Measurement device and method for measuring an optical element

Abstract

Measurement device for determining one or more parameters being indicative of the relative position of a first surface of an optical element With respect to a second surface of the optical element, the first surface and the second surface being on substantially opposing sides of the optical element, wherein at least one of the first surface and second surface is a non-planar surface, the measurement device comprising: - a supporting device comprising a support arranged for stably supporting the optical element in the measurement device in a first orientation stationary relative to the measurement device; - a measurement unit arranged for mapping, in a measurement coordinate system, main geometry data of the first surface representative of the three dimensional surface shape of the first surface, as well as reference geometry data of the second surface representative of at least three second surface reference points of the second surface in the measurement coordinate system; - a processing unit that is configured to determine the one or more parameters on the basis of provided main geometry data of the second surface representative of the three dimensional surface shape of the second surface and the main geometry data of the first surface and the reference geometry data of the second surface.

Description

The present invention relates to a , in particular for determining one or more parameters being indicative of the relative position of a first surface of an optical element with respect to a second surface of the optical element. As part ofthe process ofthe manufacturing of high-accuracy optical elements, such as lenses, it is required to measure, or map, the geometry of the optical surfaces of the optical element as part of for example quality assurance. Many optical elements comprise multiple optical surfaces which are to be measured. For the purpose ofmeasuring the various surfaces of an optical element, the optical elementmay be supported in a measurement device which employs a movable probe, such as a touch probe or an optical probe, to move across the surface to be measured to measure the surface. The optical element is supported in a position which allows the probe to access substantially the entire surface to be measured. To measure another surface, the optical element is moved to another position, to allow the probe to access the other surface. However, by moving the optical element between measuring steps, the reference with respect to which the first measured surface is measured is lost, such that the spatial relationship between the second measured surface and the first measured surface is notknown. Many devices and methods for measuring multiple surfaces of an optical elementknown in the art use a referencing device that is attached to the optical element to retain or reacquire the spatial relationship between the various positions in which the optical element is measured. However, this requires ajig that specifically fits the optical element, and the jig also obstructs part of the optical element, preventing it from being measured. Additionally or alternatively, the optical element itself may be provided by reference features, which can be remeasured to determine the relationships between the different orientations in which the optical element is measured. International patent applicationWO 2022 / 186693 A1 discloses a measurement device and method for measuring optical elements, wherein one of the two surfaces to be measured is supported on a support with aknown geometry, while the other surface is mapped by a measurement device. Geometry data of the supported surface is then provided, either based on design data or on actual measurements. Due to the fact that the locations of the contact points where the supported surface is supported are known relative to the measured surface, the geometry data of the supported surface can be related to the measured geometry data of the measured surface based on the constraints provided by the known supporting points on the supported surface.A drawback of this device and method is that a specific support is required. It is a goal of the present invention to provide for an improved measurement device and method for determining one or more parameters being indicative of the relative position of a first surface ofan optical element with respect to a second surface of the optical element. This goal, among other goals, is at least partially met by a measurement device and method according to the appended claims. More in particular, this goal, among other goals, is at least partially met by a measurement device for determining one or more parameters being indicative of the relative position of a first surface of an optical element with respect to a second surface of the optical element, the first surface and the second surface preferably being on substantially opposing sides of the optical element, wherein at least one ofthe first surface and second surface preferably is a non-planar surface, the measurement device comprising: - a supporting device comprising a support arranged for stably supporting the optical element in the measurement device in a first orientation stationary relative to the measurement device; - a measurement unit arranged for mapping main geometry data of the first surface representative of the three dimensional surface shape of the first surface, as well as reference geometry data ofthe second surface representative of at least three second surface reference points ofthe second surface; - a processing unit that is configured to determine the one or more parameters on the basis of provided main geometry data of the second surface representative of the three dimensional surface shape of the second surface and the main geometry data of the first surface and the reference geometry data ofthe second surface. The location of the second surface with respect to the first surface is thus determined on the basis of actual measurements ofthe second surface, comprised in the reference geometry data. This removes the need for referencing jigs attached to the optical element, or specific referencing features included in the optical element. In addition, the supporting device can be any supporting device suitable for stably supporting the optical element, without any particular referencing features which also removes or at least reduces the effect of such referencing features obstructing or otherwise interfering with parts of the optical element. Main geometry data of a surface, such as the above mentioned first surface, is representative of the three dimensional surface shape of the relevant surface. This means that the main geometry data comprises data that substantially describes the entirety of the mapped surface, i.e. substantially complete data of that surface. In practice, all measured geometry data comprises a (large) plurality of discrete points on the surface, as measuring the entirety of the surface required infinite discrete points. Thus, main geometry data should be understood to comprise the data required to (digitally) represent the mapped surface in manners as known in the art. Reference geometry data on the other hand should be understood to at least represent only a number ofpoints on the surface, instead of substantially the entire surface. However, there are no objections to the reference geometry data approaching the level of detail of the main geometry