GB2523346A

GB2523346A - Free form fresnel lens

Info

Publication number: GB2523346A
Application number: GB1403037.3A
Authority: GB
Inventors: Richard Lewis; Michael John Hanney; Andrew Jonathan Dennington
Original assignee: Polymer Optics Ltd
Current assignee: Polymer Optics Ltd
Priority date: 2014-02-20
Filing date: 2014-02-20
Publication date: 2015-08-26
Also published as: GB201403037D0

Abstract

An improved Fresnel lens 21 may be created on any shape of base surface and allows light 20 from any source point on one side of the lens to be focused to any point 23 on the other side where either the source or focus can be at infinity, wherein the lens comprises a free form central optical zone (1, figure 1) and a plurality of transition surfaces (2) between optical zones (4, 5). The transition surfaces preferably have a shape that reduces optical losses and scattering. The modified shape of the transition surfaces may prevent undercuts to allow the part to be removed from a mould. The lens may be formed on a cylindrical base surface (figure 4) and offers an improvement on conventional circularly symmetric Fresnel lenses.

Description

FREE-FORM FRESNEL LENS

DESCRIPTION

BACKGROUND OF THE INVENTION

The Fresnel lens is a type of compact lens originally designed by the French Physicist Augustin-Jean Fresnel for use in lighthouses. The design of the lens allows for the production of a compact, short focal length lens without the bulk of material required in a conventional lens. The lens was first used in 1823 in a lighthouse in the Gironde Estuary, France. Up until now all Fresnel lenses have been generated by taking a 2 dimensional, (2D) curve and either rotating it about an axis, creating a circular Fresnel lens or alternatively sweeping it along a curve lying in a plane perpendicular to the plane of the 2D curve. This means is used to create a cylindrical Fresnel lens. The design of these lenses is carried out by ray tracing the profile in 2D so that light from the source is bought to a focus at the desired point. The 2D curves of early Fresnel lenses were limited to being comprised of sections of arcs but more recently aspheric curves that provide for better on-axis focus quality have been used. However even the best 2D aspheric designs only work well when both the source and focus lie on the rotational axis of a circular Fresnel lens or for an extruded Fresnel lens on a line of symmetry that passes through the centre line of the 2D curve.

The advent of accurate CNC machining has allowed for the creation of highly accurate complex 3D surfaces which cannot be described by either rotating or sweeping a 2D curve. Consequently creating Fresnel lenses on to these surfaces using the existing Fresnel lens design technique of optimising a 2D curve and using this to create a 3D surface is not possible. Even creating a Fresnel lens with good focus where either the source or focus lies a significant distance from the line of symmetry through the centre of the 2D curves from which they are constructed has proved impossible. What is needed is a design of Fresnel lens that can be applied to any 3D surface to focus light from an arbitrarily positioned point source on one side of a 3D surface to another arbitrarily positioned focal point on the other side.

Although it is possible to create the 3D surfaces of Fresnel lenses using a number of methods such as laser machining, CNC machining or 3D printing, a moulding process is best suited for mass production. However if in a moulded lens the tool split line is required to be at an angle to the transition surfaces between Fresnel zones there is a problem with them forming an undercut. This prevents the part being removed from the mould tool. With conventional circularly symmetric Fresnel lenses the solution has been to angle the transition surface to meet the minimum draft requirement but this has to be applied around the full 36U of the circular zone perimeter. The problem with this approach is that the resulting large increase in the area of the transition surface leads to significant optical losses and scattering. The design of a transition surface described here is an improvement because it allows the part to be removed from a mould with the minimum effect on the optical performance of the lens.

BRIEF SUMMARY OF INVENTION

The illustrated embodiment of the invention includes the design of a Fresnel lens of any thickness that can be created on any arbitrary 3D base surface, the Fresnel lens optical surfaces being designed such that light from an arbitrarily positioned point source on one side is focused to another arbitrarily positioned focal point on the other side of the surface. (Either the source or focus can be positioned at infinity). The Fresnel lens surface can be formed on either the focus side or the source side of the base surface. The illustrated embodiment is an improvement on conventional circularly symmetric Fresnel lenses which are limited to being formed on circularly symmetric base surfaces and also limited to designs where both the source and focus lie on or close to the rotation axis of the optical surfaces.

In one illustrated embodiment the Fresnel lens is created on a planar base surface inclined to the chief ray. In another illustrated embodiment a 3D Fresnel lens is shown formed on cylindrical base surface. Other embodiments such as forming the Fresnel surface on a generalised ellipsoid are possible. In general the invention allows the creation of Fresnel lenses on any arbitrary 3D surface.

