Electro-holography can display images without inducing fatigue and three-dimensional (3D) sickness, i.e., visual discomfort due to viewing a stereoscopic display. Thus, this technology is expected to be applied to 3D media. However, there are no studies that have shown the agreement between the dynamic responses of accommodation and vergence to the reconstructed images of electro-holography and those to the real targets. This paper describes the measurement results of these responses using a developed system that can simultaneously measure the dynamic responses of accommodation and vergence. Moreover, statistical analysis for associating the accommodation and the vergence responses was achieved, and our study confirmed that these responses were in agreement.
© 2017 Optical Society of America
Three-dimensional (3D) technologies have become increasingly common . As one of the representative 3D technologies, stereograms have become popular for 3D movies, 3D games, etc.
The physiological factors of recognizing 3D shapes are accommodation, vergence, and binocular parallax . Binocular parallax is the difference between the retinal images of the right eye and left eye. Accommodation is the function of focusing on an object by adjusting the thickness of a crystalline lens to change the refractive power. Vergence is the function of the horizontal eye movement for looking at an object fixedly.
Several studies have shown that the visual fatigue and the 3D sickness experienced after watching stereo binocular images are caused by a conflict between the accommodation and the vergence [3–6]. Actually, stereo binocular displays apply binocular parallax only. The vergence stimulus matches the position of a stereo binocular image, while the accommodation stimulus matches the display . Therefore, the viewers must fight against the normal neural coupling between accommodation and vergence. That is the reason why the conflict causes discomfort.
Holography is said to be the ideal 3D technology because it reconstructs a wavefront from a real object. Reconstructing a wavefront induces the accommodation and the vergence stimuli the same as in the real world. Thus, one does not expect visual fatigue or 3D sickness in holography as compared to stereogram methods. Electro-holography also has the same characteristic theoretically. In electro-holography, electronic devices called a spatial light modulator (SLM) are used as reconstructing devices instead of silver halide plates [8, 9]. This technology is applicable to 3D media such as movies, animations, and games. However, there are few studies that have shown the agreement between the responses of accommodation and vergence to the reconstructed images of electro-holography and those of real targets [10,11].
Recently, Ohara et al. developed a simultaneous measuring system of the responses for accommodation and vergence to the reconstructed images of electro-holography . They conducted an experiment with statistically enough subjects. Consequently, the experiment demonstrated that these responses to the reconstructed images of electro-holography were equivalent to those to the real targets. However, the static responses were insufficient for verifying the usefulness for 3D media. Moreover, the experiment did not correlate the responses of accommodation and those of vergence.
In our study, we examined whether the dynamic responses of accommodation and vergence to the reconstructed images of electro-holography correspond to those of the real targets. To measure those responses, we conducted a verification experiment. In the experiment, the reconstructed images and the real targets went back and forward in the same depth range. Moreover, this study statistically analyzed the results by relating the vergence to the accommodation.
2. Electro-holographic methods
This section explains the electro-holographic display for the experiment. We used the Fourier transform optical system (FTOS) to reconstruct holographic images in order to ensure a sufficient visual field and the computer generated holograms (CGHs) techniques to calculate hologram data . Enlarging the visual field prevents the influence of the high-order diffraction light and induces the correct responses of the vergence.
In the experiment, the electro-holographic reconstructing device was an eyepiece type electro-holographic display for binocular vision, as shown in Fig. 1 . The FTOS is composed of a light emitting diode (LED) used as a point light source, a liquid crystal display (LCD) used as an SLM, and a lens. An LED is used for avoiding laser speckle because it is able to produce images that are clear enough to view, according to the study by Ito . In our study, a reflective LCD is used as an SLM. Let L1 be the lens arranged near the LCD; the role of L1 is transforming the spherical light from the LED into parallel light. When the LED is arranged at the focal distance of L1 (f1), a real image is reconstructed at the point f1 far from L1. Thus, the parallel light reflected and diffracted by the hologram pattern displayed on the LCD produces the real images at the point near the LED by passing through L1 again. Herewith, a barrier arranged in front of the viewpoint easily blocks off unnecessary light rays such as high-order diffraction light rays because those light rays converge at f1, namely the point of the LED. In addition, the virtual images can be enlarged by the lens other than L1 (L2) arranged between the viewpoint and the real images in order to make the reconstructed images less complex to view for the observers.
