intro

Progressive addition lenses (PALs) are used to provide eyeglass wearers with a spectacle lens in which optical power varies smoothly as the user looks through different regions of the lens. For example, when looking straight ahead there may be little added power, and when looking down at some angle there may be significant power. This means the same eyeglass can be used for both driving and reading.

PALs are a specific example of the more general case of free-form optics. In free-form optical design, the shape of an optical surface is not constrained to a simple expression like a conic asphere or even asphere, but is allowed to take any shape necessary to provide the optical performance needed. A free-form optic can add optical power wherever it is needed in order to provide the required correction.

Free-from optics therefore require different analysis and optimization techniques compared to classical lenses. For example, OPD and ray fans may not be so useful when power can vary across a surface in an arbitrary manner. This article describes a very simple PAL lens, and shows how to construct such systems, analyze their performance and optimize them.

Surface Types

An ideal free-form optical surface would simply be a set of data points. However, in order to be able to optimize such a surface, there must be some method to perturb the free-from surface so as to evaluate how to add or subtract power appropriately. Therefore, purely data-based surfaces, like the Grid Sag surfaces or imported CAD objects may be useful for characterizing system performance, but are not so useful for the initial design stage, which is when we want to be able to change the surface smoothly under the control of the optimizer.

The surface types most useful for initial design include:

• Cubic Spline and Extended Cubic Spline
• Radial and Toroidal NURBS
• Polynomial and Extended Polynomial
• Zernike Sag
  
  

The correction lens is made of Polycarbonate and has an Extended Polynomial front surface and a Standard rear surface.

So it has a base conic asphere (standard) surface sag upon which the polynomial terms are added. The base standard surface is very helpful, as paraxial rays can interact with it and so paraxial concepts like EFFL are still useful.

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Analyzing the Surface

The Shaded Model of the lens shows that the surface sag is very complex. The lens tends to "run away" at the edges where there are no rays to provide control. This is typical of free-form design: either a ray or some other form of constraint needs to be applied over the whole surface to prevent unrealistic sags from being produced.

The power or focal length is determined for the optical system as a whole up to and including refraction from any surface. The method used is to trace a ring of real rays around the entrance pupil at each point in the field.

In the general case, the focal length is a function of orientation in the entrance pupil. By tracing a ring of rays, the average, maximum, and minimum optical power or focal length around the pupil can be determined. The feature can display:

• spherical power
• cylinder power
• maximum and minimum power
• tangential and sagittal power
• x or y direction optical power
  
  

in diopters. Additionally it can display the same data as effective focal length (EFL) in lens units.

These plots are extremely useful in understanding how power is distributed over a freeform surface.

In addition the POWF optimization operand allows direct optimization of any of the terms computed by the Power Field Map at any point. This is vital when a known desired power map is required on a surface.

Summary

Designing freeform or progressive lenses is in principle no different to optimizing traditional surfaces. However, because power can be added or subtracted easily at any point on the freeform surface, additional analysis plots an optimization controls are needed. The Power Field Map and POWF operand give designers of freeform optics this control.

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