Angle measurements

Methods and devices for angle determination, and retroreflecting foils are presented. A retroreflecting foil (1) is arranged at a surface, an angle of which is going to be determined. The retroreflecting foil has a lens surface with a plurality of spherical microlenses (4) and a reflecting surface with a plurality of spherical mirrors (5) of a second main radius of curvature. The lens surface of the retroreflecting foil is illuminated, and transitions between darkness and light in radiation reflected from the retroreflecting foil, either upon changing a relative angle between the retroreflecting foil and the illuminating light or spatial transitions over the surface of the retroreflecting foil, are observed. An angle measure associated with the transitions is determined. The spherical mirrors present preferably at least one inner point (22) of a spherical mirror surface at which reflection according to the second main radius of curvature is prohibited.

TECHNICAL FIELD

The present invention relates in general to devices and methods for determination of angles, and in particular for such methods and devices utilising optical means.

BACKGROUND

Angle measurements are requested in many different applications. In particular in manufacturing and/or operating of mechanical devices, relative angles between different surfaces are often of vital importance. Mechanical parts having a relative motion have often to be aligned very accurately in order to ensure low wear and power consumption. Positioning of different mechanical part relative each other are also often performed by performing measurements of relative angles.

There are many approaches to angle measurements. The most straight-forward is to use mechanical means for measuring or ensuring a certain angle orientation. However, if the surfaces that are intended to be measured are sensitive for mechanical influence and/or if the space around the surfaces is limited, mechanical approaches are often difficult to perform. Furthermore, they do often involve complex assistance devices. Mechanical approaches for angle measurements are also often time consuming.

Optical means are used in prior art for angle measurements. Phenomena such as reflection, interference and diffraction are utilised. Traditional reflection measurements need highly collimated light sources, which increases cost and apparatus complexity. Interference or diffraction based methods typically need assistance parts close to the surfaces to be measured, which makes them difficult to use in applications with limited space. Furthermore, if costly parts have to be provided for each surface to be measured, the overall cost for the device becomes high.

A general problem with prior art angle measurement approaches is that they typically are time consuming, that they require complex assistance parts and/or that they are difficult to perform in limited space.

SUMMARY

A general object of the present invention is therefore to provide improved methods and devices for angle measurements. A further object of the present invention is to provide contact-free methods and devices for angle measurements, which are suitable for measurements even in small spaces.

The above objects are achieved by methods and devices according to the enclosed patent claims. In one aspect of the invention, a retroreflecting foil is presented, which comprises lens surface having a plurality of spherical microlenses with a first main radius of curvature and a reflecting surface having a plurality of spherical mirrors with a second main radius of curvature. The retroreflecting properties are caused by arranging a center of curvature of at least one of the spherical microlenses coinciding with a center of curvature of at least one of the spherical mirrors and by arranging a focal length of the spherical lenses being equal to a thickness of the retroreflecting foil. The spherical mirrors present at least one inner point of a spherical mirror surface at which reflection according to the second main radius of curvature is prohibited.

In another aspect of the present invention, a device for angle determination is presented, which comprises a retroreflecting foil. The retroreflecting foil in turn comprises a lens surface having a plurality of spherical microlenses with a first main radius of curvature and a reflecting surface having a plurality of spherical mirrors with a second main radius of curvature. A center of curvature of at least one of the spherical microlenses coincides with a center of curvature of at least one of the spherical mirrors and a focal length of the spherical lenses is equal to a thickness of the retroreflecting foil. The device for angle determination further comprises a light source arranged to illuminate the lens surface of the retroreflecting foil, means for observing transitions between darkness and light in radiation reflected from the retroreflecting foil, and means for determining angle measures associated with the transitions.

