WO2020180254A1 - Diffractive optical element and method of producing thereof - Google Patents

Abstract

The disclosure relates to a diffractive optical element (DOE) including a discretized phase matrix extending in a first plane, the discretized phase matrix including a plurality of phase elements, wherein top surfaces of the phase elements may be each non-parallel to the first plane. The disclosure also relates to an optical system including the DOE. The disclosure also relates to methods of producing 3D-print data including a 3D object model of a DOE, and methods of producing the DOE. The methods may include: transforming the pre-determined image to obtain a shifted image; determining a plurality of phase values corresponding to the plurality of phase elements based on the shifted image; determining the 3D object model of the discretized phase matrix based on the phase values, wherein determining the 3D object model may be further based on a blaze angle of a blazing cap for each of the plurality of phase elements.

Description

DIFFRACTIVE OPTICAU EUEMENT AND METHOD OF PRODUCING THEREOF

CROSS-REFERENCE TO REUATED APPUICATION

[0001] This application claims the benefit of priority of Singapore Patent Application No. 10201902061R, filed 7 March 2019, the content of which being hereby incorporated by reference in its entirety for all purposes.

TECHNICAU FIEUD

[0002] An aspect of the disclosure relates to a diffractive optical element. Another aspect of the disclosure relates to an optical system for projecting a far field holographic projection (projected image) on a screen at a projection plane. Another aspect of the disclosure relates to a method of producing 3D-print data. Another aspect of the disclosure relates to a method of producing a DOE.

BACKGROUND

[0003] Diffractive optical elements provide a compact and energy-efficient solution to project arbitrary grayscale images onto a screen in the far field. Unfortunately, they invariably suffer from the zero order spot, a central bright spot mainly caused by un-diffracted laser light that travels along the optical axis. To solve this problem, various methods have been put forward by either removing the hologram away from the zero order spot or blocking it. Blocking the zero order spots requires addition of components in the optical path, increasing the complexity of the optical system. Efforts to shift the intended projected image away from the optical axis are met with non-uniformly illuminated images as the intensity distribution falls off away from the optical axis. Therefore, there is a need to provide improved diffractive optical elements wherein their projected image is uniform and separated from the zero order spot.

SUMMARY

[0004] An aspect of the disclosure relates to a diffractive optical element (DOE) including a discretized phase matrix extending in a first plane, the discretized phase matrix including a plurality of phase elements, wherein top surfaces of the phase elements may be each non parallel to the first plane. [0005] Another aspect of the disclosure relates to an optical system for projecting a far field holographic projection (also named herein as projected image) on a screen at a projection plane. The optical system may include a source configured to emit a coherent electromagnetic energy with a first optical axis, for example laser. The optical system may include the DOE according to various embodiments, arranged on the first optical axis and between the source and the projection plane. According to various embodiments, the diffractive optical system may be selected from: augmented reality device, medical imager, laser multi-beam projector, beam shaper, interferometer, optical manipulator, anti-counterfeiting equipment.

[0006] Another aspect of the disclosure relates to a method of producing 3D-print data including a 3D object model of a DOE including a discretized phase matrix including a plurality of phase elements, the discretized phase matrix storing phase information of a shifted image. The method may include transforming a pre-determined image to obtain the shifted image. The method may further include determining a plurality of phase values corresponding to the plurality of phase elements based on the shifted image. The method may include determining the 3D object model of the discretized phase matrix based on the phase values. Determining the 3D object model may be further based on a blaze angle of a blazing cap for each of the plurality of phase elements.

[0007] Another aspect of the disclosure relates to a method of producing a DOE. The method may include producing the 3D-print data of the DOE in accordance with various embodiments. The method may further include 3D printing the DOE according to the 3D object model.

BRIEF DESCRIPTION OF THE DRAWINGS

[0008] The invention will be better understood with reference to the detailed description when considered in conjunction with the non-limiting examples and the accompanying drawings, in which:

- FIG. 1 shows in: (a) and (b) a typical process to project an image using a comparative DOE; (c) a DOE and a projected image in accordance with various embodiments;

- FIG. 2 shows in: (a) a phase block; (b) and (c) a phase element including a phase block and a blazed cap in accordance with various embodiments; (d) and (f) simulated light intensity distribution in far field of a comparative example for a single pixel and for the pre-determined image of FIG. 1(a) respectively; (e) and (g) a simulated light intensity distribution in far field of a DOE including a single phase element and for the pre determined image of FIG. 1(a) of an example in accordance with various embodiments;

- FIG. 3A shows a cross sectional profile of phase blocks and the corresponding amplitude of the projection at the Fourier plane according to a comparative example;

- FIG. 3B shows a cross sectional profile of phase elements and the corresponding amplitude of the projection at the Fourier plane in accordance with various embodiments;

- FIG. 4A and 4B show the theoretical relation between frequency domain shift and coefficient of optical path difference;

- FIG. 5 A - 5D show one example of how to transform a pre-determined image to obtain a shifted image;

- FIG. 6 shows one example in which shifting the pre-determined image is carried out by swapping the quadrants of the pre-determined image;

- FIG. 7 shows components of the 3D printing setup;

- FIG. 8 shows in: (a) and (b) printing strategy for phase blocks with the same laser writing distances in each phase block of a comparative example; and (d) and (e) printing strategy for the phase elements with gradual changing laser writing distances, in accordance with various embodiments;

- FIG. 9 shows characterizations of DOEs by optical microscope, scanning electron microscopy (SEM) and atomic force microscopy (AFM);

- FIG. 10 shows SEM images of DOE’s with different coefficient of optical path difference and their corresponding deflection of energy distribution;

- FIG. 11 shows simulated projected images at grating order (a) m = 0 and (b) m = 1, with range of phase error p of phase blocks.

