GB2557633A

GB2557633A - Method of obtaining data characterizing 3D-imaging equipment

Info

Publication number: GB2557633A
Application number: GB1621216.9A
Authority: GB
Inventors: Henry John Larkins Andrew; James Owen Richard; Rubio Navarro Leonardo
Original assignee: Fuel 3d Tech Ltd
Current assignee: Fuel 3d Tech Ltd
Priority date: 2016-12-14
Filing date: 2016-12-14
Publication date: 2018-06-27
Also published as: WO2018109479A1; GB201621216D0

Abstract

A method for determining the accuracy of a three-dimensional measurement of the surface of a target object (3-d image) comprises using a test piece target 20 which has a number of test areas (zones) 22a, 22b, 24a, 24b, , 29a, 29b. Each zone comprises a set of round bottomed or polygonal grooves with ridges between, the grooves of different zones having different spacings (separations), depths and/or orientations. The 3-d imaging equipment (fig. 1) comprises light sources (1, 2b, 3b) and image sensors (2a, 3a) and operates photogrammetrically. Comparing the measured 3-d image with the known profiles of the test areas will lead to a cut-off spacing at which the measured results become inaccurate (Fig. 4b); this is the resolution of the equipment.

Description

(71) Applicant(s):

Fuel 3D Technologies Limited (Incorporated in the United Kingdom)

Unit 2 Douglas Court, Seymour Business Park, Station Road, Chinnor, Oxfordshire, 0X39 4HA, United Kingdom (56) Documents Cited:

CN 104820217 B CN 102982550 A US 20140362184 A1 (58) Field of Search:

INT CL G01C, G01S Other: EPODOC, WPI

CN 103983961 A DE 003801381 A1 US 20140028834 A1 (72) Inventor(s):

Andrew Henry John Larkins Richard James Owen Leonardo Rubio Navarro (74) Agent and/or Address for Service:

Marks & Clerk LLP

Fletcher House (2nd Floor), Heatley Road,

The Oxford Science Park, OXFORD, ΟΧ4 4GE, United Kingdom (54) Title of the Invention: Method of obtaining data characterizing 3D-imaging equipment Abstract Title: Obtaining data characterizing 3D-imaging equipment (57) A method for determining the accuracy of a three-dimensional measurement of the surface of a target object (3-d image) comprises using a test piece target 20 which has a number of test areas (zones) 22a, 22b, 24a, 24b, ..., 29a, 29b. Each zone comprises a set of round bottomed or polygonal grooves with ridges between, the grooves of different zones having different spacings (separations), depths and/or orientations. The 3-d imaging equipment (fig. 1) comprises light sources (1, 2b, 3b) and image sensors (2a, 3a) and operates photogrammetrically. Comparing the measured 3-d image with the known profiles of the test areas will lead to a cut-off spacing at which the measured results become inaccurate (Fig. 4b); this is the resolution of the equipment.

At least one drawing originally filed was informal and the print reproduced here is taken from a later filed formal copy.

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Method of obtaining data characterizing 3D-imaqinq equipment

Field of the invention

The present invention relates to test methods and test apparatus for obtaining numerical characterization parameters characterizing three-dimensional (3-D) imaging equipment. It further relates to a method of operating 3-D imaging equipment by setting at least one operating parameter of the 3-D imaging equipment based on the numerical characterization parameters obtained by the test methods and/or test apparatus.

Background

In recent years standards have been developed for characterizing the accuracy with which three-dimensional imaging systems image three-dimensional objects. An example is the standard proposed by the ASTM (American Society for Testing and Materials) committee E57. The standards generally require the 3-D imaging equipment to image a threedimensional scene of known dimensions (“ground truth”), such as two smooth spheres of known diameter (typically a few centimetres) placed on a common flat plane. A numerical measure of the accuracy of the image created by the 3-D imaging equipment is obtained by comparing the three-dimensional image to the ground truth.

