Holographic system with improved projection quality

Abstract

The present invention relates to a method for generating a pixelated projection in a reconstruction space, the method comprising: determining a first discretized hologram, the first discretized hologram being determined to generate a desired amplitude profile of an output pixel in the reconstruction space; determining a second discretized hologram having a phase distribution determined to create a desired projection in the reconstruction space; determining a tiling hologram by tiling the second discretized hologram one or more times in one or two directions, the number of tilings and the first discretized hologram being determined subject to an output pixel constraint determined based on the magnitude of the amplitude profile of the output pixel in the reconstruction space and the pixel pitch in the reconstruction space. A composite hologram is determined based on a phasor multiplication of the first discretized hologram and the tiling hologram. A coherent input beam is phase modulated based on the composite hologram such that the phase modulated beam generates a pixelated projection in the reconstruction space. A particular application of the present invention is for volume additive manufacturing (VAM), in particular for medical applications, e.g. for implants.

Description

[Technical field]

[0001] The present invention relates to computer generated holography, and more particularly to a method for reducing speckle in computer generated holography. [Background technology]

[0002] Patent Document 1 discloses a method for providing an intensity pattern, such as an image, more particularly an adjacent intensity pattern with reduced speckle. The method includes encoding a spatial light modulator with a modulation pattern to form the intensity pattern as a diffraction pattern, the method further includes shaping an input beam such that a point spread function in an output region where the diffraction pattern is formed has suppressed side lobes, such as a point spread function having a substantially rectangular shape, and the method further includes tiling the modulation pattern such that the gaps between the individual point spread functions correspond to their widths. The effect of this is to allow the output pattern to be formed as a pattern of closely spaced point spread functions, which allows the formation of adjacent patterns with reduced speckle.

[0003] While US Pat. No. 5,999,333 presents a method for addressing the problems with speckle, the present invention is devised with the objective of further reducing image speckle and improving holographic systems. [Prior art documents] [Patent documents]

[0004] [Patent Document 1] International Publication No. 2015 / 165471 Summary of the Invention [Means for solving the problem]

[0005] It is an object of the present invention to provide an improved method for computer generated holography, in particular an improvement that addresses problems with speckle, but also other improvements.

[0006] In a first embodiment of the present invention, a method for generating a pixelated projection in a reconstruction space is presented. The method comprises: determining a first discretized hologram having a phase distribution in a plane, the first discretized hologram being determined to produce a desired amplitude profile of output pixels in the reconstruction space; determining a second discretized hologram having a phase distribution determined to produce a desired projection in the reconstruction space; determining a tiling hologram by tiling the second discretized hologram one or more times in one or two directions, the number of tilings and the first discretized hologram being determined according to the output pixel constraints determined based on the magnitude of the amplitude profile of an output pixel in a reconstruction space, e.g. ΔXpsf and / or ΔYpsf, and the pixel pitch in the reconstruction space, e.g. ΔXholo and / or ΔYholo; generating or determining a composite hologram based on a phasor multiplication of a first discretized hologram and the tiling hologram; phase modulating a coherent input beam based on the composite hologram and directing the phase modulated beam towards a reconstruction space to generate a pixelated projection in the reconstruction space; Includes.

[0007] Advantageously, the first discretized hologram is responsible for generating a specific amplitude profile of an output pixel. Since the first discretized hologram is implemented on a spatial light modulator or a fixed phase mask, no further beam shaping optics are needed to shape the input beam to generate a desired amplitude profile in the reconstruction space. Moreover, the amplitude profile of the output pixel can be adapted by modifying the first discretized hologram.

[0008] Advantageously, combining the first and second discretized holograms into a composite hologram through said phasor multiplication allows for a simple and cost-effective implementation of computer-generated holograms.

[0009] The size of the amplitude profile of the output pixel refers to the magnitude of the amplitude profile in the reconstruction space, and therefore this magnitude represents the output pixel size.

[0010] The tiling refers to distributing the second discretized hologram over an area of ​​a Spatial Light Modulator (SLM) or a fixed phase mask by copying the second discretized hologram so that at least two identical second discretized holograms are arranged adjacent to each other along their sides. The at least two second discretized holograms are arranged adjacent along at least one direction in the plane of the SLM or fixed phase mask (which may be flat or curved). For example, the second discretized holograms are repeated and arranged adjacent along a vertical direction in the plane of the SLM or fixed phase mask.

[0011] As used herein, multiplication, i.e., phasor multiplication, is a component-wise multiplication, where components z_i,j in the resulting matrix or vector Z are given by multiplication of components x_i,j and y_i,j in the respective matrices or vectors X and Y, i.e., z_i,j = x_i,j · y_i,j, for i ∈ 1..m and j ∈ 1..n. In this example, X represents the first discretized hologram, Y represents the tiling hologram, and Z represents the composite hologram. Each of the matrices / vectors X, Y, and Z has equal dimensions.

[0012] The steps of determining the first discretized hologram and the second discretized hologram may be performed in a computer. The first and second holograms may subsequently be used to control one or two spatial light modulators (SLMs), where the first hologram may be used directly and the second hologram may be tiled. Using one SLM, the SLM performs a computer-determined phasor multiplication of the first discretized hologram and the tiled hologram.

[0013] Alternatively, either one or both of the determined first discretized hologram and the determined second discretized hologram are subsequently used to generate a fixed phase mask implementing the determined hologram or a tiled form thereof.

[0014] The tiling hologram is determined in a computational manner by tiling the second discretized hologram.

[0015] Alternatively, the tiling hologram may be generated by an optical tiling system arranged to tile a phase distribution generated on the basis of the second discretized hologram by an SLM or a fixed phase mask. A combination is also feasible in which the optical tiling system optically generates a further tiling of the tiled phase distribution generated by the SLM. Thus, the SLM or the fixed phase mask generates a single second discretized hologram or a tiled, e.g. 4x4 tiled, phase distribution of the second discretized hologram and the optical tiling system generates a further tiling of the phase distribution.

[0016] The multiplication of the first discretized hologram and the tiling hologram may be determined in a computer and subsequently used to control the SLM.

