GB2444990A

GB2444990A - Holographic image display system and method using continuous amplitude and quantised phase modulators

Info

Publication number: GB2444990A
Application number: GB0625364A
Authority: GB
Inventors: Edward Buckley
Original assignee: Light Blue Optics Ltd
Current assignee: Light Blue Optics Ltd
Priority date: 2006-12-20
Filing date: 2006-12-20
Publication date: 2008-06-25
Also published as: GB0625364D0

Abstract

A holographic image display system is configured to generate a displayed image using plural holographically generated temporal subframes, being displayed sequentially in time so they are perceived as a single-reduced-noise image; each subframe is generated holographically by modulation with holographic data such that replay of a hologram defined by said holographic data defines a sub frame. The modulator in the system - also independently claimed - comprises a combination of a quantised phase modulator F and a continuous amplitude modulator N. Also independently claimed is a display method using the system comprising: phase modulation processing, for each subframe, to add noise; space frequency transformation generating complex valued transformed data; and quantization of a real / imaginary component to generate two data sets for a subframe - first quantized data for driving the quantised phase modulator and second data for driving the continuous amplitude modulator (see Figures 4 and 6).

Description

M&C Folio: GBP290821 Holographic Image Djp lay Systems

FIELD OF fl-IF 1NVENTTON

ibis invention relates to apparatus, methods and computer program code for the holographic display of images, and to related light modulation techniques.

BACKGROUND TO THE INVENTION

Many small, portable consumer electronic devices incorporate a graphical image display, generally a LCD (Liquid Crystal Display) screen. These include digital cameras, mobile phones, personal dital assistants/organisers, portable music devices such as the iPOD (trade mark), portable video devices, laptop computers and the like. in many cases it would be advantageous to be able to provide a larger and/or projected image hut to date this has not been possible, primarily because of the size of the optical system needed for such a dispLay.

We have previous described, fbr example in WO 2005/05 9660, a method for image prolection and display using appropriately calculated computer generated holograms displayed upon dynamically addressable liquid crystal (LC) spatial light modulators (SLMs). Broadly speaking in this technique an image is displayed by displaying a plurality of holograms each of which spatially overlaps in the replay field and each of which, when viewed individually, would appear relatively noisy because noise is added (by phase modulation) prior to a holographic transform of the image data. however when viewed in rapid succession the replay field images average together in the eye of a viewer to give the impression of a reduced (low) noise image. The noise in successive temporal sub frames may either be pseudo-random (substantially independent) or the noise iii a subframe may be dependent on the noise in one or niore earlier subframes with the aim of at least partially cancelling this out, or a combination of both may be employed. More details of such OSPR-type procedures are described later.

Figurc 1 shows an example a consumer electronic device 10 incorporating a holographic image projection module 12 to project a displayed image 14. Displayed image 14 comprises a plurality of holographically gcncratcd sub-images each of the same spatial extent as displaycd imagc 14, and displayed rapidly in succession so as to give the appearancc of thc displaycd image. Each holographic sub-frame is gcncratcd using an OSP.R-typc procedure.

Figure 2a shows an example optical system Ihr the holographic projection module of Figure 1. Referring to Figure 2a, a laser diode 20 (for example, at 532nm), provides substantially collimated light 22 to a spatial light modulator 24 such as a pixellated liquid crystal modulator. The SLM 24 phase modulates light 22 with a hologram and the phase modulated light is preferably provided to a demagniIing optical system 26.

Tn the illustrated embodiment, optical system 26 comprises a pair of lenses 28, 30 with respective focal lengths f1, f2, f1<zf2, spaced apart at distance f1+f2. Optical system 26 increases the size of the projected holographic image by diverging the light forming the displayed image; it effectively reduces the pixel size of the modulator, thus increasing the diffraction angle. Lenses 1.4 and T2 form a beam-expansion pair which expands the beam from the light source so that it covers the whole surface of the modulator; depending on the relative size of the beam 22 and SLM 24 this may be omitted. A filter may he included to filter out unwanted parts of the displayed image, for example a zero order undi Ifiacted spot or a repeated first order (conjugate) image, which may appear as an upside down version of the displayed image, depending upon how the holograni for displaying the image is generated.

A single optical arrangement can he used for beam expansion prior to modulation, and fbr demagrufleatiori of the modulated light. Thus the lens pair Ll and L2 and the lens pair I3 and L4 may comprise at least part of a common optical system, used in reverse, in conjunction with a relleetive SLM, for light incideni. on arid reflected from the SLM.

Figure 2b illustrates such a lens sharing arrangement, in which a polariser is included to suppress interibrence between light travelling in different directions, that is into and out of the SLM. Figure 2e shows a preferred practical configuration of such a system, in which the laser diode (LD) does not obscure a central portion of the replay field, in the arrangement of Figure 2c a polarising beam splitter is used to direct the output, modulated light at 90 degrees on the image plane, and also to provide the ftmction of the polariser in Figure 2b.

A colour holographic projection systcni may be constructed by employmg an optical system as described above to create three optical channels, red, blue and green superimposed to generate a colour image. In practice this is difficult because the different colour images must be aligned on the screen and a better approach is to create a combined red, green and blue beam and provide this to a common SLM and demagni lying optics. In this case, however, the different colour images are of di EThrent sizes; techniques to address this are described in our co-pending UK patent application no. (1B0610784.l filed 2 June 2006, hereby incorporated by reference.

Referring again to Figure 2a, a digital signal processor 100 has an input 102 to receive image data from the consumer electronic device defining the image to be displayed.

The DSP 100 implements an OSPR-type procedure to generate phase hologram data for a plurality of holographic sub-frames which is provided from an output 104 of the DSP to the SLM 24, optionally via a driver integrated circuit if needed. The DSP 100 drives SLM 24 to project a plurality of phase hologram sub-frames which combine to give the impression of displayed image 14 in the replay field (RPF). The DSP 100 may comprise dedicated hardware and/or Flash or other read-only memory storing processor control code to implement the hologram generation procedure.

