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Abstract
A two-step holographic process for the fabrication of an imageplane disk-type multiplex hologram is described in this paper. The diffraction efficiency of the transfer hologram is measured as a function of exposure. It is found to be influenced by the polarization of the light beams of the copying system, resulting in different diffraction efficiencies from different areas (under different interference conditions) of the hologram transfer. The factors which cause the phenomenon of diffraction-efficiency difference are demonstrated and the corresponding experimental results are discussed.
©2007 Optical Society of America
1. Introduction
Multiplex holography which combines off-axis holography and photography was first proposed by DeBitetto in 1969 [1], and then computer-generated data [2] or outdoor scenery were used as the subjects for hologram formation. In 1977, L. Cross developed the cylindrical-type multiplex hologram [3] with its image appeared at the center of the cylinder. In 1989, Japanese scientists invented the conical holographic stereogram [4], with the reconstructed 3D image being present at the open end. Based on this our holographic team
developed the disk-type multiplex hologram [5] by extending the apex angle of the conical hologram. Conventional multiplex holograms are composed of a series of long-thin individual holograms which consequently causes the reconstructed images overlaid with a fence structure. This annoying phenomenon is called the picket-fence effect. Image-plane method has been designed to free multiplex holograms from this fence structure. This method has been successfully applied to various formats of hologram, including the cylindrical-type [6], the conical-type [7], and the disk-type [8] holograms. More recently, we further developed a 360-degree viewable image-plane disk-type multiplex hologram (IPDTMH) which can be viewed by the surrounding observers simultaneously [9].
Owing to the possibility of using CD technology for mass production, it would be an appropriate time to utilize this kind of IPDTMH to display scientific data, tomographic data, and images of people or scenery. We are now trying to fabricate the IPDTMH for commercial production. Photo-resist materials are ordinarily used in production of master plates but we know that the exposure time needed for grating formation in photo resist is much longer than that needed for a silver halide film which of course makes it impractical for multiplex hologram fabrication. It seems that single exposure would be more efficient for mass production. In this paper, we discuss how to produce a master hologram and a simple optical system for single-beam copying. Light diffracted from different areas of the transfer hologram is measured. Unfortunately, the diffraction efficiency measured in alternate areas of the finished transfer hologram under different interference conditions is inevitably discordant, representing two polarization-influenced factors. One of the factors is formed from the linearly polarized light source (TM or TE incidence) [10] during the transferring process and the other factor is shown to be because in the second step the directions of the polarization of interfering beams are not parallel in one area of the recording film [11]. We also find the ratio of the diffraction efficiencies of two beams diffracted from these two areas. Finally, the method for producing uniform diffraction efficiency for the hologram transfer is demonstrated experimentally.
2. The parameters needed to design a master hologram
Fig. 1 shows the schematic diagrams of both the fabrication of the master hologram (H1) and the production of the transfer hologram (H2), where the image plane in the first step becomes the film plane during the transfer formation. It is assumed that observers around the transfer hologram in viewing coordinate system X-Y-Z will see a 3D reconstructed image (with its center P) at a distance dv away from the master hologram. This position is the best viewing distance (where the eye can perceive a 2D image) for the reconstruction process. The object beam (WOM) producing the master hologram in our optical system is a converging spherical wave which is focused to the point C at a distance about v d behind the master hologram. The reconstruction reference beam (WRM) in the second step is just the same as the reference beam (WCM) in the first step.
For simplicity, the reference beam below the X-Y plane is set to be a normally incident plane wave (WCM), and the same plane wave acts also as both the reconstruction reference beam (WRM) and the reference beam (WCT) in the second step.
