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Capabilities of diffractive optical elements forreal-time holographic displaysStephan Reichelt, Hagen Sahm, Norbert Leister and Armin SchwerdtnerSeeReal Technologies GmbH, Blasewitzer Str. 43, 01307 Dresden, GermanyABSTRACTThis paper illustrates one of the various capabilities of static diffractive optical elements (DOE) beneficial to realtimeholographic displays. Custom kinoform-type DOE can be used as elements for illumination of the spatiallight modulator, i.e. the display where the video hologram is encoded. For an RGB application of diffractiveoptical elements, particular issues concerning the inherent wavelength-dependence have to be addressed. MultiorderDOE offer a way to compensate for chromatic as well as monochromatic aberrations. We will discussconcepts and performance of multi-order DOE, show their application in holographic displays, describe issues offabrication and replication, and give experimental results of the multi-order DOE performance.Keywords: Electro-holography, 3D Display, Multi-order diffractive optical elements1. INTRODUCTIONReal-time holography is the ne plus ultra art and science of visualizing fast temporally changing three-dimensionalscenes. The integration of the real-time or electro-holographic principle into display technology is one of the mostpromising and challenging developments for the future consumer display and TV market. Only holography allowsthe reconstruction of natural-looking 3D scenes, and therefore provides observers with a completely comfortableviewing experience. Recently, we have developed a novel approach to real-time display holography overcomingthe challenges of classic holography by combining an overlapping sub-hologram technique with a tracked viewingwindowtechnology. 1, 2 For the first time this enables solutions for large screen interactive holographic displays.Diffractive optical elements (DOE) are versatile elements on their way to becoming state-of-the-art componentsin a variety of optical systems. DOE offer a flat, space-saving integration, high-accuracy, nearly arbitrarywavefront shaping, and high diffraction efficiency. However, when blazed for an operation at first order, a DOEexhibits a significant dispersion due to the wavelength-dependent diffraction. To overcome this limitation, socalledmulti-order or harmonic diffractive lenses were introduced independently by Sweeney and Sommargren 3and Morris and Faklis 4 in 1995. They showed that a diffractive lens with multi-wavelength path-length stepsrather than a single-wavelength step has the same optical power for a set of discrete wavelength whereby broadbandor multi-spectral applications become feasible. It has also been shown that such higher-blazed diffractiveelements have both diffractive and refractive properties. 5–7An important design aspect of a 3D holographic display is the flatness of the screen which should be in thesame dimension as today’s standard LCD. But the requirements for a backlight used in holographic displayscompletely differ from that for standard displays. In holography a well-defined, coherent wavefront is neededto reconstruct the 3D scene. When using standard refractive optics for reference wave collimation, the pricewe have to pay is a relatively large depth of the backlight to avoid aberrations. Here, multi-order DOE can beadvantageously used to provide a well-defined reference wave for the hologram reconstruction at the given RGBwavelengths.E-mail: sre@seereal.com, Phone: +49 (0)351 450 3240, Web: http://www.seereal.comProceedings of SPIE, Vol. 6912, Practical Holography XXII: Materials and Applications, Editor(s): Hans I. Bjelkhagen;Raymond K. Kostuk, p. 69120P, (2008). http://dx.doi.org/10.1117/12.76288769120

2. SEEREAL’S REAL-TIME HOLOGRAPHIC DISPLAY SOLUTIONFor the sake of a better understanding we briefly recapitulate the basic principles of our novel approach toreal-time display holography in a phenomenological way. For a more comprehensive description we refer to thereferences. 