OSPR-type techniques substantially reduce the amount of computation required for holographic image display and also provide advantages for miniaturisation, fault tolerance (in the SLM) and optical efficiency. However there remains a need for improvement.

Currently there is no liquid crystal material available which can independently modulate both the amplitude and phase of incident tight. Ferroclectrie liquid crystal (FLC) spatial light modulators can be used for binary phase modulation (L. Banks, M. birch, 1').

Kruecrke, E. Buckley, A. Cable, N. Lawrence and P. Mash, "Real-time diffractive video projector employing ferroelectric LCOS SLM", Proceedings SJD Symposium 73.4, (San Francisco, CA, 2006) 1-4) and the replayed image noise which results from quantisation of hologram pattenis to binary phase can be mitigated using the aforementioned one-step phase retrieval (OSPR) procedure (A. .1. Cable, E. Buckley, P. Mash, N.A.

Lawrence, T. D. Wilkinson, Real-time binary hologram generation (hr high-quality video projection applications, Proceedings SIP Symposium 53.1 (Seattle, WA, 2004) 1431-1433). Uowever the resultant replayed images can still exhibit a relatively low signal-to-noise ratio (SNR), depending upon the iiuniher of suhfranies used to build lip au image frame. The use of continuous phase modulators employing pnematic liquid crystal (LC) represents one possible solution since continuous phase encoding of a hologram pattern provides a replay field (RPF) which, for the same content, provides an SNR approximately four times greater than is obtainable using binary phase. Further, with only binary modulation the hologram results in a pair of' images, one spatially inverted with respect to the other, the latter being known as a conjugate image. The use of continuous phase encoding can suppress such a conjugate image, and hence the associated loss of light to this image as compared to the main, upright iniage. However such continuous phase modulators are very expensive and difficult to characterise and operate reliably.

Another possibility is to quantise a continuous complex hologram pattern so that it is represented by a quantised amplitude-only or phase-only pattern which can be displayed on readily available SLMs. Techniques (hr complex amplitude modulation by coupling two modulators have previously been described, either to cover the perimeter of a circle centred on the origin of the complex plane (constant magnitude, continuous phase) or to cover the entire region within such a circle. Such techniques are described in: P. Birch, R. Young, D. Budgett and C Chatwin, Dynamic complex wave-front modulation with an analog spatial light modulator, Opt. Let!. 26 (2001) 920-922; J. Aniako, H. Miura, T. Sonehara, Wave-front control using liquid-crystal devices, AppL Opt. 32 (1993) 4323- 4329; L. C. Neto, D. Roberge and Y. Sheng, Full-range, continuous, complex modulation by the use of two coupled-mode liquid-crystal televisions, Appl. Opt 35 (1996) 4567-4574; J.L. de Boitgrenet de Ia Tocnaye and L. Dupont, Complex amplitude modulation by use of liquid-crystal spatial light modulators, App/. Opt. 36(1997)1730- 1741; SE. Broomfield, M.A.A. Neil and E.G.S. Paigc, Programmable multiple-level

S

phase modulation that uses ferro-electric liquid-crystal spatial light modulators, AppL Opt. 34 (1995) 6652-6665; C. Stolz, L. Bigue, and Pierre Ambs, linplementation of high-resolution (ii Ifractive optical elements on coupled phase and amplitude spatial modulators, App!. Opt 40 (200 I) 6415-6424; T-L. Kelly and J. Munch, Phase-aberration correction with dual liquid-crystal spatial light modulators, App! Opt 37 1998) 5 1 84-5189). Another technique which could he employed would he to characterisc cach pixel of, say, a pneniatic hqwd crystal modulator by measuring the phase shift as a function of amplitude, then using this to provide phase shill modulation, compensating for the amplitude variation. This would, iii principle, be able to provide continuous phase modulation, although the characterisation and storage of the eharacterisation data make this technique inipractical.

There is therefore a need for improved techniques.

SUMMARY OF THE INVENTION

According to a first aspect of the invention there is therefore provided a holographic iniage display system, the image display system being configured to generate a displayed image using a plurality of holographically generated temporal subframes, said temporal subfranies being displayed sequentially in time such that they are perceived as a single-reduced-noise image, each said suhframe being generated holographically by modulation of a modulator with holographic data such that replay of a hologram defined by said holographic data defines a said subframe, and wherein said modulator comprises a combination of a quantised phase modulator and a continuous amplitude modulator, to provide a combination of controllable quarstised phase modulation and controllable amplitude modulation.

Broadly speaking the inventors have recognised that substantially improved signal-to-noise ratio perfonnance ratio can be achieved by combining continuous amplitude modulation, for exaxnpJe by placing two SLMs in close proximity. More particularly, in an OSPR-type system such an arrangement enahles modulation along the entire real (or imaginary) axis rather than simply in the range 0 to I. If binary phase modulation is employed then positive values on the real axis correspond lo a phase of 0 and negative values to a phase of r(the skilled person will recognise that, iii embodiments described later, the labelling o!'the real and imaginary axes may effectively he interchanged). A ferroelectric liquid crystal light modulator can advantageously he employed to provide such binary phase modulation. However, multiphase modulation may also be employed, for example three phase modulation or quatemary phase modulation again, For exaniple, using a ferroelectric liquid crystal light modulator In such a case the complex plane may be trisected or divided into quadrants in order to determine which quantised phase to employ in the phase modulation. In the context of an OSPR-type procedure the use of more than two phase levels enables the conjugate image to be suppressed, thus potentially, further improving the SNR (further details can be found in W02005/059660, hereby incorporated by reference).

The above-described technique is particularly advantageous for OSPR-type procedures in which quantisation along the real and/or imaginary axes can be mapped to the phase and amplitude spatial light modulators. Thus in sonic preferred embodiments the system incorporates a data processor to add noise to the input data by phase modulation, then perform a space-frequency transForm, for example an inverse Fourier translhrm, and then quantise the resulting, complex-valued data to generate data for driving the continuous amplitude aiicl q uanti sed phase modulators.

