Differential Equation for the Use of the Diffused Ring Photokeratoscope

When a small diaphragm is placed at the back focal plane of the photokeratoscope, a differential equation which can determine the corneal topology in one plane is obtained. The solution of the differential equation results in a more accurate description of corneal topology than previous methods. The solution of the equation requires computer programs. For each keratoscope ring of a variable coordinate a and a fixed coordinate b, a differential equation is obtained. One differential equation characteristic of the corneal surface was sought. For the discret values ai, the polynomial function ai = a (y) was substituted. The numerical precision was demonstrated to be exact enough for practical purposes. Experimental errors had a minor influence on keratogram evaluation. Results were corrected for corneal misalignment. Corrections for defocusing require very precise measurement of the smallest ring image diameter. When the corneal vertex-position was aligned with an accuracy of 0.2 mm, the accuracy of measurement at the corneal periphery was better than 0.02 mm.