WO2019009722A2

WO2019009722A2 - Interference light field reconstruction using sparsely distributed light points

Info

Publication number: WO2019009722A2
Application number: PCT/NL2018/050445
Authority: WO
Inventors: Martin FRANSEN
Original assignee: Stichting Nederlandse Wetenschappelijk
Priority date: 2017-07-05
Filing date: 2018-07-05
Publication date: 2019-01-10
Also published as: WO2019009722A3; NL2019189B1

Abstract

An optical system is described that is adapted to reconstruct an interference light field comprising: a spatial light modulator comprising an array of pixels optically aligned to an optical element comprising an array of light point forming elements formed in a first transparent substrate, each light point forming element including a light receiving area at the light receiving face of the first substrate and an associated light transmitting area at the light transmitting face of the first substrate; the light receiving area of a light point forming element being arranged to receive light from a reference light source and to form a light point that emits light out of the light emitting area; at least one mask element and/or refractive element in each light point forming element causing the locations of the points of light to be arranged a-periodically or randomly in at least one direction in a plane of the substrate; and, the pixels of the spatial light modulator controlling the intensity and, optionally, the phase of the light transmitted by the points of light, the transmitted light forming the interference light field at a predetermined location relative to the optical system.

Description

W027717-WTd

Interference light field reconstruction using sparsely distributed light points Field of the invention

The invention relates to interference light field reconstruction using sparsely distributed light points, and, in particular, though not exclusively, to methods and optical systems for interference light field reconstruction using sparsely distributed light points, an optical element for generating a sparse distribution of light points, a method for generating control information for use in such system and a computer program product using such method.

Background of the invention Holography is a diffraction-based coherent imaging technique in which a 3D object can be reproduced on the basis of a flat 3D holographic plate. Holography typically includes the steps of holographic recording, which includes capturing a 3D interference light field pattern, and holographic playback, which includes using the captured interference light field to reconstruct the 3D light field.

During holographic recording a wide beam of coherent light is directed onto an object that scatters incident light. The part of the beam that does not hit the object passes by unscattered. Then, the scattered light, which may be considered as the light field that ultimately is to be reconstructed, propagates and interferes with the unscattered coherent light that passed the object. A resulting interference light field is subsequently recorded on a holographic plate, the hologram, that is capable of capturing the amplitude, phase, and wavelength information of the object.

During holographic playback the recorded interference light field pattern is illuminated with a coherent light beam (also referred to as reference light). The hologram diffracts the incoming reference light, resulting in a light field identical to the original scattered light field. The hologram thus stores both phase information and amplitude information of the light field radiated from the sample. A person looking to the reproduced light field observes a holographic image of the small sample.

The interference light field may be captured with a digital sensor array, typically with a CCD camera. The resolution of the digitally captured holograms is however limited by the pixel size of the used sensor. Instead of capturing an interference light field, a desired light field may be generated using a computer. Typically, a computer-generated hologram involves the generation of holographic data (i.e. data including light intensity and a phase values) representing an interference light field. The holographic data are used to control a spatial light modulator (SLM). Coherent light is directed onto the SLM using e.g. a laser, and the resulting output is a modulated light pattern.

In order to produce a 3D holographic image of usable size and viewing angle, a large amount holographic data need to be processed requiring an SLM having a large number of pixels, e.g. 10⁸-10¹⁰. Additionally, pixels should be substantially smaller than a micron, i.e. smaller than a micron to eliminate grating effects and to provide a large viewing angle, while still producing light of sufficient intensity. The pixels of the SLM must be positioned relative to one another with a high degree of accuracy while being capable of modulating coherent light, e.g. produced by a laser. These requirements are extremely demanding and expensive to achieve in practice and so far prevents practical use of computer-based holography techniques in commercial products.

US6753990 discloses holographic display devices comprising a spatial light modulator that are configured to reproduce a computer-generated interference light field. In order to address the problem of the large number of pixels a combination of a high-speed electrically addressable SLM (EASLM) and a high-resolution optically addressable SLM (OASLM) is used for playout of a computer-generated hologram. Images displayed on an EASLM are sequentially transferred to different parts of an OASLM before the whole image on the OASLM is presented to the viewer. Hence, part of the high-bandwidth capabilities of the OASLM are given up in order to make use of the high-resolution capabilities of the optically addressable SLM. Moreover, the overall design of the holographic display device is complex in terms of hardware and software and less suitable for simple and sheep commercial applications.

US2010103486 describes a holographic reconstruction device comprising a pixelated light modulator illuminated by at least one light source, and a focusing optical element field arrangement which images the light sources in an image plane after the light modulator. For the reconstruction, only one order of diffraction of the Fourier spectrum of the hologram should be used. To that end, the light modulator is provided with an assigned filter- aperture field arrangement which is located in the area of the image plane of the light source images and which has a plurality of aperture openings. The apertures are positioned to select a diffraction order for presentation to an observer.

For many holographic applications, it is sufficient if holograms are reproduced with less accuracy than the theoretical physical limits (in terms of resolution, dynamic range, noise, contrast, etc.... ). Reconstruction or at least partial reconstruction of an interference pattern by spatially under-sampling using e.g. a spatial light modulator of a predetermined spatial resolution would be sufficient in many applications. However, due to the Nyquist limit, spatial under-sampling causes interference patterns to be incorrectly reconstructed.

Hence, there is a need in the art for improved methods and systems that enable simple reconstruction of holographic images using limited resources with a reduced number of artefacts. In particular, there is a need in the art for improved methods and systems that enable the generation of holographic images using simple optics and limited computational resources.

Summary of the invention

As will be appreciated by one skilled in the art, aspects of the present invention may be embodied as a system, method or computer program product. Accordingly, aspects of the present invention may take the form of an entirely hardware embodiment, an entirely software embodiment (including firmware, resident software, micro-code, etc.) or an embodiment combining software and hardware aspects that may all generally be referred to herein as a "circuit," "module" or "system". Functions described in this disclosure may be implemented as an algorithm executed by a microprocessor of a computer. Furthermore, aspects of the present invention may take the form of a computer program product embodied in one or more computer readable medium(s) having computer readable program code embodied, e.g., stored, thereon.

Any combination of one or more computer readable medium(s) may be utilized. The computer readable medium may be a computer readable signal medium or a computer readable storage medium. A computer readable storage medium may be, for example, but not limited to, an electronic, magnetic, optical, electromagnetic, infrared, or semiconductor system, apparatus, or device, or any suitable combination of the foregoing. More specific examples (a non- exhaustive list) of the computer readable storage medium would include the following: an electrical connection having one or more wires, a portable computer diskette, a hard disk, a random access memory (RAM), a read-only memory (ROM), an erasable programmable read-only memory (EPROM or Flash memory), an optical fiber, a portable compact disc read-only memory (CD-ROM), an optical storage device, a magnetic storage device, or any suitable combination of the foregoing. In the context of this document, a computer readable storage medium may be any tangible medium that can contain, or store a program for use by or in connection with an instruction execution system, apparatus, or device.

A computer readable signal medium may include a propagated data signal with computer readable program code embodied therein, for example, in baseband or as part of a carrier wave. Such a propagated signal may take any of a variety of forms, including, but not limited to, electro-magnetic, optical, or any suitable combination thereof. A computer readable signal medium may be any computer readable medium that is not a computer readable storage medium and that can communicate, propagate, or transport a program for use by or in connection with an instruction execution system, apparatus, or device.

Program code embodied on a computer readable medium may be transmitted using any appropriate medium, including but not limited to wireless, wireline, optical fiber, cable, RF, etc. , or any suitable combination of the foregoing. Computer program code for carrying out operations for aspects of the present invention may be written in any combination of one or more programming languages, including a functional or an object oriented programming language such as Java(TM), Scala, C++, Python or the like and conventional procedural programming languages, such as the "C" programming language or similar programming languages. The program code may execute entirely on the user's computer, partly on the user's computer, as a stand-alone software package, partly on the user's computer and partly on a remote computer, or entirely on the remote computer, server or virtualized server. In the latter scenario, the remote computer may be connected to the user's computer through any type of network, including a local area network (LAN) or a wide area network (WAN), or the connection may be made to an external computer (for example, through the Internet using an Internet Service Provider).