- FIG. 12 shows the SNR corresponding to the images in FIG. 11.

- FIG. 13 shows simulated projected images at grating order (a) m = 0 (b) m = 1, wherein the range of sub-pixel level phase error q.

- FIG. 14 shows the SNR corresponding to the images in FIG. 13.

- FIG. 15 shows a plot of the height of phase blocks at different phase levels.

- FIG. 16 shows simulated projected images in the far field with phase block size dx,y at (a) 6 pm; (b) 3 pm and (c) 1.5 pm, in accordance with various embodiments. - FIG. 17 shows a further comparative example, in which the image is shifted but comparative phase blocks are used.

[0009] FIGS. 2(d)-(f), 16, and 17 show images with inverted color, wherein the higher intensities are represented with darker colors (black) for easier visualization and to facilitate reproduction.

DETAILED DESCRIPTION

[0010] The following detailed description refers to the accompanying drawings that show, by way of illustration, specific details and embodiments in which the disclosure may be practiced. These embodiments are described in sufficient detail to enable those skilled in the art to practice the disclosure. Other embodiments may be utilized and structural, and logical changes may be made without departing from the scope of the disclosure. The various embodiments are not necessarily mutually exclusive, as some embodiments can be combined with one or more other embodiments to form new embodiments.

[0011] Embodiments described in the context of one of the diffractive optical elements, methods of producing 3D-print data, or methods of producing a DOE are analogously valid for the other diffractive optical elements, methods of producing 3D-print data, or methods of producing a DOE. Similarly, embodiments described in the context of a DOE are analogously valid for a method, and vice-versa.

[0012] Features that are described in the context of an embodiment may correspondingly be applicable to the same or similar features in the other embodiments. Features that are described in the context of an embodiment may correspondingly be applicable to the other embodiments, even if not explicitly described in these other embodiments. Furthermore, additions and/or combinations and/or alternatives as described for a feature in the context of an embodiment may correspondingly be applicable to the same or similar feature in the other embodiments.

[0013] In the context of various embodiments, the articles“a”,“an” and“the” as used with regard to a feature or element include a reference to one or more of the features or elements.

[0014] As used herein, the term“and/or” includes any and all combinations of one or more of the associated listed items.

[0015] Various embodiments relate to a DOE including a discretized phase matrix extending in a first plane. The discretized phase matrix includes a plurality of phase elements, wherein top surfaces of the phase elements may be each non-parallel to the first plane. The top surfaces may be facets.

[0016] In some embodiments the DOE may consist of the discretized phase matrix, in other embodiments, the DOE may include further elements, for example, a substrate. The substrate may be transparent for intended wavelength in which the DOE is active.

[0017] Various embodiments relate to an optical system for projecting a far field hologram projection on a screen at a projection plane. The optical system may include a source configured to emit a coherent electromagnetic energy, for example laser, with a first optical axis. The optical system may further include the DOE in accordance with various embodiments, arranged on the first optical axis and between the source and the projection plane. According to various embodiments, the diffractive optical system may be selected from: augmented reality device, medical imager, laser multi-beam projector, beam shaper, interferometer, optical manipulator, anti-counterfeiting equipment.

[0018] In the following, a comparative example will be used in connection with FIG. 1(a). to explain some aspects on which the disclosure may rely on. In the comparative example, a comparative DOE has top surfaces parallel to the plane in which the discretized phase matrix extends, thus phase elements of the comparative DOE are also called phase blocks. Firstly, the discretized phase matrix data (“Phase”) can be calculated through the iterative Fourier transform algorithms (IFTA). For the example, the Gerchberg-Saxton (GS) algorithm with iteration 100 times is employed. Secondly, the DOE (“Sample”) having the discretized phase matrix including phase blocks with different heights is fabricated by 3D printing with TPL, and finally, it is illuminated by green laser with wavelength at 532 nm to get the designed hologram, i.e., the intended image projected at the Fourier plane which is equivalent or identical to the image projected at the far field (“Projected image”). However, a bright zero order spot appears in the center of the actual far field hologram projection (the last image in FIG. 1(a) and schematic in FIG. 1(b)), which is mostly from the un-diffracted incident light. High order spots with the same periodicity of the projected image can also be observed in the projection plane (not shown in FIG. 1). Besides, the light intensity of the projected image drops quickly when increasing the distance to the beam axis, i.e., only the projected image on-axis is entirely illuminated.

[0019] FIG. 1(c) shows a DOE in accordance with various embodiments, the DOE includes an optional substrate and a discretized phase matrix (“Phase plate”) extending in a first plane, for example extending in the plane x-y. According to various embodiments, the discretized phase matrix includes a plurality of phase elements, wherein top surfaces of the phase elements may be each non-parallel to the first plane, as illustrated, each of the top surfaces of the phase plate is in a plane diagonal to the plane x-y. The phase elements may include phase blocks and blazed caps, thus, the top surfaces of the phase elements may be provided by blazed caps. Phase blocks may be of rectangular cross section, for example the cross section parallel to the x-z axis and/or parallel to the y-z axis of the phase block may be rectangular.

[0020] According to various embodiments, the discretized phase matrix data may be calculated through the iterative Fourier transform algorithms (IFTA). For the example, the Gerchberg-Saxton (GS) algorithm with iteration 100 times is employed. The DOE having the discretized phase matrix including phase elements wherein the phase blocks have different heights may be fabricated by 3D printing, e.g., with TPL.

