WO1986000146A1

WO1986000146A1 - Light diffusing lens

Info

Publication number: WO1986000146A1
Application number: PCT/SE1985/000238
Authority: WO
Inventors: Stig Berglund; Ernst GRANSTRÖM
Original assignee: Ernst Granstroem AB
Current assignee: Ernst Granstroem AB
Priority date: 1984-06-07
Filing date: 1985-06-07
Publication date: 1986-01-03
Anticipated expiration: 1986-12-07
Also published as: AU4498785A; DE3568496D1; JPS61502355A; SE8403074D0; BR8506773A; EP0185069B1; AU581670B2; EP0185069A1

Abstract

A light-diffusing lens for use with optical arrangements such as traffic signals, where the light diffusion is to vary as a function of the viewing angle and be different in two orthogonal planes comprising the optical axis of the arrangement, in which a light source projects a beam of rays towards the lens and so that the lens shows one or several light-emitting zones within the entire viewing range, especially so that the light diffusion occurs within at least one predetermined maximum angle zone calculated from the optical axis. The optical arrangement comprises a lens surface which on one side is designed with one or several non-rotation symmetrical calotte-shaped cavities and/or projections which were there are several cavities and/or projections form elementary lenses every one of which provides one or several light-emitting zones and which are designed as complete or partial toroid-shaped or two-axis aspheric toroidal (atoric) calottes, especially so that the large axis (x-x) of the calotte lies orientated in vertex (5) of the said plane through the elementary lens and parallel to that plane where the light diffusion is lowest, and so that the small axis (y-y) of the calotte lies orientated in the opposite plane, where the light diffusion is highest. A lens of the said type is well suited for diffusing light substantially only within a half-plane of a quadrant of the optical arrangement's lens surface.

Description

Light diffusing lens

The present invention relates to an optical lens or an assembly of a number of cooperating optical lenses, e.g. for use in traffic signals, which are specially designed to bring about a specific light distribution when light passes through them. It is known that with traffic signals having modern concentrated light sources the achievement of adequate diffusion of the nearly parallel beam of light reaching the lens via the given parabolic reflector gives rise to difficulties. International standards (CIE 1980) have been laid down concerning the required light distribution (see figure l), and it can be shown that present traffic signals do not meet the said international standards, especially not where traffic signals have concentrated light sources.

One object of the invention has accordingly been to produce a light diffusing lens which produces inter alia the light distribution specified according to the said CIE standard (figure 1), which must be regarded as a minimum requirement for light diffusion in traffic signals. In this connection it is sufficient to take, into account the relative levels of light. The absolute levels of light depend on the intensity of the light source. Another object of the invention has been to produce a lens enabling the energy requirement of the light source to be reduced by designing the lens in such a way that the light is substantially diffused only within the area in which this is necessary, i.e. only below the horizontal level. The light diffusing lens in accordance with the invention consists of one or preferably a large number of cooperating non- rotation symmetric elementary lenses which are substantially identical and which are so arranged on the inside of the lens body that their contribution to the light distribution on a remote plane in front of the lens is substantially the same, i.e. that the elementaiy lenses are substantially orientated in the same way in respect of the incident light. If the light diffusing lens is concave, which is normal, the elementary lenses may, as an extreme case, be arranged stepwise with parallel axes and in such a manner that the vertices substantially join so as to form a surface having the radius of curvature of the lens. By way of another extreme case it is also possible to have the axes of the elementary lenses pointing towards the centre of the lens' curvature.

Since the required light distribution is not rotation symmetric the elementary lenses must be non-rotation symmetric. Since light diffusion in an upward, direction is neither required nor desired one can in principle make use of half-lenses. If the elemental^ly lenses are concave use is made of the lower half, and if the elementary lenses are convex use is made of the upper half. This has already been described in the literature. The most readily available non-rotation symmetric surfaces suitable for this purpose are toric surfaces or surfaces constituting sections of ellipsoids of revolution. However, these surfaces are far from providing the required light distribution. In order to bring about the required light distribution a new type of two-axis aspheric toroidal surfaces has come to be introduced, and these will henceforth be referred to as atoric surfaces. in atoric surface is so designed as to have, in the same way as a toric surface, two planes of symmetry designated as a rule as the x-plane and the y-plane. Another property which they have in common with toric surfaces consists in the fact that the intersection lines ob¬ tained when the atoric surface is intercepted in a plane (p-plane) parallel to the tangential plane at the vertex consist of ellipses (p-ellipses) . As regards toric surfaces the rule applies that the intersection lines obtained with planes containing the surface normal at the vertex consist of circular arcs. With atoric surfaces the general rule applies that these intersection lines (axial intersection lines) consist of monotonic functions (functions without maxima and minima) .

