Vision-compensating device, method for controlling a vision-compensating device and binocular optometry device

A vision-compensating device allowing observation along an optical axis of observation with an optical correction of variable power includes a lens having, along the optical axis, a spherical power that is variable as a function of a first control, and an optical assembly generating, along the optical axis, a cylindrical correction that is variable as a function of at least one second control applied to the optical assembly. The vision-compensating device also includes a module for receiving at least one setpoint for the optical correction and a module for determining the first control and the second control depending on the setpoint by way of a mode taking into account the distance separating the lens and the optical assembly. A method for controlling a vision-compensating device and a binocular optometry device are also proposed.

TECHNICAL FIELD OF THE INVENTION

The present invention relates to pieces of optometry equipment that are in particular intended for subjective eye tests.

It more particularly relates to a visual compensation device, to a method for controlling a visual compensation device and to an optometric binocular device.

TECHNOLOGICAL BACKGROUND

In the context of subjective eye tests, a visual compensation device is generally used to allow observation along an optical axis of observation with an optical correction of variable power.

For example, such a device is for example known from document US 2004/032 568; this device comprises a lens having, along the optical axis, a variable spherical power that depends on a first setting, and an optical assembly generating, along the optical axis, a variable cylindrical correction that depends on at least one second setting applied to said optical assembly.

In such a system it is for example proposed to display on a screen the optical correction values obtained by applying current settings, thereby allowing the practitioner to modify the settings to obtain other optical correction values.

This solution is however impractical since it obliges the practitioner to find by trial and error the visual correction values that he desires to test during the subjective eye test.

SUBJECT OF THE INVENTION

In this context, the present invention provides a visual compensation device allowing observation along an optical axis of observation with an optical correction of variable power, comprising a lens having, along the optical axis, a variable spherical power that depends on a first setting, and an optical assembly generating, along the optical axis, a variable cylindrical correction that depends on at least one second setting applied to said optical assembly, characterized by a module for receiving at least one setpoint for said optical correction, and by a module for determining the first setting and the second setting depending on said setpoint by means of a model taking into account the distance separating said lens and said optical assembly.

Because the aforementioned distance, i.e. the spacing between the lens and the optical assembly, is taken into account, coupling effects generated by this spacing are taken into account and, after the first setting and the second setting have been applied to the lens and to the optical system, respectively, a correction that corresponds precisely to the setpoint (i.e. to the correction desired by the practitioner) is obtained.

The module for determining the first setting and the second setting may furthermore comprise a module for determining an approximate first setting value and an approximate second setting value depending on said setpoint, a module for evaluating, on the basis of said model, at least one correction value obtained by applying the approximate first setting value to the lens and the approximate second setting value to the optical assembly, and a module for determining a corrected first setting value and a corrected second setting value on the basis of a comparison between the setpoint and the evaluated correction value.

The module for determining the first setting and the second setting may then use the first corrected setting value and the second corrected setting value respectively by way of first setting and second setting.

Thus, in real-time, setting values are obtained that allow the desired setpoint values to be obtained.

According to another envisionable embodiment, the module for determining the first setting and the second setting may be designed to read the first setting (and optionally the second setting) from a look up table constructed on the basis of said model.

In certain embodiments, the optical assembly may comprise a second lens and a third lens; the model may in this case also take into account the distance separating the second lens and the third lens.

The invention also provides a method for controlling a visual compensation device allowing observation along an optical axis of observation with an optical correction of variable power and comprising a lens and an optical assembly, characterized in that it comprises the following steps:receiving at least one setpoint for said optical correction;determining a first setting and a second setting depending on said setpoint by means of a model taking into account the distance separating said lens and said optical assembly;modifying the spherical power of the lens along the optical axis depending on the first setting; andmodifying a cylindrical correction generated along the optical axis by the optical assembly depending on the second setting.

The step of determining a first setting and a second setting may comprise the following substeps:determining an approximate first setting value and an approximate second setting value depending on said setpoint;evaluating, on the basis of said model, at least one correction value obtained by applying the approximate first setting value to the lens and the approximate second setting value to the optical assembly;determining a corrected first setting value and a corrected second setting value on the basis of a comparison between the setpoint and the evaluated correction value.