Aspects of the present invention are described below with reference to flowchart illustrations and/or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of the invention. It will be understood that each block of the flowchart illustrations and/or block diagrams, and combinations of blocks in the flowchart illustrations and/or block diagrams, can be implemented by computer program instructions. These computer program instructions may be provided to a processor, in particular a microprocessor or central processing unit (CPU), or graphics processing unit (GPU), of a general purpose computer, special purpose computer, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer, other programmable data processing apparatus, or other devices create means for implementing the functions/acts specified in the flowchart and/or block diagram block or blocks.

These computer program instructions may also be stored in a computer readable medium that can direct a computer, other programmable data processing apparatus, or other devices to function in a particular manner, such that the instructions stored in the computer readable medium produce an article of manufacture including instructions which implement the function/act specified in the flowchart and/or block diagram block or blocks.

The computer program instructions may also be loaded onto a computer, other programmable data processing apparatus, or other devices to cause a series of operational steps to be performed on the computer, other programmable apparatus or other devices to produce a computer implemented process such that the instructions which execute on the computer or other programmable apparatus provide processes for implementing the functions/acts specified in the flowchart and/or block diagram block or blocks.

The flowchart and block diagrams in the figures illustrate the architecture, functionality, and operation of possible implementations of systems, methods and computer program products according to various embodiments of the present invention. In this regard, each block in the flowchart or block diagrams may represent a module, segment, or portion of code, which comprises one or more executable instructions for implementing the specified logical function(s). It should also be noted that, in some alternative implementations, the functions noted in the blocks may occur out of the order noted in the figures. For example, two blocks shown in succession may, in fact, be executed substantially concurrently, or the blocks may sometimes be executed in the reverse order, depending upon the functionality involved. It will also be noted that each block of the block diagrams and/or flowchart illustrations, and combinations of blocks in the block diagrams and/or flowchart illustrations, can be implemented by special purpose hardware-based systems that perform the specified functions or acts, or combinations of special purpose hardware and computer instructions.

It is an objective of the invention to reduce or eliminate at least one of the drawbacks known in the prior art. In particular, the methods and systems described in this disclosure are aimed at reconstructing or at least partially reconstructing an interference light field using a spatial light modulator in combination with an optical element that is configured to generate a sparse a-periodic or random distribution of light points. The optical systems described in this disclosure use the principles underlying compressive sensing to reconstruct interference light fields without artefacts, or at least with a reduced number of artefacts, on the basis of a set of sparsely distributed light points.

In an aspect, the invention relates to an optical system adapted to reconstruct or at least partially reconstruct an interference light field wherein the optical system may include a spatial light modulator comprising an array, preferably a periodic array, of pixels optically aligned to an optical element comprising an array, preferably a periodic array, of light point forming elements formed in a first transparent substrate.

In an embodiment, the light point forming elements being arranged to form an a-periodic or random distribution of light points on the basis of light of a reference light source.

In an embodiment, each light point forming element of the array of light point forming elements may comprise at least one mask element comprising at least one aperture and/or at least one refractive element comprising at least one optical axis, wherein the positions of the apertures and/or optical axes of the light point forming elements are arranged a-periodically or randomly in a plane of the substrate.

In an embodiment, the light point forming element may include a light receiving area at the light receiving face of the first substrate and an associated light transmitting area at the light transmitting face of the first substrate.

In an embodiment, the light receiving area of a light point forming element may be arranged to receive light from a reference light source and to form a point of light (a light point) that emits light out of the light emitting area.

In an embodiment, at least one mask element and/or refractive element in each light point forming element causing the locations of the light points to be arranged a- periodically or randomly in at least one direction in a plane of the substrate.

In an embodiment, pixels of the spatial light modulator may control the intensity and, optionally, the phase of the light transmitted by the points of light. The transmitted light may form the interference light field at a predetermined location relative to the optical system.

The invention enables accurate reconstruction of a predetermined interference light field in an efficient and simple way using a spatial light modulator and an optical element. The optical element is configured to generate a sparsely distribution of light points on the basis of light originating from the spatial light modulator. The light points formed by the light point forming elements of the optical element are not active opto-electronic light sources, e.g. laser diodes that generate light by converting charge carriers into light. Rather, the light points are light samples or focussing points (formed by e.g. apertures and/or focal points of refractive elements), which form light points when the optical element is illuminated with light of a reference light source.

The optical element transforms the spatially under-sampled light field of a spatial light modulator into a sparsely distributed set of light points. The optical element is further arranged to add a sub-wavelength "a-periodicity" or "randomness" to the position of the light points in the light point forming elements in order to generate an a-periodically or randomly distributed set of light points, wherein the spatial light field modulator may control the phase and/or amplitude modulation of the light emitted by the light points.

The a-periodic or random distribution light points provides the effect of suppression or elimination of high order diffraction modes. Further, it suppresses aliasing effects. The random distribution or a-periodic distribution of light points will avoid a situation wherein at certain positions the phase of the light emitted from the light points coincides in the same way so thathigher order diffraction modes are suppressed. . Thus, the a-periodic distribution of the light points is arranged such that in each point of the space where reconstruction of a predetermined interference light field is desired, the phases due to the optical path lengths to the light points vary sufficiently in order to suppress artefacts. In other words, each point in space is unique in terms of optical path lengths/phases to the light points. Additionally and inherently, the a-periodic distribution suppresses possible aliasing effects in the set of light points since aliasing effects are inherently related to periodic sampling methods.

The spatial light modulator in combination with the optical element may be regarded as an optical phased array in which the average distance between the light points is allowed to be much larger than the wavelength of the used light (e.g. light of the visible spectrum between 400 and 700 nm), while at the same time minimising 'grating' effects and effects due to spatial under-sampling. As will be described hereunder in greater detail, the optical element further allows simultaneous processing of multiple wavelengths.

The invention is scalable and can be optimized with respect required resources (data, bandwidth, computing power, etc.). Applications of the invention may include but are not limited to: holographic displays for rendering holographic video and still images for entertainment, interfacing, lithography, metrology, etc. In an embodiment, each light point forming element may comprise a masking element comprising at least one aperture.

In another embodiment, each light point forming element may comprise a polarizing layer comprising at least one area that does not exhibit the polarization effect.

The at least one aperture may be substantially smaller than the area of pixels of the spatial light modulator.

In embodiment, the masking element may be an opaque plate comprising one or more apertures.

In an embodiment, the point light forming elements may be configured such that location of the point lights exhibit an a-periodic or random offset relative to each other. The a-periodic or random offset may be in one or more directions in the plane of the substrate and/or in a direction perpendicular to the plane of the substrate.

In an embodiment, the offset may be smaller than the wavelength of the light of the reference light.

In an embodiment, apertures in mask elements of different light point forming elements may have different positions.

In an embodiment, mask elements of different light point forming elements may be arranged in different planes of the substrate.

In an embodiment, the mask elements may be arranged at the light receiving area of the light point source forming elements.

In an embodiment, elements of a transparent material of different dimensions being formed over different apertures.

In an embodiment, each light point forming element may comprise at least one refractive element arranged to focus light in a point, preferably the optical axis of different light point forming elements being located at different positions relative to the centre of the light receiving areas.

In a further embodiment, refractive elements of different light point forming elements may have different focal points.

In an embodiment, different positions of the optical axes and/or the different focal points of the light point forming elements may be varied a-periodically or randomly within a predetermined range.

In an embodiment, the light receiving area of a light point source forming element may be configured as a refractive element.

In an embodiment, the light transmitting area may include a mask element comprising at least one aperture.

In a further embodiment, the light refractive element may be configured to focus at least part of the light received by the refractive element onto the at least one aperture.

In an embodiment, the refractive element may be configured to receive light originating from two or more pixels of the spatial light modulator and to focus the light from the two or more pixels onto two or more apertures in the masking element of the light point source forming element respectively.

In an embodiment, the length of optical paths of different light point source forming elements may vary a-periodically or randomly within a predetermined range of optical path lengths

In an embodiment, the distance between a plane through the substrate and the light transmitting areas of different light point forming elements may vary a-periodically or randomly within a predetermined range.

In an embodiment, at least a second transparent substrate may be fixed to the light transmitting face of the first transparent substrate, the refractive index of the second transparent substrate being larger than the medium at the light transmitting side of the second substrate.

In an embodiment, the pixels of the spatial light modulator may be configured to control the intensity and, optionally, the phase of the light emitted by the points of light, the light of the points of light reconstructing or at least partially reconstructing the light field at a predetermined location relative to the optical element.

In an embodiment, the spatial light modulator may be an electrically addressable spatial light modulator.

