SUMMARY
This study was designed to explore practical differences between visual acuity (VA) scores measured on Snellen chart versus ETDRS chart, to grade cataracts using LOCS III system, and to compare VA on both charts depending on cataract grade and type. Prospective evaluation of uncorrected and best-corrected visual acuity was carried out on the eye scheduled for cataract surgery preoperatively and postoperatively on the Snellen and ETDRS charts. The study was carried out at Department of Eye Diseases, Clinical Center of Serbia, during a two-year period. Inclusion criteria were met by 540 patients who underwent testing, surgery, data collection and analysis. The mean VA score was better on ETDRS than on Snellen chart. The mean difference was 6.05 letters or 1.21 lines. VA results correlated with all types of cataract regardless of the chart used, with the highest statistical significance (p<0.0001) for subcapsular cataract. The ETDRS chart was found to be more discriminative and precise than Snellen chart, especially for poor VA.
Key words: Visual acuity, ETDRS chart, Snellen chart, LOCS III, Age-related cataract
Introduction
Numerous testing charts are used for evaluation of visual acuity (VA), but Snellen and Early Treatment Diabetic Retinopathy Study (ETDRS) charts are most frequently applied (1, 2). Snellen chart has some advantages as it is readily available, relatively affordable, small, does not take up much space, and testing is fast and does not require examiner training (3). However, disadvantages of Snellen chart are more numerous. There is an unequal number of symbols in rows and changes in symbol size is linear from row to row (4), crowding phenomenon is therefore amplified in rows with more letters, some chart letters (e.g., C, D, E, O) are easier to read than others (e.g., A, J, L) (5). Visual acuity testing on Snellen chart relies on the line assignment method and the term Snellen chart is not standardized, i.e. the Snellen chart definition criteria are not precisely defined (6). Snellen chart has high test-retest variability (TRV) values, e.g., more than 2 rows for healthy eyes (7, 8) and up to 3.3 rows for eyes with some ocular disease (9, 10).
The ETDRS chart has an identical number of letters per row, and equal spacing between the letters and between the rows, expressed in logarithmic values (3). Instead of Snellen letters, quadratic or so-called Sloan letters are used, which are balanced based on the ‘reading difficulty’ in each row. ETDRS chart is graded in LogMAR (Logarithm of the Minimum Angle of Resolution) units, corresponding to the logarithmic perception of the visual system (11).
Each letter read is assigned a value of 0.02 LogMAR marking based on the number of read letters, not rows. The TRV values were significantly better than for Snellen charts, and were in the range of 3.5 to 10 letters depending on whether the patient had normal VA and function (12-15). Disadvantages of the ETDRS chart are its size, insufficient knowledge of testing protocols, longer testing time, need for personnel training, and high price (16, 17).
Senile cataract is a progressive cloudiness or opacity of the lens in people older than 45 without a known source of origin such as trauma, inflammation, hypocalcemia, medicaments, or congenital factors (18, 19). The Lens Opacities Classification System III (LOCS III) is used to grade and compare the type and progression of the cataract (20, 21).
The present study investigated the degree of compliance of the measurement results of the best corrected visual acuity (BCVA) and uncorrected visual acuity (UCVA) in patients suffering from senile cataract preoperatively (poor VA) and postoperatively (good VA) using Snellen and ETDRS charts.
Patients and Methods
The study involved adult patients suffering from senile cataract and operated on at Department of Eye Diseases, Clinical Centre of Serbia, during a two-year period. Exclusion criteria were failure to show up for control check-up; VA <6/60 according to Snellen chart; diagnosed or suspected accompanying eye diseases or diseases of the central nervous system which might affect VA along with the cataract; complications during cataract surgery; oligophrenia, presenile or senile dementia, psycho-organic syndrome, poor cooperation with the patient; and patient failing to provide written consent to participate in the study.
