A comparison of stereopsis testing between red/green targets and polarized targets in children with normal binocular vision

Article Outline

• Abstract
• Methods
  • Subjects
  • Stereopsis testing protocol
    • The Random Dot Letter “E”/The RDE Stereotest
    • Random Dot Butterfly/Stereo Butterfly test
    • Stereo Numbers
    • Stereo Circles/Wirt Circles
    • Stereo Animals
  • Statistical methods
• Results
  • Stereo Circles/Wirt Circles
  • Stereo Numbers
  • Stereo Animals
  • The Random Dot Letter “E”/The RDE Stereotest
  • Random Dot Butterfly/Stereo Butterfly test
• Discussion
• Acknowledgments
• References
• Copyright

Abstract 

Background

Measurement of stereopsis is important in assessing a patient’s binocular status. Several measurement methods are available, most commonly using polarized targets. Recently, less expensive red/green targets have become available. In this study, we compare polarized versus red/green methods, using random dot and contour targets.

Methods

Sixty children with no strabismus, amblyopia, or high refractive error and normal ocular health were recruited. Stereopsis measurements were taken using the red/green and polarized versions of the Random Dot Letter “E”/RDE Test, Random Dot Butterfly/Stereo Butterfly Test, Stereo Circles/Wirt Circles, Stereo Numbers, and Stereo Animals tests. Observed agreement was used to assess agreement between results. Wilcoxon signed-rank tests were used to compare an individual’s response with both targets.

Results

There was greater than 95% agreement using any of the Random Dot–based tests and the Stereo Animals tests. However, agreement was less than 60% with the Stereo Numbers test and less than 35% with the Stereo Circles/Wirt Circles test.

Conclusion

The red/green versions of the Random Dot–based tests and the Stereo Animals test appear to be a cost-effective alternative to their polarized equivalents. Our data, however, show that the red/green versions tend to underestimate the level of stereopsis when using the Stereo Numbers and Stereo Circles/Wirt Circles tests compared to their polarized equivalents.

Keywords: Stereopsis, Depth perception, Anaglyph testing, Polarization

Stereopsis is a sensitive measure of binocular function and is an important prognostic indicator in the assessment and management of patients with strabismus.¹, ² The traditional evaluation of stereopsis includes measurement by stimulation of retinal disparity using polarized targets and polarized glasses. Targets not requiring the use of any glasses have also been developed, and stereopsis measurements with these targets have been shown to correlate well with those requiring polarized glasses.³ Another format for measuring stereopsis involves the use of red/green cancellation to induce exclusive, disparate images to the right and left eyes. This red/green testing often is referred to as anaglyph testing. These targets have been developed so that target properties, such as disparity, shape, and size, are similar to those found in the polarized equivalents. To our knowledge, there has been no formal study comparing measurement of stereopsis using red/green to traditional polarized stereo targets.

The main disadvantages of the use of polarized stereopsis instruments are cost and reports that use of polarized targets in conjunction with plastic prisms may yield false measurements.⁴ Prism is used clinically to neutralize the angle of deviation in patients with strabismus to determine if a patient appreciates stereopsis under conditions of bifoveal stimulation. Using red/green targets could eliminate this potential measurement error. However, for the red/green targets to be clinically useful, stereopsis measurements obtained with red/green targets need to correlate well with those obtained with polarized equivalents.

This study was designed to determine if there is a difference in stereopsis measurements obtained using red/green versus traditional polarized targets in children with normal binocular vision.

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Methods 

Subjects 

The protocol and informed consent forms were approved by the Pennsylvania College of Optometry’s institutional review board. The parent or guardian of each study subject gave written informed consent, and the child gave written assent, as required. The primary source of subjects was internal referrals from The Eye Institute of the Pennsylvania College of Optometry, and as such, eligibility testing was performed by interns with supervision by faculty of the Pediatric Service. Eligibility criteria are listed in Table 1.

Table 1. Eligibility and exclusion criteria

D = diopter.