The control method may then optionally comprise the following substeps:evaluating, on the basis of said model, at least one new correction value obtained by applying the corrected first setting value to the lens and the corrected second setting value to the optical assembly;determining a new corrected first setting value and a new corrected second setting value on the basis of a comparison between the setpoint and the evaluated new correction value.

In this case, the substeps of evaluating at least one new correction value and determining a new corrected first setting value and a new corrected second setting value may be reiterated provided that the distance between the setpoint and the evaluated new correction value is larger than a preset threshold.

According to the aforementioned variant, the step of determining a first setting and a second setting may comprise a sub-step of reading the first setting (and optionally the second setting) from a look up table constructed on the basis of said model.

The invention also provides an optometric binocular device comprising two optical devices, which are for example mounted on a common holder, wherein one of the two optical devices (or even each of the two optical devices) is a visual compensation device as presented above.

FIG. 1schematically shows the main optical elements of an exemplary visual compensation device according to the teachings of the invention.

These optical elements comprise a convex planar-cylindrical lens2, of cylindrical power C1(here equal to C0), a concave planar-cylindrical lens4, of cylindrical power C2(here negative and equal to −C0), and a lens6of variable spherical power SV.

The absolute value (or modulus), here C0, of the cylindrical power (here −C0) of the concave planar-cylindrical lens4is therefore equal to the absolute value (C0) (or modulus) of the cylindrical power (C0) of the convex planar-cylindrical lens2.

These three lenses2,4,6are placed on the same optical axis X. Precisely, each of the three lenses2,4,6has a generally cylindrical exterior shape centered on the optical axis X. In the example described here, the lenses2,4,6have the following diameters (quantifying their bulk), respectively: 25 mm, 25 mm, 20 mm.

It will be noted that it is preferable to use this visual compensation device10with the eye of the patient located on the side of the variable spherical power lens6so that the cylindrical power lenses2,4, which are larger in diameter, do not limit the field of view defined by the variable spherical power lens6, which itself is perceived as large due to its proximity to the eye of the patient.

Each of the three lenses2,4,6comprises a first planar face, perpendicular to the optical axis X, and a second face, opposite the first face and optically active:the optically active face of the lens2is cylindrically convex in shape (the axis Y1of the cylinder defining this face lying perpendicular to the optical axis X);the optically active face of the lens4is cylindrically concave in shape (the axis Y2of the cylinder defining this face lying perpendicular to the optical axis X); andthe optically active face of the lens6of variable spherical power SVis deformable and may thus be given a convex spherical shape (as illustrated by the line of equal length dashes inFIG. 1), a planar shape (as illustrated by the solid line) or a concave spherical shape (as illustrated by the line of unequal length dashes).

The lens6of variable spherical power SVis for example a lens of the type described in document EP 2 034 338. Such a lens comprises a cavity closed by a transparent deformable membrane and a planar movable transparent wall; the cavity contains a transparent liquid of constant volume that is constrained, to a greater or lesser degree, by the movable face, in order to deform the membrane that is thus either a spherical concave surface, or a planar surface, or a spherical convex surface. In the lens used, a transformation of motion achieved with a nut/bolt system makes it possible to ensure transformation of rotary and linear motion. Thus, rotating a ring mounted on a casing26translates a part of the lens6, thereby causing the aforementioned deformation of the transparent membrane, as explained for example in the aforementioned document EP 2 034 338. It is thus possible to vary the spherical power SVcontinuously via mechanical action on the lens6. In the example described here, the lens6has a variable focal length of between −40 mm and 40 mm, i.e. a variable spherical power SVof between −25 D and 25 D (D being the diopter, the unit for measuring vergence, inverse to the focal length expressed in meters).

Moreover, the planar-cylindrical lenses2,4have respectively as already indicated a cylindrical power of −C0and C0, here with C0=5 D.

As explained in greater detail below, the concave planar-cylindrical lens4and the convex planar-cylindrical lens2are rotatably mounted about the axis X (rotation centered on the axis X).

The axis Y1of the convex cylinder formed on the optically active face of the convex planar-cylindrical lens2may thus make a variable angle α1with a reference axis Y0(which is fixed and perpendicular to the optical axis X).

Likewise, the axis Y2of the concave cylinder formed on the optically active face of the concave planar-cylindrical lens4may make a variable angle α2with the reference axis Y0.