The atoric surfaces can be classified in different groups. The first group consists of surfaces where the axial intersection lines lack inflexion points. These surfaces are referred to as "atoric surfaces of the 0th order". In general an atoric surface where all axial intersection lines have n inflexion points is known as an "atoric surface of nth order". By a "regular atoric surface of nth order" is meant an atoric surface of nth order in which the number of inflexion points between two p-planes for different axial intersection lines differs by not more than a unit. By a "harmonic atoric surface of nth order" is meant an atoric surface of nth order where the number of inflexion points between any two p-planes for any different axial random lines is always the same. An "atoric calotte" is a part of an atoric surface located on the side of a p-plane containing the vertex. The said p-plane is known as an "atoric calotte base". An atoric surface is defined entirely by two axial intersection lines, the x-axis and the y-axis. It is advantageous to select two "orthogonal axial intersection lines", i.e. axial intersection lines obtained with two orthogonal planes - advantageously planes containing the x- and y-axes in the Euclidian system of coordinates. The said orthogonal axial intersection lines may in general be any two symmetric functions, both convex or both concave at the vertex these being known as an "atoric x-function" and an "atoric y-function" respectively. As regards the elementary lenses in the light diffusing lens it is assumed that the y-axis is substantially located in the horizontal plane. A general formula for an atoric x-function f(x) is

f(x) = ex² / [1 + Vl-(a+l)c²x²J + . a_± \ x\^X + S(x)

¹⁼³ (formula 1) where c is a constant cf curvature

38. is a constant of conicity a., i between 3 and. m, are so-called aspheric constants, and S(^x) is ^{a sum} of spline functions.

Atoric y- unctions are defined in an analogous way. formally all a. are equal to zero or also S(x) is equal to zero.When all a. are equal to zero and S(x) is equal to zero but 3^β is different from zero one always obtains atoric surfaces of 0th order. If also * equals zero both for the x-function and the y-function the result is a toric surface.

To achieve a light distribution of the type shown in figure 1 the large or long axes of the p-ellipses must be located along the x-axis, and the ratio between the large axis and the small axis of each elementary lens should be about 1.3 - 1.5.

In a first embodiment - type A - shown in figures 2 and 3 the atoric calotte is of Oth order, in a second embodiment - type B - shown in figure 4 the calotte is a regular or harmonic calotte of first order, and in a third embodiment - type C - shown in figure 5 we have a calotte of 3rd order.

With the emdobiment type A (atoric calotte without inflexion points) one sees in every elementary lens a light-emitting area which changes its position and appearance as a function of the viewing angle. With the embodiment of type B (atoric calotte with one inflexion zone in the surface of the calotte) one can see, at least from and including viewing angles larger than a certain minimum angle, two different light-emitting areas in every elementary lens, which should be deemed an advantage by comparison with the embodiment type A since the light is distributed more evenly over the surface of the lens. As a result one achieves inter alia the advantage of covered symbols on a traffic signal lens becoming clearer.

Another advant-age of the embodiment according to type B (see figure 4) consists in the fact that an atoric calotte of first order (one inflexion zone per calotte plane) does not have its maximum inclination at the edge of the atoric calotte base, which is the case with the embodiment according to type A, except in the inflexion zone. This entails that with the embodiment according to type B with negative or concave elementary lenses a larger maximum inclination of the axial intersection lines is acceptable than with the embodiment according to type A, without getting interference from adjacent elementary lenses. This also gives rise to production advantages inasmuch as more obtuse angles are achieved at the junctions between the various elementary lenses. Interference between two adjacent elementary lenses means that light from one lens passes into the other lens. This can cause problems already for the substantially parallel light coming via the parabolic reflector. The phenomenon becomes more accentuated as regards the light direct from the light source as well as in the case that when the light refraction surface of the elementary lens is rough, it may incidentally be desirable since it produces a further diffusion of the light over the surface of the lens.

