WO2023187167A1

WO2023187167A1 - Method to establish the size of the different areas of a progressive lens

Info

Publication number: WO2023187167A1
Application number: PCT/EP2023/058477
Authority: WO
Inventors: Santiago SOLER MONENTE; Pau ARTÚS COLOMER; Glòria CASANELLAS PEÑALVER; Rocío B. RODRÍGUEZ DOMÍNGUEZ; Javier Vegas Caballero
Original assignee: Horizons Optical S.L.U.
Priority date: 2022-03-31
Filing date: 2023-03-31
Publication date: 2023-10-05

Abstract

Method to establish the size of the zones of near A_c, far A_L and intermediate A_i vision_of a progressive lens by generating, thanks to virtual reality, a gaze map of the user while following a stimulus in at least two planes at two different distances. Once the gaze maps have been made in those two planes or more, the area of each zone is calculated from the maximum horizontal and vertical amplitudes and the points of maximum frequency. In this way, the lens is adapted to the way a user looks.

Description

METHOD TO ESTABLISH THE SIZE OF THE DIFFERENT AREAS OF A PROGRESSIVE LENS

TECHNICAL SECTOR

The present invention is encompassed within optical applications in particular, progressive lenses.

BACKGROUND OF THE INVENTION

A progressive lens has three distinct clear areas with different optical powers that allow objects to be focused at different distances: far, intermediate and near. There is a fourth and fifth non-clear areas, located on the sides, where aberrations inevitably appear, causing a lower optical quality (see Figure 1). This makes it difficult to use when looking through them.

It is known that multipurpose progressive lenses are characterized by being designed to have an upper zone of focus on objects located at a far distance of 5 meters or more, another in the lower part to focus on objects around 40 cm away, and a third in the central zone with progressively changing focus capacity from near to far distance, called intermediate zone or corridor.

Due to the progressive power variation of this intermediate zone, the sides of these lenses always have aberrations that do not allow the user to focus precisely. This is due to the fact that unwanted astigmatism appears with values greater than 0.50 Diopters, which is the limit value from which the human eye-brain group begins to have a perception of lack of clarity (see Figure 2).

Consequently, the clear zone of far vision of a progressive lens is defined as the area where the astigmatism value is less than 0.50 Diopters and the mean power value is less than +0.25 Diopters of the far target power value. In the upper part, the area is limited to 8 millimeters above the position of the pupil (known as the fitting cross or segment) while at the bottom it is limited to 4mm below the position of the pupil, whichusually coincides with the point known as the prism reference point (PRP).

The clear zone of near vision of a progressive lens is defined as the area where the astigmatism value is less than 0.50 Diopters and the mean power value is greater than 85% of the near average power, which takes into account the addition. At the upper part, this limit is usually about 4mm above the near reference point (known as the Near Reference Point or NRP). At the bottom, the near area is limited to 2 millimeters below the near reference point (known as the Near Reference Point or NRP).

The clear zone of intermediate vision of a progressive lens is also defined as the area where the astigmatism value is less than 0.50 Diopters and the power varies continuously from +0.25 Diopters of the objective value from far to 85% of the value of the addition. At the upper part, it is limited above the PRP, while the bottom is usually limited to about 4mm above the NRP. The corridor is defined as the vertical length of the clear zone of intermediate vision.

An example of a combined astigmatism and mean power map of a progressive lens is shown in Figure 2 with each of the three useful zones 1-3 marked, and also zones 4 and 5 not having clear vision.

It is known that for the calculation of progressive lenses, iterative optimization methods are used that incorporate as restrictions the values of power and astigmatism required in each zone described ("Optimization methods for the design of progressive lenses", Casanellas, Gloria. Polytechnic University of Catalonia, 2020. http://hdl.handle.net/10803/668877). These mathematical methods iterativelymodulate the lens surface, being understood as two surfaces containing a material ofknown refractive index, until the objective function requirements are met within specified tolerances for each point.

It is also known that the size and distribution of each of the zones (far, intermediate, near and aberrations) does not have a unique mathematical solution, so it is possibleto modify them within certain limits (“Do the progressive lenses really satisfy the Minkwitz theorem? Strategies to go beyond the Minkwitz theorem.” Innovation Department of Horizons Optical. MAFO - Ophthalmic Labs & Industry, Volume 15, pp10-17, 1/2019. ISSN 1614-1598 66527).

Consequently, there may be many possible geometries to define the contour of each of the zones once their size is established. A known model is the one constituted by polyhedrons that define the limits of the zones and that can be used for the mathematical definition of the optimization system. Specifically, one of the simplest models uses two trapezoids to define the contours of the far and near zone, and a rectangle or parallelogram for the intermediate zone, depending on whether a symmetric or asymmetric progressive lens is designed. There are also more sophisticated models in which one or more of the edges of the polyhedrons are replaced by arcs of circumference, arcs of ellipses or n degree polynomials.

A progressive lens with larger areas for near and far focus causes the fourth and fifth zones to be smaller but have high levels of aberration and image distortion. This often causes a greater difficulty in adapting to especially sensitive users. This is the case of progressive lens designs commonly known as hard.

On the contrary, an expansion of the fourth and fifth zones entails a more limited intensity of aberrations on the sides and an intermediate zone with a wider transition corridor or corridor. These types of lenses usually offer easier adaptations for some users but others do not prefer them, since they cause a greater sensation of visual restriction on the sides of far, near areas and corridor. This is the case of progressive lens designs commonly known as soft.

The location and size of these areas, especially those that are not clear, conditions the user's oculomotor movement since, for different gaze directions, users prefer to prioritize head movement over ocular rotation or vice versa, depending on the intensity of the aberrations and the sensitivity of each user to them.

