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This article describes the principles of ophthalmic lens design, and discusses the parameters of the lens, the eye and the visual environment that are critical to the lens design. A glass catalog for common ophthalmic lens materials (both glasses and polymers) is included. The article does not include progressive lens design, although progressive lenses tend to follow the general base curve principles of other ophthalmic lenses, nor does it consider specific purpose lenses such as those intended to reduce the progression of myopia.
Authored By Rod Watkins - Director of Strategic Development Optometry and Vision Science, Flinders University
Introduction
Historically, ophthalmic lens design involves solely controlling primary oblique astigmatism. It was generally accepted that spherical aberration and coma were of lesser importance due to the relatively small pupil size and because coma increases linearly with field angle while astigmaticsm increases quadratically. Similarly, other aberrations could be ignored since they were not characteristic of the given system type.
However, the advent of freeform manufacturing technology has allowed lens makers to break away from these restrictive assumptions. Coupled with OpticStudio's ability to model a large range of system and image parameters, ophthalmic lens design may be approached in a different manner, as shown in this article.
The Conventional Approach
A myopic eye has a “far point” at a distance in front of the eye that corresponds to the furthest point that can be seen clearly, since more distant points will be imaged in front of the retina. As the eye rotates, the far point remains at a constant distance from the eye and falls on the “far point sphere”. The far point is the optical conjugate of the retina, so the function of an ophthalmic lens is to form an image on the far point sphere. The aperture is the pupil of the eye, and since the eye rotates the aperture is referred to the eye’s centre of rotation. The object plane is normally taken to be at infinity, although a near object plane can result in a substantially different lens design.
The example below shows the principle. Light from infinity is diverged by a -3.00D lens and forms a virtual image on the far point sphere a third of a metre from the back vertex of the lens. Light passes through the pupil regardless of the angle of rotation. In this case, field angles of 15° and 30° are shown, although many spectacle frames allow for rotation of 50° or more. Note that this approach is independent of the optical system of the eye, apart from the pupil size, and does not consider a non-rotating eye.
For a hyperopic eye, the far point sphere is formed behind the eye.
At first glance, the design of an ophthalmic lens in OpticStudio is the ultimate in simplicity. The back vertex power can be entered directly as a surface solve on the back surface and there is only one variable, the front surface radius or base curve. The Lens Data Editor for the -3.00D example above is shown here. (The back vertex power is -0.003mm-1.) The material CR-39 is from the glass catalog OPHTHALMIC which is included here. It differs slightly from the material CR39 in the MISC catalog - see Glass Catalog below.
The issue for lens designers, however, is that the base curve that provides the best image quality depends critically on the choice of some parameters for the eye and the visual environment. In teaching optometry students at Flinders University in Australia the principles of ophthalmic lens optics we ask them whether they believe it is possible, using OpticStudio, to design a unique lens series for use at night, for rifle shooting, for desk work or for children. They are also asked to assess the value of aspheric lens surfaces and wavefront image criteria.
Lens Form Parameters
The historical design approach of minimizing Seidel oblique astigmatism can be modelled in OpticStudio by adding the operand ASTI to the merit function with a target of zero and a high weighting, and using a single wavelength. The approach of minimizing the size of the circle of least confusion on the far point sphere can also be closely approximated by using the OpticStudio default merit function and the spot radius criterion.
In the example above of a -3.00D lens with field angles of 0° and 30° OpticStudio finds the base curve to be +4.50D. This produces a conventional ophthalmic meniscus lens with a base curve close to that commonly used. However, arriving at this result depends on the process used to reach it. It depends on the incident wavefront being planar, on the choice of field angles and their weighting, on the distance chosen from the lens to the centre of rotation of the eye, on the decision to ignore some aberrations (particularly distortion) and so on.
Contrary to common belief, the accepted approach does not provide a basis for a so-called “best form” or “corrected curve” lens series in which a relatively few base curves are meant to provide good aberration correction for all lens powers. The lens form for optimum image quality may be greatly different for different wearers and for different visual environments. For example, a lens that is designed for on-axis vision (a single field angle of 00) and photopic wavelengths has a negative base curve of about -5.50D.