[0021] The DOE structure composed of phase blocks with blazed top surfaces (i.e., the phase elements) shifts the projected image off-axis along with the diffraction energy distribution, as shown in FIG. 1(c) and FIG. 2(e), while the zero order spot remains on-axis. While embodiments and examples show the blaze angle on the diagonal, the present disclosure is not limited thereto. Thus, the projected image at the Fourier plane which is equivalent or identical to the image projected at the far field is separated from the zero order spot.

[0022] According to various embodiments, an image may be encoded in the discretized phase matrix, wherein the image may be projectable on a Fourier plane off-axis upon incidence of coherent electromagnetic energy on the discretized phase matrix. The coherent electromagnetic energy may be provided by a coherent electromagnetic energy source, such as a laser source.

[0023] According to various embodiments, an angle formed between the optical axis and the off-axis holographic projection may be chosen to be substantially equal to a deflection angle of the phase elements, thereby maximizing light intensity for the wavelength of the used coherent electromagnetic energy.

[0024] According to various embodiments the image encoded in the hologram corresponds to a pre-determined image which may be shifted, for example, geometrically translated, or including diagonally swapped quadrants. The pre-determined image may be a grey-scale image, which includes intensity information for each of the pixels. A color of the projected image may be given by the wavelength used for the laser that illuminates the DOE. [0025] As used herein, and in accordance with various embodiments, the term“top” (e.g., as in“top surface”) may refer to one side of the discretized phase matrix. For example, the discretized phase matrix may include a bottom, which is an opposite side of the top. Is some embodiments, the bottom may be flat. The bottom may be the side which receives coherent electromagnetic energy, and the top may be the side which projects the image (in the far field). The bottom side may be closer to a substrate supporting the discretized phase matrix, provided that the DOE includes a substrate.

[0026] According to various embodiments, top surfaces of the phase elements may be parallel to each other, herein, the term“parallel” may include the meaning of coplanar. According to various embodiments, top surfaces of the phase elements may be each disposed at a blaze angle to the first plane. According to various embodiments, bottom surfaces of the phase elements may be parallel to the first plane.

[0027] According to various embodiments, the discretized phase matrix may include a hologram encoded in optical path lengths of the plurality of phase elements. The hologram may be a transmission hologram. The DOE may be a transmission DOE.

[0028] According to various embodiments, the discretized phase matrix may include a hologram encoded in thicknesses of the phase elements, for example, the thicknesses may be the thickness of the phase blocks of the respective phase elements of the plurality of phase elements. The hologram may be a transmission hologram. The DOE may be a transmission DOE.

[0029] FIG. 2(a) shows a comparative phase block of dimensions d_y, d_x, and height H_p. FIG. 2(b) shows a phase element including a phase block of dimensions d_y, d_x, and height H_p and a blazed cap. FIG. 2(c) is a diagonal cross section view of the phase element of FIG. 2(b) (in a plane orthogonal to the drawings page), and shows the diagonal at the bottom with dimension + d_y, the height of the blazed cap H_b, a blaze angle Q formed between the diagonal of the top surface and the first plane, a deflection angle f, and n representing the refractive index of the phase element. The refractive index of air is represented in FIG. 2(c) by 1.

[0030] While FIGS. 2(b) and (c) show one phase element for illustration purposes, in accordance with various embodiments, the plurality of phase elements of the discretized phase matrix is preferably monolithically integral to the discretized phase matrix, for example, there may be a continuity in material (thus, no gap) between neighboring phase elements of the plurality of phase elements.

[0031] FIG. 2(d) shows the simulated light intensity distributions in far field for a comparative example using a DOE with a single phase block as shown in FIG. 2(a). FIG. 2(c) shows the simulated light intensity distributions in far field for an example using a DOE with a single phase element in accordance with various embodiments as shown in FIGS. 2(b) and (c). The bar in FIG. 2 shows a normalized scale for the light intensity. In FIGS. 2(d) and (e), intense sharp pillars (black) represent generated different order spots, in which the strongest one (blackest) one denotes the zero order spot. In FIG. 2(d) the zero order spot overlaps with the projected pixel, while in FIG. 2(e), the projected pixel and the zero order spot are separated.

[0032] FIG. 2(f) shows the simulated light intensity distributions in far field for a comparative example using phase blocks with different thicknesses, each phase block similar to shown in FIG. 2(a). FIG. 2(g) shows the simulated light intensity distributions in far field for an example using phase elements, with phase blocks of different thicknesses, in accordance with various embodiments as shown in FIGS. 2(b) and (c). The bar in FIG. 2 shows a normalized scale for the light intensity. In FIGS. 2(f) and (g), intense (black) sharp pillars represent generated different order spots, in which the strongest (blackest) one denotes the zero order spot. In FIG. 2(f) the zero order spot overlaps with the projected image, while in FIG. 2(g), the projected image and the zero order spot are separated.

[0033] FIG. 3A shows simulations of a Fourier transform of a comparative DOE and FIG. 3B shows simulations of a Fourier transform of a DOE in accordance with various embodiments. Symbol x means multiplication and the symbol (X) means convolution. In the simulations, the blocks are separated by a narrow gap to simulate the defects in the physical DOEs. The exemplary DOEs are shown in one dimension for ease of reference. In FIGS. 3 A and 3B, H_p is height of the phase block; A is the amplitude of hologram projection; d_x is the phase block interval distance at phase plane; l/d_x is the hologram projection interval distance at Fourier plane; d_cx is the size of phase block.

