FI20205622A1

FI20205622A1 - Gradient-index optics

Info

Publication number: FI20205622A1
Application number: FI20205622A
Authority: FI
Inventors: Jyrki Saarinen; Jouni Partanen
Original assignee: Aalto Univ Foundation Sr; Itae Suomen Yliopisto
Priority date: 2020-06-15
Filing date: 2020-06-15
Publication date: 2021-12-16
Also published as: WO2021255337A1

Abstract

According to an example aspect of the present invention, there is provided a method comprising constructing (520) an optical element using a programmable material-jet printer by employing at least two materials having indices of refraction different from each other, and wherein internally the optical element has (530) an index of refraction which changes continuously as a function of place, wherein the constructing (520) comprises producing the continuously changing index of refraction by modifying continuously, as a function of place, a mixing ratio at which the at least two materials are ejected from the material-jet printer to construct the optical element.

Description

GRADIENT-INDEX OPTICS FIELD

[0001] The present disclosure relates to the fields of gradient-index optics material- jet printing.

BACKGROUND

[0002] Gradient-index, GRIN, optics involves materials with a variable index of refraction. While conventional lenses, constructed of material with a constant index of — refraction, perform their function based on their carefully designed shape, the GRIN principle allows construction of lenses or other optical elements which need not be specifically shaped to perform their function, rather, the distribution of the index of refraction inside the optical elements defines the functioning of the element.

[0003] Traditionally, manufacture of GRIN lenses has been difficult, which has slowed down their use in practical applications. o SUMMARY

S > 20 [0004] According to some aspects, there is provided the subject-matter of the

O LO independent claims. Some embodiments are defined in the dependent claims. E [0005] According to a first aspect of the present disclosure, there is provided a N method comprising constructing an optical element using a programmable material-jet

N D printer by employing at least two materials having indices of refraction different from each S 25 — other, and wherein internally the optical element has an index of refraction which changes continuously as a function of place, wherein the constructing comprises producing the continuously changing index of refraction by modifying continuously, as a function of place, a mixing ratio at which the at least two materials are ejected from the material-jet printer to construct the optical element.

[0006] According to a second aspect of the present disclosure, there is provided an apparatus comprising a memory configured to store information concerning an optical element, at least one processing core, configured to construct the optical element in accordance with the information by controlling a programmable material-jet printer which employs at least two materials having indices of refraction different from each other, and wherein the at least one processing core is configured to construct the optical element such that internally the optical element has an index of refraction which changes continuously as a function of place, wherein the constructing comprises producing the continuously changing index of refraction by modifying continuously, as a function of place, a mixing ratio at which the at least two materials are ejected from the material-jet printer to construct the optical element.

[0007] According to a third aspect of the present disclosure, there is provided an — apparatus comprising means for storing information concerning an optical element, constructing the optical element in accordance with the information by controlling a programmable material-jet printer which employs at least two materials having indices of refraction different from each other, and wherein the apparatus is configured to construct the optical element such that internally the optical element has an index of refraction which — changes continuously as a function of place, wherein the constructing comprises producing the continuously changing index of refraction by modifying continuously, as a function of place, a mixing ratio at which the at least two materials are ejected from the material-jet printer to construct the optical element. S [0008] According to a fourth aspect of the present disclosure, there is provided a O 25 — non-transitory computer readable medium having stored thereon a set of computer readable 0 instructions that, when executed by at least one processor, cause an apparatus to at least I store information concerning an optical element, construct the optical element in a accordance with the information by controlling a programmable material-jet printer which O employs at least two materials having indices of refraction different from each other, and N 30 wherein the at least one processing core is configured to construct the optical element such N that internally the optical element has an index of refraction which changes continuously as a function of place, wherein the constructing comprises producing the continuously changing index of refraction by modifying continuously, as a function of place, a mixing ratio at which the at least two materials are ejected from the material-jet printer to construct the optical element

BRIEF DESCRIPTION OF THE DRAWINGS

[0009] FIGURE 1A illustrates a GRIN lens in accordance with at least some embodiments of the present invention;

