The geometrical center of the pupil has often been used as the reference axis in ocular wave-front aberration measurement. However, the geometrical center of the pupil may shift when the pupil size changes under different conditions. In particular, for subjective methods, defining the center of the pupil precisely during the actual measurement is not always practical. Furthermore, the geometrical center of the pupil may not define the chief ray of the ocular optics because of the Stiles-Crawford apodization effect, which has a peak location that often deviates from the geometrical center of the pupil. We present the coefficient transformation table of the Taylor polynomial up to the sixth order with respect to reference axis shift. We illustrate the effect of wave-front aberration change with reference axis shift with experimental data. This type of wave-front aberration change could be a true measurement error if there is an error in defining the reference axis. We also propose using the coaxially sighted corneal reflex as a better reference axis in aberration measurement.
A general color difference formula has been derived based on the parameters of color discrimination ellipsoids in the CIE 1976 L*a*b* color space. By using different orders of approximation, the general formula resembles the basic forms of the current formulae. The method described in this article suggests a framework for modifying the CIE 1976 L*a*b* color difference formula.
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