NL2019189B1

NL2019189B1 - Interference light field reconstruction using sparsely distributed light points

Info

Publication number: NL2019189B1
Application number: NL2019189A
Authority: NL
Inventors: Fransen Martin
Original assignee: Stichting Nederlandse Wetenschappelijk Onderzoek Inst Vestiging Nikhef
Priority date: 2017-07-05
Filing date: 2017-07-05
Publication date: 2019-01-16
Also published as: WO2019009722A3; WO2019009722A2

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 20 by the points of light, the transmitted light forming the interference light field at a predetermined location relative to the optical system.

Description

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 10 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.

J- -3

Background of the invention

Holography is a diffraction-based coherent imaging

CL

3b holographic plate. Holography typically includes the steps

CL son,

During holographic recording a wide beam of coherent he beam, that does not hit the object passes by considered as the ligl with resu interference light field is subsequently the amplitude, phase, and wavelength information of ΐ ght field pattern is illuminated with a coherent light beam (also referred to as reference light).

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 5 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 computergenerated 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 o	utput is a	. modulated	light pattern.
I	n order to	produce a	3D holographic image of	usable
size and vi	ewing 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

For manv h theoretical physical limits range, noise, contrast, etc

..., r e s o 1 u t i ο n, d y n a m i c

CL on fficient in manv applications. However

Hence, there for improved methods and

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 or svstem. Functions described in this may be or cl computer. Furthermore, aspects o of a computer program product embodied more computer cl computer be 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 30 carrier wave. Such a propagated signal may take any of a variety of forms, including, but not limited to, electromagnetic, 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 35 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 25 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 computer readable medium that can direct cl other devices to function in

CL tha the instructions stored in the computer readable medium ture including- instructions whic block cl te cause a series of operational steps computer, other programmable appara implementing the possible implementations o systems, methods and computer cordina to various embodiments of the is regard, each block in the flowchart of code, which comprises one or more ti.on a b 1 e i n s t r u c t i ο n s ed logical function(s). It should unctions noted in the blocks may occur in the figures. For example, two blocks shown in succession t, be executed substantially concurrently, or the 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 o 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 5 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 lorm an , the light point forming· elemen a-periodic or random distribution o gh source .

In an embodiment	, the	light	poi
include a light receiving	di βά	a ts t h a	lig
tbe first, substrate and an	a a s o	ci ated	1 i g
at the light transmitting	face	of the	f ir
In an embodiment	, the	light	ISO
point forming element may	be ar	ranged	to

?·, ·

source and to form, a do or from a

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 aperiodically 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 5 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 10 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 15 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 undersampled 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 25 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 spatial light modulator in combination with the 30 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 35 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 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 t h e s u b s t r a t e .

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.

n embodiment, point forming element

	light	in a point,	preferab
	light	point formir	• g elemen
5	po s i t	ions relative	: to the
		In a fur	;· Η ν'

local points.

axes and/or ne embodiment, differen f·'. r·, o

CT

In an embodiment, the light receiving area of a ligh

In ormina element mav configured an embodiment, the ligh a mask element comprising at least one aperture

In a further embodiment, the light refractive elemen may be

CT received by the onto the

In an embodiment.

may be configured to receive light two or more more

Ο1ΧΘ onto two or more

In an embodiment, the length of optical randomly within a predetermined range o through the substrate and the ligh

In an embodiment, at least

CT ansparen second transparent substrate being larger than the medium at an embodiment, at

3.

embodiment, the spatial light modulator may be embodiment, o

tical	system may	further
l·*·; O	lectrically	addressab
age m<	edium associ	ated with
lompri:	sing· control
iapted	to use the	control
. c 31-1 y	addressable	spatial

i gn hat each point of light emits ligh he invention may relate to a method method optical element comprising an ansparen point forming element including a light receiving area at the ssociated oi substrate;

Cl of the

Cl least l··.

periodically or randomly in at least one direc 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 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 li	ght	points, tn	e holographic data
enabling the optical system	to r	econstruct	a predetermined
ho1ogr aphi c image .
I n a η o t h e r a s p e c t.,	the	invention	relates to a
c omp ut e r - imp 1 erne nt e d me t ho d	for	determinin	g 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 I_m and phase values associated light field positions p_:;i (m=l,...,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-l,...,n) determining distance dk,™ between light point k and light field position pm (m=l,...t) and calculating an intensity ik and, optionally, phase i>k of light to be emitted by each light, point on the basis dk,m and the light f ield 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 t these specific embodiments.