To determine the sample size, we performed calculations using the Power Analysis and Sample Size 2002 software⁵ (NCSS, Kaysville, Utah) with α = 0.05. Data from a similar study performed by Hatch and Richman³ were used to obtain preliminary data estimates. In the Hatch and Richman study, the correlation between stereopsis measurements obtained using different stereoacuity test procedures exceeded 0.95. We determined that to achieve 80% power to detect a reduction in the correlation from 0.95 to 0.90, a minimum of 51 subjects was required.

Eligibility testing included measuring best-corrected visual acuity (distance and near) and performing a subjective refraction and a cover test at far and near. If the refraction indicated the need for correction, all testing was performed through the appropriate eyeglass prescription. Eligibility criteria for the trial included children ages 6 years to 14 years inclusive, with at least 20/25 best-corrected visual acuity in each eye, no strabismus, and normal ocular health.

Stereopsis testing protocol 

Stereopsis was measured using red/green targets and polarized targets. Tests were administered in accordance with the manufacturer’s recommendations at a distance of 40 cm, with room lights on. The same examiner performed all testing. The specific tests administered are listed in Table 2.

Table 2. Testing materials

A coin-flip determined if the red/green or polarized testing format was to be performed first to distribute any learning effects equally among both groups. The tests were then administered again using the alternative format. The red/green format was performed first 27 times and the polarized format 33 times. The subjects were not under any time constraints in their identification of stereopsis targets. Red/green or polarized glasses were used as appropriate for each test.

For this test, the subject was presented with 2 cards, 1 with an “E” hidden within a random dot pattern and another with only scattered random dots. The letter “E” disparity is 600 seconds of arc (″) at the testing distance of 40 cm for both red/green and polarized targets. The subject was instructed to identify the card that contained the letter “E.” The cards were shuffled behind the examiner’s back and the cards were re-presented to the subject. The subject was again instructed to identify the card with the “E.” This was repeated 4 times, and the number correctly identified was recorded. Credit was given only if the subject correctly identified the figure “E” 4 times, to be reasonably confident that correct answers were not obtained by guessing.

The subject was asked to identify the picture and was given credit for either a verbal report that the picture was a butterfly or for tracing the pattern of the insect. The subject’s response was recorded as correct or incorrect. At 40 cm, the disparity of the butterfly ranges from 2,000″ at the top of the wing to 1,150″ at the bottom of the wing. The disparity at the body is 700″.

The subject was asked to identify or point to the circled number that was floating off the page. This test has 6 sets with 6 circled numbers to choose from in each set, 1 of which appears to be floating off the page (a 6-alternative forced choice test). The stereo disparities are 526″, 226″, 128″, 66″, 41″ and 28″. The measurement recorded was the last correct response before 2 consecutive errors were made.

The subject was asked to identify or point to the circle that was floating off the page. This test has 9 sets, with 4 circles to choose from in each set, 1 of which appears to be floating off the page (a 4-alternative forced choice test). The stereo disparities are 800″, 400″, 200″, 140″, 100″, 80″, 60″, 50″ and 40″. The measurement recorded was the last correct response before 2 consecutive errors were made.

The subject was asked to identify or point to the animal that was floating off the page. This test has 3 sets, with 5 animal figures to choose from in each set, 1 of which appears to be floating off the page. The stereo disparities are 400″, 200″, and 100″. The measurement recorded was the last correct response.

Statistical methods 

Observed agreement was calculated for the comparison between polarized and red/green stereopsis testing. This is the percentage of observations for which the 2 testing procedures give the same response and was calculated in 2 ways. One, the observed agreement was calculated to determine general agreement between testing methods. In other words, what was the overall level of observed agreement for a given test? Two, the observed agreement was calculated for each level of stereo disparity for the Stereo Circles/Wirt Circles, Stereo Numbers, and Stereo Animals tests. In this way, stereo disparities in which agreement is good and those in which agreement is poor are identified. Although observed agreement is easy to calculate and understand, it does suffer from at least 1 drawback in that a certain percentage of the observed agreement occurs purely by chance. For each measure of agreement, its 95% confidence interval (CI) is also reported.

