May 2007
Volume 48, Issue 5
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Visual Psychophysics and Physiological Optics  |   May 2007
Legibility Variations of Chinese Characters and Implications for Visual Acuity Measurement in Chinese Reading Population
Author Affiliations
  • Jun-Yun Zhang
    From the State Key Laboratory of Cognitive Neuroscience and Learning, Beijing Normal University, Beijing, China; the
    Institute of Neuroscience, Chinese Academy of Sciences, Shanghai, China; the
  • Ting Zhang
    From the State Key Laboratory of Cognitive Neuroscience and Learning, Beijing Normal University, Beijing, China; the
    Institute of Neuroscience, Chinese Academy of Sciences, Shanghai, China; the
  • Feng Xue
    EENT Hospital, Fudan University, Shanghai, China; and the
  • Lei Liu
    School of Optometry, University of Alabama at Birmingham, Birmingham, Alabama.
  • Cong Yu
    From the State Key Laboratory of Cognitive Neuroscience and Learning, Beijing Normal University, Beijing, China; the
    Institute of Neuroscience, Chinese Academy of Sciences, Shanghai, China; the
Investigative Ophthalmology & Visual Science May 2007, Vol.48, 2383-2390. doi:10.1167/iovs.06-1195
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      Jun-Yun Zhang, Ting Zhang, Feng Xue, Lei Liu, Cong Yu; Legibility Variations of Chinese Characters and Implications for Visual Acuity Measurement in Chinese Reading Population. Invest. Ophthalmol. Vis. Sci. 2007;48(5):2383-2390. doi: 10.1167/iovs.06-1195.

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      © 2015 Association for Research in Vision and Ophthalmology.

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Abstract

purpose. Written Chinese contains an enormous number of characters with a wide range of spatial complexities. Consequently, the legibility of Chinese characters is expected to vary significantly, and this variability offers the challenge of deriving a simple visual function measurement for the Chinese reading population. The purpose of this study was to suggest a solution to the challenge through psychophysical studies of Chinese character legibility.

methods. To illustrate legibility variations in Chinese characters, visual acuities for six groups of Chinese characters from low to high spatial complexities and one group of Sloan letters were determined in six normal-sighted Chinese observers. The relationship between legibility and optical defocus were then determined for the Landolt C, the Snellen E, and three groups of Chinese characters representing low, medium, and high spatial complexities in 26 normal-sighted Chinese readers.

results. The acuity size of Chinese characters increased steadily with stimulus complexity, though at a slower rate than would be expected if visual acuity were based on the finest details of the stimuli. The acuity size versus optical defocus functions of three Chinese character groups and the Snellen E had similar slopes and differed only by a vertical shift, depending on the optotype spatial complexity. The function of the Landolt C was significantly steeper.

conclusions. The findings indicate that visual acuity assessment in Chinese readers is complicated by the spatial complexity of Chinese characters, but the fact that the Snellen E, which is the current national standard of acuity measurement in China, and Chinese characters showed similar dependence on optical defocus may indicate a potentially valid way to infer functional vision in Chinese readers with Snellen E acuity.