[0017] Alternatively, it is understood that the phasor multiplication is determined by the result of the input light being transmitted through adjacently arranged first and second phase modifying devices, and in this case each of the first and second phase modifying devices can be embodied by a fixed phase mask or an SLM. Obviously, the transmission through two adjacent first and second phase modifying devices produces a cumulative change in the optical phase per pixel equivalent to the phasor multiplication of two holograms, in which case the phasor multiplication results in a pixel-by-pixel addition of the pixel phases of two holograms, for example the phasor multiplication of the first discretized hologram with the tiling hologram.

[0018] According to the present embodiment, the pixel constraint requires that the magnitude ΔXpsf is smaller than, equal to, or substantially equal to the pixel pitch ΔXholo. If ΔXpsf is selected to be equal to or slightly less than ΔXholo, it may in fact happen that ΔXpsf is larger than ΔXholo by a small percentage, for example 1 percent, for a fraction of the output pixels. The same applies to the width ΔYpsf and pixel pitch ΔYholo in the perpendicular second direction, which may be equal to or different from the width and spacing in the first direction. Thus, the x- and y-directions may be optimized independently of each other, and the pixel constraint is satisfied by different pixel and pitch values ​​in each direction. Obviously, the output pixels are arranged according to a coordinate system other than the Cartesian system, and therefore also in polar, cylindrical and spherical coordinate systems.

[0019] According to this embodiment, determining the tiling hologram comprises determining the tiling numbers in two directions of the tiling hologram, e.g. NT or NT1 and NT2, subject to the pixel constraint and the magnitude of the amplitude profile of the output pixel, e.g. ΔXpsf and / or ΔYpsf. Thus, the method comprises determining the tiling numbers NT, NT1, NT2 as a function of the output pixel magnitude ΔXpsf and / or ΔYpsf, such that the output pixel constraint is satisfied. Advantageously, in case the magnitudes ΔXpsf, ΔYpsf etc. are predetermined, the output pixel constraint is satisfied by determining the tiling hologram, in particular the tiling numbers.

[0020] According to this embodiment, determining the first discretized hologram comprises determining a magnitude, such as ΔXpsf and / or ΔYpsf, of the amplitude profile of the output pixel subject to the pixel constraint and the tiling numbers (NT, NT1, NT2) of the tiling hologram. Thus, the method comprises determining ΔXpsf and / or ΔYpsf as a function of the tiling numbers NT, NT1, NT2, such that the output pixel constraint is satisfied. Advantageously, when the tiling numbers are predetermined, the output pixel constraint is satisfied by determining the lateral pixel sizes ΔXpsf, ΔYpsf subject to the constraint.

[0021] According to this embodiment, the first discretized hologram is determined depending on the desired magnitudes ΔXpsf, ΔYpsf of the amplitude profile of the output pixels.

[0022] For example, the first discretized hologram may be determined such that at least 70% of the total power of the amplitude profile in the reconstruction space falls within a pixel, i.e. within the lateral dimensions ΔXpsf, ΔYpsf of the output pixel. For example, the first discretized hologram is determined such that the percentage of the total power of the amplitude profile in the reconstruction space falls within at least 50%, such as 60% or 70%, for example within a percentage range of 50% to 99%, for example 60% to 90%.

[0023] According to this embodiment, the determination of the second discretization hologram comprises determining a phase distribution such that at least some of the output pixels of a desired projection are determined to be reconstructed in a reconstruction space at different positions along the propagation direction of the input beam. Advantageously, the second discretization hologram, and thus the tiling hologram, is determined such that the positions along the propagation direction at which the output pixels are generated, i.e. reconstructed to have sharply defined pixel edges, are different for different pixels, for example with the aim of generating the projection on a curved surface or in a 3D space.

[0024] According to this embodiment, the phase modulation comprises controlling a spatial light modulator to generate a discretized phase distribution corresponding to the first discretized hologram, the tiling hologram or the composite hologram. Advantageously, a spatial light modulator is combined with a fixed phase mask, such that for example the first discretized hologram is implemented in the fixed phase mask, while the tiling hologram is implemented in the spatial light modulator.

[0025] A second embodiment of the invention relates to a holographic system arranged to generate a pixelated projection in a reconstruction space, the holographic system comprising: a data processor arranged to carry out the steps of the first embodiment; a light source generating the coherent input beam; a spatial light modulator arranged to phase modulate the coherent input beam based on the composite hologram and direct the phase-modulated beam towards a reconstruction space to generate the pixelated projection in the reconstruction space; Equipped with.

[0026] A third embodiment of the invention relates to a holographic system arranged to generate a pixelated projection in the reconstruction space according to the first embodiment, the holographic system comprising: a first fixed phase mask configured to have a discretized phase distribution according to a first discretized hologram, and a spatial light modulator arranged to generate a phase modulation according to said tiling hologram; or a spatial light modulator arranged to generate a phase modulation according to a first discretized hologram, and a second fixed phase mask configured to have a discretized phase distribution according to said tiling hologram; or a first fixed phase mask configured to have a discretized phase distribution according to a first discretization hologram and a second fixed phase mask configured to have a discretized phase distribution according to the tiling hologram or a first fixed phase mask configured to have a discretized phase distribution according to a composite hologram; a light source generating a coherent input beam, the light source being arranged to transmit light through a discretized phase distribution generated by at least a first fixed phase mask and / or a second fixed phase mask, and directing the phase-modulated beam towards a reconstruction space to generate a pixelated projection in the reconstruction space; Equipped with.

[0027] Advantageously, one of the discretized holograms is implemented in a fixed phase mask. In particular, the implementation of the compound hologram in a fixed phase mask allows for ultra-high resolution due to the higher available pixel density in a fixed phase mask compared to a controllable spatial light modulator.

[0028] In the third embodiment, it will be appreciated that the holographic system also includes a data processor arranged to carry out the relevant steps of the first embodiment, i.e. determining the first discretized hologram, the second discretized hologram, the tiling hologram and / or the composite hologram, and controlling a spatial light modulator, if present in the system.