The a priori preference of a user over progressive lenses with different area sizes, without having tried them, is one of the challenges that the ophthalmic lens sector hasbeen pursuing since the beginning of progressive lenses. For this reason, many lens manufacturers have diagnostic tests and devices that aim to improve thecharacterization of the users in order to objectify the sensations in perception and to be able to better adjust the selection of the designed or chosen lens.

For some years there have been devices on the market that attempt to measure the behavior of users and record head and eye movements with the aim of improving the prescribed progressive lenses. Some examples would be:

• Visioffice from Essilor (https://www.essilorusa.com/content/dam/essilor- redesign/visioffice/Visioffice%20Measurement%20FAQ.pdf): this device measures various parameters relevant to the optician and incorporates the measurement of the percentage of eye moving I head moving on the horizontal axis from a simple onedimensional test with a light stimulus of two LEDs located on each side of the user. There is also a more specific device from the same company called Varilux® VisionPrint System™ (http://www.luzerneoptical.com/pdf/varilux-physio-faqs.pdf) that follows the same principle. • Patent ES2264848; describes a method for measuring the visual map of the user from the tracking of the user's eyes and head while following a punctual light stimulus moving on a two-dimensional black screen.

Virtual reality is a stereoscopic simulation of reality both visually and audibly, its main characteristic being the ability to provide an immersion of the subject in a three- dimensional and, consequently, multisensory environment.

Unlike desktop or floor-standing equipment that is limited by the space it occupies and by the hardware, a virtual reality environment allows you to create scenarios specially designed for each test in which you want to record the dynamics of your gaze. The lighting conditions are controlled, and the experience is completely immersive, with which the results are more repetitive and there are no distractions or unforeseen events, resulting in an ideal experience for conducting tests related to the health world.

For example, there are many applications for training purposes for health professionals that allow simulating work environments and critical situations to help improve their reactions.

Currently available virtual reality devices have a level of precision in determining the position of the head that makes them especially effective in determining the movement of the head. They incorporate inertial sensors of the accelerometer and gyroscope type to determine the movements of the head and synchronize the movement of the virtual environment appropriately. Optionally, some devices can also incorporate pupil movement sensors (eye-tracker), which completes the information on the user's oculomotor movement. To create the stereoscopic sensation in the user, virtual reality devices project complementary images to each eye that place the objects in the relative position with respect to the background based on the calculatedposition in space.

The gaze dynamics map is known as the record of the positions in the user's gaze while carrying out certain activities. To determine the gaze dynamic’s map of each person, it is necessary to project a stimulus in the virtual space that the user is askedto follow naturally with his gaze. The virtual reality device will record the relative movement of the eyes and head to determine the frequency of use of each area of the plane where an ophthalmic lens would be located. This recording is made while the patient is asked to follow with his gaze a stimulus that is moving freely in the three dimensions of the virtual space.

In the event that the device lacks an eye-tracker, a simplification can be used assuming that the patient always faithfully follows the stimulus. This simplification is especially suitable for patients with dysfunctions in the visual system such as phoria, amblyopia or nystagmus since the tracking devices do not give a reliable answer on the real direction of the gaze.

In the case of knowing the gaze dynamics of each specific user at each distance, it is possible to adapt the size of each area of the lens to their needs and type of gaze dynamics, providing a unique and exclusive lens perfectly adapted to their way of viewing.

Additionally, the position of the near zone of a progressive lens can be adjusted vertically so that it is positioned in a comfortable position for the user when performing near and intermediate vision tasks. This change in location determines the vertical length of the intermediate vision zone, which is usually called the corridor, and consequently, the size and intensity of the lateral aberrations since the intensity of thevariation of optical power in this corridor is also interrelated with the level of aberrations (shorter corridors have higher level of lateral aberrations).

Additionally, if the progressive lens to be manufactured is not a multipurpose lens andis designed to be an occupational lens, said object focus distances will be different. For example, for an office lens the power will be adapted for the far distance to focus between 1.5 and 3m instead of the 5m or more usual ones. In contrast, for a lens for outdoor sports activities, the near distance would be optimized for focusing on the ground and would be between 1.5 and 2m, instead of the usual 40 cm for reading.

SUMMARY OF THE INVENTION

In order to physically manufacture a progressive lens adapted to the way a person looks, the present invention describes, in a first aspect, a method for determining and calculating thesize of the far, near and intermediate areas of said lens from the measurement of the dynamics of the patient's gaze. Gaze dynamics maps are obtained using a virtual reality environment within which stimuli are projected in at least two planes at at least two different distances: far and near, and recording their eye and head movement andthe calculation is done by means of processing.

The size of the far vision area (AL) in mm² of the progressive lens will be determined from the average of the maximum horizontal and vertical amplitude of the gaze dynamics map in the far plane (Aabi), expressed in degrees (°), following a linear relationship for Aabi values between 10° and 80° according to the following relationship:

A_L = i ^x Aab_L + j, wherein i values are between 1.0 mm²/⁰ and 1.4 mm²/⁰, preferably 1.2 mm²/⁰ and jhas values between 120 mm² and 160 mm², preferably 140 mm².

The size of the near vision area (Ac) in mm² of the progressive lens will be determinedfrom the average of the maximum horizontal and vertical amplitude of the gaze dynamics map in the near plane (Aabc), expressed in degrees (°), following a linear relationship for Aab_c values between 10° and 80° according to the following relationship:

A_c = k x Aabc + I wherein k has values between 0.15 mm²/⁰ and 0.25 mm²/⁰, preferably 0.20 mm²/⁰ and wherein I has values between 20 mm² and 30 mm², preferably 25 mm².

