Various Factors that Interfere with the Accurate Assessment of the Three-rods Test and Modied Three-rods Test to Resolve Monocular Cues

Binocular stereopsis is a higher-order visual function and is thought to play an important role in spatial cognition in everyday life and many occupational settings. Various stereotests are used clinically to evaluate binocular stereopsis, and the three-rods test is used to assess stereopsis in various occupations in Japan. It is known that there are factors such as monocular cues in various stereotests that make it dicult to accurately evaluate the stereoscopic function, but the existence of such factors in the three-rods test has not been claried. Here, we show that practice effect and monocular cues exist in the conventional three-rods test and that we devised a modied three-rods test to address the monocular cues. In the conventional three-rods test, performance improved when multiple tests were performed in a short time under binocular condition, and performance was signicantly better in the monocular condition compared to the blind condition, indicating the existence of practice effect and monocular cues, respectively. The modied three-rod test with a wider central rod excluded the effect of monocular cues and maintained binocular cues on test performance. Their results suggest that the three-rod test with the simple modication can be a useful method for testing stereoscopic functions.


Introduction
Stereopsis is a binocular cue to perceive the depth information of the surroundings that results from the processing of disparity in the images formed on the retina of each eye. Although stereopsis is not indispensable for depth perception, it plays a critical role in tasks involving distance estimation 1 or oculomotor coordination 2 . Several previous studies have also shown that good stereopsis may be important for daily activities such as athletics 3 , walking 4 , and car driving [5][6][7] . Therefore, accurate assessment of the degree of stereoscopic function is important from both a social and clinical perspective.
Various methods of stereo vision testing have been developed and used, but they are known to have problems such as inconsistent results and di culty in reproducibility due to a variety of factors that affect the results. It is often unclear to what extent the test results accurately re ect the stereoacuity 8,9 . Perception of depth is generally considered to be achieved by a combination of monocular and binocular cues. Stereopsis is a binocular cue, which allows us to obtain relative depth information rather than absolute distance. Furthermore, the disparity cue of two objects separated by the same distance depends on the viewing distance. Unless there is a problem such as strabismus, stereopsis develops in early childhood and is relatively free from misperception 10,11 . On the other hand, the monocular cue is characterized by skills learned based on life experiences, which provide only indirect information about the depth and are known to be susceptible to environmental and intrinsic factors 12,13 . Thus, an ideal stereoacuity test would be devoid of any monocular cues or other factors that have inappropriate effects, otherwise, these factors may give rise to the invalid results in stereotest 14,15 .
As a feasible testing method for measuring stereoacuity, the three-rods test is adopted and conducted by several Japanese governmental institutions for occupational quali cation. For example, the Japan Self Defense Forces (JSDF) and the Ministry of Land, Infrastructure, Transport, and Tourism (MLIT) enforces aircrews such as pilots to pass a depth perception standard tested by three-rods test for active duty on aircraft. The Road Tra c Act in Japan also demands drivers of large vehicles or commercial cars to pass the three-rods test. The criteria to pass the three-rods test in these institutions is common and set at the mean erred distance of 20mm or less, however, there is no standardization as regards the number of measurements. For quali cation of driver's licenses and the JSDF aircrews, three measurements are taken, and the mean of erred distance is assessed. On the other hand, for civilian pilots, the number of measurements is ve.
Previous research has shown that the statistically signi cant positive correlation of results between threerods test and stereotests used in daily ophthalmic practice (distance Randot Stereotest and Titmus Stereotest) 16 . The authors also reported that the results of the three-rods test done on separate days were positively correlated 17 . These studies collectively support the validity of the use of the three-rods test as a means of evaluating binocular stereoacuity. However, the result of stereoacuity measured by the threerods test can be affected by several factors including test distance, binocularity, masking, and direction of movement 18 . Moreover, factors such as practice effects associated with repeated measurements or monocular cues may make results in the three-rods test as if there is good binocular stereopsis.
To test this, we used an actual testing protocol employed in driver's license in Japan and testing for aircrews in JSDF -test distance of 2.5 m with the number of measurements of three-as a set of experiments. To examine a practice effect on the three-rods test, we performed the three-rods test under binocular condition multiple times over a short period of time. To examine whether monocular cues affect the outcome of the three-rods test, the three-rods test was conducted under monocular, blind, and binocular conditions with the normal or wider central moving rod. The results to be presented indicate that the repeated testing affected the outcome of the three-rods test and the monocular cue was present in the three-rods test, and this cue can be partly explained by the relative width of rods.