The convex planar-cylindrical lens2and the concave planar-cylindrical lens4are spaced apart by a distance e1along the optical axis; the concave planar-cylindrical lens4and the lens6of variable spherical power SVare spaced apart by a distance e2along the optical axis. In the embodiment described below with reference toFIG. 2, e1is for example (about) 1 mm (generally, e1may be comprised between 0.5 mm and 2 mm) and e2is for example (about) 5 mm (generally, e2may be comprised between 2 mm and 10 mm).

In order to explain the optical behavior of the system that has just been described in a simple way, the formulae for the spherical power S, the cylindrical power C and the angle of astigmatism α of the system formed from the three optical elements2,4,6will be given below, these formulae being obtained by calculating the vergence on the various meridians in a model in which the coupling effect caused by the spacings e1, e2between the various lenses is neglected:

It will be noted that the term (−C/2) in formula 3 corresponds to spherical power generated by the resultant of the 2 lenses providing cylindrical power.

By setting the rotational position of the convex planar-cylindrical lens2and the rotational position of the concave planar-cylindrical lens4independently of each other, as described below, it is possible to vary, independently, each of the angles α1and α2from 0° to 360° and thus obtain a cylindrical power C adjustable between −2.C0and 2.C0(i.e. here between −10 D and 10 D) for any angle of astigmatism, adjustable between 0° and 360°, obtained by controlling the two lenses simultaneously. As formula 3 indicates, the spherical power resulting from the resultant of the orientation of the 2 cylindrical lenses is compensated for using the spherical lens of variable power.

Moreover, by varying the spherical power SVof the spherical lens6, it is possible to adjust the spherical power S of the system formed from the three lenses2,4,6.

According to one envisionable variant, the lenses providing a set cylindrical power could have the same (positive or negative) cylindrical power C0: it could be a question of two, optionally identical, convex planar-cylindrical lenses or, as an alternative, of two, optionally identical, concave planar-cylindrical lenses.

Specifically, in this case, the spherical power S, the cylindrical power C and the angle of astigmatism α of the system formed from these two lenses and from a lens providing variable spherical power are given by the following formulae:

The term C0−C/2 corresponds to the spherical power induced by the combination of the two lenses providing cylindrical power.

It is therefore also possible in this case to adjust the spherical power S, the cylindrical power C and the angle of astigmatism α, in particular so that the hcylindrical power C is zero, by rotating the lenses providing cylindrical power (independently of each other) and by varying the spherical power of the lens providing variable spherical power.

An example visual compensation device10that uses the optical elements that have just been described is shown inFIG. 2.

Sometimes in the following description, in order to clarify the explanation, terms such as “upper” or “lower” will be used, which define an orientation inFIGS. 2, 3 and 4. It will be understood that this orientation is not necessarily applicable to the use that will possibly be made of the device described, in which use the only reference direction is the optical axis X.

The visual compensation device10comprises a casing12formed from a first portion14, a second portion16and a third portion18, which are placed in succession along the optical axis X and assembled pairwise in planes perpendicular to the optical axis X.

A first toothed wheel22is mounted so as to be able to rotate with a rotary movement centered on the optical axis X in the first portion14of the casing12and bears, at its center, in an aperture provided for this purpose, the convex planar-cylindrical lens2. The first toothed wheel22and the convex planar-cylindrical lens2are coaxial; in other words, in cross section in a plane perpendicular to the optical axis X, the exterior circumference of the first toothed wheel22and the circumference of the convex planar-cylindrical lens2form concentric circles centered on the optical axis X.

Likewise, a second toothed wheel24is mounted so as to be able to rotate with a rotary movement centered on the optical axis X in the second portion16of the casing12and bears, at its center, in an aperture provided for this purpose, the concave planar-cylindrical lens4. The second toothed wheel24and the concave planar-cylindrical lens4are coaxial; in other words, in cross section in a plane perpendicular to the optical axis X, the exterior circumference of the second toothed wheel24and the circumference of the concave planar-cylindrical lens4form concentric circles centered on the optical axis X.

A third toothed wheel27is mounted so as to be able to rotate with a rotary movement centered on the optical axis X in the third portion18of the casing12. The third toothed wheel27is securely fastened to the ring provided on the circumference of the casing26that bears the lens6of variable spherical power and allowing the spherical power SVto be controlled. The casing26of the lens6of variable spherical power is mounted in the third portion18of the casing12.