[0010] FIGURE 1B illustrates an optical element in accordance with at least some embodiments of the present invention; — [0011] FIGURE 2 illustrates a material-jet printer capable of supporting at least some embodiments of the present invention;

[0012] FIGURE 3 illustrates an example apparatus capable of supporting at least some embodiments of the present invention;

[0013] FIGURE 4 illustrates signalling in accordance with at least some embodiments of the present invention, and

[0014] FIGURE 5 is a flow graph of a method in accordance with at least some embodiments of the present invention. o EMBODIMENTS

O

N & 20 <Q 2 [0015] Using a material-jet printer, such as an ink-jet printer, a GRIN optical E element, such as a lens, may be constructed by three-dimensional, 3D, printing. The N variable index of refraction inside the optical element is obtained by adjusting a mixing

N D ratio of materials deposited into the optical element by the material-jet printer to construct S 25 — the optical element, the materials having indices of refraction which differ from each other. The index of refraction of the optical element in voxels in the optical element thus results from a mixing ratio of the materials which are deposited into the voxel by the material-jet printer. In detail, the mixing ratio is varied from voxel to voxel based on the desired distribution of the variable index of refraction inside the optical element. Advantageously, the material-jet 3D printing process may use more than two materials of different indices of refraction, to obtain the technical benefit of enhanced dynamic range in creation of the desired index of refraction. In general, optical elements may be transparent. 3D printing may be referred to as additive manufacturing. In general, by material-jet printing it is meant additively constructing a three-dimensional object by depositing material to form the object.

[0016] FIGURE 1A illustrates a GRIN lens in accordance with at least some embodiments of the present invention. GRIN lens 110 has internally an index of refraction n which varies as a function of the radial coordinate as schematically illustrated in the left- most part of the figure. As a result, when rays of light 102 enter GRIN lens 110 from one side, they are focused in the same way as by a conventional lens, as illustrated.

[0017] In a conventional lens, composed of material with an index of refraction — constant inside the lens, the focusing, or defocusing, effect is generated by a carefully designed shape of the lens. In a GRIN lens, on the other hand, the shape of the lens may be simple, as the focusing, or more generally manipulation of light paths, is defined rather by the distribution of the index of refraction inside the lens.

[0018] Manufacture of GRIN optical elements has been a challenge in the past. — Manufacturing techniques such as thallium or lithium doping of glass may be used to produce relatively simple distributions of refraction index inside a GRIN optical element. Alternatively, ion exchange using silver or lithtum may be used, again resulting in ES relatively simple distributions of refraction index inside a GRIN optical element. As will N be described herein, a material-jet printer mixing at least two different materials of S 25 different indices of refraction may be used to 3D-print a GRIN optical element such that a 2 complex distribution of the refraction index may be generated inside the optical element.

T s [0019] FIGURE 1B illustrates an optical element in accordance with at least some S embodiments of the present invention. FIGURE 1B represents schematically a three- N dimensional optical element by a two-dimensional drawing. The optical element 120 is N 30 transparent, having therein a nonuniform distribution of refractive index. Concentric circular patterns 122 schematically illustrate areas inside optical element 120 where the refractive index is higher. In the illustrated example, there are plural local maxima of refractive index, one at the centre of each concentric circular pattern 122. In particular, there are four local maxima. A ray of light 104 entering optical element 120 encounters the areas of higher and transversely gradient refractive index, which bend its path into a meandering, snake-like form illustrated in the figure. In general, using the disclosed 5 material-jet 3D printing method, optical elements having plural local minima and/or plural local maxima in the distribution of refractive index inside the optical element may be constructed. In general, the material-jet printer may be controlled to construct the optical element such that inside the optical element the refractive index has more than one local maximum and/or more than one local minimum. In some embodiments, there are more — than two local maxima and/or local minima. In addition to local minima and maxima, the refractive index can exhibit other kinds of variations with respect the spatial coordinates.

