Flexible design of progressive addition lenses for effective sizing of viewing zones using ellipse, hyperbola, parabola, and circle parametric equations

The distribution of meridian optical power is critical for controlling the far, near, and channel zones in progressive addition lenses (PALs), whether using direct or indirect design methods. Traditional power distribution functions, represented by linear functions, trigonometric functions, or higher-order polynomials, fail to effectively control the rate of change of optical power, limiting the flexibility in designing individualized PALs. To address this issue, we employ a high-order Bezier function to describe the desired meridian optical power distribution. By adjusting the control points of the Bezier curve, the rate of change in optical power can be flexibly controlled, enabling personalized management of optical power and astigmatism distribution in PALs. Two distinct PAL designs were developed for different application scenarios using this method. A comparison of computational simulations, facial analysis, and profile measurements indicates that the designed PALs meet wearable requirements, exhibiting lower astigmatism extremes and a broader area of optical power stabilization. These results demonstrate the high versatility of the Bezier curve, offering meridian flexibility and adjustability to effectively control the design's key areas, including the position and size of the distance vision, near vision, and channel zones.

Progressive addition lenses design is focused on utilizing the shape of lens surface, which is not rotationally symmetric, and provides power addition. The lenses should meet power variation progressively without allowing the aberrations to attain detrimental values. The principle and e idea of designing progressive addition lenses are introduced. Several kinds of design methods are illustrated, and their advantages and drawbacks are also represented. Based on one of design methods, which the distance and near power points are determined firstly, then an umbilic line of progressive dioptric power is optimized to satisfy realistic requirements on stability of power and binocular compatibility, the form of the progressive power surface will be gotten, a progressive addition lens design that matches the particular visual needs of the patient is given out. Progressive addition lenses were manufactured with Satisloh VFT-compact machine. The lenses manufactured were measured using the Class Plus lens analyzer to provide sphere and cylinder across the surface of the lens. The results of measurement show that the lenses having a progressive power surface with a near portion and a distance portion, the near portion being of higher power than the distance portion, the form of the progressive power surface of the lens is effective to distribute surface astigmatism. In the current study, it is also shown that the optical characteristics of the different progressive addition lenses designs are significantly different from one another. The lenses designed and manufactured meet the needs. Compared with the lenses designed using Seiko software, the performance is similar with each other.

Progressive addition lenses—measurements and ratings

Traditional progressive addition lens (PAL) design, which places the distance vision correction in the upper half of the lens,1,2 may pose a specific challenge for the short of stature. Given that ...

Progressive addition lenses are a kind of ophthalmic lenses with freeform surface. The surface curvature of the progressive addition lenses varies gradually from a minimum value in the upper, far-view zone, to a maximum value in the lower, near-view zone. The increasing mean power from far-view zone to near-view zone is called addition mean power. The far-view zone, near-view zone and the intermediate zone are called effective usable area of the lens. In this paper, the design principles of progressive addition lenses are discussed. Several kinds of design methods are illustrated, and their advantages and disadvantages are also represented. A global optimizing method using curvature compensation is proposed which can reduce the undesirable astigmatism in some regions of the progressive addition lens surface while retaining desirable optical features of the progressive lenses. The total optimizing design thought is to reduce astigmatism of each point by reducing the curvature difference using curvature compensation. The value of the surface vector height of the optimized PAL is calculated by adding the value of the surface vector height of the initially designed PAL and the value of the surface vector height of a new freeform. The contours of the power and astigmatism of the initially designed PAL and optimized PAL from the example are given. It is shown that the largest astigmatism is reduced after optimization and the effective usable area in the far-view zone is expanded obviously.

EDITOR: It is a pleasure to read the interesting case of progressive lens design.1 The authors raise an interesting topic in progressive lens prescribing and fitting, whether trigonometric construc...