8, 9The fundamental idea in our concept of an electro-holographic display is to give highest priority to reconstructthe wave field at the observer’s eyes and not the three-dimensional object itself. Figure 1 illustrates the principle.Reconstruction of a single scene pointfor fixed observer positionTracked viewing windowWastedinformationSub-HologramEssentialinformationReconstructedscene pointHologramVirtualviewing windowFigure 1. Schematic drawing of SeeReal’s approach to real-time holography, the so-called tracked viewing technology.In classic holography, the 3D scene information is encoded in the entire hologram, i.e. every pixel of thehologram contributes to each object point. When illuminated by the reference wave, the combination of allof its cells reproduces the complete scene by means of multiple interferences. A classic hologram has a largeangular spectrum, which means that a large space-bandwidth-product is required. If a classic hologram is brokeninto a number of pieces, each piece will reconstruct the original scene, even though with less resolution and insmaller size. All past attempts of transferring classic holography to display and TV applications have faileddue to two inherent challenges: (1) display resolution and (2) data volume and processing. To give an example,extreme-resolution displays with a pixel size of roughly 0.5 microns would be required, which translates to thehuge demand for calculation of millions to billions of complex values for each of the 2 Mio scene points (1920 x1080) to determine an HDTV scene in 3D.When considering the human vision system regarding to where the image of a natural environment is receivedby a viewer, it becomes obvious that only the information aimed at the pupils of the viewer is required to createthe complete scene. All other information is wasted. This basic fact allows to realize tracked real-time videoholography with the following key features.Viewing window. In our approach a wavefront originating from a 3D scene is reconstructed only in a smallregion called viewing window - its size being in the range of an eye pupil size. For an observer different viewingwindows for left and right eye are generated. Holography is based on diffraction. The pixel pitch of theholographic display determines the diffraction angle that can be used. For a viewing window type hologram onlya small diffraction angle from the display to the border of the viewing window is needed whereas in classicalholography the diffraction angle is related to the size of the 3D scene. So the constraint of small pixel pitch isdistinctly released in our approach. A display with a pitch in the range of 60 µm can be used.69121

Sub-hologram. A direct consequence of the viewing window setup is the following: For each reconstructedobject point there is only a limited region in the hologram where data from this object point is coded. Thislimited region is called sub-hologram. In contrast to a classical hologram, if a viewing window-type hologram isbroken into a number of pieces, each piece will reconstruct only part of the original scene, but with full resolution(apart from object points close to the border of the reconstructed scene fragment). The refractive analogue of asub-hologram is a small lens focusing light from the hologram to the object point.Real time calculation. Hologram calculation is done by setting the sub-hologram for each object point assimple lens function and then summing up different sub-holograms. In contrast to classical computer-generatedholograms no Fourier transform is required. Larger pixel pitch and sub-hologram approach reduce computationrequirements by a factor of 10,000 as compared to the classic approach. This allows for a real time calculationof holograms.Higher orders. Higher diffraction orders of each object point of the 3D scene are also generated. But lightfrom these points is located in higher diffraction orders outside the viewing window. They are not seen by theeye located inside its viewing window. So higher orders do not deteriorate the visible reconstruction of the scene.Tracking. In a classical film hologram with fine resolution and large diffraction angle an observer can movearound the hologram and see the reconstruction from different positions. In contrast to this the restriction oflimiting the reconstruction to a viewing window would lead to a 3D scene only visible from a fixed observerposition unless an important additional feature is added to the setup, namely tracking. User tracking has beenknown before from autostereoscopic systems where some kind of sweet spots are moved in accordance with theobserver’s eye position. Such concepts have been adapted to holography, taking care of the fact, that coherenceof the light his to be maintained during tracking. A camera system in combination with fast image processingalgorithms is used to detect the actual eye position of the observer. Then the viewing window is shifted inreal-time to the new eye position, by optical or electronical means. Simultaneously hologram content is updatedby real-time