The invention also includes an improved method for the design of transition surfaces between optical zones which reduces optical losses at the transition surface to a minimum. In another embodiment the design of improved transition surfaces for moulded Fresnel lenses are described.

These improved surfaces prevent undercuts allowing parts to be removed from a mould tool while having the minimum detrimental effect on the optical performance.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a perspective view of a free form Fresnel lens designed for an application where the chief ray is inclined at an angle of 45 degrees to a planar base surface. This shows the non-circular zones of a free form Fresnel lens optimised for this application.

FIG. 2 is a cross-section through the centre plane of the lens shown in FIG. 1. This shows that the gradient of the free form optical surfaces is not symmetric across the centre line of the lens.

FIG. 3 is a perspective view of a free form Fresnel lens designed for an application where the chief ray is normal to a cylindrical base surface. This shows the preferred embodiment where the inner and outer 3D perimeter curves of the optical surface zones are uniformly offset from the underlying base surface.

FIG. 4 is a cross-section through a plane perpendicular to the cylindrical base surface axis of the lens shown in FIG. 3. This shows the circular section of the cylindrical base surface in the section plane and that in the preferred embodiment the minimum and maximum thickness of the optical zones is the same across the lens.

FIG. 5 is a cross-section through a plane lying along the cylindrical base surface axis of the lens shown in FIG. 3. This shows the linear section of the cylindrical base surface in the section plane and that in the preferred embodiment the minimum and maximum thickness of the optical zones is the same across the lens FIG. 6 is a ray diagram showing the performance of a conventional axially symmetric Fresnel lens used in an application where the chief ray is at an angle of 20 to the planar surface of the lens. This shows how poor the focus quality of a conventional circularly symmetric Fresnel lens is with even a modest angle between the chief ray and the planar base surface.

FIG. 7 is a ray diagram showing the improved performance of a free form Fresnel lens used in an application where the chief ray is at an angle of 2O to the planar surface of the lens. This shows that for incident collimated light the free form Fresnel lens described in this invention is able to focus the incident light to a single point.

FIG. 8 shows the cross-section of a Fresnel lens where the transition surfaces are formed by extruding the outer perimeter curves of the Fresnel zones in the same vector direction. In this embodiment the vector direction is parallel to the centre line.

FIG. 9 shows the cross-section of a Fresnel lens where the transition surfaces are formed by extruding the outer perimeter curves of the Fresnel zones along a vector direction that is normal to the base surface.

FIG. 10 shows the cross-section of a Fresnel lens where the transition surfaces are formed by extruding the outer perimeter curves of the Fresnel zones along the direction vector of the refracted rays inside the lens.

FIG. 11 shows a ray diagram illustrating the total internal reflection ray paths that are the cause of optical losses and scattering that occurs from conventional transition surfaces between optical zones.

FIG. 12 shows a ray diagram illustrating the ray paths through the preferred embodiment of transition surface shown in Figure 10. This shows how in the preferred embodiment the ray paths that would have been obstructed from conventional transition surfaces are clear.

FIG. 13 shows the 3D cross-section through a moulded Fresnel lens where the transition surfaces are modified to allow it to be released from a mould where the split line is at an angle of 45 to the base surface.

FIG. 14 shows the 2D cross-section through the lens shown in Figure 12 where the transition surfaces are modified to allow it to be released from a mould where the split line is at an angle of to the base surface. The direction of ejection is arrowed.

DETAILED DESCRIPTION OF THE PREFERRED EMODIMENTS

The design of the free form Fresnel lens in this invention is characterised by the following: 1. The position of the apex of the central zone.

2. The 3D surface normal of the optical surfaces.

3. The 3D curve defining the outer extent of the optical surface of each zone.

4. The transition surface between zones.

5. The 3D curve defining the inner extent of the optical surface of each zone.

The position of the apex of the central zone of the free form Fresnel surface is unique and characterised as follows: Consider a virtual surface offset from the base surface such that it passes through the apex of the central zone. In the preferred embodiment this is the maximum thickness of the Fresnel lens. In a virtual 3D optical component that comprises this offset surface and the base surface, having a refractive index of the lens material, the position of the apex coincides with the only point on the virtual offset surface that a ray starting at the source will pass through and reach the focus point after refraction at the two surfaces.

The free form Fresnel optical surface form of the central zone is uniquely defined by the position of the apex and the direction vector of the 3D surface normal at every point on the surface. The optical surface forms of subsequent zones are defined by the 3D curve defining the inner extent of the optical surface and the direction vector of the 3D surface normal.