[0029] According to this embodiment, the spatial light modulator arrangement comprises a spatial light modulator and an optical tiling system, the spatial light modulator being arranged to generate the second discretized hologram, or the tiling hologram, and the optical tiling system being arranged to tile the second discretized hologram, or the optical tiling system being arranged to further tile the tiling hologram.

[0030] According to this embodiment, the optical tiling system includes an imaging system, for example a lens array or a mirror scanner, configured to generate a tiling and to project incident light into the reconstruction space.

[0031] The paper "Direct fabrication of seamless roller molds with gapless and shaped-controlled concave microlens arrays, Guangqing Du et al. OPTICS LETTERS Vol. 37, No. 21 November 1, 2012" provides an example of optical tiling using lens arrays.

[0032] A fourth embodiment of the invention relates to a computer program comprising instructions for causing a data processor of the second embodiment to carry out the steps of the first embodiment.

[0033] A fifth embodiment of the invention relates to the use of the method according to the first embodiment or the system according to the second or third embodiment for any one of the following: Multiphoton excitation of living cells, 3D object printing, Holographic display, Photopolymerization, e.g. two-photon photopolymerization; Laser material processing, such as one-shot material processing, Optical lithography, Structured illumination microscopy, Skin treatments, such as cosmetic skin treatments, Combined with spatiotemporal focusing of ultrafast pulsed lasers for multiphoton excitation at selected depth layers, Ultra-rapid additive manufacturing, Laser material processing performed in parallel; Fast laser engraving, welding and machining Two-photon excitation in optogenetics and voltage imaging Polychromatic and multifaceted diffraction Photon-efficient phase-only display technology Real-time adaptive optics embodiments, including aberration correction; and Space-time focusing (TF)

[0034] The spatiotemporal focusing is performed by using a fixed diffraction grating.

[0035] Advantageously, the present invention further relates to using the method according to the first embodiment or the system according to the second embodiment to print a 3D object by using Three-dimensional Additive Manufacturing (VAM), preferably for medical applications, preferably for printing a biocompatible implant, an artificial organ or part thereof or a similar object.

[0036] In general, the various aspects and embodiments of the invention may be combined or combined in any manner possible within the scope of the invention. These and other aspects, features and / or advantages of the invention will be apparent from and elucidated with reference to the embodiments described hereinafter.

[0037] Embodiments of the present invention will now be described, by way of example only, with reference to the drawings in which: [Brief description of the drawings]

[0038] [Figure 1A] FIG. 1A shows the point spread function in the reconstruction space and the side lobes of the point spread function that lead to an undesirable speckle pattern. [Figure 1B] FIG. 1B shows an improved point spread function that leads to reduced speckle. [Figure 2A] FIG. 2A shows a holographic system arranged to generate a pixelated reconstructed image projection in a reconstruction space based on the improved hologram determination method. [Figure 2B] FIG. 2B shows an alternative holographic system arranged to generate a pixelated reconstructed image projection in the reconstruction space, including one or two fixed phase arrays, for example one fixed phase array combined with one SLM. [Figure 3A] FIG. 3A illustrates the method steps of an embodiment. [Figure 3B] FIG. 3B shows how a composite hologram is determined through phasor multiplication of a PSF-shaped hologram and a tiled object hologram, the latter being determined by tiling the determined object hologram based on the desired projected image, here a two-dimensional image of the letter H. [Figure 4] FIG. 4 shows the output pixels, pixel pitch ΔXholo, and pixel width ΔXpsf in a pixel row of the pixelated reconstructed image. [Diagram 5] FIG. 5 shows the Gerchberg-Saxton algorithm for determining the PSF-shaping hologram. [Figure 6A] FIG. 6A shows an example of a first discretized hologram 311 and a tiling hologram 313. [Figure 6B] FIG. 6B shows an example of pixelated projection 201 and pixelated image formation. [Figure 7] FIG. 7 shows an embodiment within the field of 3D Additive Manufacturing (VAM) to which the present invention applies. [Figure 8] FIG. 8 shows an embodiment within the field of 3D Additive Manufacturing (VAM) to which the present invention applies. [Figure 9] FIG. 9 shows an embodiment within the field of 3D Additive Manufacturing (VAM) to which the present invention applies. [Figure 10] FIG. 10 shows an embodiment within the field of 3D Additive Manufacturing (VAM) to which the present invention applies. DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

[0039] FIG. 1A illustrates the generation of an image projection based on a computer-generated hologram. The computer-generated hologram comprises a discretized phase distribution σ(x,y) as a function of coordinates x,y in a plane. The phase distribution is determined according to known methods. For example, the phase distribution may be determined based on an image such that an identical image can be reconstructed based on the phase distribution. In general, an image generated from the phase distribution σ(x,y) is referred to as a reconstructed image. The spatial light modulator SLM is controlled according to the discretized phase distribution. In particular, the spatial light modulator SLM comprises a matrix of addressable optical components, where each element is capable of changing the phase of a portion of the input light beam 101 that interacts with it. Each component can be controlled to generate a desired phase change. And therefore the spatial light modulator can be controlled to generate the phase distribution σ(x,y) of the computer-generated hologram. The discretized phase distribution of the computer hologram is represented as a matrix of phase values, where the phase distribution and the matrix of SLM components may be of the same dimension or they may also be of different dimensions.

[0040] Spatial light modulators can be transmission-based, as illustrated in FIG. 1A, or reflection-based.

[0041] The input beam 101 is a coherent beam, such as a laser beam. The degree of spatial and temporal coherence of the input beam depends on the application. Thus, a spatially coherent LED, a superluminescent diode, or a temporally semi-coherent beam from a semi-coherent laser source will suffice. The input beam 101 may also come from a pulsed light source, for example a femtosecond laser. Pulsed lasers are used in conjunction with multi-photon excitation.

[0042] The phase modulation of the input beam can use any polarization state of the input beam, including a circular polarization state of the input light.

[0043] The spatial light modulator generates a phase-modulated light beam 102 that forms an image projection at the reconstruction space 111 due to diffraction effects. That is, interference of the phase-modulated beam in the reconstruction space results in an image, such as a desired projection, e.g., a desired intensity distribution in the reconstruction space that corresponds to a desired image, e.g., a desired intensity distribution that determines the phase distribution of a computer generated hologram.