The amplitude data 11w driving the amplitude data may de obtained by taking the absolute value of the real (and/or imaginary) part oFthc complex-valued data. The quantised phase data may be derived by quantising the phase angle, into a number of levels which corresponds to the quantised values olphase modulation available, for example two (binary), three or Four By contrast more bits, for example 6 bits, 8 bits or greater are employed to drive the continuous amplitude modulator to provide a substantially continuous range of amplitude values from which to select for amplitude modulation. Preferably each of the phase modulator and the amplitude modulator comprises an electrically controllable modulator.

When driving a binary phase modulator the phase angle may he quantised into two values, 0 and r, which effectively corresponds to positive and negative values real values. Thus the real component of the complex valued data may be used to generate a first set oF values ibr the combined modulator (Ic the sign of the real component and its absolute value), and the imaginary component of the complex valued data may be used to generate a second set of values for the combined modulator, further reducing the computational load.

Thus, broadly speaking, in some preFerred embodiments of the system the continuous amplitude data is derived f'ron-i the rca] part of the (inverse Fourier) transformed data and binary quantised phase data is derived from the sign of the real data. A second sub frame may be derived without significant further computation by taking absolute value and signed value data for the imanary component of the traiisformed data, effectively doubling the number of subframes available. Where quantisation into more than two phase values is employed the quantisation may explicitly or implicitly employ 1)0th the real and imaginary components (axes) of the complex-valued transformed data.

In embodiments the holographic image display system may he employed to provide a video image display system to display either a still or a moving video image, each frame of the video image being processed as described above.

In a related aspect the invention provides a method of displaying an image holographically using a plurality of holographically generated temporal subframcs, said temporal subframes being displayed sequentially in time such that they are perceived as a single-reduced-noise image, each said sub frame being generated holographically by modulation of a modulator with holographic data such that replay of a hologram defined by said holographic data defines a said subfranie, the modulator comprising a combination of a quantised phase modulator and a continuous amplitude modulator, the method comprising: inputting image data defining said image; processing said image data to generate said holographic data for said subframes, and wherein said processing comprises operating on said image data to perform, for each said subframe, phase modulation to add noise followed by a space- frequency transformation to generate complex valued transformed data followed by a quantisation of at least one of a real and an imaginary component of said transformed data to generate two sets of data for said holographic data defining a said subframe, a first set of data comprising quantised data for driving said quantised phase modulator and a second set of data comprising data for driving said continuous amplitude modulator and outputting said first set of data to drive said quantised phase modulator and outputting said second set of data to drive said continuous amplitude modulator.

fri preferred embodiments of the method the processing to generate the holographic data comprises an OSPR-type procedure.

The invention further provides processor control code to implement the above-described systems and methods, iii particular on a data carrier such as a disk, CD-or DVD-ROM, programmed memory such as read-only memory (Firmware), or on a data earner such as an optical or electrical signal carrier. Code (and/or data) to implement embodiments of the invention may comprise source, object or executable code in a conventional programming language (interpreted or compiled) such as C, or assembly code, code for setting up or controlling an ASIC (Application Specific Integrated Circuit) or FPGA (Field Programmable Gate Array), or code for a hardware description language such as Ycrilog (Trade Mark) or VHDL (Very high speed integrated circuit hardware Description Language). As the skilled person will appreciate such code andlor data may he distributed between a plurality of coupled components in communication with one another.

In a further related aspect the invention provides a modulator fbr a holographic image display system, the modulator comprising an electrically controllable continuous amplitude modulator in combination with an electrically controllable quantised phase modulator.

In preferred embodiments each of the modulators comprises pixellated spatial light modulator, and the modulators are positioned such that corresponding pixels in the amplitude and phase modulator align with oiie another.

In preferred embodiments the quantised phase modulator comprises a ferroeleciric liquid crystal light modulator. For convenience in such an implementation a quarter wave plate may be included between the amplitude modulator and the phase modulator, in particular in order to rotate the polansation state so that it intersects (bisects) the switching angle of the phase modulator. For example the phase modulator may switch between polarisation in a first direction and in a second direction and the quarter wave plate may be employed to convert a circular polarisation output from the continuous amplitude modulator to a linear polarisation which is in a direction which bisects the angle between the first and second polarisation directions. In some preferred embodiments the amplitude modulator comprises a linear polariser in combination with a liquid crystal SLM such as a nematic liquid crystal SLM.

in some preferred implementations the phase modulator is a reflective modulator; in this case because, in emhodinieiits, light passing through the modulator is effectively modulated twice (once going towards the reflecting surface, once away from the reflecting surface) the modulator may be modulated at a level which is half that which would otherwise he employed. Alternatively a transmissive system may be employed in which light passing through the modulator passes through the amplitude modulator and then the quantised phase modulator (optionally with an initial linear polariser; optionally with a quarter wave plate between the continuous amplitude modulator and the quantised phase modulator. Theoretically, in embodiments optically addressed modulators may he employed but this is generally impractical.

Embodiments of the above described systems, methods and modulators may be incorporated into a consumer electronics device, or into an advertising or signage system, or into a helmet mounted or head-up display or, for example, an aircraft or automobile.