[0034] The left panel in FIG. 3A shows, on top, a sequence of 5 phase blocks arranged along a direction x, having different thicknesses H_p. It can be seen that, on the Fourier plane, the projected image overlaps with the zero order spot. A sine-type energy distribution corrected signal shows that the projected image is centered at the optical axis and is identical to the pre defined image. [0035] High order spots and the drop in light intensity can be explained with the Fraunhofer approximation in the far field diffraction regime and the convolution theorem (see references 23, 29, 33). For the sake of simplicity, here one dimensional Fourier transform (FT, denoted as model is used to explain the underneath physical principle. As illustrated in Fig. 3A, the DOE structure can be regarded as a convolution between comb function and phase block with flat top surface, in which the comb function represents the positions of phase block with interval distance d_x, and the corresponding height H_p can be calculated with the phase f,Ic) from GS algorithm as

Eq. (1)

[0036] where l is the wavelength of incident light (or source of coherent electromagnetic energy), h(l) is the refractive index of the DOE material. The phase block size is d_cx, which is smaller than the interval distance, thus un-diffracted light and high order spots can be included in this model. In the Fourier plane, the designed images are periodically distributed with interval distance l/d_x (represented by dark color in FIG. 3A, and only the on-axis hologram is lightened up when they are multiplied with the sine- shape amplitude of light intensity, unfortunately, the bright zero order spot (“zero order”) from un-diffracted light occupies the zero frequency position too, leaving the overlap of them.

[0037] The left panel in FIG. 3B shows, on top, a sequence of 5 phase elements arranged along a direction x, each phase element including a phase block having different thicknesses H_p , and a blazed cap having a same blaze angle. The top surfaces of the blazed caps are parallel to each other. The blaze angles of each blaze caps are identical. It can be seen that, on the Fourier plane, that the projected image and the zero order spot do not overlap and are separated in space. A sine-type energy distribution corrected signal shows that the projected image is a shifted image corresponding to the pre-determined image shifted, at the optical axis, (e.g., by half its size) along with the diffraction energy distribution.

[0038] According to various embodiments, the pre-defined image may be redesigned to ensure the Fourier transform (FT) of comb function is shifted away from the zero frequency position. The FT of the phase element with blazing angle Q will shift the energy distribution in the Fourier plane with distance fi_x, hence an“uncontaminated” off-axis hologram with high diffraction efficiency can be obtained. [0039] In a DOE in accordance with various embodiments, the different order spots are located in the Fourier plane with 2D periodicity (see FIG. 2), and in most cases cross-type astral light exists at these positions. Therefore, in accordance with various embodiments, the blazed cap may be designed with blazing angle along a diagonal direction to keep the hologram clear from all the deleterious optical effects. Taking consideration of the Snell’s law, grating formula and basic geometrical relationship, the following equations can be obtained:

Eq. (2)

in which, Q and f are the blazing angle and deflection angle, respectively, as shown in the cross section view in Fig. 2(c), m is the grating order of the blazed caps, H_b is the height of blazed cap. According to Eqs. (1) and (2), the phase element provides a local phase change in each phase block in DOE, which turns out to be the energy distribution shift fi_x and f_/n in Fourier plane:

Eq. (3)

[0040] Through comparing the simulated far field result in Fig. 2(d) for the comparative structure with the structure shown in Fig. 2(e), it’s obvious that the energy distribution has been shifted to the deflection angle, while the hologram array and diffraction spots stay put in their initial positions (intense sharp pillars represent generated different order spots, among which the thickest one denotes the zero order spot; the zero order is highlighted by using more pixels to indicate its intensity). Furthermore, the relations between frequency domain shift and coefficient of optical path difference m at different refractive index n of phase plate material and at different phase block size d_x,y can be well explained with Eq. (3).

[0041 ] FIGS . 4A and 4B show the theoretical relation between frequency domain shift (unit: frequency domain period 1 /d_x,y)) and the coefficient of optical path difference m. The dash-dot lines are the asymptotic lines with slope value 0.5. The dashed lines are the theoretical relation when n = 1.5534 and d_x,y = 3 pm.

[0042] FIG. 4A indicates that from refractive index n = 1.4 to 1.7 (see arrow indicating the trend when n increases), the relation curve moves towards the asymptotic line, whose slope value is 0.5 obtained from Eq. (3). When the phase block size increases from 2 pm to 5 pm, (see arrow in FIG. 4B indicating the trend when the phase block size increases), it shows a similar trend as refractive index increases, while the size value has a greater influence on the shift (FIG. 4B). For larger blazing angle, the effect of changing refractive index or phase block size becomes more significant. Regarding the deflection angle, appropriate photoresists and size of phase block can be chosen expediently by exploitation of this analysis.

[0043] Further details, regarding diffraction theory are presented in the following, however the disclosure is not limited thereto.

[0044] The zero order and higher order holographic images with spots are reproduced in a theoretical model by introducing small gaps between each phase block, i.e. , enforcing the size of the phase block, d _X < d_x. The bright zero order spot from un-diffracted light occupies the zero frequency position, thus overlapping with the holographic projection. Note that there are no actual gaps between the phase blocks in physical DOEs, such as those fabricated in the experiments in accordance with various embodiments. The simplified model built here is to include the different order spots generated from the limited precision in the fabrication of phase blocks of exact heights, and light that propagates at the interface of phase blocks of significantly different heights.

