WO2002005270A1 - Method for generating a phase code for holographic data storage - Google Patents

Abstract

The invention relates to a method for generating a phase code for a reference wave for holographic data storage. In the method, a first and second phase code is selected, wherein the first phase code is compared with one or more second phase codes in an optimisation procedure. The comparison is done by calculating the difference between an object and its restored image. The restored image is calculated as being restored from a hologram created with a reference wave coded with the first and/or second phase code.

Description

METHOD FOR GENERATING A PHASE CODE FOR HOLOGRAPHIC DATA

STORAGE

Technical Field The invention concerns a method for encrypting and/or multiplexing data stored in non-Bragg selective holographic recording material. The invention also concerns a method for generating phase codes for a reference wave, for the.purposes of holographic data storage.

Background Art

Holographic data storage presents serious advantages over traditional electronic, magnetic or optical, storage systems with the potentiality of low cost, high storage capacity, high transfer rate, immunity against electromagnetic perturbations and last but not least,; hardware-based data encryption. The development of holographic storage systems was implemented mainly on thick-Braggrselective- and thin scalar holograms.

To overcome the difficulties concerning the storage media for recording scalar holograms, e.g. photoemulsion, which is not dynamic and difficult to use, or photorefractive crystals (Fe-doped LiNb0₃), which are very expensive and sensitive for mechanical impact, we use polarization-sensitive medium (polymer layer with photoinduced anisotropy), as the rapid improvement of the sensitivity, diffraction efficiency and resolution of polarization-sensitive storage media made it possible to store data in the forms of polarization holograms.

The invention is applicable with a holographic recording system using thin polarization-sensitive storage medium. In such a system the data blocks are stored in the forms of Fourier-holograms, which are possibly multiplexed, and/or security encrypted. In the recent years there has been ceaseless efforts on both multiplexed and security encrypted holographic data storage. There are many methods for multiplexing holograms, e.g. wavelength-, shift-, angle-, rotation-, and phase-coded multiplexing. Almost all of these methods have been used with both thin and thick scalar holograms, but there have been no working implementations for data storage in the form of polarization holograms.

Using the wavelength-multiplexing method, either several different lasers are needed, or one laser radiating at many wavelengths.;, These solutions are rather complicated and expensive for using in a commercial data storage system. Further, wavelength-, angle-, and rotation multiplexing demands high-Bragg selectivity of the storage material, otherwise the reconstructed beams diffracted from the multiplexed holograms overlap, the Signal to Noise Ratio (SNR).!s very low. Thus neither of these methods are appropriate for use in non-Bragg-selective holography. A known multiplexing method is phase-coded multiplexing. This method is described by C. Denz, G. Pauliat, G. Roosen, in: Volume Hologram Multiplexing Using a Deterministic Phase Encoding Method, Opt. Lett. Vol. 85, 171 (1991). Phase coded multiplexing can be carried out by a phase-modulating Spatial Light Modulator (SLM) and needs no precise mechanical actuators, lasers radiating at many wavelengths, or acousto-optical elements (modulators, scanners, etc.). The phase encoding method has the potentiality of using in non-Bragg-selective systems as there is a possibility of suppressing the noise-part of the response function of the storage system by destructive interference.

Phase encoding is also used in many ways for security encryption of data, both in the forms of thin and thick scalar holograms. The phase code used for encryption of the data blocks can be either random or deterministic. Random phase codes can be realized by transmitting the beam to be encoded through a mobile ground-glass plate, in that case the codes are generated by moving the diffuser plate, a hologram taken with a certain position of the diffuser can be properly reconstructed only if the actual position of the plate is the same during recording and reconstruction. In most applications the phase code is applied on the object beam both in the real and/or in the Fourier-plane.

As shown above, holographic data storage in highly Bragg selective bulk storage materials has been largely investigated in previous works. The practical usability of these materials is limited by the fact that they can not be applied to removable media and they require strict positioning tolerances in the data storage system. Therefore, it is proposed to realise data storage in thin layer storage material without or with limited Bragg selectivity only. The ^! use of such material presents the following advantages: ^;

feasible for removable media (e.g. memory card, tape etc.) because of the thin layer

-relaxed positioning tolerances, hence less costly optics arid mechanics

The use of different writing and reading wavelength is possible, which allows the use of certain holographic storage materials which are re-recordable, such as Side- Chain Liquid Polyesters (SCLP).

The lack of Bragg selectivity results in noise beams when reconstructing the hologram. The proposed method generates phase codes for the reference wave for holographic data storage taking into account the above noise beams. The procedure optimises the phase coded reference wave so that the noise beams interferes either destructively or positively, appropriately to allow encryption and/or multiplexing of the stored data.

Summary of the Invention

To find appropriate phase codes, we suggest a method for generating a phase code for a reference wave for holographic data storage, in particular for holographic data storage in thin layer storage material. According to the invention, the suggested method comprises the steps of: a, selecting a first phase code, and b, selecting a second phase code, preferably, but not necessarily by modifying the first phase code or by selecting from a group of predetermined phase codes, wherein the first phase code is compared with one or more second phase codes in the optimisation procedure. i

Advantageously, the difference between an object and its restored image is calculated to compare a first phase code and a second phase code, where the restored image is calculated as being restored: from a hologram created with a reference wave coded with the first and/or second phase code.

If the inventive method is used to find phase codes for encryption, it is foreseen that a, the difference between the restored image of an object and the respective object is minimised when using a first phase code for the reference wave for recording the hologram, and using the same first phase code for the reference wave for restoring the hologram and b, the difference between the restored images and the respective objects is maximised when using a first phase code for the reference wave for recording the hologram, and using a second phase code for the reference wave for restoring the hologram.

If the inventive method is used to find phase codes for multiplexing, it is foreseen that the restored image is calculated as being restored from a hologram recorded with a reference wave coded with a first phase code and a first object and the hologram also being recorded with a reference wave coded with a second phase code and a second object, and a, the difference between the restored image of a first object and the respective first object is minimised when using the first phase code for the reference wave for recording a the hologram, and using the same first phase code for the reference wave for restoring the hologram and 5 b, the difference between the restored image of a second object and the respective second object is minimised when using the second phase code for the reference wave for recording the hologram, and using the same second phase code for the i . , . reference wave for restoring the hologram. • i ,.

10 In most data storage applications a digital data array is used as object. It is therefore practical if the difference between the restored image of the digital data array and the respective digital bitmap is calculated from the bitierror rate.

It is^a particular feature of the invention that in a preferred embodiment the 15 difference between the restored images and the respective objects is calculated based on auto-correlation and/or cross correlation. This facilitates the calculation of the difference with computer simulation.

A particular application of the method is to Fourier holograms. Further, it is 20 foreseen to use the method with polarisation holograms. The invention also concerns a method for recording phase-code encrypted or multiplexed data in substantially non-Bragg selective holographic recording material, where the phase codes were generated according to the inventive method.