In an embodiment, the optical system may further comprise: a computer connected to the electrically addressable spatial light modulator and a storage medium associated with the computer, the storage medium comprising control information, the computer being adapted to use the control information to control the electrically addressable spatial light modulator so that each point of light emits light of a predetermined intensity and/or phase for reconstructing the light field.

In an aspect, the invention may relate to a method for reconstructing or at least partially reconstructing an interference light field using an optical system comprising an optical element and a spatial light modulator, the method comprising: applying coherent light of a reference light source to the light receiving face of the optical element, the optical element comprising an array of light point forming elements in a first transparent substrate, each light point forming element including a light receiving area at the light receiving face of the first substrate and an associated light transmitting area at the light transmitting face of the first substrate; the light receiving areas of the light point forming elements receiving light from the reference light source and forming a light point that emits light out of the light emitting area; wherein at least one mask element and/or refractive element in each light point forming element cause the locations of the light points to be arranged a-periodically or randomly in at least one direction in a plane of the first substrate; a computer controlling the pixels of the spatial light modulator, the pixels being optically aligned to the light point forming elements, the pixels of the spatial light modulator controlling the intensity, and optionally, the phase of the light emitted by each light point, the light emitted by each light point forming a g light field at a predetermined location the transmitted light forming the interference light field at a predetermined location relative to the optical system.

In an embodiment, the pixels may be controlled on the basis of holographic data, the holographic data representing intensity values and, optionally phase values, of the light to be emitted by each of the light points, the holographic data enabling the optical system to reconstruct a predetermined holographic image.

In another aspect, the invention relates to a computer-implemented method for determining holographic data for a spatial light modulator, the spatial light modulator and an optical element forming an optical system arranged to reconstruct an interference light field, the method comprising

receiving light field information, the light field information including intensity values l_m and phase values <t>_m associated light field positions p_m (m=1 , ... ,t); receiving optical model information, the optical model information being associated with an optical element comprising an array of light point forming elements in a substrate, the light point forming elements being arranged to form an a-periodic or random distribution of light point on the basis of light of a reference light source, the optical model information including the locations of the light points and the wavelength of the light emitted by the light points; for each light point k (k=1 ,... ,n) determining distance d_k,_m between light point k and light field position pm (m=1 , ...t) and calculating an intensity ik and, optionally, phase φκ of light to be emitted by each light point on the basis d_k._m and the light field information.

The invention may also relate of a computer program product comprising software code portions configured for, when run in the memory of a computer, executing any of the method as described above.

The invention will be further illustrated with reference to the attached drawings, which schematically will show embodiments according to the invention. It will be understood that the invention is not in any way restricted to these specific embodiments.

Brief description of the drawings FIG. 1A and FIG. 1 B depict an optical system according to one embodiment of the invention;

Fig. 2A and 2B depict cross-sectional views of optical systems according to various embodiments of the invention;

Fig. 3A-3C depict cross-sectional views of optical elements according to various embodiments of the invention;

Fig. 4A and 4B depict cross-sectional views of optical systems according to further embodiments of the invention;

Fig. 5A-5C depict cross-sectional views of optical systems according to yet other embodiments of the invention; FIG. 6 illustrates the determination of holographic data for reconstruction of a light field using an optical system according to an embodiment of the invention;

Fig. 7 depicts a flow diagram of a method for determining holographic data for an optical system according to one embodiment of the invention;

FIG. 8 illustrates the determination of holographic data for reconstruction of a light field using an optical system according to another embodiment of the invention;

Fig. 9 depicts a flow diagram of a method for determining holographic data for an optical system according to another embodiment of the invention;

FIG. 10 depicts an optical element according to an embodiment of the invention;

FIG. 11 illustrates the generation of an interference light field using a conventional optical system;

FIG. 12 illustrates the generation of an interference light field using an optical system according to an embodiment of the invention;

FIG. 13 illustrates the generation of an interference light field using an optical system according to an embodiment of the invention;

FIG. 14A-14C is a photograph of a reconstructed interference light field;

FIG. 15 is a block diagram illustrating an exemplary data computing system that may be used for executing methods and software products described in this disclosure.

Detailed description

The systems and methods described in this application address this problem. The optical systems and methods described in this application transform a spatially under- sampled light field of a spatial light modular into a sparsely distributed set of light points. A sub-wavelength a-periodicity or randomness can be added to the locations of the sparsely distributed set of light points so that artefacts due to the under-sampling can be eliminated or at least substantially reduced. Embodiments of the invention will be described hereunder in greater detail.

FIG. 1A and FIG. 1 B depict an optical system according to one embodiment of the invention. The optical system is configured to reconstruct a predetermined interference light field that may represent a holographic image of at least one object. The optical system as shown in Fig. 1A and 1 B may comprise an optical arrangement 109 comprising a spatial light controlling means 104, e.g. a spatial light modulator, and an optical element 108 configured to form spatially distributed light points on the basis of light originating from a reference light source 102. The spatial light controlling means may comprise an array of controllable pixels, which may be regarded as a regular distribution of closely packed "light sources" when it receives light from the reference light source.

As shown in Fig. 1A, the optical element may comprise a substrate 110, preferably a transparent substrate, including an array, preferably a periodic array, of so- called light point forming elements 112. Each light point forming element may include a light receiving area 114 at the light receiving face of the substrate and an associated light transmitting area 116 at the light transmitting face of the substrate. The light receiving area of a light point forming element may be arranged to receive light from the reference light source and to form a light point that emits light 120 out of the light emitting area. One or more mask elements 119 and/or refractive elements in each light point forming element may cause the locations of the light points to be arranged a-periodically or randomly in at least one direction in the plane of the substrate.

As shown in Fig. 1 B, the light points may be arranged to emit light such that a predetermined interference light field can be reconstructed at a predetermined location 117 relative to the light points.

The optical element may be configured to transform the light of a reference light source or the light of a spatial light modulator (representing an array of closely packed light sources) into a sparsely distribution of light points, wherein the dimensions of the pixels of the spatial light controlling means are substantially larger than the dimensions of the light points. Additionally, the optical element may be configured to introduce an a-periodicity or a randomness in the distribution of the light points. This way, the optical element enables the optical system to decrease artefacts that occur when trying to reconstruct a light field using an under-sampled light field data.

The spatial light controlling means may be configured to control the properties of light 120, e.g. the intensity, phase and/or polarization emitted by each light point. In an embodiment, the optical element may be configured not to modify the properties of the light emitted by the spatial light controlling means.

In an embodiment, the spatial light controlling means may be positioned between the reference light source and the optical element (e.g. a configuration as shown in Fig. 1A). Hence, in that case, the spatial light controlling means controls the light that is incident on the light receiving face of the optical element. In another embodiment, the optical element may be positioned between the reference light source and the spatial light controlling means. In that case, the spatial light controlling means controls the light that exits the light emitting face of the optical element.

In an embodiment, the optical element may be fixed to the light emitting face or light receiving face of the spatial light controlling means 104 so that the optical element is in close proximity to the spatial light modulator (as schematically depicted in Fig. 1 B). In an embodiment, the optical element may be embodied as a sheet or a foil that can be attached or fixed to the spatial light modulator. In another embodiment, the optical element may form an integral part of the spatial light controlling means.

In an embodiment, the optical arrangement, in particular the spatial light controlling means of the optical arrangement, may be controlled by a computer. In that case, the spatial light controlling means may include or may be configured as (part of) a pixelated spatial light modulator (SLM). The pixels of the SLM may be individual addressable by the computer so that it can individually control the properties of the light (e.g. intensity, phase and/or polarization) transmitted by each pixel. The spatial light modulator may be a transmitting-type SLM or a liquid crystal display (LCD).

In case of a transmitting-type SLM, a pixel of the SLM may comprise a stack of layers, wherein each layer is configured to influence one or more properties of the light that passes the pixel. For example, a first layer may be configured to control a phase and a second layer may be configured to control an intensity of light that passes the pixel.

In another embodiment, the spatial light controlling means may be implemented as a static spatial light controlling means comprising pixels that are not controlled by a computer. In that case, each pixel of the spatial light controlling means may comprise one or more layers configured to influence one or more properties of the light that passes the pixel according to a fixed value.

In case of a computer-controlled spatial light controlling means, the optical system of Fig. 1A and 1 B may comprise a computer 105 connected to the optical arrangement and a storage medium 107 comprising computer-generated control information. The control information may define for each light point a light intensity value and/or a phase value. The computer is adapted to configure the spatial light controlling means on the basis of the control information so that each light point emits light of a predetermined intensity and, optionally, of a predetermined phase. The emitted light of the plurality of light points may form an interference light field at a location relative to the optical arrangement wherein the interference light field may represent e.g. a holographic image or holographic point object. In an embodiment, the control information may be used to control the intensity and phase of the light points as a function of time. This way, the light points may emit light 120 having a time- varying intensity and phase in order to form a time-varying interference light field 117. Such time-varying light field may - for example - represent a holographic video, i.e. a sequence of holographic images 116.