This device configures the FTOS to each eye in order to enable the observers to view the reconstructed images with binocular vision because the FTOS limits the viewing zone owing to the low resolution of the SLM. The optical path to the right eye is reflected by a prism to avoid physical interference between parts of the device. In addition, the optical system for the right eye can be moved in order to adjust to the inter-ocular distance also known as the pupillary distance (PD) of each observer. Table 1 shows the parameters of each part of this device. By using the FTOS, this device has visual fields with 15 degrees in horizontal and 8 degrees in vertical, which ensures achieving experiments for moving the reconstructed images.
CGHs simulate the interference fringes between light irradiated toward a recording medium (reference light) and light reflected from an object (object light). The fringe patterns are displayed at the LCD. Furthermore, CGHs have flexibility in terms of generating objects owing to computer simulation.
In this study, we used a point light method for object light calculations . This method simulates object light by superimposing the light propagation of each point light source when objects are regarded as assemblages of point light sources. This method produces full parallax images. Furthermore, the reconstructed image for each eye was obtained because of the use of the FTOS for each eye. In order to give the correct accommodation and vergence stimuli, these images were produced in accordance with the depth of the object by affine transformations of the object data.
3. Experimental devices
3.1. Device for real targets
The motion of real targets was realized by using one meter-long rail type electro-actuators that are controlled by a computer. The pattern of the targets was the same as the reconstructed images of electro-holography. The targets were formed by a combination of two sheets of white and black paper that were illuminated by the light source. The light source was the same type of LED that the electro-holographic reconstructing device had. The brightness of the real targets was equivalent to that of the reconstructed images of electro-holography. Figure 2 shows a photo of the actuators.
3.2. Accommodation and vergence measuring instrument
The measuring instrument was the PowerRef3 (Plusoptix Inc.). This instrument measures the accommodation and the vergence responses simultaneously by a photorefraction method using a camera and infrared LEDs. This instrument can detect both myopia and hyperopia . Figure 3 shows a photo of this measuring instrument. Table 2 shows the specifications of this instrument.
3.3. Experimental optical system
The optical system as shown in Fig. 4 is used in order to measure the responses to the real targets and the reconstructed images in the same conditions. The optical device in front of a viewpoint is changed in accordance with the measurement systems: a mirror for the real targets or a hot mirror for the reconstructed images. Figure 5 shows a photo of this system.
4.1. Experimental method
The experiment measured the dynamic responses of accommodation and vergence to the reconstructed images and those to the real targets. As shown in Fig. 6, a target motion was uniform along the depth direction. Targets moved from a 1.5 m (0.67 D) point to a 0.5 m (2 D) point and back. The time one-way was five seconds. Furthermore, each target stopped for 2.5 seconds at both the 0.67 D and 2 D points.
The pattern of real targets and the reconstructed images of electro-holography formed a Maltese cross . The apparent size of the targets was in accordance with the real world, and the images were controlled at the same brightness and the same color as the targets. The visual angles of the targets were 1.3 degrees at the 0.67 D position and 4.0 degrees at the 2 D position. Figure 7 shows the reconstructed images and the real targets.
The measurement was repeated four times. The measured value was a mean value of the last three times of measurement while the first time was a test. Eye blinking was not specifically prohibited. The periods of eye blinking were excluded from the measurement results. In order to remove the eye fatigue, we provided three minutes for rest per measurement. The experiment was conducted in a dark room in order to prevent other lights and stimuli from reaching the observers’ eyes.
The subjects were 22 persons from 18 to 27 years old who have at least 20/20 vision with or without contact lenses and have normal binocular vision. There were 13 persons wearing contact lenses and 9 persons wearing no corrective lens. The subjects had never accepted any training of viewing reconstructed images of electro-holography. They were not informed the purpose of this experiment.
4.2. Experimental results
The examples of experimental results are shown from Fig. 8 and Fig. 11. The vertical axis is a reciprocal of the distance from the viewpoint to the targets, and the horizontal axis is the measuring time. The accommodation responses were recorded from the left eye. The shift of absolute values between the measuring values and the ideal values is caused by a peculiarity of the measuring instrument. Therefore, in the experiment, the criterion of agreement between the responses is the coincidence of each locus of the measuring value. Figures 8 and 9 show the examples of good agreement between the responses to the reconstructed images and the real targets. Conversely, Figs. 10 and 11 show the examples of failures, i.e., the responses to the real targets agree with the ideal curve, but the responses to the reconstructed images are nearly constant. Seventeen out of 22 measurement results showed the same tendency of the agreement of the responses, and five did not.