Ethics Statement
This study was conducted in accordance with the Declaration of Helsinki at Aeromedical Laboratory, Japan Air Self Defense Force (JASDF). All experimental procedures were approved by the institutional Ethical Committee of Aeromedical Laboratory, JASDF. All subjects were briefed on the scope and procedures of the experiment, and their written informed consent was obtained before participation.

Subjects
A total of 68 subjects (16 female, 52 male, age range 22-56 years, average:37.1) were recruited from within the JASDF and participated in the study. The exclusion criteria were a best-corrected visual acuity (BCVA) of less than 1.0 in both eyes and a history of neurological and mental illnesses. No subjects were excluded on this basis. Because not all participants were naive to this test (10 of 68 had prior three-rods test experience), we did not make it a condition of participation whether or not the subject had been tested by the three-rods test in the past. However, we did require that at least six months had passed since the last test.

Visual examinations
Subjects underwent a variety of ophthalmologic examinations, including BCVA and three types of clinical stereotests. BCVA was measured with the Landolt Chart. The subject's dominant eye was determined by using Rosenbach test 18 . The interpupillary distance (IPD) of each subject was measured by auto refractometer, NIDEK AR-330A (NIDEK Co, Tokyo, Japan).
Near stereoacuity was assessed using Randot stereotest (Stereo Optical Co, Chicago, US), Titmus Stereotest (Stereo Optical Co, Chicago, US), and New Stereo Test (Handaya, Tokyo, Japan) at the standard viewing distance of 40cm with appropriate spectacle correction.

Three-rods test
The three-rods test was conducted using an electric depth perception testing device, Kowa AS-7JS1 (Kowa Co, Tokyo, Japan). This device has a wide rectangular viewing window of 4.4 cm * 10.4 cm at the front surface. Inside the device, three black-colored rods are displayed. Each rod was 3 mm in diameter with a separation of 30 mm laterally. The rods were seen through the viewing window against an evenly illuminated white background (Fig. 1a). The center rod moves back and forth between the two xed rods at the speed of 50 mm/second. The moving range of the center rod was set at 110 mm and 100 mm for forward and backward directions respectively.
During measurements, subjects sat on a chair at the distance of 2.5m apart from xed rods and put their head on the headrest with a chin cup to avoid motion and parallax being used as a depth cue. The height of the headrest was adjusted so that the height of the eyes matches the height of the viewing window.
Three rods inside the apparatus were presented to the subjects only during measurements. Between measurements, the viewing window of the apparatus was manually covered by a cardboard panel. The direction of movement and the position of the center rod at the start of each measurement was not xed and were chosen randomly.
The subject is asked to press the switch when he/she feels that the three rods are lined up in a row. The erred distance between the planes of the xed rods and movable center rod was recorded as a plus or minus value (in mm) when the center rod was in backward or forward positions relative to the xed rods, respectively. Three measurements are taken as one set of measurements, and the mean of absolute values of measured erred distances was used for analysis.
Four sets of measurements were taken under binocular condition, followed by two sets of measurements under monocular condition, and then one set of measurements under blind condition. Measurement in the monocular condition is done rst by the subject's dominant eye, followed by the non-dominant eye. In the non-blind conditions, the measurement starts when the cardboard panel covering the viewing window is manually removed by the experimenter. On the other hand, in the blind condition, the subject was only verbally informed of the signal to start the measurement, and the subject keeps both eyes closed during the measurement.
The width of the central movable bar in the original test was 3 mm in diameter, but the test was also conducted under conditions where this was thickened to 5 mm in diameter (Fig. 1b). To increase the width of the center movable rod, a hollow cylindrical silicon tube with an inner diameter of 3 mm and an outer diameter of 5 mm was placed over this rod, and the surface of this silicon tube was painted to have a similar color and texture as the xed two peripheral rods. Under this condition, two binocular measurements were performed, followed by two monocular measurements.
Four consecutive sets of binocular measurements were taken in all 68 subjects. Of these, 50 continued testing in the monocular and blind conditions. After at least 7 days, 24 of these 50 subjects were tested in conditions with a modi ed bar width.

Statistical analysis
All data processing and statistical analysis were performed using Python (v3.7). Statistical tests are as described in text and gure legends.

