Eye accommodation is considered to function properly for three-dimensional (3D) images generated by holography. We developed a horizontally scanning holographic display technique that enlarges both the screen size and viewing zone angle. A 3D image generated by this technique can be easily seen by both eyes. In this study, we measured the accommodation responses to a 3D image generated by the horizontally scanning holographic display technique that has a horizontal viewing zone angle of 14.6° and screen size of 4.3 in. We found that the accommodation responses to a 3D image displayed within 400 mm from the display screen were similar to those of a real object.
©2012 Optical Society of America
Holography [1, 2] is a three-dimensional (3D) display technique that reconstructs wavefront emitted from objects. A holographic display can therefore generate 3D images on which eyes can focus as accurately as they do on real objects. Therefore, a holographic 3D display is expected to provide 3D images that do not result in visual fatigue caused by the accommodation-vergence conflict [3, 4]. The accommodation-vergence conflict is one of the major problems of conventional 3D displays that reconstruct rays emitted from objects, such as two-view displays, multi-view displays, and integral imaging displays. This study reports the results of accommodation measurements of holographic images generated by the recently developed horizontally scanning holographic display [5–7].
As shown in Fig. 1(a) , the wavefront reconstruction technique generates spherical waves that converge at object points in space that constitute 3D objects. When eyes focus on these points, a sharp retinal image is obtained. On the contrary, the ray reconstruction technique redirects rays to intersect with one another at points in space in order to reconstruct a 3D image, as shown in Fig. 1(b). Each ray has the smallest beam width (i.e., the beam waist), usually on the display screen. The beam width increases as the ray departs from the beam waist position. Because rays are mutually incoherent, the beam width does not decrease when multiple rays are superimposed. Therefore, when eyes focus on a 3D image displayed at points other than the beam waist position, a blurred retinal image is obtained. It is also possible to set the beam waist position outside the display screen. In this case, a sharp retinal image is obtained only when eyes focus on the beam waist position. Eyes tend to focus on the display screen or the beam waist position, because a sharp retinal image is obtained. Consequently, the accommodation function does not work properly for conventional 3D displays that are based on the ray reconstruction technique. An exception is the super multi-view display technique [8–10] that increases the ray density to allow two or more rays passing through the same point in the 3D space to simultaneously enter the pupil of eyes so that eyes can focus on that point. The accommodation responses to the integral imaging 3D displays were reported in Refs . and .
In spite of the ability to generate 3D images without causing visual fatigue, an electronic holographic display has some difficulties that prevent its practical use. The viewing zone angle and 3D image size are limited by the performance of the spatial light modulators (SLMs). For Fresnel holography, the pixel pitch p of the SLM determines the viewing zone angle ϕ, given by ϕ = 2 sin−1(λ/2p), where λ is the wavelength of light. The 3D image size is identical to the screen size of the SLM. For Fourier transform holography, the screen size w of the SLM determines the viewing zone angle as ϕ = 2 tan−1(w/2f), where f is the focal length of the Fourier transform lens. The pixel pitch of the SLM determines the 3D image width W, i.e., W = λf/p. For both types of holography, the 3D image size is usually limited to less than one or two inches and the viewing zone angle is limited to several degrees, because the pixel pitch of the SLM is not much smaller than 10 μm (typically 5–10 μm) and the screen size of the SLM is less than one or two inches. Therefore, the observation of electronically generated holographic images with both eyes has been practically impossible. To the authors’ knowledge, accommodation measurements for electrically generated holographic images have not yet been reported.
We developed a Fresnel type electronic holographic display using the time-multiplexing technique [5–7], which increases both the horizontal viewing zone angle and 3D image size. With this technique, a series of elementary holograms were scanned horizontally on the display screen by a galvano mirror to increase the image width. These holograms were generated by a high-speed SLM and projected by an anamorphic imaging system to reduce the horizontal pixel pitch and increase the image height. A holographic display with a horizontal viewing zone angle of 14.6° and a 3D image size of 4.3 in. was demonstrated .