A total of 540 patients satisfied the set criteria and were included in statistical analysis. Grading of the cataract was performed 7 days prior to the operation based on slit lamp examination through medically dilated pupils. All patients were successfully tested for VA with both test charts selected. VA testing was done by the same examiner and in the same room with a standardized ambient lighting, i.e. dark room (approximately 10 cd/m2 measured by digital lux meter MS-1500 (Voltcraft, No. 12 88 02) and standardized test chart lighting (inside lighting of the test box). Prior to VA testing, refraction was determined on both eyes, followed by possible optical correction (where necessary). Subsequently, VA was tested on the eye scheduled for operation, first on Snellen chart and then on ETDRS chart. During testing, the patient’s pupil size was adequate for the ambient lighting, i.e. the pupils were not medically dilated.
Snellen chart testing was carried out using Snellen chart with a standard back-lighting of 85 cd/m2 (Instrumentaria, Zagreb, Croatia; TIP PV/02, V 220/24, W 14.25, attest number 3024) from a 6-m distance. Snellen chart was printed in high-contrast letters on a translucent back-lit white panel and was represented in a standard light box. Only letter symbols were used during testing. VA testing was initiated from the top of the scale and progressed top-to-bottom to the final row which the patient could read clearly with all the pictured symbols (numbers). Patients were allowed only one attempt at reading the chart. The recorded results were confirmed using Tumbling E test eye chart in order to avoid the possibility of false reading (false positive result).
ETDRS Chart Testing (ETDRS chart Precision Vision, Catalog No. 2110) was carried out at a 4-meter distance from the patient, with a chart box mounted on a stand. The chart box had a standard backlighting of 300 cd/m2 (Chart Illuminator, Precision Vision, Catalog No. 2425, 230 V, 50 Hz). ETDRS chart was printed in high-contrast letters on a translucent polystyrene back-lit panel, and was shown in a standard light box. The chart had 5 letters per line, spaced in steps of 0.1 LogMAR, as per ETDRS protocol. VA testing was initiated with the first letter in the upper row of the chart and progressed top-to-bottom until the patient would erroneously read all the letters in one of the lines, or until the patient read all the letters in all the lines (on the chart). The examinees were allowed to read off the chart only once.
In order to achieve partial concordance between different methodologies of determining VA using ETDRS and Snellen charts, we partially modified testing on the ETDRS chart. We tested patients on the ETDRS chart by using line assign method (similar to Snellen chart). In other words, we did not take into account the letters from the subsequent row, instead we only counted those rows that were read in full. This principle will henceforth be labeled as the ‘modified ETDRS chart’.
Cataract grading was done 7 days prior to the operation. The examination was performed on a slit lamp through dilated pupil (tropicamide 1% and phenylephrine 2.5%). The slit lamp setup (slit height, width, slit beam angle and focus) was made according to the Harvard Medical School recommendations (LOCS III) in grading human age-related cataract (21). Classification was performed by a single ophthalmologist, based on the subjective perception of the clinical shape of the cataract and comparison with a set of standardized photographs.
Visual acuity testing was carried out under the same testing conditions and standards one month after the operation, both on Snellen and ETDRS charts.
Statistical analysis
Study results were expressed as mean ± standard deviation (SD). The normality of data distribution was assessed with Kolmogorov-Smirnov test. Statistical analysis included descriptive statistics and paired t-test used for comparison of the Snellen and ETDRS chart results. The level of statistical significance was set at p<0.05. Difference between group medians was tested by Mann-Whitney U-test.
Non-parametric data were expressed as numbers and percentages, and tested by the χ2-test. Correlation coefficient was used to test the relationship between two properties. Bland-Altman analyses were used to compare variability between the two scales.
Results
A total of 540 patients were operated on. There was no significant difference according to sex, operated eye, age, and cataract type distribution (Table 1). The mean age of patients in the posterior subcapsular cataract group was lowest and statistically significantly different.