Summary of the invention

The present inventors have found that the above system is inappropriate for certain types of imaging equipment. For example, certain important imaging applications exist in which it is important to be able to image small surface structures accurately (e.g. ones with dimensions measured in millimetres or even micrometres) on a larger object with dimensions measured in centimetres, but less important to image the overall shape of the larger object. In other words, low accuracy in estimating the shape of the larger object can be tolerated, provided that a high resolution is obtained for the finer-scale structure. The existing standards, which concentrate on measuring accuracy of the larger object do not produce useful numerical parameters characterizing the resolution of the finer-scale structure.

An example of an application in which resolution is clearly distinct from overall accuracy is provided by the three-dimensional imaging equipment described in WO 2009/122200, “3D Imaging System”. This describes a system in which, in preferred embodiments, an object to be imaged is successively illuminated by at least three directional light sources, and multiple cameras at spatially separated spatial positions capture images of the object. The object will have a number of “landmarks” which, when imaged, produce features which can be easily recognized in each of the images. Consider two images (a “stereo pair” of images) which are captured simultaneously respectively by two or more of the cameras with a known geometrical relationship, such that the relationship between the viewpoints is known. For each of a number of landmarks, the system determines the corresponding positions in the stereo pair of the corresponding features. Using this data, an initial 3D model of the object is created stereoscopically (i.e. by optical triangulation). Photometric data is generated from images captured at different times when successive ones of the directional light sources are activated. On the assumption that the object exhibits Lambertian reflection, the photometric data makes it possible to obtain an estimate the normal direction to the surface of the object with a resolution comparable to individual pixels of the image. The normal directions are then used to refine the initial model of the 3D object. Note that in this application the accuracy obtained by the stereoscopy may be accurately characterized using the known standards described above, but the fine detail obtained by the photometric imaging is not.

In general terms, the present invention proposes obtaining a plurality of numerical characterization parameters characterizing 3-D electromagnetic imaging equipment, by using the 3-D electromagnetic imaging equipment to form a three-dimensional image of a test unit including a test surface having a three-dimensional surface structure. The test surface comprises a plurality of test areas, and the three-dimensional surface structure of different ones of the test areas is formed with different respective spatial frequency characteristics. The numerical characterization parameters comprise a measure of the respective accuracy of the three-dimensional image for each of a plurality of values of a surface characterization parameter which characterizes a plurality of the test areas.

The term “3-D electromagnetic imaging equipment” is used to include all systems for forming a 3-D model of a subject using electromagnetic radiation, i.e. light (not limited to light in the visible part of the spectrum). It embraces equipment in which information is captured for different portions of the subject sequentially (e.g. systems in which the subject is gradually scanned), and equipment in which information about the whole subject is collected at once (“simultaneous capture”) such as by a camera. It embraces equipment which measures the amplitude of light reflected by the subject (e.g. cameras), and also equipment using any of time-of-flight measurement, depth-of-focus measurement, and triangulation.

The test surface may be generally planar, and may be exactly planar (to within the limits of machining or moulding accuracy) away from the test areas.

We may consider the test surface as being made up of a low-spatial-frequency surface having no spatial frequency components below a predetermined spatial wavelength (e.g. 1 cm), and we may define the surface structure as being the spatial frequency components of the test surface at or below the predetermined spatial wavelength. The low-spatial frequency surface defines the overall shape of the test surface. The low-spatial-frequency surface may be substantially flat, at least in each test area.

Considering a two-dimensional spatial frequency transform of the surface structure in each of the test areas in two orthogonal directions which are tangents to the low-spatial frequency surface, each test area may be characterized by one or more spatial frequency peaks.

In at least one test area the surface structure may be longitudinally symmetric in a first direction which is tangent to the low-spatial-frequency surface (the “symmetry direction”). In this case, the spatial frequency transform of the surface structure will be substantially zero at any direction which has a component in the symmetry direction. That is, the two-dimensional spatial frequency transform is only non-zero in positions which are displaced from the origin in a second direction orthogonal to the symmetry direction (the “test direction”). The spatial frequency transform may have a single peak in the test direction, or a plurality of peaks which are all in the test direction from the origin.