The Minkwitz theorem, which can be proven to apply to the immediate surface surrounding a line of umbilics, states that astigmatism perpendicular to the line changes twice as quickly as the rate of change of power along the line. Our objective is to test how the Minkwitz theorem applies to the design of progressive addition lenses (PALs). Our primary investigation of the astigmatism/power rate relationship used Hoya Tact lenses because they have a relatively large central region with horizontal spherical equivalent power contours and vertical astigmatism power contours. Other PALs were used for subsequent analysis. Lenses were measured with a Rotlex Class Plus lens analyzer. Zone widths in the central region of the Tact lenses exceeded those predicted by the Minkwitz theorem. Above and below this region, zone widths were narrower than predicted. When averaged along the entire corridor, zone widths approximated the Minkwitz theorem. For other PALs, the measured zone widths exceed Minkwitz theorem in the top (distance) and middle (intermediate) corridor but fell short in the lower (near) corridor. Likewise, on average along the entire corridor, they approximate the Minkwitz theorem. Although the Minkwitz theorem must apply exactly to the immediate locale of an umbilic, deviations from Minkwitz can occur within 2 mm of the corridor. Several factors enable enough local deviation from the Minkwitz theorem to "steer" the astigmatism and affect its magnitude in the peripheral portions of a lens. Although the Minkwitz relationship may be altered in some regions of the corridor, there is a global component to the Minkwitz prediction that applies to PALs. On a global level, the gains and losses of astigmatism along the corridor with respect to the Minkwitz prediction have strong tendency to cancel one another. In the end, it appears the unwanted astigmatism associated with a given power change along a given distance can be redistributed but probably not reduced.

Design a device for accurate measurements of local optical properties of progressive addition lenses (PALs). A point diffraction interferometer has been adapted to measure local prescriptions of PALs. The most basic configuration of the interferometer for the measurement of PALs showed in this work presents high dynamic range and accuracy as well as the possibility of choosing the number and position of measurement points. Measurements are taken within a region of interest within a radius of about 0.4 to 1.5 mm. Different PAL designs are measured by the method proposed here and compared with results by a last generation commercial lens mapper. With the point diffraction interferometer we also compared several PAL designs in order to analyze their properties in the progression zone. The device is compact, robust, and fairly accurate, and the operational principle is very simple. By direct measurements it provides the local dioptric power, i.e., the second order wavefront properties, of the lens for selected regions of interest. The position and area can be chosen by the user. The only mobile part of the setup allows for the selection of the measurement points without any additional prismatic correction or movement of the PAL.

The surface curvature of the progressive addition lenses varies gradually from the distance-viewing area to the near-viewing area. The curvature of the principal meridional curve varies progressively from point to point to provide a predetermined dioptric focal power at each point according to a predetermined power law. Several kinds of power laws along meridian line including linear combination and polynomials, are illustrated. The details for determining the coefficient and order of the polynomial are also introduced. Based on different power laws along meridian lines, the results of the computer evaluation are given out. Progressive addition lenses corresponding to different forms of meridional power laws have been manufactured with Satisloh VFT-compact machine. The lenses manufactured have been measured using the Class Plus lens analyzer to provide sphere, cylinder, and axis values across the surface of the lens, and distortion distributions are also presented. The results of measurement indicate that the performances of progressive addition lenses are consistent with those of the computer evaluation. These results are shown that the lenses have more wide distance-viewing or near-viewing areas and short corridor but with higher level of astigmatism in the peripheral areas while the curvature along the median line is constant in the distance zone and the rate of meridional dioptric variation is quicker, on the contrary, the lenses have more narrow distance-viewing or near-viewing areas and long corridor. The comparison and analysis prove that determining the power law along the meridian line is an important task in designs for progressive addition lenses.

Progressive addition lenses (PAL) are used to compensate presbyopia, which is induced by losing accommodation of elder eyes. These eyes need different optical power provided by eye glasses while watching objects at different distance. A smaller optical power is required in further distance and a larger one in nearer zone. A progressive addition lens can provides different power requirements in one piece of lens. This paper introduces a whole process of PAL production, from design, fabrication, to measurement. The PAL is designed by optimizing NURBS surface. Parameters of merit function are adjusted to design lenses with different specifications. The simulation results confirm that the power distributes as expected and cylinders are controlled under an acceptable level. Besides, sample lenses have been fabricated and measured. We apply precise-machining to produce the molds for plastic injection. Then, the samples are produced by injecting polycorbonate to the molds. Finally, Ultra Accuracy 3D Profilemeter is used to measure the sample PALs. Practical examinations shows that our designs are achievable and feasible in practice use.