Table 1. Patient distribution by sex, operated eye, age, and cataract type.
| Sex | Male | 244 |
|---|---|---|
| Female | 296 | |
| Operated eye, n | Right | 300 |
| Left | 240 | |
| Age (years) | Posterior subcapsular group | 62.75±6.03 |
| Cortical group | 65.85±6.54 | |
| Nuclear group | 65.92±6.92 | |
| Cataract type, n (%) | Posterior subcapsular group | 184 (34.07) |
| Cortical group | 160 (29.63) | |
| Nuclear group | 196 (36.29) |
The lowest preoperative VA value on all charts was measured on Snellen chart (0.797±0.235 LogMAR) and the best VA was recorded on ETDRS chart (0.605±0.235 LogMAR) (Fig. 1).
Fig. 1.
Mean preoperative visual acuity, uncorrected (UCVA) and best corrected (BCVA), on both charts.
Visual acuity measurements recorded postoperatively were very good, i.e. lower than 0.1 LogMAR. The lowest postoperative VA of 0.098±0.097 LogMAR was measured with UCVA on Snellen chart. When measurements were repeated on a modified ETDRS chart, the lowest recorded VA value was 0.095 LogMAR. Thus, postoperative VA measurements on the two scales were almost completely equalized. Preoperatively measured VA were statistically significantly different. The greatest difference was observed with UCVA. Its value was 6.05 letters or 1.21 sequence rows on Snellen chart compared to ETDRS chart (Table 2). However, with regard to BCVA, the values recorded on Snellen and ETDRS charts were approximately the same, i.e. 0.639 LogMAR on Snellen chart and 0.636 on modified ETDRS chart.
Table 2. Preoperative visual acuity values measured on Snellen chart vs. ETDRS chart.
| Preoperative visual acuity | Snellen chart, AM ± SD |
ETDRS chart, AM ± SD |
Statistical significance | 95% confidence interval |
|---|---|---|---|---|
| UCVA | 0.799±0.235 | 0.678±0.147 | p<0.0001 | -0.145-0.093 |
| BCVA | 0.639±0.225 | 0.605±0.155 | p=0.007 | -0.056-0.009 |
ETDRS = Early Treatment Diabetic Retinopathy Study chart; AM = arithmetic mean; SD = standard deviation; UCVA = uncorrected visual acuity; BCVA = best corrected visual acuity; p = probability value
Considering postoperative VA, statistical significance was only found with UCVA, which was lower on Snellen chart by 1 letter. Regression analysis of the preoperatively measured UCVA indicated a statistically highly significant connection (p<0.001) between the two scales with determination coefficient R2=0.6029 (Fig. 2a). These values correspond to poor VA. Similar result was also obtained on postoperative measurements, i.e. for good VA (Fig. 2b). There was a statistically highly significant connection (p<0.001) between the two scales with determination coefficient R2=0.6863. The relationship between the two charts is clearly defined, and the values obtained using one chart can be used to calculate the values on the other chart using the regression line equation.
Fig. 2.
Correlation of preoperatively (left) and postoperatively (right) measured uncorrected visual acuities (UCVA) on ETDRS and Snellen charts; X and Y axes represent visual acuity values expressed in LogMAR; X-axis represents Snellen chart values and Y-axis ETDRS chart values; solid black line is the line of regression; dashed lines represent 95% confidence interval of the regression line.
The Bland-Altman analysis of difference between the results of the preoperatively measured, native (UCVA) VA (low values, poor VA) on Snellen and ETDRS charts compared to their mean values showed that VA deterioration increased the variability between the two charts (Fig. 3a). On postoperatively measured VA (good eye sight) on Snellen and ETDRS charts, the observed difference was not so significant (Fig. 3b).
Fig. 3.
Bland-Altman graph showing differences in the values of preoperatively (left) and postoperatively (right) measured visual acuities on Snellen and ETDRS charts, expressed in LogMAR; Y- axis represents difference between measurements on the two charts, whereas X-axis represents the mean visual acuity on the two charts; solid blue line represents the mean visual acuity expressed in LogMAR (0.12 preoperatively, poor visual acuity vs. 0.01 postoperatively, good visual acuity); the area between dashed lines equals the limit of 95% overlap between the two charts; all the points below the solid line represent Snellen chart results as poorer compared to ETDRS chart results on the same eye.