Visual acuity is the most frequently used vision test in both clinical practice and basic research. Though it is not always explicitly stated, the fact is that visual acuity is measured for two related but different purposes. The first is to determine the refractive error of the eye as well as the lens correction that makes the stimulus optically conjugate to the retina. 1 For this purpose, visual acuity is usually defined as a measure of spatial resolution of the visual system and is described by the finest details (minimum angle of resolution, MAR) that can be resolved. International 2 and U.S. 1 standards recommend the eight- and four-orientation Landolt C as the primary visual acuity test optotype. Both standards stipulate that the gap of the C target is the detail to be resolved and that the width of the gap, which is one fifth of the target height, is the measure of visual acuity. In China, the standard optotype is the Snellen E, 3 whose stroke width is one fifth of the optotype height. For the purpose of refraction, visual acuity measurement should use a universal standard and should be free from the observers’ visual environment and cultural background. 
However, there are situations in which the optical conjugation between image plane and the retina is not the main concern. 4 Even when refractive errors are optimally corrected, visual performance can be impaired by diseases and trauma of the eye or of the visual neural pathway or by demanding operating conditions, such as low luminance, low contrast, and disabling glare. Therefore, for purposes such as diagnosis of ocular diseases, visual rehabilitation, job qualification, and disability benefit, visual acuity is used as a measurement of functional vision—that is, how well a person can perform vision-related activities under certain conditions. For a visual acuity measurement to be functionally relevant, the stimuli should be closely related to the observer’s visual tasks. For literate observers, the most important visual task is undoubtedly reading text of the observers’ native language. 
Because of the importance of reading text in functional vision, letter charts have become the dominant way of clinical evaluation of functional vision around the world. However, letters are complex spatial patterns, and what constitutes the “finest detail” in letters cannot be precisely defined. Therefore, uniting visual acuity for refraction and for functional vision has always been a challenge. 1 Both international and U.S. standards stipulate that alternative optotypes, such as letters, should be equivalent to the Landolt C in test results. ISO 8597 (International Organization for Standardization) 2 stipulates that a set of optotypes is equivalent to the Landolt C if they differ less than 0.05 log unit. In the U.S. standard, the allowed difference is within 5%. If an alternative set of optotypes is not equivalent to the Landolt C, a size conversion factor should be determined to scale the optotypes. In phonics-based languages, at least in those using Roman alphabets, an agreement between refraction oriented Landolt C acuity and functional vision oriented letter acuity is relatively easy to achieve. Sloan et al. 5 tested acuity in 214 eyes with various refractive errors by using the Landolt C and the uppercase English letters CDHKNORSVZ and found that the two measurements correlated highly (Pearson r = 0.90). When such agreement between primary and alternative optotypes can be established, the same unit for visual resolution, MAR (minimum angle of resolution) or logMAR, can be used for functional vision measurement, even though for letter stimuli, what is to be resolved may differ from letter to letter. 
Because many phonics-based languages employ only a small number of letters that often have simple and relatively uniform spatial complexities, a subset of 8 to 10 letters can adequately represent the spatial complexity of the entire alphabet. The letters to be used as acuity optotypes can be determined by an exhaustive testing of the legibility of the entire alphabet, to select letters with approximately identical legibility (The identical legibility requirement is essential to modern visual acuity chart design, in which multiple optotypes of nominally identical legibility are arranged on the same line to increase testing accuracy.) Once selected, the set of optotypes can be tested against the standard, such as the Landolt C, to determine acuity equivalence and a conversion factor, if necessary. This method has been used in creating visual acuity charts in English, German, Hindi and Gujarati, Thai, and Arabic. 5 6 7 8 9  
This optotype selection method, however, may not be applicable to nonalphabetic languages like Chinese. An enormous number of characters are used in written Chinese. Primary school graduates are required to learn more than 2500 frequently used characters during their 6 years of schooling. The criterion for literacy is the ability to recognize 2000 or more characters. It is thus impractical to test the legibility equivalence of even the frequently used characters. In addition, Chinese characters have a wide range of spatial complexities. While all written Chinese characters of the same font type and font size occupy the same square area, a character may consist of 1 to 52 strokes. The wide range of spatial complexity makes it difficult to use a small number of Chinese optotypes to quantify the visual demand for reading Chinese text. Efforts have been made to create visual acuity charts in Chinese. Woo and Lo10selected a small set of Chinese characters to construct a chart for distance acuity measurement. Because the authors intended to draw the characters according to the Snellen principle (stroke width = one-fifth character height), only simple characters with a few strokes could be used. Even among these simple characters, a large variation of character irradiation was found. For example, the ink area of Image Not Available and Image Not Available was almost 3:1. Such global cues could have aided observers in recognizing optotypes, and thus may have rendered acuity measurement unreliable. Cheng11selected 12 simple Chinese characters (2–5 strokes), and compared their acuity with that of the Landolt C. Although these characters were drawn according to the Snellen principle and thus had the same stroke width as the Landolt C, their mean threshold size was 12% larger. No acuity chart based on Cheng’s characters has been reported. Hao and Johnston12suggested a logarithmic Chinese near-acuity chart, in which lines of six characters progressed in 0.1-log-unit steps, and each line consisted of two 4-stroke, two 7-stroke, and two 10-stroke characters. Although their effort to capture the range of character complexity in one test chart is interesting, mixing optotypes of different legibility in the same line violates the basic principle of logMAR design, which requires that optotypes on the same line have approximately the same legibility. To date, none of the Chinese visual acuity charts have gained popularity in clinical practice. The current Chinese national standard uses a logarithmic Snellen E chart.3This chart, like the Landolt C, is preferable for refraction, but how its result can be related to the legibility of Chinese characters has not been systematically studied. 
In this article, we present a thorough investigation of the legibility of written Chinese characters to lay the groundwork for developing a more reliable way to evaluate functional vision in Chinese readers. We first measured the legibility of six groups of representative Chinese optotypes that covered the full range of spatial complexities of frequently used Chinese characters, by applying rigorous psychophysical procedures. The results showed that acuity sizes of Chinese characters increased linearly with their spatial complexity. We then studied the effects of optical defocus on acuities of the Landolt C, the Snellen E, and three Chinese character groups representing low, medium, and high spatial complexities, using a clinically accepted, forced-choice letter recognition method. We found that acuity-versus-defocus functions for the Snellen E and all three Chinese character groups, but not for the Landolt C, were parallel to each other. These results suggest that Snellen E acuity could be used to infer functional vision in Chinese readers. 