[0044] A lens 112 can be used so that the diffraction image is generated at the focal reconstruction space 111 of the lens, but a lens may also be omitted, in which case the image is generated without the Fourier lens 112. When no lens is used, this is usually referred to as Fresnel or Fraunhofer holography.

[0045] 1A illustrates the individual amplitude curves 121-123, also called point spread functions (PSF), of a reconstructed image in a reconstruction space 111. The individual amplitude curves 121-123 have different phases φ1-φ3. The reconstructed image is the result of the interference of the individual amplitude curves 121-123, i.e. the superposition of the individual amplitude curves 121-123 taking into account the individual phases φ1-φ3.

[0046] The main peaks of the amplitude curves 121-123 can be regarded as output pixels of the image projection, where the light amplitude of each output pixel can be controlled according to the phase distribution σ(x,y) of the computer generated hologram.

[0047] The interference of the side lobes of the amplitude curves 121-123 results in speckle around the main peak and therefore reduces the quality of the diffraction image.

[0048] When using a spatial light modulator operating in phase-only mode to maximize light efficiency, speckle cannot be avoided in the reconstructed intensity if a large number of pixels of the SLM are mapped to individual pixel spots at the output. If only the output amplitude value is controlled due to the finite aperture of the SLM or diffraction effects due to the expanded coherent light beam read out from the SLM, crosstalk of nearest neighbor pixel spots due to phase variations in the reconstruction space 111 cannot be avoided and speckle due to phase variations in the reconstruction space 111 cannot be avoided.

[0049] Each output light spot 121-123 or output pixel in the output light pattern is generated as a result of a global transformation of the input phase distribution σ(x,y) generated by the spatial light modulator SLM, i.e., as generated in discretized form by the SLM. However, by constraining the SLM phase distribution σ(x,y) to generate a desired output intensity pattern, control over the specific phase value of each output pixel 121-123 is essentially lost. The resulting varying output phase is due to light leakage from the tails of the point spread function (PSF) governed by the truncated aperture of the overall optical system, resulting in varying interference between nearest output pixels.

[0050] FIG. 1B shows individual amplitude curves 151-153 of a diffraction image in reconstruction space 111 generated according to a method of an embodiment of the present invention. FIG. 1B shows that side lobes are reduced at the expense of broadening of the amplitude peaks. Suppression of the side lobes reduces speckle and improves image quality. Each peak of the individual amplitude curves 151-153 represents an image output pixel 151a-153a. The amplitude curves 151-153 are equivalent to the point spread functions 121-123, but are shaped to be approximately flat-topped rectangular point spread functions 151-153.

[0051] The phase distribution of the computer generated hologram is determined such that each of the individual amplitude curves 151-153, and thus the amplitude of each output pixel 151a-153a, is generated by a group of one or more addressable elements of the spatial light modulator SLM. The amplitude of each output pixel 151a-153a can therefore be controlled by adjusting the phase distribution of the computer generated hologram.

[0052] The phase distribution determined to produce a desired amplitude profile of the output pixels in the reconstruction space, such as a flat-topped rectangular point spread function (PSF), can be determined in a variety of ways. For example, the phase distribution is determined by using the Gerchberg-Saxton algorithm for phase retrieval (see Gerchberg RW and Saxton W 0 1972 OPTIK 35 p. 237-246). In another example, the phase distribution is determined from analytical methods. These methods are described below.

[0053] The determined phase distribution is converted into a discretized hologram, this is done by discretizing the values ​​of the determined phase distribution according to the pixel size of the SLM, e.g. according to the pixel size and pixel pitch of the SLM.

[0054] FIG. 2A illustrates a holographic system 200 arranged to generate a pixelated projection 201 in the reconstruction space 111.

[0055] The holographic system comprises a data processor 210, such as a computer, arranged to determine a composite hologram or a particular SLM control device. The determination of the composite hologram is described in relation to Figures 3A and 3B. The data processor 210 is arranged to generate a single static composite hologram or a series of composite holograms to generate an image sequence in the reconstruction space 111.

[0056] The holographic system further comprises a light source 202 generating a coherent input beam 101 and a spatial light modulator SLM arranged to phase modulate the coherent input beam 101 according to a composite hologram. , the holographic system 200 may comprise a Fourier lens 112. The output beam of the spatial light modulator SLM propagates, possibly via the Fourier lens 112, towards the reconstruction space 111 to generate a pixelated projection 201 in the reconstruction space 111. Alternatively, a lens-free Fresnel or Fraunhofer method may be used.

[0057] The reconstruction space 111 is a two-dimensional image plane or a three-dimensional reconstruction space. If the reconstruction space 111 is a three-dimensional reconstruction space, the second discretized hologram 313 is determined based on the three-dimensional image.

[0058] An image in this specification is understood as any intensity distribution, which does not necessarily have to be a visible image, but also includes any intensity distribution determined by a computer, mathematically or by other methods.

[0059] 2B shows an alternative configuration of the holographic system 200. The alternative holographic system has a first phase modifying component 251 and a second phase modifying component 252. The first phase modifying component 251 is embodied by a spatial light modulator SLM or a first fixed phase mask. Similarly, the second phase modifying component 252 is embodied by a spatial light modulator SLM or a second fixed phase mask.

[0060] A fixed phase mask includes a matrix of individual fixed phase changing pixel elements that modify the pixel components, where the phase of each pixel element is set according to a determined first discretized hologram 311, a tiling hologram 313, or a composite hologram 314. Examples of fixed phase masks include Diffractive Optical Elements (DOE), polymer-based phase masks, diffractive phase masks, and metamaterial-based phase masks.

[0061] Related combinations of embodiments of the first phase correction component 251 and 2252 are: a first embodiment, in which the first phase correction component 251 is a first fixed phase mask and the second phase correction component 252 is an SLM; a second embodiment, in which the first phase correction component 251 is an SLM and the second phase correction component 252 is a second fixed phase mask; a third embodiment, in which the first phase correction component 251 is a first fixed phase mask and the second phase correction component 252 is a second fixed phase mask; and a fourth embodiment, in which the first phase correction component 251 is a first fixed phase mask and the second phase correction component 252 is omitted.