We also analyzed the relation between the values of native VA measured on Snellen and modified ETDRS chart. Once again, it was observed that the variability increased with VA reduction (Fig. 4a). Analysis of postoperatively measured VA on Snellen and modified ETDRS charts showed that there was virtually no between-chart variability at better VA (Fig. 4b).
Fig. 4.
Bland-Altman graph showing differences in the values of preoperatively (left) and postoperatively (right) measured visual acuities on Snellen and modified ETDRS charts, expressed in LogMAR; Y-axis represents difference between measurements on the two charts, whereas X-axis represents the mean visual acuity value on the two charts; solid blue line represents the mean visual acuity expressed in LogMAR (0.09 preoperatively, poor visual acuity); the area between dashed lines equals the limit of 95% overlap between the two charts; all the points below the solid line represent Snellen chart results as poorer compared to ETDRS chart results on the same eye.
The mean cataract grade was 3.96±0.686. Our results showed a statistically significant relationship between the degree of cataract progression and measured VA in all three cataract groups. The highest correlation was observed in posterior subcapsular cataract with a correlation coefficient of r=0.683 for the modified ETDRS chart (Table 3).
Table 3. Correlation between cataract progression and preoperative UCVA and BCVA for all three cataract types measured on Snellen, ETDRS and modified ETDRS charts.
| Preoperative visual acuity |
Posterior subcapsular cataract | Cortical cataract | Nuclear cataract | |||
|---|---|---|---|---|---|---|
| r | p | r | p | r | p | |
| Snellen chart, UCVA | 0.466 | 0.0346 | 0.324 | 0.042 | 0.309 | 0.048 |
| Snellen chart, BCVA | 0.519 | 0.0007 | 0.430 | 0.0041 | 0.410 | 0.0049 |
| ETDRS chart, UCVA | 0.467 | 0.0021 | 0.487 | 0.00039 | 0.483 | 0.0015 |
| ETDRS chart, BCVA | 0.685 | <0.0001 | 0.494 | 0.0003 | 0.677 | <0.0001 |
| Modified ETDRS chart, UCVA | 0.386 | 0.0081 | 0.498 | 0.0003 | 0.306 | 0.0387 |
| Modified ETDRS chart, UCVA | 0.567 | <0.0001 | 0.461 | 0.0009 | 0.496 | 0.0005 |
ETDRS = Early Treatment Diabetic Retinopathy Study chart; UCVA = uncorrected visual acuity; BCVA = best corrected visual acuity; p = probability value; r = correlation coefficient
As illustrated in Table 4, preoperatively measured UCVA in all three cataract types was statistically significant lower on Snellen chart than on the other two charts. The situation was different with BCVA, whereby the difference was statistically significant only in posterior subcapsular cataract.
Table 4. Comparison of UCVA and BCVA preoperative visual acuity measured on Snellen and ETDRS charts according to cataract type.