calculation. Each object point shift of the viewing window also means a shift of its sub-hologramin opposite direction. This principle is illustrated in Figure 1 on the right side.3. BASICS OF MULTI-ORDER DOEDesign procedure. The design of a kinoform-type 10 diffractive optical element starts with the calculationof its phase function. The continuous phase function φ of a thin diffractive phase element refers to the phasedifference between the desired output wave and the incident wave, i.e. that difference before and behind thediffractive elementφ(x, y) = φ out (x, y) − φ in (x, y), (1)where φ is related to the recording eikonal by φ(x, y) = k 0 G(x, y), with the free-space wave number k 0 = 2π/λ 0 .That is, φ is defined by the optical path difference introduced by the diffractive element and by its designwavelength λ 0 . The continuous phase function usually refers to the first diffraction order, which is designated asthe design order. In a second design step, the blazing procedure transfers the continuous phase function φ to amodulo m2π phase profileΨ(x, y) = φ(x, y) mod (m2π), (2)where the integer-valued m is the so-called blaze order. The modulo operation – which represents the foundationof diffractive optics – is based on the fact, that a monochromatic wave is insensitive to phase jumps of multiplesof 2π since the constructive interference condition is satisfied in any case. It is important to note that differentphase profiles Ψ can be created from the same underlying phase function φ, when higher orders than the usualfirst blaze order are chosen. Blazing the diffractive element for higher orders will alter the diffractive surfaceprofile toward to more moderate feature sizes although with enlarged blaze depth. In general, the blaze orderm represents an additional design parameter of diffractive optics which has already been utilized in the past foradapting the minimum feature sizes to the manufacturing feasibility or for realizing multi-order harmonic DOE,69122

which are of special interest here. The latter type is associated with a harmonic multi-wavelength operation,i.e. the diffractive element is designed for and illuminated by a number of discrete wavelengths which fulfill thecondition ofmλ 0 = qλ blaze . (3)700q = 3 q = 5 q = 7Blaze-matched wavelength λ blaze[nm]6506005505004504001000 2000 3000 4000 5000 6000 7000 8000Synthetic design wavelength λ syn[nm]Figure 2. Wavelength selection for multi-order DOE. For a given synthetic design wavelength λ syn exists N discrete wavelengthsλ blaze within the VIS spectral range for which the multi-order condition λ blaze = λ syn/q is fullfilled. Exemplary,a q = 5, 6, 7 RGB-design for λ syn = 3150 nm is marked. The larger the synthetic wavelength, the higher the number ofsuited discrete wavelengths.Here, m is again the blaze order for the design wavelength λ 0 , where q is the blaze order for another, socalledblaze-matched wavelength λ blaze . To determine suited orders m, q for a given set of discrete operationwavelengths, we search for the lowest common multiple of these wavelengths. This wavelength now becomes thesynthetic design wavelength by which the design procedure is traced back to the standard case with a maximumphase modulation of 2π at a blaze order of one. Furthermore, that means λ syn can be substituted for mλ 0 inEq. (3). Figure 2 visualizes the set of discrete blaze-matched wavelengths λ blaze within the visible spectral rangeover a synthetic design wavelength λ syn -range. The diagram may be helpful if one prefers to go the other wayaround, that is to say defining first a synthetic wavelength and then searching for suitable operation wavelengthsat different blaze orders.The final step of the design procedure is the transfer of the modulo m2π phase profile to a surface reliefprofile t which is afterwards structured in any substrate material. Here, one has to distinguish between reflectivemirror-type (M) or transmissive lens-type (L) diffractive elementst M (x, y)| blaze = mλ 02πt L (x, y)| blaze = mλ 02πΨ(x, y),2(4)Ψ(x, y)[n(λ 0 ) − 1] . (5)From the equations above it becomes obvious that a reflective multi-order DOE is completely chromaticallycorrected for the set of harmonic wavelengths, whereas for a transmissive multi-order DOE a minor refractivedispersion of the substrate material is still present. Nevertheless, also multi-order diffractive lenses offer anelegant way to correct the diffractive dispersion at distinct wavelengths.69123