Prior to the horizontally scanning holography technique, several techniques were proposed to increase the viewing zone angle and 3D image size of holographic displays. In the holographic display system proposed by MIT [13, 14], a high-resolution one-dimensional hologram distribution generated by an acousto-optic modulator is scanned two dimensionally by a mechanical scanner. An active tiling technique [15, 16] was also proposed to increase the viewing zone angle and 3D image size, which demagnified images that were generated by a high-speed SLM and tiled them onto an optically addressed SLM in a time sequential manner. A technique using a photorefractive polymer as a rewritable hologram recording material was also developed [17, 18]. The use of multiple SLMs was proposed by several research groups [19–21]. A combination of an eye tracking system and a viewing zone steering system was developed to realize a large hologram size with viewing zone enlarged by the eye tracking technique [22, 23]. Our research group also developed a resolution redistribution technique [24, 25] that increases the horizontal resolution of the SLM by several times by sacrificing the vertical resolution.
In this study, we measured the accommodation responses to a 3D image generated by the horizontally scanning holographic display that provides a large 3D image with a large viewing zone angle so that it can be easily viewed with both eyes. We also measured the accommodation responses to a real object and compared both these responses.
2. Image blur in horizontally scanning holography
Because horizontally scanning holography generates a series of elemental holograms, its reconstructed image is different from that generated by the conventional holographic displays. The accommodation responses are closely related to the blurs of a retinal image. Thus, the blur of a retinal image generated by horizontally scanning holography is derived after briefly explaining the operating principle of the horizontally scanning holographic display.
2.1 Display system’s principle
A schematic diagram of the horizontally scanning holographic display system is shown in Fig. 2 . An image generated by a high-speed SLM is compressed in the horizontal direction and enlarged in the vertical direction by an anamorphic imaging system which consists of two orthogonally aligned cylindrical lenses, and has different magnifications in the horizontal and vertical directions. The generated vertically stretched image, which is an elementary hologram, is scanned horizontally by a mechanical scanner. The high-speed SLM displays a series of elementary images in synchronization with the horizontal scanning. The pixel pitch of the SLM is reduced in the horizontal direction so that the horizontal viewing zone angle increases. The vertically enlarged image is scanned horizontally so that the hologram screen size increases. Since the vertical pixel pitch increases, this system displays a horizontal-parallax-only (HPO) hologram. A screen lens redirects light to observers, and a vertical diffuser increases the vertical viewing zone.
The resolution of the high-speed SLM is denoted by Nx × Ny and the pixel pitch is denoted by p0. The horizontal and vertical magnifications of the anamorphic imaging system are denoted by Mx and My, respectively. The number of elementary holograms displayed by a single scan is denoted by N and the horizontal pitch of the displayed elementary holograms is denoted by q. The width and height of the elementary holograms are given by MxNxp0 and MyNyp0, respectively. The horizontal viewing zone angle of the reconstructed images is given by 2sin−1(λ/2Mxp0). The width and height of the hologram screen are given by (N − 1)q + MxNxp0 and MyNyp0, respectively. The width of the elementary holograms must be equal to or larger than the horizontal pitch of the elementary holograms. In the experimental systems developed in previous studies [5–7], the width was about five times larger than the pitch. The overlapping of the elementary holograms is used to improve the grayscale reproduction of reconstructed images .
2.2 Blur on retina
Because the horizontally scanning holography technique represents a 3D object as an aggregate of many object points (as shown in Fig. 1(a)), the blur of a reconstructed image is given by the width of a converging beam at an object point. The beam width depends on the width of the elementary holograms and the method used to scan the holograms. In this study, we consider blurs in the horizontal direction because the horizontally scanning holography employed is the HPO holography.
The width of the spherical waves on elementary holograms, which generate an object point, is considered. The distance between an object point and the screen is denoted by zo. As described in Ref. , the cylindrical lens 2 and the screen lens (in Fig. 2) provide a spherical phase distribution on the screen, whose radius of curvature is denoted by t. Thus, the phase distribution of a spherical wave that generates the object point is given by ϕ = k(x2/2zo + x2/2t), where k is the wave number and x is the horizontal coordinate. The width of the elementary hologram is denoted by u, where u = MxNxp0, and the pixel pitch in the elementary hologram is denoted by px, where px = Mxp0. From the sampling theorem |dϕ/dx|px ≤ π, the maximum diameter of the spherical wave is given by λ/(1/zo + 1/t)px. In the experiments described in Sec. 3, this maximum diameter was larger than the elementary hologram’s width. The width of the spherical wave is therefore considered to be equal to the elementary hologram’s width.