| Cataract type | UCVA | BCVA | ||||
|---|---|---|---|---|---|---|
| Snellen chart AM ± SD, 95% CI |
ETDRS chart AM ± SD, 95% CI |
Statistical significance | Snellen chart AM ± SD, 95% CI |
ETDRS chart AM ± SD, 95% CI |
Statistical significance | |
| Posterior subcapsular | 0.879±0.197 CI=0.822-0.936 |
0.742±0.122 CI=0.706-0.777 | p<0.0001 | 0.729±0.211 CI=0.668-0.789 | 0.681±0.132 CI=0.643-0.719 |
p=0.0336 |
| Nuclear | 0.798±0.243 CI=0.720-0.876 |
0.654±0.167 CI=0.600–0.708 | p<0.0001 | 0.601 ± 0.232 CI=0.527–0.675 | 0.567±0.169 CI=0.513-0.622 | p=0.1442 |
| Cortical | 0.710±0.237 CI=0.639-0.780 |
0.631±0.129 CI=0.593-0.670 | p=0.0009 | 0.573±0.206 CI=0.512-0.634 |
0.556±0.135 CI=0.516-0.597 | p=0.3596 |
ETDRS = Early Treatment Diabetic Retinopathy Study chart; AM = arithmetic mean; SD = standard deviation; UCVA = uncorrected visual acuity; BCVA = best corrected visual acuity; 95% CI = 95% confidence interval
Discussion
To our understanding, based on MEDLINE database search (February 2016), our research is the only one that directly estimated VA measurement differences between Snellen and ETDRS charts based on the grade of cataract progression. Furthermore, to our knowledge, this research is the only one carried out on a significant group of patients with age-related cataract, whereby both the preoperative and postoperative VA measurements were compared on both aforementioned charts. The only known previous research of this kind included a group of cataract patients comprised of only three subjects (22). Our research showed significantly higher VA values on ETDRS than on Snellen chart with a high statistical significance (p=0.000000001). The mean difference was 6.05 letters or 1.21 lines. This could be of significance during the patient selection process for operation. Similar results have been reported by Falkenstein et al. (23), who observed a mean difference in the measured VA values on the two charts of 2.5 lines, as well as by Kaiser (22), who recorded a difference between the two charts of 6.5 letters or 1.3 lines. When we introduced the method of assigning rows to VA measurements on ETDRS chart, i.e. when the so-called modified ETDRS chart was used, with an appropriate optical correction we observed almost no difference in the mean VA values between the two charts. This questions the importance of the precision difference between the two charts from the aspect of daily clinical practice.
The mean postoperative VA showed a statistically significant difference between the two charts only when it was measured without appropriate optical correction, and it was about one letter (non-modified, standard ETDRS compared to Snellen chart). Given the lack of appropriate study to compare data, we can only compare the obtained results with those reported by Kaiser (22) and Falkenstein et al. (23), who examined VA in different patient groups suffering from a number of ophthalmologic diseases, as well as those included in the healthy group as a whole, whereby one of the ways of group sorting was based on the measured VA. Kaiser’s results (22) indicated the group of patients with good VA (VA better than 20/50) to show difference between Snellen and ETDRS charts smaller than one line. This is similar to the previous findings that patients with VA better than 20/30 exhibited difference in the two charts of 3.5 letters (23). Based on our results, as well as the results of previous research, for clinical trials/tests requiring patients with good VA, it is justified to assume that the measurements recorded on ETDRS chart largely correspond to Snellen chart measurements with a deviation of up to 1 line.
Similar results measured on the two aforementioned charts in patients with good VA, as well as a significant difference in poor VA patients can be explained by the very nature of the vision sense. Humans perceive the linear increase of a stimulus by a logarithmic increase in perception (24). Weber-Fechner law stipulates that the perception intensity is proportional to the logarithm of the stimulus intensity. At the very beginning, i.e. at lower stimulus intensities above the necessary threshold, the perception intensity increases proportionally. However, as we increase the amount of stimulus, the intensity of perception does not change at the same rate, instead it increases more slowly. Perception intensity does not increase with the absolute value of the stimulus intensity. Rather, it increases with its logarithm. For lower stimulus intensities, i.e. at lower VA as applied in our research, this logarithmic scale varies significantly from the linear scale and has a greater bandwidth. In contrast, for greater values, it contracts and achieves maximum value which tends to infinity and invariance, and thus approximates the linear scale (25).
Our research showed that there was a highly statistically significant correlation among cataract grade, cataract type and VA. The greatest level of correlation was observed in posterior subcapsular cataracts, which is in line with the existing research (26). This is somewhat in contrast to the adopted belief that the estimate of the posterior subcapsular cataract VA is somewhat less precise than for nuclear cataracts, as it is much more reliant upon ambient illumination. However, our research excluded the factor of different ambient illumination (minimal degree, darkened room, approximately 10 cd/m2), thus enabling greater light penetration for subcapsular cataracts than it is the case (at least for the majority) for nuclear and nuclear brunescent cataracts. It is possible that the reason why the best correlation of VA with cataract grade is present in posterior subcapsular cataracts is the relative structure and optical homogeneity of subcapsular cataracts compared to the relative structure and optical homogeneity of cortical and nuclear cataracts (27). In this special case, there is a possible justification for the preferential utilization of ETDRS over Snellen chart.
