Relationship between Surface Sag Error and Optical Power of Progressive Addition Lens

Progressive addition lenses (PAL) have very wide application in the modern glasses market. The unique progressive surface can make a lens have progressive refractive power, which can meet the human eye's different needs for distance-vision and near-vision. According to the national glasses fabrication standard, the difference between actual optical power after fabrication and nominal design value should be less than 0.1D over the lens effective area. The optical power distribution of PAL is determined directly by the surface. Consequently, the surface processing accuracy requirement is proposed. Beginning from the surface expressions of progressive addition lenses, the relationship equations between the surface sag and optical power distribution are derived. They are demonstrated through tolerance analysis and test of an example progressive addition lens with addition of 2.09D (5.46D-7.55D). The example addition surface is fabricated under given accuracy by a single-point diamond ultra-precision machine. The optical power of the PAL example is tested with a focal-meter after fabrication. The optical power addition difference between test result and design nominal value is 0.09D, which is less than 0.1D. The derived relationship between the surface error and optical power is verified from the PAL example simulation and test result. It can provide theoretical tolerance analysis proof for the PAL surface fabricating process.