The size of the intermediate vision area (Ai) in mm² of the progressive lens will be determined from the angle formed by the PML and PMc points with the origin of coordinates (PPMLC), expressed in degrees (°), following a linear relationship for PPMLC values between 0° and 18° according to the following relationship:

Ai = m x PPMLC + n wherein m has values between 0.5 mm²/⁰ and 1.5 mm²/⁰, preferably 1.0 mm²/⁰ and n has values between 15 mm² and 30 mm², preferably 23 mm².

Hence, the method of the first aspect of the present invention is a method to establish the size of the zones of near Ac, far AL and intermediate Ai vision of a progressive lens, comprising the following steps: a. generation of a gaze map through the use of virtual reality in a near plane and a distant plane; b. calculation of the maximum horizontal amplitude of each map in degrees, AaL.Aac; c. calculation of the maximum vertical amplitude of each map in degrees Abi, Abe; d. determination of the size of the far vision area AL in mm² from the average of the maximum horizontal and vertical amplitude in the far plane, AabL, following a linear relationship whose result for AabL values between 10° and 80° is obtained according to the following relationship: A_L = i ^x Aab_L + j, wherein i values are between 1.0 mm²/⁰ and 1.4 mm²/⁰ and j has values between 120mm² and 160 mm²; e. determination of the size of the near vision area Ac in mm² from the average of the maximum amplitude in horizontal and vertical in the near plane Aabc followinga linear relationship whose result for values of Aabc between 10° and 80° is obtainedaccording to the following relationship:

A_c = k x Aabc + I, wherein k has values between 0.15 mm²/⁰ and 0.25 mm²/⁰ and wherein I has values between 20 mm² and 30 mm²; f. determination of the size of the intermediate vision area Ai in mm² from the angle PPMLC formed by the points of maximum frequency in each plane, PML and PMc with the origin of coordinates following a linear relation whose result for PPMLC values between 0° and 18° is obtained according to the following relationship:

Ai = m x PPMLC + n wherein m has values between 0.5 mm²/⁰ and 1.5 mm²/⁰ and n has values between 15 mm² and 30 mm². wherein steps b-f are performed by a processor.

For an embodiment, i has a value of 1 .2 mm²/⁰ and j has a value of 140 mm².

According to an embodiment, k has a value of 0.02 mm²/⁰ and I has a value of 25 mm².

For an embodiment, m has a value of 1.0 mm²/⁰ and n has a value of 23 mm²

According to an embodiment, AL is the area in mm² in the far zone where the astigmatism value is less than 0.50D and the mean power value is less than +0.25D of the target far power value; said area AL limiting, in its upper part, 8mm above the pupil position, and, in its lower part, 4mm below the pupil at the prism reference point.

According to an embodiment, Ac is the area in mm² in the near zone where the astigmatism value is less than 0.50D and the mean power value is greater than 85% of the target value of addition; said area Ac limiting, at the bottom, 2 mm below the near reference point.

According to an embodiment, Ai is the area in mm² in the intermediate zone where the value of astigmatism is less than 0.50D, and the value of the mean power is greater than + 0.25D of the far target power value and the average power value is less than 85% of the target value of the addition. For an embodiment, the above mentioned origin of coordinates is the origin (0,0,0) of a Cartesian coordinate system at the midpoint of a vector joining the user's pupils, wherein the xy plane is defined parallel to the ground and the z axis perpendicular to the ground.

In a second aspect, the present invention relates to a method for manufacturing a progressive lens comprising delimiting the size of the areas of the near Ac, far AL and intermediate Ai vision zones, wherein said size has been calculated according to the method of the first aspect of the invention.

In a third aspect, the present invention relates to a computer program product comprising program code means which, when loaded into a processor, causes said program code means to execute the method of the first aspect of the invention.

The astigmatism of the three different zones of the progressive lens (far, near and intermediate areas) manufactured or whose size is determined according to the methods of the invention, corresponds to the residual aberrations, and thus issues related to the control of aberrations are indeed addressed by the present invention.

As mentioned in the above section, consequently, there may be many possible geometries to define the contour of each of the zones once their size is established. A known model is the one constituted by polyhedrons that define the limits of the zones and that can be used for the mathematical definition of the optimization system. Specifically, one of the simplest models uses two trapezoids to define the contours of the far and near zone, and a rectangle or parallelogram for the intermediate zone, depending on whether a symmetric or asymmetric progressive lens is designed. There are also more sophisticated models in which one or more of the edges of the polyhedrons are replaced by arcs of circumference, arcs of ellipses or n degree polynomials.

The shape alternatives disclosed in any of those known models indeed allow the skilled person to design a progressive lens with the information provided by the present invention, and particularly to establish a dependence between the size and shape of the different zones (near, far and intermediate) and the amount of residual aberrations, as indeed the astigmatism of the three different zones is defined above, and that astigmatism corresponds to the residual aberrations. Therefore, the skilled person would just use the information provided by the models/methods of the present invention together with any of those (or others) known prior art models, to design a viable progressive lens.

This is further supported in a section below, where detailed embodiments are described using some of those prior art models/methods to design a progressive lens with the information provided by the methods of the present invention.

BRIEF DESCRIPTION OF THE FIGURES

In order to help a better understanding of the features of the invention and to complement this description, the following Figures are attached as an integral part thereof, the nature of which is illustrative and not limiting.

Figure 1 : schematic representation of the zones of a progressive lens.