[0020] GRIN lenses with complex distributions of refractive index may be employed in spreading light from pointwise or linear to uniform light distributions, guiding light into optical fibres and/or obtaining a more densely packed assembly of lenses compared to use of'traditional lenses. In particular, GRIN lenses need not be curved, and a GRIN lens may be engineered to perform the functions of at least two traditional lenses. Thus a GRIN lens may find application as a lens in a smartphone camera assembly, for example, which typically has a constrained space available for lenses.

[0021] By local minimum it is meant a location, such as a voxel or group of voxels, in the optical element with neighbouring locations, for example neighbouring voxels or neighbouring groups of voxels, which have higher refractive index. Likewise a local maximum is a location, such as a voxel or group of voxels, in the optical element with neighbouring locations, for example neighbouring voxels or neighbouring groups of S voxels, which have lower refractive index. The trend to higher or lower refractive index O 25 — need not take place in all directions, but in at least two directions. Thus a local minimum or o local maximum need not be point-like, rather it may take the shape of a ring or a line. In = the example of FIGURE 1B, there are four local maxima 122 and one minimum which a occupies the inside of the optical element where densifications 122 are not present. In the O example of FIGURE 1A, there is a single linear maximum at coordinate xo.

S S 30 [0022] Optical elements, such as lenses, are used in imaging, in controlling illumination and in other applications of light. In the most common case, light is understood to mean visible light that is optical radiation in the wavelength range 400 — 700 nanometres. The refractive indices of optical elements, in general, are not constant through the visible wavelength range. For simplicity, in the present disclosure we discuss single values of refractive indices, omitting the complications that wavelength dependent behaviour brings. Single values for refractive indices are good for the case when optics are used in of laser applications, for example. Typically, lasers have very a narrow wavelength range, wherefore the single refractive index is a good approximation in the case of laser applications.

[0023] In optics with white light, or otherwise at least light with a somewhat wider range of wavelengths, or two or more narrow wavelength bands, different optical materials — may be used to maintain optical behaviour similar at different wavelengths, as needed in the application. The result may be a multicomponent lens that often has even 10 individual optical components made from a number of different optical materials. The refractive indices of these materials behave differently as function of wavelength. This is described by the Abbe number of the material. Smaller Abbe numbers mean stronger dependence on wavelength and larger Abbe numbers mean weaker dependence on wavelength. The relevance of this for 3D printed GRIN optics is that for being able to have optical elements to work at certain wavelength range, materials with different refractive indices and different Abbe numbers are needed. We would expect that 3 — 10 materials would be needed depending on their properties making a well-functioning optical device. The materials may be used as input materials in the material-jet printing process to obtain an optical component which maintains optical behaviour similar at different wavelengths.

[0024] In general, this discussion applies to a much wider range of wavelengths than o merely visible light, at least visible to infra red.

O N [0025] When producing a useful optical effect using a GRIN optical element, it is S 25 often useful to obtain, inside the optical element, an index of refraction which changes - continuously as a function of place. This kind of distribution can be used to approximate z the effect of a conventional lens, the surface of which tends to have a smooth shape. The N GRIN optical element could in that case be a GRIN lens, for example. A place may be D expressed as a voxel, for example, where each voxel may have a location inside the optical S 30 element defined in, for example, a three-dimensional voxel coordinate system (x, y, z) where each voxel has size one, or the actual voxel size. The refractive index which changes continuously as a function of place may be obtained in the construction of the optical element by a mixing ratio of the input materials of the material-jet printer which changes continuously as a function of place. The shape of the mixing ratio distribution in the optical element may thus correspond to the shape of the refractive index distribution.

[0026] Where a material-jet printer is used to construct the optical element based on information concerning the optical element, the result may be an optical element constructed voxel by voxel by the material-jet printer. The information concerning the optical element may define, for example, explicitly or implicitly, the desired refractive index for each voxel of the optical element, the optical element being comprised of the voxels. In such a case, the voxel size may define the resolution at which the continuous — nature of the distribution of the refractive index is achieved.