Optionally, for a given symmetry direction, there may be more than one test area which is longitudinally symmetric in this symmetry direction. The respective spatial frequency transforms for the multiple test areas which share a common symmetry direction may be different. For example, they may each have a single peak at different respective spatial wavelength in the test direction.

For a given symmetry direction and a given spatial wavelength in the test direction, there may be multiple test areas which have a spatial frequency at that wavelength in the test direction with different respective amplitudes. This possibility is particularly useful for testing a property of 3-D imaging equipment which is the extent to which surface structure is resolved less accurately as the “height” of the surface structure (i.e. the extent of variations transverse to the low-spatial-frequency surface) becomes greater.

Optionally, there may be multiple test areas all sharing a given test direction, a given spatial wavelength in the test direction and a given surface structure amplitude, but spaced apart on the test surface. These test areas may be used to measure the consistency with which the 3D imaging equipment measures 3-D structure at different locations on the test unit, for example at different respective distances from an imaging centre of the 3-D imaging equipment.

Preferably, for at least one pair of test areas, the respective test directions are at a non-zero angle to each other. For example, the respective test directions may be orthogonal to each other. More generally, there may be n test areas, where n is an integer which is at least two, and the test directions may be spaced from each other at directions which are 180/n apart, where n is an integer which is at least two, and may be at least three. The test surface may include one or more test areas for each respective test direction.

For example, since a 3-D imaging system which employs photometry typically includes at least three directional light sources, it may be appropriate for the test unit to include at least three test areas with different respective test directions, e.g. a number of test directions equal to, or a multiple of, the number of light sources in the 3-D imaging equipment. In the case that there are three directional light sources, and three corresponding test directions, the three test directions may be spaced pairwise from each other by 60 degrees. Each test direction may be parallel to the component parallel to the low-spatial-frequency surface of the respective propagation direction.

This is an example of how, during the testing of the 3-D imaging equipment, the test unit may be arranged with at least one test direction aligned with a critical direction of the imaging equipment. More generally, the test direction and/or symmetry direction of at least one of the test areas is aligned with the component parallel to the low-spatial-frequency surface of the propagation direction of at least one directional light source. Another example would be aligning at least one test direction with a row or column of the image sensor (e.g. camera) of the 3-D imaging equipment. In another example, when the 3-D imaging equipment includes multiple cameras (as in 3-D imaging equipment which uses stereoscopy), the spacing direction of two cameras (or at least the component of the spacing direction transverse to the low-spatial-frequency surface) may be chosen to be parallel to a test direction of one or more of the test areas, or parallel to a symmetry direction of one or more of the test areas

There is some similarity between the 3-dimensional test surface proposed by the present invention, and two-dimensional “resolution charts” which are sometimes used to test twodimensional imaging equipment. However, in resolution charts, different areas of the chart have different reflectivity levels (e.g. each area of the chart is either black or white), whereas the present 3-dimensional test unit may have substantially constant reflectivity properties in all areas. Furthermore, whereas many conventional two-dimensional resolution charts which are used to characterize two-dimensional imaging equipment are generally circularly symmetric about a central position (which, in use, is typically arranged to lie on an optical axis of a lens arrangement of the two-dimensional imaging equipment), the present 35 dimensional test surface may be optimised according to the principles used in threedimensional imaging. For example, it may be optimised to provide correspondence between test directions and illumination directions, as mentioned above; or a test direction of the test unit may be aligned with a separation direction of two cameras used for stereoscopic imaging.

Once the 3-D imaging equipment has formed a 3-D image of the test surface, one or more numerical characterization parameters may be obtained by comparing the 3-D image with known properties of the test surface. At least one numerical characterization parameter may be obtained for each test area.

The comparison may be carried out in the spatial frequency domain. Alternatively, the comparison may be carried out in the distance domain; for example, by comparing a known distance transverse to the low-spatial-frequency surface (that is a known “height”) between peaks and troughs in a given test area with the corresponding distance in the 3-D image.

