incidence, experiencing optical dispersion due to a transverse refractive gradient of the optical-element with a positive GRIN Abbe-number. The optical-dispersion of light ray  52  causes beam separation, exemplified by a short wavelength  52 A (short-ray) and a long wavelength ray  52 B (long-ray). One skilled in the art will recognize ray separation is dramatized for explanatory purposes. 
     Short-ray  52 A and long-ray  52 B propagate through the optical-element, the GRIN Abbe-number changes smoothly from positive to negative, thereby reducing the refraction of the short-beam, while increasing refraction of the long-beam resulting in recombination of beams at a point  53 . The change in the optical-element&#39;s GRIN Abbe-number, from negative to positive, causes increased refraction of the short-beam and reduced refraction of the long-beam, resulting in beam-separation. The optical-element&#39;s GRIN Abbe-number changes again from positive to negative resulting in aforementioned beam recombination at element-air interface  42 B. The angle-of-incidence on an interface  42 B is such that the refraction at the interface results in the short-ray and the long-ray exiting optical-element  40  at about a same angle, co-propagating towards a focal point  54 A, thereby experiencing about no focal shift. 
     Although only two rays are shown, one skilled in the art will recognize that additional wavelengths can be corrected by the aforementioned technique as well as continuous bands of wavelengths otherwise known as broadband. The change in the GRIN Abbe-number does not necessarily align with beam separation and change in the GRIN Abbe-number can occur resulting in no beam overlap until the element-air exit interface. The GRIN Abbe-number need not be a smooth function, nor sinusoidal as shown. Likewise, beam overlap may occur multiple times across multiple wavelengths within the optical-element. The GRIN Abbe-number is spatially dependent on incoming rays and will experience different values dependent on the angle entering the optical-element and entrance location. 
       FIG. 3C  schematically illustrates that shown in  FIG. 3B , wherein light-rays  51 ,  52 , and  53  approach at an angle-of-incidence not parallel to optical-axis  41  resulting in an off-axis focal position  54 B. The off-axis focal position  54 B in a plane transverse to the optical-axis  41 , the plane also containing focal point  54 A. 
       FIG. 3B  details correction of axial chromatic-aberration. Axial chromatic aberration is characterized by focus shift of different wavelength along the optical-axis.  FIG. 3C  details correction of transverse chromatic-aberration. Transverse chromatic-aberration is characterized by focus shift of different wavelength in the focal plane. In addition to chromatic-aberration correction, the optical-element can correct geometric-aberrations. 
     Some nonlimiting geometric-aberrations include spherical aberration, coma, astigmatism, curvature of field, and distortion, known as Seidel aberrations. Spherical aberration is characterized by on-axis defocus. Coma is characterized by defocus of off-axis field-points. Astigmatism is characterized by asymmetric power in transverse planes to the optical-axis. Curvature of field is characterized by focus on a curved surface rather than a preferred planar surface. Distortion is characterized by nonlinear power as function of distance from the optical-axis, resulting in pincushion or barrel distortion. As aforementioned, the disclosed technique allows for complex refractive-gradient profiles which can correct for, in addition to chromatic aberration, those geometric-aberrations listed and combinations thereof. Further, geometric-aberrations of the substrate of the optical-element can be measured, before deposition of nanocomposite-ink, and corrected in the final optical-element by altering the gradient-index of the optical-element to correct for the geometric-aberrations measured. 
     A variety of techniques can be used to measure geometric-aberration. For a constant refractive-index optic, geometric-aberration can be determined with knowledge of the optic surfaces and material. The material of the optic is generally known or can be determined. Inexpensive methods include reflective and transmission spectrometry or refractometry, which are well known techniques in the art. Detailed element material analysis can be accomplished with scanning electron microscopy, x-ray spectrometry, and other advanced techniques. Surface properties can be measured using interferometry, profilometery, and other related techniques. Instruments capable of measuring those geometric aberrations aforementioned as well as others are commercially available from optical metrology companies such as ZYGO Corporation, of Middlefield, Conn. 
       FIG. 4A  and  FIG. 4B  schematically illustrate another preferred embodiment of the present disclosure. An optical-element  60  is a GRIN optic with a parabolic GRIN profile like that shown generally in  FIG. 3A . Here, the optical-element has nanocomposite deposited such that the GRIN Abbe-number changes radially from optical axis  41  along symmetric cylindrical according to an exemplary GRIN Abbe-number profile  64 . GRIN Abbe-number profile  64  has an inflection point  62 A,  62 B, and  62 C thereby correcting beam separation caused by optical-dispersion. 