[0027] Where the voxel size defines the resolution of the achieved distribution of refractive index, an index of refraction which changes continuously as a function of place may be defined as a distribution where the index of refraction changes locally by the same amount in consecutive inter-voxel boundaries in a certain direction. The direction may be aligned with the voxels, or be oblique to a grid of voxels, for example. A small variation of these changes is allowed to account for an accuracy of the material-jet printer and variation in how the input materials blend in each voxel. A small variation may be 5% of the change per inter-voxel boundary, for example.

[0028] In a first example, the index of refraction continuously changing as a function of place comprises the index of refraction changing over a sequence of five consecutive voxels such that the total change over the five consecutive voxels is distributed between four inter-voxel boundaries in the sequence of the five consecutive voxels such that each inter-voxel boundary comprises between 20% and 30% of the total change.

O

N © [0029] In a second example, the index of refraction continuously changing as a 2 25 function of place comprises the index of refraction changing over a sequence of ten = consecutive voxels such that the total change over the ten consecutive voxels is distributed * between nine inter-voxel boundaries in the sequence of the ten consecutive voxels such S that each inter-voxel boundary comprises between 10% and 12% of the total change

S I [0030] FIGURE 2 illustrates a material-jet printer 220 capable of supporting at least some embodiments of the present invention. In the figure, material-jet printer 220 is 3D-

printing a GRIN optical element 210. The optical element 210 is unfinished, with a grid of locations 202 for a next layer of voxels schematically illustrated in the figure.

[0031] Material-jet printer 220 is controlled by controller 230, which may comprise a microprocessor or other control device. Controller 230 may comprise, for example, at least one processing core and memory. The memory may store information concerning optical element 210, to enable material-jet printer 220 to 3D-print the optical element 210 based on the information. The information may take the form of a digital file, for example.

In effect, the material-jet printer 220 is programmable by providing the information concerning the optical element.

[0032] Material-jet printer 220 has at least two input material reservoirs 240. The printer can extract input material from each of the input material reservoirs 240, via input material leads 242, to eject through nozzles 252 installed in printer head 250. Printer head 250 may be movable to enable depositing new voxels on the partially constructed optical element 210. In detail, material-jet printer 220 may deposit new voxels onto optical element 210, such that the refractive index of each new voxel is determined based on the information concerning the optical element. Material-jet printer 220 may obtain the correct refractive index for each new voxel by selecting the mixing ratio of the input materials from material reservoirs 240, the input materials having refractive indices different from each other. The material-jet printer may calculate the correct input material mixing ratio — for the new voxels using the refractive indices of the input materials, such that their linear combination in the correct mixing ratio is the desired refractive index. Optical element 210 may thus be constructed to have the internally varying refractive index distribution, as described above in connection with FIGUREs 1A and 1B. In some embodiments, S controller 230 and/or material reservoirs 240 are connected with material-jet printer 220, O 25 — but not comprised in the material-jet printer. The input materials may be mixed in printer LO head 250, in nozzles 252, during flight between nozzles 252 and optical element 210, or in z situ on the optical element. Nozzles 252 may be configured to eject the input material by a + shape-changing piezoelectric element method or a thermal drop generation method, for N example.

5 S 30 — [0033] In some embodiments, material-jet printer 220 is configured to eject plural droplets of the input materials, such that the droplets merge during flight before reaching optical element 210. For example one to ten such droplets may be ejected. A mixing ratio may thus be obtained in the material reaching optical element 210 by selecting the number of droplets of each of the input materials. For example, by ejecting three droplets of a first input material and two droplets of a second input material for merging into a single larger droplet, a 3:2 mixing ratio is obtained.

[0034] The material-jet, such as ink-jet, 3D printing process may comprise a curing phase, or curing phases, where the mixed input materials are cured onto optical element 210, for example using blue light or ultra-violet light. Curing parameters may be static or configured dynamically by controller 230 based on the information concerning the optical element.

[0035] The number of material reservoirs 240, and correspondingly the number of different input materials of different refractive indices, may be more than two. In particular, the number may be at least three, at least five or at least fifteen. Using a larger number of input materials, of differing refractive indices, provides the technical benefit of enabling a construction of voxels with an accurate refractive index over a larger dynamic range than with fewer input materials.