[0062] According to the first embodiment, a first fixed phase mask implements a determined first discretized hologram 311 and an SLM controlled by a data processor 210 (not shown in FIG. 3B) implements a tiling hologram 313 (see FIG. 3B).

[0063] According to the second embodiment, the second fixed phase mask implements the determined tiling hologram 313 and the SLM implements the first discretized hologram 311 .

[0064] According to the third embodiment, the first fixed phase mask implements a first discretization hologram 311 and the second fixed phase mask implements a tiling hologram 313 .

[0065] According to the fourth embodiment, the first fixed phase mask implements a determined multiplication of the first discretized hologram 311 and the tiling hologram 313 , i.e. the first fixed phase mask incorporates a composite hologram 314 .

[0066] The spatial phase distribution of light propagating through the first phase correction component 251 and the second phase correction component 252, when illuminated by the input beam 101, is first modified by the first phase correction component 251 and then modified by the second phase correction component 252, such that the cumulative final phase correction of the first phase correction component 251 and the second phase correction component 252 corresponds to the determination of a composite hologram 314 based on phasor multiplication of the first discretized hologram and the tiling hologram.

[0067] Thus, the first phase modification component 251 and the second phase modification component 252 generate a phase modulation of the coherent input beam 101 based on the cumulative effect of the phase modification components 251, 252 corresponding to the composite hologram 314 or corresponding to the phasor multiplication of the first discretized hologram and the tiling hologram.

[0068] The spatial phase modulation of the input light can be performed by static or dynamic spatial light modulation, such as that described in “GPC-based optical micromanipulation in 3D real-time using a single spatial light modulator”, PJ Rodrigo, IR Perch-Nielsen, CA Alonzo, J. Gluckstad, Optics Express 14(26), 13107-13112 (2006)” and “GPC light shaper: static and dynamic experimental demonstrations”, A. Banas, O. Kopylov, M. Villangca, D. Palima, J. Gluckstad, Optics Express 22 (20), 23759-23769 (2014), the contents of which are incorporated herein by reference. In general, spatial phase modulation can be performed by any known spatial light modulator, including Liquid Crystal SLM (LC-SLM), Liquid Crystal on Silicon SLM (LCoS-SLM), Micro Electro-Mechanical Systems SLM (MEMS-SLM), Deformable Mirror SLM (DM-SLM), Digital Mirror Device (DMD), Acousto-Optic SLM (AO-SLM), or any other type of SLM. Furthermore, spatial phase modulation does not necessarily require a spatially moving component of a spatial light modulator or phase mask. Rather, local properties of the elementary units or pixels (such as transparency, refractive index, or optical path length) can be modified. It is also possible to encode the required spatial phase modulation onto an amplitude-limited SLM by encoding the phase onto a spatial amplitude carrier wave, such as that provided by synthetic interference fringes.The so-called Lee method is particularly useful for encoding phase modulation onto amplitude-only modulators.

[0069] FIG. 3A illustrates the steps that would be performed by data processor 210 to determine a compound hologram that is a discretized compound hologram.

[0070] In step 301, a first discretized hologram 311 is determined by determining a first two-dimensional phase distribution σ1(x,y) such that the first discretized hologram generates the desired amplitude profiles 151-153 of the pixels 151a-153a in the reconstruction space 111.

[0071] Methods for determining the first phase distribution σ1(x,y) include the Gerchberg-Saxon algorithm mentioned above or analytical methods.

[0072] The Gerchberg-Saxon algorithm, shown in Figure 5, takes as input three user-defined variables: the target intensity IR in the reconstruction space 111, the source intensity distribution Ih in the hologram plane 113, and some initial guess Φ0 for the phase in the reconstruction space 111. The algorithm iteratively propagates through the complex space between the hologram and the reconstruction space, calculating the amplitude at each plane as √I h and √I R The target intensity for shaping the point spread functions 151-153 is unit square, with side width ΔXpsf, padded with zeros according to the resolution of the SLM. The exact width of the unit square psf can be calculated by the formula ΔXpsf≦(N T1The phase estimate is determined from (λ×λ×f) / Dslm (see derivation below) and depends on the number of desired tilings of the object hologram, i.e. the second discretized hologram 312. The source amplitude is a Gaussian beam profile with shape determined using an optical beam profiler. The first phase estimate is a quadratic phase profile with curvature coefficients q and p calculated by q=π / M and P=π / N, where M×N is the SLM resolution, i.e. the number of SLM pixels in X and Y directions.

[0073] Analytical methods have shown that lossless shaping of an input Gaussian beam into a flat-top beam by using a phase-modulating SLM can be achieved by the phase pattern σ1(x,y)=[βx Φx(x)+βy Φy(y)] This can be done by calculating:

number

number

number

number

[0074] In step 302, a second phase distribution σ2(x,y) of the second discretized hologram 312 is determined based on a desired projection, such that the desired projection is reproduced as a reconstructed image 201 in the reconstruction space 111.

[0075] The second phase distribution σ2(x,y) is determined according to known methods of computer generated holography. This can be based on an iterative Fourier transform algorithm or can use machine learning optimization as demonstrated in this recently published paper in Optics Communications: Comparison of state-of-the-art Computer Generated Holography algorithms and a machine learning approach, Optics Communications Volume 505, 15 February 2022, Andreas Erik Gejl Madsen, Rene Lynge Eriksen, Jesper Gluckstad.

[0076] The determination of the first and second phase distributions σ 1 (x,y) and σ 2 (x,y) can be easily extended to 3D in the case of a 3D reconstruction space 111 .

[0077] In step 303, the second discretized hologram 312 is tiled, i.e., repeated along one or two vertical directions in a matrix, to generate a discretized tiling hologram 313. That is, the second discretized hologram 312 is tiled in a first direction, such as the x-direction, such that the N T1 The second discretized hologram 312 is tiled N times along the first direction. T1 Similarly, the second discretized hologram 312 appears N times in a second direction, such as the y direction. T2 In the case of a rectangular spatial light modulator (SLM), the hologram is tiled equally in both directions, i.e. N T =N T1 =N T2 The image is tiled according to the

[0078] In step 304 a discretized composite hologram 314 is determined by phasor multiplying the matrix of the first discretized hologram with the matrix of the tiled second discretized hologram determined in step 303 .

