Higher-order wavefront correction

With completely custom lens surfaces comes the opportunity to try and address higher order aberrations. The changing gaze angle of the eye during normal vision makes correction difficult in general use. However, researchers have claimed some improvements in vision using aspheric designs. Further, vision is a very active process, wherein eye movements  are undertaken to improve understanding of the current scene. This suggests that the eye might discover and utilize a special high-order correction zone.

FormuLens provides the ability to incorporate various types of high-order corrections in freeform lenses.




Progressive Addition Lens Anatomy

With digital lens surfacing (a.k.a freeform) one or both surfaces of a lens can be completely specified by the Lens Design System (LDS). For example the LDS can provide a height map, giving points on a grid of some chosen spacing. This surface will be produced with very high accuracy by the generator.

The optical performance of a freeform lens when used in spectacles, is difficult to predict. Either the lens must be manufactured and analyzed with a complex apparatus that can measure optical properties for a range of realistic view directions, or the lens must be simulated computationally using sophisticated ray-tracing algorithms.


Fast & Robust Wavefront Sensing

Rapidly rising levels of myopia, particularly in the developing world, have led to an increased need for inexpensive and automated approaches to optometry. A simple and robust technique is provided for estimating major ophthalmic aberrations using a gradient-based wavefront sensor. The approach is based on the use of numerical calculations to produce diverse combinations of phase components, followed by Fourier transforms to calculate the coefficients. The approach does not utilize phase unwrapping nor iterative solution of inverse problems. This makes the method very fast and tolerant to image artifacts, which do not need to be detected and masked or interpolated as is needed in other techniques. These features make it a promising algorithm on which to base low-cost devices for applications that may have limited access to expert maintenance and operation.

Dillon K; “Fast and robust estimation of ophthalmic wavefront aberrations“. J. Biomed. Opt. 0001;21(12):121511.  doi:10.1117/1.JBO.21.12.121511. (pdf)


Custom Generic Progressive Lens

The FormuLens Custom Generic PAL (Progressive Addition Lens) is a single product which can be adjusted through a wide range of performance requirements. With adjustable fitting heights from 12 to 22 mm, and “hardness” ranging between the extremes offered by designs from major vendors, and everything in between. The design is optimized computationally using our lens design system SimPAL for a dense grid of setting combinations.



SimuLens performs a realistic simulation of a spectacle lens in use. The lens is to be described by arbitrary sets of points describing the front and back surfaces (e.g. generator points-files), and a refractive index. The eye position relative to the points is computed based on fitting parameters.


Zernike Polynomials

Truncated expansions such as Zernike polynomials provide a powerful approach for describing wavefront data. However, many simple calculations with data in this form can require significant computational effort. Important examples include recentering, renormalizing, and translating the wavefront data. This paper describes a technique whereby these operations and many others can be performed with a simple matrix approach using monomials. The technique may be applied to other expansions by reordering the data and applying transformations. The key is the use of the vectorization operator to convert data between vector and matrix descriptions. With this conversion, one-dimensional polynomial techniques may be employed to perform separable operations. Examples are also given for differentiation and integration of wavefronts.

Keith Dillon, “Bilinear wavefront transformation,” J. Opt. Soc. Am. A 26, 1839-1846 (2009) (pdf)