Figure 2: graphical representation of the areas of a progressive lens calculated from the astigmatism and addition values (diamonds: far vision zone; circles: intermediatevision zone; squares: near vision zone; gray: zones 4 and 5 without clear vision). Thecross shows the location of the fitting cross point. The dot shows the location of the NRP.

Figure 3: diagram of the test where the position of the user is seen with respect to the coordinate system, and the two planes with the stimulus path, in dashed line. DR is the gaze point of rest.

Figure 4: graphic representation of the vertical and horizontal amplitudes Aa and Ab of a gaze dynamics map. The different intensities of gray show the values of frequencyof use.

Figure 5: diagram of the relative position of the frequency maps and the points (PML y PMc) of maximum frequency in far and near projected on the plane of the lens, as well as the angle (PPMLC) formed by these two points with respect to the coordinates origin.

Figure 6: lower and upper limits of the far, intermediate and near zones.

Figure 7: trapezoid for the near zone, and far zone and rectangle for the intermediate zone. Far zone is represented with dash-dotted line, intermediate zone with dotted line and near zone with solid line.

Figure 8: elevations of the shapes of the far, intermediate and near vision areas. Far zone is represented with dash-dotted line, intermediate zone with dotted line and near zone with solid line.

Figure 9: astigmatism and power maps of two equivalent progressive lenses. Figure of the thesis “Optimization methods for the design of progressive lenses”, Casanellas, Gloria. Polytechnic University of Catalonia, 2020. http://hdl.handle.net/10803/668877 cited before.

Figure 10: shapes of the trapezoids obtained for Example 1. Far zone is represented with dotted pattern, intermediate zone with cross pattern and near zone with star pattern.

Figure 11 : Astigmatism map of the progressive lens obtained from Figure 10 using the trapezoid calculation method. Far zone is represented with dotted pattern, intermediate zone with cross pattern and near zone with star pattern.

Figure 12: Shapes of the far, intermediate, and near vision areas for Example 2. Far zone is represented with dotted pattern, intermediate zone with cross pattern and near zone with star pattern.

Figure 13: Astigmatism map of the progressive lens obtained from Figure 12. Far zone is represented with dotted pattern, intermediate zone with cross pattern and near zone with star pattern.

DETAILED DESCRIPTION

For each user, the following sequence of steps is followed:

1 . Protocol to ensure the correct fit of a virtual reality glasses to the user's head (adjustment of fastening straps, correct position of the glasses in front of the eyes, etc.).

2. Transfer of the patient to the virtual space where the test will be performed. It is a relaxed and distraction-free environment.

3. Preparation of the patient to ensure a natural position of the back and neck.

4. The patient is asked to look at infinity and the tilt of the head relative to the ground is recorded as their Resting Position and the patient's gaze direction relative to the ground as the Direction of Rest (DR).

5. A Cartesian coordinate system is defined with the origin (0,0,0) at the midpoint of the vector joining the user's pupils. The xy plane is defined parallel to the ground and the z axis perpendicular to the ground. A vector is defined that has the origin of the coordinate system as its origin and has the direction of rest (DR) as its direction. It is defined that the xz plane contains this vector. 6. The Far Zone is defined as the portion of the plane parallel to yz with a value of x corresponding to the far distance for which the Far Area (AL) of the progressive lens is to be adjusted (for example, 5 meters or more for a multipurpose progressive lens) and having a horizontal size of at least 100° and a vertical size of at least 80°. These angles are measured from the origin of coordinates (0m, 0m, 0m).

7. The Near Zone is defined as the portion of the plane parallel to yz with a value of x corresponding to the near distance for which the Near Area (Ac) of the progressive lens is to be adjusted (for example, 0.4 meters for a multipurpose progressive lens) and having a horizontal size of at least 100° and a vertical size of at least 80°. These angles are measured from the origin of coordinates (0m, 0m, 0m).

8. A stimulus appears on the Far Zone of the virtual space located at the point of intersection between this zone and the resting gaze vector DR. The stimulus can be a flying object such as a bird, an insect, a drone, etc.

9. The stimulus moves over the Far Zone following a predetermined path with a homogeneous time distribution in all its portions. The linear velocity of the stimulus will be set between 0.2m/s and 0.6m/s, preferably 0.4m/s. The virtual reality device records eye and head movements as the patient follows the stimulus with his/her gaze.

10. At the end of the path established over the Far Zone, the stimulus moves to the Near Zone and makes a path analogous to that of the Far Zone, covering the same opening angle and at an equivalent angular speed. The virtual reality device records eye and head movements.

11 . End of test and registration.

12. The device calculates and shows the gaze dynamics map in each plane to the patient.

With the recording of head and eye movements in each plane (Figure 3), a map of frequency of use of the lens plane can be calculated when the stimulus is in the far plane and another map when it is in the near plane.

Consequently, two gaze dynamics or frequency of use maps will be generated, one for each distance. The following parameters will be extracted from each of these maps (Figures 4 and 5):

• Aa maximum horizontal amplitude of the far map in degrees (Figure 4).

• Ab maximum vertical amplitude of the far map in degrees (Figure 4).

• Aab average value in degrees of the maximum horizontal amplitude Aa_L and maximum vertical amplitude Abi. of the far map.

• Aac: maximum horizontal amplitude of the near map in degrees (Figure 4).

• Abe: maximum vertical amplitude of the near map in degrees (Figure 4).

• Aabc: average value in degrees of the maximum horizontal amplitude Aac and maximum vertical amplitude Abe of the near map.

• PML: point of maximum frequency of use of the lens plane when the stimulusis in the far plane. If there is more than one point with the same maximum frequency value, a point having as horizontal coordinate the average of the horizontal coordinates of the maximum points found, and as vertical coordinate the average of the vertical coordinates of the maximum points found (Figure 5).

