These early empirical investigations used the criterion of singleness of vision, or absence of diplopia to determine the horopter. Today the horopter is usually defined by the criterion of "identical visual directions" (similar in principle to the "apparent motion horopter", according that identical visual directions cause no apparent motion). Other criteria used over the years include the "apparent fronto-parallel plane horopter", the "equi-distance horopter", the "drop-test horopter" or the "plumb-line horopter". Although these various horopters are measured using different techniques and have different theoretical motivations, the shape of the horopter remains identical regardless of the criterion used for its determination.