Color holographic 3D display unit with aperture field division Weronika Zaperty, Tomasz Kozacki, Malgorzata Kujawinska, Grzegorz Finke Photonics Engineering Division, Faculty of Mechatronics Warsaw University of Technology Warsaw, Poland Abstract In this paper application of the aperture field division (AFD) method to provide color imaging in 3D holographic display is presented. The ways to improve the performance of the AFD solution, in terms of its suitability as a component unit of wide angle color 3D holographic displays, are discussed. Keywords-digital holography; color holography; 3D display, aperture field division method I. INTRODUCTION Holography, due to the ability to record both the amplitude and phase of an object stand out from the other 3D imaging techniques providing the true 3D effect [1]. Ideal 3D display expectations are primarily: wide angular field of view, large aperture, high resolution with real color reproduction. So far technological limitations of spatial light modulators (SLM) used for holographic displays (large pixel size, small aperture) forced to seek solutions to increase the imaging dimension and viewing angle. For this purpose the monochrome displays employ spatial, temporal or spatio-temporal multiplexing methods [2]. In our work we consider multi-slms monochrome display with circular configuration [3] Introduction of color in this display requires increasing the number of SLM [4, 5] or refresh rate requirements [6]. To realize holographic display with color imaging and wide viewing angle the system complexity has to be low. One of the feasible and attractive solutions is applying an aperture field division method (AFD) [7], in which the change of the monochrome display base design into the color one requires minimal modification. II. APERTURE FIELD DIVISION METHOD In the AFD solution an individual SLM, present in a monochrome display, can be converted into the color holographic display unit. In this paper the method is applied to reflective type modulator, however it can be used for transmissive one. A. Unit concept Three illuminating beams are provided simultaneously to the SLM surface in a common path (fig.1). An active area of the modulator is divided into three regions corresponding to red, green and blue component holograms. A color filter mask placed in front of the SLM surface distributes illuminating beams accordingly to the displayed information. Modulated Figure 1. The scheme explaining the principle of aperture field division method for digital color hologram reconstruction wavefronts representing R, G, B channels pass through the filter mask and after propagation overlap in space and create a color real image. Due to the lateral separation of the channels a triple keyhole problem (color channel separation) occurs when image is observed with a naked eye. It is therefore necessary, to apply a method which supports color mixing at the image plane. At this paper we propose a color image observation with an asymmetrical diffuser placed at the image plane [8]. This technique provides color mixing by expanding every channel viewing window in vertical direction, but at the expanse of vertical parallax and scene depth limitation up to 30mm. B. Theory of the method Due to the wavelengths diversity of separate color channels and their lateral displacement the basic reconstruction parameters differ from the parameters of monochrome display [9] and need to be discussed. The component color reconstruction images overlap properly in a limited cone area only, as shown in Fig.1. In the most general case, the location of this area most of all depends on the angular field of view (afov) and the minimum reconstruction distance (z rec ) of each channel, but their lateral separation and order are also relevant. A single channel afov is determined by the light wavelength λ and the SLM pixel pitch Δ [9]: afov = 2α = From the above formula it follows that the narrowest field of view we obtain for the shortest light wavelength. It means that the blue channel limits color reconstruction area, so the most (1) The research leading to these results has received funding from the National Science Centre, Poland, within the projects under agreement 2011/02/A/ST7/00365.