data, except that more steps are required. The measurement unit preferably takes measurements, such as the mapping of the main geometry data of the first surface as well as the reference geometry data of the second surface, in the same coordinate system, preferably a coordinate system that is stationary relative to the measurement device, in other words a measurement coordinate system. It should be noted that it is not necessary that the measurement coordinate system is calibrated in some way in relation to the optical element supported in the measurement device. By mapping the main geometry data of the first surface as well as the reference geometry data of the second surface while the optical element is supported in the first position, said main geometry data of the first surface and reference geometry data of the second surface is provided in the same reference frame, or coordinate system. The one or more parameters being indicative of the relative position of a first surface of an optical element with respect to a second surface of the optical elementmay comprise a number of parameters, such as the tilt of the datum axis ofone of the surfaces relative to the datum axis of the other surface, or to another reference axis.A thickness of the optical elementmay be determined, as well as a coaxiality of the first and second surfaces. The parameters that can be determined are also described in for example normNEN-ISO 10110-6. It should be noted that it is preferred that at least one of the surfaces is non-planar, such that three reference points provide sufficient constraints to locate the surface in the three lateral dimensions. It is not necessarily required that the non-planar surface is continuous, as it could also comprise multiple surfaces located at a non-zero angle relative to each other. It should further be noted that the various surfaces and orientations / positions listed herein of the optical element are arbitrary, and merely act to differentiate different (parts of) surfaces and different positions of the optical element. The main geometry data ofthe second surfacemay be provided in a coordinate system different from the measurement coordinate system as mentioned above, for instance in a coordinate system stationary relative to the optical element, referred to as the optical element coordinate system. It is not required that any relationship between the measurement coordinate system and the optical element coordinate system is known beforehand, as the device as described above allows this relationship to be determined based on the above mentioned measurements. Said optical element coordinate system may be defined by a datum axis as defined in IS0101 10-6. The reference geometry data of the second surface collected by the measurement unit is known to correspond to points, preferably at least three, on the second surface of the optical element. These reference points can thus be used as constraints to virtually place the second surface geometry as provided onto the reference points, to virtually construct a model of the first and second surface in the same reference frame. This then allows the one or more parameters being indicative for the relative position of the first surface and second surface of the optical element to be determined. The three reference points provide sufficient constraints to virtually place a spherical second surface in the correct location relative to the first surface. More reference points may be mapped to provide more constraints. More constraints allow for a more accurate determination of the position of the second surface relative to the first surface, and / or for a more complex geometry of the second surface to be accurately referenced to the first surface, and / or to account for errors in the actual geometry of the second surface, etcetera. Preferably, the processing unit is configured to determine a coordinate transformation T to transform the measurement coordinate system to an optical element coordinate system, or vice versa, preferably by using as constraints at least that the at least three second surface reference points lay on the three dimensional surface shape of the second surface, wherein the processing unit is configured to determine the one or more parameters by applying the coordinate transformationT to either the main geometry data of the first surface or the main geometry data of the second surface. In practice, main geometry data of either surface comprises a plurality of discrete measurement points, rather than a continuous mathematical function to represent the surface shape. Thus, the reference points comprised in the reference geometry data of the second surface are virtually placed onto the second surface represented by the main geometry data of the second surface by means ofknown interpolation techniques. The at least three second surface reference points provide three equations, which can be solved to obtain the transformation T. By mapping more reference points, as part of the reference geometry data of the second surface, more constraints are obtained, allowing for a more accurate determination of the transformation, and / or allows for the transformationT to be determined for a second surface with a more complex geometry than a spherical geometry, and / or to account and / or compensate for manufacturing errors in the second surface, etcetera. In an embodiment, the processing unit is additionally configured to determine the one or more parameters on the basis of additionally provided reference geometry data of the first surface representative of the location, in the optical element coordinate system, of at least three first surface reference points, preferably by using as additional constraints that the at least three first surface reference points lay on the three dimensional surface shape of the first surface. Thus, at least six constraints are obtained, providing the above mentioned benefits. Preferably, the supporting device is additionally arranged to support the optical element in a second orientation, different from the first orientation, and wherein the measurement device is additionally arranged for mapping, preferably in the optical element coordinate system, main geometry data ofthe second surface representative of the three dimensional surface shape of the second surface. Thus, the main geometry data of the second surface is determined based on measurements taken of the actual second surface, rather than for example relying on design data that is indicative of the actual geometry of the second surface, but wherein the actual geometry of the second surfacemay differ from said design data due to manufacturing errors. As said above, the optical element coordinate system may be arbitrary. In case the main geometry data of the second surface is mapped by the measurement unit while the optical element is supported in the second position, the main geometry data of the second surface is measured with respect to a coordinate system stationary relative to the measurement device, for example the same coordinate system as mentioned above, in which the main geometry data of the first surface is measured. However, as the orientation of the optical element changes when the optical element is moved from the first position to the second position, without necessarily retaining aknown reference, the spatial relationship between the main geometry data of the first surface and the main geometry data of the second surface is not known. This is illustrated