[0079] The first discretized hologram 311 can be represented by a matrix M1 of phase values ​​σ1(x,y). The second discretized hologram 312 can be represented by a matrix M2 of phase values ​​σ2(x,y). The tiling hologram 313 can be represented by a matrix M2 T Therefore, the discretized composite hologram is a simple addition of the respective phase values ​​M comp =M1+M2 T is given by the element-wise phasor multiplication of two matrices corresponding to

[0080] The phasor multiplication of the matrix of the first discretized hologram and the matrix of the tiled second discretized hologram is not a normal matrix multiplication, but a multiplication in which only the components at the same matrix positions i, j are multiplied. Therefore, each component exp(i M comp (i,j)) is the sum of exp(i M1(i,j)) and exp(i M2 T (i,j) where i is the

number

[0081] In step 305 , the discretized composite hologram 314 is applied to a spatial light modulator SLM to generate a phase modulation of the coherent input beam 101 and an output pixelated projection 201 in the reconstruction space 111 .

[0082] 3B illustrates the generation of a pixelated reconstructed image 201 based on a discretized composite hologram 314. The determination of the discretized composite hologram 314 is based on tiling a second discretized hologram 312 (object hologram) onto a tiling hologram 313 and phasor multiplication with the first discretized hologram 311. As illustrated, the second discretized hologram 312 is tiled or repeated six times in the x and y directions.

[0083] As described above, the first discretized hologram 311 and the second discretized hologram 312 can be determined such that the pixelated reconstructed image 201 is optimized for the 3D reconstruction space 111. For example, the holograms in this example are determined to produce an image projection of an "H" on a curved surface.

[0084] In general, a pixelated projection can be a single pixel, i.e., a point projection image, a line of pixels forming a 1D projection image, a surface projection forming a 2D image, or a space or volume projection forming a 3D projection image. Thus, the reconstruction space can be a surface or plane in two or three dimensions, i.e., a flat or curved surface, or the reconstruction space can be a volume, i.e., a three-dimensional space.

[0085] FIG. 4 shows output pixels 151a-153a in a pixel row of a pixelated projection 201. The height of an output pixel indicates the pixel amplitude. The output pixels have a width ΔXpsf in a first direction, e.g. the x-direction, of the pixel row, and adjacent output pixels are separated by a distance ΔXholo measured between the centers of adjacent pixels. Thus, the output pixel pitch in the reconstruction space 111 is given by ΔXholo. The width ΔYpsf and pixel pitch ΔYholo in a perpendicular second direction (not shown) may be equal to or different from the width and spacing in the first direction.

[0086] In order to prevent the pixels 151a to 153a from overlapping in the first discretized hologram 311, the tiling numbers NT1 and NT2 are determined so that the output pixel constraint ΔXpsf≦ΔXholo is satisfied in both the first and second directions.

[0087] ΔXholo is, ΔXholo=(NT×λ×f) / (Dslm) where NT is the number of hologram tiles to be generated on the SLM and Dslm is the size of the pixel area of ​​the SLM, assuming a square shape, i.e., equal dimensions in X and Y.

[0088] Using this formula for ΔXholo, the output pixel constraint becomes ΔXpsf≦ΔXholo ΔXpsf≦(NT1×λ×f) / Dslm NT ≧ (ΔXpsf × Dslm) / (λ × f), and similarly for the Y direction, except that the point spread function usually has the same magnitude in both directions. Dslm can be equal in both directions or different in the X and Y directions.

[0089] Thus, for a given first discretized hologram 311, the pixel width ΔXpsf is fixed and the tiling numbers NT, NT1, NT2 are therefore determined subject to the pixel constraints.

[0090] Alternatively, if the tiling numbers NT, NT1, NT2 are predetermined, the pixel width ΔXpsf, and therefore the first discretized hologram 311, must be determined subject to pixel constraints.

[0091] It is also possible that neither the given first discretized hologram 311 nor the tiling numbers NT, NT1, NT2 are pre-determined, in which case an iterative calculation process can be used to determine both the first discretized hologram 311 and the tiling numbers subject to pixel constraints.

[0092] The above equations for determining the first discretized hologram 311, the second discretized hologram 312 and the pixel constraints are based on Fourier lens reconstruction. Similar equations for the lensless Fresnel setup can be obtained in a similar manner.

[0093] The method of generating a pixelated projection in the reconstruction space has several applications, including, for example: Multiphoton excitation. In multiphoton applications, such as two-photon applications, speckle dramatically degrades the excitation in the reconstruction space due to the intensity-squaring effect, where side lobes of the amplitude curves 121-123 create interference patterns. For example, multiphoton excitation can be used for optical excitation of biological materials, such as living cells, in vivo or in vitro, e.g. in neurophotonics and optogenetics. Another example is 3D stimulation of neurons.

[0094] 3D printing. The reconstructed image in a 2D or 3D plane can be used for 3D printing of an object. 3D printing includes photopolymerization, e.g., two-photon photopolymerization, using the generated reconstructed image. A detailed embodiment, referred to as volume additive manufacturing (VAM), is described in more detail below. Holographic display. Laser material processing, e.g. one shot material processing. Photolithography. Quantum Optics and Photonics. Structured illumination microscopy. Treatment of the skin, for example cosmetic treatment of the skin, for example for the removal of tattoos.

[0095] FIG. 6A is a diagram showing an example of phase fluctuations of a first discretized hologram 311 and a tiling hologram 313 into which an enlarged portion corresponding to a second discretized hologram 312 has been inserted.

[0096] 6B shows an example of a pixelated projection 201 and individual pixels of the projected image, with the inset zoomed in portion showing the individual output pixels.