It has been discovered that a comparison in the spatial frequency domain can be useful in observing “aliasing”, which is an undesirable artefact of many 3-D imaging systems, involving the generation of false peaks at spatial frequencies below the true spatial frequency peaks of the test surface. Furthermore, a comparison in the spatial frequency domain can be useful in observing undesirable harmonics in the spatial frequency domain.

The test areas may include a plurality of test areas with a respective periodicity in a corresponding test direction. Such test areas may be referred to as “periodic” test areas. For example, each of the periodic test areas may comprise a plurality of parallel ridges extending in a corresponding symmetry direction, and spaced apart by equal amounts in a corresponding test direction transverse to the symmetry direction, with the peaks of the ridges lying in a common plane. Considering a convex hull of the test surface for each of the test areas, the portions of the convex hull corresponding to the respective periodic test areas may be substantially flat. For the periodic test areas, the surface characterization parameter may be (or be indicative of) the period of the periodic test area in the test direction.

Alternatively or additionally, the test areas may include one of more test areas with a single transition in a corresponding test direction. The transition may be a step-change increase in height (i.e. a step) transverse to the low-spatial-frequency surface (e.g. the test surface away from the test areas). Such test areas are referred to here as “step-change” test areas. The step-change test areas thus have a corresponding test direction which is from one side of the transition to the other. The step-change areas have a corresponding symmetry direction which is transverse to the test direction. For the step-change test areas, the surface characterization parameter may be (or be indicative of) the height of the step.

In either case, at least one numerical characterization parameter which is a measure of imaging accuracy is obtained for each of a plurality of respective values of the surface characterization parameter. The numerical characterization parameters may be used to generate a graph representing the variation of the numerical characterization parameter with the surface characterization parameter. Following the terminology used in 2-D imaging systems, this may be referred to as a “modulation transfer function”.

Thus, a first modulation transfer function may be defined using the periodic test areas (or periodic test areas which share a symmetry direction) and their corresponding spatial periods, and a second modulation transfer function may be defined using the step-change test areas (or step-change test areas which share a symmetry direction) and the corresponding heights of their respective steps.

Using the obtained numerical characterization parameter(s), at least one operating parameter of the 3-D imaging equipment may be selected. For example, if given 3-D imaging equipment has two imaging modalities (e.g. stereoscopic and photometric imaging), the characterization parameter(s) may be used to select one or more spatial frequency ranges in which each imaging modality is used.

Furthermore, the numerical characterization parameter(s) may be used to derive a model of the 3-D imaging equipment which can be used to estimate numerical characterization parameter(s) of the performance of the 3-D imaging equipment in different optical conditions from those in which the 3-D imaging equipment was tested, such as different lighting conditions (e.g. a different number of light sources, and/or at different respective positions). The results may be used in a process of selecting at least one operating parameter of the 3D imaging equipment, e.g. as value(s) of the operating parameter(s) which give an optimal trade off between one or more numerical characterization parameter(s) in the different optical conditions.

Brief description of the figures

Non-limiting embodiments of the invention will now be described for the sake of example only with reference to the following figures in which:

Fig. 1 shows schematically a known imaging 3-D imaging apparatus;

Fig. 2 which shows the steps of a method according to the invention;

Fig. 3, which is composed of Figs. 3(a), 3(b) and 3(c), includes three views of a test unit defining a test surface comprising a number of test areas;

Fig. 4, which is composed of Figs. 4(a) and 4(b), shows a cross-section of a 3-D image which can be obtained by 3-D imaging equipment from a test area of the test unit of Fig. 2, and a graph which may be obtained when the measurement of Fig. 2 is carried out for different test areas of the test unit of Fig. 3;

Fig. 5, is composed of Figs. 5(a) which shows the spatial frequencies of an accurate image of one of the test areas of the test unit of Fig. 2, and Fig. 5(b) which shows the spatial frequencies which may be produced by real 3-D imaging equipment;

Fig. 6 shows how the chart of Fig. 6 would appear for 3-D imaging equipment having two imaging modalities;

Fig. 7 shows another possible form of a test unit which may be used in the method of

Fig. 1;

Fig. 8 is cross-sectional view of two test areas of a further test unit which may be used in the method of Fig 1;

Fig. 9 shows the steps of another method which is an embodiment of the invention; and

Fig. 10 shows the configuration of a computer system which can perform a method according to Fig. 2 or Fig. 9.