Methods
Optotype Selection
Besides Chinese optotypes, three sets of visual acuity optotypes were used in this study: Landolt Cs and Snellen Es at four orientations, and the 10 Sloan letters. All these optotypes had equal width and height. The stroke width was uniform and equal to one fifth of the optotype height. 1 2 13 14 The Landolt C was the primary optotype of international and U.S. visual acuity measurement standards. 1 2 The Snellen E was the optotype stipulated by the Chinese national visual acuity measurement standard. 3 The Sloan letters had intermediate legibility among the 26 uppercase English letters. 5 They were recommended letter optotypes 1 and were used in the popular ETDRS (Early Treatment Diabetic Retinopathy Study) visual acuity charts. 
A unique method was developed to select Chinese optotypes (see the Appendix). Six groups, 10 characters in each, were selected according to the number of strokes per letter (2–4, 5–6, 8–9, 11–12, 13–15, and 16–18 strokes/letter). Characters in each group had sufficient physical similarity, judged by the Euclidian distances among them, and thus might have similar legibility. 15 16 17 These Chinese optotypes were drawn in standard bold Heiti (black) font face, which has a relatively uniform stroke width and no flaring or tapering at the beginning or end. The resultant Chinese optotypes, CC1 through CC6, are shown in Figure 1a . For further quantification of the spatial complexity of these Chinese optotypes further, their stroke frequencies were calculated (see the Appendix and Fig. 1b ). 
In the rest of the article, unless specifically indicated, “letter” refers to a Sloan letter or a Chinese character or both. 
Apparatus
The stimuli were generated by a MatLab-based (The MathWorks, Natick, MA) WinVis program (Neurometrics Institute, Oakland, CA) and were presented on a 21-in. color monitor (2048 × 1536 pixels, 0.189 × 0.189 mm/pixel, 75-Hz frame rate). The maximum and minimum luminance of the monitor was 89 and 0.02 cd/m2. All optotypes were minimal-luminance, black figures on a maximum-luminance white background. Observers viewed the displays binocularly in a dimly lit room. An instrument table with a chin–headrest combo was used to maintain correct viewing distance. 
Observers and Procedures
In the two parts of the study, determination of the legibility of Chinese characters and the measurement of the effects of optical defocus on Chinese character legibility, different sets of observers and different procedures were used. 
Chinese Character Legibility
Six young (mean age, 22.8 years) native Chinese speakers with normal or corrected-to-normal vision served as observers. All observers had a college education and at least 7 years of training in reading and writing English. Except ZJ, a coauthor, all were new to psychophysical observations and were unaware of the purpose of the study. Each observer first underwent refractive testing by a trained technician using a Snellen E light box at the designated viewing distance of 5 m. Most observers were slightly myopic and wore corrections. The average best corrected acuity was −0.114 ± 0.049 logMAR. 
Sloan letters and the Chinese optotypes CC1 through CC6 were used. A method of constant stimuli was used to measure the acuity size of a stimulus group. A single letter stimulus was presented at the center of the screen with unrestricted duration. The observer’s task was to report the stimulus letter from a 10-letter list with a key-press (0–9). Auditory feedback was given on incorrect responses. Six levels of stimulus angular sizes were tested for each stimulus group. The stimulus angular size was changed by changing viewing distance without changing the physical stimuli on the screen (40 × 40 pixels for Sloan letter and 50 × 50 pixels for Chinese characters). Letter recognition for a specific stimulus group at a specific angular size formed one experimental session (10 letters × 5 trials). One round of experiments consisted of 42 sessions (seven stimulus groups × six stimulus sizes), which were run according to a randomly permuted table for each observer and were typically completed in several days. Four observers performed 10 rounds of experiments, and the other two performed six rounds. 
The percentage of correct data for each stimulus group was fitted with a Weibull function: P=1−(1−γ) e −(x/th)β , where P was the percentage correct, γ was the guessing rate (0.1 in a 10-AFC trial), x was the stimulus size in arc minutes, β was the slope of the psychometric function, and th was the threshold size at a 66.9% correct level. In the rest of this article we use “acuity size” to refer to the full height of the threshold optotype in arc minutes, and use “MAR” to refer to one fifth of the acuity size, even though for complex Chinese characters, MAR was not a well-defined stimulus feature. 
The Effects of Optical Defocus on Chinese Character Legibility
Twenty-six observers (mean age, 25.9 years) with normal or corrected-to-normal vision served as observers. Landolt Cs and Snellen Es at four orientations and three groups of Chinese optotypes representing low, medium, and high spatial complexities were used. Each stimulus group contained five optotypes (see 2 3 Fig. 4a ). The Chinese optotypes were extracted from the original CC1, CC3, and CC6 groups shown in Figure 1 . They were shown to have intermediate empiric legibility within their groups (Table 1) . The largest optotypes were 125 × 125 pixels, and the smallest were 25 × 25 pixels. This range was used to ensure good pixel image quality and a close match of logarithmic steps. 
The stimuli consisted of one line of five optotypes randomly selected from the same stimulus group. In each line, the five optotypes were randomly ordered and up to two repetitions of the same optotype were allowed. The separations between optotypes were always the width of the optotype. The stimulus line was presented at the center of the screen. There was a black rectangular marker on each side of the stimulus line, which had the same height and one-fifth width of the optotype and was separated from the stimulus line by one optotype width. 
All observers were first refracted with a Snellen E light box at the designated viewing distance of 5 m. The mean best corrected visual acuity was −0.126 ± 0.054 logMAR. An observer used his or her dominant eye to view the stimulus display from a distance of 6 m, with his or her best correction in a trial frame. Acuity sizes were measured under four conditions: best corrected vision with an additional 0-, +0.5-, +1.0-, and +2.0-D spherical lens in a random testing order. The order of the five optotype groups under each condition was also randomized. If an observer failed to recognize the largest optotype at 6 m due to the addition of a +1.0- or +2.0-D lens, the viewing distance was halved. The experiment was conducted in a dimly lit room. A front surface mirror was used to increase optical distance. 
The observer’s task was to report the five optotypes from left to right. The stimulus was shown continuously until all five optotypes were reported. The observers knew the tested letters well, and they had a list of the tested optotypes in large print at hand. The test began with a large optotype size (usually 0.2 or 0.3 log unit larger than the threshold size estimated in pilot studies). If the observer reported four or five optotypes of a possible five correctly, the optotype size was reduced by approximately 0.05 log unit. If the observer reported three or fewer optotypes correctly, the same optotype size was repeated with a new line of optotypes. If the observer was then able to report four or five optotypes correctly, the optotypes size was reduced, and the test continued. Otherwise, the mean number of correctly read optotypes of this size was recorded, and their contribution to acuity was considered according to the letter-by-letter scoring principle. Acuity was recorded in terms of one fifth of the threshold letter size. 