• PMc: point of maximum frequency of use of the lens plane when the stimulus is in the near plane. In the event that there is more than one point with the same value of maximum frequency, a point having as horizontal coordinate the average of the horizontal coordinates of the maximum points found, and as vertical coordinate the average of the vertical coordinates of the maximum points found (Figure 5).

• PPMLC: angle formed by PML y PMc points with the origin of coordinates (Figure 5).

Thus, a total of 9 parameters are obtained for each user.

The areas of a progressive lens are defined as:

Ai (intermediate vision area or "intermediate vision clear zone"): area in mm² in the intermediate zone where the value of astigmatism is less than 0.50, and the value of the mean power is greater than + 0.25D of the far target power value and the average power value is less than 85% of the target value of the addition.

The size of the intermediate vision area (Ai) in mm² of the progressive lens will be determined from the angle formed by the PML and PMc points with the origin of coordinates (PPMLC), expressed in degrees (°), following a linear relationship forpPMi_c values between 0° and 18° according to the following relationship:

Ai = m x PPML + n wherein m has values between 0.5 mm²/⁰ and 1.5 mm²/⁰, preferably 1.0 mm²/⁰ and nhas values between 15 mm² and 30 mm², preferably 23 mm².

AL (far vision area or "far vision clear zone "): area in mm² in the far zone where the astigmatism value is less than 0.50D and the mean power value is less than +0.25D of the target far power value. In the upper part, the area limits 8mm above the pupil position (known as the fitting cross or segment). The lower part limits 4mm below thepupil at the point known as PRP.

The size of the far vision area (A_L) in mm² of the progressive lens will be determined from the average of the maximum horizontal and vertical amplitude of the gaze dynamics map in the far plane (Aabi), expressed in degrees (°), following a linear relationship for Aabi values between 10° and 80° according to the following relationship:

A_L = i x A.ab_L + j

Wherein i values are between 1.0mm²/° and 1.4mm²/⁰, preferably 1.2mm²/° and j values are between 120mm² and 160mm², preferably 140mm².

Ac (near vision area or “near vision clear zone”): area in mm² in the near zone where the astigmatism value is less than 0.50D and the mean power value is greater than 85% of the target value of addition. At the bottom, the area limits 2 mm below the near reference point (known as the Near Reference Point or NRP).

The size of the near vision area (Ac) in mm² of the progressive lens will be determined from the average of the maximum horizontal and vertical amplitude of the gaze dynamics map in the near plane (Aabc), expressed in degrees (°) , following a linear relationship for Aabc values between 10° and 80° according to the following relationship:

Ac = k x Aab_c + I wherein k values are between 0.15mm²/⁰ and O.25mm²/⁰, preferably 0.20mm²/° and where I values are between 20mm² and 30mm², preferably 25mm².

By virtue of the method of the invention it is possible to design a lens whose areas are specially adapted to the dynamics of the user's gaze.

As stated in a previous section, some examples are described below to design a progressive lens with the information provided by the methods of the present invention using some of those prior art known models/methods.

DESIGN OF A PROGRESSIVE LENS USING THE VALUES OBTAINED WITH THE CLAIMED METHOD:

Next, it is shown that, given some values of the sizes of the far, near and intermediate vision area, obtained with the method of the first aspect of the invention, and using the known trapezoid model/method, one can calculate a progressive lens with these values. In addition, given the same values of the near and intermediate distance vision area, using the known models/methods of arcs of circumference, ellipses or polynomials of degree n, in case of obtaining some variants, these variants will be equivalent.

An example for calculating a progressive lens using polynomials of different degrees and arcs of circumference, from some given values of the sizes of the far, near and intermediate vision area, is also provided below.

The objective of this disclosure is to demonstrate that, from some values of sizes of said areas, using the trapezoidal model/method or other more sophisticated known models/methods, a unique progressive lens that consequently has a unique shape and a unique amount of aberrations is obtained. The amount of residual aberrations are the amount of astigmatism. Two lenses with the same shape, have the same isolines of astigmatism, and consequently they have the same amount of residual aberrations. The relation between the astigmatism map and the amount of residual aberrations is explained in articles:

D. Meister, S.W Fisher. Progress in the spectacle correction of presbyopia. Part 1 : Design and development of progressive lenses, Clinical and Experimental Optometry, 91 , 240-250, 2008. https://doi.Org/10.1111/j.1444-

0938.2007.00245.x; and Eloy A. Villegas, Pablo Artal, Comparison of aberrations in different types of progressive power lenses, Ophthalmic & Physiological Optics (OPO) ,2004. https://doi.orq/10.1111/i.1475-1313.2004.00214.x

It is remarked that using other models/methods, for example more sophisticated models/methods where the arcs of trapezoids or polygons can be replaced by arcs of circumference, ellipse, etc., equivalent progressive lenses are obtained. Given the same size of areas, combined with the differences introduced by the mathematical optimization system in the result and together with the variation also provided by the FreeForm manufacturing system, the effective differences in the perception of use of these more sophisticated variants with respect to those of the trapezoidal method will be insignificant.

Calculation of the maximum and minimum values of the far, near and intermediate vision areas according to the invention

Based on the values of the parameters and formulas described in claim 1 , we then calculate the maximum and minimum values of the far (AL), near (Ac) and intermediate (Ai) vision areas.

