Method of fabricating an imaging system and corresponding imaging system

Abstract

A method of fabricating an imaging system as well as to a corresponding imaging system. The method includes providing a substrate; and forming, by means of a 3D-printing technique, a 3D structure on the substrate, wherein the forming of the 3D structure includes forming a stack of at least two diffractive optical elements in a single printing step.

Claims

1. A method of fabricating an imaging system, the method comprising: providing a substrate; and forming, using a 3D printing technique, a 3D structure on the substrate, wherein the forming of the 3D structure comprises forming a stack of at least two diffractive optical elements in a single printing step.

2. The method of claim 1, wherein each of the at least two diffractive optical elements has a thickness-to-diameter ratio which is at least 1:200 and not more than 1:5.

3. The method of claim 1, further comprising forming a supporting structure for supporting the at least two diffractive optical elements.

4. The method of claim 3, further comprising forming at least one discharge opening in the supporting structure between the at least two diffractive optical elements so that an unexposed photoresist is able to discharge during or after the 3D printing.

5. The method of claim 4, wherein a volume ratio of the at least one discharge opening with respect to the supporting structure is between 0.2 and 5.

6. The method of claim 1, further comprising exposing a photoresist deposited on the substrate, wherein the exposing of the photoresist is performed on a voxel by a voxel basis by guiding an exposing beam on concentric circle tracks, wherein a starting point of the exposing beam on each of the concentric circle tracks is determined randomly.

7. The method of claim 1, further comprising exposing a photoresist deposited on the substrate, wherein the exposing of the photoresist is performed such that writing tracks of subsequent writing layers to be exposed are laterally shifted in an alternating manner by a predefined distance.

8. The method of claim 1, wherein the at least two diffractive optical elements have edge structures, wherein the edge structures are formed by using an exposing dose of a 3D printer that differs from a standard exposing dose that is used for structures other than edges.

9. The method of claim 1, wherein the at least two diffractive optical elements have edge structures, and wherein the edge structures are formed such that at least one of the following is present: (a) an additional edge optimizing track is written on an upper boundary of desired edge structures; and (b) a target track is omitted on a lower boundary of the desired edge structures.

10. The method of claim 1, wherein the at least two diffractive optical elements have edge structures with undercuts.

11. An imaging system, comprising: a substrate; and a 3D structure positioned on the substrate, wherein the 3D structure comprises a stack of at least two diffractive optical elements that have been printed using a 3D printing technique in a single printing step, and wherein each of the at least two diffractive optical elements has a thickness-to-diameter ratio that is at least 1:200 and not more than 1:5.

12. The imaging system of claim 11, wherein the 3D structure is formed by exposing a photoresist deposited on the substrate, wherein the exposing of the photoresist is performed on a voxel by a voxel basis by guiding an exposing beam on concentric circle tracks, wherein a starting point of the exposing beam on each concentric circle track is determined randomly.

13. The imaging system of claim 11, wherein the 3D structure is formed by exposing a photoresist deposited on the substrate, wherein the exposing of the photoresist is performed such that writing tracks of subsequent writing layers of the photoresist are laterally shifted in an alternating manner by a predefined distance.

14. The imaging system of claim 11, wherein the at least two diffractive optical elements have edge structures that are formed by using an exposing dose of a 3D printer that differs from a standard exposing dose that is used for structures other than edges.

15. The imaging system of claim 11, wherein the at least two diffractive optical elements have edge structures that are formed such that at least one of the following is present: (a) an additional edge optimizing track is written on an upper boundary of desired edge structures; and (b) a target track is omitted on a lower boundary of the desired edge structures.

16. The imaging system of claim 11, wherein the diffractive optical elements have edge structures with undercuts.

17. An imaging system, comprising: a substrate; and a 3D structure positioned on the substrate, wherein the 3D structure comprises a stack of at least two diffractive optical elements that have been printed using a 3D printing technique in a single printing step; and a supporting structure configured to support the at least two diffractive optical elements, wherein the supporting structure comprises at least one discharge opening located between the at least two diffractive optical elements so that an unexposed photoresist is able to discharge during or after the 3D printing technique.

18. The imaging system of claim 17, wherein a volume ratio of the at least one discharge opening with respect to the supporting structure is between 0.2 and 5.