As may be clearly seen inFIG. 3, the first toothed wheel22is rotated (about the optical axis X) by means of a first motor42a drive axis of which bears a first worm screw32that engages with the first toothed wheel22. The first motor42is for example mounted in the first portion14of the casing12.

The current position of the first toothed wheel22is monitored by a first optical cell52.

Likewise, the second toothed wheel24is rotated about the optical axis X by means of a second motor44a drive axis of which bears a second worm screw34that engages with the second toothed wheel24. The second motor44is for example mounted in the second portion16of the casing12.

The current position of the second toothed wheel24is monitored by a second optical cell54.

As shown inFIG. 4, the third toothed wheel27is for its part rotated (about the optical axis X) by means of a third motor46that has a drive axis on which a third worm screw36that engages with the third toothed wheel27is mounted. The third motor46is for example mounted in the third portion18of the casing12.

The current position of the third toothed wheel27is monitored by a third optical cell56.

Each optical cell52,54,56is for example formed from a pair of elements comprising at least one optical sensor; the other element of the pair is for example an optical emitter (or, as a variant, a reflective element, in which case an optical emitter is associated with the optical sensor).

The first, second and third motors42,44,46are for example stepper motors having a resolution of 20 steps/turn, here set in 8ths of a step (referred to as micro-steps below). As a variant, these motors could be set in 16ths of a step. As a variant, it could be a question of DC motors with coders.

The internal volume of the casing12(and moreover the internal volume of each of the first, second and third portions14,16,18in the same way) may be subdivided into a space for receiving the motors42,44,46(upper region of the casing12inFIGS. 2, 3 and 4) and a space for receiving the optical elements2,4,6(lower region of the casing12inFIGS. 2, 3 and 4).

The space for receiving the motors42,44,46has an essentially parallelepipedal shape open (toward the bottom in the figures) in the direction of the space for receiving the optical elements2,4,6and closed at the opposite end (toward the top in the figures) by an upper face19of the casing12(the upper face19of the casing12being formed by the assembled upper faces of the first, second and third portions14,16,18of the casing12, respectively).

The arrangement of the motors42,44and46is such as to advantageously make it possible to use a circular geometry over 180°, said circular geometry being centered on the optical axis as close as possible to the useful radius of the lenses.

The space for receiving the optical elements2,4,6has, in contrast to the space for receiving the motors, a cylindrical shape (bounded by the walls of the casing12) that matches that of the third toothed wheel27over half the circumference of the latter.

In other words, the casing12(and therefore each of the first, second and third portions14,16,18of the casing12) has, in the space for receiving the optical elements2,4,6, a cylindrical shape with a diameter (perpendicular to the optical axis X) that is about the same as, and slightly larger than, that of the third toothed wheel27.

The respective diameters of the toothed wheels22,24,27are chosen so as to promote preservation of the field despite the thickness of the optical system.

The first motor42and the first worm screw32extend in the casing12in a direction Z perpendicular to the upper face of the casing12(and therefore especially perpendicular to the optical axis X) in such a way that the first motor42is housed in the space for receiving the motors whereas the first worm screw32lies in the space for receiving the optical elements.

As for the second motor44and the second worm screw34, they extend in the casing12in the same direction, but opposite the first motor42and the first worm screw34relative to the cylindrical power lenses2,4. The second motor44is housed in the space for receiving the motors whereas the second worm screw34lies in the space for receiving the optical elements.

Thus, it will be noted that the first worm screw32and the second worm screw34are located on either side of the assembly formed by the first toothed wheel22and the second toothed wheel24, and that the lateral bulk (along an axis Y perpendicular to the aforementioned axes X and Z) of these various parts (first worm screw32, second worm screw34, first or second toothed wheel22,24) is smaller than the diameter of the third toothed wheel27so that the first and second worm screws32,34are contained in the space for receiving the optical elements without extra room being required to receive them.

Moreover, the first and second motors42,44each have a bulk along the optical axis X larger than that of each of the first and second toothed wheels22,24, and even larger than that of each of the first and second portions14,16of the casing12. However, because these first and second motors42,44are placed as indicated above on each side of the casing12(relative to the axis Z), they may each occupy a space that extends, along the optical axis X, in line with the first portion14and the second portion16of the casing12.