BRIEF DESCRIPTION OF TIlE DRAWINGS

T]iesc and other aspects of the invention will now be further described, by way of example only, with reference to the accompanying figures in which: figure 1 shows an example of a consumer electronic device incorporating a holographic proj ecti on module; Figures 2a to 2c show, respectively, an example of an optical system for thc holographic projection module of figure 1, and lens sharing aiTangemcllts used with a reflective SLM; Figure 3 shows a block diagram of a hologram data calculation system; Figure 4 shows the operations performed within the hardware block of Figure 3; Figure 5 shows the energy spectra of a sample mi age before and after multiplication by a random phase matrix; Figure 6 shows an example of a hologram data calculation system with parallel quantisers for the simultaneous generation of' two sub-frames from real and imaginary components of' complex holographic sub-frame data respectively; Figures 7a to 7e show, respectively, a continuous amplitude-only pattern, a binary phase-only pattern, and a simulated reconstructed image employing continuous real axis modulation using coupled modulators according to an embodiment of an aspect of the invention; Figures Ra to 8d show degradation in a reconstructed image Fyy =1 FLIi,J 12 as the phase modulation depth air decreases, the figures illustrating, respectively, a = 1, a = 0.8, az0.6,and a=0.4; Figure 9 shows replay field SNR values for a coupled modulator as a function of decrease in phase modulation depth a, for pixel coverage proportions of 20% coverage (circles), 40% coverage (squares), and 80% coverage (triangles), the dotted line indicating a = 0.50 and the solid line a = 0.63, values at which the replay field SNR of the coupled modulator would exceed that of binary and continuous phase holograms respectively; and Figure 10 shows a schematic diagram of a integrated modulator to perform continuous real axis modulation, using a reflective quantized phase spatial light modulator F in combination with a transrnissive continuous amplitude spatial light modulator N, in which incident light V is modulated along substantially the entire real axis resulting in a wavefront V', according to an embodiment of the invention.

DETAILED DESCRWTTON OF PREFERRED EMBODIMENTS

It is first helpful, for understanding embodiments of the invention, to review the OSPR procedure. Although we refer to this procedure in a shorthand way as One Step Phase Retrieval (OSPR) strictly speaking u-i implementations it cold be considered that more than one step is employed (as described for example in GB0518912.1 and GBO6O 1481.5, incorporated by reference, where "noise" in one sub-frame is compensated in a subsequent sub-frame).

OSPR

Broadly speaking in our prelbrred method the SLM is modulated with holographic data approximating a hologram of the image to be displayed. However this holographic data is chosen in a special way, the displayed image being made up of a plurality of temporal sub-frames, each generated by modulating the SLM with a respective sub-frame hologram. These sub-frames are displayed successively and sufficiently fast that in the eye of a (human) observer the sub-frames (each of which have the spatial extent of the displayed image) are inlegrated together to create the desired image for display.

Each of' the sub-frame holograms may itself' be relatively noisy, for example as a result of quantising the holographic data into two (binary) or more phases, hut temporal averaging amongst the sub-frames reduces the perceived level of noise. Embodiments of such a system can provide visually high quality displays even though each sub-frame, were it to be viewed separately, would appear relatively noisy.

The precedure is a method of generating, for each still or video frame I = h,, sets of N binary-phase holograms -h. In embodiments such sets of holograms form replay fields that exhibit mutually independent additive noise. An example is shown below: 1. Let kexp (,/p) where is uniformly distributed between o and 2m foi I C n C N/2 arid s. y in 2. t,et I [G)] where p1 rejrescnts the two-dimensional inverse Fourier Iran sform operatot; for I = n = N/2 3. Let m 9tjge1. } tor I z s N/2 4. Let ni FN/2) {g} for I = n NJ2 5. Let I4Y [ -i irn4V whei Q') = median (rn?) I ifm Q(fl) and I <n = N Step 1 forms N targets equal to the amplitude of the supplied intensity target I., but with independent identically-distributed (i.i.t.), uniformly-random phase. Step 2 computes the N corresponding full complex Fourier transform holograms g. Steps 3 and 4 compute the real part and imaginary part of the holograms, respectively.

Binarisation of each of the real and imaginary parts of the holograms is then performed in step 5: thrcsholding around the median of in ensures equal numbers of -1 and 1 points are present in the holograms, achieving DC balance (by definition) and also minimal reconstruction error. The median value of rn,2 may be assumed to be zero with minimal effect on perceived image quality.

Figure 3 (from GBO51 1962.3, filed 14 ' June 2005, incorporated by reference) shows a block diagram of a hologram data calculation system configured to implement this procedure. The input to the system is prelèrahly image data from a source such as a computer, although other sources are equally applicable. The input data is temporarily stored in one or more input buffer, with control signals for this process being supplied from one or more controller units within the system. The input (and output) buffers preferably comprise dual-port memory such that data may be written into the buffer and read out from the huftbr simultaneously. The control signals comprise timing, initialisation and how-control information and preferably ensure that one or more holographic sub-frames are produced and sent to the SLM per video frame period.

The output from the input comprises an image frame, labelled I, and this becomes the input to a hardware block (although in other embodiments sonic or all of the processing may he perhbrnied in software). The hardware block perfonns a series oh' operations on each of the afbrementioned image frames, I, and for each one produces one or more holographic sub-frames, ii, which are sent to one or more output huller. The sub-frames are supplied from the output buffer to a display device, such as a STIM, optionally via a driver chip.

Figure 4 shows details of the hardware block of Figure 3; this comprises a set of elements designed to generate one or more holographic sub-frames for each image frame that is supplied to the block. Preibrably one image frame, 1,, is supplied one or more times per video frame period as an input. Each image frame, h3, is then used to produce one or more holographic sub-frames by means of a set of operations comprising one or more of: a phase modulation stage, a space-frequency transformation stage and a quantisation stage. In embodiments, a set of N sub-frames, where N is greater than or equal to one, is generated per frame period by means of using either one sequential set of the aforementioned operations, or a several sets of such operations acting in parallel on different sub-frames, or a mixture of these two approaches.

The purpose of the phase-modulation block is to redistribute the energy of the input frame in the spatial-frequency domain, such that improvements in final image quality are obtained after performing later operations. Figure 5 shows an example of how the energy of a sample image is distributed before and after a phase-modulation stage in which a pseudo-random phase distribution is used. It can be seen that modulating an image by such a phase distribution has the effect of' redistributing the energy more evenly throughout the spatial-frequency domain. The skilled person will appreciate that there arc many ways in which pseudo-random binary-phase modulation data may he generated (for example, a shift register with feedback).

The quantisation block takes complex hologram data, which is produced as the output of the preceding space-frequency transform block, and maps it to a restricted set of values, which correspond to actual modulation levels that can be achieved on a target SLM. As we describe Ilirther later, in embodiments the number of phase

quantisation Levels is set at two (phase retardations of U or it at each pixel) but the amplitude is substantially non-quantised (continuous). In other embodiments, the number of phase quantisation levels (and corresponding phase retardations) may be greater than two. The dificrent quantised phase retardation levels may have either a regular distribution or an irregular distribution, or a combination of the two may be employed.

