Impact of contact lens zone geometry and ocular optics on bifocal retinal image quality

Abstract

Purpose: To examine the separate and combined influences of zone geometry, pupil size, diffraction, apodisation and spherical aberration on the optical performance of concentric zonal bifocals.

Methods: Zonal bifocal pupil functions representing eye + ophthalmic correction were defined by interleaving wavefronts from separate optical zones of the bifocal. A two-zone design (a central circular inner zone surrounded by an annular outer-zone which is bounded by the pupil) and a five-zone design (a central small circular zone surrounded by four concentric annuli) were configured with programmable zone geometry, wavefront phase and pupil transmission characteristics. Using computational methods, we examined the effects of diffraction, Stiles Crawford apodisation, pupil size and spherical aberration on optical transfer functions for different target distances.

Results: Apodisation alters the relative weighting of each zone, and thus the balance of near and distance optical quality. When spherical aberration is included, the effective distance correction, add power and image quality depend on zone-geometry and Stiles Crawford Effect apodisation. When the outer zone width is narrow, diffraction limits the available image contrast when focused, but as pupil dilates and outer zone width increases, aberrations will limit the best achievable image quality. With two-zone designs, balancing near and distance image quality is not achieved with equal area inner and outer zones. With significant levels of spherical aberration, multi-zone designs effectively become multifocals.

Conclusion: Wave optics and pupil varying ocular optics significantly affect the imaging capabilities of different optical zones of concentric bifocals. With two-zone bifocal designs, diffraction, pupil apodisation spherical aberration, and zone size influence both the effective add power and the pupil size required to balance near and distance image quality. Five-zone bifocal designs achieve a high degree of pupil size independence, and thus will provide more consistent performance as pupil size varies with light level and convergence amplitude.

Keywords: annular pupils; apodisation; diffraction; pupil size; spherical aberration; zonal bifocal.

Figure 1

Wavefront error profiles for two-zone (left) and five-zone (right) bifocal lenses produced by distant (A, B), intermediate (C,D) and near (E,F) target distances. A +2 dioptre add was used in each case. Gray indicates optical zone with +2 add power. Black lines show aberration-free case, red lines show WFE in presence of Seidel spherical aberration (C₄⁰=0.15 microns, C₂⁰=SQRT(15) × 0.15 microns).

Figure 2

Examples of diffraction limited MTFs for the individual circular and annular zones and combined apertures for the distance optic of a five-zone bifocal (zones A, C and E, see Figure 1). Inserts show schematic maps of zone geometry.

Figure 3

MTF plots for individual and combined zones of zonal bifocal lenses: A, a 2-zone (6 mm diameter pupil, 3 mm inner zone diameter) and B, 5 zone (6 mm pupil, same zone geometry as described in Figure 1). For reference, the diffraction limited MTF of a monofocal diffraction limited 6 mm optic is also shown (black line). In both panels, solid lines show the diffraction limited MTFs for the focussed separate inner (blue) and outer (red) zone optics (A) and distance (red) and near (blue) optics of the five-zone design (B), while the dashed lines show the MTFs for the full 6 mm aperture with one optic focused and the other defocused by 2 dioptres. Aperture geometries are shown schematically, white=focused, black = defocussed, and gray is opaque.

Figure 4

Radially averaged modulation transfer functions (MTFs) for a centre-distance two-zone bifocal with a 3 mm an inner-zone diameter and +2D add power for several pupil sizes. Solid lines show MTFs when the central distance optic is focussed, and dashed lines when the annular near optic is focused. Numbers on each curve indicate pupil diameter in mm. This model included diffraction and uniform pupil transmission.

Figure 5

Sample images of a logMAR chart computed for a two-zone centre-distance +2D bifocal with 3 mm diameter inner-zone (A: top two rows). Row 1 and 2 show images calculated for distant (target vergence, TV = 0) and near (TV = −2) targets, respectively. The left to right series are calculated with pupil diameters of 3, 4, 5, and 6 mm. DHEVP line = logMAR of 0.3. Sample images of a logMAR chart computed for a five-zone centre-distance +2D bifocal are shown in the bottom two rows (B). Rows 3 and 4 show images calculated for distant (TV = 0) and near (TV = −2) targets, respectively.

Figure 6

Impact of Stiles Crawford effect (SCE) apodisation on diffraction limited modulation transfer functions for a 6mm circular pupil, and for a two-zone bifocal with 3 mm and a 3 to 6 mm annulus. Add power is 2 dioptres. Modulation transfer functions computed with SCE (dashed lines) are compared to those w/o SCE (solid lines) when either the inner-zone (blue) or the outer-zone (red) are focussed.

Figure 7

Wavefront vergence errors are plotted as a function of radial position in the pupil for a two-zone centre distance bifocal (A), a two-zone centre near bifocal (B) and a centre distance five-zone bifocal (C). In each case we plot the vergence error in the absence of any aberrations (solid black line), with Seidel spherical aberration added (red dotted lines, C₄⁰=0.15 microns, C₂⁰=SQRT(15) × 0.15 microns) and with Zernike spherical aberration added (blue dotted lines, C₄⁰=0.15 microns, C₂⁰=0). Zones with the near add are indicated with gray in each panel.

Figure 8

Through focus image quality (diffraction-limited normalized Area Under the MTF) was computed for three zonal bifocals (2-zone centre distance (A), two-zone centre near (B) and five-zone (C)) as a function of target vergence in dioptres. In each case a 6 mm pupil was used. MTFs for each bifocal lens were calculated with a +2 dioptre add power, and either without spherical aberration (black lines), or with 0.15 microns of Seidel spherical aberration (dashed lines) added. The combined impact of Seidel spherical aberration and Stiles Crawford Effect apodisation is also shown (dotted lines). Image quality is quantified by the areaMTF metric in which all values are normalized to the areaMTF generated by a DL 6 mm pupil.

Figure 9

Percentage of pupil area covered by the distance (blue) and near (red) optics as a function of pupil diameter in mm for a two-zone bifocal with a 3 mm diameter inner-zone (A) and a five-zone design with zones diameters of 2.0, 3.2, 4.4, 5.3, and 6.0 mm (B). Pupil area calculations are performed either with (filled symbols) or without (open symbols) Stiles Crawford Effect central weighting of the pupil.

Figure 10

MTFs for a two-zone bifocal with +2D add power and a 3mm inner-zone diameter calculated for a 4.2 mm diameter pupil, which equates the area of the inner-zone and outer-zone. Blue shows MTF when inner-zone is focussed, and red when outer-one is focused.

Figure 11

Peak near (red) and distance (blue) image quality (AreaMTF) obtained with through-focus analysis (see Figure 6) for a two-zone centre-distance bifocal is plotted as a function of pupil diameter in mm. In this example, the areaMTF metrics are normalised by the areaMTF for a diffraction-limited 6 mm pupil. Open symbols represent uniform pupil, while filled symbols show data for a Stiles Crawford Effect apodised pupil, the model includes 0.15 microns of primary spherical aberration (scaled for pupil diameters less than 6 mm).

Figure 12

Image quality for a five-zone bifocal as a function of pupil diameter. 0.15 microns of spherical aberration was included. AreaMTF with (solid) and without (open) Stiles Crawford Effect apodisation are calculated for distant (blue) and near (red) target vergences. In this example, the areaMTF metrics are normalised by the areaMTF for a diffraction limited 6 mm pupil. Panel A shows data when the eye is paraxially focused, equivalent to adding Seidel spherical aberration to the lens, whereas panel B shows image quality for an eye which had a minRMS refraction, which is equivalent to adding Zernike spherical aberration to the lens.