For example, each of the first and second motors42,44has a lateral bulk (outside diameter of the motor) comprised between 6 and 12, for example 10 mm, whereas the first and second toothed wheels22,24each have a thickness (bulk along the axis X) comprised between 1 and 4, for example 2.5 mm.

The third motor46and the third worm screw36are in contrast located in the space for receiving the motors, in the region that extends along the axis X in line with the third portion18of the casing12. Thus, the third worm screw36engages with the third toothed wheel27in an upper portion of the latter, thereby making it possible for the casing12to follow closely the shape of the casing12in the lower portion of the third toothed wheel27, as indicated above.

In the example described, as shown inFIG. 4, the axis of the third motor46and the third worm screw36is slightly inclined relative to the upper face of the casing12(specifically relative to the aforementioned axis Y).

Provision is for example made for the thickness of the third toothed wheel27to be comprised between 0.3 mm and 2 mm.

This arrangement of the various elements allows a relatively thin casing to be obtained, typically having a thickness comprised between 15 and 20 mm.

The casing12also comprises, for example in the upper region of the space for receiving the motors, a control element50, here formed of a plurality of integrated circuits borne by a common printed circuit board.

Moreover a device for storing electrical power, here a battery58(though, as a variant, it could be a supercapacitor), is provided in order to make the apparatus standalone. Provision is for example also made for contactless elements for recharging the power storing device58. The battery58especially allows the motors42,44,46and the control element50to be supplied with electrical power.

The main elements of such a control element50, and their connections to the aforementioned motors42,44,46and to the aforementioned optical cells52,54,56, are schematically shown inFIG. 5.

The control element50comprises a receiving module60designed to receive, here via a wireless link, setpoint information, i.e. information indicating the values desired by the user for the spherical power S, the cylindrical power C and the angle of astigmatism α that define the compensation generated by the optical system formed from the optical elements2,4,6.

The receiving module60is for example an infrared receiving module that receives this setpoint information from an infrared emitting remote control controlled by the user. As a variant, provision could be made for this setpoint information to be received from a personal computer via a wireless link, for example a local wireless network; the user could in this case choose values of spherical power S, cylindrical power C and angle of astigmatism α for the visual compensation device by interactive selection on the computer.

The receiving module60transmits the setpoint information S, C, α received to a computing machine66(for example consisting of a processor executing a computer program so as to perform the functions of the computing machine, as described below), specifically to a converting module68implemented by this computing machine66.

The converting module68determines the values of the angles α1, α2and the value of the spherical power SVrequired to obtain the setpoint values S, C, α received as input, in accordance with what is described below with reference toFIG. 6.

The computing machine66also implements a control module70that receives as input the values of angles α1, α2and spherical power SVcomputed by the converting module68and emits control signals to the motors42,44,46, in order to control each of the motors42,44,46independently of the others so as to obtain respective positions for the toothed wheels22,24,27that allow the desired values to be obtained:the control module70controls the first motor42so as to make the first toothed wheel22turn about the optical axis X as far as the position in which the axis Y1of the optically active cylindrical surface of the convex planar-cylindrical lens2(borne by the first toothed wheel22) makes an angle α1with the reference direction Y0;the control module70controls the second motor44so as to make the second toothed wheel24turn about the optical axis X as far as the position in which the axis Y2of the optically active cylindrical surface of the concave planar-cylindrical lens4(borne by the second toothed wheel24) makes an angle α2with the reference direction Y0; andthe control module70controls the third motor46so as to make the third toothed wheel27turn about the optical axis X as far as the position in which the ring for controlling the variable spherical power sets the spherical power SVto the power computed by the converting module68.

The position of each toothed wheel22,24,27is known at each instant by virtue of the optical cells52,54,56, respectively, which each measure, on the toothed wheel with which each is associated, the number of teeth that have passed through the optical cell relative to a reference point on the circumference of the wheel in question (for example a point devoid of teeth).

In the example described here, the first motor42/first worm screw32/first toothed wheel22assembly, just like the second motor44/second worm screw34/second toothed wheel24assembly, has a gear ratio such that one turn of the toothed wheel22,24corresponds to 15040 micro-steps of the associated motor42,44. The resolution (angle of rotation of the toothed wheels22,24for one micro-step) is therefore 0.024° for the angles α1and α2.