The 3D surface normal is calculated from the incident and output vectors of the light rays at the Fresnel lens surface and the refractive index of the lens material. As light can be considered reversible in conventional optics the focus and source are interchangeable, it is therefore preferred for the purposes of defining the Fresnel lens surface form that rays start from the focal point on the base surface side of the lens, whether or not this is the actual direction of light propagation.

The 3D surface normal at every point on the Fresnel lens optical surfaces is defined by the following 3D vector equation.

= ft * I-flQ * 5 Where: = Fresnel lens optical surface Normal vector.

ml = Refractive Index of the material on the incident ray side of the Fresnel surface optical boundary.

I = Unit incident ray vector at the Fresnel surface.

no = Refractive Index of the material on the output ray side of the Fresnel surface optical boundary.

0 = Unit output ray vector at the Fresnel surface.

It is usual for the normal vector to be scaled to a unit vector in which case the normal vector becomes: -+ t * * d -.

nj * I -no * The 3D incident unit ray direction vector fin the equation above is the direction of the ray which started at the focal point on the base surface side of the lens and was subsequently refracted at the base surface optical boundary before being incident on the Fresnel optical surface.

The 3D output unit ray direction vector 0 in the equation above is the direction vector pointing towards the focal point on the Fresnel surface side of the lens.

The refractive index no on the output ray side of a Fresnel lens will be 1 if the lens has an air interface. The refractive index ni on the incident ray side of the Fresnel optical surface will be that of the material from which the lens is made, for most common optical materials will lie between 1.5 and 1.9.

In the preferred embodiment the 3D curve that defines the outer perimeter of the free form Fresnel lens optical zones is defined by the intersection between the optical surface having the surface normal characteristics described above and a surface offset from the base surface by the minimum required lens thickness. If the thickness of the lens at the maximum extent of the optical zones is not required to be constant across the lens) the intersection of the optical surfaces with a surface that has the required variation in thickness from the base surface is used to define the outer perimeter curve.

Between the optical surfaces of the Fresnel zones there is a transition surface between the curve on the outer perimeter that has the minimum lens thickness and the inner perimeter curve of the next zone which is defined by points that have the maximum specified lenses thickness. The preferred embodiment that is most optically efficient is a transition surface formed by the translation of each point on the 3D outer perimeter curve of each zone along the refracted 3D ray direction vector inside the lens at that point to a point that is the maximum desired thickness from the base surface.

In another embodiment the translation vector used is the normal to the base surface. In yet another embodiment a fixed direction vector is used for translating the 3D curve defining the outer perimeter of one zone to produce the transition surface to the next zone.

In one particular embodiment where the Fresnel lens is to be manufactured by moulding, the translation vector for translating the outer perimeter of one zone to create the inner perimeter of the next zone must result in a transition surface that allows the part to be ejected from the mould tool. To allow the part to be ejected cleanly from the mould tool the draft angle of the transition surface must meet or exceed a desired minimum draft angle relative to the direction that the lens will be extracted from the mould tool. In this preferred embodiment where the translation vector around the perimeter of an optical zone, (whether defined by the refracted ray vector, the offset base normal vector, a fixed direction vector or some other means), does not meet the minimum draft angle it is replaced by a translation vector that is calculated to produce a transition surface meeting the draft angle requirement.

In the preferred embodiment the 3D curve that defines the inner perimeter of the free form Fresnel lens optical zones is defined by the intersection between the transition surface and a surface offset from the base surface by the maximum required lens thickness. If the thickness of the lens at the inner extent of the optical zones is not required to be constant across the lens, the intersection of the optical surfaces with a surface that has the required variation in thickness from the base surface is used to define the inner perimeter curve.

Turn now to Figures 1 & 2. Figure 1 shows a 3D view and Figure 2 shows a 2D cross-sectional view of a free form Fresnel lens designed to focus light from a source at infinity on the planar side to point focus on the Fresnel optical surface side where the planar base surfaceS is inclined at an angle of 2O to the chief ray. The surface form of the central optical zone 1 is defined by the position of the apex 6 and the direction of the surface normal as defined in the equations above. In the illustrated preferred embodiment the thickness of the lens is the same at all points around the outer bounding curve of the central zone 2 this being the minimum desired thickness of the lens. The lens thickness is also the same around all the other outer bounding curves of the first zone 4, the second zoneS and all other subsequent zones. The transition surface 7 is formed by translating the outer boundary curves along a direction vector that is defined at all points around the boundary curve. In the illustrated preferred embodiment shown in Figures 1 & 2 the thickness of the lens is the same at all points around the upper edge of the transition surface 3 for the central zone and all subsequent optical zones, this being the maximum desired thickness of the lens.