Detailed description of the embodiments

Referring firstly to Fig. 1, a known item of 3-D imaging equipment is shown. The imaging assembly includes an energy source 1. It further includes units 2, 3 which each include a respective energy sensor 2a, 3a in form of an image capturing device, and a respective energy source 2b, 3b (note that in variations of the 3-D imaging equipment, the energy sensors 2a, 3a are not part of the same units as the energy sources 2b, 3b). The units 2, 3 are fixedly mounted to each other by a strut 6, and both are fixedly mounted to the energy source 1 by struts 4, 5. The exact form of the mechanical connection between the units 2, 3 and the energy source 1 is different in other forms of the 3-D imaging equipment, but it is preferable if it maintains the energy source 1 and the units 2, 3 at fixed distances from each other and at fixed relative orientations. The relative positions of the energy sources 1,2b, 3b and sensors 2a, 3a are pre-known. The energy sources 1,2b, 3b and image capturing devices 2a, 3a may be incorporated in a portable, hand-held instrument. In addition to the assembly shown in Fig. 1, the embodiment includes a processor which is in electronic communication with the energy sources 1,2b, 3b and image capturing devices 2a, 3a.

The energy sources 1,2b, 3b are each adapted to generate directional electromagnetic radiation, such as visible light or infra-red radiation. The energy sources 1,2b, 3b are all controlled by the processor. The output of the image capturing devices 2a, 3a is transmitted to the processor.

Each of the image capturing devices 2a, 3a is arranged to capture an image of an object 7 (in Fig. 1, a dodecahedron) positioned in both the respective fields of view of the image capturing devices 2a, 3a. The image capturing devices 2a, 3a are spatially separated, and preferably also arranged with converging fields of view, so the apparatus is capable of providing two separated viewpoints of the object 7, so that stereoscopic imaging of the object 7 is possible.

The case of two viewpoints is often referred to as a “stereo pair”, although it will be appreciated that more than two spatially-separated image capturing devices may be provided, so that the object 7 is imaged from more than two viewpoints. This may increase the precision and/or visible range of the apparatus. The words “stereo” and “stereoscopic” as used herein are intend to encompass, in addition to the possibility of the subject being imaged from two viewpoints, the possibility of the subject being imaged from more than two viewpoints. Suitable image capture devices include the 1/3-lnch CMOS Digital Image Sensor (AR0330) provided by ON Semiconductor of Arizona, US.

The processor is adapted to perform large scale imaging of the object 7 by stereoscopy using a stereo pair of the images captured by the image capturing devices 2a, 3a (e.g. when any one or more of the directional energy sources 1,2b, 3b are illuminated). The processor is further adapted to perform surface detail imaging of the object 7 by photometry using three images captured by one of the image capturing devices 2a, 3a when respective ones of the directional energy sources 1,2b, 3b are illuminated.

Fig. 2 shows the steps of a method 100 which is an embodiment of the invention. The method employs a test unit 20, for example as shown in Fig. 3(a), (b) and (c). The test unit 20 has a test surface 21 with a known three-dimensional surface structure. Fig. 3(a) is a front view looking towards the test surface 21. Fig. 3(b) is a first perspective view, and Fig. 3(c) is a second perspective view.