[0036] The input materials may comprise suitably selected materials of different refractive indices to enable obtaining a range of refractive indices by mixing. For example, the input materials may comprise suitably selected acrylate, silicone and/or epoxy materials. In detail, the input materials may comprise different acrylates. In some embodiments, the input materials may comprise different silicone materials, In yet further embodiments, the input materials comprise different epoxy materials. In some embodiments, at least one of the input materials is an acrylate and at least one other input material is a silicone. In some embodiments, at least one of the input materials is an N acrylate and at least one other input material is an epoxy. In some embodiments, at least S 25 one of the input materials is a silicone material and at least one other input material is an - epoxy. i

[0037] In some embodiments, the material-jet printer is configured to obtain the S desired refractive index for the voxels by first selecting the mixing ratio, as described N above, and then fine-tuning the resulting refractive index by selecting parameters of the N 30 curing process. For example, material-jet printer 220 may know that increasing the intensity of light used in the curing, or prolonging the duration of the curing, results in a slight increase (or decrease, depending on the materials) in the refractive index when the current input materials are used. In other words, the refractive index of new voxels may be determined based on a combination of a selected mixing ratio of input materials and a selected set of curing process parameters. This may enable obtaining a more precise value for the refractive index of the new voxels when they are complete, for example in case the mixing ratio can only be achieved up to a limited resolution in printer head 250 and/or nozzles 252.

[0038] In some embodiments, the information concerning optical element 210 comprises a definition of a shape of a surface of optical element 210 in addition to the distribution of refractive index inside optical element 210. In such a case, optical element 210 may have a so-called freeform surface in addition to having an internally anisotropic refractive index distribution. In other words, the optical element would be a GRIN optical element with a freeform surface, constructed by 3D material-jet printing. For example, a freeform surface may have a shape which comprises at least two raised areas and/or at least two recessed areas.

[0039] FIGURE 3 illustrates an example apparatus capable of supporting at least some embodiments of the present invention. Illustrated is device 300, which may comprise, for example, controller 230 FIGURE 2. Comprised in device 300 is processor 310, which may comprise, for example, a single- or multi-core processor wherein a single- core processor comprises one processing core and a multi-core processor comprises more — than one processing core. Processor 310 may comprise, in general, a control device. Processor 310 may comprise more than one processor. Processor 310 may be a control device. A processing core may comprise, for example, a Cortex-A8 processing core manufactured by ARM Holdings or a Zen processing core designed by Advanced Micro S Devices Corporation. Processor 310 may comprise at least one Qualcomm Snapdragon O 25 and/or Intel Atom processor. Processor 310 may comprise at least one application-specific o integrated circuit, ASIC. Processor 310 may comprise at least one field-programmable gate = array, FPGA. Processor 310 may be means for performing method steps in device 300, a such as storing and controlling. Processor 310 may be configured, at least in part by O computer instructions, to perform actions, such as controlling a material-jet printer.

S S 30 — [0040] Device 300 may comprise memory 320. Memory 320 may comprise random- access memory and/or permanent memory. Memory 320 may comprise at least one RAM chip. Memory 320 may comprise solid-state, magnetic, optical and/or holographic memory, for example. Memory 320 may be at least in part accessible to processor 310. Memory 320 may be at least in part comprised in processor 310. Memory 320 may be means for storing information. Memory 320 may comprise computer instructions that processor 310 is configured to execute. When computer instructions configured to cause processor 310 to perform certain actions are stored in memory 320, and device 300 overall is configured to run under the direction of processor 310 using computer instructions from memory 320, processor 310 and/or its at least one processing core may be considered to be configured to perform said certain actions. Memory 320 may be at least in part comprised in processor 310. Memory 320 may be at least in part external to device 300 but accessible to device 300.

[0041] Device 300 may comprise a transmitter 330. Device 300 may comprise a receiver 340. Transmitter 330 and receiver 340 may be configured to transmit and receive, respectively, information in accordance with at least one communication protocol.