The optical arrangement may form the plurality of light points on the basis of light originating from the reference light source. The reference light source may be configured to produce coherent light 103. The light of the reference light source may be coherent to a degree that is sufficient for a specific application. The coherent length of the light may be equal or more than the maximum difference in path length from the reference source 102 to any actively involved point source and from point source to a point on the holographic object 116. In case of a normal rectangular screen the largest path length difference is (approximately) twice the screen diagonal. A coherent length of more than this will be sufficient in all cases.

The formation of an interference light field in a space 117 using the optical system is schematically depicted in Fig. 1 B. The cross-sectional view of the optical system in Fig. 1 B includes an optical arrangement 109 comprising a spatial light controlling means 104 and an optical element 108 configured to form spatially distributed light points on the basis of light originating from a reference light source 102. The light 120 emitted by the light points forms a desired interference pattern representing a holographic image 116 of an object (in this example a cube) by controlling the intensities and phases of the light points. When an observer 118 is positioned in area 117, he may perceive a light field that is identical, both in phase and amplitude, to a light field that would be emitted by a real object. Hence, the observer sees a holographic image of the cube and is able to see the respective sides of the cube by moving his head from one point in area 117 to another point in this area.

The optical element may be implemented in different ways. In one embodiment, the optical element 108 may comprise a substrate including masking elements 119 including a-periodically or randomly distributed apertures 122 as shown in Fig. 1A. Light of the reference light source that is positioned behind the optical element may pass the mask at the aperture sites. This way, a light point at the position of an aperture may be formed.

In another embodiment, the optical element may comprise a plurality of refractive elements (e.g. micro-lenses). The light receiving face of a transparent substrate may include micro-lenses that receive the light of the reference light source and focus the light into a point. An a-periodicity or randomness is added to the position of the optical axis (in the plane of the substrate) of each refractive element. This way, a plurality of a- periodically or randomly distributed light points may be realized. In further embodiments, combinations of apertures and refractive elements may be used in order to form an optical element for generating an aperiodic distribution of light points on the basis of light of a reference light source.

Each light point forming element of the array of light point forming elements may comprise at least one mask element comprising at least one aperture and/or at least one refractive element comprising at least one optical axis, wherein the positions of the apertures and/or optical axes of the light point forming elements are arranged a-periodically or randomly in a plane of the substrate. The a-periodic or random distribution light points provides the effect of suppression or elimination of high order diffraction modes. Further, it suppresses aliasing effects. The random distribution or a-periodic distribution of light points will avoid a situation wherein at certain positions the phase of the light emitted from the light points coincides in the same way so that unwanted interference patterns can occur.

The SLM and the optical element may be optically aligned such that one or more pixels of the SLM are associated with at least one light point forming element of the optical element. For example, in the embodiment depicted in Fig. 1 A the optical element includes an array of light point forming elements, wherein each light receiving area of each light point forming element may receive the light of at least one pixel of the SLM

In one embodiment, a plurality of SLM pixels may be associated with one light point forming element 112. For example, in an embodiment, a light point forming element may receive light from a set of colour pixels, e.g. RGB pixels. This way, each light point forming element may be configured to form light points that emit light of a different wavelength. In another embodiment, a plurality of SLM pixels per light point forming element may be used to increase the range of irradiance that the light source forming element receives or transmits. This way the intensity range of the light received by or transmitted by a light point forming element may be increased. In a further embodiment, a plurality of SLM pixels may be used to modulate the phase the light a light point forming elements receives or emits. For example, in an embodiment, a plurality of pixels per light source may be positioned such that each of the plurality of pixels has a different (optical) distance from the reference light source. Light of each pixel may arrive at the light point forming element, wherein the light of each pixel has a different phase at the position of the light point forming element. This way the resulting phase of light at the light source may be controlled by controlling the intensity of light emitted by the respective pixels.

The optical element may be adapted to provide a certain aperiodic distribution of light points on the basis of light of a reference light source. The light points may be distributed in a flat plane (e.g. as depicted in Fig. 1A) or a curved plane. Alternatively, the light points may be distributed in a volume, e.g. a rectangular volume. In an embodiment, the rectangular volume may have a z-dimension which is substantially smaller than the x and y dimensions. Alternatively, the volume may be a spherical volume.

In one embodiment, the dimensions of the light points may be substantially smaller than the dimensions of the pixels of the spatial light modulator. The pixels of the spatial light modulator 104 may have a surface area in the range of 1 -500.000 pm². In one embodiment, the SLM pixels 106 may have a size between 5 and 10 pm, e.g. 7 pm by 7 pm.

The dimensions of a light point may be selected in a range between 0.1 and 25 pm, more preferably 0.1 and 10 pm, most preferably between 0.1 and 5 pm. In one embodiment, the effective dimensions of a light point may be selected between 1 and 5 pm, e.g. 2 pm by 2 pm. Here, the effective dimensions of the light point may be defined by the size of the apertures (in case of an aperture-type light point) or the size of the focal point (in case of a focal-point type light point).

In one embodiment, the positions of the light sources can be determined with an error margin that is smaller than the smallest detail in the to be constructed interference light field and/or than the smallest detail of the holographic image, preferably with an error margin that is smaller than a wavelength of light that is used to construct the interference light field. The positions may be obtainable by analysing the optical element using a microscope. In another example, the exact positions of the light sources can be derived from the design parameters of the optical element, which may be known prior to fabrication of the optical element.

For creating different holographic images, different interference light fields need to be constructed by the optical system. The different interference light fields can be constructed, because the phase and/or intensity of the light 120 originating from the light sources can be varied by controlling the spatial light controlling means by a computer 105. The computer may use control information stored on a storage medium in order to control individually addressable pixels of the spatial light controlling means. Thus, the optical element may be a static optical element that can be used in combination with a computer- generated spatial light controlling means, e.g. an SLM, for creating different holographic images, e.g. a sequence of holographic images forming a holographic movie, with a reduced number of artefacts.

Detailed embodiments of optical elements according to various embodiments of the invention are described hereunder with reference to Fig. 2-4.

Fig. 2A and 2B depict cross-sectional views of optical systems according to various embodiments of the invention. As shown in Fig. 2A, the system comprises a spatial light modulator 204, comprising an array of pixels 206. The optical element may comprise a transparent substrate 222 wherein the light receiving face of the substrate (the surface facing the spatial light modulator) is covered with an opaque mask 224 (e.g. a metal mask) comprising a-periodically distributed apertures 212. An aperture may be part of a light point forming element 228. The light point forming elements may form a regular array in the substrate as described with reference to Fig. 1A. This way, each light forming element may be associated with at least one pixel of the spatial light modulator. Apertures may be located at different positions in the area defining the light receiving area of the light point forming elements. The positions may be defined such that the apertures may be a-periodically distributed with one or more directions in the plane of the substrate.

Fig. 2B illustrates a system according to another embodiment of the invention. This embodiment includes an optical system including a spatial light modulator and an optical element 208 wherein an array of light source forming elements 222 include a mask structure including apertures wherein the apertures may have a-periodic distribution in one or more directions of the plane of the substrate.

In this particular embodiment, the mask structure 224 comprising the apertures has a 3D structure such that the z-position of the masking element in a first light point forming element 230 differs from the z-position of the masking element in a second light point forming element 232. This way, an aperture structure is realized wherein the position of the apertures are a-periodically or randomly distributed in the optical element. Such an aperiodic distribution is advantageous for preventing artefacts and twin images. In particular, the a-periodic or random distribution of the light points in the z-direction result in the elimination of so-called ghost images. Fig. 3A-3C depict cross-sectional views of optical elements according to various embodiments of the invention. These embodiments represent optical elements 308i wherein light source forming elements 328,330 include a mask structure 324 including apertures 312 wherein the apertures may have a-periodic distribution in one or more directions of the plane of the substrate. Additionally, dielectric material elements 332₁ ,334!. ,336i of different dimensions and shapes may be formed over the apertures. This way, the length of the optical paths for different light points forming elements may be varied, either a- periodically or randomly. Additionally, by selecting the size and shape of the dielectric material elements, e.g. rectangular (Fig. 3B), cylindrical and/or (semi)spherical (Fig. 3C), the opening angle of the light exiting an aperture may be increased. This way, the viewing angle of the holographic image may be improved.