25 The inventive method is applicable for different optical arrangements. In a first arrangement, the reference wave generating device is imaged onto the holographic storage layer. In an other optical arrangement, the reference wave generating device is projected onto the holographic storage layer by non-geometrical imaging, particularly by Fourier transformation. Brief Description of Drawings

The invention will be explained below with the help of the ensuing detailed description and the attached figures, where Fig. 1 is a perspective view of a card used for the recording of holograms coded with the phase codes obtained with the invention, Fig. 2 is a side and top view of the card shown in Fig. 1 , Fig. 3 shows the structure of the medium of the card show in Fig. 1 in cross section, Fig. 4. is a diagram of a first optical arrangement, which is simulated in the calculations when the method is performed, :« > Fig. 5 ;is a principal drawing of the ray propagation of the object beam in the optical system shown in Fig. 4, Fig. 6. s a principal drawing of the ray propagation of the reference beam in ^{• ' ■•} the optical system shown in Fig. 4,

Fig. 7 is an optical layout of a modified optical system similar to that of Fig.

: - 4, Fig. 8 is a principal drawing of the ray propagation of the reference beam in the optical system shown in Fig. 7, Fig. 9 is a schematic figure of the phase code on the phase SLM in Figs. 4 and 7, Fig. 10a is a schematic figure of the amplitude modulation of the amplitude

SLM of Figs. 4 and 7, Fig. 10b is a schematic figure of the phase modulation of the random phase mask of Figs. 4 and 7,

Fig. 10c is a schematic figure of the polarising layer of one of the polarising beam splitters of Figs. 4 and 7, Fig. 11 illustrates the formation of the code elements of a phase code,

Fig. 12 illustrates a one-dimensional phase code, Fig. 13 and 14 illustrates the composition of a phase code from code elements

Fig. 15 illustrates multiple codes for a phase code SLM,

Fig. 16 illustrates the selection of multiplexing phase codes from a set of phase codes, Fig. 17. show calculated results of an optimised autocorrelation function for a one-dimensional phase code, similar in structure to that shown in Fig.

12, Fig. 18. i show calculated results of an optimised cross-correlation function for the one-dimensional phase code, similar in structure to that shown in Fig. 12, ■

Fig. 19. show calculated results of an optimised autocorrelation function for a two-dimensional phase code, similar in structure to that shown in Fig.

9, Fig. 20. show calculated results of an optimised crossi-correlation function for a ^! two-dimensional phase code, similar in structure to that shown in Fig.

9, Fig. 21. shows the angle selectivity as a function of recording layer thickness,

Fig. 22 is an alternative embodiment of the optical system shown in Fig.4,

Fig. 23 is a modified embodiment of the optical system shown in Fig.22, Fig. 24 illustrates the common SLM of the optical systems shown in Figs. 22 and 23.

Best Mode for Carrying out the Invention

The data encrypting and multiplexing method of the invention will be explained with reference to a recording on an optical card 1, which is shown in Figs. 1-3. The card 1 is equipped with an optical medium 2, which is suitable for holographic recording. The optical medium 2 comprises a mechanical support layer, which carries an optical layer structure 3. The specific physical data storage medium is actually the optical layer structure 3. The optical card 1 is recorded and read by an optical recording apparatus, which is not shown here in all detail. The apparatus comprises a suitable write/read optical unit. Certain details of the write-read optical unit will be explained below.

The card 1 may be multiply written (recorded), read and erased, which latter is ensured by the material of the storage layer in the optical layer structure 3. There is a separate carrier. (substrate) layer 5 within the optical layer structure 3 on the optical medium 2. The carrier layer 5 provides an optical quality surface, and it is attached to the surface of the card with a bonding layer 4. The carrier layer 5 is covered with a mirror layer 6, the storage layer 7 and the protective layer 8. The . card 1 is sized as a standard credit card, but other sizes are also applicable. In the .. figures, the layer structure 3 stands out from the plane of the card 1, but it is not necessary. Optionally, the top layer of the layer structure 3, i.e. the protective ayer 8 may completely flush with the plane of the card 1, or may be even below this. plane. In this case the medium 2 is sunk into the card 1.

In the following, the holographic recording and readout of data on the optical layer structure 3 is presented. An image of a two-dimensional data source is recorded in a hologram on an optical medium. In the examples shown below, the two-dimensional data source is realised with an SLM matrix. The recorded hologram is resulting from an interference between an object beam and reference beam in a Fourier-plane associated to the image of the data source. In the present case the optical medium is the optical medium 2 on the card 1. During the readout, the recorded hologram, more precisely, the image restored from the hologram, is detected with a two- dimensional detector.

Polarization holograms can be recorded in media with photoinduced anisotropy by using a reference and an object beam of orthogonal polarization. The most effective way to record polarization holograms is to use orthogonal circularly polarized beams for object and reference. In that case the a diffraction efficiency of 100 % can be achieved considering ideal storage medium for recording the polarization hologram (the ideal material would have a transmittance of 100 %, a very fine domain structure -i.e. the size of the domains are below the wavelength of the light-, and a deep modulation of the optical anisotropy).

Using a reference beam of the same polarization -i.e. left-, or right-handed circular- for reconstruction of the hologram, as for recording it, the reconstructed beam will propagate in the direction of the original object beam, i.e. the light will be diffracted only in the (+l)-th order. Considering real -not ideal- storage medium we observe the reference to be diffracted both in the 0 and «+l orders of diffraction, but unlike noticed for thin scalar holograms, no light is diffracted in any other orders. If the polarization states of the reconstructing and recording references are orthogonal, the reconstructing beam will be diffracted in the (-l)-th order. The proposed method for encrypting and multiplexing is developed with an eye

, . towards the use of thin -not Bragg selective- storage layers. With such layers the diffraction efficiency is independent of the mutual angle of the reference beams used for recording and reconstruction of a particular hologram, but the direction of the reconstructed beam -the (+l)-th order of diffraction- "rotates" together with the reconstructing reference, the angle subtended by the directions of the object-, and reconstructed beams is equal to the angle of the recording and reconstructing reference beams, respectively.

Next, the formation of a polarization hologram will be explained, considering the method discussed above. The object beam is a circularly polarized plane wave, the reference beam also a plane wave of orthogonal circular polarization. The directions of the waves are symmetrical, subtending an angle ±θ with the normal of incidence at the holographic plane, respectively. The resultant field at the hologram plane then has a constant intensity, only the polarization state is space dependent. The spatial frequency depends on the angle 2Θ subtended by the object and reference beams, the frequency is proportional with the sinus of this angle. The polarization state of the total field is elliptical, the shape and the position of the polarization ellipse depends on the local phase difference of the plane waves generating the hologram. For small θ angles of incidence the total field can be considered as linearly polarized, with a Jones-vector lying the hologram plane. The axis of the polarization rotates with respect to the variation of the phase difference of the beams. For greater angles the electric field vector of the total field does not fall in the hologram plane, the field can not be described as linearly polarized. Instead, the electric field varies in three dimensions.

The calculations shown below were performed for non-Bragg selective material, but it is also possible to include the Bragg-selectivity of the storage medium in the calculations, in order to take into account a certain level of Bragg-selectivity. The diffraction efficiency of thick polarization holograms has an analogous dependence on the angle subtended by the recording and reconstructing reference beams as observed in case of thick scalar holograms. The response of a polarization holographic arrangement can be obtained in two steps. First, the response of the arrangement has to be determined in terms of the angle considering thin storage layer, next this response function must be multiplied with the angular selectivity, i.e. the function showing the diffraction efficiency vs. the angle difference between the recording and reconstructing reference waves.