The test surface 21 is generally flat, although it is optionally surrounded by a rim which is not flat. The test surface 21 comprises sixteen periodic test areas, which are in eight pairs: periodic test areas 22a and 22b; periodic test areas 23a and 23b; periodic test areas 24a and 24b; periodic test areas 25a and 25b; periodic test areas 26a and 26b; periodic test areas 27a and 27b; periodic test areas 28a and 28b; and periodic test areas 29a and 29b. Each of the periodic test areas 22a, 22b, 23a, 23b, 24a, 24b, 25a, 25b, 26a, 26b, 27a, 27b,

28a, 28b, 29a, 29b has a set of five equally-spaced, parallel, round-bottomed grooves, thereby defining four ridges between adjacent pairs of the grooves. In different test units which can be used in the method 100, there are a different number of grooves/ridges, although there are preferably at least three grooves and/or ridges in each periodic test area.

The grooves and ridges are longitudinally symmetric in one direction (the “symmetry direction”), and spaced apart in an orthogonal direction (the “test direction”). The respective symmetry directions of each pair of periodic test areas are orthogonal to each other. In Fig. 3(a), the symmetry direction is the vertical direction in the diagram for the periodic test areas 22a, 23a, 24a, 25a, 26a, 27a, 28a and 29a, and it is the horizontal direction in the diagram for the periodic test areas 22b, 23b, 24b, 25b, 26b, 27b, 28b, 29b.

The number on Fig. 3(a) near each pair of periodic test areas shows the depth of the groove measured in mm. In each case, the distance between the bottoms of adjacent pairs of grooves in each of that pair of periodic test areas is four times the depth of the grooves. This is referred to here as the spacing value, and is equal to the periodicity of the periodic test area. Thus, the spacing values for the eight pairs of periodic test areas are respectively 12mm (for periodic test areas 22a and 22b), 8mm (for periodic test areas 23a and 23b),

4mm (for periodic test areas 24a and 24b), 3.2mm (for periodic test areas 25a and 25b), 2mm (for periodic test areas 26a and 26b), 1.2mm (for periodic test areas 27a and 27b), 0.8mm (for periodic test areas 28a and 28b) and 0.4mm (for periodic test areas 29a and 29b).

If a two-dimensional spatial Fourier transform is carried out of the surface of a given one of the periodic test areas, with axes which are the symmetry direction and test direction respectively, the spatial Fourier transform would only have non-zero components in the test direction. The lowest spatial frequency would be at a wavelength in the test direction which is equal to the reciprocal of the spacing value for the periodic test area.

The test surface 21 may be considered as the combination of (i) a low-spatial-frequency (e.g. flat) surface, with no spatial frequencies as high as a cut-off spatial frequency of 1/(3mm), i.e. 3.33x10³m¹, and (ii) the sixteen periodic test areas which each provide a surface structure with a spatial-frequency of at least (1/3mm).

In other test units which can be used in the method 100, the number of periodic test areas is different. However, preferably for each spacing value, there are at least two periodic test areas having spatial periodicity equal to that spacing value. The at least two periodic test areas comprise at least one pair of periodic test areas which have respective test directions which are non-parallel, preferably orthogonal to each other.

Furthermore, in other test units which can be used in the method 100 the spacing values are different. However, preferably there is at least one periodic test area for each of a number of respective spacing values which is at least four, at least six or at least 8. At least one of the spacing values is preferably below 1mm, and at least one is preferably below 0.5mm. At least one of the spacing values is preferably above 1mm, and at least one is preferably above 4mm.

The profile of each groove/ridge in each periodic test area may be different in different test units. For example, the gooves/ridges may have a sinusoidal cross-section as viewed in the longitudinal direction (i.e. such that a spatial Fourier transform of the cross-section only includes one Fourier component).

The rim of the test unit 20 comprises eight flat regions 221,222, 223, 224, 225, 226, 227, 228 which are each parallel the test surface 21 but which are displaced from it (in the depth direction from the test surface 21 towards the opposite major face of the test unit 20; we refer to the opposite direction as “height”) by 3mm, 2mm, 1 mm, 0.8mm, 0.5mm, 0.3mm, 0.2mm and 0.1mm respectively. Each of the flat regions 221,222, 223, 224, 225, 226, 227, 228 touches a respective flat portion of the test surface 21. Thus, there are step changes of height at the eight respective lines of transition between the eight respective regions 221, 222, 223, 224, 225, 226, 227, 228 and the respective flat portion of the test surface 21.