Description

BRIEF DESCRIPTION OF THE FIGURES

(1) The above and other objects, features and advantages of the present invention will become more apparent upon reading of the following description of preferred embodiments and accompanying drawings. Other features and advantages of the subject-matter described herein will be apparent from the description and the drawings and from the claims. It should be understood that even though embodiments are separately described, single features and functionalities thereof may be combined without prejudice to additional embodiments. The present disclosure is illustrated by way of example and not limited by the accompanying figures.

(2) Preferred embodiments of the present invention are exemplarily described regarding the following figures:

(3) FIG. 1 shows schematics regarding a phase shift as a function of entrance pupil radius r and angle of incidence α for A) a single DOE and B) a combination of two DOEs;

(4) FIG. 2A shows a schematic with geometric relations used for theoretical considerations regarding a correction of monochromatic aberrations by combining DOEs;

(5) FIG. 2B shows schematics regarding field dependent aberrations of a single perfect DOE whose phase function creates a converging spherical wave;

(6) FIG. 2C shows schematics regarding field dependent aberrations for a combination of two DOEs, wherein both DOEs are optimized for a minimum point spread function over the whole field of view;

(7) FIG. 2D shows schematics regarding field dependent aberrations for a combination of three DOEs with a full field of view of 120°;

(8) FIG. 3A shows a schematic representation of an optical design (left hand side) and a corresponding CAD design (right hand side) for a single diffractive lens with a numerical aperture of 0.8;

(9) FIG. 3B shows a schematic representation of an optical design (left hand side) and a corresponding CAD design (right hand side) for an imaging system comprising a stack of two DOEs, according to an exemplary embodiment of the present invention;

(10) FIG. 3C shows a schematic representation of an optical design (left hand side) and a corresponding CAD design (right hand side) for an imaging system comprising a stack of three DOEs, according to an exemplary embodiment of the present invention;

(11) FIG. 4A shows a schematic representation in a plan view of a conventional Cartesian writing process;

(12) FIG. 4B shows a schematic representation in a plan view of a polar writing process as used according to a preferred embodiment of the present invention;

(13) FIG. 4C shows a schematic representation in a cross sectional view of a 3D writing process according to a preferred embodiment of the present invention;

(14) FIG. 5A shows a schematic representation in a cross sectional view of ideal edge structures of a DOE;

(15) FIG. 5B shows a schematic representation in a cross sectional view of target writing tracks for forming edge structures of a DOE;

(16) FIG. 5C shows a schematic representation in a cross sectional view of resulting edge structures formed by means of a 3D printing technique when writing the target writing tracks as shown in FIG. 3B;

(17) FIG. 5D shows a schematic representation in a cross sectional view of optimized writing tracks for forming edge structures of a DOE, according to a preferred embodiment of the present invention;

(18) FIG. 5E shows a schematic representation in a cross sectional view of resulting edge structures formed by means of a 3D printing technique when writing the optimized writing tracks as shown in FIG. 3D;

(19) FIG. 6A shows a schematic representation in a cross sectional view of the scattering behavior of a DOE having edge structures without undercuts;

(20) FIG. 6B shows a schematic representation in a cross sectional view of the scattering behavior of a DOE having edge structures with undercuts;

(21) FIG. 6C shows a schematic representation in a cross sectional view of a writing process from the target profile (top sketch) over an optimized arrangement of writing tracks (middle sketch) to the result after developing the exposed structures; and

(22) FIG. 6D shows a schematic representation in a cross sectional view of a DOE having edge structures with undercuts.

DETAILED DESCRIPTION OF THE FIGURES

(23) The following detailed description relates to exemplary embodiments of the present invention. Other embodiments of the invention are possible within the scope of the invention as defined by the appended claims. Throughout the figures, same reference signs are used for the same or similar elements.

(24) If flat lenses or DOEs are used for imaging, strong color and coma aberrations may lead to a significant decrease in image quality. For example, color dispersion is an inherant property of diffractive lenses. In order to correct dispersions and/or aberrations of a DOE, at least one additional DOE may be used to compensate the dispersions and/or aberrations. In other words, a combination or a cascade of at least two DOEs may compensate the dispersions and/or aberrations of the individual DOEs and thus increase the imaging quality. This is explained in more details below in connection with FIGS. 1 and 2.

