Design and fabrication of stacked, computer generated holograms for multicolor image generation

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1 Design and fabrication of stacked, computer generated holograms for multicolor image generation Thomas Kämpfe, 1, * Ernst-Bernhard Kley, 1 Andreas Tünnermann, 1 and Peter Dannberg 2 1 Friedrich-Schiller-University Jena, Institute of Applied Physics, Max-Wien-Platz 1, Jena, Germany 2 Fraunhofer Institut Angewandte Optik und Feinmechanik, Albert-Einstein-Strasse 7, Jena, Germany *Corresponding author: kaempfe@iap.uni-jena.de Received 5 March 2007; revised 29 May 2007; accepted 1 June 2007; posted 6 June 2007 (Doc. ID 80545); published 23 July 2007 We present a diffractive optical element consisting of computer-generated holograms and dielectric multilayer mirrors in a stratified setup. Illuminated with a white laser beam, consisting of three single lasers with wavelengths of 635 nm, 543 nm, and 473 nm, this element enables the far field projection of arbitrary, multicolor images. Certain advantages of holographic image generation, e.g., the possibility of a large depth of focus and a very easy optical setup, are maintained with the new element Optical Society of America OCIS codes: , , , Introduction Diffractive optical elements in the form of computer generated holograms (CGHs) are generally used to influence the wave front of a propagating light beam in a very flexible way. In contrast to optically recorded holograms, which require a physically existing object to record the fringe pattern, a CGH is calculated in a computer and then fabricated by appropriate writing and structuring techniques, depending on the required feature size. One interesting area is the use of CGHs for the projection of static images onto a screen. Such a projection system can be realized with some unique properties (very large depth of focus, very simple, adjustment insensitive optical setup). It consists only of a laser, the CGH, and a focusing lens if necessary (Fig. 1). Therefore, this setup is especially interesting for very small handheld systems, like the known laser pointer caps. With the common setup and a single CGH the projection is usually limited to monochromatic images. To encode the red, green, and blue parts of a multicolor image, three separate elements can be used. Placing them side by side [1] in the optical setup results in a loss of depth of focus, since the three images emerge from separate /07/ $15.00/ Optical Society of America sources. A more complicate setup overcomes this limitation by merging the colors after the CGHs [2], yet this approach requires a laser setup adapted to the specific CGH layout. In this paper we want to develop elements that are capable of generating screenfilling, multicolor images from one white laser beam, consisting of three single lasers beams of red, green, and blue color. In this case there are widely known approaches to encode the specific information for the single wavelengths not in separated elements, but in the structure profile itself, as first proposed by Dammann [3] in the case of grating structures. With the optimal rotation angle method [4,5], even the creation of multicolor images from a single element, illuminated by an RGB laser beam is possible. However, this method is only suited for signals consisting of a limited number of points. Images filling the whole signal plane would be limited regarding the SNR and furthermore cause excessive computational effort. The introduction of a phase delay, increased significantly beyond 2, can be used to improve such a multi-wavelength element [6,7] but in this case the choice of wavelengths is limited and, especially for covering the typical RGB wavelengths, the required structure depth can be very high and thus make the fabrication more difficult if small pixel sizes are of interest. Another known possibility is the use of a stratified setup of CGHs, where the optical nearfield 5482 APPLIED OPTICS Vol. 46, No August 2007