The blur on the retina is given by the addition of an out-of-focus blur, diffraction blur, and scanning blur. The behavior of the first two blurs depends on whether the pupil diameter is larger or smaller than the beam diameter just in front of the pupil. As shown in Fig. 3(a) , when the beam diameter is larger than the pupil diameter, the beam diameter is decreased to the pupil diameter. As shown in Fig. 3(b), when the beam diameter is smaller than the pupil diameter, the beam diameter does not change. For simplicity, we do not consider the condition in which the beam exits at the circumference of the pupil. If the distance between the screen and the eye is denoted by l and the pupil diameter is denoted by d, the beam width just in front of the pupil is given by u(l − zo)/zo. The critical distance zc that discriminates the above two cases is given by zc = l/(1 + d/u).
The out-of-focus blur is then calculated. The distance between the screen and the plane at which an eye focuses is denoted by z. When the beam diameter is larger than the pupil diameter (zo ≤ zc) (see Fig. 3(a)), the out-of-focus blur on the retina is obtained by imaging the bold line on the eye-focusing plane onto the retina. Then, the out-of-focus blur on the eye-focusing plane is given by |z − zo| d/(l − zo). When the beam diameter is smaller than the pupil diameter (zo ≥ zc), (see Fig. 3(b)), the bold line shifts as the elementary hologram moves on the screen. The total length of the range at which the bold line exists on the eye-focusing plane is given by |z − zo| d/(l − zo). For both cases, the out-of-focus blur is given by the same formula. When the image distance of the eye imaging system is denoted by le, the magnification is given as le/(l − z). Therefore, the out-of-focus blur on the retina is given by
Next, the diffraction blur is calculated. If the beam width after passing through the pupil is denoted by d’, the diffraction blur on the retina is given by 1.22λle/d’. In the case when the beam diameter is larger than the pupil diameter (Fig. 3(a)), d’ = d and the diffraction blur is constant. In the case when the beam diameter is smaller than the pupil diameter (Fig. 3(b)), d’ = (l/zo − 1)u. The diffraction blur increases when the depth of the object point increases, and is given by
Scanning the elementary holograms causes the scanning blur. The elementary hologram pattern does not change while the elementary hologram moves on the scan plane. This scanning blur can be reduced by decreasing the time for which the laser illuminates the SLM . The laser should be modulated to avoid illumination of the SLM while the state of the SLM changes. If the ratio of the illumination time to the image updating time is denoted by m:1, the scanning blur on the retina is given by
Finally, the summation of the above three blurs gives the total blur on the retina by the scanning holography:
The derivative of Eq. (4) with respect to distance z provides the following equations:
When z ≥ zo, the relation dδscan/dz > 0 is always true. When z ≤ zo, the relation dδscan/dz < 0 holds if the condition d > mq is satisfied. Therefore, the blur becomes minimum when the eye focuses at the depth position of the object point (z = zo) if d > mq is satisfied.
3. Measurements of accommodation responses
The accommodation responses to the horizontally scanning holographic display were measured.
3.1 Experimental system
The horizontally scanning holographic display system used for accommodation measurements is the same as that described in Ref. .
A digital micromirror device (DMD) (DiscoveryTM 3000, Texas Instruments) was used as the high-speed SLM, with a resolution of 1,024 × 768 and pixel pitch of 13.68 μm. A laser diode with a wavelength of 635 nm was used as the light source. The horizontal and vertical magnifications of the anamorphic imaging system were 0.183 and 5.00, respectively. The size of the elementary hologram was 2.56 × 52.5 mm2. The horizontal pixel pitch was reduced to 2.50 μm so as to increase the horizontal viewing angle to 14.6°. The frame rate of the DMD was 13.333 kHz and the horizontal scan rate was 60 scans/s. The horizontal pitch of the elementary holograms was q = 0.51 mm. Although the DMD can display 222 images during each scan period, 186 elementary holograms were displayed for each of the forward and backward scans, while avoiding the nonlinear scan regions. The hologram size was 96.9 × 52.5 mm2 (4.3 in.).
To avoid light illumination during the mirror transition state of the DMD and to reduce scanning errors, the DMD was illuminated by a pulse-modulated laser light. The frame time of the image update of the DMD was 75.0 μs and the pulse width was 37.5 μs. Thus, the modulation of the illumination laser was m = 0.50.
A photograph of the experimental system is shown in Fig. 4 .
The measurement method for the accommodation responses to a holographic image and a real object is explained.