favorable for the other system parameters is to place it at the SLM center. As shown in Fig.1, color mixing occurs as soon as three wavefronts start to overlap, but since we are interested in fully utilizing the capabilities of the SLM, color reconstruction area is defined as beams superposition covering whole blue afov. Hence, the scene size at AFD method d is equal to the blue component maximum image size at given reconstruction distance z rec and can be described by the following equation [9]: d = where λ B is the wavelength of blue component illumination and z rec is the reconstruction distance longer than minimal color reconstruction distance z min. The principle of a minimal color reconstruction distance z min determination is presented in fig.2. The z min value is the z coordinate of the furthest from the SLM component afov intersection points, i.e. blue and green (BG) or blue and red (BR) depending on lateral channels separation. After some mathematical manipulations, for a small afov values, we can calculate z min using the following equation: (2) z = max, (3) where s BG and s BR are relevant component channels separations in pixel number and λ R, λ G, λ B are corresponding to red, green and blue illumination light wavelengths. Referring to (3) in a situation where component areas are same size and adjacent to each other (s BG = s BR ), the point BG defines minimal reconstruction distance. The last parameter of the color reconstruction with AFD method on which we want to draw an attention is image resolution. In general case, a resolution of holographic image reconstruction d r is described by the equation [7]: d = where N is a number of SLM pixels. Since a single color channel of the image is created using a third of the SLM area, the spatial bandwidth product of such a hologram is three times lower than for a whole surface reconstruction. For the (4) equal component hologram areas, as with other color holographic display techniques, we obtain the highest resolution for blue and the lowest for red channel. The AFD method gives us an additional opportunity of the resolution difference compensation, by developing more complex filter mask patterns which will take into account light wavelengths ratio and SLM dimensions. III. UNIT CALIBRATION High-quality color holographic reconstruction requires a precise system calibration and additional data processing. In AFD method different areas of single SLM are used for holograms of different wavelengths. This requires precise location of pixel areas corresponding to the region of individual mask responsible to holographic reconstruction of different colors. Then at each of these regions the phase response characteristic corresponding to the used wavelength has to be applied. A. Phase response calibration The expected phase pixel response of the SLM is linear 8- bit modulation within a range 0-2. This characteristic is strongly dispersive for different illumination wavelengths in visible region [9]. Because we are using a single device for a color reconstruction, and the modulation range is defined simultaneously for its entire area, we are not able to use three different phase response settings for component holograms. Since the longer the light wavelength, the shorter the range of modulation, we decided to exploit the longest among used wavelengths for the base phase response characteristic determination and the bit depth compensation for the other wavelengths. Using a double slit interferometer method [10], first we calibrated SLM for the red channel (λ R = 660nm), next we measured phase response for the rest of the wavelengths i.e. λ G = 532nm and λ B = 445nm. The experimental results are show in fig.3. As expected, the inclination of phase responses different for each wavelength. However, it shall be noticed, that all of the characteristics are linear. This finding allows for a simple compensation of dispersion using reduction of bit depth. For Figure 2. The principle of a minimal color reconstruction distance z min determination Figure 3. SLM phase response characteristics with red channel calibration 0-2 settings
compensation of dispersion using reduction of bit depth. For example for a blue component the bit depth is decreased from 256 to 156 levels. It was proven [8] that such a bit depth reduction does not affect significantly quality of image reconstruction. B. Color filter mask position calibration Precise matching of the filter mask position and component holograms at the SLM plane is a crucial feature for the high efficiency of the presented method. To achieve this aim a method based on the displayed by the SLM phase patterns and its observation through a filter mask has been developed. Within this process, the SLM, which is displaying the phase masks, is imaged on the CCD camera. At first roughly positioned filter mask joints must be adjusted to their minimal width position (tilt correction), and match to the vertical lines created by the phase pattern (fig.4a and fig.4b). Next step is a definition of the precise measurement range by the two symmetrical vertical lines scanning from the image center to the edges (fig.4c). The measurement range must cover filter mask joints and a small area around. In the final measurement step the position between mask s is determined. Defined area was scanned with three single pixel point test (fig.4d). The coordinates of the points covered by the joints allows for a linear approximation of active area borders for each channel, in fig.4e shown 24-bit mask. In our experiment, we achieved only 3.3% loss of the active SLM area in favor of joints (black color in fig.4e). This Figure 5. Data processing scheme at