Conversely, a lens that is used for reading may have a much higher front surface power. OpticStudio shows that the optimized lens for a -5.50D myope who is also presbyopic and wears a -3.00D lens for reading at 40cm has a base curve of +28D.
Any attempt to manage distortion in the image also results in a very steep base curve.
Clearly, to make all lenses of a given power to a single base curve regardless of the parameters of the wearer or the application does not provide optimum image quality for many people. The issues for lens designers and manufacturers are whether it is commercially practical to vary the base curve within the limits of cost and cosmetic factors and, even when all of the important design parameters are taken into account, whether the improvement in image quality translates into an improvement in visual acuity.
Materials Catalog
The materials catalog file OPHTHALMIC.AGF for common ophthalmic lens materials is included here. For use, the file must be copied to the OpticStudio materials catalog folder. To find the folder location go to Setup | Project Preferences | Folders | Glass and copy to the folder GLASSCAT. After copying, the Libraries | Materials Catalog window should verify that OpticStudio can see the catalog OPHTHALMIC.
The glass materials data (Corning_1.523, Corning_1.6, Corning_1.7, Corning_1.8 and Corning_1.9) are taken from data sheets provided by Corning SAS, a major manufacturer of ophthalmic glass. The source of the data sheets is given in the glass catalog. Refractive indices are provided for six wavelengths and to five decimal places, so the Schott formula is used. The Corning Unicrown (Corning_1.523) glass is of some interest as it is true 1.523 index (Nd 1.52300, Vd 58.8) ophthalmic glass. Without it, ophthalmic lens designers have commonly used the Schott glass B270 (Nd 1.5231, Vd 58.571) as an approximation. Data sheets for tinted and photochromic ophthalmic glasses are also available1. All data sheets include material density, which allows calculation of the relative weights of high index glass lenses.
The other materials in the catalog are polymers including CR-39, polycarbonate and a range of common ophthalmic thiourethanes. The information has been taken from major manufacturers of the materials or lenses, but nevertheless is less reliable than that for ophthalmic glasses. The refractive index of any ophthalmic polymer can vary within and between manufacturers from the use of additives such as UV absorbers, plasticizers and mould release agents, and with normal variations in monomer and polymer manufacture and in lens casting or injection moulding cycles. For this reason, material and lens manufacturers are often reluctant to provide refractive index data beyond the second decimal place (and in at least one case beyond the first decimal place) and very little data is available apart from refractive index and V value for a single wavelength. The wavelength is sometimes the d line at 587.6 nm, but often the e line at 546.1 nm since it is closer to the peak of the relative luminosity curve.
To create the files here, the NF and NC refractive indices have been inferred from Nd and Vd or Ne and Ve values. Sultanova et al2 have published refractive index data at eight wavelengths for 15 optical polymers and have calculated V values for each. The starting point for each of the OpticStudio material files included here has been to assume that the dispersion curve for each ophthalmic polymer is similar to that for a Sultanova polymer with similar refractive index and V value. From NF, Nd or Ne, and NC values the Conrady formula has then been used to create the material files.
The wavelength range in the glass catalog has been extended for all of the materials to 400-800 nm, to include the whole visible spectrum and to allow them to be used in conjunction with the OpticStudio photopic or scotopic wavelengths.
The standard OpticStudio materials catalog MISC contains materials CR39 and POLYCARB. These differ slightly from the OPHTHALMIC materials CR-39 and POLYCARBONATE in that the CR-39 data has been taken from the major monomer manufacturer PPG Industries and the wavelength range has been extended to include the whole visible spectrum, and the POLYCARBONATE data is supplied by Essilor International S.A. (the parent company of Gentex Corp., a major polycarbonate ophthalmic lens manufacturer) to allow for material properties specific to ophthalmic lens manufacture. The MISC catalog also includes the materials ACRYLIC, PMMA and STYRENE which are useful in contact lens and intraocular lens optics.
References
- Corning. 2019. Glass Products Data Sheets. Accessed Feb 15, 2015. www.corning.com/worldwide/en/products/advanced-optics/product-materials/specialty-glass-and-glass-ceramics/ophthalmic-glass/glass-products-data-sheets.html.
- Sultanova K., Karasova S., Nikolov I., (2009), Dispersion Properties of Optical Polymers, Acta Physica Polonica A, 116:4, 585-587.
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