For Stereo Circles/Wirt Circles, Stereo Numbers, and Stereo Animals tests, a Wilcoxon signed-rank test was also used to compare the results obtained from the 2 testing methods. A significant finding would indicate that the 2 methods (red/green and polarized methods), on average, produce different responses.

Correlation coefficients have been used to quantify agreement between tests in many published reports. Although correlations do describe the strength of the linear relationship between test results, they should not be used to quantify agreement. As such, no correlation coefficients are reported.

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Results 

A total of 60 subjects, 6 years to 14 years of age were recruited. The mean age of the subjects was 9.6 years (standard deviation = 2.0), and 63% were girls.

Stereo Circles/Wirt Circles 

There was a much larger range of results when the Stereo Circles/Wirt Circles test was performed with red/green glasses (range 40″ to 400″) than with polarized glasses (range 40″ to 80″). For example, although 48 of 60 subjects achieved 40″ of stereoacuity when performing the test with polarized glasses, only 16 of 60 achieved 40″ of stereoacuity when using red/green glasses (see Table 3). This low level of agreement was consistent across response outcomes with observed agreement ranging from 0.406 to 0.089 (see Table 4). This result is confirmed by the Wilcoxon signed-rank test, which also showed a statistically significant difference between the results obtained using the 2 different glasses (P < 0.001). With the polarized targets, 55 of 60 subjects (92%) achieved 60″ of stereoacuity or better, whereas with the red/green glasses only 40 of 60 (67%) achieved this level.

Table 3. Stereo Circles/Wirt Circles

Note: Numbers in table indicate number of subjects. For instance, 14 indicates that there were 14 subjects who achieved 40″ with both polarized and red/green formats of this test.

Table 4. Observed and specific agreement between red/green versus polarized targets for Stereo Circles/Wirt Circles

	Estimate	95% CI
Overall observed agreement:	0.317	0.199,0.434
Observed agreement at:
40″	0.406	0.282,0.530
50″	0.089	0.017,0.161
60″	0
80″	0.128	0.043,0.212
100″	0
140″	0
200″	0
400″	0

Note: Agreement is a percentage for which the 2 testing procedures give the same response. The number 0.000 indicates 0% agreement, and 1.000 indicates 100% agreement between polarized and red/green formats. For example, 31.7% of subjects achieved the same stereoscopic result on the Stereo Circles/Wirt Circles test between the polarized and red/green formats.

Stereo Numbers 

There was low agreement between the 2 test conditions (see Table 5). For example, although 50 of 60 subjects scored 28″ when performing the test with polarized glasses, only 34 of 60 also scored 28″ when using red/green glasses. This is confirmed with the low overall observed agreement (0.567, 95% CI 0.441, 0.692). Interestingly, for the response outcome at 28″, there was considerably better observed agreement between the 2 testing methods (0.698, 95% CI 0.581, 0.814) and the overall low observed agreement is driven by the poor observed agreements at outcomes 41″ (0.235, 95% CI 0.128, 0.342) and 66″ (0). The Wilcoxon signed-rank test also indicates that the 2 testing methods give different results (P = 0.002).

Table 5. Stereo Numbers

Note: Numbers in table indicate number of subjects. For instance, 50 of 60 subjects achieved 28″ with the polarized format of the Stereo Numbers test, whereas only 34 of 60 subjects achieved the same level with the red/green format of the same test.

Stereo Animals 

For this test, there was good agreement between the 2 formats. Fifty-seven of the 58 subjects who scored 100″ using red/green glasses also scored 100″ when using polarized glasses. This is confirmed by the overall observed agreement estimate of 0.950 (95% CI 0.895, 1.000) and the observed agreement at outcome 100″ (0.974, 95% CI 0.934, 1.000). Agreement was also indicated by the Wilcoxon signed-rank test, which showed no difference between the outcomes obtained via the 2 methods (P = 0.50).

The Random Dot Letter “E”/The RDE Stereotest 

As with the Stereo Animals test, there appears to be good agreement in the results obtained between the 2 formats. Fifty-nine of the 60 subjects who correctly identified the “E” using red/green glasses in 4 of 4 trials also identified them when using polarized glasses. The Wilcoxon signed-rank test indicates good agreement between the 2 glasses (P = 0.99).