Practice effects on the error distance in three-rods test
To investigate whether there is a practice effect in the three-rods test, we rst performed 4 sets of consecutive measurements under binocular condition. We found a signi cant decrease in error distance in the third set compared to the rst set (Fig2a. Nemenyi post-hoc test following Friedman test; p = 0.006). Since the legal acceptance criterion for the three-rod test in Japan is set at less than or equal to 20 mm, we further divided the data set into two groups: those whose average error distance in the rst set was less than or equal to 20 mm (pass group) and those whose average error distance was greater than 20 mm (fail group). In the fail group, as in the overall group, there was a signi cant decrease in error distance between the rst set and the third set (Fig2b. Nemenyi post-hoc test following Friedman test; p = 0.005). However, in the pass group, there was no signi cant change in the score due to the repetition of measurement (Fig2c. Friedman test; p = 0.241). The fail group consisted of 14 subjects, of which 9, 10, and 10 reached scores within the acceptance criteria on the second, third, and fourth measurements, respectively. Taken together, these results indicate that scores of subjects who failed in the rst set of measurements improved with repetition, indicating the practice effect in the three-rods test.
Effects of monocular cues on the depth perception in threerods test We next examined the ability to perceive depth using only monocular cues in the three-rods test. We measured erred distances under the monocular condition and compared them with the erred distances under the binocular and the blind conditions (Fig. 3). Of the 68 subjects who performed continuous measurements under the binocular condition, 50 subjects continued to perform measurements under the monocular condition. In the monocular condition, one set of measurements was performed rst by the dominant eye and then by the non-dominant eye. We found that the erred distances under the monocular condition were signi cantly longer than those in the binocular condition, indicating the existence of binocular cue in the three-rods test ( To test the ability to perceive depth by monocular cues, we performed one set of measurements under the blind condition following the measurement by the monocular eye. We found that both binocular and monocular conditions performed signi cantly better than blind condition (Fig3a. Nemenyi post-hoc test following Friedman test; p < 0.001 in each of the blind and other conditions). In blind condition, only 8 out of 50 subjects reached the passing criterion, whereas 19 and 23 subjects reached the passing criterion by the dominant and non-dominant eyes, respectively. These results indicate that there is an approximate 40% chance of passing the test with the monocular eye alone.
Of these 50 subjects, there were two subjects with suppression in one eye due to anisometropia or exotropia and had no binocular stereopsis. These two subjects were able to reach the passing criteria in three out of four measurements and two out of four measurements under the binocular condition respectively. In the monocular condition, they all reached the passing criteria in all measurements of the three-rods test. In addition, there was one subject whose binocular stereopsis was poorer than 60 arcsec in other clinical stereotests (Titmus Stereo Test, Randot Stereo Test, and New Stereo Test). The subject exceeded the passing criteria in all measurements under both binocular and monocular conditions. (Fig3b,3c) Our results indicate that the three-rods test has a statistically signi cantly higher probability of reaching the passing criteria even under monocular conditions compared to blind conditions. Although the small sample size did not allow us to show a statistical signi cance, the results suggest that even humans with no or inferior binocular stereoscopic function may have a higher pass rate than chance. Taken together, our results indicated the existence of both binocular and monocular cues as factors that affect results in the three-rods test.
Effects of rod width on the depth perception in the threerods test.
It is known that some kinds of monocular cues allow us to determine relative distance and depth. These include relative size, interposition, linear perspective, aerial perspective, light and shade, and monocular motion parallax 19 . We investigated what type of monocular cue is used in the three-rods test. In the threerods test, subjects know before the start of the measurements that the widths of all the rods are equal.
We hypothesized that subjects use the cognitive information that all rods are the same width as a monocular cue. To test this hypothesis, we modi ed the width of the central movable rod from 3mm to 5mm and performed measurements under binocular and monocular conditions. First, two sets of measurements were performed under the binocular condition, followed by two measurements under the monocular condition using one of the dominant and non-dominant eyes. This measurement was done on 24 of the 50 people who had done all the measurements.
The results showed that neither of the two monocular conditions differed signi cantly from the blind condition (Fig4a. Nemenyi post-hoc test following Friedman test; p = 0.680 for blind vs dominant eye, p = 0.900 for blind vs non-dominant eye). Furthermore, in the monocular condition, no subject could score above the criterion for both the dominant eye and the non-dominant eye. (Fig4a) We also compared the results of the measurements before and after changing the width of the central rod. Changing the width of the rod did not result in signi cant changes in the measurements under binocular condition (Fig4b. Nemenyi post-hoc test following Friedman test; p = 0.887). In contrast, the use of the wider rod signi cantly increased the error distance compared to the measurements when the width of rods is equal under the monocular condition (Fig4b. Nemenyi post-hoc test following Friedman test; p = 0.0012) and resulted in no signi cant difference between the monocular condition and the blind condition (Fig4b. Nemenyi post-hoc test following Friedman test; p = 0.784). These data demonstrate that when the width of the rod is increased, the binocular cue is preserved but the monocular cue is lost, thus indicating that the equal width of rods is a potent monocular cue in the three-rods test.
Of these 24 subjects who performed experiments under conditions where the width of the rods was wider, two of the three people with weak or no stereopsis participated (Fig4c, see also Fig. 3b and c). When the width of the central rod was made wider, neither subject could pass the criterion in all cases in contrast to the results using the normal width of the rod. This result suggests that these subjects passed the criterion in the three-rod test with the normal width of the rod by using the information of equal width of rods as a monocular cue.
Effects of the interpupillary distance on the performance of the three-rods test Stereopsis is typically quanti ed by stereoacuity, which is the threshold angular disparity that can be seen in binocular vision. One of the factors which affect stereoacuity is the interpupillary distance (IPD) 20 . The angular disparity depends on IPD, and the larger IPD would give subjects a better depth perception, which may result in a smaller erred distance in the three-rods test.
To examine this, the mean error distance was plotted against IPD for the normal rod condition and the wider rod condition. The mean error distance in three-rods test showed low correlation with IPD in both normal rod condition (Fig5a. Pearson correlation; n = 68, r = 0.102, p = 0.409) and wider rod condition (Fig5b. Pearson correlation; n = 24, r = 0.067, p = 0.756). These results indicate that differences in IPD in the physiological range do not make a signi cant difference in the results of the three-rods test.
Correlation between the results of the three-rods test under various conditions and clinical stereopsis tests.
Finally, to investigate the reproducibility and correlation between the three-loss test and the clinical stereopsis test under various conditions, we calculated the Spearman correlation coe cient between each test. (Fig6) There was a signi cant positive correlation between the results of the rst and second sets of the normal three-rods test performed under binocular condition (Fig6a. Spearman correlation; n = 24, ρ = 0.67, p = 0.0003). However, we did not nd a signi cant correlation between these results and the results of clinically used stereotests. The same result was observed when the width of the rod was increased or tests were done under monocular or blind conditions. A signi cant positive correlation was found only between Randot stereotest and Titmus stereotest among the clinical stereoscopic tests (Fig6a. Spearman correlation; n = 24, ρ = 0.69, p = 0.0002). We did not nd a signi cant correlation for the other combinations.