This invention partly concerns a method to define phase codes for coding the reference beams. The method is shown with the use of thin polarization holograms, but the method is also applicable for other types of holograms. It is sought to find codes in which the parasitic waves of the response function interfere destructively, thus yielding an acceptable SNR (Signal to Noise Ratio) of the storage system, if multiplexing is contemplated. Or, on the contrary in the case of encryption, the method provides phase codes, with which the parasitic waves of the response function interfere to destroy the actual data, if not the correct phase codes are used for readout.

There are two basic arrangements for writing and reading phase-encoded polarization Fourier-holograms of an amplitude SLM (Spatial Light Modulator) with object-, and reference beams of orthogonal circular polarization, using a phase SLM for generating the phase code. Below, both of these arrangements will be discussed.

In the case of both arrangements above the object - an illuminated amplitude SLM - is Fourier-transformed to the hologram plane through a Fourier-lens, the reconstructed beam is also transformed by a Fourier-lens and in practice it is captured by a CCD. The difference between the arrangements is in the method of generating the phase-encoded reference beam. The reference can be generated either as Fourier-transformed or simple (geometrical) imaging of a phase- SLM on the hologram plane. An imaging is considered as a geometrical imaging when a real image of the imaged object is created.

Turning now to Fig. 4, there is shown a schematic first optical arrangement for phase encoded data storage with geometrically imaged reference beam. The light emitted by the laser 31 passes through the beam expander optics 32, then it is divided in an object beam 35 and a reference beam 36 by a beam splitter 34. The reference beam 36 passes through a beam forming optics 40 and spherical beam converter 41 until the phase-SLM 42. This phase-SLM 42 generates the phase code and it is imaged through the first Fourier-lens 52 and the second Fourier-lens 48 on the hologram plane of the optical card 1 through the other beam splitters 45 and 46. The object beam 36 passes through an amplitude modulating SLM 44, which is generating the data blocks. The SLM 44 is imaged through Fourier-lenses 47 and 48 and through polarising beam splitters 45 and 46 on the optical card 1. The total field generates the holographic pattern at the recording layer 7 of the optical card 1. During reconstruction the reference beam is diffracted from the hologram, the diffracted wave is imaged by the Fourier-lens 48 to the image plane of a CCD-array 54.

The light source of the optical system is constituted by a laser 31, in the present example a green diode laser. The beam of the laser 31 has a Gaussian distribution, and the beam is expanded by a spherical beam expander 32 to an appropriate size. In order to achieve a better wavefront, it is also possible to apply spatial filtering in this location with the pinhole method.

The beam is divided into two beams with appropriate intensity, by the beam splitter cube 34, namely into an object beam 35 and a reference beam 36. Optionally, the intensity ratio between the object and reference beams may be modified with the division ratio of the beam splitter cube 34.

The object beam 35 and the reference beam 36 propagates along the sides of a rectangle, and the opposing sides of the rectangle constitute the two arms of an interferometer. The beam diversion on the three comers of the rectangle is made by the plane mirrors 37,38 and 43, having dielectric mirror layers. With the appropriate adjustment of the side lengths of the rectangle, the equal length of the optical path of the object and reference beams until the layer structure 3 may be ensured.

In the object beam arm, the expanded object beam 35 having a Gaussian distribution is transformed into a homogenous plane wave with the beam forming optics 39. This latter is a single piece lens with two aspheric surfaces. Similarly, in the reference arm the expanded Gaussian beam is transformed into a homogenous plane wave with the beam forming optics 40. The homogenous beam is compressed to the appropriate size with a spherical beam converter 41. Optionally, the aspheric beam forming optics 40 may be omitted, or substituted by a plane parallel plate, which allows the use of an illuminating beam having a Gaussian profile in the reference arm. In this case this factor must be taken into consideration when the beam converter 41 is designed.

In the reference arm, there is a further mirror 43 following the beam converter 41-, followed by the phase SLM 42. The phase-SLM 42 is imaged onto the card 1 with the reference beam 36. In the present case the used phase-SLM has the form of a square, but SLM-s in the form of a circle or other shape could be equally applicable. The coupling of the object beam 35 and the reference beam 36 is done along one side of the rectangle. The object beam 35 is coupled onto the SLM 44 with the mirror 38. The SLM 44 constitutes a two-dimensional data source ( in the presented embodiment an LCD-based transmission mode SLM is used). The hologram of the active area of the SLM 44 is recorded on the card 1, in the recording layer 7 of the layer structure 3. As shown in Fig. 10a, the SLM 44 is an amplitude modulating SLM. The central area 69 of the SLM 44 is not modulated, as the rays going through these pixels would coincide with the rays of the reference beam 35.

The optical axis of the Fourier holographic optics, which provides an object/image imaging, is perpendicular to the beams illuminating the 44 SLM and the phase SLM 42. The SLM 44 constitutes the object of the holographic optical system, while the phase SLM 42 serves as the image plane of the reference of the holographic optical system. The principle of this Fourier holographic system is shown in a folded-out position in Figs. 5 and 6. The object/image arm, which is constituted by the object beam 35, is realised as a so-called 8f system, and it is shown in Fig. 5. This object arm also comprises the polarising splitter prisms 45 and 46 (the polarising splitter prisms are not shown in the Figs. 5,6 and 8, because they have no role in the imaging itself, but only serve the coupling of the object and reference beams into the optical path. The write/read system comprises two identical Fourier objectives 47 and 48. There is a mirror in each Fourier plane (focal plane) 49 and 50 of the Fourier objectives 47 and 48, so in this manner it is possible to use only two Fourier objectives for the 8f system, instead of the four objectives that are theoretically required. The first mirror is the mirror 51, which is also used as spatial filtering means. The other mirror is the hologram 9 itself, which is recorded in the layer structure 3 of the holographic card, and the mirror layer 6 below the hologram 9 in the layer structure 3 (see also Fig. 3.). As it is apparent from Fig. 4, the splitter prisms 45 and 46 are between the two Fourier objectives 47 and 48.

The reference arm, which is constituted by the reference beam 36, is a so-called 4f system (see also Fig. 6), which images the image of the reference aperture 42 onto the hologram 9. The system comprises two Fourier objectives, which are different in design and focal length. The first Fourier objective 52 is a single piece optics, and it is located between the reference phase SLM 42 and the coupling polarising splitter prism 45. The second objective is common with the second Fourier objective 48 of the object/image arm. With the appropriate selection of the focal lengths of the Fourier objectives 52 and 48, the phase SLM 42 may be imaged onto the holographic card 1 with suitable magnification or reduction.

The object beam 35 and the reference beam 36 is coupled together through the first polarising splitter prism 45. The polarising splitter layer 58 deflects the object beam 35 upwards, towards the first Fourier objective 47, while the reference beam 36 is directed downwards, towards the common focal plane of the Fourier objectives 52 and 48.

The SLM 44 constituting the object is positioned in the first focal plane of the optical imaging system embodied by the first Fourier objective 47. A mirror 51 is placed in the rear focal plane, in the so-called Fourier plane. In the presented embodiment the mirror 51 is a plane mirror of with a predetermined size. Thus the optical system comprises a further Fourier plane, beside the necessary Fourier plane for creating the hologram itself. This further Fourier plane is formed before the hologram on the optical path. The mirror 51 is placed in this further Fourier plane.

During the writing of the holograms, the mirror 51 serves asm spatial filtering, means in the holographic optical system.