Brief description of the drawings

FIG. 1A and FIG. IB 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 vi	.ews of optical
systems according to yet other embodiments of	the invention;
FIG. 6 illustrates the determinatior	i of holograph.!

data for reconstruction of a light field

Fig. 7 oh

3.

method tor to one embodiment of the invention;

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

Fig. 9 Ct C JO 1 Ό 3 ö 3 x low 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	r h θ	genera t i ο η o f a	n interference
ght field using·	a conventional	optical system;
FIG. 12	illustrates	the	generation of a	n interference
ght field using	an optical	s y s t	em according to	an embodiment
the invention;
£ Xk? . X J?	illustrates	the	generation of a	n interference
ght field using	an optical	syst	em according to	an embodiment
the .1 n v e n t. i ο n;
FIG. 14	is a photog	raph	of a reconstruc	ted
terference light	. field;
FIG. 15	is a block	diag	ram illustrating	an exemplary

data computing system that may be used for executing methods and software products described in this disclosure.

For many holographic applications, are racv than ΐ of resolution, dynamic range, no

Oil 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.

The systems address this problem.

and methods described in this application

The optical systems and methods described in this application transform a spatially under30 sampled light field of a spatial light modular into a sparsely distributed set of light, points. A sub-wavelength aperiodicity 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.

ng· to one embodiment of the inventio s configured to reconstruct a predetermined image op c omp rising a s ρ a ΐ o form light point.s on the b controlling means may comprise an mi on of closely packed light sources when it o

As shown in Fig. 1A, elements 112. Each light mi ng element

Cl ng

area 116	at the light	Iran	emitting face	of the substr	ate. The
light rec	eiving area	ΟΓ 3.	light point f	orming element	may be
arranged	to receive 1	ight	f r o m t h e r e f e	r e n c e .1 i gh t s o	urce and
to form a	light point	that	emits light	120 out of the	light

119 emittina area. One or more mask elemen ming element elements in each light point, for:

a-’O randomlv in at least one direction in uw the to err 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 em.bodi.ment, 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 m 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.

2 5	In an	embodiment,	the optical element	may be fixed t·
	the 1	ight emitt	ing face or	light receiving face	of the spatial
	light.	contro11i	ng means 104	so that the ooticaJ	element is in
	C10 S Θ	proximity	to the spat	ial light modulator	(as

schematically depicted in Fig. IB). 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 d1s P1a y (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 i	nay comprise one or m	tore layers	configured to influence
2 0	one or	more properties of t	he light t	hat passes the pixel
	accord.	inq- to a fixed value.

In case of a computer-controlled spatial light controlling means, the optical system of Fig. 1A and IB 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 predet.erm.ined 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 10 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 15 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 mere 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. IB. The cross-sectional view of the optical system in Fig. IB 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.

field that would be emitted by a real object. Hence, the observer sees a holographic image of the cube and i see

The optical element may be implemented in different

In one embodiment, the optical

108 may compr1s e π

a substrate including masking elements 119 including aperiodically or randomly distributed apertures 122 as shown

Fig. 1A. Light of ΐ position of an ma ν formed.

In another embodiment, the optical element may

The light receiving face of a transparent substrate axi s (in the plane of the substrate) of each randomly distributed light points may be realized. In further embodiments, combinations of apertures and refractive elements distribution o ight points on the basis of rg op aliened wi at the op cal element includes icfht each ligr may receive the lig' pixel of the SLM

In one embodiment, a ré

This way, each light point forming element may be configured tha wavelengt

OI poi forming element may be range

0 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 nave 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 may have a

The dimensions effective dimensions of a may be selected between pm. Here, the effective dimensions (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 5 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 10 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 15 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 20 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 me t a J_ masn) comprisiiig a perioo.ica n.y 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 5 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

3Π ao re 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 socalled ghost images.