herein by using a different term for the coordinate system wherein the main geometry data of the first surface is described (the measurement coordinate system) and the coordinate system wherein the main geometry data ofthe second surface is described (the optical element coordinate system). The above mentioned transformation T allows the main geometry data of the first surface and the main geometry data ofthe second surface to be related to each other. In an embodiment, the measurement unit is additionally arranged for mapping reference geometry data of the first surface representative of the location, when the optical element is supported in the second orientation, preferably in the optical element coordinate system, of at least three first surface reference points. Thus, at least three additional constraints are determined based on actual measurements of the actual surfaces, rather than relying on for example design data representative of the shapes of the first and second surfaces, as elaborated upon above. In a preferred embodiment, the measurement unit is additionally arranged for mapping, preferably in the measurement device coordinate system, while the optical element is supported in the first orientation, reference geometry data representative of the location of at least one reference point on a third surface of the optical element, wherein the processing unit is additionally configured to determine the one or more parameters on the basis ofprovided main geometry data of the third surface representative ofthe three dimensional surface shape of the third surface relative to the second surface, preferably defined in the optical element coordinate system fixed to the optical element, and the reference geometry data representative of the location of the at least one reference point on the third surface, preferably defined in the measurement device coordinate system. The at least one reference point comprised in the reference geometry data of the third surface thus provides at least one additional constraint to derive the coordinate transformation T, as it is known that the at least one reference point on the third surface (preferably defined in the measurement coordinate system) lays on the third surface, represented by the main geometry data of the third surface, which is preferably defined in the optical element coordinate system. Preferably, the measurement unit is arranged for mapping, as the third surface, at least part of a side surface ofthe optical element, which is preferably substantially cylindrical, wherein the side surface connects the first surface and the second surface. Additionally or alternatively, the third surface may be part of a planar, annular surface extending around the first or second surface. However, any surface ofthe optical elementmay be chosen as the third surface, even (part of) the first and second surface. Preferably, the measurement unit is additionally arranged for mapping, while the optical element is supported in the second orientation, main geometry data representative of at least the location of the third surface, preferably defined in the optical element coordinate system. The third surface is thus measured both in the first position and in the second position. The main geometry data of the third surface does not necessarily have to comprise an entire mapping of the third surface, and it can also be equivalent to reference geometry data comprising a number ofreference points on the third surface. Either way, these measurements ofthe third surface in both the first and second orientation of the optical element can be used as a reference to relate the first surface, defined with respect to a first coordinate system (such as the measurement coordinate system described above), to the second surface, defined with respect to a second coordinate system (such as the optical element coordinate system described above). The measurements representative of the location of the third surface in the measurement coordinate system and the measurements representative of the location ofthe third surface in the optical element coordinate system can thus be used as constraints to relate the locations of the first surface and the second surface to each other. It should be noted that main geometry data representative of the shape of the third surface may be provided, for example as design data, or determined based on measurements taken of the third surface in the first position and / or the second position. If the main geometry data representative of the shape ofthe third surface is provided, for example as design data, itmay be sufficient to perform a number ofmeasurements of the third surface in both the first position and the second position thatmay determine the location of the third surface with sufficient accuracy both in the first position and in the second position. Ifthe main geometry data is not available before any measurements are taken, it is preferred that the third surface is mapped with sufficient accuracy in at least one of the first position and the second position to obtain the shape and location of the third surface, such that in the other ofthe first or second position, the location of the third surface relative to the first and / or the second surface may be determined by taking a limited number of reference measurements ofthe third surface. Alternatively, the third surface may be mapped substantially entirely in both the first and the second position, such that main geometry data representative of both the shape and location ofthe third surface is obtained relative to at least the first surface in the first position, and at least the second surface in the second position. Preferably, the coordinate transformationT is additionally determined by using as constraint that the at least one reference point comprised in the reference geometry data of the third surface lays on the three dimensional surface shape of the third surface represented by the main geometry data of the third surface. As the same surface, the third surface, is measured at least partially in both the first position and the second position, the third surface thus serves as a reference to relate the measurements taken of the first surface in the first position to the measurements taken of the second surface in the second position. If the measurements of the third surface are taken both in the first and in the second position, either of the entire third surface, or a number ofreference point measurements in combination with other geometry data describing the shape of the third surface, such as design data, only these measurements may be required to determine a parameter being indicative ofthe position ofthe surface of the optical element and the coordinate transformation T between the first and second positions of the optical element, i.e. between the measurement coordinate system and the optical element coordinate system. Preferably, the measurement device comprises a movable measurement head arranged to measure surfaces of the optical element. This allows the measurement head to move to multiple positions to at least partially measure the first, second and optionally third surfaces in the first and optionally second positions. Preferably, the measurement head comprises a probe member extending substantially horizontally. In other words, said probe member preferably extends substantially perpendicular to a side surface, and / or a centre line and / or a datum axis of the optical element. The probe