2 Fig. 1. (Color online) Principle of monochromatic image generation by a CGH. Fig. 2. (Color online) Creation of a multicolor image from the three primary colors, using three laterally separated CGHs. of one hologram is directly influenced by the following CGH. Such stratified setups have already been analyzed and fabricated for periodic, grating like structures [8]. They also enable the encoding of arbitrary, wavelength-selective functions [9]. In contrast to conventional CGHs these elements are extremely sensitive to variations in the illumination angle and thus sacrifice one of the main advantages a projection setup with CGHs. Furthermore, they are very challenging for the fabrication, since they require almost pixel-exact adjustment of the stratified CGHs in the lateral direction. The herein proposed element is a new approach to a simple projection system based on CGHs that is realized as a stacked setup consisting of common surface relief phase holograms and dielectric multilayer mirrors. In the following we first describe the calculation method used for the monochromatic CGHs. Then design and fabrication of the stacked setup for color image generation are explained and optical measurements of the resulting images are given. 2. Design of the Computer Generated Hologram for the Monochromatic Case Binary phase only diffractive elements can be used to influence a coherent, monochromatic laser beam in such a way that during further propagation of the light a desired image is formed (Fig. 1). To calculate the required phase function we use an iterative approach based on the Gerchberg Saxton algorithm [10]. The Fraunhofer approximation is used for the simulation of the propagation between element and image plane, thus the image is calculated as the Fourier transform of the optical function of the CGH. This means that after a certain propagation length, necessary to reach the far field, the image only scales with the distance. Furthermore, we chose the lateral size of the phase function to be considerably smaller than the beam size and assumed plane wave illumination. This unit cell was then repeated several times to form the final CGH, having a size of about 1 cm 1 cm. These two approaches lead to a translation invariance of the image formation, i.e., the CGH can be moved through the laser beam without influencing the image. The setup is also very insensitive to the actual intensity distribution of the laser beam on the CGH as long as the laser spot in the image plane is sufficiently small. Therefore it is no problem to use, for example, stacked diode lasers with a rather inhomogeneous intensity profile. Due to the repetition of the unit cell, the CGH works as a beam splitter. The image is therefore composed of pixels having the size and shape of the undisturbed laser beam and thus stays sharp as long as the laser beam diameter is sufficient to sample the image in the corresponding plane. With a proper choice of parameters the projection onto strongly tilted or curved screens is possible. As a rule of thumb, at least about 3 3 repetitions of the unit cell must lay inside the laser beam diameter. This separates the image pixels enough to prevent large intensity modulations due to phase dislocations and at the same time retains a quite smooth appearance of the image. In our experimental setup we used 250 mw diode pumped solid state lasers for blue and green (473 nm and 532 nm) and a 300 mw stacked diode laser for red 635 nm. The beam diameter was for all three lasers about 3 mm which results in a unit cell of about 1 1 mm. The pixel number was then chosen according to the pixel size (see Section 4). Furthermore we used a Fourier lens after the CGH adapted to the screen distance (standard screen distance: 2 m) to achieve a laser spot small enough to sample the image. Of course this reduces the depth of focus. For a projection on tilted or curved screens one has to bear this limit in mind and probably chose a smaller image resolution, which would allow a smaller beam diameter and thus a larger depth of focus. It is very straightforward to use this rather simple optical setup to create a multicolor image by illuminating three elements for the primary colors, which are placed side by side. However, this sacrifices the large depth of focus to a far greater extent (Fig. 2). 3. New Approach to Create Color Images by Computer Generated Holograms Our approach is to place the elements directly behind each other, giving the separate primary color images almost the same source point. It is thus comparable with a multicolor volume hologram, yet it is created synthetically from single elements. The wavelength selectivity is achieved by dielectric multilayer mirrors, which are designed to reflect one of the RGB wavelengths and transmit the other two. These mir- 1 August 2007 Vol. 46, No. 22 APPLIED OPTICS 5483