The Fourier-objectives 47 and 48, the mirror 51 and the hologram 9 constitutes a symmetrical optical system, and in the middle part of this system (between the polarising splitter prisms 45 and 46) a real image of the SLM 44 is created. In this image plane a random distribution phase mask 53 is placed, with a pixel arrangement. The position, size and number of the pixels of the phase mask 53 is the same as the corresponding data of the SLM 44. The phase mask 53 adds a random phase shift in the object beam 35, which is changing at every pixel. With this phase mask 53 the appearance of the large Fourier components is prevented, which would result from the periodicity of the bitmap image written onto the SLM 44, and those large components are also eliminated, which result from the diffraction on the aperture of the SLM 44, appearing around the zero spatial frequency.

The Fourier transform of the Phase SLM 42 in the reference arm appears in the middle of the phase mask 53. For this reason, there is no phase modulation in a central region 63 of the phase mask 53, as shown in Fig. 10b. Following the phase mask 53, the object and reference beams propagate through the second polarising splitter prism, and the second Fourier objective 48, in order to generate/reconstruct/erase the hologram on the card. During readout, the reconstructed image of the hologram 9 is imaged by the reflected object beam 38 through the second Fourier objective 48, and it is deflected towards the CCD detector matrix 54 by the second polarising splitter prism 46. After the polarising splitter prisms there are 1/4 plates 55 and 56, which perform a linear-circular, and circular-linear polarisation transformations, respectively. Thereby the light going through the 1/4 plate 55, being reflected on the mirror 51, and again going through the 1/4 plate 55 will have a linear polarisation, perpendicular to its previous state of polarisation.

In the polarising layer 57 of the second splitter prism 46, which is closer to the card 1, there is a small central region 61 without a splitter layer. This latter is also illustrated in Fig. 10c. This central region 61 serves for the lead-through of the reference beam 36. In this manner the reference beam 36, which propagates towards the card 1 with an orthogonal polarisation relative to the object beam 35, will go through the splitter layer 57 without reflection. With other words, there is a separate channel in the optics for the propagation of the reference beam 36, and this channel comprises two principal elements: the non-modulating region 63 in the centre of the phase mask 53 (see Fig. 10b), and the region 61 without the splitter layer formed in the polarising splitter layer 57 of the polarising splitter prism 46.

The reference beam 36, which is reflected from the card 1 without diffraction, and other components thereof reflected from the lens surfaces will not reach the detector, because these will pass twice through the 1/4 plate 56. Even so, a further polarising filter or a shutter 60 may be placed before the CCD detector matrix 54, in order to filter out eventual scattered light. This optical arrangement shown in Fig. 4 is more suitable for encrypted data recording.

The optical arrangement of Fig. 7 and 8 shows a second optical arrangement for phase encoded data storage with a Fourier-transformed reference beam. The arrangement works similarly as the optical system discussed with reference to Figs. 4. The optical path of the object beam 36 follows the same route as explained above and shown in Fig 5. The difference is that the lens 52 is substituted by the reference objective 62, which images the phase SLM 42 on the plane of the random phase mask 53. Thereafter, this image of the code-generating phase SLM 42 is Fourier- transformed on the hologram plane. This optical arrangement is more suitable for multiplexed recording.

On the optical card 1 the data blocks are stored in forms of Fourier-holograms. A point-like object at a particular position at the object plane will give rise then to a plane-wave of a particular direction at the hologram plane. By determining the response of the holographic arrangement given for a plane- wave object, we can obtain the Point Response Function (PRF) of the system. In view of the PRF, the output of the system -i.e. the complex amplitude-distribution at the image plane- can be calculated from the input -i.e. of the amplitude at the object plane- as a convolution.

(i)

A^Pic (w,z) = A°^bj (w,z)® PRF(w,z)

On the grounds of the plane-wave response non-Fourier holograms can also be described by a consequent application of the Fourier-analysis. To obtain the plane wave response of a thin Fourier-hologram recorded and reconstructed with complex reference beams, the object beam is assumed to be a simple plane wave and the reference beams to consist of a few plane waves of different directions (Fig. 1.).

For the sake of simplicity, some further assumptions are made:

I. The local anisotropy created by superposed holograms or successive exposures add up linearly until the index change of the material saturates.

II. The different plane- wave components of a complex reference beam interfere one by one with the corresponding object wave and create a holographic pattern.

III. The resulting hologram is the coherent sum of these partial .holograms, the diffracted beams from the elementary gratings add up linearly. Considering these assumptions, the reconstructed beam can be relatively easily described in case of an optical setup shown on Figs. 5, 7 and 8. The object-, and reference beams can be written in the form of a linear combination of plane waves, i.e.: complex exponentials.

2^0bJ - _a ^obJ . j o j (2)

N Jref HMC _ ^ _Qref\ Jkj-Z =1

2^ref2>HMC =

a re/2² ■ e k^'-yt /=ι

_A ^reβ,HMc_^ ^reβ.^HMC _{denote the} complex amplitudes of the recording and reconstructing reference beams at the hologram plane, respectively, the tilde-sign refers to the plane-wave composition. aj^ef1'² are the amplitudes, k_j the wave vectors of the plane wave components of the reference beams.

The plane wave-composition of a beam on a plane can be obtanied from its complex amplitude-distribution as a two-dimensional Fourier-transform. The operation of Fourier transform can be considered as transforming a function to a continual superposition of two-variable complex exponentials, the variables (e.g.: ω,ξ) in the Fourier domain correspond to the planar components (k_x, k_y) of the wave vector of a particular plane wave.

As mentioned, each of the plane wave components of the reconstructing reference wave interferes with the object wave and generates an elementary anisotropy- grating. During reconstruction each plane wave-component of the reconstructing reference is diffracted from each of the elementary gratings, which results N² diffracted plane waves.

The direction of the diffracted waves depends on the direction of the reference components generating the grating and diffracted from it. If these directions of the writing and reading plane waves coincide, the diffracted beam propagates along the direction of the object beam. Otherwise, the . direction of the diffracted plane wave is rotated by an angle equal to the angle subtended by the recording and reconstructing reference components. The waves propagating in directions different from the object beam (parasitic waves) give rise to noise around the image of a bright object point. The reconstructed beam can also be written as the superposition of plane waves.

2" =

e ik rtL (4) l=-N+l

k denotes a wave vector subtending an angle (l-θ) with the direction of the object beam, bj the amplitude of a plane wave propagating in the direction of the vector kf . It's easy to prove, that the bj amplitudes can be obtained as the discrete correlation of the plane wave amplitudes of the recording and reconstructing references. oo

ι =—oo

It's also easy to generalize this expression to reference beams of continuous direction-dependence.

2^dVr(ω,ξ) = 2^r -^HMC (ω,ξ)φ 2^{ref2 MC} (ω,ξ) rø

The sign ® denotes the operation of correlation, each of the beams are written in the form of plane wave-decomposition. On the grounds of Eq. (6) -describing the plane wave-decomposition of the diffracted beam at the hologram plane- we can^; determine the PRF of holographic storage system for arbitrary arrangement.

In the case of the second arrangement (see Figs 7 and 8) each pixels of the reference code-generating SLM 42 -just like the pixels of the object SLM 44 - results a plane wave at the hologram plane, i. e. at the layer 3. First we investigate that case.