An atoric calotte of third order - type C - such as shown in figure 5 yields in its turn and from certain viewing angles up to four light-emitting areas per calotte surface, which contributes to a more even light distribution over the surface of the traffic signal. One advantage of negative or concave elementary lenses consists in the fact that with identical strength requirements less material is required, and as the abcve comment on interference between adjacent elementary lenses indicates the use of concave lenses is facilitated if they are designed in accordance with type B or possibly type C. The maximum inclination (Of) with the y- or x-function can, if the largest viewing angle ( ) in the horizontal or vertical direction is known, be simply calculated using a formula as such known, the designations being as shown in the following figure:

°t = _,+arctg(sin( )/(n • cos(arcsin(sin(β)/n))-l)) (formula 2)

So as to be able to achieve a light distribution of the type shown in figure 1 it is necessary with the embodiment according to type A that the y-function of the atoric calotte base has an inclination of not less than about 50°. To avoid, with re erence to parallel incident light interference between adjacent elementary lenses the same inclination must not exceed 6θ° if the elementary lenses are concave. This is a condition affecting the choice of parameters in formula 1. Another condition consists in the "atoric calotte height", i.e. the distance along the surface normal at the vertex from the atoric calotte base. For practical reasons the calotte height should not be higher than about 0.5 times the "atoric calotte width", i.e. the extent of the atoric calotte base along the y-axis. From a functional point of view it is not advisable for the atoric calotte height to be less than 0.2 times the atoric calotte width. With practical embodiments factors in the range 0.25-0.30 have been found suitable.

In practice it has proved that the ratio between the extent of the calotte base along the large axis (x-x in figure 1) and the small axis ( - in figure 1) should be about 1.3-1_*5_. whereas the calotte height advantageously has a value of 0.2-0.5 or preferably 0.25-0.30 in relation to the extent of the calotte base along the small axis (j-j) .

The maximum inclination of an intersection line in relation to the plane in which the light diffusion is highest, subsequently referred to as the 1-plane should, with lenses having a refraction index of for instance 1.4-1.6 be preferably 40-60°, and the ratio between the maximum inclination of the intersection line between the plane where the light diffusion is lowest, subsequently referred to as the s-plane, and the maximum inclination of an intersection line in relation to the 1-plane should be about 0.7-0.8. As regards the atoric x-function the rule correspondingly applies that the inclination at the edge of the calotte base should be at least 40°. With the embodiment type A there are therefore two conditions for both the atoric y-functions and the atoric x-function, i.e. on the one hand the inclination at the calotte base and on the other hand also the condition concerning the ratio between calotte height and calotte width, which in the case where in formula 1 all a.=0 and S is equal to zero substantially determines the two remaining parameter values c and ^«* . For solutions as regards type B and type C embodiments the same conditions apply in respect of the calotte height as with type A, however the minimum value of the maximum inclination is in this case governed by the inflexion points of the x- and -functions, where in this case the inclinations are after all largest.

A hybrid embodiment (type D) is also feasible, where the atoric x-function has no inflexion points whereas the atoric y-function has an inflexion point or vice versa (type E). By choosing atoric surfaces of higher orders than the first order, i.e. surfaces with several inflexion points, it is possible to achieve several light-emitting zones with each elementary lens thus further evening out the distribution of light over the surface of the lens. In practice it should however be sufficient not to go beyond atoric calottes of the first or possibly the third order.

The invention will now be described in greater detail with reference to the attached drawings. It should however be noted that the invention is not limited to the embodiments shown in the drawings and described in the text but that these should be regarded only as illustrative examples.

In the drawings figure 1 shows, as previously discussed, a schematic presentation of the standard recommended by CIE (1 80) concerning the distribution of light with a red traffic signal. Figure 2 shows the surface of a lens or elementary lens of 0th order in accordance with the above embodiment type A. Figure 3a shows a horizontal projection of the elementary lens surface in figure 2 viewed in the plane of the lens, and figures 3b and 3^G show horizontal projections of the same elementary lens surface in the x-plane and in the y-plane. Figures 4a, b and c show in the same way as figure 3 three different horizontal projections of an elementary lens surface of 1st order in accordance with type B as described above, and figure 5 shows likewise in the same way three different horizontal projections of an elementary lens surface of 3rd order in accordance with the said type C. Figure 6 shows an axial section through a traffic signal provided with a lens in accordance with the invention. Figures 7_> 8 and show different possible embodiments and distributions of elementary lenses within the inner surface of the lens. Figure 10 shows a section through a small part of a lens of concave type viewed along the line x-x in figure S, and figure 11 shows a plan view from within the lens in figure 10. Figure 12 shows in schematic form the path of the rays through the lens in figures 10-11 with one of the numerous cavities in the vertical plane, and figure 13 shows in corresponding manner the path of the rays through the cavity viewed in the horizontal plane. The figures 14 and 15 show in the same way as figures 12 and 13 the path of rays through a convex elementary lens intended for traffic lights. Figures 16 and 17 show two different alternative embodiments of negative or positive lenses or elementary lenses according to the invention. Figures 18 and 19 show curves corresponding to the form of the y-function or x-function, respectively with atoric surfaces of the Oth respective 1st order.