Fig. 3A-3C depict cross-sectional views of optical elements according to various embodiments of the invention. These embodiments represent optical elements 3081-3 wherein light source forming elements 328,330 include a mask structure 324 including apertures 312 wherein the apertures may have a35 periodic distribution in one or more directions of the plane of the substrate. Additionally, dielectric material elements 332i,2, 334i-5,336i-5 of different dimensions and shapes may be randomly. Additionally, by elements, e.g. rectangu

-r· o , cylindrical and/or angle o ross-sectional views o

Cl o

on perpendicular to the elements may be designed such that the position of the optical axi s each this particular, embodiment the light emitting forming elements having a

Cl

-Λ V this embodiment, the light emitting e ol the substrate may comprise masking elements 426, each pos local poir cl embodiment, the refractive element. Hence, embodiment, sking elements with apertures are provided cl

4 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-perlogically 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 dif fractive element.

Fig. 5A--5C depict cross-sectional views of optical systems according to yet other embodiments of the invention.

These embodiments represent optical elements 5081,2 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 20 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 25 5101,2 formed in a first transparent substrate 502i, refractive elements 5121-3 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 aperiodically 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.

transparent substrate may be configured to refractive i ansparen angle associated witr

each	of the	light
ref	m Ci C tl 1V Θ	index
ubst.	rate may	be
ndex	of the	medium

typically air . This way, light originating rrom a away from a direction normal to the co emitting face of the second transparent substrate.

embodiment advantageously increases ne v iqht emitted by the light points by taking bene

Fig. 5B illustrates an optical element in which multiple pixels 5261-3 of a spatial light modulator 504 are 15 associated with one light points forming element 5201,2. 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 5221-3 and the light, transmitting 20 face of the substrate may include mask elements 5281,2 comprising multiple apertures 5241-3. 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 25 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 5251,3 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 30 will be largely blocked by the masking element 528i. A similar blocking effect takes place with light 523₂,523₃ o r .1 g i n a t i n g 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 35 wavelengths in the visible and, optionally, the invisible spectrum.

6

Hence, in this embodiment, the optical element may

CL plurality of color light source forming elements, qe points of different wavelengths, e.g. RGB or colours defined bv another images.

element 508s comprising a transparent substrate gh emitting face. The t rans p a r e n t enses or transmitting areas forming elements may include a masking eiemenu comprising point in the direction normal element may be the res in

CL l··,

1-5 enable accurate reconstruction of a sing limited computational and hardware

7 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=l,...,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 612k.

Fig. 7 depict.s a slow diagram of a method tor 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 computerreadable 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 612k may be determined or known in advance.

In a second step 704, the processor may receive ligh 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 intensityand 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 represents 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 I_A and/or phase value Φ_Α 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=l,...,n) of the optical system, a distance dk 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 ik of light to be emitted by each of the light points 612k may be determined on the basis of

2Ü point A. In a further embodiment, (Dk of the light emitted by the light points

In this calculation, r om

Optionally, in an embodiment, the calculation of the

Cl <pk~ Φα-Δ®].; . This inversion may be required for correctly pos j ioning the perceived holographic image with res the light sources, e.g. in front of the light sources as seen

Hence, based on the method as

r.

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 inform.at.ion 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 (e.g. a of holographic system according to another embodiment of the invention, m this particular embodiment, the optical system may be used to generate an interference light field of a holographic image 35 816 (in thi s 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=l,...,n, wherein n is a positive integer) ii 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 15 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 20 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 i	.ntensity i	and ]	phase for e	:ach light point
25	When	the s	emulation £	jrogram is execu	ted, the
	pr oce s s or may ,	in a	first step	902,	receive or	>tical 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 30 distribution of light points and the wavelength emitted by the light points.

In a second step 904, the processor may receive ligh 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 I_m and phase values Φ® at a predetermined number of light field positions p_;!1(1=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 I_R and phase value Φ. associated with a reference source R at reference position PR .

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 I_m and phase values Φ_;Γ, at light, field positions p_;;i (m=l,...,t) representing in this example points of a cube may include a first light intensity value Ii at position pi (point A in Fig. 8) and a second light, intensity value 12 at.

position p₂ (point B in Fig. 8) and, optionally, a first phase Φι at light field position pi and a second phase Φ2 at light field position p₂, wherein phase Φι and phase Φ2 may 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 = l,...,n) of the simulated optical system, a distance rx between light points k and reference light source R.

Similarly, in a fifth step 910, the computer may det.erm.ine distances dk,m between light point, k and light field position p_;r. (m-l,...t; k—l,...n) . These distances then can be used to determine for each light point k (k=l,...,n) an intensity value ik and, optionally, a phase value φ:< of light to be emitted by light point k.