Our goal is to find phase codes with an SNR allowing us to store encrypted/multiplexed data. In order to construct the proper codes, we will determine the point response function (PRF) of the system, i.e. the complex amplitude-distribution observed at the image plane considering a point-like object in a simple form fit for computer simulations. Then we calculate the output as the convolution of the input and the response function and generate an optimized set of codes. The complex amplitude ^IC'^CCD _at the image plane can be obtained as the Fourier- transform of the amplitude of the diffracted beam while reconstruction of the hologram (A^pιc'^HMC).

PRF (w, z) = A^pic>CCD (w, z) = FT [A^^HMC (X, y)} oo

We denoted the spatial coordinates at the hologram-, and the image plane by (x,y) and (w,z), respectively. The reconstructed beam, which is needed for determining the PRF, is given in the form of plane wave-composition in Eq. (6) As we need the complex amplitude of the diffracted beam we take the inverse Fourier-transform of the plane wave-composition.

4^pic'^HMC (x, y) = FT^'l {2^pic'^HMC (ω,ξ)} (8)

Substituting Eq. (7) and the formula into Eq. (6) of the plane wave-composition of the diffracted beam l^p,c-^HMC(ω,ξ) in Eq. (8), we get a formula determining the response of the arrangement in terms of the writing and reading reference beams.

PRF(w, Z) = FT[FT-¹ {2^r^^HMC (ω,ξ)θ 2^ref2>HMC (ω, ξ (9)

The successive operations of Fourier-, and inverse Fourier-transforms can be omitted.

This formula is not really effective, as it contains not the complex amplitudes of the reference beams at the phase code-generating SLM, but the plane wave-composition of them at the hologram plane. We can determine the former expression in terms of the latter in quite a similar way as done with the diffracted beam.

(10) ₂ref,HMC fafl

First we wrote the plane wave composition of the beam as the Fourier-transform of the complex amplitude. Then -considering, that the code-generating SLM is imaged onto the hologram plane through a Fourier-lens- we substituted the Fourier transform of the phase-modulated encoding amplitude generated by the phase SLM ₍ f^,s^iM^ -_{nto e eX}p_ressi_on of the reference beam's complex amplitude A ^ef'^HMC _at the hologram plane. For determining the last term of Eq (10) we used a theorem about duplex Fourier- transforms, which states that the duplex Fourier transform can be eliminated similarly as the operations of successive Fourier-, and inverse Fourier-transforms,, but the duplex Fourier transform of a function is its mirror image, i.e. the argument is negative. The complex factors introduced by the Fourier-tansforms are omitted in our discussion.

Substituting Eq. (10) into Eq (9) determining the PRF of the system, we get a more effective formula.

PRF(w,z) = A^ref>SLM (- l -m)θ A^ref>SLM (- l -m) dD

Thus the point response of the holographic arrangement considering Fourier- transformed reference beam can be obtained as the correlation function of the mirror images of the reference codes -i.e. the complex amplitude-distributions at the plane of the code-generating SLM- used for recording and reconstruction of the hologram.

This formula is very efficient for computer simulations considering that the image of the pixels of the code-generating phase-SLM is fitted to the image pixels. It is satisfactory to sample both the object amplitude and the PRF at one point in each of their pixels and convolving them. The effect of the shape of the pixel masks of the SLM-s, the imperfections of the optical imaging, etc. can be considered at a later stage of the simulation as a Fourier-filtering.

Calculations were performed to determine the effect of both one and two- dimensional phase codes.

An algorithm was made for reference beams consisting of N=8 reference, beam components with binary adjustable phases (0 or.π). The algorithm computes the total amplitude of the diffracted beams for different ^angles k θ (-(N-l)< k < (N-l)) for arbitrary recording and reconstructing codes. This corresponds to the use a one- dimensional (strip-like) binary phase-SLM of 8-pixel size (a one-dimensional, phase code of eight pixels width is shown in Fig: 12).

Results of the specific calculation are shown in Figs. 17 and 18. Fig. 17. shows the amplitudes in an autocorrelation PRF, writing and reading with the same code, while Fig. 18. shows the amplitudes in a cross-correlation PRF, writing and reading with different codes.

To qualify the codes, the following quantities concerning the PRF of the holographic arrangement were introduced:

Autocorrelation SNR (Signal-to-Noise-Ratio): The intensity (squared absolute value of the complex amplitude) of the reconstructed object amplitude (auto-correlation peak), divided by the total intensity of the side-lobes of the PRF (i.e. the intensity carried by the parasitic waves).

Cross-correlation noise: The total intensity of the PRF. The geometry of the present holographic system permits reference pixels to be arranged in the forms of 2D arrays, so the investigations were also extended to 2D reference beam arrays. Consequently, the following calculations will be carried out on code matrices rather than code vectors.

It was found that the invention is suitable to find optimised sets of codes, resulting the smallest added noise in the data pages recorded in the holograms 9 on the optical card 1. Calculations were performed for phase codes of size 8x8 pixels. This code size was chosen because there are a large number of code combinations and the output images can be calculated at a satisfactory computing speed. We also investigated other code sizes from 3x3 to 10x10 and ID codes of size 1x8 to 1x160 pixels. However, the invention is applicable, to other phase code sizes as well. As an example, Fig. 9 shows a possible phase code with 6 x 6 pixel size. The different phases are indicated by the white and black colouring of the pixels, but it is noted - that no amplitude modulation is added to the reference beam. Fig. 12 shows an example of a one-dimensional code, where the pixels 12 of the phase SLM 42 have the same state along one direction. This may be useful if the positioning tolerances are lower along one dimension, typically in the direction of the movement of the optics, which is indicated by the arrow in Fig. 12.

The method for finding the proper codes is illustrated with reference to Figs. 11 and 13-15.

Both data encryption and multiplexing requires that the readout with the correct phase code (i. e. the recording phase code) provides high readout SNR. Therefore, a computer program was constructed for searching a set of codes with high autocorrelation SNR. The goal of this algorithm is to generate a set of phase codes with the maximal autocorrelation SNR. The systematic calculation of all the possible code combinations is practically impossible due to the high number of possible codes (2⁶⁴). Instead, it is proposed to use a stochastic algorithm.

It is suggested to select a first phase code, and thereafter to select a second phase code, wherein the first phase code is compared with one or more modified second phase codes in an optimisation procedure. The second phase code may be obtained by modifying the first phase ;code, or by selecting from a predetermined group of phase codes.

More particularly, the method is practically performed by calculating the difference between an object and its restored image to compare a first phase code and a second phase code, where the restored image is calculated as being restored from a hologram created with a reference wave coded with the first and/or second phase code.

Depending on whether it is sought to find phase codes for encrypting purposes or for multiplexing purposes, the same or different objects are used, and the resulting differences between images and respective objects are calculated.

In order to create effective encrypting codes, a complete phase code is divided into multiple code elements. A phase code is effective for encryption if the coded data becomes unreadable already if a small number of pixels in the phase code are changed. The phase code will have high number of variations if it consists of a large number of pixels. However, due to the physics of the hologram, the data is still readable if only a few pixels of the phase code are changed. It is sought to provide phase codes where the number of allowed deviations from the correct code is as low as possible. Therefore, a complete phase code is regarded as being composed of phase code elements, where the code elements are selected so as to result in a substantially complete destruction. For the purposes of the encryption method, the term substantially complete destruction" is to be construed as a destruction, which is satisfactory if the errors in the readout data can not be compensated with traditional error-restoring coding schemes. Standard error correcting codes can usually correct a BER of max. 4-5%. With other words, we may achieve a substantially complete destruction of the readout image, if a relatively large number of the readout pixels are incorrect. This state is normally achieved, if a certain portion of the pixels constituting the code elements are in the wrong state.