In another aspect of the present invention, a method for angle determination is presented, which comprises the step of arranging a retroreflecting foil at a surface. The retroreflecting foil has a lens surface with a plurality of spherical microlenses of a first main radius of curvature, and a reflecting surface with a plurality of spherical mirrors of a second main radius of curvature. A center of curvature of at least one of the spherical microlenses coinciding with a center of curvature of at least one of the spherical mirrors, and the spherical microlenses have a focal length equal to a thickness of said retroreflecting foil. The method further comprises the steps of illuminating the lens surface of the retroreflecting foil, observing transitions between darkness and light in radiation reflected from the retroreflecting foil, and determining angle measures associated with the transitions.

One advantage with the present invention is that the parts intended to be attached to surfaces to be measured are of relative low cost. Furthermore, devices for performing the actual angle determinations may be designed in very simple manners, further restricting the overall cost. Another advantage is that the present invention utilises contact-free methods, which easily can be applied in limited spaces.

DETAILED DESCRIPTION

The present invention is based on the use of retroreflecting foils. The present detailed description will therefore start with a summary of properties of retroreflecting foils, together with a general discussion about how to utilise these properties for angle measurements.

FIG. 1illustrates a retroreflecting foil1in cross-section. The foil1is a microlens array retroreflector. A general microlens array retroreflector as such is known in prior art, see e.g. the published international patent applications WO 95/34006 and WO 00/34807. In these disclosures, the retroreflectivity properties as such are described. However, applications for angle measurements using angle properties of the microlens array retroreflector are not mentioned.

The foil1comprises an optically transparent material6having a refractive index n. An upper lens surface2comprises a matrix of spherical bulges, which constitute densely packed spherical microlenses4. The surface of the spherical microlenses4has a main radius of curvature of R1. The spherical microlenses4have in the present embodiment a diameter d, and are separated by minor flat sections7. A lower reflecting surface3of the retroreflecting foil1also comprises a matrix of spherical bulges. The outer surface is typically coated to give a reflecting surface9, whereby the bulges at the reflecting surface3constitute densely packed spherical mirrors5. The surface of the spherical mirrors5has a main radius of curvature of Rm. The spherical mirrors5have in the present embodiment a diameter d, and are separated by minor flat sections8. The foil has a total thickness t.

The foils illustrated inFIG. 1achieves retroreflecting properties when the focal point of the spherical microlenses4are located in the plane of the reflecting surface9, and when the radii of curvature of the spherical microlenses4and the spherical mirrors5have common centres10. The centre of the spherical microlens4and the centre of the corresponding spherical mirror5have to be situated on a common line11, perpendicular to the main extension of the foil1. Furthermore, a focal length of the spherical microlenses2is equal to the thickness t of the retroreflecting foil1.

The properties are illustrated by two light rays12,13incident to the retroreflecting foil1at an angle β relative to the common line11. The light ray12hits the retroreflecting foil upper surface2at a right angle, i.e. perpendicular to the surface. The ray will not be refracted and will continue in a straight line through the centres of curvature10to the surface9of the spherical mirror5. Also the spherical mirror5is reached at a perpendicular fashion and the light ray12will be reflected back along the same path as it entered. A light ray13being incident on the upper surface2at a non-perpendicular angle, will indeed be refracted by the spherical microlens4. Since the focal length of the spherical microlens4coincides with the surface9of the spherical mirror5, the light ray13will reach the spherical mirror5at the same position as the light ray12does. However, light ray13will hit the surface9of the spherical mirror5at an angle α. Light ray13will be reflected into a reflected ray14by the spherical mirror5, again at an angle α. When the reflected ray14reaches the spherical microlens4, it refracts once more and leaves the retroreflecting foil1at the same angle β, as it entered the retroreflecting foil1. A conclusion from this description is that every light ray, within a certain angle interval, will be reflected in the same direction from where it came. This property is thus very different from a normally reflecting surface, and may, according to the present invention, be used for angle measurements.

It should be noted that the description above represents an ideal situation. In practice spherical aberrations of the spherical microlenses4give rise to a minor divergence of the retroreflected beam.