Discussion
The present study demonstrated that the result in the three-rods test is affected by repeated measurement. In addition, we showed that this test had both monocular and binocular cues. By using only monocular cues, the average erred distance of 20mm, which is the passing standard for the threerods test set by various physical examinations conducted in Japan, can be exceeded with a probability of about 40%. We hypothesized that relative size (the information that the examinee was informed before the test that all rods were equal in width) is one of the monocular cues. Based on this hypothesis, we devised a modi ed three-rods test with a wider central rod. With this modi ed device, we succeeded in reducing the monocular cue while maintaining the binocular cue in the three-rods test, proving our hypothesis. Furthermore, in both conventional and modi ed three-rods tests, IPD was not shown to be a factor affecting the results.
A recent study has shown a positive correlation between the three-rods test and stereotests used in clinical practice 16 . However, a previous report has suggested that the two-rods-based Howard-Dolman test, which is similar in principle to the three-rods test, may not be able to accurately assess stereoscopic function 21 , suggesting that the three-rods test may not be also able to assess stereoscopic function. In our three-rods test con guration, the test distance is 2.5m. When the subject's IPD is 60 mm, the theoretical disparity threshold corresponding to an error distance of 20 mm in the three-rods test is 39.3 arcsec. Inconsistency between the results of the three-rods test and those of other stereotests has often been reported. Even when the disparity thresholds obtained from other stereotests are far greater than the theoretical disparity threshold of the three-rods test, the actual error distances obtained from the threerods test tend to be below the legal standard of 20 mm error distance. A similar trend was observed in the previous report 16 , suggesting the presence of factors that could skew the results in the three-rods test.
In Japan, the average of the absolute values of the three repeated measurements is used in the three-rods test for aviation workers in the JSDF and automobile drivers in the MLIT. The MLIT uses the average of the ve repeated measurements in the test for commercial pilots. However, in the case of commercial pilots, the three-rod test is performed only in the cases of anisometropia, where the refractive powers of the two eyes differ by more than two diopters. For this reason, the average of three measurements is considered to be the standard number of measurements in Japan, and the average of three measurements was used in this study. Our results showed no statistically signi cant difference between the rst and second sets of four consecutive sets of measurements. Therefore, it is considered that the number of measurements of three or ve times, which is the unit of one set, is unlikely to distort the results due to obvious practice effects, and these numbers are reasonable. However, since statistically signi cant differences were observed between the rst and third sets, care should be taken to minimize the number of tests performed.
A number of studies investigating the existence of non-stereoscopic cues in commonly used clinical stereotests suggest that the use of monocular cues can help pass these tests 14,15,[22][23][24] . The previous study has shown that results measured in the three-rod test are affected by several factors 18 , but whether monocular cues are used to pass the test criteria has not been explored. Unlike other clinical stereotests that use static planar images, the three-rod test is a dynamic test that uses actual three-dimensional objects. However, our study revealed that both binocular and monocular cues are present in the conventional three-rods test as in other clinical stereotests, and the test results re ect the results of perceptual recognition of both cues. In assessing the stereoscopic function of the subject, it may be preferable to make a comprehensive judgment based on the results of other stereotests as well, rather than using only the results of the three-rods test.
The positive correlation between the three-rods test and clinically used stereotests could not be replicated in this study, and this may be due to the population difference 16 . This could also be due to the small number of people who performed all the experiments in our study. The group of subjects in this study was ordinary members of the JASDF who are required to pass physical examinations in terms of visual, physical, and mental functions. Past reports show that about as high as 30% of the general population has problems with stereopsis 25 , but in this study, the percentage of people with abnormal stereopsis was small (3 out of 68). Further studies targeting the general population with a larger number of subjects may be necessary to clarify the correlation between conventional and modi ed three-rods tests and clinically used stereotests.
In conclusion, this study identi es that practice effect and monocular cue are present in the conventional three-rods test and that one of the monocular cues is the evenness of the width of all rods. In the modi ed version of the three-rods test with a wider central rod we did, binocular cues were not lost, but monocular cues were signi cantly reduced, and may therefore be useful as a more accurate tool to assess binocular stereoacuity. To demonstrate the usefulness of our method, further studies in the general population are needed. Furthermore, it may be possible to develop a more effective three-rods test in the future, for example, by optimizing the width of each rod.