Given the imaging properties of the lenses, we design the holographic optical system shown in Fig. 2. Light coming from a laser source is split into two beams by the beam splitter BS. The object beam is directed into the optical system by the reflecting mirrors M1 and M2, after which it is spatially expanded by the spatial filter SF1. It is designed to be focused by the lens 1 L onto the second lens L 2, where zeroth-order filtering is performed. The 2D image is transmitted to the input object plane (LCTV) on which the image may be taken by a CCD camera aimed at a 3D object on the rotational stage or generated by a computer. The object information is enlarged by the optical system (lenses L 2 and L 3) and imaged onto the image plane (H2) behind the recording holographic film (H1), where the illuminating light source (WOM) is focused at a distance dv behind the plane of the recording film. The distance from the film plane to the image plane is IT d, and the place where the laser light source is imaged is the best viewing position for the observer. The reference beam is expanded by the spatial filter SF2 and then collimated by the lens L4 to become a plane wave (WCM), before falling on the holographic film. An aperture placed right in front of the holographic film allows only the passage of useful information. After the appropriate exposure, the 2D object is recorded as a hologram. Before making the next exposure, the 3D object on the rotational stage as well as the recording film is rotated by a suitable small angle θf. This process continues until both the object and the film have been rotated by a full round.
Taking a closer look at the object beam in Fig. 3, the equation for the tilt angle δ of the LCTV can be calculated utilizing the imaging properties of lenses L2 and L3
from which we obtain a suitable set of parameters for hologram fabrication (Fig. 3): θ1=36.50°, d1=14.53cm, d 23=65.00cm, q3=37.86cm, dv=53.62cm, f2=15.00cm, f3=38.00cm, and δ=61.32°.
Fig. 4(a) shows the 3D image captured by the CCD camera and Fig. 4(b) shows the formation of the final image point (Pv). In Fig. 4(b) we can see that the reconstructed image will float above the master hologram because of the intersection of the lines of sight. Note that, to form a plane wave, the white-light source (WRT) must be very far away from the master hologram plane or placed near the back focal plane of a lens.
Fig. 4. Schematic diagrams of the object coordinate system and image-reconstruction coordinate system.
By a simple geometrical relationship, the parallax (θv) of the 3D image as seen by the observer is shown in the table below.
Table 1. Relationship among the parameters in the reconstruction process
According to the similar triangle theorem, the distance (di) from the master plane to the 3D image can be found. Then the inclination angle (θa) of the CCD can be found by θv=θhsinθa.
Now, on the basis of coordinate transformation, the relationship between image point (Pv) and original object point (Po) in object coordinates can be performed. Referring to Fig. 5, an object point Pf on the film can be determined from the corresponding original object point Po in Fig. 4(a). With computer simulation, we can find whether the reconstructed image ray can reach the eye of the observer or not. When the hologram is shone by a light source (WRT), and given the condition that both eyes of the observer can see the respective object points which belong to the same original object point, the image point Pv will be viewed by the observer (Fig. 4(b)) at the intersection of the lines of sight of the two eyes of the observer. Also, through numerical simulation we can determine the effects on the reconstructed image by changing the holographic parameters, so as to find the most suitable parameters for hologram fabrication.
With the multiple exposure process (Fig. 6), sequential 2D images of the letter “i” (as shown in Fig. 7), which provide continuous parallax (with slightly different viewing angles), are sent to the optical system to form the master hologram. In this study we make the holograms more compact and thus more suitable for mass production, for example in security applications such as security labels. The set of parameters is as follows: dv=53.62cm, θ1=36.50, δ=61.32°, Am=3.75cm, At=1.25cm, Rm=5.00cm, Rt=2.50cm, dIT=1.85cm, θ=0.36°, and θa=53.55°. Fig. 8 shows several experimentally reconstructed images corresponding to the original images in Fig. 7, with a viewing distance of dv.
The movie (in Fig. 9) shows a typical 360-degree viewable IPDTMH display. During the reconstruction process, each eye of the observer will see its own respective 2D image. These two images become a 3D image in space when fused together by the brain.