Random Dot Butterfly/Stereo Butterfly test 

For this particular test, all subjects were able to identify the butterfly within the random dot pattern regardless of glasses used. As such, no statistics are reported.

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Discussion 

Stereoacuity testing results were very similar for the Random Dot Letter “E”/RDE Stereotest, the Random Dot Butterfly/Stereo Butterfly test, and Stereo Animals tests between the polarized and red/green testing format. However, for the Stereo Circles/Wirt Circles and Stereo Numbers tests, there was low agreement between the polarized and red/green formats; subjects scored poorer on the red/green version of each test compared with the polarized equivalents. For example, 90% of the subjects scored 50″ or better when tested with the Wirt circles using polarized targets, but only 52% scored this well when the red/green target version was used. Whereas luminous transmittance and contrast between the right and left sides are identical for the polarized format, investigators have found that these properties may differ significantly between the red and green filters for those that undergo anaglyph testing.⁶ Such differences in contrast and luminous transmittance between the 2 eyes during testing may affect suppression tendencies and may explain the overall decreased stereopsis found in this study.

The assessment of stereopsis is important for at least 2 reasons. One important use of stereopsis data is to determine the presence of strabismus. Investigators have found that the presence of random dot stereopsis can be used to help rule out constant strabismus.⁷ Conceptually, the ability to identify random dot stereopsis figures requires bifoveal fixation and therefore alignment at least during the administration of the stereopsis test.⁸ This determination is a critical element of the examination of strabismic patients because the treatment and prognosis differ significantly if the patient does not have a constant strabismus. In rare instances, a patient may appreciate random dot stereopsis despite having microstrabismus or small-angle esotropia, as described in a case study by Garcia and Richman.⁹ The results of our study suggest that either red/green or polarized targets should yield similar results for the purpose of helping to rule out constant strabismus. False positives, that is, patients who are identified as having strabismus (cannot see the random dot pattern, butterfly or “E”) even though they are capable of alignment, should be low based on our data.

We have not included subjects with strabismus in this study; therefore, we cannot state with absolute certainty that the red/green method will identify those patients with strabismus equally as with the polarized method. Identification rates for true positives (patients with strabismus who do not see the random dot pattern) are, therefore, not known. The false-negative rate (patients who see the random dot pattern even though they have strabismus) is also unknown for the same reason.

Another important clinical reason for the assessment of stereopsis is to follow the progress of patients being treated for binocular vision disorders using lenses, prism, and vision therapy. For this purpose, the ability to quantify the level of stereopsis is important. Improved stereopsis after treatment suggests a possible decrease in suppression, increased fusional vergence ranges, and more stable alignment.¹⁰, ¹¹ In this study, of the tests that are able to quantify stereopsis, Stereo Numbers or Stereo Circles/Wirt Circles, we found a low level of agreement between the red/green and polarized testing methods. Our data suggest that the polarized tests may be more useful for the clinical objective of quantifying the level of stereopsis and change in stereopsis.

The red/green method yields results comparable to the polarized equivalent, especially for testing the presence of random dot or global stereopsis in patients. The red/green version of the Random Dot Butterfly/Butterfly Stereopsis Test and the Random Dot Letter “E”/RDE tests offer a cost-effective alternative for clinicians when attempting to rule out the presence of constant strabismus. For measuring the level of contour stereopsis, our data suggest lower agreement between red/green and polarized methods. Therefore, if the objective is to quantify improvement of contour stereopsis after treatment, polarized versions of stereopsis tests may be more useful.

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Acknowledgments 

Stereo Butterfly Test, Wirt Circles, Stereo Animals, Stereo Numbers, The RDE Stereotest are available from Bernell VTP, 4016 N. Home Street, Mishawaka, Indiana 46545. Red/Green Stereo Vision Tests are available from Synthetic Optics, 747 Butternut Drive, Franklin Lakes, New Jersey 07417. Red/Green Stereo testing materials were provided by Synthetic Optics as a donation to The Eye Institute of the Pennsylvania College of Optometry. The investigators have no financial interest in either company.

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