3 Fig. 3. (Color online) Principle of a wavelength selective, reflective CGH. rors are applied to the diffractive elements, forming a wavelength selective, reflective CGH. If furthermore the structure is embedded so that both sides have only plane interfaces, the transmitted light does not suffer any phase modulation (Fig. 3). Therefore, a stacked setup, consisting of three of these CGHs designed for red, green, and blue, allows the encoding of three different optical functions for the three wavelengths (Fig. 4). The multilayer mirror, which is to be applied upon the CGHs, must be optimized with regard to two aspects: Firstly, in order to ensure a good efficiency of the resulting element, the reflectivity should be as high as possible for one of the RGB wavelengths (in the following called reflection wavelength ). Secondly, the two other wavelengths (in the following called transmission wavelengths ) should propagate through the element without being disturbed. This means the bandwidth of the reflection peak should be as small as possible and the reflectivity for the transmission wavelengths should be as close to zero as possible. The suppression of any reflection of the transmission wavelengths is the most important condition here, since even a small reflection would result in an additional image on the screen, wrong in size and in color. Normally, to design such an optical coating, one would choose a very thick coating with many layers, using the large number of degrees of freedom in the design for better wavelength selectivity. However, in our case the mirror is put upon a binary surface relief structure, whose shape should be maintained by the mirror to preserve the CGH s function for the reflected light. If the mirror gets thicker, the Fig. 5. Wavelength characteristic of dielectric multilayer mirrors of different total thicknesses, designed for reflection at 543 nm. edges get increasingly rounded, therefore, regarding the optical function of the CGH, a mirror as thin as possible is preferable. As a further constraint due to adhesion problems in the final, quite complex stacked element, only a limited number of materials is available for the dielectric layers. We chose SiO 2 n 1.46 and TiO 2 n 2.5 as layer stack materials. The wavelength characteristics that can be achieved by a layer stack of 4.6 m, 2.5 m, and 1.5 m thickness, optimized for reflection at 543 nm and transmission at 473 nm and 635 nm, is shown in Fig. 5. The important parameter (suppression at 473 nm and 632 nm), depends very much on the actual layer system (small changes in layer thickness due to fabrication tolerances shift the sidelobes) and no significant improvement is possible by using the thicker systems. Since the bandwidth and the peak reflectivity of the thinnest system is still sufficient, we decided to use the 1.5 m thick layer system for the element of the green part of the image. For the red and blue part an edge filter can be applied. For these filters even fewer layers are required to get the same suppression behavior as for the green part. Therefore, layer systems of 1.1 m and 1.0 m total thickness were chosen. The calculated and the measured wavelength characteristics of the multilayer mirrors, realized with these parameters, are shown in Fig. 6. Fig. 4. (Color online) Principle of stacked setup, creating a reflective RGB-CGH. Fig. 6. (Color online) Calculated and measured wavelength characteristics of the dielectric multilayer mirrors, used for the stacked, wavelength selective CGH APPLIED OPTICS Vol. 46, No August 2007

4 4. Fabrication of the Stacked Computer Generated Hologram As basic material for the wavelength selective CGH as shown in Fig. 3, a UV hardening polymer was used, because it is possible to structure it by UV molding and also apply a dielectric filter onto it. Additionally, the polymer can be applied upon already fabricated wavelength selective CGHs and further processed to form a stacked setup as in Fig. 4. A. Fabrication of the Computer Generated Hologram Masters by Electron-Beam Lithography The phase function of the CGH was realized as a binary surface relief structure in a fused silica substrate. We used an electron-beam writer SB350 OS (Vistec Electron Beam GmbH) for writing the phase information into resist, which after developing acts as an etching mask for the underlying chromium layer. Then, this chromium mask was transferred by reactive ion beam etching into the fused silica substrate, where the height was chosen to realize a step for the reflected light of the corresponding wavelength and the refractive index of the UV polymer. To evaluate the influence of the feature size on the stacked setup, we created the phase function with pixel sizes of 0.5, 0.7, 1.0, 2.0, 4.0, and 8.0 m. For the unit cell of about 1 1 mm (see Section 2) we chose a pixel number of , , , , , and pixels respectively. Therefore the appearance of the images is comparable, only the resolution and the aperture angle changes. There are several fabrication tolerances that influence