The third motor46/third worm screw36/third toothed wheel46assembly for its part has a gear ratio of 16640 micro-steps per turn. The ring for controlling the variable spherical power is adjustable over an angular span of 120° (therefore corresponding to 5547 micro-steps) so as to obtain the variation in spherical power from −25 D to 25 D (i.e. a span of variation of 50 D). The resolution (variation in spherical power SVfor one micro-step) is therefore 0.009 D.

According to one envisionable embodiment, provision may be made for the control element50to take into account the distance between the entrance face of the spherical lens6and the vertex of the cornea of an eye observing through the visual compensation device, in order optionally to correct the power setpoints of the visual compensation device in question. This distance (sometimes denoted LED for “lens-eye distance”) may be obtained by known means for doing so.

Taking the example of a spherical power S of equivalent focal length F, a positioning error ε would mean a correction of focal length F′ would be required, equivalent to a spherical power S′, where:
F′=F−ε and

which to a first approximation gives S′=S·(1+ε·S).

The control element50therefore determines, according to this embodiment, the values of the angles α1, α2and the value of spherical power SV(and the control signals to respectively be applied to the motors as indicated above) not only depending on the setpoint values S, C, α received as input but also depending on the eye-device (here the cornea-entrance face of the lens6) distance. It will be noted that the lens-eye distance is here taken into account by the control element50, which receives raw setpoints (i.e. without the lens-eye distance accounted for).

Moreover, provision may be made, during passage from initial setpoint values α1, α2, SVto new setpoint values α′1, α′2, S′V, for each of the first, second and third motors42,44,46to be actuated for a given length of time T (in seconds) that may optionally depend on the amplitude of one of the setpoint changes (for example on the variation, in absolute value, in spherical power |S′V−SV|, where |x| is the absolute value of x).

To do this, the computing machine66for example determines the number p1of micro-steps of the motor42allowing passage from the angle α1to the angle α′1, the number p2of micro-steps of the motor44allowing passage from the angle α2to the angle α′2and the number p3of micro-steps of the motor46allowing passage from the spherical power SVto the spherical power S′V. The computing machine66then commands the motor42to rotate at a speed of p1/T micro-steps per second, the motor44to rotate at a speed of p2/T micro-steps per second and the motor46to rotate at a speed of p3/T micro-steps per second.

The control element50also comprises a temperature sensor62, which delivers information on measured ambient temperature, and an inclinometer64, for example taking the form of an accelerometer, which delivers information on the orientation of the visual compensation device10, for example relative to the vertical.

The computing machine66receives the item of temperature information generated by the temperature sensor62and the item of orientation information generated by the inclinometer64and uses these items of information in the context of the determination of the commands to send to the motors42,44,46.

In the example described, the control module70uses the item of temperature information in order to compensate for variations in the spherical power of the lens6due to temperature (about 0.06 D/° C. in the described example) and the item of orientation information in order to compensate for possible disturbances of the drive system (motors, worm screws, toothed wheels) due to changes in the orientation of the visual compensation device10.

An example of a way in which the converting module68may be constructed will now be described with reference toFIG. 6.

As already indicated, this converting module68is designed to determine the values of the angles α1, α2and the value of spherical power SVrequired to obtain the setpoint values S, C, α received as input, here using a model taking into account the distances e1, e2separating the various lenses.

As already indicated for the computing machine66, the converting module68is shown inFIG. 6in the form of functional blocks, but could in practice be implemented via the execution, by a processor (for example a microprocessor), of computer program instructions.

The converting module68comprises a first block80that receives as input the setpoint values S, C, α and determines on this basis approximate values {tilde over (α)}1, {tilde over (α)}2, {tilde over (S)}Vfor the angles α1, α2and the spherical power SV, for example as follows:

It will be noted that these formulae are based on those given above and do not take into account the spacings e1, e2separating the various lenses (hence the obtained results are designated as “approximate values”).

The approximate values {tilde over (α)}1, {tilde over (α)}2, {tilde over (S)}Vare transmitted to a second block82and to an adder block88.

The second block82receives as input the approximate values and estimates the values of spherical power S′, cylindrical power C′ and angle of astigmatism α′ that would be obtained (with the optical system formed from the two cylindrical lenses2,4and the lens6of variable spherical power) if the approximate values {tilde over (α)}1, {tilde over (α)}2, {tilde over (S)}Vreceived were used in the device. This estimation is based on a model taking into account the distances e1, e2separating the various lenses.