The special type of light diffusion required with a traffic light as discussed above and illustrated in figure 1 makes great demands on the lens, and a lens suitable for this purpose is provided with a large number of elementary lenses which cooperate so as to produce the required light diffusion. An example of an elementary lens surface of concave or convex form is shown in figure 2. This lens surface forms a two-axis aspheric toroidal surface of concave form, which according to the above definition is designated in the present context as an "atoric surface". The longitudinal axis or large axis is designated as the axis x-x and the small axis or short axis is designated as the axis J-J. The cavities may be impressed or cast on the inside of the lens or possibly the outside with the x-axis of the elementary lens surface extending in the calculated vertical direction of the lens, with the y-axis of the lens surface extending in the calculated horizontal direction of the lens. As indicated in figures 75 8, 9 and 11 the cavities can be arranged in different ways within the lens, and they can be designed in different sizes and located at different distances from one another depending on the required effect. In figures 2, 3_? 4 and 5 the calotte base is designated with the number 2, the atoric surface with 3₅ the transversely cut upper edge with 4, the vertex with 5_. the atoric y-function with 11 and the atoric x-function with 12.

Every cavity or projection according to figure 2 constitutes an atoric surface of the 1st or Oth order, designated according to the above definition as an atoric calotte surface. Such an atoric calotte surface is characterised in that it has two planes of symmetry, i.e. x-x and J-J, and in that all sections (p-plane) parallel to the vertex consist of ellipses (p-ellipses). Calotte surface 1 is bounded by a base surface or calotte base 2, a back or calotte surface 3 and a substantially transversely cut upper edge 4- In "the example shown, where the atoric surface is calculated for a traffic light the light pattern of which is shown in figure 1 and where the light diffusion in an upward direction is to be at a minimum surface 3 is °ut at vertex 5 of the surface. So as to enable a simple, tight and effective arrange¬ ment of the cavities these can be designed with a substantially hexagonal base surface but they can also be provided inscribed within a square, rectangle or circle or impressed or cast in the surface of the lens quite independently from one another as indicated in figure 11. The illustrated atoric calotte surface 1 is so designed that the calotte base 2 has a semi-elliptical projected surface, each section in the surface parallel to vertex 5 and calotte base 2 forming an ellipse. The atoric surface is so calculated that its x-function corresponds to the above formula 1. The cavity being designed in this manner one obtains a visible light-emitting zone β in each elementary lens formed by the cavity or projection, the intensity of the light ostensibly differing when viewed in different directions in relation to the optical axis of the lens.. Viewed from above the intensity of light is small, its maximum value being along the optical axis of the cavity at right angles to vertex 5_» and it decreases gradually and in a predetermined manner outward in all directions from the optical axis. The intensity of the light decreases at a higher rate in the downward direction than towards the sides and it has its minimum value in the upward direction. Within the elementary lenses optical light refraction occurs, causing the light-emitting zone β in every elementary lens 7 ^"fc° apparently change position as the viewer steps back from the optical axis, i.e. as a function of the viewing angle, and the light-emitting zone 6 does not entirely disappear from view before the viewer is outside the actual range of visibility.

In order to achieve a special effect the aspheric surface can be designed as shown in figure 4- In this case the atoric surface is of the 1st order, and it will be seen that the transverse back line, i.e. the y-plane has a double curvature so that emanating from an inflexion point 8 on either side of the vertex it forms a convex part of the elementary lens cavity. As a result it is possible to observe from

» certain side angles two light zones in every elementary lens thus achieving a tighter light pattern.