the resulting height structure. Most critical are an inadequate e-beam dose during the lithography, which will result in a change in the fill factor (that is, the ratio between the lateral size of and zero pixels), and a limited accuracy in the reactive ion beam etching time, which will result in a different step height of the binary structure. In our case we achieved for the several fabricated elements a fill factor accuracy of about 5% for the smallest pixel size and a depth accuracy of about 5 nm, which corresponds to a relative error of the step height of about 5%. However, within the thin element approximation, small deviations of this kind mainly cause a slight increase in the zeroth order efficiency, but do not significantly influence the optical function. Since the effects caused by distortions of the profile due to the coating process is much greater, the tolerances during the CGH fabrication are in our case not critical for the final result. B. Replication into the Polymer Layer In this process, the surface of the substrate (which may already be a reflection coated CGH) was covered with a thin polymer layer and subsequently structured by a replication process. Thus the planarization of the previous and the generation of the next CGH in the stack were accomplished simultaneously. The compatibility of the two processes replication and dielectric filter generation (in our case by ionizedplasma assisted evaporation, APS) can be critical due to low adhesion, different coefficients of thermal expansion, or limited polymer stability. We succeeded with an approach consisting of UV molding of thin polymer layers, inorganic organic hybrid polymer material, optimized curing, and a special dielectric APS coating design and process [11]. UV molding is a reliable technology, which is well established, i.e., in the generation of large quantities of temperature stable micro optical elements [12]. In particular the replication assures that the quality of the fused silica master element can be transferred to a high number of polymer-on-glass elements. The UV molding was carried out in an MA6 mask aligner (SUSS MicroTec) with embossing hardware using the fused-silica CGH master as stamper and fused silica as well as borofloat B33 glass wafers as substrates [13]. After the parallel orientation of stamper and wafer to each other (wedge error compensation), the UV resin (Zipcone UA Gelest, Inc.) was dispensed, master and substrate were laterally and axially aligned, and the polymer film was then cured by a UV dose of 1 J cm 2 at 365 nm and subsequently separated from the master. Maximum stability against the following APS coating step was achieved by low polymer thickness of 10 m and by full UV cure with no oxygen present, followed by a thermal curing step for 30 min at 160 C. After dielectric coating, the top layer SiO 2 was treated with an adhesion promoting silane, so the whole cycle could be repeated. Whereas single layer AR coated UV polymer elements were thoroughly tested concerning mechanical and thermal stability [11], these tests have still to be carried out for the generated stacks, but up to now no defects due to the repeated hardbake procedure at 165 C and the plasma load during the APS coating process were found. In addition, we could demonstrate the separation of a wafer with stacked elements on a dicing saw (DAD341 Disco), showing the capability of a parallel fabrication of elements on a wafer scale. Fig. 7. SEM image of a cross section of the stacked, wavelength selective CGH. 1 August 2007 Vol. 46, No. 22 APPLIED OPTICS 5485

5 Fig. 8. Detail of Fig. 7, showing the influence of layer growth on the surface relief profile (CGH with 0.7 m pixel size). Fig. 9. Ratio of the transmittance in a structured area T s to the transmittance in an unstructured area T u, measured for the red CGH. Due to the shift invariance of the Fourier transform and the independent manner, in which the single color phase functions are applied to the incoming beam, the CGHs only have to be aligned regarding rotation, but not translation. In Fig. 7 SEM pictures of cross sections of the stacked element can be seen, showing the different layer systems. The layer growth during the APS coating has a significant influence on the surface relief structure: the edges of the structure are rounded and the fill factor (ratio of lateral size of pixels at and at zero level) is changed (Fig. 8). 