Such code elements are substantially orthogonal, since using a phase code for readout containing these code elements in their wrong state essentially result in zero readout data. More precisely, two arbitrary phase codes will be substantially orthogonal, if they contain the same code element, but in one of them all pixels of this code element are reversed. From the above it follows that further, substantially orthogonal phase codes may be generated with the help of the code elements.

It must be mentioned that if all code elements are in the opposite state, the image will be clear again, but all readout bits will be reversed again.

As an illustration, the encryption phase code pattern on the phase SLM 42 in Fig. 9 and 13 is determined as follows: a, The difference between the restored image of an object and the respective object is minimised when using a first phase code for the reference wave for recording the hologram, and using the same first phase code for the reference wave for restoring the hologram and b, the difference between the restored images and the respective objects is maximised when using a first phase code for the reference wave for recording the hologram, and using a second phase code for the reference wave for restoring the hologram.

As a first step, a phase code 31 (See Fig. 11) with all pixels 12 in an arbitrary state is selected (For better understanding, all pixels in the phase code 31 in Fig. 11 are in the same state). This is the first phase code. The recording of a hologram is simulated with the calculations above, applying this first phase code. Now this hologram may be retrieved with the best quality if the same phase code for reconstruction. The variations in the quality of the reconstructed image depend only ' bn th differences between the phase codes used for recording and reconstruction. Therefore, it is simulated to reconstruct the recorded hologram with a second phase code. -The method aims to find sets of differential pixels in the phase code, i. e. pixel sets which together strongly influence the quality of the readout image. These pixel sets will constitute the code elements., If the difference between the recording and reconstructing codes is at least as much as one or more code elements, the quality of the output image is already destroyed enough to prevent satisfactory data retrieval.

The search for the code elements starts with an array of pixels in a uniform state representing equal recording and reconstructing phase codes (i. e. where no code difference exists). Thereafter, a pixel 13 is changed. The resulting phase code is considered as the second phase code for the invention. At the same time, pixel 13 will be the first pixel in code element 1. Calculating the output image for the same object with the code difference between the first phase code and the second phase code will be confined to the pixel 13. With the second phase code now the BER of the imaging system is calculated.

The calculations are repeated by adding a randomly selected second pixel 14 to the pixel 13. If the pixels 13 and 14 together increase the BER, both are stored (at least temporarily) as belonging to code element 1. If the added pixel 14 do not increase the BER, a new one is sought.

Further pixels 15ι-15_j are added to the code element 1 in this manner. If the total effect of the pixels in the code element 1 reaches a certain threshold, e.g. BER of 20%, the code element 1 is regarded as completed, and a new code element is calculated from the remaining pixels in the phase code SLM 42. It has been found practical that the, total effect on the BER for a code element may not be to high either (e. g. not more than 40%), because this means that too many „strong" pixels are added, and -the effect of the other code elements decreases as the result. Such „strong" pixels; are usually the central pixels in the, phase code, which contribute more effectively to the readout image, than peripheral pixels. Also, it is preferable that the number of pixels in a code element is minimised to achieve the highest number of code elements from a given number of pixels. This can also be done by limiting the quality decay resulted by , a certain code element e.g. to 20%<BER<40%.

Experience showed that a phase code consisting of 8x8 pixels could be composed of ten to twenty code elements.

Fig. 13 illustrates that the phase code 70 is composed of code elements 71-75. Generally, a complete phase code 70 may contain n complementary code elements, as shown in Fig. 14. With other words, phase codes are generated as a series of complementary code elements. The code elements are complementary, since they have no common pixel, and their sum provides the total phase code.

The invention also allows the generation of phase codes for security encrypted data storage using multi-level phase codes, i. e. where the added phases of the pixels in the phase SLM may have other values beside 0 or p. Such phase codes were obtained for codes of size 8x8 pixels with an autocorrelation SNR of 74%. For comparison the highest SNR-s obtained with binary codes of this size was 100%. With the use of this code the possibility of data storage with an error rate of 3% was found.

It must be noted that the SNR can be improved by increasing the Bragg-selectivity of the storage medium to a certain extent. As mentioned, the angular selectivity of the medium can be easily included in the above shown model by multiplying the plane wave decomposition of the response function calculated for the non-selective case with the selectivity-function of the layer. Calculations with a 10. μm thick layer made of the same material show he possibility of recording non-selective polarization holograms (the former -thin- layer _.was 1 μm of thickness). Our calculations have shown that there is a possibility of multiplexing ten data pages considering Bragg-selective material. This is because the point response function can be improved if a limited Bragg selectivity is taken into account. In this case, the noise beams will be reduced, since the Bragg condition is not completely matched. The angular selectivity of a holographic grating (FWHM angle deviation from the Bragg condition) can be estimated. Figure 21 shows the estimated angle selectivity for symmetric incidence of the two beams under +/- 25 degrees, as a function of material thickness.

If the angle separation between the reference wave components are e.g. 3 times higher than the angular selectivity, the noises will be suppressed by about a factor 100. This corresponds to a reference beam spacing of about 10 degrees and 6 degrees for 13μm and 25μm thick layer respectively. Within a reference angle of about 35 degrees, 3x3 or 6x6 different angles may be used for the reference beams. That would correspond to a multiplexing factor of 9 and 36 for 13μm and 25μm thick layer respectively. The achievable multiplexing factor and the raw data density is shown by the table below.

Above we have discussed calculations applicable with Fourier-transformed reference code, i.e. the phase-SLM which applied a phase modulation on the _* ^'■^■ reference wave, was imaged to the hologram plane through a Fourier-lens. Such an arrangement is shown in Fig. 5 and 8. Next, the matheinatical description is ■ i discussed for the simulation of phase-encoding with reference SLM imaged on the storage layer instead' of being Fourier transformed together with the object beam. Such an arrangement is shown in Fig. 4 and 6. ,

In this case, firstly the PRF (Point Response Function) of the holographic arrangement is determined, then -on the base of the PRF calculated- computer simulations are implemented for evaluating the data storage properties of the phase- encoding method with imaged references. Note, that in the case of a Fourier-transformed reference beam, when the reference transforms together with the object beam, the point response function (the output of the system when reconstructing the hologram of a point-like object) is the correlation function of the references used for recording and reconstructing the hologram. More strictly, the PRF is a correlation function of the mirror images of the two complex amplitude distributions on the plane of the reference code- generating SLM when recording and reconstructing the hologram.

Now we will start up with our calculations from the formula in Eq. (9) This expression determines the PRF in terms of the plane wave-composition of the reference beam at the hologram plane. In the previous chapter we substituted here the duplex Fourier-transform of the complex amplitude distribution at the code- generating SLM, i.e. it's mirror image. In the recent case the complex amplitudes at the hologram equals with the amplitudes at the SLM. The plane wave composition we need for substituting into Eq. (9) is obtained by performing a Fourier-transform on the amplitude distribution (first equation of Eq. (10)).