The results we obtained in our research clearly indicated that in poorer VA, the ETDRS chart (modified or non-modified) was more discriminative and precise than Snellen chart. The ETDRS chart should find its place in prospective clinical trials. In everyday clinical practice, it is possible to predict results on ETRDS chart using regression analysis of the results obtained with Snellen chart. Furthermore, in accordance with the theory and analysis of the existing literature on the subject, it is also recommended to utilize ETDRS chart for medico-legal purpose, as well as for establishing decision-making standards on the appropriateness of certain medical procedures.
References
- 1.Bailey IL. Visual acuity. In: Benjamin WJ, editor. Borish’s Clinical Refraction. Philadelphia: W.B. Saunders Company; 1998. pp. 179-202. [Google Scholar]
- 2.Dong LM, Marsh MJ, Hawkins BS. Measurement and analysis of visual acuity in multicenter randomized clinical trials in the United States: findings from a survey. Ophthalmic Epidemiol. 2003;10(3):149–65. 10.1076/opep.10.3.149.15080 [DOI] [PubMed] [Google Scholar]
- 3.Bailey IL, Lovie JE. New design principles for visual acuity letter charts. Am J Optom Physiol Opt. 1976;53(11):740–5. 10.1097/00006324-197611000-00006 [DOI] [PubMed] [Google Scholar]
- 4.Flom MC, Heath G, Takahashi E. Contour interaction and visual resolution: contralateral effect. Science. 1963;142(3594):979–80. 10.1126/science.142.3594.979 [DOI] [PubMed] [Google Scholar]
- 5.Kniestedt C, Stamper RL. Visual acuity and its measurement. Ophthalmol Clin North Am. 2003;16(2):155–70. 10.1016/S0896-1549(03)00013-0 [DOI] [PubMed] [Google Scholar]
- 6.Leinonen J, Laakkonen E, Laatikainen L. Random measurement error in visual acuity measurement in clinical settings. Acta Ophthalmol Scand. 2005;83(3):328–32. 10.1111/j.1600-0420.2005.00469.x [DOI] [PubMed] [Google Scholar]
- 7.Laidlaw DA, Abbott A, Rosser DA. Development of a clinically feasible logMAR alternative to the Snellen chart: performance of the ‘compact reduced logMAR’ visual acuity chart in amblyopic children. Br J Ophthalmol. 2003;87(10):1232–4. 10.1136/bjo.87.10.1232 [DOI] [PMC free article] [PubMed] [Google Scholar]
- 8.Rosser DA, Laidlaw DA, Murdoch IE. The development of a ‘reduced logMAR’ visual acuity chart for use in routine clinical practice. Br J Ophthalmol. 2001;85(4):432–6. 10.1136/bjo.85.4.432 [DOI] [PMC free article] [PubMed] [Google Scholar]
- 9.Loumann Knudsen L. Visual acuity testing in diabetic subjects: the decimal progression chart versus the Freiburg visual acuity test. Graefes Arch Clin Exp Ophthalmol. 2003;241(8):615–8. 10.1007/s00417-003-0707-8 [DOI] [PubMed] [Google Scholar]
- 10.Gibson RA, Sanderson HF. Observer variation in ophthalmology. Br J Ophthalmol. 1980;64(6):457–60. 10.1136/bjo.64.6.457 [DOI] [PMC free article] [PubMed] [Google Scholar]
- 11.Ferris FL, 3rd, Kassoff A, Bresnick GH, Bailey I. New visual acuity charts for clinical research. Am J Ophthalmol. 1982;94(1):91–6. 10.1016/0002-9394(82)90197-0 [DOI] [PubMed] [Google Scholar]
- 12.Dorn Lj, Petrinović-Dorešić J. Contrast sensitivity in strabologic functional tests. Acta Clin Croat. 2008;47 Suppl 1:15–9. [cited 2021 November 1] Available at https://hrcak.srce.hr/22759 [Internet] [Google Scholar]