One might think that the same single-beam (transferring) system (Fig. 10) could be used easily for this master hologram. However we found that for bigger image display (the height of the duck image is 7 cm, and R′t=9cm, R′m=18cm) a large-diameter (2R′m) lens is required. Due to the lack of a high priced lens, one may produce a duplicate of the master by contact-copying replication techniques [12]. Note that in this case the parameters have to be designed for image-plane hologram.
3. Optical system for fabricating a transfer hologram
Once the master hologram H1 is finished, we can start making the transfer hologram H2. In the second step, a single-beam copying optical system is designed to transfer the master hologram as shown in Fig. 10.
Light (WRM) coming from a laser source is spatially expanded by the spatial filter SF and collimated by the lens L before being shone on the master hologram. The images recorded in the master hologram (H1) will be reconstructed and reappear on the image plane at a distance dIT away from the holographic plane. The geometric relationship between the master hologram and the transfer hologram is illustrated in Fig. 11 and Fig. 12. The distance between H2 and H1 for the experiment is 1.85 cm and Rt (Rm) is equal to 2.5 (5.0) cm. At the same time,
a part of the plane wave (WRM) becomes reference wave (WCT) and passes through the central zone of the master hologram. A holographic film H2 is used to record the interference fringes to form a transfer hologram on which each of the 2D objects is recorded as an image-plane hologram. Fig. 13 shows the reconstructed images from the transfer hologram under whitelight illumination (WRT).
4. Polarization-influenced factors in this type of copying system
In this kind of system, there are two important factors which can make an obvious difference between the diffraction efficiencies of image rays from areas A2t and A1t (Fig. 10) in a finished duplicate hologram. The first has to do with the polarization of the light source in the transferring system (linearly polarized light; see Fig. 10 and Fig. 15). The fringe structure of our disk-type multiplex hologram is like a Fresnel zone plate (Fig. 15). In area A1 (Fig. 14), we can see that the direction of the formed fringes, as well as the directions of the polarization of both the object beam and the reference beam, is perpendicular to the Y-Z plane. However, the fringes in area A2 are formed (as mentioned in section 2) by rotating the recording film (stepping motor) by 90° (=250*θf) for the recording of a master hologram (Fig. 2), and hence the direction of fringes that form in area A2 is parallel to the Y-Z plane. When the master is illuminated by the linearly polarized plane wave in the second step, as shown in Fig. 15, the diffraction efficiency of the diffracted light corresponding to area A2 is different from
that corresponding to A1. We divide these two conditions into TE and TM polarized reconstruction. The diffraction efficiency is expected to be higher under TE incidence. We note that the fringes in area closer to A1 (A2) are more (less) perpendicular to the Y-Z plane.
Second, since the direction of polarization of the light beam WCT or WOT (still linearly polarized light) is perpendicular to its own optical axis, as illustrated in Fig. 16(a), there will be an angle e (90*-θ 2) between the directions of polarization of the interfering beams. The diffraction efficiency, corresponding to area A1t of the transfer, will obviously be better [11], because its interference pattern is formed under two light beams which are polarized in the same direction, as shown in Fig. 16(b).
5. Experimental measurements and discussion
Fig. 17 shows the diffraction efficiency as a function of exposure for single exposure (η;Es) and multiple-exposure (η;Emm for M multiple exposures, and M=100) holograms, where the diffraction efficiency η is defined by
Pi (Po) is the power of the diffracted (incident) wave. The intensities of the two interfering beams are adjusted to be equal to yield the fringe visibility equal to 1 for highest diffraction efficiency of our hologram. This is somewhat different from nonimage-plane type display
holography for which equal intensity for two interfering beams is generally not an optimum condition [3]. The object beam we use in this section is just a converging spherical wave (without extended object image). Solid line curve represents an approximating polynomial that fits the data points. Comparing these two curves, we can see that the reduction factor (RF=38.47/0.003923) of diffraction efficiency for multiple-exposure holograms is about M2 [11] when the exposure is Emm=Es=629µJ/cm2 (peak value of the single exposure curve) which is not a surprising result at all. However, maximum diffraction efficiency for the disktype multiplex hologram occurs when the exposure is equal to Es/4 rather than at Es. This is an interesting point worthwhile for a closer look in the future. Similar behavior is seen in the diffraction efficiency curves (η;Etm) for the transfer holograms (Fig. 18).