Written informed consent was obtained from all observers. The research adhered to the tenets of the Declaration of Helsinki. 
Results
Legibility of Chinese Characters
Figure 2a shows each observer’s psychometric function and Weibull fitting for all stimulus groups (each data point represents the average correct responses for 10 letters). Acuity sizes estimated from Weibull fittings for all individual optotypes were plotted against stroke frequencies in Figure 2b , shown as small symbols, and the average acuity sizes for each stimulus group were shown as large bold symbols. ANOVA suggested a significant stimulus group effect (F6,30 = 89.88, P < 0.0005), in that more complex optotypes had larger acuity sizes. The acuity size of the Sloan letters, 3.68 arcmin, was significantly lower than that of all CC groups—a topic that will be discussed later. After the Sloan letter group was removed, the stimulus group effect among the six CC groups was still significant (F5,25 = 29.62, P < 0.0005). For Chinese stimuli, acuity character size increased linearly as a function of the stroke frequency (Fig. 2b) . However, the best-fitting line (the straight line in Fig. 2b ) had a shallow slope (0.435). From the simplest to the most complicated CC groups (CC1 vs. CC6), a 2.5-fold increase in mean stroke frequency (2.22–5.52 strokes/letter) was accompanied with a 1.28-fold, or 0.1-log-unit, increase in acuity size (4.68–5.99 arcmin), which was equivalent to one full line on the Bailey-Lovie acuity chart. 14 These data indicate that character recognition may not be totally based on discrimination of the finest details. Otherwise, the acuity size would have increased with a much steeper slope. 
Figure 2bshows that Sloan letters had significantly smaller acuity sizes than CC1 stimuli (average 3.41 vs. 4.68 arcmin; F1,5 = 96.29, P < 0.0005), even though both groups had similar stroke frequencies (2.02 vs. 2.22 strokes/letter). This difference may be accounted for by thicker strokes of Sloan letters (Fig. 1) . To test this hypothesis, eight Chinese characters were selected that had structures similar to that of eight of the Sloan letters, with the exception of maybe a rotation and some minor differences, such as the straightness of strokes or stroke endings. These Chinese characters were rendered in two ways, with normal bold Heiti strokes and with graphically thickened strokes similar to those of Sloan letters (CCthin and CCthick in Fig. 3a ). CCthin and CCthick stimuli had stroke frequencies similar to those of the corresponding Sloan letters. 
Acuity sizes of these groups were obtained from three young observers in the same way as in the main experiment, and the average acuity sizes of individual optotypes are shown in Figure 3b . The acuity size difference between Sloan letters and regular Chinese bold Heiti characters was reproduced (mean = 3.88 and 4.66 arcmin for Sloan and CCthin, respectively; F1,2 =30.09, P = 0.032). Thickening the strokes reduced the threshold size (mean acuity size from 4.66 arcmin for CCthin to 4.31 arcmin for CCthick; F1,2 = 17.87, P = 0.052). Moreover, the mean acuity size of CCthick was not significantly different from that of Sloan (3.88 arcmin; F1,2 = 9.35, P = 0.092). These results indicate that the smaller acuity sizes of Sloan letters shown in Figure 2bwere at least partially due to their thicker stroke width. Other factors that may have contributed to the acuity size difference will be analyzed in the Discussion section. 
Effects of Optical Defocus on Chinese Character Legibility
The variation of legibility of Chinese characters shown in Figure 2bwas wide. However, we argue (see the Discussion section) that the task of deriving a simple visual function measure would become much more complicated if the pattern of variation changes from one viewing condition to another. To estimate changes of legibility of Chinese characters quantitatively, we tested legibility under a set of most common clinical conditions—namely, different refractive errors. We added plus lenses to simulate various degrees of refractive errors and measured changes of acuity sizes of the Landolt C, the Snellen E, and the three groups of Chinese characters representing simple, medium, and complex spatial complexities (Fig. 4a)
When no plus lenses were added (Fig. 4b , at 0.0 D), there was a strong effect of stimulus type (F4.22 = 56.17, P < 0.0005). The Landolt C and the Snellen E had similar logMARs (−0.159 and −0.167; F1,25 = 0.334, P = 0.568). The three CC groups all had significantly larger logMARs (−0.044, 0.037, and 0.137, for CC1, CC3 and CC6, respectively) than the Landolt C and the Snellen E (F1,25 = 206.40, P < 0.0005). The differences among CC groups were also significant (CC1 vs. CC3: F1,25 = 27.78, P < 0.0005; and CC3 vs. CC6: F1,25 = 43.19, P < 0.0005). CC1, CC3, and CC6 acuity sizes were 0.115, 0.195, and 0.296 logMAR larger than the Landolt C acuity size, respectively. According to ISO 8597, 2 these Chinese optotypes were not equivalent to the Landolt C. 
When optical defocus was introduced, the logMARs of all five stimulus groups increased linearly with optical defocus (F3,23 = 44.34, P < 0.0005; Fig. 4b ). A linear function, logMAR = a + bD, where D is the added optical defocus in diopters, b is the slope, and a is the logMAR at 0-D optical defocus, provided excellent fits (coefficient of determination, r 2 > 0.995) for all five sets of data. Notice that the fitting lines for the Snellen E, CC1, CC3, and CC6 in Figure 4bwere almost parallel, as demonstrated by the best-fitting slopes in Figure 4c . The main difference between the Snellen E and the three groups of Chinese characters groups was an upward shift of the line with increasing optotype complexity. Specifically, calculated by the y-intercepts of the best fitting lines, acuities of CC1, CC3, and CC6 were 0.117, 0.210, and 0.291 log units higher than that of the Snellen E, respectively. In other words, acuities of CC1, CC3, and CC6 were roughly 1, 2, and 3 lines of a Bailey-Lovie chart higher than that of the Snellen E, regardless of the amount of optical defocus (up to +2.0 D). On the one hand, the common slopes of these optotypes indicated that a common mechanism might underlie their recognition. The line for the Landolt C optotype, on the other hand, had a steeper slope than others (Figs. 4b 4c) , indicated by a significant interaction between the stimulus groups and optical defocus (F12,14 = 20.92, P < 0.0005). 
Discussion
Legibility of Chinese Characters
Visual acuity of Chinese characters has been studied previously in a less systematic and comprehensive manner. Hao and Johnston 12 arranged simplified Chinese characters of the same number of strokes into logarithmic charts, and measured visual acuities from 4-stroke to 10-stroke character charts. They found that acuity size increased with the number of strokes. Because the stroke distribution of simplified Chinese characters peaks at approximately 9, Hao and Johnston’s stimuli covered only the lower half of the spatial complexities. Hao and Johnston’s stimuli in the same character groups were not prescreened for gross shape differences. As they acknowledged, their characters in the same line could have quite different legibility, which may have compromised the accuracy of their acuity measurements, since these characters were assigned the same score. In comparison, the optotypes we used had rather uniform legibility, due to the prescreening procedure described in the Appendix. Hao and Johnston 12 used two step-sizes between lines: 0.1 and 0.05 log unit. They noted that even at 0.05-log-unit step, observers sometimes could recognize all characters correctly in one line, but performed at only a random level in the next line. These relatively coarse steps may have further impaired the accuracy of acuity assessment. In our experiment, we adjusted viewing distance to achieve greater stimulus size resolution. As shown in Figure 2a , most of our data points fall on the sloping part of the psychometric functions. Therefore, our experiments provided a more accurate and comprehensive assessment of acuity sizes of Chinese characters. 
