title: Kappa and Hirschberg ratio measured with an automated video gaze tracker.
abstract: OBJECTIVE
  To develop a fast automated procedure to measure kappa and the Hirschberg ratio for immediate use in a video gaze tracker.
  
  
  METHODS
  Using the hardware platform of the PowerRefractor and a 200 mm lens, the pupil was imaged with a resolution of 57 pixels/mm, at a camera distance of 90 cm. Both the positions of the first Purkinje image and the edges of the pupil were located at 25 Hz sampling rate with subpixel resolution using video image processing software developed under Borland C++. Subjects fixated on a red spot on the left side of the monitor. If their fixation was stable (standard deviation <0.2 degrees in 25 subsequent measurements evaluated in 1 s), the fixation spot appeared automatically on the right side, and the procedure was repeated. Data on the angular position of the optical axis for both targets were stored and provided kappa and the Hirschberg ratio with a standard deviation of about 0.2 degrees or better. This enabled the system to track fixation with a resolution of about 0.2 degrees.
  
  
  RESULTS
  (1) Kappa was +3.91+/-2.73 degrees (right eyes), -3.93+/-2.68 degrees (left eyes, mean +/- SD from 24 young adults). Kappa was highly correlated in both eyes (r = 0.8996), but there were significant asymmetries between both eyes in three subjects (delta up to 3 degrees). (2) The Hirschberg ratios were 12.93+/-1.23 degrees/mm = 22.56 delta/mm (right eyes) and 12.82+/-1.49 degrees/mm = 22.38 delta/mm (left eyes). They were also highly correlated in both eyes (r = 0.931). (3) Neither kappa nor the Hirschberg ratios were correlated to refractive errors (range +0.50 to -7.75 D, mean -1.73+/-2.29 D [spherical equivalents]).
  
  
  CONCLUSIONS
  (1) The video gaze tracker measured fixation with an angular resolution high enough to display the eye position during reading of individual words on the computer screen. (2) The applicable Hirschberg ratio changed with the power of the spectacles of the subjects by about 3% per diopter. (3) In some subjects, there were significant differences in the geometry of both eyeballs, which may be important in the analysis of strabismus. (4) Consistent with the assumption of retinal stretching, the linear distance of the fovea from the optical axis appeared to increase in myopia.
authors.affiliation: Section of Neurobiology of the Eye, University Eye Hospital, Tuebingen, Germany. frank.schaeffel@uni-tuebingen.de
authors.forename: Frank
authors.initials: F
authors.lastname: Schaeffel
mesh_terms: D000328:Adult; D001331:Automation; D005139:Eyeglasses; D005403:Fixation, Ocular; D006801:Humans; D008875:Middle Aged; D011680:Pupil; D012030:Refractive Errors / Q000503:physiopathology; D013690:Television