It is also possible to achieve at certain angles in respect of the optical axis more than two light-emitting zones, by using atoric surfaces of the 2nd or a higher order. An atoric surface of the 2nd order designed with two inflexion zones may entail excessively large angles in relation to the calotte base at the edge of the base, in which case undesirable interference between adjacent atoric surfaces may occur with concave elementary lenses, this design being accordingly less suitable. Figure 5 shows a more advantageous embodiment, where the surface is of the 3rd order and so designed that the axial intersection lines have three inflexion zones at either side of the vertex, and such a surface will at certain angles possess up to four light-emitting zones for each elementary lens.

Figure 12 shows in schematic manner the path of rays in the- vertical plane through a concave elementary lens in accordance with figures 10 and 11. It will be seen that theelementary lens does not refract any light rays in the upward direction but that the rays nearest to the upper edge of the toric surface pass substantially unrefracted and that the remaining parallel incident rays are refracted in directions downward from the horizontal plane as they pass through the lens.

Figure 13 shows how the rays in the horizontal plane are refracted in the manner of a fan. As can be seen in figure 1 the light intensity declines in a predetermined manner from a maximum value at an angle of 0-5° down to about 15-7« ^ light intensity at an angle of 30° at either side of the optical horizontal axis.

Figures1 and 17 show twoalternative embodiments of a lens or an elementary lens in accordance with the invention, intended to produce light diffusion substantially only within a quadrant, i.e. in the case of concave lenses in the quadrants from the horizontal plane and downward, i.e. in figure 16 between 270° and 360° and in figure 17 in the zone between angles 180° and 270°. With convex lens surfaces the light diffusion is opposite, i.e. in figure 16 in the zone between 0° and 180° and in figure 17 in the zone between 0° and 90°. Figures 18 and 19 show the principal forms of the optimal y- and x-functions of atoric surfaces of the Oth order or 1st order, respective¬ ly. The y-function is designated with 21 or 21 ' , respectively, and the x-function with 22 or 22', respectively. As regards figure 19 it should be noted that the inclinations at the edge points 23 of the y-function or 24 of the x-function should preferably be such that the viewing angle is between 3 and 8°. The inclination can be calculated from formula 2 on page 5-

It is quite possible to combine concave and convex atoric surfaces in the lens surface in order to produce special effects and the concave and convex elementary lens surfaces can be arranged alternately or so that arranged in pairs, three by three etc. they form angle formations, optical text or pictorial symbols and similar effects. Even though the above description has dealt mainly with optical systems having a large number of elementary lenses of atoric type it will be obvious to any specialist that for certain purposes use can also be made of a single atoric lens, and the invention covers also this possibility.

Claims

P a t e n t C l a i m s

1. A light-diffusing lens for use with optical apparatus in which the light diffusion is to vary as a function of the viewing angle while being different in two orthogonal planes comprising the optical axis, and in which a light source projects a beam of rays towards the lens and so that the lens shows one or several light-emitting points within the viewing range, especially so that the light diffusion occurs within a predetermined maximum angle zone calculated from the optical axis, c h a r a c t e r i s e d in that the -lens is on one side designed with one or several non-rotation symmetric calotte-shaped cavities and/ or projections forming a lens or elementary lenses (7) every one of which provides one or several light-emitting zones (6, 9) and whereby the calotte-shaped cavities and/or projections are designed as complete or partially two-axis aspheric toroidal (subsequently jointly designated as atoric) calottes, especially so that the large axis (x-x) of the calotte base (2) lies orientated within vertex (5) of the said plane through the lens or elementary lens (7) and parallel to the said^' plane, at which point the light diffusion is least (subsequently designated the s-plane) whereas the small axis (y-y) lies in the corresponding plane (designated below as the 1-plane), where the light diffusion is highest. 2. A lens in accordance with claim 1 c h a r a c t e r i s e d in that the ratio between the extent of calotte base (2) along the large axis (x-x) and along the small axis (y-y) is about 1.3-1_*5, whereas the calotte height has a value corresponding to about 0.2-0.5 or preferably 0.25 to 0.30 of the extent along the small axis (y-y) of the calotte base.