AFD method configuration provides normal display illumination which ensures the smallest possible area waste of applied filter mask. It can be noticed should noticed, that this pixel loss depends on filter manufacturing precision as well as angle of illumination at YZ plane. IV. DATA PROCESSING Referring to Section III there are two necessary elements of data processing, which have to be included to achieve color holographic display. Having any single view holograms given for the selected wavelength and with size matching SLM area, the necessary elements of data processing are (1) application of spatial masking found in the calibration process and (2) modulation bit depth scaling according to the phase calibration curves. In practice the correction of bit depth information can be stored in the color distribution mask and applied by multiplying by the mask over a set of holograms on the scale 8-bit image saved as 24-bit color (fig.5). V. EXPERIMENTAL RESULTS In this section we present an implementation of the color holographic 3D display unit with aperture field division and compare it with another single SLM color reconstruction technique, i.e. time division multiplexing (TDM) [6]. Color holographic reconstruction experimental setup with AFD module setup is presented in fig.6a and 6b. Red, green and blue laser beams components are collimated and mixed with the use of mirror M1, and beam splitting prisms BS1, BS2. SLM is illuminated normally to its surface via beam splitter plate BS3. At a distance of approximately 2mm to the SLM front surface, a color filter mask is placed. Modulated Figure 4. Exemplary images of calibration of color filter mask position: a) SLM view at the rough calibration with line vertical line phase pattern, b) rough calibration vertical line phase pattern, c) vertical line scanning phase pattern, d) precise scanning points set, e) color channels distribution at SLM plane. Figure 6. Color holographic 3D display unit with aperture field division: a) reconstruction setup, b) an AFD unit prototype
wavefront is passing this filter mask and beam splitter plate BS3. A real holographic image is observed on an asymmetrical diffuser placed at its reconstruction plane. Most important color holographic display parameters using a single SLM are listed in Table 1. In fig.8 the holographic reconstruction obtained using both holographic displays techniques (AFD, TDM) are presented. There are showed reconstructions of Fresnel holograms calculated from 2D images and 3D objects [12] (fig.7). The holograms were calculated for SLM with pixel pitch Δ=8µm, 1920x1080 resolution, frame rate 60Hz, light sources wavelengths: 660nm, 532nm and 445nm, and reconstruction distance z=750mm. TABLE 1. Parameter Name R/G/B image vertical resolution R/G/B image horizontal resolution Max. image size afov Min. reconstruction distance Color image observation mode Color image display frame rate Synchronization mode Figure 7. Synthetic objects used for color reconstruction: a) 2D object, b) 3D object A SET OF PARAMETERS FOR THE SELECTED COLOR HOLOGRAPHIC DISPLAY METHODS Aperture field division Time division multiplexing 172µm / 139µm / 116µm 57µm / 46µm / 38µm 32µm / 26 µm / 22 µm 32µm / 26µm / 22µm 41.71mm 41.71mm 3.19⁰ 3.19⁰ 529mm 276mm Asymmetrical diffuser Asymmetrical diffuser, naked-eye 60Hz (native) 20Hz (1/3 native) none data and light source synchronization Most of the parameters of the two compared displays methods are equal or comparable (e.g. image size, reconstruction distance, angular fields of view). On the one hand, time multiplexing division technique has superiority in terms of image resolution (fig.9b), but on the other hand it has low frame rate and system complexity, which makes system much harder to apply in consumer products. The AFD unit is more suitable as a method for a wide viewing angle color holographic display system due to providing color image with a native operating frequency of the SLM. Accordingly it leaves us a field of activity for a widening angular field of view or image quality improvement with a number of multiplexing solutions. However, as SLM parameters improvement is expected, the greatest problem to solve at the aperture field division technique remains the triple keyhole effect, i.e. holographic 3D image observation conditions. Figure 8. Color holographic display experimental results with asymmetrical diffuser screen for aperture field division unit Figure 9. Color holographic display experimental results with symmetrical diffuser: a) aperture field division unit, b) time multiplexing method VI. CONCLUSIONS In this paper a color holographic 3D display unit with aperture field division was presented. Basic parameters and calibration methods are described. Experimental results are shown, and comparison to other single SLM color display technique (time division multiplexing) is performed. Since a single color channel of the image is created using a third of the SLM area, the spatial bandwidth product of such a hologram is three times lower than for the case of color multiplexing methods. Despite this fact, AFD unit has a chance to be used at wide viewing angle holographic displays, due to its native operating frame rate usage. However a proposition of triple keyhole effect solution with asymmetrically diffusing screen was presented, observation mode is the most relevant limitation of this method and some other solution must be developed in the future work. ACKNOWLEDGMENT The research leading to these results has received funding from the National Science Centre, Poland, within the projects under agreement 2011/02/A/ST7/00365.
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