member may be a touch probe that touches the optical element to take measurements. The probe member extending horizontally allows it to reach both a surface facing partially upwards, and a surface facing partially downwards. This for example allows the measurement head to measure both the first and second, and optionally also the third, surfaces of the optical element while one of the surfaces faces partially downwards, and one surface faces partially upwards. Additionally or alternatively, the measurement device comprises a movable measurement head comprising an optical probe. An optical (scanning) probe scans a part of the surface rather than taking point measurements, which allows it to gather more detailed measurement data of the measured surface compared to a touch probe. This is especially advantageous when measuring an aspherical optical surface, and in particular a freeform optical surface. Preferably, the supporting device is arranged to support the optical element in the first orientation with the first surface facing substantially upwards, and in the second orientation with the second surface facing substantially facing upwards. Usually, the optical element to be measured comprises a first and second surface on substantially opposite sides. Thus, while either surface faces upwards, the other may be securely supported on the measurement device. Preferably, the measurement head is arranged to determine main geometry data ofone of the first surface or the second surface facing substantially upwards, and to determine reference geometry data of the other of the first surface and the second surface facing substantially downwards. The surface facing downwards likely touches the supporting device, and is thus partially obstructed for the measurement units. Thus, it is beneficially only required to measure part of the downwards facing surface, to map reference geometry Preferably, the supporting device is substantially fixed to the measurement device. This prevents the optical element from moving relative to the measurement device while being supported in the first and / or second position. Preferably, the coordinate transformationT transforms the measurement device coordinate system to the optical element coordinate system, and wherein the transformationT is applied to the main geometry data ofthe first surface. Alternatively, the coordinate transformationT transforms the optical element coordinate system to the measurement device coordinate system, and wherein the transformationT is applied to the main geometry data of the second surface. Another aspect relates to a method for determining one or more parameters being indicative for the relative position of a first surface of an optical element with respect to a second surface of an optical element, the first surface and the second surface preferably being on substantially opposing sides ofthe optical element, wherein at least one of the first surface and second surface is a non- planar, wherein the method comprises the steps of: supporting the optical element in a first orientation in the measurement device; mapping, preferably in a measurement device coordinate system fixed to the measurement device, main geometry data of the first surface representative of the three dimensional surface shape of the first surface, as well as reference geometry data of the second surface representative of at least three second surface reference points of the second surface, preferably defined in the measurement device coordinate system; providing main geometry data of the second surface representative of the three dimensional surface shape of the second surface; determining the one or more parameters on the basis ofprovided main geometry data of the second surface and the main geometry data of the first surface and the reference geometry data ofthe second surface. The at least three reference points comprised in the reference geometry data of the second surface provide three constraints to virtually locate the second surface, represented by the main geometry data of the second surface, provided in a coordinate system that is preferably stationary relative to the optical element (the optical element coordinate system), relative to the first surface, represented by the main geometry data of the first surface that is provided in a reference frame different from the reference frame of the main geometry data of the second surface, namely preferably the measurement coordinate system. As the second surface is, in the first position, also partially measured, no additional references are required to relate the main geometry data of the first surface to the main geometry data of the second surface. Preferably, the method additionally comprises a step of determining a coordinate transformationT to transform the measurement device coordinate system to the optical element coordinate system, or vice versa, by using as constraints at least that the at least three second surface reference points comprised in the reference geometry data of the second surface lay on the three dimensional surface shape of the second surface represented by the main geometry data of the second surface, wherein the processing unit is configured to determine the one or more parameters by applying the coordinate transformationT to either the main geometry data of the first surface or the main geometry data ofthe second surface. The larger the number ofreference points that is represented in the reference geometry data, the more constraints are obtained for calculating the transformation matrix T. Preferably, the method additionally comprises a step of determining the one or more parameters on the basis of additionally provided reference geometry data of the first surface representative of the location, in the optical element coordinate system, of at least three first surface reference points, by using as additional constraints that the at least three first surface reference points lay on the three dimensional surface shape of the first surface. Thus, at least six reference points are provided. In an embodiment, the step ofproviding the providing main geometry data of the second surface comprises providing predetermined main geometry data, for instance based on design data of the second surface, or otherwise determined main geometry data of the second surface. However, the method preferably additionally comprises a step of supporting the optical element in the second orientation, wherein the step ofproviding the providing main geometry data of the second surface comprises mapping, preferably in the optical element coordinate system, main geometry data ofthe second surface representative of the three dimensional surface shape of the second surface. This provides actual measurements of the second surface which can be used instead of or in addition to provided design data of the second surface, which is representative of the intended shape of the second surface, but not necessarily corresponds to the actual shape of the second surface. The same applies to the relationship between design data of the first and / or surface and the actual shapes of the first and / or third surface. Preferably, the method additionally comprises a step ofmapping reference geometry data of the first surface representative of the location, in the optical element coordinate system, of at least three first surface reference points. This provides the above mentioned additional reference points, and thus constraints, to for example derive