According to the values of Aabi (between 10° and 80°), i (between 1.0mm²/⁰ and 1 ,4mm²/⁰) and j (between 120mm² and 160mm²), the area for far vision (AL) in mm² of the progressive lens (according to the formula A_L = i x Aab_L + j) can take values between 130 mm² and 272 mm².

According to the values of Aabc (between 10° and 80°), k (between 0.15mm²/⁰ and O.25mm²/⁰) and I (between 20mm² and 30mm²), the area for near vision (Ac) in mm² (according to the formula A_c = k x Aab_c + /) can take values between 21.5 mm² and 50 mm².

According to the values of PPMLC (between 0° and 18°), m (between O.5mm²/⁰ and 1.5mm²/⁰) and n (between 15mm² and 30mm²), the area for intermediate vision (Ai) in mm² (according to the formula 4/ = m x fiPM_LC + n) can take values between 15 mm² and 57 mm².

A first representation for the construction of a progressive lens from the gaze angles of a user is shown below. Definition of the "trapezoids method'

Method definition:

Given certain values of the area (in mm²) for far (AL), near (Ac), and intermediate (Ai) vision, let's see that for a 0.0mm inset lens, the shape of the trapezoid for the far area, trapezoid for the near area, and the rectangle for the area of intermediate vision are unique.

Firs, the development for building a lens that is as symmetrical as possible, and consequently using isosceles trapezoids, will be made. Once the rectangle for intermediate vision and trapezoids for far and near vision have been defined, one will see that the progressive lens that meets these shapes is unique and also the amount of residual aberrations will be the same.

In a first and second examples described below, an asymmetric lens will be built and one will see that using the trapezoid method and also using circumference arcs and polynomials to define the zones, the lenses obtained are equivalent.

Development:

Step 1 : Calculation of the upper and lower limits of the far, intermediate and near zone areas

As stated in a previous sections, for some embodiments, the far vision zone is limited to 8mm above fitting cross and 4mm below fitting cross. Usually (and for this example), the FC (Fitting Cross) is 4mm above the PRP (Prism Reference Point). Consequently this zone has a height of 12mm (3L=12). It is remarked that the FC is aligned with the pupil position, i.e., according to Lens Marking Guidelines Version 2.0, Developed by Lens Division of The Vision Council, Lens marking Task Force, June 2014: (the) "FITTING CROSS (abbr. FC): That point on a lens as specified by the manufacturer to be used as a reference point for positioning the lens in front of a patient’s eye."

As stated in a previous sections, for some embodiments, the near vision area is limited to 4mm above the NRP (Near Reference Point) and 2mm below the NRP Consequently this zone has a height of 6mm (ac=6).

As stated in a previous sections, for some embodiments, the intermediate viewing area is limited at the upper part by the PRP and in the lower part 4mm above the NRP. We define the height of this zone as ai, which will depend on the value of the NRP. According to the definitions of the present invention, the limits of the zones of Figure 6 are thus obtained.

The far and near area will be considered now in the form of a trapezoid, and the intermediate area in a rectangular shape (see Figure 7). Next, the shapes of these areas will be calculated and one will see that they are unique.

Step 2: Calculating the shape of the intermediate vision area

Once the limits of Figure 6 are established, for the intermediate zone there is only one way to obtain a rectangle that has area Ai. The height of said rectangle is defined according to the NRP (for example ai=8mm for a NRP located at y=-12mm and x=0mm). Once the NRP is defined, the value of ai is fixed. Consequently, the base of said rectangle is also fixed by the formula b =

since the area of the rectangle Apb ai.

At this point there have been defined (and fixed) the values of ai and b in Figure 8.

Note on the notation: note that AL (area in mm² of the far vision zone) is different from 3L, which is the value of the height of the far vision trapezoid expressed in mm.

The following references and dimensions are shown in Figure 8: bi= upper base of far vision trapezius

3L = height of the trapezium of the intermediate vision area b = base of the rectangle of the intermediate vision zone ai = height of the rectangle of the intermediate vision zone be = lower base of near vision trapezium ac = height of the trapezoid of the near vision zone

A progressive lens is defined by two continuous, derivable (smooth) surfaces. Consequently the lower base of the far vision trapezium coincides with b. And the upper base of the near vision trapezoid also coincides with b.

Step 3: Calculation of the shape of the far vision area

The distance vision area is an isosceles trapezoid with lower base b (calculated in the previous section) and area AL also previously fixed. The formula for the area of the trapezoid is SL (DL + b) 12, which takes the value of AL. The values of b, 3L and AL are defined above. Consequently, the value of bL is calculated as follows:

and consequently the isosceles trapezoid of the far zone is uniquely defined.

Step 4: Calculating the shape of the near vision area

The near vision area is an isosceles trapezoid with upper base b (calculated above) and area Ac also fixed above. The formula for the area of the trapezoid is ac (be + b) 12, which takes the value of Ac. The values of b, ac and Ac are defined above. Consequently, the value of be is calculated as follows:

and consequently the isosceles trapezoid of the near zone is uniquely defined.

Note that the rectangle of the intermediate zone and the isosceles trapezoids of the far and near zones are centered laterally (according to the line y=0) since a lens with inset=0mm is considered here.

Step 5: Calculation of the progressive lens

Once the bases and heights of the far and near vision trapezoids and the base and height of the intermediate vision rectangle have been defined, the shapes of the far, near and intermediate vision areas are defined and one can proceed to calculate the entire shape of the progressive lens. For this calculation the method in Cartesian coordinates defined in chapter 4 of the doctoral thesis (“Optimization methods for the design of progressive lenses”, Casanellas, Gloria. Polytechnic University of Catalonia, 2020. http://hdl.handle.net/10803/668877) will be used. Once the objective function has been chosen, the progressive lens obtained will be unique, as explained in chapter 4 of that doctoral thesis.

