' s ▁area , ▁although ▁recently ▁that ▁has ▁been ▁taken ▁to ▁mean ▁the ▁area ▁in ▁the ▁horizontal ▁plane , ▁around ▁the ▁Vi eth - M üller ▁circle , ▁where ▁any ▁point ▁appears ▁single . ▁ ▁These ▁early ▁empir ical ▁investig ations ▁used ▁the ▁criter ion ▁of ▁sing len ess ▁of ▁vision , ▁or ▁absence ▁of ▁dip lop ia ▁to ▁determine ▁the ▁hor opter . ▁Today ▁the ▁hor opter ▁is ▁usually ▁defined ▁by ▁the ▁criter ion ▁of ▁identical ▁visual ▁directions ▁( similar ▁in ▁principle ▁to ▁the ▁apparent ▁motion ▁hor opter , ▁according ▁that ▁identical ▁visual ▁directions ▁cause ▁no ▁apparent ▁motion ). ▁Other ▁criteria ▁used ▁over ▁the ▁years ▁include ▁the ▁apparent ▁fr onto - parallel ▁plane ▁hor opter , ▁the ▁equ i - distance ▁hor opter , ▁the ▁drop - test ▁hor opter ▁or ▁the ▁pl umb - line ▁hor opter . ▁Although ▁these ▁various ▁hor op ters ▁are ▁measured ▁using ▁different ▁techniques ▁and ▁have ▁different ▁theoretical ▁motiv ations , ▁the ▁shape ▁of ▁the ▁hor opter ▁remains ▁identical ▁regardless ▁of ▁the ▁criter ion ▁used ▁for ▁its ▁determ ination . ▁ ▁Cons ist ently , ▁the ▁shape ▁of ▁the ▁empir ical ▁hor opter ▁have ▁been ▁found ▁to ▁devi ate ▁from ▁the ▁geomet rical ▁hor opter . ▁For ▁the ▁horizontal ▁hor opter ▁this ▁is ▁called ▁the ▁Her ing - H ille brand ▁deviation . ▁The ▁empir ical ▁hor opter ▁is ▁fl atter ▁than ▁predicted ▁from ▁geometry ▁at ▁short ▁fix ation ▁distances ▁and ▁becomes ▁convex ▁for ▁farther ▁fix ation ▁distances . ▁Moreover ▁the ▁vertical ▁hor opter ▁have ▁been