the transformation matrix T, based on actual measurements of the actual first surface. Preferably, the method additionally comprises a step ofmapping, preferably in the measurement device coordinate system while the optical element is supported in the first orientation, reference geometry data representative of the location of at least one reference point representative of the location of a third surface in the measurement device coordinate system, and wherein the method further comprises a step ofdetermining the one or more parameters on the basis ofprovided main geometry data ofthe third surface representative of the three dimensional surface shape of the third surface, preferably defined in the optical element coordinate system fixed to the optical element, and the reference geometry data representative of the location of the at least one reference point representative of the location of the third surface in the measurement device coordinate system. The third surface is preferably different from the first surface and second surface, but itmay also be part ofone or more of the first surface and second surface. The third surface may for example comprise, if applicable, a cylindrical sidewall of the optical element, and / or (parts of) the edges connecting the third surface with the first and / or second surfaces. Preferably, the method additionally comprises a step ofmapping, in the optical element coordinate system while the optical element is supported in the second orientation, main geometry data of the third surface in the optical element coordinate system. This main geometry data may be obtained by measuring, and thus mapping, substantially the entirety of the third surface. Alternatively, it may be constructed based on partial measurements (i.e. reference geometry data comprising a number ofreference points) augmented by design geometry data which is combined using for example the same method of deriving a transformation matrix based on the knowledge that the reference points comprised in the reference geometry data correspond to points on the surface represented in the (more) complete, namely for example the design data, geometry data of the third surface. Thus, preferably the coordinate transformationT is additionally determined by using as constraint that the reference geometry data of the third surface lays on the three dimensional surface shape of the third surface. The present invention is further illustrated by the following figures, which show a preferred embodiment of the device according to the invention, and are not intended to limit the scope of the invention in any way, wherein: - figure 1 shows an overview of the measurement device; - figure 2 shows an example ofmeasurements taken of the surfaces of the optical element; - figure 3 shows a first example of a step-by-step overview of the process ofmapping the surfaces of an optical element; - figure 4 shows a second example of a step-by-step overview of the process ofmapping the surfaces of an optical element; and - figure 5 shows a third example of a step-by-step overview of the process ofmapping the surfaces of an optical element Figure 1 shows an overview of the measurement device 1. An optical element 2 is supported by a supporting device 3, comprising a plurality of supports 31, 32 on which the optical element rests. the optical element comprises a first surface 21, a second surface 22 opposite the first surface 21, and a third surface 23, which is a cylindrical sidewall 23 connecting the first surface 21 and the second surface 22. Different types of optical elements 2 may be measured, such as optical elements without a sidewall, or optical elements with spherical, aspherical and / or freeform surfaces, and / or with one or more concave surfaces, rather than the convex surfaces shown in the embodiment of the figure. The optical element 2 is shown in a first position, with the first surface 21 facing upwards, and the second surface 22 facing downwards, and contacting the supporting device 3.A measurement unit 10 comprises a probe 11, in this embodiment a contact probe 11 but other probes, such as optical probes, may also be used. The probe 11 comprises a probe section 12 extending horizontally, and ending in a contact tip 13 which is arranged to contact the optical element to register a measurement. The probe 11 is rotatable around axis Rp to rotate the optical element, and / or the supporting device 3 is rotatable around axis Rd. By moving in the horizontal plane and vertical direction, in combination with a rotation of the probe 11 around axis Rp, and / or a rotation of the supporting device around axis Rd allows the probe tip 13 to touch substantially the entirety of the first surface 21 tomap substantially the entire first surface 21, as well as substantially the entirety ofthe third surface (sidewall) 23. In addition, the probe tip 13 can access parts of the second surface 22 facing downwards. Figure 2 shows an example ofmeasurements taken of the surfaces 21, 22, 23 of the optical element 2. Substantially the entire first surface 21 may be mapped to generate main geometry data S1 which is representative of the three-dimensional surface shape of the first surface 21. In addition, substantially the entire third surface 23 may be mapped to generate main geometry data S3 which is representative of the three-dimensional surface shape of the third surface 23. The second surface 22, facing downwards in the first position shown in the figure, is only partially accessible by the probe 11, and thus part of the second surface 22may be mapped to generate reference geometry data S2 which is representative of the location in space, relative to S1 and S3, of a number of reference points on the second surface 22. Figure 3 shows a first example of a step-by-step overview of a process ofmapping surfaces ofan optical element using a measurement device and method as described herein. Steps 1.1, 1.2, 1.3 show measurements taken of an optical element in the first position or orientation, and step 2.1 shows measurements taken of the optical element in the second position. In step 1.1 main and / or reference geometry data S3 of the third surface, here corresponding to a sidewall of the optical element, is collected by taking repeated measurements of the third surface by the measurement probe 11. In an embodiment, the geometry of the third surface is known or estimated beforehand, for example based on design data used to design and manufacture the optical element. Itmay then be sufficient to collect the equivalent ofreference geometry data S3 of the third surface, which allows the location of the third surface in a measurement coordinate system to be determined by the measurement unit using the probe 11. It is also possible to measure substantially the entirety of the third surface, to obtain the equivalent ofmain geometry data S3 of the third surface. Based on the main or reference geometry data S3 collected, various parameters of the sidewall may be determined, such as a diameter C0. In step 1.2 reference geometry data S2 of the second surface is collected by measuring a number ofreference points P1, P2 on the second, downwards facing, surface using the probe 11. If the second surface is for example spherical, itmay be sufficient to measure three or more reference points, as this provides sufficient constraints to locate the second surface in the three lateral dimensions. In step 1.3 the first, upwards facing, surface is mapped to acquire main geometry