Relative Legibility
Relative legibility of optotypes within each stimulus group was calculated and summarized in Table 1 . (Relative legibility indicates the ranking of legibility among a group of letters involved in an acuity test. We used the proportion of correct recognition as the measure of relative legibility. Note that relative legibility is experiment specific. The rankings shown in Table 1were derived from experiments in which10 stimulus letters were used, and thus may not be generalized to other situations. For example, S was the third least legible among the 10 Sloan letters, but when all 26 uppercase letters were tested together, S was almost always the least legible. 18 ) The χ2 tests showed that the legibility of optotypes within each stimulus group was not homogeneous (P < 0.0005), indicating that optotypes within each group were not equally legible. In contrast, the variances of relative legibility in our data (Table 1)and that of Ferris et al. 19 were not significantly different (F9,9 = 1.228, P = 0.382), indicating the same level of test accuracy. The variances of relative legibility in our CC1 through CC5 data were not significantly different from that of our Sloan data (F9,9 = 2.746, P = 0.427). CC6 had a significantly smaller variance than did the Sloan letters (F9,9 = 7.996, P = 0.037). Therefore, although each Chinese character group contained more legible and less legible characters, the scattering of relative legibility within these stimulus groups was no greater than that of the Sloan letters observed in field tests. 19 Therefore, these CC optotypes are acceptable stimuli for assessing legibility at different spatial complexities. These results also suggest that computer evaluation of Euclidean distances among bitmaps is an acceptable way to preselect optotypes of similar legibility. 
This study is the first of a series of studies on the visual psychophysics of Chinese character recognition. In later experiments including the optical defocus experiment (Fig. 4) , five optotypes with the intermediate relative legibility from each group were used as representative optotypes of that group. These five optotypes can be treated as equally legible and interchangeable optotypes. 
Further Analysis of Acuity Differences between Sloan Letters and Chinese Characters
In Figure 3 , some acuity differences between Chinese characters and Sloan letters remained even when stroke width was equalized. Such differences may be explained by the structural similarity among the eight Chinese characters in the CCthick group. To demonstrate, raw data from the Sloan and CCthick experimental sessions that yielded correct rates between 45% and 85% were organized into letter confusion matrices (Fig. 5) , in which prominent confusions are highlighted by boxes. In a typical letter acuity experiment, the correct rate of a letter stimulus depends on how confusable it is with its fellow members in the stimulus group.20Among the eight Sloan letters used in our experiment, the three most legible letters were V, H, and Z (91%, 88%, and 76% correct, respectively). The chalice, the two vertical bars, and the two horizontal bars were unique within the group. These letters were not confused consistently with other letters (Fig. 5a) . In CCthick, however, the chalice of V was replaced by a blade of Image Not Available, and the two vertical bars of H were replaced by two horizontal bars of Image Not Available. Although these replacements did not change the overall complexity of the group, they introduced more confusion (Fig. 5b) . Now, the horizontal bars of Image Not Available could be confused with those of Image Not Available. The blade of Image Not Available was now shared by part of Image Not Available. Indeed, stimulus Image Not Available was confused with Image Not Available 12% of the time, and stimulus Image Not Available was confused with Image Not Available 11% of the time (Fig. 5b) . As a consequence, the correct rates of stimuli Image Not Available, Image Not Available, and Image Not Available were 76%, 65%, and 62%, respectively—lower than the correct rates of V, H, and Z. The increased confusions in CCthick could account for a large portion of the difference between acuity size of this group and that of the Sloan letters. Therefore, in addition to spatial complexity measures such as stroke frequency, the structural similarity among optotypes may influence acuity outcomes. 
Legibility of Chinese Characters, Roman Letters, and Short Words
Roman letters are highly abstracted symbols that consist of many regularities, such as symmetry, repetition, and uniformity in strokes. In contrast, Chinese characters are either pictographs (single-body) or compounds of pictographs. Because pictographs are more realistic depictions of natural objects or events, they do not always have the regularities of Roman letters. As a consequence, the stroke types and their placement in Chinese characters are much less predictable. From a Gestalt psychology point of view, Chinese characters are not as good patterns as Roman alphabets, because Chinese characters offer many more alternatives, and good patterns have few alternatives. 21 Not-so-good patterns with more unique features should be harder to recognize than good patterns with fewer unique features. Indeed, Pelli et al. 22 found that human efficiency for recognizing Chinese characters was only one third of the efficiency for recognizing regular English letters. In our study, however, CC1 was approximately one-third less legible than Sloan letters (Fig. 2b) , rather than two-thirds less legible if predicted by the efficiency difference. The acuity difference even became statistically nonsignificant at equal stroke widths (Fig. 3b) . The vanishing advantage of English letters over Chinese characters can be explained by the nature of the acuity task. Acuity is a unique task in which subjects are forced to perform recognition or identification based solely on the global features of the stimulus, because fine features have been significantly attenuated or completely removed by ocular optics. This low-pass filtering becomes an ultimate equalizer that wipes out most of the graphical differences between stimulus groups. In a separate theoretical study, we demonstrated that the distances among optotypes in a space defined by a few low-order geometric moments, which captured the global characteristics of two-dimensional images, could account for most of the errors made by human observers in recognizing near-acuity Sloan letters and Chinese characters. 
A Chinese character expresses a meaning and is thus functionally equivalent to an English word. Chinese can be read twice as fast as English. 23 Recognition of Chinese characters is four times as efficient as recognition of five-letter English words (five letters is the average length of English words). 22 However, this advantage of Chinese character over English words does not hold at acuity. Our result showed that CC1 was 37.2% less legible than Sloan letters. Meanwhile, Sheedy et al. 24 compared acuities of single Sloan letters and lowercase English words (five to six letters) in four font faces and found that lowercase words were 4.5% to 7% less legible than Sloan letters. These data together indicate that CC1 is approximately 33% less legible than lowercase English words. We speculate that in an acuity test, the global properties of the physical structure of the stimulus, whether it is a letter, a character or a word, determine the acuity size. Familiarity with the stimulus or the meaning of the stimulus may have little effect. 