110.90.90.80.8Diffraction efficiency η0.70.60.50.40.30.2q = 7q = m = 6q = 5Diffraction efficiency η0.70.60.50.40.30.2q = 7q = m = 6q = 50.10.10400 450 500 550 600 650 700Illumination wavelength λ [nm]0400 450 500 550 600 650 700Illumination wavelength λ [nm](a) Mirror-type(b) Lens-type (acrylate)Figure 3. Diffraction efficiency over the wavelength for a multi-order DOE with m = 6 for λ 0 = 525 nm. The marginalshift of the sinc-functions for blue and red wavelengths in (b) is due to material dispersion n(λ). The blaze depth isassumed to be ideal (µ = 1).Optical performance. The optical performance of diffractive optical elements strongly depends on how accuratethe operation corresponds to the ideal situation which the DOE is designed for. This applies to bothvariations in the optical setup (operation wavelength, alignment), as well as minor fabrication inaccuracies (profiledepth, pattern distortion) of the DOE itself. Apart from alignment errors, which can be avoided by a carefuladjustment, a wavelength change will have an impact on the diffraction efficiency and the phase reconstruction.To address these influences a parameter α was established 11α = λ [ ]0 n(λ) − 1. (6)λ n(λ 0 ) − 1Profile depth scaling errors will also influence the diffraction efficiency. In case of a constant profile depth errorthis can be addressed by introducing a parameter 6 µ = t′t , (7)with t as the nominal and t ′ as the actual profile depth. With the parameters α and µ the scalar diffractionefficiency of a multi-order DOE for the qth diffraction order is then given byη q = sinc 2 (αµm − q) . (8)If the argument of the sinc-function equals to zero, the diffraction efficiency will have a maximum. Fig. 3shows the diffraction efficiency vs. wavelength of a ’5/6/7’ multi-order DOE designed for λ 0 = 525 nm and m = 6.As it can be seen in Fig. 3(a) besides the green efficiency peak there are further maxima at the blaze-matchedwavelengths of 450 nm (q = 7) and 630 nm (q = 5). To illustrate the minor influence of material dispersion wehave distinguished between (a) reflective and (b) transmissive multi-order DOE. Figure 4 indicates the efficiencydependence on blaze depth scaling errors for different blaze orders. In contrast to a standard first-order blazedDOE, the multi-order DOE’s efficiency is much more sensitive to potential fabrication inaccuracies. For theabove mentioned ’5/6/7’-design for example, a variation in the blaze depth of only 5% will result in an efficiencydrop to 65% (blue) or 81% (red), respectively.On the other hand, the aberrations of multi-order DOE are highly wavelength-sensitive too. Unaberratedwavefronts for all wavelengths will be generated only if the operation wavelengths exactly match the design69124

wavelengths. In addition to the amount of ∆λ = λ 0 − λ the accompanied phase error depends on the shape andpower of the recording eikonal G(x, y), since the design eikonal is a function of the DOE coordinates. In otherwords, the phase error will be different for a high or low power diffractive lens or for a spherical or aspheric DOEof the same power. The phase error introduced by a wavelength mismatch is given by the difference between theactual reconstructed phase and the nominal design phase φ(λ) − φ(λ 0 ), i.e.∆φ = 2πλ 0G (α − 1). (9)10.90.8Diffraction efficiency η0.70.60.50.40.30.20.1q = 7q = m = 6q = 5q = 100.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4Parameter μFigure 4. Diffraction efficiency in dependence of blaze depth variations µ = t ′ /t for a multi-order DOE. The higher theblaze order the more critical are deviations in the blaze depth from its nominal value. For comparison, the dashed linecorresponds to the first blaze order of standard diffractive elements.4. RGB-DOE IN HOLOGRAPHIC DISPLAYSGeneral issues. As the analysis in the previous section shows, multi-order DOE can designed such thatthey are chromatically as well as monochromatically corrected for a set of discrete wavelengths. These specialproperties make multi-order DOE very attractive to all optical systems and applications which operate at morethan one distinct wavelength. Especially all laser display systems – for projection or direct view – are well-suitedfor the application of multi-order DOE since by it all color channels can pass through a common optical path,and only three wavelengths are needed. It is well-known that a colored image can be generated by superimposing(simultaneously or time-sequentially) the three basic colors red (R), green (G), and blue (B) simply by adjustingthe brightness of each basic color. Therefore, for display applications a multi-order DOE has to be designed forthree