Main design parameters of retroreflecting foils, deciding the optical performance are the diameter of the spherical microlenses4, the diameter of the spherical mirrors5, the total thickness t of the foil, the refractive index n of the foil material and the respective radii or curvature R1, Rmfor the spherical microlenses4and the spherical mirrors5. Retroreflecting foils are as such known in prior art, and the retroreflecting foils can easily be manufactured as thin foils with a thickness of typically 50-300 μm. The manufacturing can also typically be performed at very low costs according to principles known in prior art.

The properties of the retroreflecting foil that are used by the present invention are the angle dependency of the reflecting properties. This is illustrated by cross-sectional views inFIGS. 2A-D. InFIG. 2A, a light beam16impinges to the retroreflecting foil1at a right angle, i.e. the incident angle β=0. A focal point15at the spherical mirror5is then located at the centre of the spherical mirror5. InFIG. 2B, the light beam16impinges to the retroreflecting foil1at an incident angle β≠0, but still relatively small. The focal point15has now moved to the side of the spherical mirror5, but still within the mirror surface. InFIG. 2C, light beam16impinges to the retroreflecting foil1at an incident angle β=βmax. The light beam is here focussed exactly at the edge17of the spherical mirror5. Finally, inFIG. 2D, the incident angle β>βmax, which means that the focal point15is placed at the theoretical extension18of the mirror surface. Instead of being reflected back to the corresponding spherical microlens4, the beam is instead spread over the entire foil and the foil is not retroreflective with respect of light impinging at angles larger than βmax.

A summary of these finding are shown as a diagram inFIG. 3. Here, a property100, typically intensity of the reflected light, is illustrated as a function of angle of incidence β. Due to the retroreflecting properties of the foil, the reflected intensity100is almost independent of the angle of incidence β at low angles101up to the maximum angle of βmax. An abrupt change102to a very low reflected intensity103occurs at the maximum angle of βmax. The sharpness of the transition will depend mainly on the aberrations of the spherical microlens4and the accuracy of the edges of the spherical mirror5. A more accurate spherical microlens4, the sharper the transition will be. This property of abrupt change between light and dark is used for angle measurements according to the present invention.

FIG. 4illustrates the principles for angle measurements by using retroreflecting foils. A retroreflecting foil1is attached on a surface20having a normal N. The surface20is arranged relative to a reference direction by an angle δ, which is going to be determined. The retroreflecting foil1is by the design known to have a maximum angle of reflection βmax. Light is radiated onto and reflected from the retroreflecting foil1at an angle γ relative to the reference direction. The angle of incidence γ is varied, until the transition from light to dark appears at a detection point21, i.e. when the maximum angle of reflection βmaxhas been reached. At this angle γmaxhas the incident light a focal point essentially at the edge of the spherical mirror5. The angle δ of the surface20is then easily found as:
δ=βmax−γmax

The transition between reflection and no reflection according to the principles presented so far takes place at the edges of the spherical mirror5. However, additional advantages can be achieved by on purpose introduce non-reflecting structures also in the interior of the spherical mirror5. In other words, if at least one inner point of a spherical mirror surface prohibits reflection according to the main radius of curvature of the spherical mirror, additional transitions between dark and light can be achieved.

FIGS. 5A-Eillustrates the effects of non-reflecting inner points of the spherical mirror in cross-section. At the spherical mirror5surface, a number of ridges22are arranged, which prohibits reflection according to the main radius of curvature of the spherical mirror. The non-reflecting inner points form a pattern on the spherical mirror surface at which reflection according to the second main radius of curvature is prohibited. InFIG. 5A, a light ray impinges at the upper surface spherical microlens4with an angle β1, which is smaller than βmax. The light ray16is focussed at a point15at the spherical mirror5, which is reflecting according to the main radius of curvature. The light ray is therefore reflected back in the same direction as it came from. An observer will see a reflected light ray. InFIG. 5B, the light impinges at an angle β2>β1, which still is smaller than βmax. However, in this case, the spherical microlens4refracts the ray to a point24at one of the ridges22. The light ray is reflected in a non-useful direction26and contributes only to a general enlightening of the foil. An observer will thereby notice a sharp transition into a darker surface. InFIG. 5C, the incidence angle is again increased to β3. Once again, the point15at which the ray is focussed corresponds to a reflecting part of the spherical mirror5surface, and the observer will experience a light foil. InFIG. 5D, the incidence angle is β4, which corresponds to the next ridge22, and a new transition into a dark foil will occur. Finally, inFIG. 5E, the angle β5corresponds again to a reflecting point15.