Deriving a Visual Function Measurement from Snellen E Acuity
The difference between the easiest among our 60 Chinese characters ( Image Not Available, 3.77 arcmin) and the most difficult ( Image Not Available, 6.90 arcmin) was 0.263 log unit. The legibility variability of characters in real Chinese text is likely to be even larger. Can we designate one CC group of intermediate legibility and use its acuity size as the functional measure for Chinese readers? Before we can speculate on a solution, we must know how the legibility of characters of different complexities change when viewing condition changes. If they all change in proportion, then the acuity of one group may be designated as the functional measure for all conditions, which was exactly what we demonstrated when we used plus lenses to simulate refractive errors. The parallel straight lines of the Snellen E, CC1, CC3, and CC6 shown in Figure 4benable a practitioner to use a patient’s Snellen E acuity to infer the patient’s performance with Chinese characters of different spatial complexities. The next question is which CC group best represents the visual demand for reading Chinese? One solution would be to use the number of strokes that occur most frequently in daily Chinese text. Shu et al.25studied properties of the 2570 Chinese characters listed in the official elementary school textbooks in Beijing. The distribution of stroke numbers ranged from 1 to 24 and could be fitted with a Gaussian with the mean at 9.10 ± 0.09 strokes. Our CC3 group (eight to nine strokes) is the closest to this mean. The acuity size for CC3 is 0.210 log unit larger than that of the Snellen E (Fig. 4b) , which converts to a scaling factor of 1.622. Therefore, if a road sign is designed to be read 100 m away by a driver with 20/20 vision, the Chinese characters on the sign have to be at least 1.622 × 100 × tan(5 arcmin) = 0.236 m, or 23.6 cm tall. Because the driver’s vision is determined by a Snellen E chart, the 1.622 factor compensates for the acuity size difference between the Snellen E and average Chinese characters. 
It is worth noting that the Chinese characters used in this study were “simplified” characters, which are standard in mainland China and Singapore. Many simplified characters have fewer strokes than the corresponding traditional characters. For instance, the simplified character Image Not Available (none, void) in CC2 would be Image Not Available as a traditional character. The distribution of the number of strokes and thus the mean acuity size are likely to be larger for traditional Chinese characters, and for Kanji in Japanese, because most of them are traditional Chinese characters. 
Finally, it is also worth pointing out that the parallel relationship between the Snellen E and the Chinese characters shown in Figure 4bwas obtained by introducing optical defocus. While this method (dioptric blur) has been widely used to simulate refractive errors in the eye, subtle differences may exist. We are currently working on a clinical population to see whether the same relationship holds in naturally occurring refractive errors. 
Conclusions
Measurements of visual acuities of Sloan letters and Chinese characters of different numbers of strokes revealed that more complex optotypes had larger acuity sizes. The increase of acuity size with optotype spatial complexity, however, was not fast enough to support the notion that visual acuity was determined by discrimination of the smallest details. Sloan letters had significantly smaller acuity size than the simplest group of Chinese characters, even though the two groups had comparable spatial complexity. This difference, however, could partially be explained by the stroke width difference between these optotypes. When optical defocus was introduced, the acuity sizes of Chinese characters increased in the same way as Snellen E optotypes. Such simple relationships may help to derive a functional measure from Snellen E acuity that is relevant to Chinese reading. 
Appendix 1
Selection of Chinese Optotypes
First, the 500 most frequently used Chinese characters (CCs) were selected from an official character-frequency table, 26 which was compiled based on a linguistic corpus of 138 million CCs. Six groups of CCs were selected based on the number of strokes (i.e., 2–4, 5–6, 8–9, 11–12, 13–15, and 16–18 strokes). To reduce testing characters to a manageable number, a computer analysis of physical similarity among characters in each group was conducted. The 50 × 50 bitmap of each character was considered as a point in a 50 × 50-dimension space, with the coordinates x 1, x 2, x 3, … , x 2500). These coordinates were either 0 (a black pixel) or 1 (a white pixel). The Euclidean distance between the ith and the jth characters in this space was  
\[d_{ij}{=}\left[{{\sum}_{k{=}1}^{2500}}(x_{ik}{-}x_{jk})^{2}\right]\ ^{1/2}\]
. All pair-wise Euclidean distances among representing points of all characters within each group were calculated. Several studies 15 16 17 have shown that Euclidean distances correlated with perceived similarity between English letters. From each CC group, 12 to 14 characters with intermediate Euclidean distances from each other were selected. This procedure excluded characters that were either physically too similar or too different. Additional considerations of pronunciation and spatial configurations further reduced the number of characters in each group to 10. The resultant six sets of Chinese optotypes are shown in Figure 1a(CC1–CC6). 
Calculation of Optotype Stroke Frequency
Although the number of strokes has been used in many studies of letter recognition to index the complexity of stimuli, it is not a good measure of spatial complexity because the total number of strokes ignores the spatial arrangement of strokes, and thus may not provide a good measurement of stroke density. For example, although the character Image Not Availablecontains four straight line segments, there are only two line segments in the horizontal or vertical direction. Characters Image Not Available(three) and Image Not Available(river) have only three strokes each, but the stroke density in the vertical or horizontal direction is 1.5 times of that of Image Not Available. A more objective measurement of spatial complexity of optotypes is stroke frequency.27It was originally defined as the average number of strokes crossed by a slice through the letter width. Because many Chinese characters have unbalanced top–bottom or left–right configurations (for example, the second and third characters in CC4 in Fig. 1a ), and because some Chinese characters have predominantly oblique strokes (the last character of CC3), a more sophisticated method was used to calculate stroke frequencies of our optotypes. As shown in Figure 1b , each letter was sliced in one-pixel steps into six direction–position combinations: horizontally on the upper and lower halves, vertically on the left and right halves, and obliquely at 45° and 135° on the central portion of the optotype. A mean of crossed strokes was obtained from each slicing, and the maximum of the six slices was taken as the stroke frequency of the optotype. The average stroke frequency for the Sloan letters was 2.0 strokes/letter, slightly larger than that obtained in one horizontal slice (1.6 strokes/letter).27The average stroke frequencies in the six groups of Chinese characters increased monotonically from 2.2 to 5.5 strokes/letter. 
Another measurement of spatial complexity of patterns is perimetric complexity. 22 28 Perimetric complexity is a size-invariant measure of dispersion and is defined as the square of inside-and-outside perimeter of a pattern, divided by the ink area. We calculated perimetric complexities of all the optotypes used in our study and found they correlated highly with stroke frequencies (r = 0.956). Because stroke frequency is the more intuitive of the two measurements, we chose to use stroke frequency as our measurement of optotype complexity. 
 