Since we want to know the difference in the diffraction efficiency between the two orthogonal areas (A2t and A1t), it is necessary to get correct diffraction efficiency values. Also, in order to obtain high diffraction efficiency, the number of multiple exposures (M) must be decreased. We then make a master for which a circle is selected as the input pattern. The gray circles in Fig. 6 indicate 2D images recorded on the hologram; the diameter of each circle is 1.8 cm; the angle between every exposure is still 0.36 degrees (M≅50). After finishing fabricating H1 and when the master is under laser (linearly polarized) light reconstruction (Fig. 15), we measure the diffraction efficiencies of the diffracted light beams from A2 (TM incidence) and A1 (TE incidence). The ratio of the diffraction efficiencies of light beams from those two areas is 0.83.
Fig. 16 shows the use of a single-beam optical system to produce a duplicated hologram (WRM, WOT, and WCT), where the reference beam (WCT) will become a reconstruction reference beam (WRT) for the measurement process (WRT, WT2, and WT1). Similarly the diffraction efficiencies (PT2/PRT and PT1/PRT) are measured as shown in Fig. 18 (ηt;Etm), where the value (ηt) of a data point is determined by the following equation (as the condition that H2 is generally illuminated with an unpolarized light source):
where ηTM(ηTE) is the diffraction efficiency for TM (TE) incidence. Approximation curve is plotted as solid line. The maximum diffraction efficiency for H2 occurs at Etm=157.25µJ/cm2, which is about one fourth of proper exposure for a single-exposure hologram. Finally we can get the ratio of the diffraction efficiencies PT2/PT1 to be about 0.37.
One approach to alleviate the above problem is to make a double-exposure duplicate hologram. We can make the first exposure with the direction of the polarization of the light source being perpendicular to Y-Z plane (Fig. 10.), and make another exposure after changing the direction of the polarization of the light source to be perpendicular to the X-Z plane by applying a half-wave plate. Then the finished double-exposure hologram H2 is illuminated with the reconstruction reference beam (a normally incident plane wave) as shown in Fig. 16. We then measure the diffraction efficiencies of the diffracted beams from A2t and A1t. In this way, the ratio PT2/PT1 of the diffraction efficiencies of the two beams corresponding to the transfer areas A2t and A1t can be improved to 0.95, from our experimental value.
6. Conclusion
To summarize, a two-step process for image-plane disk-type multiplex holography for mass production is proposed. A plane wave is used both as the recording reference wave and the reconstruction reference wave for the master hologram H1. The plane reference wave going through the central hole of the master hologram may be attenuated by a neutral density filter to adjust the fringe contrast for the transfer hologram H2. Computer simulation is used to find the set of parameters for hologram fabrication, where both eyes of an observer can see the respective object points belonging to the same original object point. The effect of polarization on the difference in diffraction efficiency in different regions of the transfer hologram is discussed and experimentally demonstrated.
When the reconstruction process is done under linearly polarized light illumination, the beams diffracted from areas A2 and A1 will be discordant due to TE and TM diffractions. There will also be an obvious diffraction efficiency difference produced by the different interference conditions for areas A2t and A1t formed during the second-step holographic process. However, the double-exposure technique can improve the ratio between the diffraction efficiencies of the two beams corresponding to the two areas on transfer hologram to be about 0.95, which is quite uniform for unpolarized light illumination. These results should be helpful in the design of a single-beam holographic transferring system in the near future.
Acknowledgements
This work is financially supported by the National Science Council of the Republic of China under grant number NSC-94-2215-E-008-012.
References and links
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