(25) A single surface can act as a perfect lens with focal length f for focusing on the optical axis if it adds a parabolic phase of φ(r)=−2π/λ√{square root over (r.sup.2+f.sup.2)} to an incident wave front. However, if light is impinging under a certain angle α, the lens will not form a perfect focus unless an angle-dependent phase term φ(α) is added to the lens phase which at the same time deteriorates the performance for angles other than α. Thus, a single flat phase element cannot provide aberration free imaging over an extended field of view. This problem can be solved if the phase surface is not flat but has a curved shape. However, fabrication of such surfaces is challenging. Another option is the combination of two or more flat lenses (i.e. DOEs), inspired by the combination of two or more lenses for monochromatic aberration corrections of 1.sup.st (defocusing, distortion) and 3.sup.rd (spherical aberration, astigmatism, coma, Petzval field curvature) order in multi-element lens systems. In this case, the additional degrees of freedom introduced by the distance between first and second element leads to a total phase shift which is a function of both, the pupil radius as well as the angle of incidence.

(26) FIG. 1 shows schematics regarding a phase shift as a function of entrance pupil radius r and angle of incidence α for A) a single DOE and B) a combination of two DOEs. According to FIG. 1A, one flat lens leads to a parabolic phase shift φ(r) but does not allow for an angle dependent control of the phase φ(r,α). This leads to strong aberrations for fields with oblique incidence. According to FIG. 1B, if two or more lenses are combined, the phase shift φ(r,α) can be chosen as a function of both variables and thus can lead to an aberration free system over a wide field of view.

(27) FIG. 2A shows a schematic with geometric relations used for the following theoretical considerations. FIG. 2B shows schematics regarding field dependent aberrations of a single perfect DOE whose phase function creates a converging spherical wave. FIG. 2C shows schematics regarding field dependent aberrations for a combination of two DOEs, wherein both DOEs have been optimized for a minimum point spread function over the whole field of view. And FIG. 2D shows schematics regarding field dependent aberrations for a combination of three DOEs with a full field of view of 120°.

(28) The analysis on aberrations of flat lenses can be expressed in terms of optical path differences. In this formulation, the third-order off-axis wave aberrations of a perfect flat lens are given with respect to the ray c.sub.1 (see FIG. 2A) in dependence of the angle of incidence α, the focal length f, and the ray height r.sub.2 by

(29) $\begin{matrix} OPD (r_{2}) = \frac{α}{2 f^{2}} r_{2}^{3} - \frac{3 α^{2}}{4 f} r_{2}^{2}, & [1] \end{matrix}$
wherein “OPD” stands for the optical path difference.

(30) The first term which represents 3.sup.rd order coma starts to become dominant for low f-numbers, the second term which denotes astigmatism and Petzval field curvature is more dominant in systems with high f-numbers and high angles-of-view. Within the present invention, designs with low f-numbers, i.e. high numerical aperture, resulting in a dominant coma term are preferred.

(31) If an aperture is introduced before the lens element (radial coordinate: r.sub.1), the wave aberration with respect to the chief ray c.sub.2 can be expressed as

(32) $\begin{matrix} OPD (r_{2} + r_{1}) - OPD (r_{2}) = \frac{α}{2 f^{2}} {(r_{1} + r_{2})}^{3} - \frac{3 α^{2}}{4 f} {(r_{1} + r_{2})}^{3} - \frac{α}{2 f^{2}} r_{2}^{3} + \frac{3 α^{2}}{4 f} r_{2}^{2} . & [2] \end{matrix}$

(33) Since the main goal is to correct the 3.sup.rd order comatic aberration, additional terms with r.sup.3 dependence have to be introduced. This can be achieved by additionally considering the spherical aberration term prevalent at the flat lens (radial coordinate: r.sub.2), which is expressed as

(34) $\begin{matrix} - s \frac{r_{2}^{4}}{8 f^{3}} . & [3] \end{matrix}$

(35) Here the factor s can later be chosen such that the third order coma disappears. After inserting this expression into Eq. 2, the total aberration changes to

(36) $\begin{matrix} - s \frac{{(r_{1} + r_{2})}^{4}}{8 f^{3}} + \frac{α}{2 f^{2}} {(r_{1} + r_{2})}^{3} - \frac{3 α^{2}}{4 f} {(r_{1} + r_{2})}^{2} + s \frac{r_{2}^{4}}{8 f^{3}} - \frac{α}{2 f^{2}} r_{2}^{3} + \frac{3 α^{2}}{4 f} r_{2}^{2} . & [4] \end{matrix}$

(37) Expansion of the products allows to isolate the following terms with cubic dependency of r.sub.1 or r.sub.2:
−4αfr.sub.1.sup.3+4s(r.sub.1.sup.3r.sub.2+r.sub.1r.sub.2.sup.3) [5].