5. Characterization We fabricated several CGHs for just one of the primary colors (according to Fig. 3) as well as several CGHs for all three colors (stack in Fig. 4) to be able to investigate both the optical behavior of a wavelength selective CGH on its own and the capability of the stacked setup to create multicolor images. A. Influence of the Mirror Structuring on the Optical Function While measuring the reflection and the transmission behavior of the structured mirrors we encountered variations due to fabrication related variations in the thicknesses of the layers of the mirror that overlay the intended measurements (comparison between structured and unstructured regions, influence of front backside measurements). Therefore we had to stick to measurements at the same point on the substrate or at very closely neighboring points 1 mm to get reliable data. Bearing these restrictions in mind we carried out several optical measurements summarized in Fig. 9 and Table 1. However, due to the holographic nature of the image generation, these fluctuations do not create significant disturbances in the created images, compared with conventional monochromatic transmission-type CGH. For comparison of front and backside illumination we measured the ratio between all diffracted light in reflection and all reflected light (including zeroth order) for elements with a pixel size of 1 m (Table 1). This is not the efficiency for the diffraction of the light into the desired signal (because stray light, mirror images, and higher order images are included here) but it nevertheless can serve as a measure for the influences of the layer coating on the diffraction properties of the CGH. We found that of the reflection wavelength (bold numbers in Table 1) is significantly lower for frontside illumination. This is due to the changes in fill factor and depth of the structure during the growth of the layer system (Fig. 8) that both increase the zeroth order efficiency. For the two transmission wavelengths the element does not have the right depth for maximal diffraction efficiency anyway; therefore a change in fill factor and depth can cause an increase as well as a decrease of (regular numbers in Table 1). Thus no side can be generally preferred, but in our case backside illumination is slightly advantageous. To estimate the influence of the pixel size we compared the ratio of the totally transmitted intensity T in a structured T s and an unstructured T u area (Fig. 9). For smaller pixel sizes, the part of the mirror that is located in the vicinity of the pixel edges and is therefore bended and disturbed in its optical function (Fig. 8) gets bigger in relation to the whole mirror size. Therefore, decreasing the pixel size results in a higher transmission of the reflection wavelength and a lower transmission of the transmission wavelength (Fig. 9, example for red CGH). Since we assume no significant absorption inside the element this means Fig. 10. (Color online) Optical setup for the stacked, wavelength selective CGH for multicolor image generation APPLIED OPTICS Vol. 46, No August 2007

6 Table 1. Total Reflective Diffraction Efficiency in % (All Reflected Light Minus Reflected Zeroth Order) of One-Color Elements for Front Backside Illumination Element s Reflection Wavelength, Illumination Direction Red Illumination (635 nm) Illumination Wavelength Green Illumination (543 nm) Blue Illumination (473 nm) 635 nm, frontside ill nm, backside ill nm, frontside ill nm, backside ill nm, frontside ill nm, backside ill that the desired image from the reflection wavelength will get darker and the unwanted images from the transmission wavelengths will get brighter with decreasing pixel size. B. Analysis of the Created Multicolor Images The single, wavelength selective CGHs (as in Fig. 3) were illuminated with the three primary colors. The resulting pictures were sharp and showed a noiselevel comparable to a conventional transmission-type CGH. This means the structured multilayer mirror is able to realize the optical function of the CGH very well despite the rounding of the pixels. The visible wrong color images (Fig. 11) have different intensities, which is partly due to the different residual suppression of the transmission wavelengths, which the fabricated multilayer mirrors are actually able to achieve. Also the sizes of these ghost images are different due to different diffraction angles of the primary colors, meaning they appear dimmer or brighter even if they carry about the same energy. Altogether the blue element works best (intensity of green image 5%, red image 1%), followed by the green element (blue image 10%, red image 1%) and the red element (green image 25%, blue image 10%). For the stacked element we expect two possible wrong color images from the topmost layer, since it is illuminated with all three