As shown in Fig. 8, the int ensity ik and phase φκ of a light point k may be simply calculated as a superposition of

W ci V Θ S v aiue 11

{ J_ , £ „	~~ ri e
) may	be i
it ies	of .

ƒ ··’ ƒ lie ight field position pi may be determined by pos on pi (point A) and the position of the first light cl

-J square of the distance between light field position pi (point

B) and the position oy s mining each light field points p_m.

gn (nn dif i by xr stance between light field

B and light source 812i by the waveleno l··, of the which inversion may be ources,

Hence, for each light point

CL the phase contributions that travel from a gn that originate from 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 10 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 15 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 illu strates the top-view of an optical element according to one embodiment of the invention. The

O JJ L J- C cl 1 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 25 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 30 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 35 elements have a one-to-one correspondence with the pixels of a SLM. For illustrative purpose the optical element 1008 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 Moiré pattern will appear. Based on this Moiré 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 c o r re spοndence).

In an embodiment, the optical element may comprise alignment regions 10201-4. In the length and width directions of these alignment regions a 'mismatch' of one pixel may be applied, resulting in a cross-shaped Moiré pattern when properly aligned with the underlying spatial light modulator.

Figs. 11-13 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 20 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 35 spatial light modulator faces the light receiving face of the optical element. The optical element comprises sparsely aperiodically distributed apertures in order to generate a distribution of light point which are a-periodically distributed (as explained in detail with reference to Fig. 15). 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 10 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. 11 snows the simulation results for an optical system that comprises a computer-controlled spatial light 15 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 and phase) of the spatial light modulator calculated for this system. The configured pixels of the spatial light, modulator should give 20 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 25 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 30 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.

6

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 ydirection (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 x20 and y-direction. Each aperture is 2 pm 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 12121, 12121, and 1212a. 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 12061, 12062 and 1206s. Aperture 12121 receives light from pixel 12061, aperture 1212a receives light from pixel 1206a, aperture 12123 receives light from

0 pixel I2O63.

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.

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. 14 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 midair .

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 incl	ude at least one processor	1502	coupled to	memory
Θ1 ΘΓιϊΘ n is s	1504 through a system bus	1506.	As such,	the data

processing system may store programt 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 10 1508 and one or more bulk storacre devices 1510. The local random access memory or other non execution the program may be

CL storage one or orage least some program code in order to reduce the number 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 physical object, such as e.g. a stylus or a tinge on or near the touch screen display.

of a user

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 5 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 10 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 30 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 computerreadable media, with the sole exception being a transitory, 35 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 10 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 15 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 20 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, 25 or act for performing the function in combination with other claimed elements as specifically claimed. The description of

embodiments	of	the present	invent.	i. ο n	has been	presented for
purposes of	i 1	lustration, b	ut is	not	intended	to be exhaustive
or limited t	o	the implement	ations	in	the form	disclosed. Many
modification	.	and variation	s will	be	apparent	to those of
ordinary ski	11	in the art w	_L U 11 O IJ. U	dep	art.ing f:	roro 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 35 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

CONCLUSIONS

An optical system arranged 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 with 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 being a a light receiving area on the light receiving side of the first substrate and an associated light emitting area on the light emitting side of the first substrate; wherein the light receiving area of a light point-forming element is arranged to receive light from a reference light source and to form a light point which emits light from the light-emitting area; wherein at least one mask element and / or light refracting element in each light point forming element is arranged to cause the positions of the light points to be arranged aperiodically or randomly in at least one direction in a plane of the substrate; and wherein the pixels of the spatial light modulator are arranged to control the intensity, and optionally the phase, of the light emitted by the light points, the emitted light forming the interference light field at a predetermined location relative to the optical system.

An optical system according to claim 1, wherein each light-point-forming element comprises a mask element comprising at least one opening, the at least one opening being substantially smaller than the area of pixels of the spatial light modulator, preferably the openings in mask elements of different light-point-forming elements have different positions; and / or, mask elements of different light-point-forming elements are arranged in different planes of the substrate.

The optical system according to claim 2, wherein the mask elements are arranged on the light receiving side of the light-point forming elements and wherein elements of a transparent material of different dimensions are formed over different openings.