There were five subjects, including four males and one female, and their ages ranged from 22 to 24 years. All subjects had normal or corrected-to-normal visual acuity. All measurements were done in a dark room.
The horizontally scanning holographic display system generated a test image between the display screen and the subjects used in the experiment. The subjects observed the test image with both eyes. The accommodation responses of the subjects’ dominant eye were measured. The responses to the test image were measured by displaying the test image at different depth positions. Similarly, the accommodation responses to a real object were measured by placing the object at different depth positions. During the accommodation measurements, the binocular vision was used as mentioned above, because it is known that there is a close relationship between the accommodation and vergence . The conflict between the accommodation and vergence is considered to be responsible for the visual fatigue experienced while observing the conventional 3D displays.
An auto refractometer was used to measure the accommodation responses. We used an FR-5000S optometer (Grand Seiko Co., Ltd.), which has a window through which the subjects can see the test image and real object. The measured result is found using the Diopter unit [D], which is the reciprocal of the length expressed in meters. The equipment provides the measured results with a time interval of 0.2 s and an accuracy of 0.01 D. A video image of the eye during the measurement was fed through a video output, and the pupil diameter was measured using this video output.
The observation distance between the screen and subjects’ eyes was 1,100 mm. This distance was chosen because a certain minimum distance is required in front of the eyes to place the auto refractometer, and the accommodation is known to work for objects that are placed approximately within 2 m from eyes.
Figure 5 shows the test image used for the measurements. The size of the test image is constant for a visual angle of 1.1° × 1.1°. This test image was printed on a paper for using it as the real target. The test image should have contained both horizontal and vertical lines. However, we did not include the horizontal line because this line becomes darker than the vertical line owing to the nature of the display system. The horizontal line can be made to be as bright as the vertical line using the grayscale improving technique , although the entire reconstruction image becomes darker using this technique. Therefore, two diagonal lines were added to the test image instead of the horizontal line. The removal of the vertical line may affect the accommodation responses because the display system provides only horizontal parallax; the vertical line may trigger only the horizontal depth cue. The addition of the diagonal lines may trigger both vertical and horizontal depth cues.
The accommodation responses were measured three times for each distance. The measurements were performed for 10 s, and the responses for 2 s without blink were averaged to obtain an experimental result.
We first measured the accommodation responses to the test images displayed within 300 mm from the screen because the horizontally scanning display system has the scanning error, which was corrected using alignment patterns displayed at several depths up to 100 mm from the screen, as described in Ref. . We found that proper accommodation responses were obtained over this depth range. Therefore, we extended the measurement depth range to 550 mm in order to find the depth at which proper accommodation still cannot be obtained. The test images were displayed from 50 mm to 550 mm in increments of 50 mm from the screen toward the subjects.
The measured accommodation responses to the test image are shown in Fig. 6 . The horizontal axis shows the positions of the test images and the vertical axis shows the measured accommodation responses; both are represented in the diopter unit. The circles show the average accommodation responses for 2 s, and the error bars show the standard deviation. Three circles are shown at each displayed position corresponding to the three measurements. The diamonds show the measured pupil diameters. Figure 7 shows the measured accommodation responses to the real objects.
From the results shown in Fig. 6, the accommodation changed when the depth position of the test image changed. The circles locate on the diagonal dashed line if the eye correctly focused at the depth of the test image. Three subjects Y.U., M.Y., and M.M. tended to focus at further positions, and the other two subjects Y.S. and Y.T. tended to focus at nearer positions. From Fig. 7, same tendencies are observed for the results of the real objects.
The characteristic of the accommodation response differs for different subjects. However, from Figs. 6 and 7, for each subject, the accommodation responses to the test images are similar to those to the real objects. Therefore, the accommodation responses to the test images are compared with those to the real objects by drawing them in one graph, as shown in Fig. 8 . The horizontal axis shows the accommodation responses to the real objects and the vertical axis shows those to the test images. The symbols show the average of the three measurements. For three subjects Y.U., Y.T., and M.M, the accommodation responses to the test images are almost identical to those to the real objects, except at depths of 500 mm and 550 mm. For the other two subjects Y. S. and M. Y., the responses are again almost identical, except for depths of 450 mm, 500 mm, and 550 mm. Therefore, the holographic images produced by the horizontally scanning holography resulted in accommodation responses that were similar to those caused by real objects when they were produced within 400 mm of the screen.