[0045] With Fraunhofer approximation in the far field diffraction regime and the convolution theorem, we can express the transmittance function of the pixelated DOEs as

[0046] where L_x=Md_x, L_y=Nd_x, d_x, d_y are the width and length of the whole rectangular DOE structure and the phase block (or phase element), respectively. The pixel number of original image is MxN. t_c(x, y ) is the transmittance function of all the central parts of the phase elements with the size of each phase element as d _X d_C\ t_e(x, y ) is the transmittance function of all the edge parts of the phase elements; rect function denotes the rectangular shape of the whole DOE and phase blocks (or phase elements); comb function represents the spatial positions of phase blocks (or phase elements) in xy plane with 2D periods d_x and d_y. f>_c(x, y) is the central phase of phase element and f_e(c, y) is the edge phase of the phase element at coordinates (x, y), respectively. <j>_b{xi, yi ) is the local phase within one phase block, which is the same for all blocks since it is repeated along with the rect function for the blazed top surface DOE. When the DOE is illuminated by a normally incident laser, the projected image is the Fourier transform of the transmittance function (Eq.(4)), which can be expressed as

T{f_xJ_y ) = L_xL_{y S}ine (/A, /A ) ® [T_C {f_xJ_y ) + T_e ( f_{x y} )]

^Tc {fx _y ) = ^άL_g ^SinC [( - /_fa ) ^d ( fy - f_by ) ^dc_y ]

g[_' ^C°mb(f_xd_x, f_yd_y ) ®3r{exp[i<f>_c (x, y )]}} , Eq. (5)

^T _e {f_{x y} ) = [^d _x ^d _y ^sinc ( f_x ^d _x f_y ^d _y ) - d_ad_v sine ( f_xd_{a ,} f_yd_cy )]

^comb ( f_xd_{x ,} f_yd_y ) ®J^{exp [¾ ( y ) ]}}

[0047] here, T(f_x, f_y) is the FT of t(x, y), T_c(f_x, _,/i) and T_e(f_x, _,/i) are corresponding to t_c(x, y ) and t_e(x, y), respectively. The sinc functions represent 2D sine-type envelope from the shapes of DOE (the outer one multiplied by L_xL_y ) and pixelated phase block or phase element (the inner one multiplied by d_cxd_cy), in which the outer one makes negligible effect on the energy distribution when compared with the inner one, owning to L_x»d_x and L_y»d_y.f_bx and/_/,_v indicate the shifts of the inner sinc function in the frequency domain, i.e., in the reconstructed image plane. The comb function means the FT of phases f_e(c, y) and f_e(c, y) with uniform incident light will repeat periodically by l/d_cx and l/d_x in the Fourier plane.

[0048] For the ideal situation, d_x=d,_x and d_y=d_cy, thus T_e(f_x,f_y) will disappear. The diffraction energy distribution from T_c(f_x, _,/i ) will shed light on the 2D repetitive images with no shift because of the comparative DOE holding FB(CI, yi) to be zero, hence a bright on-axis holographic image without zero order can be seen in the screen. For experiments with fabricated DOE, d_x~d_cx and d_y~d_ty, consequently, T_e(f_x,f_y) causes diffraction spots to appear at the center of every repeated image. In particular, the brightest zero order spot appears in the center of the on-axis holographic image, which is detrimental to the performance of the DOE.

[0049] For the comparative DOE structure, fi_x and f_/ are zeros, thus the bright zero order spot is overlapped with the energy distribution center. The holographic image cannot be separated from the zero order spot in this situation. While for the DOE with blazed top surface in accordance with various embodiments, fi_x and /_/,_v can be steered by changing the blaze angle, therefore the far field energy distribution can be shifted to be off-axis. Hence, an off-axis projected images with high diffraction efficiency and free of zero order can be obtained through the described embodiments. The herein presented theoretical analysis is provided for ease of understanding of the disclosure, however the disclosure is not limited thereto.

[0050] Various embodiments relate to a method of producing 3D-print data including a 3D object model of a DOE. The term“producing” in this context may mean calculating, for example, using a computer and/or a microprocessor. The DOE may include a discretized phase matrix including a plurality of phase elements. The discretized phase matrix may store phase information of a shifted image obtained from the pre-determined image. The method may include transforming the pre-determined image to obtain a shifted image.

[0051] An example for image preparation is illustrated in connection with FIGS. 5 A - 5C and FIG. 6. FIG. 5A shows a pre-determined image including quadrants A, B, C, and D. A circle represents the center of the pattern which corresponds to a center of the hologram when projected in the far field (the projected image) and with the position of the zero order spot (bright area). The center of the pre-determined image also coincides with the position that the circle is shown. The pre-determined image may be shifted in the diagonal by half of the diagonal length, as shown, wherein the pattern is circularly shifted right (FIG. 5B) and downwards (FIG. 5C). Alternatively to a circular shift, the image may be padded, the padded area may be filled, e.g., with repeated image portions. It can be seen in FIG. 5D, that the resulting shifted image has diagonally swapped quadrants, being D, C, B, A (instead of A, B, C, D). According to various embodiments, shifting may be performed by pixel registration, translation, or it may be performed by diagonally swapping the quadrants of the pre-determined image.

[0052] FIG. 6 is used to illustrate an example of a pre-determined image which may be used to provide the DOE. The top portion of FIG. 6 shows a square, e.g. which may be an image boundary, divided into quadrants A, B, C, D. The shifted image may be transformed by circular shifting the image in the diagonal, e.g., separately in a horizontal direction and then in a vertical direction, each time by half the image width (or height, respectively) as shown in FIG. 5A-5D. Alternatively, the shifted image may be provided by diagonally swapping the quadrants, such as swapping A with D, and swapping B with C. The lower portion of FIG. 6 shows an example of an image with a specific pattern and the resulting shifted image.

[0053] The method of producing 3D-print data may further include determining a plurality of phase values corresponding to the plurality of phase elements based on the shifted image. The method may further include determining the 3D object model of the discretized phase matrix based on the phase values. Determining the 3D object model may be further based on a blaze angle ( Q ) of a blazing cap for each of the plurality of phase elements.

[0054] According to various embodiments determining the 3D object model of the discretized phase matrix based on the phase values may include determining optical path lengths corresponding to the phase values.