- 13.Lovie-Kitchin JE, Brown B. Repeatability and intercorrelations of standard vision tests as a function of age. Optom Vis Sci. 2000;77(8):412–20. 10.1097/00006324-200008000-00008 [DOI] [PubMed] [Google Scholar]
- 14.Manny RE, Hussein M, Gwiazda J, Marsh-Tootle W, Group CS. Repeatability of ETDRS visual acuity in children. Invest Ophthalmol Vis Sci. 2003;44(8):3294–300. 10.1167/iovs.02-1199 [DOI] [PubMed] [Google Scholar]
- 15.Stewart CE, Hussey A, Davies N, Moseley MJ. Comparison of logMAR ETDRS chart and a new computerised staircased procedure for assessment of the visual acuity of children. Ophthalmic Physiol Opt. 2006;26(6):597–601. 10.1111/j.1475-1313.2006.00407.x [DOI] [PubMed] [Google Scholar]
- 16.Williams MA, Moutray TN, Jackson AJ. Uniformity of visual acuity measures in published studies. Invest Ophthalmol Vis Sci. 2008;49(10):4321–7. 10.1167/iovs.07-0511 [DOI] [PubMed] [Google Scholar]
- 17.Sprague JB, Stock LA, Connett J, Bromberg J. Study of chart designs and optotypes for preschool vision screening – I Comparability of chart designs. J Pediatr Ophthalmol Strabismus. 1989;26(4):189–97. 10.3928/0191-3913-19890701-09 [DOI] [PubMed] [Google Scholar]
- 18.Cataract AD. BMJ. Clin Evid. 2011;2011:0708. [PMC free article] [PubMed] [Google Scholar]
- 19.Thylefors B, Negrel AD, Pararajasegaram R, Dadzie KY. Global data on blindness. Bull World Health Organ. 1995;73(1):115–21. [PMC free article] [PubMed] [Google Scholar]
- 20.Kanski JJ. Clinical Ophthalmology, 5th edn. Oxford: Butterworth-Heinemann; 2003. [Google Scholar]
- 21.Chylack LT, Jr, Wolfe JK, Singer DM, et al. LOCS III cataract grading. Arch Ophthalmol. 1993;111(6):831–6. 10.1001/archopht.1993.01090060119035 [DOI] [PubMed] [Google Scholar]
- 22.Kaiser PK. Prospective evaluation of visual acuity assessment: a comparison of Snellen versus ETDRS in clinical practice (an AOS thesis). Trans Am Ophthalmol Soc. 2009;107:311-24. [PMC free article] [PubMed] [Google Scholar]
- 23.Falkenstein IA, Cochran D, Azen S, et al. Comparison of visual acuity in macular degeneration patients measured with Snellen and early treatment diabetic retinopathy study charts. Ophthalmology. 2008;115(2):319–23. 10.1016/j.ophtha.2007.05.028 [DOI] [PMC free article] [PubMed] [Google Scholar]
- 24.Dehaene S. The neural basis of the Weber-Fechner law: a logarithmic mental number line. Trends Cogn Sci. 2003;7(4):145–7. 10.1016/S1364-6613(03)00055-X [DOI] [PubMed] [Google Scholar]
- 25.Portugal RD, Svaiter BF. Weber-Fechner law and the optimality of the logarithmic scale. Minds Mach. 2011;21(1):73–81. 10.1007/s11023-010-9221-z [DOI] [Google Scholar]
- 26.Stifter E, Sacu S, Benesch T, Weghaupt H. Impairment of visual acuity and reading performance and the relationship with cataract type and density. Invest Ophthalmol Vis Sci. 2005;46(6):2071–5. 10.1167/iovs.04-0890 [DOI] [PubMed] [Google Scholar]
- 27.Chua BE, Mitchell P, Cumming RG. Effects of cataract type and location on visual function: the Blue Mountains Eye Study. Eye (Lond). 2004;18(8):765–72. 10.1038/sj.eye.6701366 [DOI] [PubMed] [Google Scholar]