[0042] Device 300 may comprise user interface, UI, 360. UI 360 may comprise at least one of a display, a keyboard, a touchscreen, a vibrator arranged to signal to a user by causing device 300 to vibrate, a speaker and a microphone. A user may be able to operate device 300 via UI 360, for example to input information concerning an optical element.

[0043] Processor 310 may be furnished with a transmitter arranged to output information from processor 310, via electrical leads internal to device 300, to other devices — comprised in device 300. Such a transmitter may comprise a serial bus transmitter arranged to, for example, output information via at least one electrical lead to memory 320 for storage therein. Alternatively to a serial bus, the transmitter may comprise a parallel bus ES transmitter. Likewise processor 310 may comprise a receiver arranged to receive N information in processor 310, via electrical leads internal to device 300, from other devices S 25 comprised in device 300. Such a receiver may comprise a serial bus receiver arranged to, - for example, receive information via at least one electrical lead from receiver 340 for s processing in processor 310. Alternatively to a serial bus, the receiver may comprise a N parallel bus receiver.

O N [0044] Device 300 may comprise further devices not illustrated in FIGURE 3. In N 30 some embodiments, device 300 lacks at least one device described above.

[0045] Processor 310, memory 320, transmitter 330, receiver 340 and/or UI 360 may be interconnected by electrical leads internal to device 300 in a multitude of different ways. For example, each of the aforementioned devices may be separately connected to a master bus internal to device 300, to allow for the devices to exchange information. However, as the skilled person will appreciate, this is only one example and depending on the embodiment various ways of interconnecting at least two of the aforementioned devices may be selected without departing from the scope of the present invention.

[0046] FIGURE 4 illustrates signalling in accordance with at least some embodiments of the present invention. On the vertical axes are disposed, on the left, controller 230 of FIGURE 2, in the centre actuators MTR which are configured to move printer head 250 to plural locations for 3D printing, and printer head 250 on the right. Time advances from the top toward the bottom.

[0047] In phase 410, controller 230 receives information concerning an optical element to 3D-print. The received information is stored in phase 420, wherein this phase — may further comprise, for example, deriving mixing ratios for voxels of the optical element based on properties of the input materials of the material-jet printer, controller 230 knowing the properties of the input materials, such as their refractive indices.

[0048] In phases 430 and 440, controller 230 controls actuators MTR and printer head 250 to construct the optical element in based on the information received in controller 230 in phase 410. Phases 430 and 440 may comprise receiving feedback from actuators MTR and/or printer head 250 concerning completion of actions directed by controller 230.

[0049] In phase 450, the optical element is completed, such that any curing phase(s) N have also been successfully completed. The completion of the construction of the optical » element may be reported to a user using a suitable mechanism, such as a user interface, for hi 25 — example. E [0050] FIGURE 5 is a flow graph of a method in accordance with at least some N embodiments of the present invention. The phases of the illustrated method may be D performed in a machine-jet printer device, such as controller 230, for example, or in S general in a control device of a material-jet printer. — [0051] Phase 510 comprises storing information concerning an optical element. Phase 520 comprises constructing an optical element using a programmable material-jet printer by employing at least two materials having indices of refraction different from each other. Finally, phase 530 comprises specifying that internally the constructed optical element has an index of refraction which changes continuously as a function of place, wherein the constructing comprises producing the continuously changing index of refraction by modifying continuously, as a function of place in the optical element, a mixing ratio at which the at least two materials are ejected from the material-jet printer to construct the optical element.

[0052] It is to be understood that the embodiments of the invention disclosed are not limited to the particular structures, process steps, or materials disclosed herein, but are — extended to equivalents thereof as would be recognized by those ordinarily skilled in the relevant arts. It should also be understood that terminology employed herein is used for the purpose of describing particular embodiments only and is not intended to be limiting.

[0053] Reference throughout this specification to one embodiment or an embodiment means that a particular feature, structure, or characteristic described in — connection with the embodiment is included in at least one embodiment of the present invention. Thus, appearances of the phrases “in one embodiment” or “in an embodiment” in various places throughout this specification are not necessarily all referring to the same embodiment. Where reference is made to a numerical value using a term such as, for example, about or substantially, the exact numerical value is also disclosed.