(38) These terms vanish if

(39) $\begin{matrix} s = \frac{α {fr}_{1}^{2}}{r_{1}^{2} r_{2} + r_{2}^{3}} . & [6] \end{matrix}$

(40) Within the present invention, the factor s was calculated for the example system displayed in FIG. 2a, where α=25°, f=100 μm and r.sub.1=r.sub.2=50 μm. The resulting value of 0.44 was then multiplied with the 4.sup.th order term of the phase function of the DOE, leading to an imaging system with strongly reduced aberrations. However, in such a system spherical aberration becomes dominant.

(41) The spherical or residual aberrations can be corrected by adding an extra DOE at the position of the aperture (i.e. radial coordinate r.sub.1). Balancing of these aberrations within raytracing software can finally lead to an aplanatic design with diffraction limited performance (see FIG. 2C).

(42) By using more than two DOEs, a distribution of diffractive power allows for aberration corrected designs with very high fields of view of up to 120°. FIG. 2D shows a corresponding design example. A higher number of DOEs generally enables an improved correction of aberrations, particularly for large field angles and high numerical apertures.

(43) FIG. 3A shows a single diffractive lens design having a numerical aperture of 0.8. On the left hand side a schematic representation of the optical design and on the right hand side a schematic representation of the corresponding CAD design is illustrated. The diffractive lens comprises a diffractive optical element 10 which has a diffractive relief or a diffractive surface 13 with a predefined phase function. The DOE 10 is a thin and/or flat disk having a thickness-to-diameter ratio which is at least 1:200 and not more than 1:5.

(44) FIG. 3B shows a schematic representation of an optical design (left hand side) and a corresponding CAD design (right hand side) for an imaging system according to a first exemplary embodiment of the present invention. The imaging system according to the first embodiment comprises a 3D-structure 100 with a stack of two DOEs 10, wherein each DOE 10 has a diffractive surface 13.

(45) FIG. 3C shows a schematic representation of an optical design (left hand side) and a corresponding CAD design (right hand side) for an imaging system according to a second exemplary embodiment of the present invention. The imaging system according to the second embodiment comprises a 3D-structure 100 with a stack of three DOEs 10, wherein each DOE 10 has a diffractive surface 13.

(46) In both embodiments the DOEs 10 are stacked on each other along the optical axis (i.e. the z-axis) of the imaging system, wherein the optical axis is a longitudinal axis of each DOEs and/or the 3D-structure 100 and/or the imaging system.

(47) As shown in FIGS. 3B and 3C, the 3D-structure 100 further comprises a supporting structure or a shell 20 for supporting and/or connecting the at least two DOEs 10. The supporting structure 20 comprises a plurality of pillars 25 that are arranged between two subsequent DOEs 10 and that hold and stabilize the DOEs 10 at the rim or the periphery of the DOEs 10. The supporting structure 20 separates the DOEs by a distinct distance.

(48) The supporting structure 20 further comprises a plurality of discharge openings 30. Like the pillars 25, also the discharge openings 30 are arranged in the 3D-structure between two subsequent DOEs 10. By means of the discharge openings 30 an unexposed photoresist is able to discharge during or after the 3D-printing, particularly after exposing and during developing the exposed photoresist. The discharge openings 30 are lateral accesses for the developer.

(49) The supporting structure or shell 20 has to be formed such that the discharge openings 30 are sufficiently large for an effective discharge of the unexposed photoresist and that the 3D-structure has a sufficient stability and robustness. Within the present invention, it turned out that the volume ratio of the discharge openings with respect to the shell 20 has to be between 0, 2 and 5 in order to fulfill the above criteria.