In this way, several transitions into relative darkness occur when successively increasing the incidence angle. This is indicated by the broken curve104inFIG. 3. By selecting a proper pattern of the ridges22, the transitions can easily be adapted for use in different applications. Different distances between two successive ridges helps in identifying which of the ridges that is in action for the moment. Also two-dimensional angle information can easily be achieved, which will be discussed in more detail further below.

In theFIGS. 5A-E, ridges were used as means for prohibiting reflection according to the main radius of curvature of the spherical mirror. In other words, the point prohibiting reflection according to the main radius of curvature of the spherical mirror presents a protrusion from the spherical mirror surface, having straight flanks. However, there are also other possibilities. Non-exclusive other examples of means for prohibiting reflection according to the main radius of curvature of the spherical mirror are given in cross-sections inFIGS. 6A-E. Other types of geometrical deviation from the main mirror curvature are possible.FIG. 6Aillustrates ridges, but of a different shape, in this embodiment having a rounded off shape.FIG. 6Billustrates an embodiment, where the point presents a recess23from the spherical mirror surface, also prohibiting normal reflection. InFIG. 6C, holes25are provided in the reflecting coating of the spherical mirror5surface, also creating non-reflecting inner points. InFIG. 6D, certain points are instead covered with an extra coating of a non-reflecting material27also creating non-reflective inner points. The proportion between light and dark areas can be varied arbitrarily. InFIG. 6E, the dark areas prevail. The points prohibiting reflection according to the main radius of curvature of the spherical mirror cover a major part of the spherical mirror5surface, and the observed pattern will then be a few light areas surrounded by a generally dark background. The main radius of curvature of the spherical mirror is, however, still defined by the reflecting portions.

Anyone skilled in the art realizes that many more examples are possible, and also combinations of the different types of means for prohibiting reflection. A single spherical mirror5surface may e.g. have means of different types, prohibiting reflection. Since the different examples typically give different detailed transition behaviors, different types of reflection prohibiting means can e.g. be used for identify which of a plurality of non-reflecting points that presently is under consideration. The size of the means for prohibiting reflection will also directly correspond to angle width between the intensity transition to and from relative darkness. Non-reflecting spots of differing sizes can therefore also be used to identify the specific spot under consideration.

The non-reflecting points at the spherical mirror surface may be point shaped. However, since the arrangement is built by spherical symmetric lenses and mirrors, the angle sensitivity is typically present in two dimensions. The pattern constituted by the non-reflecting points is thus a two-dimensional pattern. If only the angle relative to the normal direction is to be measured, the non-reflecting points at the spherical mirror surface may be shaped as concentric rings30, as illustrated in an elevation view byFIG. 7A. In such a case, it will, however, not be possible to determine any azimuth angle.FIG. 7Billustrates another geometrical shape of the non-reflecting points at the spherical mirror surface. Here, the concentric rings are combined with radially directed lines32of non-reflecting points. By also rotating the surface to be angle determined in an azimuth manner, transitions between light and dark are also obtained by such a movement. Furthermore, by providing the lines32in a non-regular manner, it may be possible to determine which of the lines32that is presently hit by the focussed incident light.FIG. 7Cillustrates a pattern comprising a spiral structure34and a single radial line32.FIG. 7Dillustrates a pattern having an inner circle30surrounded by a star-shaped structure36. Anyone skilled in the art realizes that the possibilities for variations are endless, and that the geometrical design may be adapted to the particular application.