In that doctoral thesis it is indicated that if one solves the problem defined in Cartesian coordinates using the LOQO or KNITRO solver using the direct algorithm method, the solutions obtained are optimal and can be considered equivalent to each other. That is, the relative error is less than 0.3 and the results (although numerically they may be somewhat different, since they are iterative optimization methods, and a stop condition must be indicated), the solutions obtained in practice do not differ between them.

Specifically, the last paragraph of page 45 reads:

“All the problem instances calculated with LOQO and KNITRO using direct algorithm 1 have a relative error of fewer than 0.30, and we may therefore consider that these two solvers can produce a correct optimal lens for all of the 72 problem instances computed.”

For example, the legend of Figure 4.15 (see Fig. 9) of the doctoral thesis, page 48, states: “Figure 4.15: Astigmatism (left) and power (right) of the lens of family F7 and type T 1 using LOQO 6.0.6 (top) and KNITRO with the direct algorithm 1 (bottom), with a relative error of 0.29.” One can see that the power and astigmatism maps in Figure 11 are very similar, and in a manufactured lens they would be two lenses that could not be differentiated. It must be taken into account that according to the ISO standard (see ISO 8980-1 , Ophthalmic optics, Uncut finished spectacle lenses, Part i : Specifications for single-vision and multifocal lenses, 2017) and (ISO 8980-2, Ophthalmic optic, Uncut finished spectacle lenses, Part 2: Specifications for power-va nation lenses, 2017.), the manufacturing error can be up to 0.12D, and the isolines of these lenses are represented every 0.25D. It has to be remarked that the isolines of astigmatism (that are represented every 0.25D) are the same in both obtained solutions, and so on the amount of residual aberrations is also the same in both lenses.

Conclusion: the trapezoidal method allows, once the far, intermediate and near zone areas are defined, to calculate a single progressive lens that has said zone areas.

Example 1 : Example of construction of a progressive lens from the values of the far, near and intermediate vision areas using trapezoids

A progressive lens is going to be built herein with the NRP located at x=1.5mm, y=-11 mm that has the values (in mm²) of the following areas: the area of far vision (AL) is 201.48mm², the size of the area for near vision (Ac) is 47.25mm² and the size of the area for intermediate vision (Ai) is 17.5mm².

The trapezoids that have these areas according to the method described above (steps 1 , 2, 3 and 4) are built and then the trapezoids drawn in Figure 10 are obtained.

Specifically, to define the shape of the area for intermediate vision, a parallelogram with an area of 17.5mm² is considered. Said parallelogram limits in the upper part by the PRP and in the lower zone it limits 4mm above the near reference point (since the near zone limits 4mm above the near point (x=1.5, y=-11 mm), as described in a previous section. Consequently, the height of said trapezoid goes from y=0 to y=- 7mm, and the height of said trapezoid is 7mm. In order for it to have an area of 16.25mm², the only solution is that it has a base of 2.5mm. In this way, the area for intermediate vision is (7.0) * 2.5 = 17.5mm².

For the area for distant vision a lower base trapezoid of 2.5mm and a height of 12mm is defined. For it to have an area of 201.48mm², the only solution is for the upper base to have 31.08mm. See Figure 10.

The area of said trapezoid is then: height * [(lower base + upper base)/2] = 12 * [(2.5 + 31.08)/2 ]= 201.48mm².

To define the shape of the area for near vision, a trapezoid with a 2.5mm upper base is considered. The height of said trapezium is from y=-7.0mm (where the intermediate vision ends) to y=-13mm (2mm below the NRP). The height of said trapezoid is therefore 6.0mm. With these characteristics, the only trapezoid that has an area of 50.625 mm² must have a lower base of 11 mm. The near zone trapezoid is laterally centered at x=1.5mm (since the example lens has inset 1.5mm). Consequently, the lower base of the trapezium of the area for near vision goes from x=-4mm to x=7mm.

The area of said trapezoid is then: height * [(lower base + upper base)/2] = 6.0 * [(2.5 + 11)/2 ]= 47.25mm².

In Figure 10 the three zones that characterize the progressive lens design are shown.

Finally, the Cartesian coordinate model described in the above identified doctoral thesis is used and obtain the progressive lens of Figure 11.

One can see that the isolines of power and astigmatism in Figure 11 have some undulations. Using some other solver (as defined in chapter 4 of the aforementioned thesis) one could obtain other progressive lenses that have other astigmatism isolines that are slightly different, but these lenses would be equivalent to each other. In other words, they would differ just as little as the two progressive lenses in Figure 9, and consequently, according to the aforementioned ISO standards, they could not be differentiated once they were manufactured. It is also remarked that the amount of residual aberrations can be calculated using the astigmatism map.

Example 2: Example of construction of a progressive lens from the same values of the far, near and intermediate vision areas of Example 1 using polynomials of different degrees and arcs of circumference In Figure 12 the shapes of the far, intermediate, and near vision areas of Example 2 are shown.

Using the shapes of Figure 12, the progressive lens of Figure 13 is obtained.

The progressive lens obtained in Figure 13 is equivalent to the progressive lens obtained in Figure 11.

In this way it has been shown that, given the sizes of the near, intermediate and near areas of a progressive lens, and also given the point of DRP, FC and NRP, the progressive lens that is obtained using the trapezoid method is unique in terms of its specification. It is also unique if geometric shapes of equal area are used. Again, the amount of residual aberrations can be calculated from the astigmatism map. There may be slightly different physical lenses induced by convergence of mathematical process and manufacturing process variations but being below the threshold of human perception the different physical lenses can be considered the same once manufactured.