Fig. 4A and 4B depict cross-sectional views of optical systems according to further embodiments of the invention. These embodiments represent optical elements 408i,₂ wherein light source forming elements 410^ include a refractive element 412_1-4 wherein the position of the focal point 413i., of the refractive elements may have an a-periodic or random distribution in one or more directions of the plane of the substrate and/or in the direction perpendicular to the plane of the substrate. As shown in Fig. 4A, refractive elements may be designed such that the position of the optical axis 414i.₄ exhibit an a-periodic or random offset relative to each other. In this particular, embodiment the light emitting face of the substrate is substantially flat.

Fig. 4B depicts a similar optical element as described with reference to Fig. 4A, including light points forming elements 420i_>2, refractive elements 422_1i2 at the light receiving areas of the light points forming elements and the positions of the optical axis 424 of the light points forming elements having an a-periodic or random offset relative to each other. In this embodiment, the light emitting face of the substrate may comprise masking elements 426, each masking element comprising at least one aperture 428.

In an embodiment, the masking element may be positioned at an axial height such that it coincides with the focal point of the refractive element. In a further embodiment, the position of the aperture in the plane of the substrate may be selected such that it coincides with the focal point of the refractive element. Hence, in this embodiment, masking elements with apertures are provided at the light emitting area of each light point forming element, wherein the position of the masking element and the position of the aperture in the masking element is selected such that the focal points (which are a-periodically or randomly distributed in the substrate) coincide with the apertures.

The fact the focal points coincide with the apertures allows reduction of the dimensions of the light point beyond the theoretical minimum size of a focussed light spot, and, additionally, it allows blocking of stray light in the transparent substrate and allows light to be emitted under a larger opening angle when compared with the usage of only a diffractive element. Fig. 5A-5C depict cross-sectional views of optical systems according to yet other embodiments of the invention. These embodiments represent optical elements 508i,2 wherein light source forming elements include a refractive element wherein the position of the focal point of the refractive elements may have an a-periodic or random distribution in one or more directions of the plane of the substrate and/or in the direction perpendicular to the plane of the substrate, in a similar way as described with reference to Fig. 4A and 4B.

In particular, Fig. 5A depicts an optical element that is similar to the optical element as described with reference to Fig. 4B, including light points forming elements 510i,₂ formed in a first transparent substrate 502i, refractive elements 512i.₃ implemented as the light receiving area of the light points forming elements, masking elements 504 including at least one aperture 506, wherein the position of the masking element and the position of the aperture in the masking element is selected such that the focal points (which are a- periodically or randomly distributed in the substrate) coincide with the apertures. As shown in Fig. 5A, the optical element further includes a second transparent substrate 502₂ that is fixed to the light emitting face of the first substrate. The light emitting surface of the second substrate may be substantially flat.

The second transparent substrate may be configured to increase the viewing angle associated with each of the light points. To that end, in one embodiment, the refractive index of the material of the second transparent substrate may be selected to be larger than the refractive index of the medium at the light transmitting face of the second substrate, typically air. This way, light originating from a light points will diffract away from a direction normal to the light emitting face of the second transparent substrate. This embodiment advantageously increases the viewing angle of light emitted by the light points by taking benefit from Snell's law.

Fig. 5B illustrates an optical element in which multiple pixels 526i_-3 of a spatial light modulator 504 are associated with one light points forming element 520i_>2. The optical element may comprise at least one transparent substrate comprising a light receiving face and a light emitting face. The light receiving face of the substrate may comprise refractive elements 522i_-3 and the light transmitting face of the substrate may include mask elements 528i,2 comprising multiple apertures 524i_-3. A refractive element at the light receiving area of a light point forming element may be configured to direct light of different pixels to different apertures in a masking element at the light transmitting area of the light point forming element. For example, refractive element 522₂ may receive light form a first pixel 526i and focusses at least part of the light 525i,₃ onto a first aperture 524₄. Part of the light of the first pixel may be scattered into a neighbouring light point forming element 520i, which will be largely blocked by the masking element 528i. A similar blocking effect takes place with light 523₂,523₃ originating from the other pixel 526₃. This way, undesired effects due to stray light will be reduced. The light of the different pixels may be light of different wavelength, e.g. different wavelengths in the visible and, optionally, the invisible spectrum. Hence, in this embodiment, the optical element may comprise a plurality of color light source forming elements, wherein each colour light source forming element may generate a light points of different wavelengths, e.g. RGB or colours defined by another colour space. The plurality of colour light source forming elements may generate a sparse a- periodic or random distribution of light points of different colours, which may be used in the reconstruction of holographic colour images.

FIG. 5C illustrates an embodiment of an optical element 5083 comprising a transparent substrate comprising a light receiving and a light emitting face. The transparent substrate may comprise an array of light point forming element wherein the light receiving areas of the light point forming elements may include refractive elements 532i,2, e.g. micro- lenses or the like, and wherein the light transmitting areas of the light point forming elements may include a masking element comprising at least one aperture.

In this embodiment, the refractive elements may have the same focal point in the direction normal to the plane of the substrate. Further, the focal point of a light point element may be selected to coincide with the aperture 538i,2 of the masking elements. Further, the position in the plane of the substrate of the optical axis of a refractive element may vary so that the position of the optical axis 534i,₂ may have an a-periodic or random distribution in the plane of the substrate. This way a sparse distribution of light points may be realized that have an a-periodic or random distribution in the plane of the substrate.

Additionally, dielectric material elements 536_1|2 of different dimensions and shapes may be formed over the apertures in a similar way as described with reference to Fig. 3A-3C.

The optical systems and optical elements described with reference to Fig. 1 -5 enable accurate reconstruction of a light field and elimination or at least substantial reduction of artefacts using limited computational and hardware resources, e.g. a computer and a conventional spatial light modulator. The optical systems may be advantageously used in the reconstruction of computer-generated holographic images or objects. The generation of a computer-generated holographic image involves the generation of holographic data (i.e. data including light intensity and phase values) representing an interference light field. The holographic data are used to control a spatial light modulator (SLM) so that when coherent light (or at least partially coherent light) is directed onto the SLM a modulated light pattern is generated which will create an interference light field at a certain position relative to the optical system.

To that end, a processor may be used to generate holographic data, which may include a graphics computer program that is configured to create/design/model an object for holographic reconstruction. For example, a 3D scanner may be used to create 3D image data of a certain object for holographic playback. The 3D image data and the information about the specific configuration of the optical element may be used to calculate the holographic data, which may be used to control a spatial light modulator. The holographic data generated by the processor enables a real world optical system to construct an interference light field that is associated with a holographic image. This process is described in more detail with reference to Fig. 6-9.

FIG. 6 illustrates an example of determining holographic data for reconstruction of a light field using an optical system according to an embodiment of the invention. The optical system may comprise an optical element 608, e.g. a mask comprising an a-periodic or random distribution of apertures for generating a plurality of a-periodically or randomly distributed light points 612k (k=1 ,... ,n wherein n is a positive integer). The optical system may be used to generate an interference light field, e.g. an interference light field defining a point A 618, at a certain position relative to the light points 612_k.

Fig. 7 depicts a flow diagram of a method for determining holographic data for an optical system according to one embodiment of the invention. The method may include a computer executing a simulation program comprising computer-readable code for simulating an optical system, comprising e.g. an optical element as depicted in Fig. 6, for which holographic data is generated. When the simulation program is executed, the processor may, in a first step 702, receive optical model information describing the optical system in terms of a number of parameters, including e.g. the number of light points, the position of the light points in space, the wavelength used for generating the light points, etc. The positions of the light points 612_k may be determined or known in advance.

In a second step 704, the processor may receive light field information defining a predetermined interference light field at a predetermined location relative to the locations of the a-periodically or randomly distributed light points. This information may define a light field in terms of intensity- and phase values at predetermined positions relative to the positions of the light points of the modelled optical system. As illustrated in Fig. 6, the interference light field may represent a simple holographic point image. Thus, the

interference light field information may include position information, e.g. at least one 3D coordinate, associated with a position A in space relative to the positions of the light points. The information may further include a predetermined light intensity value l_A and/or phase value ΦΑ of the light field at position A.