(50) According to the present invention, a 3D-structure 100 such as shown in FIGS. 3B and 3C is formed, by means of a 3D-printing technique, on a substrate (not shown in FIG. 3). The forming of the 3D-structure 100 comprises forming a stack of at least two DOEs 10 in a single printing step. Thereby, aplanatic imaging systems, namely singlets, doublets, and triplets of DOEs are provided. They can be fabricated without the need for further alignment by femtosecond direct laser writing in one single step and from one material with sizes of below 200 μm in diameter and 100 μm in height. The resulting lenses allow highly efficient sub-pm resolution imaging at visible wavelengths over a bandwidth of 40 nm, combined with a field-of-view of up to 70°. As additional benefit, these stacked flat lenses dramatically reduce the writing times of 3D printed lens systems with superior imaging quality.

(51) FIG. 4A shows a schematic representation in a plan view of a Cartesian writing process, which is conventionally used for printing 3D-structures with a 3D-printing technique. By means of the Cartesian writing process, tracks are written line by line. However, within the present invention, it turned out that for printing high quality DOEs, a homogeneous exposure of voluminous regions is important. To this extent, a printing process in concentric circles has been found to be advantageous. Such a polar writing process is illustrated in FIG. 4B. In case of the polar writing process, the exposure is performed on a voxel by voxel basis by guiding an exposing beam on concentric circle tracks 40, wherein a starting point 41 of each circle track 40 (marked with an arrow in FIG. 4B) is distributed randomly on each circle track 40.

(52) Especially for writing voluminous objects, it has been found out by the inventors that it is advantageous that the writing tracks 40 of subsequent writing layers 50a-50c are laterally shifted to each other, as it is illustrated in FIG. 4C. According to FIG. 4C, the writing tracks 40 of writing layer 50b are laterally shifted with respect to the writing tracks 40 of writing layers 50a and 50c, respectively. In particular, the writing tracks 40 of writing layer 50b are arranged between the writing tracks 40 of writing layer 50a in a lateral direction, i.e. with respect to the x-y-plane. Also, the writing tracks 40 of writing layer 50b are arranged between the writing tracks 40 of writing layer 50c in a lateral direction, i.e. with respect to the x-y-plane. In other words, the exposing is performed such that writing tracks 40 of subsequent writing layers 50a-50c of the photoresist are laterally shifted in an alternating manner, i.e., in the example of FIG. 4C, a writing track 40 of layer 50b is shifted to the left with respect to a corresponding writing track 40 of layer 50a and a corresponding writing track 40 of layer 50c is shifted to the right with respect to the corresponding writing track 40 of layer 50b. Accordingly, the writing tracks 40 of writing layer 50a and the writing tracks 40 of writing layer 50c are not shifted to each other in the lateral direction, i.e. in the x-y-plane.

(53) For the diffractive structures, it is important that high line densities and at the same time a high aspect ratio is realized. The resolution of the 2-photon-lithography is in the range of about 200 nm. This is helpful for the formation of high frequency diffractive structures. Within the present invention, an additional optimization in the 3D-printing of edge structure of the DOEs has been developed in order to increase the diffraction efficiency. This boundary optimization technique is described in the following in connection with FIG. 5A to 5E.

(54) It is intended that the printed profile of the diffractive structure is as much as possible equal to the desired target profile according to a predefined design. For the 3D-print, this profile is fragmented in a plurality of individual writing layers 50a-50c (see FIG. 4C). Subsequent writing layers (e.g. layers 50a and 50b) preferably have a distance to each other of about 150 nm. The rounding of structures due to the exposing process and the subsequent washing-out lead for this layer distance to a sufficiently flat surface. However, at the edges of the individual zones, a rounding is not desired, since this would degrade the diffraction efficiency. A possible rounding is counteracted by a corresponding overcompensation. That is, at the highest point of the zone, an additional track with adjusted writing or exposing dose is written, which strongly washes-out, but which protects the subjacent profile. Correspondingly, a writing track is omitted in the trench of the zone, i.e. at its deepest point, which leads to the opposite effect.