[0055] According to various embodiments determining optical path lengths may include determining thicknesses of the plurality of phase elements.

[0056] Determining the 3D object model may be processed numerically, as explained herein, for example, using the GS algorithm.

[0057] According to various embodiments, the 3D-print data may be used to print the discretized phase matrix on a substrate or on a carrier. For example, the substrate may be a glass substrate. FIG. 7 shows components of the 3D printing setup. It is shown a substrate which is scanned by a focused laser beam, of a laser (e.g. with wavelength of 780 nm) being focused by a lens (e.g. 63x/1.4 oil immersion lens) onto a volume portion in a photoresist (e.g. IP-Dip) on the substrate. The relative x, y, z, positions of the lens to the substrate may be adjusted, and therefore provide a 3D scanning of the photoresist. According to various embodiments, the photoresist may be a polymerizable solution which polymerizes with two- photons or multi-photons (3 or more photons) hatching distance and slicing distances are shown in the inset and may be adjustable parameters for the 3D printing.

[0058] Various embodiments of the disclosure relate to a method of producing a DOE. The method may include producing the 3D-print data of the DOE in accordance with various embodiments. The method may further include 3D printing the DOE according to the 3D object model. 3D printing may further include providing a polymerizable solution; and scanning the polymerizable solution with a focal spot of a laser beam along a scanning path so as to polymerize the polymerizable solution at a light focal spot (e.g. a laser focal spot), wherein the scanning path may be determined based on the 3D-print data. The laser may be a femtosecond laser, e.g., which emits laser pulses with pulse duration of 600 fs or less, for example 200 fs or 100 fs.

[0059] According to various embodiments polymerizing may be a two-photon polymerization or a multiphoton polymerization. [0060] The theory described herein, for example, in connection with FIGS. 2 and 3, may be implemented in a computer program product, for example using MATLAB code to simulate the diffractive effects.

[0061] To experimentally prove the concept, 3D printing by two-photon polymerization (TPL), using a Photonic Professional GT system (Nanoscribe GmbH) was used to fabricate the DOEs in accordance with various embodiments. A 780 nm femtosecond pulsed laser with 100 fs pulse duration and 80 MHz repetition rate was focused into the photoresist IP-Dip (which, after polymerization, has a refractive index of n=1.5534 at light wavelength 532 nm, according to reference 35) on glass substrate (fused silica, 25x25 mm squares with thickness 0.7 mm) with an immersion objective lens (Zeiss Plan Apo 63x, 1.4 NA) to print structures by inducing two-photon polymerization, as illustrated in FIG. 7.

[0062] The beam position in the xy plane was controlled by galvanometric mirrors within one writing field (in this example, 120 pm x 120 pm) and along z direction is regulated with a piezoelectric translation stage by moving the substrate. In order to get a relatively smooth profile for the phase block, the hatching distance between two lines is chosen as 250 nm at laser scan speed 20000 pm/s with laser power 45 mW. Slicing distance between two levels (FIG. 7) is calculated to be around 120 nm from Eq. (1), due to the phase <j>_c{x, y ) from GS algorithm is discretized into 8 levels to get a balance between performance of hologram and accuracy of fabrication. The printing strategy (FIG. 8(a)-(e)) is determined as follows: the laser beam scans along y axis in one-way method and moves to next x value, and once the layer in the current writing field is completed, laser beam scan in a new z layer is started z\ all the scan lengths are same for traditional phase blocks while for the proposed structure they are adjusted to fit the profile of blazed caps with the same slicing distance; the final DOEs are stitched by different writing fields on substrate. Thus, as closer to the top comer of the blazed cap (increasing z direction), the shorter the printed line. In consideration of printing time and fineness of blazed caps, here the image of FIG. 1(a) with 300x300 pixels is used for illustration purposes, and the size of phase block is chosen to be 3 pm x 3 pm. After lithography with Nanoscribe, the samples are developed in polyethylene glycol methyl ether acetate (PGMEA) for 10 min, then transferred into isopropyl alcohol (IPA) for 5 min, with the last step immersion in nonafluorobutyl methyl ether (NFBME) for 5 min to release the surface tension and dried in air. [0063] The structural details of the printed DOEs can be seen in FIG. 9. The scale bars are 10 pm for FIG. 9(a), (b), (d), and (e), and 3 pm for FIG. 9 (c) and (f). FIGS. 9 (a)-(c) show images of comparative examples acquired by an optical microscope (Nikon Eclipse FV 100ND, lOOx, 0.8 NA, captured with inclination angle 30° along a diagonal direction) and FIGS. 9 (d)- (f) show images of DOEs in accordance with various embodiments obtained by SEM (JEOF JSM-7600F and Raith eFINE Plus), demonstrating that both the traditional flat-top phase blocks (FIGS. 9 (a)-(c), corresponding to FIG. 2(a)) and the DOE including phase elements including blazed cap (FIGS. 9 (d)-(f), corresponding to FIG. 3(b)) are successfully fabricated with high quality. FIGS. 9 (a) and (d) are optical microscopy images, and FIGS. 9 (b), (c), (e), and (f) are SEM images.

[0064] Significant gradient can be observed from the blazed structures which yet retain smooth topography, as shown in the top viewed image with gradually changed grayscale in FIG. 9(f), which proves the efficacy of the presented printing strategy. Furthermore, the blazing angles retrieved from AFM measurement for integral grating orders 1, 2, 3 are around 12.6°, 22.8° and 30.2°, which are quite close to the values 12.59°, 23.19° and 30.96° calculated from Eq. (2). The root-mean square (RMS) height profile determined from the image as shown in FIG. 9(g) is 11.3 nm, and the phase image obtained with AFM (Asylum Research Oxford Instruments, MFP-3D Origin) in FIG. 9(h) shows that the periodicity is close to the designed hatching distance 250 nm, quantitatively verifying the precision of the methods in accordance with various embodiments.