(10)

PRF (w, z) = 2^refl>HMC (ω,ξ)® ^efl>HMC (ω,ξ) = Fτ {A^{ref SLM} (l, m)}® .Fτ {A^ref2'^SLM (l,

Thus the new PRF is the correlation runction of the Fourier-transformed phase codes. This formula is quite simple, but not efficient for numerical investigations. To perform a simulation based on this formula, it is needed to sample in many points the Fourier-transformed amplitudes, and calculate the discrete correlation of these large arrays. To calculate the output image a high resolution sampling is needed from both the PRF and the input image and calculate their convolution. This demands large memory area and computing time to achieve an acceptable accuracy. By the use of some mathematical transformations we obtain a much more efficient formula. The output image is the convolution of the input and the PRF. Substituting the PRF in Eq. 10 above, an equation is obtained which determines the output directly in terms of the input image and the reference codes used for recording and reconstruction of the hologram.

PRF(W, Z) = FT[FT-¹

Fτ{A^reΛSLM(l,m)}® Fτ{A^ref2-^SLM (l,m)}

(11)

Thus the new response function is the correlation function of the Fourier transformed phase code amplitudes generated by the phase-SLM. The operations of convolution and correlation are not efficient for numerical calculations, Fourier- transformations are much more feasible this purpose. These operations can be eliminated by the use of the theorem of convolution and a similar theorem, which is valid to the operation of correlation. By the use of the second theorem we eliminate the correlation from the last term of Eq. (11).

PRF{w,z) = FT^'1

(p,q)} <¹²>

Eq. (12) may be substituted into Eq. (1), which determins the output of the system in terms of the input and the PRF. At the same time, the operation of convolution may be eliminated based on a second theorem. A simple and efficient formula is obtained, which is very suitable for computer simulations.

(13)

A^Plc>CCD (w, z) = A^0bj>SLM (_w, z) ® PRF (w, z) = FT ^~λ [FT {A°^^SLM }■ {j^refl'^SLM ■ A^ref2'^SLM }]

In Eq (13) it is predicated that the effect of the phase encoding with imaged reference beams can be simulated by the Fourier-filtering of the input image. The filtering mask is the product of the mirror image of the recording reference code ( z^re/lffiM ) and the reconstructing code ( A^ref2SLM ).

A simulation program was constructed on the grounds of Eq. (13). It was found that for thin holograms the readout with a phase code different from the recording phase code results in high level of noise. In practice, totally random-like reconstructed simulated images were obtained for reconstruction of holograms, where size of the applied phase codes were still reasonable, i. e. not too large and not too small. It has been found that using the correct phase code readout - i.e. the same phase code which was used for recording, single data pages could be recorded and read in good quality, with a BER of 0%. The recording was calculated with a geometrically imaged reference beam. As a data block recorded with a particular phase code can be reconstructed only with a phase code identical or highly similar to the one used for recording the hologram, it has been shown that phase coding is feasible for hardware-based security encryption also in non-Bragg selective material.

Calculations for phase encoded data storage on thin polarization Fourier-holograms showed that an encryption providing a number of code combinations of about (2²⁵) is achievable, with a practical phase code size, of 10 x 10 pixels. Accordingly, the total number n of useful codes constitute the applicable code set for a certain phase ry code size, where. n may be as large as 2 (Fig. 15). The different codes in the code set may comprise the same or different code elements. This- means that the phase- encoding method - with or without the concurrent use of electronic encryption methods - provides a high security hardware encryption of the data stored on the optical card 1. While the number of combination do not seem very large considering the presently available computing speed, in fact this number is more than sufficient. Firstly, the readout speed of the holographic material is limited, being below 1000 1/s, which means that the average number of readouts with systematically calculated codes would take over three years to complete. Another obstacle is the limited reading and writing cycle of the recording material, which limits the number of readouts, before being completely unreadable due to saturation and other destruction effects.

It has been shown that the non-Bragg selective material may also be used for multiplexed recording with the careful selection of appropriate phase codes. If such phase codes for multiplexing are to be generated, it means that several multiplexed images of different objects are stored in one hologram. In this case the restored image should be calculated as being restored from a hologram recorded with a reference wave coded with a first phase code and a first object, while the hologram also was recorded with a reference wave coded with a second phase code and a second object. (In theory, the first and second objects may be identical, but normally this is not the case).

During the optimisation for multiplexing, the following steps are performed: a, the difference between the restored image of a first object and the respective first object is minimised when using the first phase code for the reference wave for recording a the hologram, and using the same first phase code for the reference wave for restoring the hologram and b, the difference between the restored image of a second object and the respective second object is minimised when using the second phase .code for the reference wave for recording the hologram, and using the same second phase code for the reference wave for restoring the hologram.

The method to calculate the phase codes for multiplexing was modelled with a computer program using the functions of the calculations above. The program simulated an algorithm which optimizes an initial phase code or first phase code by randomly changing the code components with the auto-correlation noise as goal parameter. The randomly changed code is considered as the second phase code. The specific algorithm implemented the following operations:

Step 1. Generating a random phase code matrix and computing its autocorrelation SNR Step 2. Changing one random element of the code matrix and computing the new autocorrelation SNR Step 3. If auto correlation SNR improves with a predetermined amount (e.g. 1 %), then keeping changes and back to step 2 with another element

Step 4. If SNR reduces, then throwing changes and back to step 2 Step 5. If autocorrelation SNR stagnates below a given limit (e. g. the change is less than 1%) then saving the code in a file and start again at step 1 Step 6. If autocorrelation SNR stagnates above a given limit, it may mean that the algorithm has found a local maximum in the SNR. For avoiding such local maximums in the SNR, perturbations can be implemented in the method by changing more than one pixels at the same step. As an example the phase code may be changed in three pixels (with a probability of e.g. 75%) and directed back to step 2. Alternatively, the process may start again with a new code at step 1 (with a probability of e.g. 25%).

After several runs - each taking for a few hours on a 300 MHz PC-145 optimized codes with SNR-s beyond 75% were obtained. These codes constituted code set.1 (see Fig. .16.).

A large number codes with optimized autocorrelation properties were generat . _^ code set 1 , where a threshold of 75% SNR was used as benchmark for the ¹ optimisation. Thereafter, a sub-set of codes with low cross-correlation noise values was selected from the elements of code set 1.

The goal of this process is to choose a code set 2, which is a sub-set of code set 1 (see Fig. 16), where code set 2 contains codes with minimal cross-correlation noise values with each of the other codes within this code set 2. This algorithm creates the sub-set, i. e. code set 2 by adding further codes to a randomly chosen starting code. The selecting criteria for the next added code to code set 2, that the cross-correlation noise values of the new code with each of the codes already accepted into code set 2 must remain under a given limit.

The resultant sub-sets are codes applicable for multiplexing. As mentioned above, here the benchmark for the optimisation is the cross correlation noise values, which must remain below a certain percentage of the signal intensity (e. g. 50%), among all the elements of the sub-set of the original code set 1. The signal intensity value was considered as the squared abs value of the central peak of the autocorrelation PRF (See eq. 9).

Figure 19. shows the auto-correlation point response functions of a code within code set 2. Figure 20. shows the cross-correlation point response functions of two different codes of code set 2.

The achievable storage capacity of the system can be determined the best by simulating the output of the system for random data blocks on the grounds of the PRF calculated above. We constructed another computer program for simulating the multiplexed output and evaluating it.

While running, an M number of binary random objects (M≤N) is generated, where ^•■ N is the number of the elements in the code sets to be investigated. Then all of the . PRF-s between the reconstructing (i-th) and all the other (j-th, j=l,2..M) codes are calculated and a convolution is performed between the data page no. j and the correlation function of code no. i with code no. j. With other words, in this implementation the data pages, which were practically digital bitmaps, functioned as the objects of the method, e. g. data page j could be considered as the first object, while data page i could be considered as the second object.