In some preferred embodiments the quantiser is configured to separately quantise real and imaginary components of the holographic sub-frame data to generate a pair of holographic sub-frames for the output buffer. Figure 6 shows an example of such a system. It can be shown that for discretely pixellated fields, the real and imaginary components of the complex holographic sub-frame data are uncorrelated, which is why it is valid to treat the real and imaginary components independently and produce two uncorrelated holographic sub-frames.

Continuous real axis modulation We now describe a method of representing hologram patterns in which two SLMs, when placed in close proximity, perform modulation of both the amplitude anti phase of the incident light, resulting in substantially improved SNIP. performance. Furthermore, it is shown that if an OSPR-type procedure is used to determine the holograms, then binary phase and continuous ampJitude SLMs can he employed. As a consequence of using this modulation scheme, it is demonstrated that if the phase-only SLM is a perfect binary phase modulator, then the reconstructed image may contain no reconstruction noise and the SNIR is effectively infinite. It is further shown that, if the phase-only SLM is imperfect, then the SNR can still be considerably higher than can he ohtairme(l using continuous phase modulation. A example realisation of such a composite device using reflective anti transrnissive SLM components is also described.

We first consider a variant of the OSPR procedure (B. Buckley, A. S. Cable, T. Ti Wilkinson, Viewing angle enhancement for two and three dimensional holographic displays using random super-resolution phase masks, App!. Opt. (2006) 1-8; see also W02005/059659, hereby incorporated by reference). More particularly we consider the following steps, which generate real holograms in such that -l = ni = I where çc? is uniformly distributed I. Let 7t1 = \/7 exp çt-?) in the interval [0; 2x1 and 1 = ii S N/2, 1 =x4y =P where F represents the 2]) 2. Let,ç? = 71 [TZ2] inverse Fourier transform operator.

tor I < a = N/2 3. Let in? = {s} I = a = N/2 the algorithm is able to generate sets of N distinct Px P pixel binary phase holograms h,, each of which produces a reconstruction that approximates the same target image In this example, each of the N holograms generates reconstructions containing independent identically distributed (i.i.d.) noise fields. The algorithm begins with the specification of a target intensity pattern J,, and proceeds as follows.

Step I forms N targets equal to the amplitude of the supplied intensity target, but with i.i.d. unilbrmly-random phase, so that the power spectrum ol 7') is smooth. In step 2, N/2 complex and continuous-valued holograms are obtained by applying the inverse Fourier translhrm, and in step 3 the real part is taken giving N/2 holograms; the remaining N/2 holograms can be obtained by taking the imaginary part.

The following discussion is simplified by setting 1% = 1, so that the result of the Procedure is a pixellated Fourier hologram nc, with pixel values that are both continuous and real, lying in the range -l = ni1 = I; appropriate thresholding of this hologram would then produce a binary hologram. 1-lowever when such holograms are displayed on a binary SLM and illuminated with coherent light, a noisy conjugate-symmetric approximation to T, results, limiting reconstruction SNR.

We show later that LSNR may be improved by approximately a factor of four if the hologram is quantised and displayed as a continuous phase representation. However we further show that if instead a SLM device is constructed to represent the continuous real hologram m11 then the reconstruction is still conjugate symmetric, but the absence of quantisation noise would produce a perfect reconstruction of I with theoretically infinite SNR.

We thercibre describe a coupled-modulator approach which allows the continuous real set of values represented by rn, to he encoded. Broadly, the concept is to encode the positive part of these values using a continuous amplitude modulator, and the negative part using the same device but with an additional phase shift of it radians. A binary phase modulator can be used to provide the required phase shifts oil) and it radians respectively.

In practice, such a coupled-modulator technique may be realised by placing binary phase and continuous amplitude modulating SLMs in close proximity, with the pixels of each device accurately registered. An example of a suitable binary phase SLM is an SXGA (1280 1024) reflective binary phase modulating spatial light modulator made by CRL Opto (Forth Dimension Displays Limited, of Scotland. UK). For continuous amplitude modulation a conventional nematic LC devicc may be employed. When a pixel of the FLC SLM imparts a phase shift of = 0 radians, the corresponding NLC SLM pixel can encode the positive half of the real axis. 1-lowever, when the FLC SLM pixel imparts a phase shift of 8,,,, = 21 radians, then the resultant modulation is exp/r -I times that of the corresponding NLC SLM pixel. Hence, the negative hail' of the real axis can be encoded.

An example reconstructed image (I F [h,,,]12) provided by this technique is shown in Figure 7c, together with the corresponding phase-only pattern cxp JO, [-1,1] in Figure 7h, and the amplitude-only pattern A, [0;1] in Figure 7a. The effective modulal ion imparted by the coupled modulators can be written as: = A,,, exp /O,, (I) and the negative and positive parts of the real axis were encoded by setting the amplitude A, = 91 {nç } and by choosing the phase 6,, = 21 if rn, <0, or 0,,,, 0 otherwise. 1'he resultant pixcllatcd amplitude pattern contains values that lie in the set A,,,, 10; ii, whilst the phase pattern pixels are binary and hence 8,, e [0,]. Since the combination of the modulation from both devices spans the entire real axis, there is no quantisation noise in the reconstructed image i =1 Lk,i 12, although a conjugate image is present due to the pLtrely real nature ol equation (1). In practice, imperfections in the modulation depth provided by the binary phase-only SIJM will introduce RPF noise and an analysis of this effect and its impact on reconstruction SNR is provided in the next section.

Effect of inspfficient phase modulation depth In a conventional phase-modulating holographic display, the use of a LC material with insufficient switching angle causes a large bright spot in the centre of the reconstruction.

rrl1s spot is unmodulatcd light, at a spatial frequency of zero, and is the result of a modulation depth of less than it in the LC material. A related effect occurs in the coupled-modulator design, except that additional noise is distributed across thc RPF as a result of the introduction of error into the hologram pattern.

