The crossed-cylinder aberroscope: an alternative method of calculation of the aberrations

The distorted retinal grid image in the cross-cylinder aberroscope is conventionally analysed using a method based upon orthogonal polynomials. This method restricts the amount of data that can be extracted from the grid image and requires the real grid that is placed between the cross-cylinders to be pre-distorted, with the amount of pre-distortion depending upon the vertex distance. We present an alternative method based upon the minimization of least squares that does not have these restrictions and show that it gives essentially the same results as the original orthogonal polynomial method. Furthermore, the minimization of least squares method also provides a measure of 'goodness' of fit (e.g. the minimum of the sum of the squares of the deviations.