[0065] With the fabricated DOE illuminated by a laser, for example at a wavelength 532 nm, far field projected images can be observed on the screen, as depicted in FIG. 1(a). In experiments, the screen is placed perpendicular to the deflection angle f (see FIG. 2(c)) to show the positions of the projected images at different grating order m. Projected images obtained at grating order 1, 2, 3 are presented in FIG. 10(b(i)-b(iv)), which fit perfectly with the corresponding results from simulation in FIG. 10(c(i)-c(iv)).

[0066] The original pre-determined image (FIG. 1(a), 300x300 pixels) is redesigned by diagonally swapping the previous quadrants (see FIG. 6) to make the zero order spot located at the comer of hologram when m = 1. The small distortions in experimental images are caused by the unevenness of the screen and the high order spots in simulated results are not clear in FIG. 10 owing to they taking up only one pixel each in simulation. It is obvious that the 2D sine-type energy distribution has been shifted along the diagonal direction and got itself far away from the zero order spot, lighting up the 2D repetitive holograms (projected images) located there in the Fourier plane, which is consistent with the theoretical description provided herein.

[0067] Since the phase blocks are designed to be of square base (in plan view), /_to equals to f_by and d_x equals to d_y, rendering the frequency domain shift in Fourier plane along x and y axes the same as described in Eq. (3). From FIG. 10(d), we can see that the shift values in unit frequency domain period 1 /d_x,y from theory (circles with corresponding values 0.49, 0.95, and 1.32 for grating order 1, 2, and 3), simulation (triangles) and experiment (asterisks with error bar) match perfectly, proving the concept and methods in accordance with various embodiments. Simulated and experimental results of hologram with almost uniform off-axis illumination and zero order spot blocked are shown in FIGS. 10(e) and (f), respectively. The input image is obtained by padding the original image with zeros into 600x600 pixels. The measured diffraction efficiencies are around 86% for all the central holograms, in consistency with the comparative DOE structure, thus also confirming that the DOE structure in accordance with various embodiments can realize off-axis hologram with high diffraction efficiency.

[0068] Phase error analysis is discussed below in connection with FIGS. 11 to 14, showing the correlation between signal to noise ratio (SNR) values and the range of phase error.

[0069] According to various embodiments, the phase error p of phase blocks may be kept lower or equal to 6, in which situation, the projected image still can be observed. FIG. 11 shows simulated projected images at grating order (a) m = 0 and (b) m = 1, with range of phase error p of phase blocks varies from 0 to 8 and one level represents 120 nm in fabrication. The uniformly distributed phase errors in range [-rp/8, +rp/8] are added to the phase obtained from GS algorithm. The zero order spot is denoted as the central bright dot in (a). The values are normalized to show the relative intensities under different phase error levels. FIG. 12 shows the signal to noise ratios for m = 0 (line with circle) and m = 1 (line with triangle). The markers represent the SNR values, corresponding to the images in FIG. 11 (a) and (b). In the calculation, the target image is the binary image with 300x300 pixels in FIG. 1(a).

[0070] FIG. 13 shows simulated projected images at grating order (a) m = 0 (b) m = 1, wherein the range of sub-pixel level phase error q varies from 0 to 8 and one level represents 120 nm in fabrication. The uniformly distributed sub-pixel phase errors in range [-q /8, -K_|p/8] are added to the phase obtained from GS algorithm. As the size of one phase block is 3 pm and hatching distance is 250 nm in our experiment, one original phase is divided into 12x12 sections to introduce the sub-pixel phase error. The zero order spot is denoted as the central bright dot in (a). The values are normalized to show the relative intensities under different phase error levels. The value of q may be kept lower or equal to 7 to observe the projected image. FIG. 14 shows SNRs for m = 0 (line with circle) and m = 1 (line with triangle). The markers represent the SNR values, corresponding to the images in FIG. 13 (a) and (b). In the calculation, the target image is the binary image with 300x300 pixels in FIG. 1(a).

[0071] FIG. 15 shows a plot of the height ( H_p ) of phase blocks at different phase levels. According to various embodiments, the 2p phase may be discretized into a number of levels, for example, selected from 5 to 25 levels. In examples herein, the 2p phase may be discretized is discretized into 8 levels with level height 120 nm for IP-Dip at wavelength 532 nm. The dashed line represents the calculated height and the continuous line with circle is the measured result.

[0072] FIG. 16 shows simulated far field holographic projections with phase block size d_x,y at (a) 6 pm; (b) 3 pm and (c) 1.5 pm. For the simulations, the original image is redesigned by diagonally swapping the quadrants to make the zero order spot located at the corner of holographic image when m = 1, see FIG. 6. As shown in FIG. 16, the size of far field holograhic projection will increase when the phase block size decreases, since the periodicity in Fourier plane is the reciprocal of phase block size d_x,y in hologram plane. According to Fourier transform, the sine function is the Fourier transform of a rect function, and it has a value of zero at ± 1 /d_x,y in the Fourier plane. Therefore, the central energy distribution has a radius of about l/d_x,y, thus most of the diffraction energy is effectively used to illuminate the central image.