Thus, as the phasc modulation depth decreases, the introduction of RPF noise causes a concomitant SNR degradation in addition to the decrease in diffraction efficiency to the zero-order spot. To demonstrate this, Figure 8 shows simulated images resulting from a coupled modulator technique in which the modulation depth oF the phase-only FLC SLM is reduced from it by a factor a between 0 and 1. For a = 1, a perfect reconstniction of the target image results. The pixel coverage is 50% ot'the entire field in each ease. The increase in RPF noise and the zero-order component can be seen, and it therefore becomes important to determine at what point the SNR is degraded to such an extent that the performance of the real axis modulation technique is no better than pure binary phase modulation.

Simulations were used to characterise SNR degradation as a function of phase modulation depth. The phase depth was controlled by the parameter a, where 0 = a = 1, so that the effective phase modulation took the form = A,, exp jaO, (2) Again, the negative and positive parts olthe real axis were encoded by calculating an amplitude pattern A = 9t{rn} and a phase pattern 9, = it if nç <0, and O = 0 otherwise.

Results arc shown in Figure 9, for target images rj in which the pixel coverage was 20%, 40% and 80% of the entire field. As shown in below, the RPF of a perfect (a -I) binary phase hologram with 100% pixel coverage has a theoretical SNR of I.75 (2.4 dB), and there ibre such reduced coverage RPFs have proportionally greater SNRs of 9.4 cIB, 6.4 dB arid 3.4 dB respectively. Similarly, and for the same pixel covcrages, the RPFs resulting from continuous phase holograms would have SNRs of approximately 15.7 dB, 12.7 dB and 9.7 dB respectively. Measured values of the SNR of the RPF F,, =1 P rk.1 2 are plotted, in decibels, as a function oitlie modulation depth a. Vertical lines illustrate the value of a at which the reconstruction SNR exceeds that due to binary phase (dotted) and continuous phase (solid) modulation. It can he seen that the SNR performance of the coupled modulator technique exceeds that of binary phase modulation when a = 0.50, and continuous phase for a = 0.63.

The 1C material currently employed in a SXGA FIJC SlIM man ufactured by Forth Dimension Displays (4DD) was measured and found to have a phase modulation depth of approximately 0.3,r which, if used in a coupled modulator arrangement, would result in a worse reconstruction SNR. than for binary phase alone. However, 4DD have previously demonstrated stable FLC mixtures which exhibit switching angles of 75 degrees at room temperature (see K. Heggarty, B. Fracasso, J.-L. de Bougrenet de la Tocnaye, M. Birch and D. Krueerke, A silicon backplane FLC spatial light modulator lbr uses within an optical telecommunications environment, Ferroelectrics, (2004) 39- 55). l'he use of such a FLC SLM in the coupled-modulator arrangement, providing a phase modulation depth of 0.83zr, would result in RPFs with SNRs of 3.5 and 15 times greater than could he achieved using continuous or binary phase SI1Ms, respectively.

Implementation The real axis modulation technique can be conveniently realised by coupling reflective FLC and transmissive NLC SLM devices. The configuration of an embodiment of an integrated device, using these SLMs in a double-pass arrangement with their respective pixels aligned and in close contact, is shown in Figure 10.

the device of Figure 10 comprises a continuous amplitude SLM followed by a quarter wave plate Q arid a quantized phase SLIM (FLC), F'. In the illustrated embodinient the continuous amplitude SLM comprises a linear polarizer P followed by a transmissive SLM comprising, for example, a NLC SLM, N. The initial polarizer P may be omitted, br example if the incident light is polarized. The light from the amplitude SLM is circularly polarized (because a NLC is employed), and in the illustrated embodiment a quarter wave plate Q is employed to rotate one component of this such that it bisects the PLC switching angle, that is the angle between (he two switched states of the FLC. The light both incident on and reflected from the PLC is circularly polarized; it remains circularly polarized until it is output (V') from the linear polarizer P. The quarter wave plate is optional the alignment to bisect the switching may he physical or alternatively sub-optimal (or no alignment) may be employed. In this latter case the modulation depth is affected and some light is unmodulated but this can be flltered out by the linear polarizer P (where present) so that it does not appear in the final image.

A reflective system is illustrated in Figure 10 but a transmissive quantized phase LSLM such as a transmissive FLC may alternatively be employed (although a transmissive FLC is generally less preferable because a silicon backplane is not used and addressing can therefore be slower). In a transmissive system a linear polarizer is provided on the output side of the modulator, ie to the right of the FLC in a variant of the Figure 10 arrangement with a transmissive PLC.

In the device of Figure 10 each pixel of the NTFC device N can take an amplitude from 0 to I', whilst the FLC pixels F are able to retard the phase of the light by either 0 or r radians. An optical wave V, of amplitude V, is incident from the left and passes through a polariser P, quarter waveplate (QWP) Q, and each modulator twice resulting in a modulated wavefront V' If the incident light V is linearly polarised at an angle of 45 degrees and assuming a maximum switching angle of 90 degrees for the PLC material then, as shown in later, the modulated light due to each pixel of the coupled modulator has a Jones matrix representation of JV [ii I (3) 2 L'i This demonstrates that, as the FLC SLM pixels switch between each of their states and the NEC SLM pixels vary their amplitude between 0 and 1', this configuration is able to encode the positive and negative parts of the real axis. Such a configuration facilitates the manufacture of very compact integrated devices using readily-available SLMs.

SNR properties We now exarriine the SNR properties ofquantised holograms resulting from an OSPR-type procedure. Consider a quantisation operation, which is applied to the random variable m(u) to obtain a quantised random variable h(u) such that fa rn(u)cQ (4) [h rn(u) =Q where Q is the quantisation threshold and a and h are arbitrary values.