FIG. 8Aillustrates a schematic illustration of main parts of an embodiment of a device for angle determination80according to the present invention. The device for angle determination80comprises a retroreflecting foil1arranged at a surface20, an angle of which is to be determined. The retroreflecting foil1is designed according to the principles described above, i.e. comprising a lens surface having a plurality of spherical microlenses with a first main radius of curvature, a reflecting surface having a plurality of spherical mirrors with a second main radius of curvature. The center of curvature of the spherical microlenses coincides with a center of curvature of the spherical mirrors for at least one pair of microlens and spherical mirror. The focal length of the spherical lenses is furthermore equal to a thickness of the retroreflecting foil1. The device for angle determination80is operable using the edge transition of a retroreflecting foil according to prior art. However, preferably, a retroreflecting foil1, having spherical mirrors presenting at least one inner point of a spherical mirror surface at which reflection according to the second main radius of curvature is prohibited, is used.

The device for angle determination80further comprises a light source82arranged to illuminate the retroreflecting foil1and a light detector84. In the present embodiment, the light source82and the light detector84are integrated into one single unit, but could also be provided as separate units. The light source82in the present embodiment emits at least a narrow light beam16towards the retroreflecting foil1. The light detector84in the present embodiment is arranged for measuring the intensity of the reflected light and is therefore capable of observing e.g. transitions between darkness and light in radiation reflected from the retroreflecting foil1. The device for angle determination80of the present embodiment comprises a detector support86along which the combined light source82and the light detector84is movable. The detector support86in turn comprises means88for determining angle measures in form of scale indications, whereby angles connected to transitions between light and dark can be determined.

In use of the present embodiment, the combined light source82and the light detector84is moved along the detector support86, as indicated by the arrow40. When a transition between light and dark occurs, the scale indications determine an angle measure associated with the transition. As described earlier in connection withFIG. 4, such an angle measure can easily be interpreted as a relative angle between the light beam16direction and the surface normal of the retroreflecting foil1. The motion of the combined light source82and the light detector84and/or the scale indication readout can be performed manually, partially automised or fully automised. The means for observing transitions, i.e. the light detector84is in this embodiment arranged to observe transitions occurring upon changing a relative angle between the illumination by the light source82and a surface of the retroreflecting foil1.

FIG. 8Billustrates another embodiment of a device for angle determination80according to the present invention. In this embodiment, the light source82and the light detector84are stationary. Instead, the object having the surface20is mounted at a movable part48of a goniometer arrangement42. The movable part48is movable, as indicated by the arrow44, relative to a stationary part46of the goniometer arrangement42. The means88for determining angle measures are provided in form of scale indications, either at the stationary part46or, as indicated in the figure, at the movable part48. In such a way, an angle measure associated with a transition between light and dark can be obtained.

FIG. 8Cillustrates another embodiment of a device for angle determination80according to the present invention. In this embodiment, the light source82and the light detector84as well as the retroreflecting foil1are stationary. Instead, an optical arrangement50is provided between the light source82/the light detector84and the retroreflecting foil1, illustrated in this embodiment as a prism. The optical arrangement50has the property of changing the direction of a light beam16in a predetermined manner. By altering the amount of direction change, e.g. by turning a prism, as indicated by the arrow52, the relative angle between the illumination and the surface of the retroreflecting foil1can be changed. The means88for determining angle measures are provided in form of scale indications in connection with the means for altering the direction change. In such a way, an angle measure associated with a transition between light and dark can be obtained.

The light source82should be a point light source, as experienced from the retroreflecting foil1. A laser is typically a good choice, but other conventional point light sources are also possible. The light detector inFIGS. 8A-Ccan e.g. be a photosensor. The output of the photosensor can then be connected to a control unit, which also senses the different angles. An automated correlation between angles and light/dark transitions can thereby be obtained.

In another simpler setup, the light detector84is simply an eye of an observer. The angle can then be changed e.g. until a certain light/dark transition is experienced by the observer. The extraction of information can thus be performed by manual actions as well as by physical means, possibly also automated.