Figure 1.
 
(a) Sloan letters and six groups of CCs used in the study. The number of strokes was 2 to 4, 5 to 6, 8 to 9, 11 to 12, 13 to 15, and 16 to 18 for the CC groups 1 through 6, respectively. (b) An illustration of stroke frequency calculation.
Figure 1.
 
(a) Sloan letters and six groups of CCs used in the study. The number of strokes was 2 to 4, 5 to 6, 8 to 9, 11 to 12, 13 to 15, and 16 to 18 for the CC groups 1 through 6, respectively. (b) An illustration of stroke frequency calculation.
Table 1.
 
Relative Legibilities of Sloan Letters and Chinese Characters
Table 1.
 
Relative Legibilities of Sloan Letters and Chinese Characters
Figure 2.
 
(a) Individual observers’ psychometric functions for seven stimulus groups and their Weibull fittings. (b) Acuity sizes as a function of the stroke frequency. Large solid symbols: acuity sizes for individual letter stimuli averaged over six observers are shown as small, hollow symbols, and group acuity sizes averaged over 10 letters and six observers. Straight line: best fit of CC data (CC1–CC6).
Figure 2.
 
(a) Individual observers’ psychometric functions for seven stimulus groups and their Weibull fittings. (b) Acuity sizes as a function of the stroke frequency. Large solid symbols: acuity sizes for individual letter stimuli averaged over six observers are shown as small, hollow symbols, and group acuity sizes averaged over 10 letters and six observers. Straight line: best fit of CC data (CC1–CC6).
Figure 3.
 
Effect of stroke width. (a) Stimuli. CCthin were characters in the regular bold Heiti font. CCthick were the same characters with thicker strokes. The stroke width was roughly one fifth of the character height. (b) Acuity letter sizes for the three groups of stimuli. Horizontal lines: mean acuity sizes.
Figure 3.
 