[0054] As used herein, a plurality of items, structural elements, compositional elements, and/or materials may be presented in a common list for convenience. However, these lists should be construed as though each member of the list is individually identified o as a separate and unigue member. Thus, no individual member of such list should be O construed as a de facto eguivalent of any other member of the same list solely based on O 25 — their presentation in a common group without indications to the contrary. In addition, 0 various embodiments and example of the present invention may be referred to herein along I with alternatives for the various components thereof. It is understood that such a embodiments, examples, and alternatives are not to be construed as de facto equivalents of O one another, but are to be considered as separate and autonomous representations of the ä 30 present invention.

[0055] Furthermore, the described features, structures, or characteristics may be combined in any suitable manner in one or more embodiments. In the preceding description, numerous specific details are provided, such as examples of lengths, widths, shapes, etc., to provide a thorough understanding of embodiments of the invention. One skilled in the relevant art will recognize, however, that the invention can be practiced without one or more of the specific details, or with other methods, components, materials, etc. In other instances, well-known structures, materials, or operations are not shown or described in detail to avoid obscuring aspects of the invention.

[0056] While the forgoing examples are illustrative of the principles of the present invention in one or more particular applications, it will be apparent to those of ordinary skill in the art that numerous modifications in form, usage and details of implementation can be made without the exercise of inventive faculty, and without departing from the principles and concepts of the invention. Accordingly, it is not intended that the invention be limited, except as by the claims set forth below.

[0057] The verbs “to comprise” and “to include” are used in this document as open limitations that neither exclude nor require the existence of also un-recited features. The — features recited in depending claims are mutually freely combinable unless otherwise explicitly stated. Furthermore, it is to be understood that the use of "a" or "an", that is, a singular form, throughout this document does not exclude a plurality.

INDUSTRIAL APPLICABILITY

[0058] At least some embodiments of the present invention find industrial — application in manufacture of optical elements, such as lenses.

ACRONYMS LIST N GRIN gradient-index (optics)

N S UI user interface

O

REFERENCE SIGNS LIST i ;

input material leads material-jet printer grid of locations 300 — 360 structure of the device of FIGURE 3 410 — 450 phases of the process of FIGURE 4 510 — 530 phases of the method of FIGURE 5

O N O N O I LO

I a a

N N O LO O N O N

Claims

CLAIMS:

1. A method comprising: — constructing an optical element using a programmable material-jet printer by employing at least two materials having indices of refraction different from each other, and — wherein internally the optical element has an index of refraction which changes continuously as a function of place, wherein the constructing comprises producing the continuously changing index of refraction by modifying continuously, as a function of place, a mixing ratio at which the at least two materials are ejected from the material-jet printer to construct the optical element.

2. The method according to claim 1, wherein the material-jet printer uses at least three — materials having indices of refraction different from each other in constructing the optical element.

3. The method according to claim 1 or 2, wherein the material-jet printer uses at least six materials having indices of refraction different from each other in constructing the optical — element.

4. The method according to at least one of claims 1 — 3, wherein the optical element is a gradient-index lens.

S | 25 5. The method according to any of claims 1 — 4, wherein the materials are acrylate and/or S epoxy materials.

O z

6. The method according to any of claims 1 — 5, wherein the continuously changing index a of refraction is also constructed by modifying parameters of a curing phase of the material- O 30 jet construction.

O

S

7. The method according to any of claims 1 — 6, wherein the index of refraction continuously changing as a function of place comprises the index of refraction changing over a sequence of five consecutive voxels such that the total change over the five consecutive voxels is distributed between four inter-voxel boundaries in the sequence of five consecutive voxels such that each inter-voxel boundary comprises between 20% and 30% of the total change.

8. The method according to any of claims 1 — 7, wherein the index of refraction continuously changing as a function of place comprises the index of refraction changing over a sequence of ten consecutive voxels such that the total change over the ten consecutive voxels is distributed between nine inter-voxel boundaries in the sequence of ten consecutive voxels such that each inter-voxel boundary comprises between 10% and 12% of the total change.