[0097] HoloTile for Volumetric Additive Manufacturing (VAM) Tomographic volumetric additive manufacturing (VAM) is a 3D bioprinting method that simultaneously solidifies an entire three-dimensional object by irradiating a cell-loaded hydrogel with dynamically reconfigured light patterns from multiple angles. Tomographic VAM can, in principle, bioprint complex centimeter-scale organoids in seconds instead of hours, even without support structures. Typically, a violet light source is applied for curing. Tomographic VAM has the potential to fabricate highly complex structures with higher throughput than conventional layer-by-layer additive manufacturing, and with a wide range of printable materials, but currently its resolution is limited by the large etendue of the applied illumination system. Typically, etendue is a property of light in an optical system that essentially characterizes how much light is spread out in an area and angle. It corresponds, for example, to the beam-parameter product (BPP) in Gaussian beam optics.

[0098] Currently, the light-inefficient Digital Light Projection of a powerful multimode light source is applied to the tomographic VAM based on a simple binary on / off amplitude modulation. By rethinking the entire optical addressing for the tomographic VAM, not only can the light inefficiency and etendue bottleneck inherent in the current bioprinting systems be avoided, but real-time aberration correction can be applied using the holographic system or method according to the present invention, hereafter referred to as "Holotile".

[0099] The experimentally demonstrated >90% photon-efficient phase-only projection of holotile essentially solves the challenge of fast, speckle-free stereolithography for high-fidelity, ultrafast 3D bioprinting by multiplexing the point spread function (PSF) of the phase shape of our holographic system to match the spatial inter-spectral spacing in the far-field reconstruction resulting from tiling on a high-resolution phase-only spatial light modulator. The main advantages of this holotile light engine include a 100x speedup over standard holography, substantial speckle reduction due to matched tiling and PSF shaping, real-time dynamic pixel discretized projection, lens-free scaling and zoom with software-adaptive phase encoding, and / or very fast camera-in-the-loop aberration control.

[0100] FIG. 7 shows the reconstruction of the SDU logo mark with holotiles on an LCoS spatial light modulator for different output diffraction pattern resolutions.

[0101] Holotile (experimental results of phase-only projection diffraction patterns with photon efficiency of over 90% are shown in Figure 7) aims to solve the challenge of fast, speckle-free stereolithography without the need for time-averaging techniques, a challenge that exists in several fields of optics, biophotonics, additive manufacturing, display technologies, and other areas.

[0102] The holotile, i.e., a holographic system or method according to the present invention, provides fast, speckle-reduced digital holography by multiplexing the phase-shaped point spread function (PSF) of the holographic system to match the spatial inter-spectral spacing in the far-field reconstruction resulting from tiling on a high-resolution SLM or Diffractive Optical Element (DOE). In particular, the holotile offers four new and unique key capabilities as a CGH modality for high-resolution phase-only SLMs, reconfigurable DOEs, or novel metasurfaces / meta-optical elements (MOEs): 100x speed improvement over standard CGH modalities Significant speckle reduction through consistent tiling and PSF shaping Real-time dynamic output of "pixel" discretized digital holograms Lens-free scaling or zooming with software-adaptive holotile phase encoding

[0103] Extremely fast camera-in-the-loop in-situ optimization is possible, with a speed increase of 100x over standard CGH modalities, making holotiles potentially very attractive for a variety of applications, including: Ultra-fast additive manufacturing Parallel Laser Material Processing High speed laser engraving, welding and machining Two-photon excitation in optogenetics and voltage imaging Multi-color and multi-plane diffraction Highly photon-efficient phase-only display technology Realization of real-time adaptive optics including aberration correction · Space-time focusing (TF holotile) Digital Quantum Holography etc.

[0104] Future research and development will enable the demonstration of some of these potential advantages of the holotile in one or more of the above mentioned dynamic or static light diffraction applications. The aim is to use the holotile as a stand-alone light engine that can be easily integrated, both hardware-wise and software-wise, in existing optical and photonic setups for both industry and academia.

[0105] Holotiles for volumetric bioprinting Tomographic volumetric additive manufacturing (VAM) is a relatively recent 3D bioprinting method that simultaneously solidifies an entire three-dimensional object by irradiating, for example, a cell-loaded hydrogel with dynamic light patterns in the violet wavelength range from multiple angles. Tomographic VAM can print complex centimeter-scale objects in seconds instead of hours, even without support structures. Although tomographic VAM has the potential to produce highly complex structures with a higher throughput and a wider range of printable materials than conventional layer-by-layer additive manufacturing, its resolution is currently limited by the typically large étendue of the applied illumination systems. Typically, so-called Digital Light Projection (DLP) illumination systems are applied based on very light and inefficient digital micromirrors operating in a binary amplitude mode. For sparse tomographic projections, typically calculated by the Radon transform, only a small fraction of the digital micromirrors are deflected towards the 3D bioprinting volume, thus essentially requiring a substantial light source, which is typically a multimode large étendue source.

[0106] Figure 8 shows a tomographic VAM system based on a phase-only SLM encoded with a holotile, i.e., a holographic system or method according to the invention. Figure 9 shows a holotile for tomography and real-time aberration-corrected VAM using a simple camera-in-the-loop approach.

[0107] By rethinking optical addressing for tomographic VAM, this inherent bottleneck of current 3D bioprinting system configurations can be circumvented. The following are just a few of the inherent advantages that can be gained by using the previously described holotile approach, illustrated diagrammatically in Figures 8 and 9: · The phase-only modality of holotile provides a significantly more efficient light modulation engine. A side effect of higher optical efficiency is the ability to use single spatial mode laser diode sources with optimal optical etendue, improving spatial resolution for 3D bioprinting. Spatially coherent holotile projection offers the advantage of 100x faster refresh rates than standard phase-only diffractive optics or Computer Generated Holography (CGH) and unique 3D Point Spread Function (PSF) shaping capabilities. The combination of pattern projections in Volume Additive Manufacturing (VAM) can be spatially controlled by unique PSF shaping to produce higher fidelity 3D bioprinting objects. · The number of optical components required is less in a holotile light projection engine. Fast refresh rate enables real-time aberration-corrected VAM.

[0108] Ultimately, the Holotile holographic system and method is expected to pave the way for light-efficient VAM of centimeter-scale 3D bioprinting objects with optimal etendue and micron-sized features in tens of seconds.