FIG. 8Dillustrates yet another embodiment of a device for angle determination80according to the present invention. In this embodiment, it is even more preferred that the retroreflecting foil1has spherical mirrors presenting at least one inner point of a spherical mirror surface at which reflection according to the second main radius of curvature is prohibited. In this embodiment, the light source82is arranged to give a diverging light beam56, preferably covering the entire retroreflecting foil1. The light reaching the retroreflecting foil1will then impinge onto the surface at slightly differing angles. In the figure, this is illustrated by the angles α1and aα2. The light will be retroreflected in approximately the same angles, except where a point of a spherical mirror surface at which reflection according to the second main radius of curvature is prohibited is reached. The light detector84in this embodiment comprises a small aperture57allowing the retroreflected light to pass to an imaging device58. Such an imaging device could e.g. be a multichannel plate connected to a camera59, for recording a light pattern occurring at the multichannel plate. The imaging device58will present a pattern of light and dark areas, which are completely determined by the pattern of the inner point of a spherical mirror surface at which reflection according to the second main radius of curvature is prohibited and the relative angle between the retroreflecting foil1and the light detector84. Thus, the means84for observing transitions between light and dark is in this embodiment arranged to observe spatial transitions associated with a surface area of the retroreflecting foil.

The camera59can in one embodiment be connected to a computer, in which a pattern recognition software is available. The recorded image can then easily be interpreted as corresponding to a certain angle.

FIG. 9Aillustrates an example of a light/dark pattern that could be obtained at the imaging device58. The pattern of the inner point of a spherical mirror surface at which reflection according to the second main radius of curvature is prohibited comprises in this example concentric rings. This gives rise to concentric dark rings64on the imaging device58. The centre of the pattern60is here seen to be displaced62from the centre of the imaging device58, which indicates that there is a misalignment between the light detector and the retroreflecting foil1. The displacement62vector gives information about the size and the direction of this misalignment. A perfectly aligned setup will instead give the pattern illustrated inFIG. 9B. In order to achieve alignment, either the amount and direction of misalignment is determined and corrected for, or the alignment is changed according to any other principles until the aligned pattern (FIG. 9B) is achieved.

Also pattern recognition can be performed manually, using the eyes of an observer as imaging device. Preferably, the relative angles are adjusted until a certain requested pattern is observed, i.e. a pattern centered at a certain point at the foil.

Main steps of an embodiment of a method for angle determination according to the present invention are illustrated as a flow diagram inFIG. 10A. The procedure starts in step200. In step210, a retroreflecting foil is arranged at a surface, an angle of which is going to be determined. The retroreflecting foil has a lens surface with a plurality of spherical microlenses of a first main radius of curvature, and a reflecting surface with a plurality of spherical mirrors of a second main radius of curvature. A center of curvature of at least one of the spherical microlenses coincides with a center of curvature of at least one of the spherical mirrors. Furthermore, the spherical microlenses have a focal length equal to a thickness of the retroreflecting foil.

In step212, the lens surface of the retroreflecting foil is illuminated. In step213, a relative angle between the illumination and a surface of the retroreflecting foil is changed. Transitions between darkness and light in radiation reflected from the retroreflecting foil as caused by the angle changes are observed in step214. Finally, in step216, angle measures associated with the transitions are determined. The procedure ends in step299.

Main steps of another embodiment of a method for angle determination according to the present invention are illustrated as a flow diagram inFIG. 10B. The procedure starts in step200. In step210, a retroreflecting foil is arranged at a surface, an angle of which is going to be determined. The retroreflecting foil has in this embodiment preferably at least one inner point of a spherical mirror surface at which reflection according to said second main radius of curvature is prohibited.

In step212, the lens surface of the retroreflecting foil is illuminated. Transitions between darkness and light in radiation reflected from different areas of the retroreflecting foil are observed in step214, i.e. the transitions are spatial transitions associated with a surface area of the retroreflecting foil.

Finally, in step216, angle measures associated with the spatial transitions are determined. The procedure ends in step299.