Next, some examples from the bibliography where it is defined how to design a progressive lens from the contour design of different zones are cited. To use said contours, polygonal Figures are used, in a similar way to that described above in a previous section.

[1] Fanhuan Zhou: Design of Progressive Additional Lens with Wavefront Tracing Method. A dissertation submitted to the faculty of the graduate school of the University of Minnesota. Doctor of Philosophy, September 2010.

Especially relevant are pages 78-84 where there is an example of progressive lens design from polygon shapes or piecewise functions.

[2] Wei Jiang, Weizhu Bao, Qinglin Tang, Hanquan Wang, A variational-difference numerical method for designing progressive-addition lenses, Computer-Aided Design, Volume 48, 2014, Pages 17-27, ISSN 0010-4485, htps://doi.Org/10.1016/i.cad.2013.10.011.

Especially relevant is Figure 3 on page 10, where a partition of seven subregions of the computational domain Q is shown.

On page 10 lines 13-17 of article [2] it is defined: “As shown by Figure 3, the large red subregion is used for distance-view, the small blue subregion is used for near-view, and while the green subregion which connected with the two is used for intermediate-view. The rest of the subregions in Q belong to the blending zones, and we divided them into four in order to easily assign them the values of the weight functions and the prescribed mean curvature function.”

In reference [2] it is explained how to calculate a progressive lens from the definition of the anterior regions. Finally, in the thesis [3] already cited above,

[3] "Casanellas, Gloria; Optimization methods for the design of progressive lenses". Polytechnic University of Catalonia, 2020.

⁷ , in Figure 4.6 on page 32 the zones used to calculate a progressive lens are defined from arcs of ellipses, circumferences, polygonal shapes and polynomials of different degrees. In addition, in said doctoral thesis it is explained how to calculate a progressive lens from the definition of said zones.

Consequently, these three bibliographic references explain different methods for designing progressive lenses in the way proposed by the present invention, i.e. from the size of the areas, calculating the shape of the areas, and finally the progressive lens. In view of this description and Figures, the person skilled in the art will be able to understand that the invention has been described according to some preferred embodiments thereof, but that multiple variations can be introduced in said preferred embodiments, without exceeding the object of the invention as claimed.

Claims

1 . Method to establish the size of the zones of near Ac, far AL and intermediate Ai vision of a progressive lens, characterized in that it comprises the following stages: a. generation of a gaze map through the use of virtual reality in a near plane and a distant plane; b. calculation of the maximum horizontal amplitude of each map in degrees, AaL.Aac; c. calculation of the maximum vertical amplitude of each map in degrees Abi, Abe; d. determination of the size of the far vision area AL in mm² from the average of the maximum horizontal and vertical amplitude in the far plane, AabL, following a linear relationship whose result for AabL values between 10° and 80° is obtained according to the following relationship:

A_L = i ^x Aab_L + j, wherein i values are between 1.0 mm²/⁰ and 1.4 mm²/⁰ and j has values between 120mm² and 160 mm²; e. determination of the size of the near vision area Ac in mm² from the average of the maximum amplitude in horizontal and vertical in the near plane Aabc followinga linear relationship whose result for values of Aabc between 10° and 80° is obtainedaccording to the following relationship:

2. Method to establish the size of the zones of near Ac, far AL and intermediate Ai vision of a progressive lens according to claim 1 , wherein i has a value of 1 .2 mm²/⁰ and j has a value of 140 mm².

3. Method to establish the size of the zones of near Ac, far AL and intermediate Ai vision of a progressive lens according to any of the preceding claims, wherein k has a value of 0.02 mm²/⁰ and I has a value of 25 mm².

4. Method to establish the size of the zones of near Ac, far AL and intermediate Ai vision of a progressive lens according to any of the preceding claims, wherein m has a value of 1.0 mm²/⁰ and n has a value of 23 mm².

5. Method to establish the size of the zones of near Ac, far AL and intermediate Ai vision of a progressive lens according to any of the preceding claims, wherein AL is the area in mm² in the far zone where the astigmatism value is less than 0.50D and the mean power value is less than +0.25D of the target far power value; said area AL limiting, in its upper part, 8mm above the pupil position, and, in its lower part, 4mm below the pupil at the prism reference point.

6. Method to establish the size of the zones of near Ac, far AL and intermediate Ai vision of a progressive lens according to any of the preceding claims, wherein Ac is the area in mm² in the near zone where the astigmatism value is less than 0.50D and the mean power value is greater than 85% of the target value of addition; said area Ac limiting, at the bottom, 2 mm below the near reference point.

7. Method to establish the size of the zones of near Ac, far AL and intermediate Ai vision of a progressive lens according to any of the preceding claims, wherein Ai is the area in mm² in the intermediate zone where the value of astigmatism is less than 0.50D, and the value of the mean power is greater than + 0.25D of the far target power value and the average power value is less than 85% of the target value of the addition.

8. Method to establish the size of the zones of near Ac, far AL and intermediate Ai vision of a progressive lens according to any of the preceding claims, wherein said origin of coordinates is the origin (0,0,0) of a Cartesian coordinate system at the midpoint of a vector joining the user's pupils, wherein the xy plane is defined parallel to the ground and the z axis perpendicular to the ground.

9. Method for manufacturing a progressive lens comprising delimiting the size of the areas of the near Ac, far AL and intermediate Ai vision zones, wherein said size has been calculated according to any of the preceding claims.

10. A computer program product comprising program code means which, when loaded into a processor, causes said program code means to execute the method of claims 1-8.