Optical system according to one or more of claims

1-3, wherein each light-point-forming element comprises at least one light-refracting element, arranged to focus light at a point, preferably the optical axis of different light-point-forming elements being at different positions with respect to the center of the light receiving areas; and / or, the refractive elements of different light-forming elements have different focal points, preferably the different positions of the optical axes and / or the different focal points vary aperiodically or randomly within a predetermined range.

Optical system according to one or more of claims 1-4, wherein the light receiving area of a light-point-forming element is arranged as a light-refracting element, the light-emitting area comprising a mask element comprising at least one opening, preferably the light-refracting element being arranged to focus at least a portion of the light received by the refractive element on the at least one opening.

Optical system according to one or more of claims 1 to 5, wherein the light-refracting element is adapted to receive light from two or more pixels of the spatial light modulator and to focus the light from the two or more pixels on two or more openings in the mask element of the light-point-forming element, respectively.

Optical system according to one or more of claims

1-6 wherein the length of optical paths of different light-shaping elements varies aperiodically or randomly within a predetermined range of optical path lengths, preferably the distance between a plane through the substrate and the light-emitting regions of different light-formed elements varying aperiodically or randomly within a predetermined range of optical path lengths certain range.

Optical system according to one or more of claims

1-7, wherein at least a second transparent substrate is attached to the light-emitting side of the first transparent substrate, wherein the refractive index of the second transparent substrate is greater than the refractive index of the medium on the light-emitting side of the second substrate.

Optical system according to one or more of claims

1-8, wherein the pixels of the spatial light modulator are arranged to control the intensity, and optionally the phase, of the light emitted by the light points, the light from the light points reconstructing or at least partially reconstructing the light field at a predetermined position relative to the optical element.

The optical system according to any of claims 1 to 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 arranged to use the control information to control the electrically addressable spatial light modulator so that each light point emits light from a predetermined intensity and / or phase for reconstructing the light field.

An optical element arranged to form an aperiodic or random distribution of light points, preferably the optical element being used in an optical system according to one or more of claims 1-10, the optical element comprising:

an arrangement, preferably a periodic arrangement, of light-point-forming elements formed in a first transparent substrate, each light-point-forming element comprising a light receiving area on the light receiving side of the first substrate and an associated light emitting area on the light emitting side of the first substrate; wherein the light receiving area of a light point forming element is arranged to receive light from a reference light source and to form a light point which emits light from the light emitting area; and, at least one mask element and / or light refracting element in each light point forming element arranged to cause the positions of the light points to be arranged aperiodically or randomly in at least one direction in a plane of the first substrate.

A method of 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 from a reference light source to the light receiving side of the optical element, the optical element comprising an arrangement of light point forming elements and a first transparent substrate, each light point forming element comprising a light receiving area on the light receiving side of the first substrate and an associated light emitting area on the light-emitting side of the first substrate;

receiving by the light receiving areas of the light point forming elements light from the reference light source and forming a light point which emits light from the light emitting area; wherein at least one mask element and / or light refractive element in each light point forming element cause the locations of the light points to be arranged aperiodically or randomly in at least one direction in a plane of the first substrate;

controlling by a computer the pixels of the spatial light modulator, the pixels being optically aligned with the light-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 from each light point forming a light field at a predetermined location relative to the optical system.

The methods of claim 12, wherein the pixels are controlled based on holographic data, the holographic data representing intensity values, and optionally phase values, of the light to be emitted from the light points, the holographic data enabling the optical system to reconstruct a predetermined holographic image.

A computer-implemented method of determining holographic data for a spatial light modulator, wherein the spatial light modulator and an optical element form an optical system adapted to reconstruct an interference light field, the method comprising receiving light field information, wherein the light field information intensity values I _m and phase values and associated light field positions p _m (m = 1, ..., t);

receiving optical model information, the optical model information associated with an optical element comprising an arrangement of light-point-forming elements in a substrate, the light-point-forming elements arranged to form an aperiodic or random distribution of light points based on light from a reference light source, wherein the optical model information includes the locations of the light points and the wavelength of the light emitted by the light points;

determining for each light point k (k = l, ..., n) the distance dk, ® between the light point k and the light field position p _m (m = l, ..., t) and calculating an intensity i and, optionally phase <j> k, of light to be emitted by each light point based on dk, m and the light field information.

A computer program or suite of computer programs comprising at least one software code section or a computer program product that has stored at least one software code section, the software code section, when executed on a computer system, being configured to perform the method of claims 12-14.

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