Refraction Holodiagrams

Holodiagrams using Mahalanobis distance

“…If the correlation coefficients r are both zero and, if both variances are equal in the first point and also equal in the second (but eventually a different value), then the MHD are Cartesian ovals of the egg and apple types and correspond to the surfaces that conjugate one point into the other by refraction between two media [3,4] and rays from one source obey Snell's Law in each point of the HD. In the case of the MHD then the relative refractive index can be obtained from the values of the corresponding variances s.…”

“…The concept soon proved to encompass several other optical phenomena and some generalizations have been proposed that involve the solutions of reflection and refraction in arbitrary surfaces [2][3][4][5][6][7], both for isotropic and birefringent materials.…”

Refracting profiles and generalized holodiagrams

“…Using the profiles R a we can construct generalizations of both kinds of refraction holodiagrams: one when both source and image are real (8), and the other when the source is virtual (or the image is virtual) (9). The sheets R a 2 correspond to generalizations of the first case and the sheets R a 1 to the second.…”

A method to construct refracting profiles

“…See [2] for a detailed study of these ovals. Reference [3] contains some applications of these ovals to holography. A complete Cartesian oval is symmetric with respect to the straight line determined by the foci F 1 and F 2 .…”