In a third step 706, the method may include the processor of the computer determining for each light point k (k=1 , ... ,n) of the optical system, a distance d_k between light points k and the light field position of the holographic point image, e.g. a distance di between the light point 612i and the position of the light field (the light field position) of the holographic point image (point A in Fig. 6) as defined in the interference light field information. Then, in a fourth step 708, a light intensity value k of light to be emitted by each of the light points 612_k may be determined on the basis of the distance d_k (as determined in step 706) and the intensity and phase ΦΑ in point A. In a further embodiment, a phase value k of the light emitted by the light points may be determined, e.g. a phase value of light 615i emitted by a light point 612i. In this calculation, it is assumed that point A emits light that has a phase Φ_Α at point A and that light 615i travels from point A to light point 612i. Optionally, in an embodiment, the calculation of the phase value >i may include calculating a phase difference Acpk by dividing the distance di between point A and light point 612k by the predetermined wavelength. This phase difference may be inverted (multiplied by -1 ) to arrive at phase value, i.e. φ«= Φ_Α-Δφκ. This inversion may be required for correctly positioning the perceived holographic image with respect to the light sources, e.g. in front of the light sources as seen by an observer.

Hence, based on the method as described with reference to Fig. 6 and 7, holographic data (i.e. intensity and phase values of each light point in the optical system) are generated by the computer. The holographic data may be used to determine control information for the spatial light modulator of a real-world optical system. The control information control pixels of the SLM so that each light point of the optical system transmits light in accordance with the intensities and phases of the holographic data. This way, the optical system is able to reconstruct a light field representing a predetermined holographic image (e.g. a holographic light point) wherein artefacts are eliminated or at least substantially reduced.

FIG. 8 illustrates the determination of holographic data for reconstruction of a light field using an optical system according to another embodiment of the invention. In this particular embodiment, the optical system may be used to generate an interference light field of a holographic image 816 (in this example a cube) at a certain position relative to the light points 812k. Fig. 9 depicts a flow diagram of a method for determining holographic data for an optical system as depicted in Fig. 8. Similar to the embodiments of Fig. 6 and 7, the method may include a computer executing a simulation program comprising computer- readable code for simulating at least part of an optical system as depicted in Fig. 8. The simulated optical system may include a reference light source 802 and an optical arrangement adapted to generate a plurality of a-periodically or randomly distributed light points 812k (k=1 ,... ,n, wherein n is a positive integer) in a transparent substrate. Further, in this embodiment, the holographic data that is generated by the method may enable a real- world optical system to construct an interference light field representing holographic image 816.

The light field information may define a holographic image 816 (e.g. a cube) on the basis of points associated with the shape of the holographic image, e.g. points positioned at edges of the cube having a relatively high light intensity value when compared to points positioned away from the edges of the cube.

In the example of FIG. 8, the light field positions at which the light intensity values are defined by the holographic information may coincide with the holographic image to be formed (in a similar way as described with reference to Fig. 6 and 7) thus allowing a straightforward calculation of the intensity i and phase for each light point.

When the simulation program is executed, the processor may, in a first step 902, receive optical model information describing an optical system for which the control information needs to be determined. The optical model information may include locations of an a-periodical or random distribution of light points and the wavelength emitted by the light points.

In a second step 904, the processor may receive light field information defining a predetermined interference light field at predetermined location in space, wherein the interference light field represents a holographic image. Generally, the light field information associated with such holographic image may include intensity values l_m and phase values i>_m at a predetermined number of light field positions p_m (i=1 t). Such set of holographic light field data may define e.g. a point cloud representing e.g. the surface of a 3D object.

In a third optional step 906, the computer may further receive at least one intensity value IR and phase value <£R associated with a reference source R at reference position p_R.

The light field information may define light field data values, i.e. intensity values and associated phase values, wherein each data value may be linked to a certain position in space and wherein the total set of data values represents a 3D light field. For the sake of simplicity, hereunder the embodiment is illustrated on the basis of two field positions A and B of the light field as shown in Fig. 8. Intensity values l_m and phase values Φ™ at light field positions p_m (m=1 , ... ,t) representing in this example points of a cube may include a first light intensity value at position pi (point A in Fig. 8) and a second light intensity value at position p₂ (point B in Fig. 8) and, optionally, a first phase Φι at light field position pi and a second phase ₂ at light field position p₂, wherein phase Φι and phase Φ₂ η^ have different phase values. Hence, the whole light field can be expressed in terms of intensity and phase values at predetermined positions.

In a fourth optional step 908, the computer may determine for each light point k (k=1 , ... ,n) of the simulated optical system, a distance r_k between light points k and reference light source R.

Similarly, in a fifth step 910, the computer may determine distances d_k,_m between light point k and light field position p_m (m=1 ,... t; k=1 , ... n). These distances then can be used to determine for each light point k (k=1 , ... ,n) an intensity value k and, optionally, a phase value φκ of light to be emitted by light point k.

As shown in Fig. 8, the intensity i_k and phase φκ of a light point k may be simply calculated as a superposition of the intensities and phases associated with all light waves travelling the reference light source R to light point k and all the light waves travelling from all points of the light field.

Hence, the intensity value /? (i.e. the intensity value of light emitted by light point 1 ) may be calculated by determining the superposition of intensities of light waves that travel to all light field positions p_m (m=1 ,... ,t). These intensities include an intensity value associated with light field position pi (point A) and p₂ (point B), wherein the intensity value of light field position p may be determined by dividing by a square of the distance between light field position pi (point A) and the position of the first light point 312i and the intensity value of p₂ includes dividing l₂ by a square of the distance between light field position p₂ (point B) and the position of light point 312i. Intensity value is obtained by summing all intensity contributions of all light waves travelling to each light field points p_m.

Further, a phase value >i (i.e. the phase of the light emitted by light point 1) may be calculated by determining the superposition of the light waves travelling to all light field positions p_m (m=1 ,... ,t). As already explained with reference to Fig. 6 and 7, the calculation of the phase of the light wave travelling to light field point B may include:

calculating a phase difference by dividing the distance between light field point B and light source 812i by the wavelength of the light of the reference light source. This phase difference may be inverted (multiplied by -1) to arrive at a phase value associated with light field point B which inversion may be required for correctly positioning the perceived holographic image with respect to the light sources, e.g. in front of the light sources as seen by an observer.

Hence, for each light point an intensity value and a phase value may be obtained by summing the phase contributions of the light waves that travel from a light point towards the light field points and the light waves that originate from reference light source and that travel towards the light point. Effectively, the method thus includes the calculation of a superposition at the position of the light points of these light waves. The control information for controlling the spatial light modulator may be determined based on and/or comprise the light intensity value and/or phase value of light to be emitted by the light points.

Optionally, in an embodiment, an intensity value and a phase value associated with a particular point, e.g. point B, may be disregarded in the steps of Fig. 9. The phase and intensity contribution of the specific point may be disregarded if the condition are satisfied that the particular point of the holographic image should not be visible for an observer in an area of obstructed view (in the far field). This may be the case, for example, because the specific point is positioned behind a "solid" holographic object, wherein the solid holographic object should block the view onto the specific point for the observer in the area of obstructed view.

Fig. 10 illustrates the top-view of an optical element according to one embodiment of the invention. The optical element 1008 may include a substrate, e.g. an transparent substrate, comprising a light receiving and a light transmitting face. The substrate may be divided in a plurality of light points forming elements 1010, wherein the light receiving or light transmitting area of each light point forming element may comprise at least one aperture 1012. Each aperture may be provided with a different offset relative to the centre of the a light receiving or light transmitting area wherein the offset is selected such that the apertures have an a-periodic or random distribution in the plane of the substrate. .

In one embodiment, the light receiving area 1010 of a point light forming element may be selected such that when the optical element is aligned with a SLM, the point light forming elements have a one-to-one correspondence with the pixels of a SLM. For illustrative purpose the optical element 1008 was designed to match a 100 x 100 pixel light modulator.

If the optical element comprising the light point forming elements is optically aligned to pixels of a spatial light modulator, a Moire pattern will appear. Based on this Moire pattern, a user may be able to determine that the optical element is properly aligned with respect to a spatial light modulator, or more in particular, that the light point forming elements are correctly aligned with pixels of the spatial light modulator (e.g. aligned in a one-to-one correspondence).

In an embodiment, the optical element may comprise alignment regions 1020i. 4 In the length and width directions of these alignment regions a 'mismatch' of one pixel may be applied, resulting in a cross-shaped Moire pattern when properly aligned with the underlying spatial light modulator.

Figs. 1 1 -13 illustrate the generation of an interference field using an optical system according to an embodiment of the invention.