colors. The second layer should produce only one visible wrong color image, since the color from the topmost layer is already reflected, while the last element should not produce any distorting image, since the main parts of the other two colors are already reflected. With respect to the images from the single elements (Fig. 11) we used the sequence red-green-blue, with red being the lowermost element. It was illuminated according to Fig. 10. As expected, colored images are created (Fig. 12). The wrong color images appear only very faint but are still visible, especially if they appear in dark areas of the image. To measure the achievable depth of focus we chose a fixed Fourier lens of 1.4 m focus distance and place the image screen 2 m and 0.7 m from the CGH. In contrast to the laterally separated CGHs (Fig. 2) that were used in the same optical setup, no color displacement is visible with the stacked element (Fig. 12). Fig. 11. Monochromatic images created from an RGB laser beam. Fig. 12. Photographs of a color images, created by a wavelength selective, reflective CGH. Magnified detail illustrates large depth of focus without color separation. 1 August 2007 Vol. 46, No. 22 APPLIED OPTICS 5487

7 6. Conclusion We designed and realized stratified CGHs for the creation of screen filling, multicolor images, based on combining dielectric multilayer mirrors with phase only CGHs. The typical, adjustment insensitive optical setup is preserved and the resulting image quality is comparable to the monochromatic case. There is no color displacement as in the case of laterally separated CGHs and thus the complete depth of focus, provided by the optical setup, can be used. The concept of the stacked element is not limited to binary elements. Also multilevel elements (e.g., 4 or 8 height level elements) can be used, which will result in a better overall image quality (lower noise level) and better efficiency (no mirror image). Further investigations are necessary to improve the color separation in order to avoid any residual wrong color images. To this end a more detailed investigation of the reflection properties of structured multilayer mirrors will be necessary. Another approach is the encoding of the wavelength selectivity by a contact holographic step, which transfers the optical function of regular CGHs into thickfilm holograms. This idea is comparable to the herein proposed setup, yet it might be more compatible for large-scale production, and will be tackled in a forthcoming paper. The authors would like to thank MSO Jena GmbH for help with the selection process of the multilayer coating, H. J. Fuchs, H. Schmidt, and W. Gräf for the fabrication of the CGH master, and C. Otto for preparing the elements for the SEM pictures. This work was funded by the Deutsche Forschungsgemeinschaft within the project 3D Micro- and Nanostructured Optics. References 1. H. H. Suh, Color-image generation by use of binary-phase holograms, Opt. Lett. 24, (1999). 2. J. R. Fienup and J. W. Goodman, New ways to make computer generated color holograms, Nouv. Rev. Opt. Appl. 5(5), (1974). 3. H. Dammann, Color separation gratings, Appl. Opt. 17, (1978). 4. J. Bengtsson, Kinoform design with an optimal-rotation-angle method, Appl. Opt. 33, (1994). 5. J. Bengtsson, Kinoforms designed to produce different fan-out patterns for two wavelengths, Appl. Opt. 37, (1998). 6. I. Barton, P. Blair, and M. R. Taghizadeh, Dual-wavelength operation diffractive phase elements for pattern formation, Opt. Express 1, (1997). 7. Y. Ogura, N. Shirai, J. Tanida, and Y. Ichioka, Wavelengthmultiplexing diffractive phase elements: design, fabrication, and performance evaluation, J. Opt. Soc. Am. A 18, (2001). 8. G. Nordin, R. Johnson, and A. Tanguay, Jr., Diffraction properties of stratified volume holographic optical elements, J. Opt. Soc. Am. A 9, (1992). 9. S. Borgsmüller, S. Noethe, C. Dietrich, T. Kresse, and R. Männer, Computer-generated stratified diffractive optical elements, Appl. Opt. 42, (2003). 10. R. W. Gerchberg and W. O. Saxton, A practical algorithm for the determination of phase from image and diffraction plane pictures, Optik 35, (1972). 11. U. Schulz, U. B. Schallenberg, and N. Kaiser, Antireflective coating design for plastic optics, Appl. Opt. 42, (2003). 12. H. Rudmann and M. Rossi, Design and fabrication technologies for ultraviolet replicated micro-optics, Opt. Eng. 43, (2004). 13. P. Dannberg, R. Bierbaum, L. Erdmann, A. Krehl, A. Braeuer, and E. B. Kley, Micro-optical elements and their integration to glass and optoelectronic wafers, Microsys. Technol. 6, (1999) APPLIED OPTICS Vol. 46, No August 2007