Bifocal lenses are eyeglass lenses designed to help individuals who have difficulty seeing objects both near and far, a condition called presbyopia. These lenses are divided into two distinct parts: the upper part is for distance vision, and the lower part is for close-up tasks such as reading. The line separating the two prescriptions is typically visible, and the shift from one vision zone to the other can take some adjustment. Figure below is a typical scheme of eyewear with bifocal lens.

Figure 1 Bifocal lens in eyewear

Intraocular bifocal lens are artificial lenses implanted into the eye, typically after cataract surgery, to correct vision at multiple distances. These lenses replace the eye's natural lens, which is removed during cataract surgery or in procedures to address presbyopia or refractive errors. They are designed to help patients see clearly both at a distance and up close, reducing the need for glasses. Such intraocular bifocal lens Improves vision at both near and far distances and can reduce or eliminates the need for bifocal glasses or contact lenses after surgery.

Figure 2 Intraocular bifocal lens in human eye

Modeling intraocular bifocal lens in Zemax requires Binary 2 surface. The Binary 2 surface is a diffractive surface in which the phase added to each light ray varies according to a rotationally symmetric polynomial. The phase is either delayed or advanced based on the following equation. Coefficient Ai is radians.

In this context, N represents the number of polynomial coefficients in the series, M denotes the diffraction order, and p is the normalized radial aperture coordinate, with the coefficients expressed by the A terms. To initiate this design, assume the far vision focus is 0^{th} diffractive order, and near vision focus is 1^{st} diffractive order. Both front and back surfaces are diffractive. A dual-configuration scheme is applied to divide two focal statuses, as below:

Figure 3 Configuration 1 – Near vision focus

Figure 4 Configuration 2 – Far vision focus

OpticStudio uses the phase advance or delay represented by the surface locally to change the direction of propagation of the ray. Other effects, such as scattering, efficiency, or multiple order diffraction are ignored. Binary surfaces can have zero thickness, with no index change across the surface, or may have different media on either side of the surface.

The shape of the binary optic 2 surface is identical to the even asphere surface type; planes, spheres, conics, and polynomial aspheres up to order 16 are supported. The sag of the surface is given by the following expression, where the terms are identical to those in the Even Asphere Surface model.

The intraocular lens is made of PMMA, with main structure parameters of the listed below:

Figure 5 Basic parameters of eye and bifocal IOL

The diffractive and aspherical term is listed below:

Figure 6 Diffractive order parameters of bifocal IOL

In this structure, surface 6 corresponds to the front surface of the IOL. Given that the design requirements specify the need for diffractive power on the front surface of the IOL. which is demonstrated in Binary 2. This change will introduce several new parameters in the LDE for this surface, including diffraction order, aspheric coefficients, and the maximum number of terms along with the normalization radius for the Binary 2 phase expansion.

The multi-configuration definition is shown below. FLTP denotes field type, 0 for angle in degrees, 1 for object height. THIC is thickness of surface. Here in configuration 1, infinite distance is defined, where in configuration 2, 250 mm is defined.

Figure 7 Multi-configuration list to distinguish far and near vision

Here we use FFT MTF to compute the diffraction modulation transfer function (MTF) data for all field positions using an FFT algorithm in Figure 8, with the maximum spatial frequency of 50 lp/mm. The diffraction MTF computation is based upon an FFT of the pupil data. The resulting MTF is the modulation as a function of spatial frequency for a sine wave object.

Figure 8 FFT MTF of three different fields at Config. 1 (far field)

Figure 9 FFT MTF of three different fields at Config. 2 (near field)

Below shows a bitmap analysis with the far field configuration, using 0. 10 and 20 degrees of field position. This image result suggests image blur in large field, which accord with MTF analysis.

Figure 10 Original image in bitmap analysis

Figure 11 Geometric bitmap image analysis of Config. 1 in 0 degree

Figure 12 Geometric bitmap image analysis of Config. 1 in 10 degrees

Figure 13 Geometric bitmap image analysis of Config. 1 in 20 degrees

In summary, bi-focus intraocular lens can be modeled in Zemax with multi-configuration setting. Zemax also provides various image analysis tools to assist IOL optimization.

September 10, 2024