Consider an OSPR-type procedure which begins by applying uniformly random phase to a pixellated target intensity pattern I, proceeding then to take the discrete Fourier transform resulting in a complex hologram g11. If the number of pixels is large, then the central limit theorem applies, and samples of the Fourier transform g,,,, are Normally distributed. hence the continuous, real hologram samples n have a zero-mean Gaussian probability density function (PDF) f,, (u) with variance a2, which can alternatively be written as ni(u) N[0,c721.

The effect of the quantisation operation is to introduce quantisation error into the hologram, which is expressed as Ill-a u<Q CQ(U) = (5) ku-b u =Q If the hologram is appropriately balanced so that the average pixel value is zero, the mean quantisation noise E[e21 = 0. To determine the effect of quantisation upon the reconstructed SNR, it simply remains to calculate the quantisation noise energy E[e 1 where E[e]= f (u-a)2f(u)du-F f(u_h)2f(u)du (6) for binary and continuous phase modulation respectively.

Binary phase quantization The noise in the RPF due to quantisation can be determined by evaluation of equation 6 at the appropriate reconstruction points a and b. For binary phase quantisation, the points lie on the centroids of the positive and negative real axes respectively so that a=guf(u)du=crji (7) and b = -a. Hence, the REF noise due to binary phase quantisation is ELej=a2 -2 0362 (8) so that the effect of quantisation is to modify the variance of the (Jaussiaii random variable rn(u) from a2 to approximately 0.36a2 -Tithe total signal energy of the Gaussian variable P1(11) is v.2, then using the result of equation 8, the SNR can be shown to be S:[0l036l.75 (9) E[ej 0.36 assuming that the pixel coverage is 1 00% of the total field; as the pixel coverage decreases, the SNR increases in proportion. Note that the total energy directed into the conjugate-symmetric first order by the OSPR algorithm, a2 -E[e1. is approximately 64% of the total available Continuous phase guaiitizatioii For the case of' phase quantisation of complex samples, four reconstruction points are used to determine in which quadrant of the complex plane the sample lies. From communications theory the resultant mean-squared error E[e 1 = Oil 88, giving a maximum SNR of 7.42 assuming that the pixel coverage is 100%. 88% of the incident optical energy is therefore directed into the first order oithe reconstruction by a continuous phase hologram designed using OSPR.

Jones matrix analysis We here describe a Jones matrix analysis which shows that the combination of reflective FLC and transmissive NLC SLMs oriented as described below can periorm real axis modulation. The SLM devices, together with a polariser and QWP, are shown in figure 10. Consider incident light V, of amplitude J', which is linearly polarised at an angle of 45 degrees which, using Jones calculus, can be expressed as v=v[] (10) Proceeding from left to right, each of the components in figure 10 can be analysed using Jones matrices. The polariser P is also oriented at 45W, and is written as ri ii P=-I I (11) 2L1 lJ Ncxt is the NLC device N, which performs the amplitude modulation. This is oriented so that the extraordinary (or fast) axis is vertical so that, if each pixel has retardance I', then the Jones matrix is cxp-j-0 N= 2 (12) 0 expj This parbcular NTJC SLM con liguration has the QWP Q is rotated such that its fast axis is vertical, in which case i [i-i 0 1 (13) 12L 0 l+jj After passing through the QWP, the light should bisect the switching angle U of the PLC fin optimum phase modulation. If the retardanee of the FTC device pixels is F then its Jones matrix F is S F.28,.F.

cxp(-j -)cos --r exp(j -)sin - 3 sin -sin 0 2 2 2 2 -2 (14) sin --sin 9 cxp(/1-) cos2 + exp(-/i)sin2.9 Using these matrices, the operation of the entire device can he prcdictcd. However, the analysis should tac account of the double-pass nature of the system, and a coordinate transformation is therefore employed. A ti-ans formation R is defined such that the Jones matrix olan optical componcnt in reflection is given by r_1 01 =1 MM (15) [0 ii so that the output Jones matrix of the integrated device, V', can be represented as V9 *:PR N' -QM F' V (16) Assuming that the retardation of each pixel in the PLC S LM can be either 0 or t radians, then each pixel of the hybrid device has a Jones matrix representation of' /17 [ii V'= __Lsin6sinF.l I (17) 2 [ij Hence, this device is able to perform real axis modulation using a combination of transniissive NLC and reflective PLC SLMs. Transmission of light through the FTIC STJM pixels, and hence efficiency of modulation, will be at a maximum when the switching angle 6 is 7r/2 radians.

Suininy We have described a method of encoding computer-generated hologi'ams which is particularly suitable for OSPR- typc procedures. Embodiments of the technique encode the entire real axis between -1 and 1, thereby matching an intermediate result of an OSPR-type procedure, using coupled binary phase and continuous amplitude SLMs.

An implementation using readily available transmissive NLC and reflective FTC SLMs operating as amplitude and phase modulators has been described, which facilitates the manutheture of a suitable eoupled-niodulator SLM. It has been shown that even if the switching angle of the PLC device is suboptimal, leading to a phase modulation depth of less than 7r, substantial reconstruction SNR gains over continuous phase modulation can be achieved. Furthcrmore, the use of' a high switching angle PLC SLM in such a coupled modulator arrangement could result in reconstructed images with SNR gains of approximately 3.5 and 15 times compared to those i-esulting from continuous and linary phase modulation, respcctively.

Applications for the described techniques and modulators include, hut arc not limited to the following: mobile phone; PDA; laptop; digital camera; digital video camera; games console; in-car cinema; navigation systems (in-car or personal cg. wristwatch GPS); head-up and helmet-mounted displays for automobiles and aviation; watch; personal media player (e.g. MP3 player, personal video player); dashboard mounted display; laser light show box; personal video projector (a "video iPod (RIM)" concept); advertising and signagc systems; computer (including desktop); remote control unit; an architectural fixture incorporating a holographic image display system; more generally any device where it is desirable to share pictures and/or for more than one person at once to view an image.

No doubt many effective alternatives will occur to the skilled person. For example, although we have described regular quantised phase retardation levels the quantised phase retardation levels may have an irregular distribution since this does not affect the operating principle, merely the efficiency of the technique.