In addition, we calculate the mean squared error (MSE) between the ideal values and the measuring values of the real targets or the reconstructed images in these results of the vergence and the accommodation to quantify and clearly compare these results. Further, we prepared in advance for the calculation of the MSE values. First, we calculated a remainder between the mean of the ideal values and the mean of the measuring values of the reconstructed images or the real targets. Next, the remainder was subtracted from the measuring values. The purpose of those processes was to fill in the disparity between the absolute value of a measuring value and that of an ideal value due to a peculiarity of the measuring device. Let n, I, M, ī, and m̄ be the number of samples, the vector of n ideal values, the vector of n measuring values, the mean of ideal values, and the mean of measuring values. Then, the MSE is estimated by the following formula.
Responses have a wide range from one person to the next, such as accommodation domination, vergence domination, monovision, etc. In spite of that, the vision of each person is expected to respond to the same stimuli in the same way. Therefore, we studied the differences of responses between the reconstructed images and the real targets. Figure 12 shows the quantities and directions of the difference between the two MSE values. One is the MSE value between the ideal values and the measuring values of the real targets, and the other is the MSE value between the ideal values and those of the reconstructed images of electro-holography. The vertical axis is the MSE value of the responses of vergence, and the horizontal axis is that of accommodation. The origin means that there is no difference between the two MSE values. The barycenter of this scatter plot is located in the vicinity of the origin. These values are random and featureless. Therefore, it can be considered that the distribution of the difference between the two MSE values follow the normal distribution.
We evaluated the agreement between the responses to the reconstructed images of electro-holography and the responses to the real targets by t-test.
The t-test is a statistical method evaluating whether or not there are significant differences by comparing each mean value of two samples. When the significance level is 5%, the alternative hypothesis is accepted on the condition that the p-value is below the significance level (0.05). Conversely, the null hypothesis is accepted on the condition that the p-value is above 0.1. In the study, the paired t-test was used for the analysis of the agreement between the responses to the reconstructed images and those to the real targets owing to the fact that the same subjects measured the accommodation and the vergence responses to the reconstructed images and the real targets. The null hypothesis defined that there is no difference between the MSE values of the accommodation or the vergence responses to the reconstructed images and those to the real targets, and the alternative hypothesis defined that there are differences.
The result of the t-test to the accommodation responses was p = 0.13(> 0.05), and the result of the t-test to the vergence responses was p = 0.25(> 0.05). Moreover, both results were above 0.1. Hence, the null hypothesis cannot be rejected because there is no significant difference for each result.
In addition, Fig. 13 shows 95% confidence ellipses of the two MSE values in order to assess the agreement by associating the accommodation and the vergence responses. The vertical axis and the horizontal axis are the same as those of Fig. 12. The blue line and points mean the MSE values between the ideal values and the measuring values of the real targets. The orange line and points mean the MSE values between the ideal values and the measuring values of the reconstructed images. 95% of the whole values were distributed in 95% confidence ellipses. The shifts of the positive direction for all points were caused by accommodative lag . Accommodative lag means that the responses of the accommodations shift from the actual position. Further, the scattering of the MSE values might be caused by a difference of the visual function of each subject owing to the fact that the results of the t-test were following the normal distribution.
The two confidence ellipses were highly coincident. Moreover, the barycenter coordinates of the confidence ellipses were Accommodation = 0.13, Vergence = 0.10 to the reconstructed images and Accommodation = 0.11, Vergence = 0.10 to the real targets. Thus, each barycenter is located in each confidence ellipse. The origin, which means no difference between the ideal values and the measuring values, is also located in the two confidence ellipses.
The responses of accommodation and vergence to the reconstructed images and the real targets were proved to follow the normal distribution by the scatter plot of the MSE values and the t-test. Moreover, there was no significant difference between the responses of the reconstructed images and those to the real targets according to the results of the t-test and the analysis of 95% confidence ellipses of those MSE values. Consequently, the experiment confirmed that the dynamic responses of accommodation and vergence to the reconstructed images of electro-holography agreed with those to the real targets.
In the proposed study, we measured the dynamic responses of accommodation and vergence to the reconstructed images and those to the real targets and performed statistical analysis on the results. It indicated that the dynamic visual responses to the reconstructed images agreed with those to the real targets. In the future, it is needed to analyze gain, phase and lag of the measurement data in order to obtain various characteristics further. Moreover, the reconstructed images were blurred because the reconstructing device used the LED with the spread of the light source and the wavelength. The experiment did not verify whether the blurring of the images has any influence on accommodation responses. That is also needed to be verified in future research. In addition, comparing these responses to the responses to stereo binocular images is required to clearly verify the superiority of electro-holography.
Japan Society for the Promotion of Science (JSPS) KAKENHI (16H02852).
We would like to thank the Yoshida Gakuen Medical & Dental College Department of Orthoptics for cooperating in our experiments. This work was supported by JSPS KAKENHI Grant Number 16H02852.
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