(55) FIG. 5A shows a schematic representation in a cross sectional view of ideal, i.e. desired edge structures 60 of a DOE 10, the edge structure having an upper boundary or peak 62 and a lower boundary or trench 64. FIG. 5B shows a schematic representation in a cross sectional view of a plurality of writing tracks 40a, 40b for forming edge structures 60 of a DOE. The writing tracks 40a and 40b are target writing tracks, i.e. writing tracks 40 that, according to a predefined design, are intended to or should be written. FIG. 5C illustrates the resulting edge structures 66 which are formed by means of a 3D printing technique when writing the target writing tracks 40a, 40b, as shown in FIG. 3B. FIG. 5D shows an optimization of the writing tracks 40 for forming the edge structures 60 of a DOE. As can be seen in FIG. 5D, an additional edge optimizing track 40c is written on the upper boundary 62 of the desired edge structure 60, while target tracks 40b (see FIG. 5B) are omitted on a lower boundary 64 of the desired edge structure 60. Thus, the writing tracks 40a, 40c as shown in FIG. 5D are actually or really written tracks. Target tracks 40a, as exemplarily indicated in FIGS. 5B and 5D, are tracks that are present both in FIG. 5B and FIG. 5D. Thus, all target tracks 40a are actually written. Target tracks 40b, however, are only present in FIG. 5B and not in FIG. 5D, i.e., target tracks 40b are not actually written but omitted. Such a boundary optimization technique leads to improved 3D-printed edge structures 68 (FIG. 5E) compared to edge structures 66 that are written without the boundary optimization technique (FIG. 5C). In particular, the edges of FIG. 5E are more pronounced and sharper than the edges of FIG. 5C. This results in an improved diffraction efficiency and thus in an improved imaging quality of the DOEs and the imaging system.

(56) An important aspect for optimizing the efficiency of diffractive lenses is the minimization of scattering losses on the edges. This can be achieved by an inclination of the edge flanks, i.e. by providing the edge structures with an undercut, as illustrated in FIGS. 6A to 6D.

(57) FIG. 6A shows a schematic representation in a cross sectional view of the scattering behavior of a DOE having edge structures without undercuts, while FIG. 6B shows a schematic representation in a cross sectional view of the scattering behavior of a DOE having edge structures with undercuts. In case of oblique incident light (in FIGS. 6A and 6B from the bottom to the top), perpendicular flanks (FIG. 6A) result in an internal total reflection and thus to an energy loss in the focal point F, since due to the total reflection a portion of the light is scattered away. If the flanks of the edges are inclined in the direction of arrival, i.e. by means of edges having undercuts (FIG. 6B), these energy losses can significantly be reduced or even avoided. FIG. 6C shows a schematic representation in a cross sectional view of a writing process from the target profile (top sketch) over an optimized arrangement of writing tracks (middle sketch) to the result after developing the exposed structures. As already described above in connection with FIG. 5D, additional edge optimizing tracks 40c are written on an upper boundary of the desired edge structure, while a target track 40b (see FIG. 5B) is omitted on a lower boundary of the desired edge structure. FIG. 6D shows a schematic representation in a cross sectional view of a DOE 10 having edge structures with undercuts 70, i.e. with inclined flanks. Depending on the angle of incidence, the improvements due to the formation of undercuts can be significant. With respect to axially symmetric structures such as DOEs, the formation of undercuts cannot be realized with conventional 2.5D processing techniques such as dry etching. However, by means of a 3D-printing technique, undercuts also for axially symmetric structures can reproducibly be formed.

(58) In the lateral direction, i.e. in the x-y-plane, the writing spot is shifted by means of a Galvo-mirror. In the z-direction, the sample itself may be shifted by means of a Piezo-unit. Thus, the 3D printing process is free from adjustment in the lateral direction. Possible deviations from the target design only depend on random fluctuations of the beam and/or object positioning mechanisms. In the z-direction, a Piezo-unit can be used, which has a precision in the low two-digit nanometer range. The smallest structure periods (radial width of a zone) are in the range of about 700 nm. In order to reduce the writing time, the supporting structure, which does not have an optical function, can be written with a larger layer- and track distance than the optically relevant regions.

(59) Within the present invention, designs with a high numerical aperture of up to 0.8 have been developed. This ensures that the ratio of height to diameter of the lens stacks remains small, thus reducing the amount of straylight which easily propagates through the all-transparent device from unwanted directions. The phase reliefs may be designed and optimized for a wavelength of 543 nm with the raytracing software ZEMAX using a global optimization algorithm. The optimum phase φ as a function of radius r can be determined in terms of coefficients α.sub.i as φ(r)=Σ.sub.i=1.sup.Nα.sub.ir.sup.2i by using raytracing based on a local grating approximation (LGA). The necessary relief to create this phase in air can be calculated by modulating the function in steps of 2π and multiplying the result with

(60) $\frac{λ}{2 π (n - 1)},$
where n is the refractive index of the photoresist at the used wavelength λ. For example, a photoresist with n=1.548 may be used.