Figures 3 to 5 show the design of a free form Fresnel lens formed on a cylindrical base surface according to the invention described herein. In the illustrated design the source is positioned at infinity on the cylindrical side of the lens, the point focus is on the Fresnel optical surface side and the chief ray is normal to the cylindrical axis of the surface. Figure 3 shows a 3D view of the free form Fresnel lens, figure 4 shows a cross-section through a plane perpendicular to the cylindrical axis of the base surface) figures shows a cross-section through a plane parallel to the cylindrical axis of the base surface.

Figure 6 shows a ray trace through a conventional circularly symmetric lens 17 where the planar base surface is angled at 2O to the chief ray. The incident rays 16 are focused from a point source at infinity on to the focal plane 18. It can be seen that the rays are not brought to a point focus at 19 but suffer significant optical aberration.

Figure 7 shows the improvement in the focus quality of this invention compared to the conventional circularly symmetric lens shown in Figure 6. As in Figure 6 the planar base surface is angled at 2O to the chief ray and the incident rays 20 are focused from a point source at infinity to the focal plane 22. With this invention the rays are focused to a perfect point source which is a clear improvement over the conventional lens.

Figure 8 shows a cross-section through a free form Fresnel lens where the transition surfaces 25 are formed by the outer perimeter curve of the optical zones translated along the arrowed vectors 24 which are all pointing in the same direction.

Figure 9 shows a cross-section through a free form Fresnel lens where the transition surfaces 27 are formed by the outer perimeter curve of the optical zones translated along the arrowed vectors 26 that are all pointing in a direction that is normal to the base surface.

Figure 10 shows a cross-section through a free form Fresnel lens where the transition surfaces 29 are formed by the outer perimeter curve of the optical zones translated along the arrowed vectors 28 that are pointing in a direction that is aligned with the refracted ray direction inside the lens material at those points. To illustrate why Figure 10 is the preferred embodiment, Figure 11 shows a ray trace through an enlarged cross-section of the lens in Figure 8. In the embodiment shown in FigureS the incident rays 32 intercept the transition surface 31 and undergo total internal reflection before being refracted in a direction 30 away from the focus. This results in a reduction in the lens optical efficiency. In contrast Figure 12 shows an enlarged cross-section through the preferred embodiment shown in Figure 10 where the transition surface 34 is formed by a translation vector aligned with the ray direction inside the material. It can be seen that the rays 35 in contrast with those in Figure 11 are refracted towards the focus point of the lens, so improving the lens efficiency.

Figure 13 & 14 show a 3D and 2D cross-sectional view respectively through a planar Fresnel lens that has transition surfaces optimised for a moulding process where the split line of the mould tool is not parallel with the base surface. The direction of extraction of the Fresnel lens from the mould tool is arrowed 39. In this illustration part of the transition surfaces 36 & 38 have been modified to prevent an undercut by replacing the translation vector that forms the transition surface from the outer perimeter curve with a translation vector that meets the minimum draft angle requirement. The replacement of the translation vector is only required around part of the perimeter curve. It can be seen on the opposite side of the lens centre line the transition surfaces 37 & 40 are unmodified.

Modifying the transition surface to remove the undercut reduces the optical efficiency of the Fresnel lens because it reduces the useful optical area of the lens. This embodiment has the minimum effect on the optical performance because only the part of the transition surface that does not meet the draft angle requirement is replaced. a

Claims

FREE-FORM FRESNEL LENSCLAIMS1. An improvement in a Fresnel lens that allows a Fresnel lens structure to be created on any shape of base surface, furthermore the improvement allows light from any source point on one side of the lens to be focused to any point on the other side where either the source or focus can be at infinity) the invention comprising: a free form central optical zone defined by the position of the central zone apex, the surface normal of every point on the optical surface and the 3D curve defining the outer extent of the central optical zone; and a plurality of transition surfaces between optical zones; and a plurality of subsequent optical zones each defined by a 3D curve defining the inner extent of each zone, the surface normal of every point on the optical surface and a 3D curve defining the outer extent of each zone.
2. The improvement of claim 1 wherein the transition surface between the Fresnel optical zones has a shape that reduces the optical losses and scattering from the transition surface.
3. An improvement of claim 2 wherein the transition surface between the Fresnel optical zones has a modified shape that prevents undercuts to allow the part to be removed from a mould while minimising optical losses and scattering from the transition surface.