wavelengths only, which reduces the required maximum order q for each wavelength, and thus the overallprofile depth of the diffractive structure.To beneficially apply multi-order DOE as a passive component to displays, the selection of the RGB wavelengthsrequires the careful consideration of the following three aspects:Light sources. Main criteria is the availability of high-quality light sources with sufficient coherence, beamquality and power that match as best as possible the blaze-constraint of multi-order DOE given in Eq. (3).Due to the phase error and diffraction efficiency sensitivity this will be the key point. Furthermore, thesize, cost and system integration are issues that have to be considered as well.Smallest common multiple of the three wavelengths. A larger synthetic wavelength means that there aremore blaze-matched wavelengths which can be selected (cf. Fig. 2). Admittedly, this simplifies the lightsource selection issue, but it comes with an increased profile depth, which is quite unfavorable in termsof the efficiency sensitivity to profile depth errors. Therefore, the smallest common multiple of threeRGB-wavelengths which corresponds to the smallest possible synthetic wavelength is the best choice.69125

Color gamut and color sensitivity of the eye. Nowadays, in standard non-laser display technology thereis a demand for large color gamut. By using laser light at RGB a high color gamut is always provided sincethe spectrally clear colors lay at the edge of the color tongue. However, also the sensitivity of the humaneye to different colors must be taken into consideration to find best-suited wavelengths.In fact, there will be always a trade-off between these aspects.Illumination issues for holographic displays. We continue our discussion with an exemplary design ofthe focusing element of a backlight unit for holographic displays. In contrast to standard liquid-crystal-displays,where the backlight provides an incoherent illumination of the LC-pixel and a large angular spread in its radiationto ensure large viewing angle, holographic displays have completely different demands to its backlight. Thebacklight of a holographic display have to be coherent and must have a defined or well-known phase and amplitudedistribution. To put it into holographic terms, this wave corresponds to the reference wave which is required toreconstruct the object encoded in the hologram.SeeReal’s approach to holography requires coherence in the illumination only over a hologram area whichequals approximately the maximum sub-hologram size. This simplifies the demand to the used optical components,since not a single light source must serve for the entire 20-inch or even larger sized hologram. Instead,a light source matrix can be used to illuminate the hologram. By doing so, the depth of the backlight can bedramatically decreased, since the closest distance between the point source and the focusing element is limitedby the maximum f-number which is achievable by classic optics.The proposed backlight unit for holographic displays is shown schematically in Fig. 5. It consists basically ofa point source array (PSA), at which the three RGB-colors are emitting in a time-sequential manner. The PSAis followed by a multi-order DOE-lens array which is placed at focal distance behind the sources. Thereby, thelight coming from one point source is collimated to a size corresponding to the clear aperture of an individualDOE. The entire hologram panel is then illuminated by a ‘quasi-planar’ wave, which is actually composed ofan entire set of planar wavefronts. To achieve a homogeneous intensity behind the DOE-lens array, a 100% fillfactor of the array is essential.RGB pointsourcearrayMulti-order DOElensarrayVideo hologram(display panel)Figure 5. Schematic explosion view of an illumination unit (backlight) for direct-view holographic displays.At this point one may ask what are the specific advantages for using multi-order DOE in holographic displaybacklights compared to standard spherical or even aspherical refractive singlets? To answer this question we69126

