PROGRESSIVE POWERED LENSES - THE MINKWITZ THEOREM

James Sheedy

Abstract

PURPOSE: The Minkwitz Theorem (MT) states that astigmatism perpendicular to the power vertex line changes twice as quickly as the rate of change of power along the vertex line. Our objective is to test the validity of this theorem as it applies to astigmatism-limited zone widths of progressive addition lenses (PALs).

METHODS: The MT can be derived using a theoretical lens with constant rate of power change, resulting in horizontal spherical equivalent power contours and vertical astigmatism power contours. Most current PAL designs are more complex. Hoya Tact (an occupational progressive) has a relatively large central region with constant zone width and is closest to meeting these criteria. Our primary investigation of the astigmatism/power rate relationship used Hoya Tact lenses (adds of 1.00-2.50 D in 0.25 D steps); other PALs were used for subsequent analysis. Lenses were measured with a Rotlex Class Plus lens analyzer that calibrated accurately to Humphrey Lensmeter measurements in peripheral areas of PALs.

RESULTS: Although we hypothesized that the MT would apply in the constant zone width region of Tact lenses, zone widths in that region exceeded those predicted by MT. Above and below this region zone widths were narrower than predicted. When averaged along the entire corridor, zone widths approximated the MT. A polynomial equation was developed (r2=0.98) to describe the zone width as a function of power rate and magnitude of astigmatism in the middle region of Tact lenses. For other PALs the measured zone widths exceed MT in the top (distance) and middle (intermediate) corridor but fall short in the lower (near) corridor. Likewise, on average along the entire corridor, they approximate the MT. The polynomial equation developed with Tact lenses approximates the best zone width attained in the middle portion (intermediate) of other tested PAL designs.

CONCLUSIONS: Zone widths can deviate considerably from the MT at locations along the corridor, but average zone width along the entire corridor approximates MT.

Details

Year: 2004

Program Number: n/a

Resource Type: Scientific Program

Author Affiliation: The Ohio State University, College of Optometry

Co-Authors: Ewen King-Smith, John R. Hayes

Co-Author Affiliation: The Ohio State University, College of Optometry, The Ohio State University, College of Optometry

Room: n/a