data S1 of the first surface. If the first surface is spherical, the radius R1 and centre point C1 of the first spherical surface can be determined from the main geometry data S1. It is, however, not required that the first or second surface is spherical, as also for example aspherical surfaces are compatible with the device and method described herein. Additionally or alternatively to the contact probe 11, an optical probe 111 may be used. In step 2.1, the optical element is ipped and placed in the second position, with the second surface facing upwards. The probe 11 is used to gather main geometry data S2 of the second surface. These measurements are also taken in a coordinate system that is fixed to the measurement device, usually the same coordinate system as the coordinate system in which the measurements of steps 1.1-1.3 are taken. However, the optical element has moved, and the measurement coordinate system has thus moved relative to the optical element. The measurements in the second position are thus performed in a different coordinate system as seen from the perspective of the optical element. For simplicity, the coordinate system in which the main geometry data S2 of the second surface is gathered is referred to as the optical element coordinate system. In step 3, the measurements S1, S2 and S3 taken in steps 1.1-1.3 with respect to the measurement device coordinate system are combined with the measurement S2 taken in step 2.A transformation matrix is derived to translate the measurement coordinate system to the optical element coordinate system (or vice versa) by solving a number of equations constrained by the fact that the reference points P1, P2 correspond to locations on the second surface represented by the main geometry data S2 of the second surface. For the two-dimensional example shown in the figure, a minimum oftwo constraints, provided by reference points P1, P2 is required. For a three-dimensional second surface, at least three constraints, corresponding to three distinct reference points measured as part of the reference geometry data S2 of the second surface, are required. By applying the transformation matrix to either the dataset comprising S1, S3 and S2 or the dataset comprising S2, S1, S2 and S3 are obtained in a single reference frame, for example the measurement device coordinate system or the optical element coordinate system. Figure 4 shows a second example of a step-by-step overview of a process ofmapping surfaces of an optical element using a measurement device and method as described herein. In step 1.1 main geometry data S3, or reference geometry data S3, as explained in reference to figure 3, is collected. The shape and location, as well as a centreline A0 in case the third surface is for example cylindrical, of the third surfacemay be determined based on only main geometry data, indicative for the shape and location of substantially the entire third surface as measured by the probe 11. Said parameters of the third surface may also be approximated based on reference geometry data S3, comprising a more limited number ofmeasurements of the third surface, optionally in combination with design data of the third surface. In step 1.2, reference geometry data S2 of the second surface is collected by the probe 11 by measuring a limited number ofreference points P1, P2. In step 1.3 main geometry data S1 of substantially the entire first surface is collected. This may be performed using an optical probe 111. In step 2.1, the third surface is measured by the probe, either partially or substantially entirely, generating main or reference geometry data S3. The more reference points on the third surface are measured, the more constraints are obtained for deriving a transformation matrix based on S3 and S3. Itmay also be that only particular parts of the third surface, for example the edge on the junction of the third surface and the second surface are measured as part of the reference geometry data S3 of the third surface. Based on S3, parameters of the third surface, such as a centreline AO, may be derived. In step 2.2, main geometry data S2 of the second surface is collected, by touch probe 11 or more preferably an optical probe 111, or another type ofprobe. In step 3, a transformation matrix is derived based to translate the geometry data collected in steps 1.1-1.3 (with respect to the measurement device coordinate system) or 2.223 (the optical element coordinate system) to the other of the two coordinate systems, based on the constraints provided by the reference geometry data S2, in particular reference points P1, P2, and the main geometry data S2. Additionally or alternatively, the transformation matrixmay be derived based on the constraints provided by S3 and S3. For example, if S3 and S3 each comprise geometry data representative of substantially the entirety of the third surface, and the location of the third surface, the transformation matrixmay be derived based only on S3 and S3. While the figures do not show any specific reference points on the third surface, the principle of obtaining the constraints to derive the transformation matrix is the same as explained with reference to S2 and S2 (which comprises indicated reference points P1, P2). Figure 5 shows a third example of a step-by-step overview of a process ofmapping surfaces of an optical element comprising a concave first surface surrounded by a planar annular third surface. In step 1.1 the optical element is in the first position, and the annular third surface is measured substantially entirely, to generate main geometry data S3 of the third surface. In step 1.2, reference geometry data S2 of the second surface is collected by measuring a number ofreference points P1, P2. If the second surface is spherical, a radius R2 and centre point C2 may be derived from the reference geometry data S2. In step 1.3, main geometry data S1 of the first surface is collected by probe 111, in the shown embodiment an optical probe. In step 2.1, the optical element is ipped to the second position, and reference geometry data S3 is gathered of the third surface. Main geometry data S2 ofthe second surface is also gathered in step 2.3, preferably by optical probe 111. As explained above, S1, S3 and S2 are obtained with respect to a certain reference relative to the optical element, such as the measurement device coordinate system. S2 and S3 are obtained with respect to a different reference (as the optical element has been moved from the first to the second position), which may be called the optical element coordinate system. To translate S1, S2 and S3 to the optical element coordinate system, or alternatively to translate S2 and S3 to the measurement device coordinate system, a transformation matrix is obtained by solving a number of equations that are constrained by the fact that the reference points measured as part of the reference geometry data S2 lie on the main geometry data S2 of the second surface, and by the fact that the reference points measured as part of S3 lie on the geometry data S3 of the third surface. By applying the thus obtained transformation matrix, S1, S2 and S3 are obtained in the same reference frame, for example either the measurement device coordinate system or the optical element coordinate system. Optionally main or reference geometry data of an outside surface S4 may be gathered in the coordinate system of S1, S3 and S2, as well as in the coordinate system ofS2 and S3, to serve as additional reference.