3. A lens in accordance with claim 1 or 2 c h a r a c t e r i s e d in that the maximum inclination (Of) of an intersection line between an elementary lens and the 1-plane is expressed by the formula

Q< = +. arctg(sin (β))/(n- cos(arcsin( i )/n))-1)) (formula 2)

where the absolute value of the angle (ft) is within the range 30-45° and n is the index of refraction of the lens material. 4. A lens in accordance with claim 2 and/or 3 c h a r a c t e r¬ i s e d in that the inclination (oς¹) at the edge points for the y-function (23) is expressed by the formula

o = ± arctg(sin(ft', )/(n . cos(arcsin(sin(Λ')/n))-!))

where the absolutevalue of the angle β' is preferably within the range 3-8° and n is the index of refraction of the lens material whereby the minimum inclination of the line of intersection with the plane where the light diffusion is lowest (s-plane) and the maximum inclination of the line of intersection with the 1-plane is about 0.7-0.8. 5. A lens in accordance with any of claims 1-4 c h a r a c t e r¬ i s e d in that every elementary lens surface consists wholely or partially of atoric calottes of the Oth order (without inflexion zones).

6. A lens in accordance with any of claims 1-4 c h a r a c t e r¬ i s e d in that every elementary lens surface consists of atoric surfaces of the 1st order with one inflexion zone.

7. A lens in accordance with any of claims 1-4 c h a r a c t e r¬ i s e d in that every elementary lens surface consists wholely or partially of an atoric surface such that the intersection of the surface with the s-plane (x-x) has one inflexion point whereas the intersection of the surface with the 1-plane (y-y) has no inflexion point.

8. A lens in accordance with any of claims 1-4 c h a r a c t e r¬ i s e d in that every elementary lens surface consists wholely or partially of atoric surfaces such that the intersection of the surface with the s-plane (x-x) has no inflexion point whereasthe intersection of the surface with the 1-plane (y-y) has one inflexion point.

9. A lens in accordance with any of claims 1-4 c h a r a c t e r¬ i s e d in that every elementary lens surface consists wholely or partially of atoric surfaces of the 2nd order with two inflexion zones.

10. A lens in accordance with any of claims 1-4 c h a r a c t e r- i s e d in that every elementary lens surface consists wholely or partially of atoric surfaces of the 3rd order with three inflexion zones.

11. A lens in accordance with claim 5 c h a r a c t e r i s e d in that the surface has substantially one y-function (21) and one x-function (22) in accordance with the curves shown in figure 18.

12. A lens in accordance with claim 6 c h a r a c t e r i s e d in that the surface has substantially one y-function (21*) and one x-function (22') in accordance with the curves shown in figure 19- 13» A lens in accordance with claim 1 intended for diffusing light only on that one side of a plane (subsequently referred to as the light half-plane) comprising the optical axis of the arrangement, e.g. for use in traffic signals, c h a r a c t e r i s e d in that use is made substantially of half a section of atoric calottes which if the lens or elementary lens is concave (impressed) are located in the half-plane through the vertex (5) of the calotte which is a translation equivalent of the said light half-plane and which if the lens or elementary lens is convex (projecting) is located in the half- plane through vertex (5) of the calotte which is the translation equivalent of the half-plane opposite to the light half-plane.

14- A lens in accordance with any of claims 1-12 c h a r a c t e r i s e d in that the light half-plane is the plane below the horizontal line and in that the s-plane (x-x) is vertical (figures 12-15).

15« A lens in accordance with any of claims 1-12 for diffusing light substantially only within a quadrant (subsequently referred to as the light quadrant) relative to the optical axis of the arrangement, e.g. for use in traffic signals, c a r a c t e r i s e d in that use is made of substantially quadrant sections of atoric calottes, which if the lens or elementary lens is concave is the translation equivalent of the light quadrant and if the lens or elementary lens is convex is the translation equivalent of the quadrant opposite to the light quadrant (figures 16 and 17)• l6. A lens in accordance with claim 15 c h a r a c t e r i s e d in that the light quadrant consists either of the left or the right quadrant below the horizontal line and in that the s-plane (x-x) is either vertical or horizontal.

17- A lens in accordance with any of the above claims c h a r a c t e r i s e d in that the atoric calotte of the lens or elementary lens is so orientated that the tangential plane at the vertex (5) of the calotte is substantially parallel to the tangential plane of the surface of the optical arrangement, which can be flat or curved.

18. A lens in accordance with any of patent claims 1-16 c h a r a c t e r i s e- d in that every atoric calotte is so orientated that the tangential plane at vertex (5) of the calotte is substantially parallel to the tangential plane at the optical axis of the surface of the optical arrangement, which can be flat or curved.