       FIG. 5A  and  FIG. 5B  schematically illustrate yet another preferred embodiment of the present disclosure. An optical-element  70  is a GRIN optic with a parabolic profile like that shown generally in  FIG. 3A . Here, optical-element  70  has nanocomposite deposited such the GRIN Abbe-number changes radially from optical axis  41  and varies along optical axis. A GRIN Abbe-number profile  74 A at air-element interface  76 A has an inflection points  72 A,  72 B, and  72 C. The Abbe-number profile changes through the optical-element resulting in GRIN a Abbe-number profile  74 B. 
       FIG. 6A ,  FIG. 6B ,  FIG. 6C  and  FIG. 6D  schematically illustrate other preferred embodiments of the present disclosure wherein darker shaded areas represent higher refractive index of the optical-element. In each of  FIGS. 6A-6D  the techniques aforementioned, or combinations thereof, can be implemented.  FIG. 6A  schematically illustrate an optical-element  80 A where the optical power is negative, causing an incoming beam  82 A to diverge from an optical axis  41 .  FIG. 6B  schematically illustrates an imaging optical-element  80 B, where a field-point  84 A is imaged to a image-point  84 B.  FIG. 6C  schematically illustrate an optical-element  80 C, where the optical power changes from negative to positive along the optical axis  41 , causing an incoming collimated beam  82 C to diverge then converge such that it exits optical-element  80 A expanded and collimated.  FIG. 6D  schematically illustrate an optical-element  80 D, where positive optical power varies in along optical-axis  41 , causing an incoming beam  82 D to focus within the optical-element and then diverge and expand, finally exiting optical-element  80 D expanded and collimated. 
       FIG. 7A  schematically illustrates an optical-system  90 A with chromatic aberration. Optical-system  90  has a light ray  91 A,  92 A, and  93 A propagating toward a plano-convex lens  94 , the plano-convex lens made of glass. Light-rays  92 A, consisting of at least two different wavelengths, enters plano-convex lens  94  at an air-glass interface  95 A along optical-axis  41  at zero degree angle-of-incidence, whereby light-ray  92 A experiences no optical-dispersion. Light-ray  91 A and  93 A, symmetric about optical-axis  41 , experience the same optical effects, light-ray  91 A explained in detail herein. Light-ray  91 A, consisting of at least two different wavelengths, enters optical element  94  at air-glass interference  95 A at an angle-of incidence due to the convex lens shape of lens  94 . Light-ray  91 A experiences chromatic aberrations due to the optical-dispersion of the glass, exemplified by a short-wavelength ray  91 B (short-ray) refracting towards the optical-axis more than a long-wavelength ray  91 C (long-ray). Short-ray  91 B and long-ray  91 C propagate through the glass to glass-air interface  95 B, where refraction occurs again, resulting in short-ray  91 B focusing on optical-axis  41  at a point  96 A and long-ray  91 C focusing on optical-axis  41  at a point  96 B. 
       FIG. 7B  schematically illustrate the optical system shown in  FIG. 7A  with the addition of an optical-element  96 , in accordance with the present disclosure, positioned after plano-convex lens  94 . Short-ray  91 B and long-ray  91 C enter optical element  96  at a air-element interface  95 C, experiencing refraction into optical-element  96 . The optical-element comprises of at least two nanocomposite-inks, whereby the distribution of the nanocomposite-inks, using aforementioned techniques, direct short-ray and long-ray towards an element-air interface  95 D at an angle such that refraction at the interface  95 D results in short-ray  91 B and long-ray  91 C exit optical-element  96  overlapping and co-propagating towards an overlapping point  96 C, thereby correcting the chromatic aberration of optical system  90 . 
     While this shows one particular example, other positions and other optical systems can be corrected. For example, the optical-element may be positioned before plano-convex lens  94  correcting for later experienced chromatic-aberration. Alternatively other optical systems that consist of lenses, mirrors, fibers, diffractive-optics, other optical components, the optical-element disclosed, and combinations thereof can be corrected with the optical-element in accordance with the present disclosure. 
       FIG. 8A  is a cross section view, schematically illustrating an optical-element  100 A. Optical-element  100 A has a substrate  102 , where the substrate is a plano-convex optic made of glass. The nanocomposite-ink is deposited to form the refractive-gradients of a bulk nanocomposite  104  with a nanofiller  106 , correcting chromatic-aberrations and geometric aberrations of the plano-convex optic. An element-air interface  108  is shown planar, but can be printed in a manner to be conformal to the underlying substrate or other geometries. 
       FIG. 8B  is a cross-section view, schematically illustrating a shaped optical-element  100 B wherein optical-element  100 B is shaped after deposition. Nanocomposite-ink is first deposited, then partially removed by methods such as single point diamond turning or chemical mechanically polishing, or solvent based removal of uncured polymers, forming an air-element interface  112 , where the interface has curvature. The remaining nanocomposite-ink and nanofillers  106 , structured using aforementioned techniques, correcting chromatic-aberrations and geometric-aberrations. 