[0109] For certain configurations of holotiles for volumetric addressing, it may be advantageous to apply arbitrarily shaped PSF encodings such as spirals, circles, rings, straight edges, crosshairs, etc. An experimental example of such PSF shaping is shown in FIG.

Claims

1. determining a first discretized hologram having a phase distribution in a plane, the first discretized hologram being determined to produce a desired amplitude profile of an output pixel in a reconstruction space; determining a second discretized hologram having a phase distribution determined to produce a desired projection in the reconstruction space; determining or generating a tiled hologram by tiling the second discretized hologram one or more times (NT, NT1, NT2) in one or two directions, the number of tilings and the first discretized hologram being determined according to an output pixel constraint determined based on a magnitude (ΔXpsf, ΔYpsf) of an amplitude profile of an output pixel in the reconstruction space and a pixel pitch (ΔXholo, ΔYholo) in the reconstruction space; determining a composite hologram based on a phasor multiplication of the first discretized hologram and the tiling hologram; phase modulating a coherent input beam based on the composite hologram and directing the phase modulated beam towards a reconstruction space to generate a pixelated projection in the reconstruction space; A method for generating a pixelated projection in a reconstruction space, comprising:

2. 2. The method of claim 1, wherein the pixel constraint requires that the magnitude (ΔXpsf, ΔYpsf) of an output pixel amplitude profile is less than or equal to the pixel pitch (ΔXholo, ΔYholo).

3. 3. The pixelated projection generating method of claim 1 or 2, wherein in the tiling hologram determination step, the number of tilings (NT, NT1, NT2) of the tiling hologram is determined based on the pixel constraint and the magnitude (ΔXpsf, ΔYpsf) of the amplitude profile of the output pixel.

4. 4. The pixelated projection generating method according to claim 1, wherein in the step of determining the first discretized hologram, a magnitude (ΔXpsf, ΔYpsf) of an amplitude profile of an output pixel is determined subject to the pixel constraint and the number of tilings (NT, NT1, NT2) of the tiling hologram.

5. 5. The method for generating a pixelated projection according to claim 1, wherein the first discretized hologram is determined according to a desired magnitude (ΔXpsf, ΔYpsf) of the amplitude profile of the output pixel.

6. 6. The method for generating a pixelated projection according to claim 5, wherein the first discretized hologram is determined such that at least 70% of the total power of the amplitude profile in the reconstruction space falls within the range of an output of the pixel.

7. 7. The method for generating a pixelated projection according to claim 1, wherein in the step of determining the second discretized hologram a phase distribution is determined such that at least some of the output pixels of the desired projection are determined to be reconstructed in the reconstruction space at different positions along different propagation directions of the input beam.

8. 8. The method for generating a pixelated projection according to claim 1, wherein the phase modulation comprises controlling a spatial light modulator (SLM) to generate a discretized phase distribution corresponding to the first discretized hologram, the tiling hologram, or the composite hologram.

9. 9. The method for generating a pixelated projection according to claim 1, wherein the reconstruction space is a surface in two or three dimensions, or a volume in three dimensions.

10. A data processor arranged to carry out the steps of claim 1; a light source generating the coherent input beam; a spatial light modulator (SLM) arranged to phase modulate the coherent input beam based on the composite hologram, and directing the phase modulated beam towards the reconstruction space to generate a pixelated projection in the reconstruction space; 1. A holographic system arranged to generate a pixelated projection in a reconstruction space, comprising:

11. a first fixed phase mask configured to have a discretized phase distribution according to the first discretized hologram, and a spatial light modulator arrangement arranged to generate a phase modulation according to the tiling hologram; or a spatial light modulator (SLM) arranged to generate a phase modulation according to the first discretized hologram, and a second fixed phase mask configured to have a discretized phase distribution according to the tiling hologram; or a first fixed phase mask configured to have a discretized phase distribution according to the first discretized hologram, and a second fixed phase mask configured to have a discretized phase distribution according to the tiling hologram; or a first fixed phase mask configured to have a discretized phase distribution according to the compound hologram; and a light source generating the coherent input beam, the light source being arranged to transmit light through two discretized phase distributions generated by two of the first fixed phase mask, the second fixed phase mask, the spatial light modulator, and the spatial light modulator arrangement, or generated by a first fixed phase mask configured to have a discretized phase distribution according to the composite hologram, and directing the phase-modulated beam towards a reconstruction space to generate a pixelated projection in the reconstruction space; 13. A holographic system arranged to generate a pixelated projection in a reconstruction space according to the method of claim 1, comprising:

12. the spatial light modulator arrangement comprising a spatial light modulator and an optical tiling system; the spatial light modulator is arranged to generate the second discretized hologram or the tiling hologram; 12. The holographic system of claim 11, wherein the optical tiling system is arranged to tile the second discretized hologram or the optical tiling system is arranged to further tile the tiling hologram.

13. The holographic system of claim 12 , wherein the optical tiling system comprises an imaging system, such as a lens array or a mirror scanner, configured to generate the tiling and to project incident light into the reconstruction space.

14. A computer program comprising instructions for causing a data processor to carry out the steps of the method according to claim 1.

15. Multiphoton excitation of living cells, Printing 3D objects, Holographic display, Quantum Optics and Photonics, Photopolymerization, e.g. two-photon photopolymerization; Laser material processing, such as one-shot material processing, Optical lithography, Structured illumination microscopy, Skin treatments, such as cosmetic skin treatments, Combined with spatiotemporal focusing of ultrafast pulsed lasers for multiphoton excitation at selected depth layers, Ultra-rapid additive manufacturing, Laser material processing performed in parallel; Fast laser engraving, welding and machining Two-photon excitation in optogenetics and voltage imaging Polychromatic and multifaceted diffraction Photon-efficient phase-only display technology Real-time adaptive optics embodiments, including aberration correction; and Spatiotemporal focusing (TF) 12. A method using the method of claim 1 or the system of claim 10 or 11, comprising:

16. 12. A method of using the method according to claim 1 or the system according to claim 10 or 11 for printing a 3D object using Volumetric Additive Manufacturing (VAM), preferably for printing a 3D object intended for medical applications, preferably a biocompatible implant, an artificial organ or part thereof or a similar object.

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