It will be understood that the invention is not limited to the described embodiments and encompasses modifications apparent to those skilled in the art lying within the spirit and scope of the claims appended hereto.

Claims

CLAiMS: 1. A holographic image display system, the image display system

being configured to generate a displayed image using a plurality of holographically gerìerated temporal subframes, said temporal sub tiames being displayed sequentially in time such that they are perceived as a single-reduced-noise image, each said subframe being generated holographically by modulation of a modulator with holographic data such that replay of a hologram defined by said holographic data deFines a said suhframe, and wherein said modulator comprises a combination of a quantised phase modulator and a continuous amplitude modulator, lo provide a combination of controllable quantised phase modulator and controllable anipli tude modulation.
2. A holographic image display system as claimed in claim 1 comprising an input for image data defining said displayed image, and a data processor coupled to said input to generate said holographic data, and wherein said data processor is configured to operate on said input data to pcrlbrm a phase modulation to add noise followed by a space-frequency transfonnation to generate complex valued transformed data followed by a quantisation of at least one of a real and an imaginary component of said transformed data to generate two sets of data for said holographic data defining a said subfraine, a first sct of data compnsing quantised data for driving said quantised phase modulation and a second set of data for driving said continuous amplitude modulator.
3. A holographic image display system as claimed in claim 2 wherein said quantisation comprises quantisation into a number of levels corresponding to a number of said quantised values of said quantised phase modulator.
4. A holographic image display system as claimed in claim I, 2 or 3 wherein said quantised phase modulator has four or fewer quantised phase values.
5. A holographic image display system as claimed in claim 1, 2, 3 or 4 wherein said quantised phase modulator comprises a binary phase modulator.
6. A holographic image display system as claimed in claim 5 when dependent on claim 2, wherein said first set of data comprises sign data and wherein second set of data comprises absolute value data for said at least one component of said transformed data.
7. A holographic image display system as claimed in any preceding claim wherein said quantised phase modulator and said continuous amplitude modulator each comprise an electrically controllable modLLlator.
8. A holographic image display system as claimed in claim 7 wherein said quantised phase modulator comprises a ferroelectric liquid crystal light modulator.
9. A holographic image display system as claimed in any preceding claim whcrein the holographic image display system comprises a video image display system, and wherein said displayed image conipnses a video frame.
10. A method of displaying an image holographically using a plurality of holographically generated temporal subframcs, said temporal subframes being displayed sequentially in time such that they are perceived as a single-reduced-noise image, each said subframe being generated holographically by modulation of a modulator with holographic data such that replay of a hologram defined by said holographic data defines a said sub frame, the modulator comprising a combination of a quantised phase modulator and a continuous amplitude modulator, the method comprising: inputting image data defining said image; processing said image data to generate said holographic data for said sub frames, and wherein said processing comprises operating on said image data to perform, for each said subframe, phase modulation to add noise followed by a space-frequency transformation to generate complex valued transformed data followed by a quantisation of at least one of a real and an imaginary component of said transformed data to generate two sets of data for said holographic data defining a said subframe, a first set of data comprising quantised data for driving said quantised phase modulator and a second set of data comprising data for driving said continuous amplitude modulator and outputting said first set of data to drive said quantised phase modulator and outputting said second set of data to drive said continuous amplitudc modulator.
1 I. A method as claimed in claim 10 wherein said quantisation comprises quantisation into a number of levels corresponding to a number of said quantised values of said quantiscd phase modulator.
12. A method as claimed in claim 10 or 11 wherein said quantiscd phase modulator has four or fewer quantiscd phase values.
13. A method as claimed in claim 10, 11 or 12 wherein said quantised phase modulator comprises a binary phase modulator.
14. A method as claimed in claim 13 wherein said first set of data comprises sign data and wherein second set of data comprises absolute value data for said at least one component of said transformed data.
15. A method as claimed in any one of claims 10 to 14 wherein said quantised phase modulator comprises a fcrroclectric liquid crystal light modulator.
16. A method as claimed in any one of claims 10 to 1 5 wherein said processing to generate said ho1oaphic data comprises an OSPR-type procedure.
17. A method as claimed in any onc of claims 10 to 16, for video image display, and wherein said displayed image comprises a vidco frame.
IS. A carrier carrying computer proccssor control code to, when runn]ng, implement the method of any one of claims 10 to 17.
19. A modulator for a holographic image display system, the modulator comprising an electrically controllable continuous amplitude modulator in combination with an electrically controllable quantised phase modulator.
20. A modulator as claimed in claim 19 wherein said quantised phase modulator has four or fewer quantised phase values.
21. A modulator as claimed in claim 19 or 20 wherein said quantised phase modulator comprises a binary phase modulator.
22. A modulator as claimed in any one of claims 19 to 21 wherein said quantised phase modulator comprises a felToelectric liquid crystal light modulator.
23. A modulator as claimed in any one ol' claims 19 to 22 further comprising a quarter wave plate between said continuous amplitude modulator and said quantiscd phase modulator.
24. A modulator as claimed in any one of claims 19 to 23 comprising a linear polariser at one or both of an input an output of said modulator.
25. A modulator as claimed in any one ol'clainis 19 to 24 wherein said modulator is a reflective modulator.
26. A modulator as claimed in any one oF claims 19 to 25 wherein said continuous amplitude modulator comprises a liquid crystal light modulator in combination with a polariser.
27. A consumer electronic device including the system of any one of claims I to 9, or the carrier of claim 18 or the modulator of any one of claims 19 to 26 or configured to operate in accordance with the method of' any one of claims 10 to 17.
28. An advertising or signage system including the system of any one of claims ito 9, or the carrier of claim 18 or the modulator of any one of claims 19 to 26 or configured to operate in accordance with the method of'any one of claims 10 to 17.
29. A helmet-mounted or head-up display including the system of any one of claims Ito 9, or the carrier of claim 18 or the modulator of any one olelaims 19 to 26 or configured to operate in accordance with the method of' any one of claims 10 to 17.