Claims

1. Measuring device for determining one or more parameters that are indicative of the relative position of a first surface of an optical element with respect to a second surface of the optical element, where the first surface and the second surface on essentially opposite sides of the optical element are located, where at least one of the first surface and the second surface is a is a non-flat surface, where the measuring device comprises: a support device comprising a support designed for stability supporting the optical element in the measuring device in an initial orientation stationary relative to the measuring device; a unit of measurement designed for mapping, in a measurement coordinate system, main geometry data of the first surface that be representative of the three-dimensional surface shape of the first surface, as well as reference geometry data of the second surface that are representative for at least three second surface reference points of the second surface in the measurement coordinate system; - a processing unit that is configured to the one or more parameters determine based on provided main geometry data of the second surface that be representative of the three-dimensional surface shape of the second surface and the main geometry data of the first surface and the reference- geometry data of the second surface.

2. Measuring device within the meaning of claim 1, where the processing unit is configured to to determine a coordinate transformation T to the measurement coordinate system to a to transform an optical element coordinate system that is stationary with respect to the optical element, or vice versa, by using as boundary conditions at least that the at least three second surface reference points that are passed through the reference geometric data of the second surface included be on the three-dimensional surface shape of the second surface lie which is represented by the main geometry data of the second surface, where the processing unit is configured to determine one or more parameters by the coordinate transformation to apply T to either the main geometry data of the first surface or the main geometry data of the second surface.