Effect of stroke width. (a) Stimuli. CCthin were characters in the regular bold Heiti font. CCthick were the same characters with thicker strokes. The stroke width was roughly one fifth of the character height. (b) Acuity letter sizes for the three groups of stimuli. Horizontal lines: mean acuity sizes.
Figure 4.
 
(a) Stimuli used in the experiment. (b) LogMARs averaged over all observers for each stimulus group plotted as a function of optical defocus in diopters. The straight lines are the best fitting lines. (c) Slopes of the best-fitting lines in (b).
Figure 4.
 
(a) Stimuli used in the experiment. (b) LogMARs averaged over all observers for each stimulus group plotted as a function of optical defocus in diopters. The straight lines are the best fitting lines. (c) Slopes of the best-fitting lines in (b).
Figure 5.
 
Letter confusion matrices for the Sloan letters (a) and CCthick optotypes (b). The ith, jth cell of a confusion matrix contains the empiric probability that the ith optotype will be reported as the jth optotype. The diagonal line cells (bold) contain the correct rates and the off-diagonal line cells contain perceptual errors, or confusions. Each column contains all responses to the corresponding stimulus optotype, and thus sums to 1.0. Prominent confusions (>0.10) are highlighted.
Figure 5.
 
Letter confusion matrices for the Sloan letters (a) and CCthick optotypes (b). The ith, jth cell of a confusion matrix contains the empiric probability that the ith optotype will be reported as the jth optotype. The diagonal line cells (bold) contain the correct rates and the off-diagonal line cells contain perceptual errors, or confusions. Each column contains all responses to the corresponding stimulus optotype, and thus sums to 1.0. Prominent confusions (>0.10) are highlighted.
The authors thank Patti Fuhr (VA Medical Center, Birmingham, AL) for careful reading of the manuscript and for lending her clinical insight and Shu-Guang Kuai for helping to write software programs for the study. 
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Figure 1.
 
(a) Sloan letters and six groups of CCs used in the study. The number of strokes was 2 to 4, 5 to 6, 8 to 9, 11 to 12, 13 to 15, and 16 to 18 for the CC groups 1 through 6, respectively. (b) An illustration of stroke frequency calculation.
Figure 1.
 
(a) Sloan letters and six groups of CCs used in the study. The number of strokes was 2 to 4, 5 to 6, 8 to 9, 11 to 12, 13 to 15, and 16 to 18 for the CC groups 1 through 6, respectively. (b) An illustration of stroke frequency calculation.
Figure 2.
 
(a) Individual observers’ psychometric functions for seven stimulus groups and their Weibull fittings. (b) Acuity sizes as a function of the stroke frequency. Large solid symbols: acuity sizes for individual letter stimuli averaged over six observers are shown as small, hollow symbols, and group acuity sizes averaged over 10 letters and six observers. Straight line: best fit of CC data (CC1–CC6).
Figure 2.
 
(a) Individual observers’ psychometric functions for seven stimulus groups and their Weibull fittings. (b) Acuity sizes as a function of the stroke frequency. Large solid symbols: acuity sizes for individual letter stimuli averaged over six observers are shown as small, hollow symbols, and group acuity sizes averaged over 10 letters and six observers. Straight line: best fit of CC data (CC1–CC6).
Figure 3.
 
Effect of stroke width. (a) Stimuli. CCthin were characters in the regular bold Heiti font. CCthick were the same characters with thicker strokes. The stroke width was roughly one fifth of the character height. (b) Acuity letter sizes for the three groups of stimuli. Horizontal lines: mean acuity sizes.
Figure 3.
 
Effect of stroke width. (a) Stimuli. CCthin were characters in the regular bold Heiti font. CCthick were the same characters with thicker strokes. The stroke width was roughly one fifth of the character height. (b) Acuity letter sizes for the three groups of stimuli. Horizontal lines: mean acuity sizes.
Figure 4.
 
(a) Stimuli used in the experiment. (b) LogMARs averaged over all observers for each stimulus group plotted as a function of optical defocus in diopters. The straight lines are the best fitting lines. (c) Slopes of the best-fitting lines in (b).
Figure 4.
 
(a) Stimuli used in the experiment. (b) LogMARs averaged over all observers for each stimulus group plotted as a function of optical defocus in diopters. The straight lines are the best fitting lines. (c) Slopes of the best-fitting lines in (b).
Figure 5.
 
Letter confusion matrices for the Sloan letters (a) and CCthick optotypes (b). The ith, jth cell of a confusion matrix contains the empiric probability that the ith optotype will be reported as the jth optotype. The diagonal line cells (bold) contain the correct rates and the off-diagonal line cells contain perceptual errors, or confusions. Each column contains all responses to the corresponding stimulus optotype, and thus sums to 1.0. Prominent confusions (>0.10) are highlighted.
Figure 5.
 
Letter confusion matrices for the Sloan letters (a) and CCthick optotypes (b). The ith, jth cell of a confusion matrix contains the empiric probability that the ith optotype will be reported as the jth optotype. The diagonal line cells (bold) contain the correct rates and the off-diagonal line cells contain perceptual errors, or confusions. Each column contains all responses to the corresponding stimulus optotype, and thus sums to 1.0. Prominent confusions (>0.10) are highlighted.
Table 1.
 
Relative Legibilities of Sloan Letters and Chinese Characters
Table 1.
 
Relative Legibilities of Sloan Letters and Chinese Characters
Copyright 2007 The Association for Research in Vision and Ophthalmology, Inc.
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