sizes the geometry of the stylus itself will distort the measurement. The total height is estimated to be approx.6.0 - 6.1 µm.0Profile [µm]-2-4-60 0.2 0.4 0.6 0.8 1Radial coordinate r [mm]Figure 8. Measured surface profile of the fabricated multi-order lens (central zones).Wavefront quality. To evaluate the wavefront quality a simple interferometric collimation test was performed.The multi-order DOE was placed at its focal distance of f ′ = 40 mm behind a pinhole to image a point sourceto infinity. A wedge shear plate was used to laterally shear the collimated wavefront with itself. Fig. 9 showslateral shearing interferograms obtained for red, green and blue laser light illumination.(a) λ = 633 nm (b) λ = 532 nm (c) λ = 475 nmFigure 9. Lateral shearing interferograms.For red and green we observed a wavefront quality of about λ/2, which is quite well considering the largenumerical aperture of the DOE. As expected from the theory, the strong wavelength dependence to both efficiencyand aberrations became apparent during the experiment. In our experiments we used a red HeNe-laser andgreen and blue solid state laser operating at 633 nm, 532 nm and 475 nm, respectively. That is, the operationwavelengths differ from that of the design by ∆λ R = 3 nm, ∆λ G = 7 nm and ∆λ B = 25 nm. For a smallwavelength mismatch as for red and green, this basically results in a focal shift. Therefore, we have had toreadjust the best collimation state between the tests at different colors. First, the experimental setup was bestadjusted by using the red HeNe-laser. Due to the ∆λ R of 3 nm this best adjusted focus is already 195 µm shiftedfrom its nominal value. Second, the test was performed with green light, where the multi-order lens has to shiftedabout 355 µm, which corresponds well to the ZEMAX R raytracing simulation (348 µm). Third, the collimationwith 532 nm was tested. Besides a large focal shift of we observed a primary spherical aberration of ∼ 1λ.69129

7. CONCLUSIONSIn conclusion, capabilities of multi-order diffractive optical elements for real-time holographic displays have beendiscussed. A backlight design incorporating an array of multi-order DOE having a large numerical aperture hasbeen proposed. To evaluate its performance experimentally, we have fabricated a single multi-order DOE lenswith an f-number of 2 by diamond turning and molding in acrylate. We have characterized the surface qualityand profile and analyzed the optical performance by interferometric tests. From both theoretical analysis andexperimental studies it became apparent that the most crucial parameters of multi-order DOE are best-matchedoperation wavelengths and an accurate blaze depth. In spite of their needs in tight tolerances, multi-orderdiffractive elements possess significant potential for holographic displays, since they can be designed very flexiblyand operate multi-spectrally.ACKNOWLEDGEMENTSThe authors wish to gratefully acknowledge Steffen Buschbeck for his help in performing some of the experiments.REFERENCES1. A. Schwerdtner, N. Leister, and R. Häussler, “A new approach to electro-holography for TV and projectiondisplays,” in SID, p. 32.3, 2007.2. A. Schwerdtner, R. Häussler, and N. Leister, “A new approach to electro-holographic displays for largeobject reconstructions,” in Adaptive Optics: Analysis and Methods/Computational Optical Sensing andImaging/Information Photonics/Signal Recovery and Synthesis Topical Meetings on CD-ROM, p. PMA5,Optical Society of America, 2007.3. D. W. Sweeney and G. E. Sommargren, “Harmonic diffractive lenses,” Applied Optics 34(14), p. 2469, 1995.4. D. Faklis and G. M. Morris, “Spectral properties of multiorder diffractive lenses,” Applied Optics 34(14),p. 2462, 1995.5. S. Sinzinger and M. Testorf, “Transition between diffractive and refractive micro-optical components,”Applied Optics 34, pp. 5970–+, Sept. 1995.6. M. Rossi, R. E. Kunz, and H. P. Herzig, “Refractive and diffractive properties of planar micro-opticalelements,” Applied Optics 34, pp. 5996–6006, Sept. 1995.7. T. R. M. Sales and G. M. Morris, “Diffractive refractive behavior of kinoform lenses,” Applied Optics 36,pp. 253–257, Jan. 1997.8. A. Schwerdtner, R. Häussler, and N. Leister, “Large holographic displays for real-time applications,” in PracticalHolography XXII: Materials and Applications, Proceedings of the SPIE 6912, SPIE–The InternationalSociety for Optical Engineering, 2008.9. A. Schwerdtner, R. Häussler, and N. Leister, “Large holographic displays as an alternative to stereoscopicdisplays,” in Stereoscopic Displays and Applications XIX, Proceedings of the SPIE 6803, SPIE–The InternationalSociety for Optical Engineering, 2008.10. L. B. Lesem, P. M. Hirsch, and J. A. Jordan, Jr, “The kinoform: a new wavefront reconstruction device,”IBM J. Res. Develop. 13, pp. 150–155, 1969.11. D. A. Buralli, G. M. Morris, and J. R. Rogers, “Optical performance of holographic kinoforms,” AppliedOptics 28(5), pp. 976–983, 1989.12. S. Sinzinger and J. Jahns, Microoptics, Wiley-VCH, 2nd ed., 2003.69130