[0073] FIG. 17 shows a further comparative example, in which the image (same as in FIG. 1(a)) is shifted. FIG. 17 shows image projections by linear phase technique along x axis and (b) along a diagonal direction. The desired image is marked by the white dashed line. The designed holographic image can be shifted off-axis along x/y axis (FIG. 17(a)) or along a diagonal direction (FIG. 17(b)) to avoid the overlapping with the bright zero order spot by linear phase technique. However, the comparative DOE composed of phase blocks with flat top facets determines the 2D sine-type energy distribution in the center of the Fourier plane. Thus as shown from the simulation, the desired image (marked by white dashed line) is falling within the dark fringe and, in contrast with embodiments of the present disclosure, suffers from the non-uniform illumination. [0074] In summary, a DOE structure composed of phase elements with blazed top surfaces is disclosed to solve the problem of bright zero order spot in hologram. By shifting the diffraction energy distribution away from zero order spot along a diagonal direction, hologram free of zero order and with uniform off-axis illumination is achieved. The physical principle is elaborated with diffraction theory. Besides, relations between frequency domain shift at different refractive indexes of photoresist material and at different phase block sizes are disclosed. With advanced 3D printing technology, e.g., based on two-photon or multiphoton lithography, high quality DOEs are fabricated and characterized by optical microscopy, SEM and AFM. Off-axis holograms without zero order spot disturbed experimentally obtained with the new structure at grating order 1, 2, and 3, fit well with simulation and theory, thus confirming the effectiveness of the DOEs and methods in accordance with various embodiments. Diffraction efficiency of the DOEs in accordance with various embodiments is as high as 86%, similar to the comparative examples using DOE with flat top facet. The concept of local manipulation of DOE structure by 3D printing described here brings up a reliable solution to the hologram with zero order spot.

[0075] Simulations and/or calculations described herein, may be performed with a computer. For example, the computer may be used for the method of producing 3D-print data in accordance with various embodiments. The computer may include a bus through which one or more of the devices may communicate with each other. One or more of the following devices may be connected to the bus: a microprocessor; a main memory, for example a RAM; a storage device, for example a hard disk drive, a solid state drive, and/or a flash drive; a communication device, for example for wired or wireless communication, e.g. WiFi, USB, and/or Bluetooth; a display interface, and other user interfaces, for example for user input; however the disclosure is not limited thereto, and more or less devices may be included in the computer and the computer and/or bus may have other architectures than the one illustrated.

[0076] While the disclosure has been particularly shown and described with reference to specific embodiments, it should be understood by those skilled in the art that various changes in form and detail may be made therein without departing from the spirit and scope of the invention as defined by the appended claims. The scope of the invention is thus indicated by the appended claims and all changes which come within the meaning and range of equivalency of the claims are therefore intended to be embraced. REFERENCES

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Claims

1. A diffractive optical element (DOE) comprising a discretized phase matrix extending in a first plane, the discretized phase matrix comprising a plurality of phase elements, wherein top surfaces of the phase elements are each non-parallel to the first plane.

2. The DOE of claim 1, wherein top surfaces of the phase elements are parallel to each other.

3. The DOE of claim 1 or claim 2, wherein top surfaces of the phase elements are each at a blaze angle ( Q ) to the first plane.

4. The DOE of any one of the preceding claims, wherein bottom surfaces of the phase elements are parallel to the first plane.

5. The DOE of any one of the preceding claims, wherein the discretized phase matrix comprises a hologram encoded in optical path lengths of the plurality of phase elements.

6. The DOE of any one of claims 1 to 4, wherein the discretized phase matrix comprises a hologram encoded in thicknesses of the plurality of phase elements.

7. The DOE of any one of the preceding claims, wherein an image is encoded in the discretized phase matrix, wherein the image is projectable, as a projected image, on a Fourier plane off-axis upon incidence of coherent electromagnetic energy on the discretized phase matrix.

8. The DOE of claim 7, wherein an angle formed between a zero order axis and the off-axis holographic projection is chosen to be substantially equal to a deflection angle (f) of the phase elements.

9. The DOE of any of claims 7 or 8, wherein the image encoded in the hologram corresponds to a pre-determined image which is shifted.

10. An optical system for projecting a far field holographic projection on a screen at a projection plane, the optical system comprising:

- a source configured to emit a coherent electromagnetic energy, for example laser, with a first optical axis;

- the DOE according to any of the previous claims, arranged on the first optical axis and between the source and the projection plane.

11. The diffractive optical system of claim 10 being selected from: augmented reality device, medical imager, laser multi-beam projector, beam shaper, interferometer, optical manipulator, anti-counterfeiting equipment.

12. A method of producing 3D-print data including a 3D object model of a DOE comprising a discretized phase matrix comprising a plurality of phase elements, the discretized phase matrix storing phase information of a shifted image, wherein the method comprises:

- transforming a pre-determined image to obtain the shifted image;

- determining a plurality of phase values corresponding to the plurality of phase elements based on the shifted image;

- determining the 3D object model of the discretized phase matrix based on the phase values,

wherein determining the 3D object model is further based on a blaze angle of a blazing cap for each of the plurality of phase elements.

13. The method of claim 12, wherein determining the 3D object model of the discretized phase matrix based on the phase values comprises determining optical path lengths corresponding to the phase values.

14. The method of claim 13, wherein determining optical path lengths comprises determining thicknesses of the plurality of phase elements.

15. A method of producing a DOE comprising

- producing the 3D-print data of the DOE according to any of claims 12 to 16; and - 3D printing the DOE according to the 3D object model.

16. The method of claim 15, wherein 3D printing comprises:

providing a polymerizable solution; and

scanning the polarizable solution with a focal spot of a laser beam along a scanning path so as to polymerize the polymerizable solution at the focal spot, wherein the scanning path is determined based on the 3D-print data.

17. The method of claim 16, wherein polymerizing is a two-photon polymerization or a multiphoton polymerization.