3. Measuring device according to at least one of the preceding claims, where the The support device is additionally configured to support the optical element in a second to support orientation, other than the first orientation, and where the measuring device additionally configured for mapping main geometry data of the second surface that are representative of the three-dimensional surface shape of the second surface.

4. Measuring device according to at least one of the preceding claims, where the measuring device is further configured for mapping, while the optical element supported in the first orientation, reference geometry data that are representative are for the location of at least one reference point on a third surface of the optical element, where the processing unit is additionally configured to the one or to determine more parameters based on provided main geometry data of the third surface that are representative of the three-dimensional shape of the third surface relative to the second surface, and the reference geometry data that be representative of the location of at least one reference point on the third surface.

5. Measuring device within the meaning of claim 4, where the unit of measurement is additionally configured for mapping of, as the third surface, at least a part of a substantially cylindrical side surface of the optical element.

6. Measuring device according to at least claims 3 and 4, where the unit of measurement is additional configured for mapping, while the optical element is in the second orientation is supported, main geometry data representative of the location of the third surface relative to the second surface.

7. Measuring device according to at least claims 2 and 4, where the coordinate transformation T additionally is determined by using as a boundary condition that at least one reference point that is encompassed by the reference geometry data of the third surface on the three-dimensional surface shape of the third surface lies that through The main geometry data of the third surface is represented.

8. Measuring device according to at least one of the preceding claims, where the measuring device comprises a movable measuring head that is designed to measure surfaces of the to measure optical element.

9. Measuring device within the meaning of claim 8, where the measuring head comprises a probe element which is located extends mainly horizontally.

10. Measuring device according to at least one of the preceding claims, where the The support device is configured to the optical element in the first orientation support with the first surface facing mainly upwards, and in the second orientation with the second surface primarily facing upwards.

11. Measuring device in accordance with at least claims 8 and 10, where the measuring head is configured to to determine main geometry data of one of the first surface or second surface that is primarily directed upwards, and to determine reference geometry data of the other of the first surface or second surface that is essentially downwards targeted 12. Measuring device according to at least one of the preceding claims, where the support device is primarily fixed to the measuring device.

13. Method for determining one or more parameters that are indicative of the relative position of a first surface of an optical element with respect to a second surface of an optical element, where the first surface and the second surface on essentially opposite sides of the optical element are located, where at least one of the first surface and the second surface is a is not flat, where the method includes the steps of: - supporting the optical element in an initial orientation in the measuring device; mapping of, in a surveying device coordinate system, main geometry data of the first surface that are representative of the three-dimensional surface shape of the first surface, as well as reference geometry data of the second surface that are representative of at least three second surface reference points of the second surface; determining one or more parameters based on provided main geometry data of the second surface that are representative of the three-dimensional surface shape of the second surface, and the main geometry data of the first surface and the reference geometry data of the second surface.

14. Method according to conclusion 13, whereby the method further comprises a step of the determining a coordinate transformation T to the measuring device coordinate system transform to an optical element coordinate system that is stationary with respect to of the optical element, or vice versa, by using at least as boundary conditions that the at least three second-surface reference points that are comprised by the reference geometry data of the second surface on the three-dimensional surface shape of the second surface lie which is represented by the main geometry data of the second surface, where the processing unit is configured to determine one or more parameters by applying the coordinate transformation T to fit either the main geometry data of the first surface or the main geometry data of the second surface.

15. Method of working in accordance with at least one of the preceding method of working claims, whereby the method additionally includes a step of supporting the optical element in a second orientation, different from the first orientation, and mapping out main geometry data of the second surface that are representative of the three-dimensional surface shape of the second surface.

16. Method of working in accordance with at least one of the preceding method of working claims, whereby the method further includes a step of mapping, while the optical element in the first orientation is supported, reference geometry data that are representative are for the location of at least one reference point on a third surface in the measuring device coordinate system, and where the method further comprises a step of the determine one or more parameters based on provided main geometry data of the third surface that are representative of the three-dimensional surface shape of the third surface, and the reference geometry data that are representative of the location of at least one reference point that is representative of the location of the third surface.

17. Method in accordance with at least conclusions 15 and 16, whereby the method takes a further step includes mapping, while the optical element in the second orientation is supported, main geometry data representative of the location of the third surface relative to the second surface.

18. Method according to at least claims 14 and 16, where the coordinate transformation T additionally is determined by using as a boundary condition that at least one reference point that is encompassed by the reference geometry data of the third surface lies on the three-dimensional surface shape of the third surface that is represented by the main geometry data of the third surface.

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