The optical system comprises a computer-controlled spatial light modulator comprising an array of pixels, in this case 160 x 60 pixels wherein the pixels having a pixel pitch of 60 pm (similar to a 5.5 inch HD screen). The spatial light modulator is a transmissive- type spatial light modulator comprising a light receiving and a light emitting face.

The optical system may comprise a reference light source that is positioned 1 meter behind the light receiving face of the spatial light modulator, at the centre (as viewed from the z-direction) of the spatial light modulator. The wavelength of the (coherent) light emitted by the reference light source is selected to be approximately 650 nm (red light).

Further, the optical system comprises an optical element comprising a light receiving and a light emitting face. The optical element is positioned in front of the spatial light modulator so that the light emitting face of the spatial light modulator faces the light receiving face of the optical element. The optical element comprises sparsely a-periodically distributed apertures in order to generate a distribution of light point which are a-periodically distributed (as explained in detail with reference to Fig. 1 -5). Each light point is associated with one or more pixels of the spatial light modulator. Each light point source can be controlled by controlling the one or more pixels that are associated with an aperture. Control information is used to control the intensity of each light point so that the optical system generates an interference light field representing a holographic image of a point-like light source situated at +50 mm from the light emitting face of the optical element in the z- direction. Hereto, for each optical system, a state of the spatial light modulator was calculated.

Fig. 1 1 shows the simulation results for an optical system that comprises a computer-controlled spatial light modulator 1104 but does not comprise an optical element according to the invention. The top left inset of Fig. 11 illustrates the state of the pixels (intensity) of the spatial light modulator calculated for this system. The configured pixels of the spatial light modulator should give rise to an interference light field representing a light point.

The graphs 1126 and 1128 show the resulting holographic images as perceived by a viewer when the main light source (defined by the boundary conditions) emits light onto the spatial light modulator. A viewer will see a first holographic image 1128 in front of the spatial light modulator 1104 in the +z direction, and a second holographic image 1126 behind the spatial light modulator in the -z direction. The second holographic image 1126 is referred to as a so-called "ghost images" and appear because the two-dimensional interference pattern encoded into the spatial light modulator can be associated with either one of a point-like image at +50mm in the z-direction or with a point-like image at -50mm in the z-direction. As a result, a viewer experience images both in front of and behind the spatial light modulator, which is undesired.

Both graphs show a maximum relative intensity at 5 mm in the x-direction (at the centre of the spatial light modulator) corresponding to the intended image, a holographic point source. However, in addition to these peaks, both holographic images 1126, 1128 comprises additional side peaks, which a viewer observes as additional point-like light sources next to the intended point-like light source. These side peaks are the result of high order diffraction occurring because of the periodic pixel array of the spatial light modulator. Such high-order diffraction images may also be present in the y-direction (not shown).

Hence, a conventional optical system cannot produce a light field that accurately represents a desired image without artefacts and without a ghost image.

Fig. 12 shows the simulation result for an optical system according to one embodiment of the invention. The optical system comprises a spatial light modulator 1204 and an optical element 1208 according to one embodiment of the invention. The optical element 1208 comprises 160 x 60 apertures 1212 that are a-periodically distributed in the x- and y-direction. Each aperture is 2 μιτι x 2 pm. The inset at the bottom right of Fig. 12 shows fifteen apertures 1212 of the optical element 1208, among which are apertures 1212i, 1212i, and 12123. The apertures 1212 of the optical element 1208 are associated one-to-one with the pixels 1206 of the spatial light modulator. To illustrate, call-out 1230 shows fifteen individual pixels of the spatial light modulator 1204, among which pixels are pixels 1206i, 12062 and 12063. Aperture 1212i receives light from pixel 1206-t , aperture 1212₂ receives light from pixel 12062, aperture 1212a receives light from pixel 12063.

The inset at the top left of Fig. 12 shows the calculated state of the spatial light modulator 1204 for this optical system that should give rise to an interference light field representing the point-like holographic image. This state may be calculated by performing the method described above with reference to FIG. 6 and 7.

Again, the optical system causes a ghost holographic image 1226 behind the screen. However, both graphs 1226, 1228 show that the artefacts are reduced significantly with respect to the optical system discussed with reference to Fig. 11. The high-order artefacts are reduced both in the x-direction (shown) and in the y-direction (not shown). The light points that are caused by the apertures 1212 are not organized in regular arrays yet are distributed a-periodically. A viewer who receives the light field constructed by this optical system thus sees two point-like holographic images, one in front of and one behind the spatial light modulator 1204.

Fig. 13 depicts a variant an optical element is used wherein the apertures are also a-periodically distributed in the z-direction (the direction normal to the substrate plane). As shown by the graphs 1326, 1328 the a-periodic or alternatively random distribution of the light points in the z-direction result in the elimination of the ghost image. The ambiguity with respect to the position of the image, in front of or behind the spatial light modulator, no longer exists. Suppressing the ghost image in this manner conveniently does not require to alter the direction of incoming reference light. The ghost image can be suppressed with the reference light source right behind the screen, in line with the holographic image and viewer.

FIG. 14A is a photograph taken by a camera that is present in an interference light field. A holographic image, an oval structure, is perceived that seems to be floating mid- air.

Fig. 14B depicts a photograph of a point hologram that is generated using an SLM comprising a regular array of pixels. The photograph clearly shows artefacts caused by higher order effects and/or aliasing.

Fig. 14C is a photograph of a point hologram that is generated using an SLM and a light point forming element according to an embodiment of the invention. The photograph clearly shows that the arrangement of the light point forming element, in this case a random arrangement of light point forming elements eliminates a substantial part of the artefacts.

Fig. 15 depicts a block diagram illustrating an exemplary data processing system that may be used in a computer system as described herein.

As shown in Fig. 15, the data processing system 1500 may include at least one processor 1502 coupled to memory elements 1504 through a system bus 1506. As such, the data processing system may store program code within memory elements 1504. Further, the processor 1502 may execute the program code accessed from the memory elements 1504 via a system bus 1506. In one aspect, the data processing system may be

implemented as a computer that is suitable for storing and/or executing program code. It should be appreciated, however, that the data processing system 1500 may be implemented in the form of any system including a processor and a memory that is capable of performing the functions described within this specification.

The memory elements 1504 may include one or more physical memory devices such as, for example, local memory 1508 and one or more bulk storage devices 1510. The local memory may refer to random access memory or other non-persistent memory device(s) generally used during actual execution of the program code. A bulk storage device may be implemented as a hard drive or other persistent data storage device. The processing system 1500 may also include one or more cache memories (not shown) that provide temporary storage of at least some program code in order to reduce the number of times program code must be retrieved from the bulk storage device 1510 during execution.

Input/output (I/O) devices depicted as an input device 1512 and an output device 1514 optionally can be coupled to the data processing system. Examples of input devices may include, but are not limited to, a keyboard, a pointing device such as a mouse, or the like. Examples of output devices may include, but are not limited to, a monitor or a display, speakers, or the like. Input and/or output devices may be coupled to the data processing system either directly or through intervening I/O controllers.

In an embodiment, the input and the output devices may be implemented as a combined input/output device. An example of such a combined device is a touch sensitive display, also sometimes referred to as a "touch screen display" or simply "touch screen". In such an embodiment, input to the device may be provided by a movement of a physical object, such as e.g. a stylus or a finger of a user, on or near the touch screen display.

A network adapter 1516 may also be coupled to the data processing system to enable it to become coupled to other systems, computer systems, remote network devices, and/or remote storage devices through intervening private or public networks. The network adapter may comprise a data receiver for receiving data that is transmitted by said systems, devices and/or networks to the data processing system 1500, and a data transmitter for transmitting data from the data processing system 1500 to said systems, devices and/or networks. Modems, cable modems, and Ethernet cards are examples of different types of network adapter that may be used with the data processing system 1500.

As pictured in Fig. 15, the memory elements 1504 may store an application 1518. In various embodiments, the application 1518 may be stored in the local memory

1508, the one or more bulk storage devices 1510, or apart from the local memory and the bulk storage devices. It should be appreciated that the data processing system 1500 may further execute an operating system (not shown in Fig. 15) that can facilitate execution of the application 1518. The application 1518, being implemented in the form of executable program code, can be executed by the data processing system 1500, e.g. , by the processor 1502. Responsive to executing the application, the data processing system 1500 may be configured to perform one or more operations or method steps described herein.