       FIG. 8C  is a cross-section view, schematically illustrates a mold for printing an optical-element  114 . Here the mold is the substrate and has curvature at a nanocomposite-mold interface  118 , causing nanocomposite-ink to conform to the mold curvature, resulting in optical-element  114  retaining the curvature of the mold interface upon removal. The nanocomposite-ink and nanofillers  106 , are structured using aforementioned techniques, correcting chromatic-aberrations and geometric-aberrations of the resultant optical element. 
       FIG. 9A  is a perspective view of an imaging system  200 . Imaging system  200  has an optical-dispersion corrected optical-element  210  for imaging onto an image sensor  230  and more particularly an image plane array  232 . The optical-dispersion element has with a first surface  212  and a second surface  214  with a first nanocomposite-ink with a first nanofiller dispersed in a cured organic-matrix and a second nanocomposite-ink with a second nanofiller dispersed in the cured organic-matrix. Optical-dispersion of the second nanocomposite-ink is different than optical-dispersion of the first nanocomposite-ink. The distribution of the first nanocomposite-ink and second nanocomposite-ink corrects chromatic aberration and creates a volumetric cross-section with a radially asymmetric refractive gradient to correct optical aberration within the aspect ratio of an image plane array. 
     Image sensors or more particularly image plane arrays are also referred to in the art as camera sensors, focal plane arrays (FPA), pixelated detectors and other such terms. The optical-element of the present disclosure applies to all such sensors wherein pixels are non-radially symmetric. A typical image plane array, such as image plane array  230 , is an equal-angle quadrilateral, i.e. a square or a rectangle. Such image plane arrays typically have aspect ratios (length:width) that are 1:1, 4:3, or 16:9, although other aspect rations exist and the optical-element can be designed to accommodate other aspect ratios. Here, image sensor  230  has image plane array  232  with an aspect ratio of about 3:2. Typical imaging systems have an f-number of about f/1.4, f/2, f/4, or f/8 although larger and smaller f-numbers can be accommodated. 
     The radially asymmetric cross-section corrects optical aberration by optimizing imaging within a field-of-view  236  that is about matched to the aspect ratio of the image plane array. As described above, the concentration of nanoparticles within any volumetric are determine the local refractive index. The concentration of nanoparticles, or the proportional index of refraction, of the radially asymmetric refractive gradient can be described by high order mutually orthogonal cross terms or any other such freeform equations. The ABBE number and GRIN Abbe number compensation can be implemented as described above. 
     In some embodiments, the cross-section of the entire optical-element has the radially asymmetric refractive gradient and the overall asymmetry of the radially asymmetric refractive gradient is optimized for imaging within the image sensor. In other embodiments, a smaller volumetric cross-section is used and the radially asymmetric refractive gradient has a higher asymmetry to compensate for radially symmetric cross-sections. In yet other embodiments, a plurality of cross-section have radially asymmetric refractive gradients and can include distinct or continuously changing radially asymmetric refractive gradients along the optical axis. 
     The first surface, the second surface, or both can have surface curvature. The surface curvature can be radially symmetric or asymmetric, including freeform. Using inkjet printing, the shape of the lens can be arbitrarily chosen and can include circular, square, rectangular, including segmented pieces and annular shapes with center of mass located on or off-axis. 
     From the description of the present disclosure provided herein one skilled in the art can design the optical-elements in accordance with the present disclosure. For example, one skilled in the art could design an optical-element describing the GRIN material by using commercially available optical design software, such as ZEMAX available from the Zemax Corporation, of Belleview, Wash. 
     Those skilled in the art to which the present disclosure pertains will recognize that while above-described embodiments of the inventive optical-element and method of manufacture are exemplified using particular refractive profiles, GRIN Abbe-number profiles, and materials, others may be combined using these embodiments without departing from the spirit and scope of the present disclosure. 
     While some of the embodiments explained above and assume symmetry around the optical-axis, one skilled in the art will recognize that radial symmetry is not a requirement and cylindrical optical-elements can implemented with the disclosed techniques. While embodiments of the present disclosure are described above with respect to chromatic aberration, the disclosure is equally applicable to alternate optical-aberration correction. Further, the techniques described allow for a thermal design allowing the optical-element disclosed to correct for Temperature Coefficient of Refractive Index (dn/dT). 
     In summary, the present invention is described above in terms of particular embodiments. The invention, however, is not limited to the embodiments described and depicted herein. Rather, the invention is limited only by the claims appended hereto.