(61) A minimum DOE feature size of ˜0.7 μm may result in case of the singlet lens. The final geometry of the lens stacks are optimized to reduce the amount of printed resist volume and at the same time to minimize the writing time in that the diffractive surfaces are placed on thin disks which are mounted on pillars. All lenses may be restricted to a maximum diameter of 200 μm.

(62) Within the present invention, the designs have been 3D-printed in dip-in configuration with a Nanoscribe ‘Photonic Professional GT’ device using IP-DIP photoresist which was specifically developed for highest resolutions. As substrates, 170 μm thick BK7 slides with a thin layer of indium tin oxide were used. Typical writing times of imaging systems such as the one displayed in FIG. 3B was in the range of 15 minutes but can be further reduced.

(63) In summary, the combination of multiple diffractive lenses, fabricated in one single step by femtosecond 3D printing, allows highly compact imaging systems for visible wavelengths. According to theory, one diffractive lens element allows perfect imaging only for one point, two surfaces permit a correction of the main first-order aberrations, and three surfaces help to further improve the performance at high numerical apertures or high angle-of-views. In contrast to concepts using metasurfaces, the phase relief lenses are basically insensitive to polarization and transmit light over a broad spectral range with high efficiencies.

(64) With sizes of below 200 μm in diameter and 100 μm in height, the 3D-printed lenses resolve line spacings of 550 nm at a wavelength of 550 nm and over a FWHM bandwidth of 40 nm. With three planar lenses, a resolution of below 800 nm over a wide field of view of 70° can be achieved, lower than the pixel pitch of today's image sensors. As expected, the performance deteriorates clearly when broadband illumination is used. However, some of these color effects can be significantly reduced by digital means.

(65) The fabrication method of femtosecond 3D printing is inherently alignment free and highly precise at the same time. One of its main drawbacks, hour-long fabrication times, is diminished because the lenses only require a small amount of material. This is due to the fact that diffraction happens only at the phase relief layers which are less than 1 μm in thickness. Currently, the writing time is about 15 minutes for a doublet lens but can be further reduced if the mounting disks are made thinner and the support structures are written with a coarser line spacing.

(66) The present invention opens the possibility for high resolution imaging on smallest scales which is particularly interesting for applications in endoscopy, drone vision, or security, as well as for smartphones, imaging sensors, and augmented/virtual reality displays. Moreover, if used in reverse, the lenses could act as small scale microscope objective lenses with diffraction-limited imaging quality.

LIST OF REFERENCE NUMERALS

(67) 10 diffractive optical element (DOE)/flat diffractive lens

(68) 13 diffractive surface

(69) 20 supporting structure/shell/housing

(70) 25 pillar

(71) 30 discharge opening/aperture

(72) 40 writing track/concentric circle track

(73) 40a target writing track (actually written)

(74) 40b target writing track (omitted, i.e., not actually written)

(75) 40c edge optimizing track

(76) 41 starting point

(77) 50a writing layer

(78) 50b writing layer

(79) 50c writing layer

(80) 60 desired (target) edge/desired (target) edge structure

(81) 62 upper boundary/peak

(82) 64 lower boundary/trench

(83) 66 3D-printed edge structure without boundary optimization technique

(84) 68 3D-printed edge structure with boundary optimization technique

(85) 70 undercut/inclined flank

(86) 100 3D-structure

(87) F focal point

Method of fabricating an imaging system and corresponding imaging system

Assignee

Inventors

Cpc classification

Classification Explorer

B29C64/106

PERFORMING OPERATIONS; TRANSPORTING

Classification Explorer

B33Y10/00

PERFORMING OPERATIONS; TRANSPORTING

Classification Explorer

G02B27/4205

PHYSICS

Classification Explorer

B33Y80/00

PERFORMING OPERATIONS; TRANSPORTING

Classification Explorer

G02B5/188

PHYSICS

Classification Explorer

G02B5/1857

PHYSICS

International classification

Classification Explorer

G02B5/18

PHYSICS

Abstract

Claims

Description