Here for example, using Gullstrand's equations, the optical power for each meridian (indicated by an angle ϕ) is (with the optical system formed from the two cylindrical lenses2,4and the lens6of variable spherical power):
P(ϕ)=SV+A1(SV)·P1(ϕ)+A2(SV)·P2(ϕ)+A3(SV)·P1(ϕ)·P2(ϕ)
where
P1(ϕ)=C1sin2({tilde over (α)}1−ϕ)
P2(ϕ)=C2sin2({tilde over (α)}2−ϕ)
A1(SV)=1+(e1−e2−K)·SV
A2(SV)=1−(e2+K)·SV
A3(SV)=−e1·(1−(K(SV)+e2)·SV)

K=w0-h·(1-1nLV),
where w0is the bow of the lens6, h the thickness of the lens6and nLVthe index of the liquid filling the lens6, K being the distance between the rest position of the membrane and the principal object plane of the variable lens.

The parameters A1, A2 and A3 are therefore variable functions of SV, whereas the other parameters are constants of the system (which may be calibrated).

By definition of the spherical power, of the cylindrical power and of the angle of astigmatism of the optical system, this optical power P may also be written, for each meridian:
P(ϕ)=S′+C′ sin2(α′−ϕ).

It is thus for example possible to obtain C′ and a′ by calculating the derivative dP/dϕ) of the function P(ϕ) and by taking 2 particular values (for example ϕ=0 and ϕ=π/4), this allowing tan 2α′ and C′2to be obtained.

The constant portion of P(ϕ) moreover gives access to S′ according to the above equation.

The values of spherical power S′, of cylindrical power C′ and of angle of astigmatism α′ generated as output from the second block82are transmitted to a subtracter block84, which computes the difference between each of these values and the corresponding setpoint value S, C, α. The subtracter block84thus outputs the following values (which represent, for each parameter, the error due to the use of the approximate values):
ΔS=S−S′; ΔC=C−C′; Δα=α−α′.

The error values ΔS, ΔC, Δα output from the subtracter block84are input into a third block86that is designed to determine the respective variations Δα1, Δα2, ΔSVin the settings α1, α2, SVassociated with these error values ΔS, ΔC, Δα (for example by linearization of the equality:
S′+C′ sin2(α′−ϕ)=SV+A1(SV)·P1(ϕ)+A2(SV)·P2(ϕ)+A3(SV)·P1(ϕ)·P2(ϕ)
around the values S′, C′, α′ and {tilde over (α)}1, {tilde over (α)}2, {tilde over (S)}V). The values of ΔS are for example obtained for {tilde over (α)}1, {tilde over (α)}2and {tilde over (S)}Vby respectively taking the derivatives dS′/d({tilde over (α)}1), dS′/d({tilde over (α)}2), and dS′/d({tilde over (S)}V). The process is identical for ΔC and Δα. Next, the obtained system of equations is solved conventionally using particular values.

The setting variations Δα1, Δα2, ΔSVare then input into the adder block88that also receives as input, as already indicated, the approximate values {tilde over (α)}1, {tilde over (α)}2, {tilde over (S)}Vgenerated by the first block80.

This adder block88therefore generates as output the following setting values:
α1={tilde over (α)}1+Δα1;
α2={tilde over (α)}2+Δα2;
ΔSV={tilde over (S)}V+ΔSV.

By virtue of the calculations performed above, these setting values α1, α2, SVallow the setpoint values S, C, α to be obtained while taking into account coupling effects related to the spacing of the lenses, with a minimum error related to the approximation made during the linearization used within the third block86.

According to one envisionable variant, as shown by the dashed line inFIG. 6, it is possible to apply one or more new iterations of the process described above in order to make each of the error values ΔS, ΔC, Δα converge toward 0 (the iterative process for example stopping when each of the error values is lower than a preset threshold). For these subsequent iterations, the setting values α1, α2, SVoutput from the preceding iteration are used by way of approximate values {tilde over (α)}1, {tilde over (α)}2, {tilde over (S)}Vin the current iteration.

It will be understood that the process that has just been described allows, depending on setpoint values S, C, α, setting values α1, α2, SVto be determined in real-time by means of a model taking into account the distances e1, e2separating the various lenses2,4,6.