Various embodiments of the invention may be implemented as a program product for use with a computer system, where the program(s) of the program product define functions of the embodiments (including the methods described herein). In one embodiment, the program(s) can be contained on a variety of non-transitory computer-readable storage media, where, as used herein, the expression "non-transitory computer readable storage media" comprises all computer-readable media, with the sole exception being a transitory, propagating signal. In another embodiment, the program(s) can be contained on a variety of transitory computer-readable storage media. Illustrative computer-readable storage media include, but are not limited to: (i) non-writable storage media (e.g., read-only memory devices within a computer such as CD-ROM disks readable by a CD-ROM drive, ROM chips or any type of solid-state non-volatile semiconductor memory) on which information is permanently stored; and (ii) writable storage media (e.g., flash memory, floppy disks within a diskette drive or hard-disk drive or any type of solid-state random-access semiconductor memory) on which alterable information is stored. The computer program may be run on the processor 1502 described herein.

The terminology used herein is for the purpose of describing particular embodiments only and is not intended to be limiting of the invention. As used herein, the singular forms "a," "an," and "the" are intended to include the plural forms as well, unless the context clearly indicates otherwise. It will be further understood that the terms "comprises" and/or "comprising," when used in this specification, specify the presence of stated features, integers, steps, operations, elements, and/or components, but do not preclude the presence or addition of one or more other features, integers, steps, operations, elements, components, and/or groups thereof.

The corresponding structures, materials, acts, and equivalents of all means or step plus function elements in the claims below are intended to include any structure, material, or act for performing the function in combination with other claimed elements as specifically claimed. The description of embodiments of the present invention has been presented for purposes of illustration, but is not intended to be exhaustive or limited to the implementations in the form disclosed. Many modifications and variations will be apparent to those of ordinary skill in the art without departing from the scope and spirit of the present invention. The embodiments were chosen and described in order to best explain the principles and some practical applications of the present invention, and to enable others of ordinary skill in the art to understand the present invention for various embodiments with various modifications as are suited to the particular use contemplated.

Claims

CLAIMS . An optical system adapted to reconstruct or at least partially reconstruct an interference light field comprising:

a spatial light modulator comprising an array, preferably a periodic array, of pixels optically aligned to an optical element comprising an array, preferably a periodic array, of light point forming elements formed in a first transparent substrate, each light point forming element including a light receiving area at the light receiving face of the first substrate and an associated light transmitting area at the light transmitting face of the first substrate;

the light receiving area of a light point forming element being arranged to receive light from a reference light source and to form a light point that emits light out of the light emitting area;

each light point forming element comprising at least one mask element comprising at least one aperture and/or at least one refactive element comprising at least one optical axis, wherein the positions of the apertures and/or optical axes of the light point forming elements are arranged a-periodically or randomly in a plane of the substrate; and, the pixels of the spatial light modulator controlling the intensity and, optionally, the phase of the light transmitted by the points of light, the transmitted light forming the interference light field at a predetermined location relative to the optical system.

2. Optical system according to claim 1 , wherein each light point forming element comprises a mask element comprising at least one aperture, the at least one aperture being substantially smaller than the area of pixels of the spatial light modulator, preferably apertures in mask elements of different light point forming elements having different positions; and/or, mask elements of different light point forming elements being arranged in different planes of the substrate.

3. Optical system according to claim 2, wherein the mask elements are arranged at the light receiving area of the light point source forming elements and wherein elements of a transparent material of different dimensions being formed over different apertures.

4. Optical system according to any of claims 1-3, wherein each light point forming element comprises at least one refractive element arranged to focus light in a point, preferably the optical axis of different light point forming elements being located at different positions relative to the centre of the light receiving areas; and/or, the refractive elements of different light point forming elements having different focal points, preferably the different positions of the optical axes and/or the different focal points varying a-periodically or randomly within a predetermined range.

5. Optical system according to any of claims 1-4, wherein the light receiving area of a light point source forming element is configured as a refractive element, the light transmitting area including a mask element comprising at least one aperture, preferably the light refractive element being configured to focus at least part of the light received by the refractive element onto the at least one aperture.

6. Optical system according to any of claims 1-5, wherein the refractive element is configured to receive light originating from two or more pixels of the spatial light modulator and to focus the light from the two or more pixels onto two or more apertures in the masking element of the light point source forming element respectively.

7. Optical system according to any of claims 1-6 wherein the length of optical paths of different light point source forming elements varies a-periodically or randomly within a predetermined range of optical path lengths, preferably the distance between a plane through the substrate and the light transmitting areas of different light point forming elements varying a-periodically or randomly within a predetermined range.

8. Optical system according to any of claims 1-7, wherein at least a second transparent substrate is fixed to the light transmitting face of the first transparent substrate, the refractive index of the second transparent substrate being larger than the refractive index of the medium at the light transmitting face of the second substrate.

9. Optical system according to claims 1-8 wherein the pixels of the spatial light modulator being configured to control the intensity and, optionally, the phase of the light emitted by the points of light, the light of the points of light reconstructing or at least partially reconstructing the light field at a predetermined location relative to the optical element.

10. Optical system according to claims 1-9 wherein the spatial light modulator is an electrically addressable spatial light modulator, the optical system further comprising:

a computer connected to the electrically addressable spatial light modulator and a storage medium associated with the computer, the storage medium comprising control information,

the computer being adapted to use the control information to control the electrically addressable spatial light modulator so that each point of light emits light of a predetermined intensity and/or phase for reconstructing the light field.

11. An optical element adapted to form an a-periodic or random distribution of light points, preferably the optical element being used in an optical system according to any of claims 1-10, the optical element comprising:

an array, preferably a periodic array, of light point forming elements formed in a first transparent substrate, each light point forming element including a light receiving area at the light receiving face of the first substrate and an associated light transmitting area at the light transmitting face of the first substrate;

the light receiving area of a light point forming element being arranged to receive light from a reference light source and to form a light point that emits light out of the light emitting area; and,

at least one mask element and/or refractive element in each light point forming element causing the locations of the light points to be arranged a-periodically or randomly in at least one direction in a plane of the first substrate.

12. A method for reconstructing or at least partially reconstructing an interference light field using an optical system comprising an optical element and a spatial light modulator, the method comprising:

applying coherent light of a reference light source to the light receiving face of the optical element, the optical element comprising an array of light point forming elements in a first transparent substrate, each light point forming element including a light receiving area at the light receiving face of the first substrate and an associated light transmitting area at the light transmitting face of the first substrate;

the light receiving areas of the light point forming elements receiving light from the reference light source and forming a light point that emits light out of the light emitting area, wherein each light point forming element comprises at least one mask element comprising at least one aperture and/or at least one refractive element comprising at least one optical axis, wherein the positions of the apertures and/or optical axes of the light point forming elements are arranged a-periodically or randomly in a plane of the substrate;

a computer controlling the pixels of the spatial light modulator, the pixels being optically aligned to the light point forming elements, the pixels of the spatial light modulator controlling the intensity, and optionally, the phase of the light emitted by each light point, the light emitted by each light point forming a light field at a predetermined location the transmitted light forming the interference light field at a predetermined location relative to the optical system.

13. Methods according to claim 12, wherein the pixels are controlled on the basis of holographic data, the holographic data representing intensity values and, optionally phase values, of the light to be emitted by each of the light points, the holographic data enabling the optical system to reconstruct a predetermined holographic image.

14. A computer-implemented method for determining holographic data for a spatial light modulator, the spatial light modulator and an optical element forming an optical system arranged to reconstruct an interference light field, the method comprising

receiving light field information, the light field information including intensity values l_m and phase values O_m associated light field positions p_m (m=1 ,... ,t);

receiving optical model information, the optical model information being associated with an optical element comprising an array of light point forming elements in a substrate, wherein each light point forming element comprises at least one mask element comprising at least one aperture and/or at least one refractive element comprising at least one optical axis, wherein the positions of the apertures and/or optical axes of the light point forming elements are arranged a-periodically or randomly in a plane of the substrate, the light point forming elements being arranged to form an a-periodic or random distribution of light points on the basis of light of a reference light source, the optical model information including the locations of the light points and the wavelength of the light emitted by the light points;

for each light point k (k=1 ,... ,n) determining distance dk._m between light point k and light field position pm (m=1 ,... t) and calculating an intensity i_k and, optionally, phase <|>k of light to be emitted by each light point on the basis d_k,m and the light field information.

15. A computer program or suite of computer programs comprising at least one software code portion or a computer program product storing at least one software code portion, the software code portion, when run on a computer system, being configured for executing the method according to claims 12-14.