9. The method according to any of claims 1 — 8, further comprising constructing at least one surface of the optical element, using the material-jet printer, to have a shape which comprises at least two raised areas and/or at least two recessed areas.

10. The method according to any of claims 1 — 9, wherein inside the optical element the refractive index has more than one local maximum and/or more than one local minimum.

11. An apparatus comprising: — a memory configured to store information concerning an optical element; — at least one processing core, configured to construct the optical element in accordance with the information by controlling a programmable material-jet printer which employs at least two materials having indices of refraction different from each other, and

S < 25 — wherein the at least one processing core is configured to construct the optical O element such that internally the optical element has an index of refraction which 0 changes continuously as a function of place, wherein the constructing comprises =E producing the continuously changing index of refraction by modifying a continuously, as a function of place, a mixing ratio at which the at least two O 30 materials are ejected from the material-jet printer to construct the optical element.

S N

12. The apparatus according to claim 11, wherein the apparatus is configured to control the material-jet printer to use at least three materials having indices of refraction different from each other in constructing the optical element.

13. The apparatus according to claim 11 or 12, wherein the apparatus is configured to control the material-jet printer to use at least six materials having indices of refraction different from each other in constructing the optical element.

14. The apparatus according to at least one of claims 11 — 13, wherein the optical element isa gradient-index lens.

15. The apparatus according to any of claims 11 — 14, wherein the materials are acrylate — and/or epoxy materials.

16. The apparatus according to any of claims 11 — 15, wherein the apparatus is configured to control the material-jet printer to construct the continuously changing index of refraction is also by modifying parameters of a curing phase of the material-jet construction.

17. The apparatus according to any of claims 11 — 16, wherein the index of refraction continuously changing as a function of place comprises the index of refraction changing over a seguence of five consecutive voxels such that the total change over the five consecutive voxels is distributed between four inter-voxel changes in the seguence of five — consecutive voxels such that each inter-voxel change comprises between 20% and 30% of the total change.

18. The apparatus according to any of claims 11 — 17, wherein the index of refraction 5 continuously changing as a function of place comprises the index of refraction changing O 25 over a sequence of ten consecutive voxels such that the total change over the ten O consecutive voxels is distributed between nine inter-voxel changes in the seguence of ten 0 consecutive voxels such that each inter-voxel change comprises between 10% and 12% of z the total change. a © 30

19. The apparatus according to any of claims 1 — 8, wherein the at least one processing N core is further configured to control the material-jet printer to construct at least one surface N of the optical element to have a shape which comprises at least two raised areas and/or at least two recessed areas.

20. The apparatus according to any of claims 1 — 9, wherein the at least one processing core is further configured to control the material-jet printer to construct the optical element such that inside the optical element the refractive index has more than one local maximum and/or more than one local minimum.

21. An apparatus comprising means for: — storing information concerning an optical element; — constructing the optical element in accordance with the information by controlling a programmable material-jet printer which employs at least two materials having indices of refraction different from each other, and — wherein the apparatus is configured to construct the optical element such that internally the optical element has an index of refraction which changes continuously as a function of place, wherein the constructing comprises producing the continuously changing index of refraction by modifying continuously, as a function of place, a mixing ratio at which the at least two materials are ejected from the material-jet printer to construct the optical element.

22. A non-transitory computer readable medium having stored thereon a set of computer readable instructions that, when executed by at least one processor, cause an apparatus to at — least: — storeinformation concerning an optical element; — construct the optical element in accordance with the information by controlling a programmable material-jet printer which employs at least two materials having o indices of refraction different from each other, and O 25 — wherein the at least one processing core is configured to construct the optical S element such that internally the optical element has an index of refraction which O changes continuously as a function of place, wherein the constructing comprises E producing the continuously changing index of refraction by modifying N continuously, as a function of place, a mixing ratio at which the at least two 3 30 materials are ejected from the material-jet printer to construct the optical element.

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