A new digitised screen test for strabismus measurement

Abstract

Purpose: Our study presents a digitised tangent screen test for ocular motility analysis according to the Harms and Hess tests (measurement of the squint angle in all fields of vision). This test uses an image beamer to display the tangent screen, a position sensor to measure the patient's head orientation, and a distance sensor to measure the fixation distance. Digital measurement of head orientation allows for a test procedure that eliminates the conventional requirement for a light pointer in the patient's hand. Thus, the digital screen test is presented, and the uncertainty of the measurement system is evaluated.

Methods: A mathematical relationship was given between the measured squint angles, as well as the angle of diagnostic gaze direction, and the influence quantities on their measurement uncertainty. The individual uncertainties resulted from deviations in the measured values by the position and distance sensors, the calibration of the projection image of the beamer in length units, and the finite image resolution of the beamer. The individual standard uncertainties of the influence quantities were determined. The combined standard measurement uncertainties of the squint and gaze direction angles were given based on the model equation of the error propagation law at the tangent table according to Harms at a test distance of 2.5 m. The patient's uncertainty contribution to the mobility analysis was not considered.

Results: The combined standard uncertainty of the measurement system (coverage factor k = 2 for 95% confidence level) for the squint angle is ≤ 0.43° for the angle of diagnostic gaze direction ≤ 3.13° at the test distance of 2.5 m. The individual standard uncertainties of the influence quantities on the angles are (k = 1): 1.55°/1.01° (horizontal/vertical angle of the position sensor), 0.19° (distance sensor), 0.06° (calibration of the projection image of the beamer), and 0.02° (image resolution of the beamer). The maximum valid test distance of the digital screen test is 3.8 m.

Conclusion: The digital screen test is compact and can be used at different locations. Compared to the traditional test, the time required for examination via the digitised test is less; additionally, its documentation is simplified. The measurement uncertainty of the diagnostic gaze direction angle is dominated by the sensor drift of the position sensor in the horizontal direction (yaw angle) and is due to the sensor technology. However, this drift error does not affect the squint angle measurement result nor its measurement uncertainty because the measurement principle used here is based on the congruence between the position cross and the fixation object and the confusion principle and compensates for the drift error. The measurement uncertainties of the determined measurement system are the lower limits of the uncertainties in the clinical use of the digital screen test if there are no effects due to significant patient deviations.

Keywords: Digital tangent screen test; Measurement uncertainty; Ocular motility analysis; Strabismus.

Figure 1

Digital screen test in motility analysis according to Harms (here, using a dummy head and camera tripod with swivel joint for measurement uncertainty analysis). A beamer projects the tangent grid on the wall. The patient fixes with the left eye (red glass) the centre of the chart (red square). The right eye to be examined sees only the position cross (blue cross) with the given gaze direction and head orientation. The small picture shows the glasses with the colour filters and the measuring unit with the controller, position sensor and distance sensor attached to their frame. The diode laser is used to analyse the measurement accuracy of the position sensor and is not part of the digital screen test.

Figure 2

Horizontal (yaw) and vertical (pitch) angular deviations of the position sensor BNO055 in 9 directions of gaze (N = 21). The measurement starts with the central (0°/0°), then with the primary (15°/0°) direction of gaze and continues counterclockwise. The values in brackets indicate the horizontal/vertical standard uncertainty.

Figure 3

Measured distances and their repeatability (N = 18) of the VL53L1X sensor. With the error limit of 37 mm, the valid distance range is 0.4 m–3.8 m.