Experimental results showed that the accommodation responses to the holographic images generated by the horizontally scanning holographic display system were similar to the responses to the real objects. The measured pupil diameters shown in Fig. 6 were much larger than mq = 0.26 mm. Therefore, from Eq. (5), the blur δscan may become minimum (dδscan/dz = 0) when the eye focused at a position at which the test image was generated (z = zo). The blur of the reconstructed images may also become minimum at the position at which the blur of the real objects became minimum.
The blur on the retina was investigated using an image sensor. A cooled CCD camera (U2000, Apogee Instruments, Inc.) was placed at the eye positions of the subjects, i.e., at a distance of 1,100 mm from the display screen with a horizontal shift of ±32.5 mm. The resolution of the camera was 1,600 × 1,200 and the pixel pitch was 7.4 μm. The focal length of the lens was 25 mm. The aperture diameter of the lens was set to 7 mm, which was the average of the measured pupil diameters shown in Fig. 6. The focus of the camera was changed to evaluate the blur. Figure 9 shows the captured images when the test images were displayed at distances of 50 mm, 100 mm, and 150 mm. The line width became minimum when the focus was close to the depth position of the test image, and the line width increased as the focus departed from the depth position. When the depth of the test image was 50 mm, the change of the line width was not obvious because the line width was comparable to the pixel pitch of the CCD. Figure 10 shows the captured images when the test images were displayed at distances of 200 mm, 300 mm, and 400 mm. Even when the focus of the camera was at the depth of the test images, the blur remained obvious. The critical distance zc derived in Sec. 2.2 was 295 mm for the experimental system. From Eq. (2), the diffraction blur may increase when the test image was displayed further from the screen when zo ≥ zc. The blur was also caused by the scanning error, because the scanning error was corrected for the depth range within 100 mm from the screen, as described in Sec. 3.3. Figure 11 shows the blurs when the test images were displayed at distances of 500 mm and 550 mm from the screen. The blur was large and did not become minimum when the focus of the camera was at the depth of the test images. This unexpected blur behavior may be caused by the scanning error. The incorrect accommodation responses to the test images displayed at these depths can be explained by this unusual blur behavior, which was smaller when the camera focused at depth positions that were nearer to the screen than when it focused at the depth positions of the test image. The subjects reported that obvious blur was observed for the test images displayed at these depths.
For most subjects, when the holographic image was displayed at a depth of not more than 400 mm, the accommodation responses to the holographic images were similar to those to the real object. This depth range exceeded our expectations prior to performing the experiments. The scanning error was corrected using alignment images that were displayed at depths of 50 mm, 70 mm, and 100 mm, as described in Ref. . The depth range can be increased by correcting the scanning system using the alignment images displayed at greater depth positions, but in this case, the blur at smaller depth positions might increase.
We compared the theoretical blur derived in Sec. 2.2 with the experimentally obtained blur. There was good agreement when the test image was displayed near the screen. For the experimental results shown in Fig. 9, the theoretically predicted blur widths are 8.8 μm, 9.1 μm, and 9.5 μm when the test images are displayed at depths of 50, 100, and 150 mm, respectively, and the focus of the camera is on these depths. The smallest half-widths of the corresponding lines in the reconstructed images shown in Fig. 9 were approximately one, two, and two CCD pixels (the pixel pitch was 7.4 μm). The line widths became larger when the focus of the camera shifted further from the depth positions of the test images. However, the experimentally obtained blur became larger than the theoretical blur when the test image was displayed far from the screen. This was because the scanning error increased when the test image was displayed further from the screen. In Sec. 2.2, we did not consider the case when the beam exits at the circumference of the pupil for simplicity. A more detailed analysis is required to develop a more precise theory to explain the blur.
From Figs. 10 and 11, when the test image was displayed far from the screen, the line width in the vertical direction was observed to be larger than that in the horizontal direction. This means that the vertical blur was larger than the horizontal blur because the horizontally scanning holography employed is the HPO holography. It is important to better understand the effect of the vertical blur because both the horizontal and vertical blurs may influence the accommodation responses.
We measured the accommodation responses to a holographic image generated by horizontally scanning holography. For comparison purposes, the responses to a real object were also measured. Experimental results showed that the accommodation responses to the holographic image were in good agreement with those to the real object when the holographic image was displayed at a depth position of not more than 400 mm. We also investigated retinal images using an image sensor. We found that the blur became minimum when the focus of the camera was set near the depth position of the holographic image.
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