Data availability
The datasets obtained and analyzed in this study are available from the corresponding author upon reasonable request. Figure 1 Wide rectangular viewing window at the front surface of normal, conventional three-rods test machine (a) and modi ed version of the three-rods test with a wider central rod (b). In both cases, three rods are lined up in a row.    Correlation between interpupillary distance (IPD) and error distance in the normal, conventional three-rods test (a) and modi ed three-rods test with a wider central rod (b).

Figure 6
Heat map showing the Spearman correlation coe cient and signi cance levels between the results of the three-rods test under several conditions and the results of clinical stereotests. The color bar to the right of the gure displays the mapping of correlation coe cient values to the color map. bset1-Set1 under binocular condition using the normal three-rods test. bset2-Set2 under binocular condition using the normal three-rods test. wbset1-Set1 under binocular condition using the modi ed three-rods test. wbset2-Set2 under binocular condition using the modi ed three-rods test. mset1-Set1 under monocular condition using the normal three-rods test. mset2-Set2 under monocular condition using the normal three-rods test. wmset1-Set1 under monocular condition using the modi ed three-rods test. wmset2-Set2 under monocular condition using the modi ed three-rods test. blind-Set under blind condition using the normal three-rods test. titmus-stereo threshold quanti ed by Titmus stereo test. randot-stereo threshold quanti ed by Randot stereo test. new-stereo threshold quanti ed by New stereo test. *p < 0.05, **p < 0.01, ****p < 0.001.