Method for calculating a customized progressive addition surface; method for manufacturing a progressive addition lens

A computer implemented method for calculating, using a processor, a customized progressive addition surface S′″ of a progressive addition lens (PAL) made of a material having an optical index of n, the method, comprising at least the successive steps of:

• a) providing N initial progressive addition surfaces where N≧1, each initial progressive addition surface, Sk, where 1≦k≦N, being provided with characteristic data comprising:
• Mk points, Pk,i, where 1≦i≦Mk,
• the sphere Sph(Pk,i), the cylinder Cyl(Pk,i) and the axe Axe(Pk,i) at each point Pk,i
• the near vision point Pk,nv, and
• the far vision point Pk,fv,
• and selecting for each initial progressive addition surface Sk a reference point Pk,r among the Mk points Pk,i of each initial progressive addition surface,
• b) calculating, by the processor, N intermediate surfaces S′k by flattening each initial progressive addition surfaces Sk so as to have for each intermediate surface S′k the value of the Sphere Sph(Pk,fv) at the far vision point smaller or equal to 1 diopter and the Sphere Sph(Pk,nv) at the near vision point smaller or equal to 1 diopter,
• c) calculating, by the processor, a transformed intermediate surface S″ by applying
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• where Tpk,r;εk is an isotropic function applied to each point Pk,i of each intermediate surface S′k and αk a coefficient specific to each intermediate surface S′k, each isotropic function Tpk,r;εk is defined by the selected reference point Pk,r of the intermediate surface S′k, and a scaling parameter εk, with εk≠1 when N=1,
• d) calculating, by the processor, the customized progressive addition surface S′″ by cambering the transformed intermediate surface S″ so as to have the desired value of the sphere in at least two points of the customized surface S′″.