The output image is the sum of all the images obtained from these convolutions, i.e. from all the multiplexed pages a pattern of cross-correlation noise is added to the signal-image, which already carries the noise resulted by the side-lobes of the autocorrelation PRF.

The evaluation of the output image were performed by calculating the Bit Error Rate (BER) by comparing the pixels of the output and input images. It has been found that for very thin layers a high level of multiplexing is not possible, e. g. for 7 fold multiplexing with a hologram layer thickness of approx. lmm a bit error rate of 45 % was found. That means, that the output is random noise, practically independent of the input. For this very same reason, the thin layers are very suitable for hardware encryption in combination with single page recording. In particular, 0% BER was obtained with long ID codes for single page recording.

The invention may be used to find phase codes for multi-level codes as well. In this case- codesxonsisting of pixels with phase shifts of Δφ=0, 2π/8... 7-2π/8 may be used, as an example.

Fig. 22 illustrates a modified embodiment of the optical system shown in Fig. 4. The SLM 44 of Fig. 4 is now substituted with the SLM 144. The object beam 35 follows . the same route from the SLM 144 which is explained and shown with reference to Fig. 6. In this case the reference arm of the interferometer is coupled into the optical path between the two Fourier planes 49 and 50 (see also Fig. 6) from the same side as the object beam 35. Instead of the splitter prism 34, the reference and object beams are separated by the beam splitter 140. The object beam 35 is formed by the spherical mirror 136, after passing through the 1/4 plate 132 twice. The diverging object beam 35 is collimated by the lens 134, from which it falls onto the SLM 144 through the 1/2 plate 139. The lens 134 has a central hole 149 for allowing the passing through of the reference beam 36. This latter first passes through the beam splitter 140, than reflects from the adjustable mirror 135. Another 1/4 plate 131 provides the proper polarisation of the reference beam 36. The reference beam 36 passes through the beam splitter 45, and it is returned from the mirror 137, after passing twice through further 1/4 plate 133 and reference objective 64. Finally, the reference beam 36 is also reflected from the polarising layer 58 of the beam splitter 45 towards the optical card 1. The main advantage of this embodiment is that the same SLM 144 is used for coding the phase code of the reference beam 36 and the amplitude modulation of the object beam 35. For this purpose, the SLM 144 must be of the type which is simultaneously capable of phase coding and amplitude coding. Such devices are the SLM' s sold by SONY Corp. under the identification number LCX 029 or LCX 023. Fig. 23 is a similar arrangement, but the formation of the reference beam 36 and the object beam 35 is done slightly differently. Instead of the spherical mirror 136, both beams are expanded by the expander optics 141. After separation by the beam splitter 140, the object beam is reflected towards the SLM 144 by the mirror 146. The reference beam 36 is concentrated to the central region of the SLM 144 by the concave mirror 145/and the collimator lens 143.

Fig. 24 illustrates that the central region 150 of the SLM 144 only provides phase modulation, while the peripheral parts provide the amplitude modulation. With both optical systems, the reference beam 36 may follow the optical path shown schematically in Figs. 6 or 8, depending on the design of the reference objective 64, i. e. the phase code on the central region 150 of the SLM 144 may be imaged or Fourier-transformed onto the optical layer 3 through the lenses 64 and 48.

It should be understood that the methods and optical systems of the invention described above are not limited to the specific exemplary embodiments explained and shown, unless indicated otherwise. For example, various types of optics or other components may be used with or perform operations in accordance with the disclosed teachings. The claims should not be read as limited to the described order or elements unless stated to that effect. Therefore, all embodiments that come within the scope and spirit of the following claims and equivalents thereto are claimed as the invention.

Claims

Claims:

1. Method for generating a phase code for a reference wave for holographic data storage, comprising the steps of: a, selecting a first phase code, and b, selecting a second phase code, wherein the first phase code is compared with one or more second phase codes in an optimization procedure.

2. The method according to claim 1, wherein the difference. between an object and its restored image is calculated to compare a first phase code and aisecond phase code, where the restored image is calculated as being restored from a hologram created with a reference wave coded with the first and/or second phase code.

3. The method according to claim 2, wherein a, the difference between the restored image of an object and the respective object is minimised when using a first phase code for the reference wave for recording the hologram, and using the same first phase code for the reference wave for restoring the hologram and b, the difference between the restored images and the respective objects is maximised when using a first phase code for the reference wave for recording the hologram and using a second phase code for the reference wave for restoring the hologram.

4. The method according to claim 2, wherein the restored image is calculated as being restored from a hologram recorded with a reference wave coded with a first phase code and a first object and the hologram also being recorded with a reference wave coded with a second phase code and a second object, and a, the difference between the restored image of a first object and the respective first object is minimised when using the first phase code for the reference wave for recording a the hologram, and using the same first phase code for the reference wave for restoring the hologram and b, the difference between the restored image of a second object and the respective second object is minimised when using the second phase code for the reference wave for recording the hologram, and using the same second phase code for the reference wave for restoring the hologram.

5. The method according to any one of claims 1 to 4, wherein a digital data array is used as object, and the difference between the restored image of the digital data array and the respective digital data array is calculated from the bit error rate.

6. The method according to any one of claims 1 to 5, wherein the difference' between the restored images and the respective objects is calculated based on autocorrelation and/or cross correlation.

7. The method according to any one of claims 1 to 6, wherein the holograms are Fourier holograms.

8. The method according to any one of claims 1 to 7, wherein the holograms are polarisation holograms.

9. The method according to any one of claims 1 to 8, wherein the reference wave generating device is an array of amplitude and/or phase modulating elements

10. The method according to any one of claims 1 to 9, wherein the reference wave generating device is imaged onto the holographic storage layer.

11. The method according to any one of claims 1 to 9, wherein the reference wave generating device is projected onto the holographic storage layer by non-geometrical imaging.

12. The method according to claim 10, wherein the reference wave generating device is projected onto the holographic storage layer by Fourier transformation.

13. The method according to any one of claims 1 to 12, wherein the second phase code is selected by modifying the first phase code.

14. The method according to any one of claims 1 to 12, wherein the second phase code is selected from a group of predetermined phase codes.

15. The method according to any one of claims 1 to 14, wherein the first phase code is generated as a series of complementary code elements.

16. The method according to claim 15, wherein a code element of a phase code is selected so as to provide substantially complete destruction of the readout data when all pixels of that code element are incorrect in the readout phase code.

17. A computer program product comprising executable instructions of a program to perform the method according to any of the claims 1 to 16, when the program is run on a computer.

18. A method for recording encrypted data stored in substantially non-Bragg selective holographic recording material, wherein the data is recorded and encrypted with optimised phase codes, the phase codes being calculated according to the method of any one of the claims 1 to 3 and 5 to 16.

19. The method according to claim 18, using holographic recording material with limited Bragg-selectivity.

20. A method for recording multiplexed data stored in substantially non-Bragg selective holographic recording material, wherein the data is recorded and multiplexed with optimised phase codes, the phase codes being calculated according to the method of any one of the claims 1 to 2 and 4 to 16.

21. The method according to claim 20, using holographic recording material with limited Bragg-selectivity.