Design of progressive addition lens is to obtain the desired power distribution, and control the unwanted astigmatism. And newly developed curvature polynomials are ideal candidate for representing the power and astigmatism distribution of a PAL.

This study demonstrates that appropriate measurement procedures can detect differences in head movement in a near reading task when using three different progressive addition lenses (PALs). The movements were measured using an anatomical reference system with a biomechanical rationale. This reference system was capable of representing rotations for comparing head flexion relative to trunk, head flexion relative to neck, head rotation relative to trunk and trunk flexion. The subject sample comprised 31 volunteers and three PAL designs with different viewing zones were selected. Significant differences were found between the lenses for three of the seven movement parameters examined. The differences occurred for both vertical and horizontal head movements and could be attributed to aspects of the PAL design. The measurement of the complete kinematic trunk–neck–head chain improved the number of differences that were found over those in previous studies. Statement of Relevance: The study proposes a methodology based on a biomechanical rationale able to differentiate head–neck–trunk posture and movements caused by different progressive addition lens designs with minimum invasiveness. This methodology could also be applied to analyse the ergonomics of other devices that restrict the user's field of view, such as helmets, personal protective equipment or helmet-mounted displays for pilots. This analysis will allow designers to optimise designs offering higher comfort and performance.

In this study, we developed a new method for designing progressive addition-multifocus defocused freeform lenses. We used two independent meridians and achieved a smooth gradient transition of additional optical power from the center to the peripheral area of the lens, along with an asymmetric distribution of additional optical power on the nasal-temporal side of the lens. To improve the optical performance of the lenses, we developed three different designs based on the distribution of the additional optical power on the meridians. We conducted simulations and processing on the three different designs. The lenses designed using improved logistic regression and sine functions for meridian optical power distribution exhibited stable optical performance in the central focus area. They also met the design requirements for additional optical power. However, significant distortion was still observed in the peripheral region, which required further optimization. Lenses designed using piecewise linear functions for meridian optical power distribution exhibited relatively poor optical performance with significant optimization potential. Thus, combining the optical power distribution and surface-type factors for optimization is necessary. The proposed method enabled designing of defocus-free curved mirror lenses that satisfy the optical performance requirements. Thus, this method provides a new approach for the design of progressive addition lenses.

A new method for characterizing the design of progressive addition lens is presented. The power gradient of the lens is measured in a small area using an automatic lensmeter. This measurement, designated PV, is repeated on selected, separated areas of the lens to create a profile of the lens gradient change. Results of measurements taken on lens of different designs are presented.

Insufficient accommodative response is assumed to result in myopia progression. We have investigated if the accommodative lag in myopes is different between a single vision lens (SVL) and the progressive addition lens PAL 2, clinically trialled for its ability to reduce progression of myopia, and if there exist differences in accommodative lag between PAL 2 and other PALs with the same addition power (+1.50 D). The influence of spherical SVL and four different designs of PALs that differ in the near zone width (PAL 1) or that have different signs and magnitude of horizontal gradients of mean power adjacent to their near vision zones (PAL 3 and PAL 4) on the accommodative response was investigated for different near viewing distances (40, 33, and 25 cm) in 31 subjects, aged 18 to 25 years. The SVL correction resulted in insufficient accommodative response for the near object viewing distances tested. PAL 2 did significantly reduce accommodative lag for all near object distances tested. The PAL design with a more negative horizontal mean power gradient (PAL 4) provided a lower lag of accommodation when compared with PAL 2 at the shortest object distance of 25 cm (P = 0.03) and was able to reduce the lag of accommodation to a level below the depth of focus for the higher near working distances tested. Designs of PAL with more negative horizontal mean power gradients are the most effective in lowering the lag of accommodation in myopes. This could make them good test candidates for myopia control applications.