According to another envisionable embodiment, the converting module68could store in memory (within a look up table or LUT) many triplets (α1, α2, SV) of setting values and, for each triplet (α1, α2, SV), the triplet of values (S, C, α) obtained using the setting values α1, α2, SVin question.

The triplets of values (S, C, α) associated with a triplet of setting values (α1, α2, SV) are computed beforehand using a module taking into account the distances separating the lenses2,4,6(for example by means of the equations given above) and stored in memory, as already indicated, in the converting module68.

In practice, triplets associated with possible values of S and C that are regularly distributed over the envisionable value ranges are stored in memory. For example, 160 values of S in the range [−20 D, 20 D] (this corresponding to an interval of 0.25 D) and 32 values of C in the range [0, 8 D] (this also corresponding to an interval of 0.25 D) are used and the parameter α is processed by simple rotation, this allowing only 5120 triplets of setting values (α1, α2, SV), each associated with one pair (S, C), to be stored in memory.

In operation, the converting module68selects, from the stored triplets (S, C, α), the triplet the values of which are closest to the setpoint values S, C, α received as input; the converting module68then reads the triplet of setting values (α1, α2, SV) that is associated (in the look up table) with the selected triplet and outputs the values read.

In the practical example that was just mentioned, the triplets (α1, α2, SV) are stored in memory each in association with a pair (S, C), and the converting module68reads the values (α1, α2, SV) associated with the pair the values of which are closest to the setpoint values S, C and makes a rotational correction in order to take into account the angle α.

According to one envisionable variant, it is possible to furthermore take into account temperature (in order to compensate, as indicated above, for variations in the spherical power of the lens6due to temperature). The converting module68for example in this case stores in memory a plurality of look up tables each associated with one given temperature. In use, the converting module68selects the look up table associated with the item of temperature information delivered by the temperature sensor62and performs the processing described above using the selected look up table.

According to another envisionable embodiment, the converting module68could determine the values of the angles α1, α2and the value of the spherical power SVrequired to obtain the setpoint values S, C, α received as input by means of a ray-tracing simulation, the ray tracing being carried out in an environment in which the lenses2,4,6are modelled in their respective positions and that therefore takes into account the distances separating these lenses2,4,6.

The visual compensation device10may be used to provide the Jackson-cross-cylinder function, Jackson cross-cylinders also being referred to as flip cross cylinders.

According to a first example, this function may be used to verify (or even find) an angle α0of required cylindrical correction (parameter sometimes denoted “cylinder axis”). Here, it is assumed that a spherical power correction value S0and a cylindrical power correction value C0have also been determined beforehand.

The Jackson-cross-cylinder function is then for example provided by applying in rapid alternation two sets of setpoints, namely a first set of setpoints corresponding to an addition of cylindrical power Cvar(for example 0.5 D) at 45° from the axis defined by the angle α0:an angle of astigmatism setpoint α1=α0−0.5·a tan(Cvar/C0);a cylindrical power setpoint C1=Root(C02+Cvar2), where Root is the square root function; anda spherical power setpoint S1=S0+C0/2−C1/2,

and a second set of setpoints corresponding to an addition of cylindrical power −Cvarat 45° from the axis defined by the angle α0:an angle of astigmatism setpoint α2=α0−0.5·a tan(Cvar/C0);a cylindrical power setpoint C2=Root(C02+Cvar2); anda spherical power setpoint S2=S0+C0/2−C2/2,

According to a second example, this function may be used to verify (or even find) the value of the required cylindrical power correction value C0. Here, it is assumed that a spherical power correction value S0and an angle of astigmatism value α0have also been determined beforehand.

The Jackson-cross-cylinder function is then for example provided by applying in rapid alternation two sets of setpoints, namely a first set of setpoints corresponding to an addition of cylindrical power Cvar(for example 0.5 D) on the axis defined by the angle α0:an angle of astigmatism setpoint α1=α0;a cylindrical power setpoint C1=C0+Cvar; anda spherical power setpoint S1=S0−Cvar/2,

and a second set of setpoints corresponding to an addition of cylindrical power −Cvaron the axis defined by the angle α0:an angle of astigmatism setpoint α2=α0;a cylindrical power setpoint C2=C0−Cvar; anda spherical power setpoint S2=S0+Cvar/2.