The dashed areas 231,232, 233, 234, 235, 236, 237, 238 show “step-change” test areas which each consist of a portion of a respective one of the flat regions 221,222, 223, 224, 225, 226, 227, 228 and a respective flat portion of the flat test surface 21. Note that each step-change test area has a corresponding symmetry direction (e.g. the horizontal direction in Fig. 3(a) for step-change areas 231,232, 235 and 236; and the vertical direction in Fig. 3(a) for step-change areas 233, 234, 237 and 238), and a test direction which is transverse to the symmetry direction. The symmetry direction of the step-change test areas is equal to the symmetry direction of corresponding ones of the periodic test areas.

In a further possible test unit which can be used in the method 100, the test surface may be non-flat. For example, it may be a portion of a spherical surface. Nevertheless, the portions of the test surface away from the test areas may have a spatial frequency below the cut-off spatial frequency. The axis directions used to define the spatial Fourier transform for a given test area may be defined as orthogonal directions tangential to a low-spatial-frequency surface derived from the test surface in the proximity of the test area.

In a first step 101 of the method 100, the test unit 20 is positioned in relation to 3-D imaging equipment (for example, the known equipment of Fig. 1). This may be done such that the two have a known relative positional relationship (including both translational position and rotational position). A central portion of the test unit 20 is preferably placed in the centre of a visual field of the 3-D imaging equipment.

Step 101 may include aligning the symmetry direction and/or test direction of at least one test area with an axis of the 3-D imaging equipment. For example, the horizontal direction of Fig. 1 may be aligned (made parallel) with the horizontal direction of Fig. 3(a), because this means that the spacing direction of the imaging devices 2a, 3a is parallel to the test direction of the periodic test areas 22a, 23a, 24a, 25a, 26a, 27a, 28a and 29a. Note that 3-D imaging equipment which employs stereoscopy often has different imaging performance in the spacing direction of the cameras, and in the transverse direction, so it is useful to be able to produce independent numerical characterization parameter(s) for each using the method 100.

In step 102, the 3-D imaging equipment is used to form at least one 3-D image of the test surface 21.

In step 103, the 3-D image is compared computationally with the known 3-D structure of the test surface 21, i.e. a ground truth 3-D model of the surface of the test unit 20. The comparison may be carried out individually for each of the periodic test areas 22a, 22b, 23a, 23b, 24a, 24b, 25a, 25b, 26a, 26b, 27a, 27b, 28a, 28b, 29a, 29b, to obtain at least one numerical characterization parameter for each periodic test area.

Fig. 4 shows schematically a first way this may be done. Fig. 4(a) shows, for a given periodic test area, a cross-section of the 3-D image looking in the symmetry direction. The ratio R may be found of (i) the height difference h of the tops of the ridges and the bottoms of the grooves in the portion of the 3-D image corresponding to the periodic test area, (ii) the ground truth value of h. This ratio R is a numerical characterization parameter of the 3-D imaging equipment for the corresponding test direction and the corresponding spacing value. In this way the value of R may be found for all the test images for which the test direction is the same. These R values are plotted in Fig. 4(b), and typically have the profile shown by the line 31. The horizontal axis represents the inverse of the spacing value (equivalent to a spatial frequency of the surface structure), and may be a log scale. For many imaging techniques the intercept with the vertical axis is often at 100%, since very large structures are relatively easy to image using such imaging techniques. However, it may be different from 100% because of a scale error.

It is known to produce similar graphs to Fig. 4(b) in the field of characterizing twodimensional imaging equipment, where they are known as “modulation transfer functions”, and this terminology is followed here to describe the line 31. Thus, Fig. 4(b) shows a measure of the respective accuracy of the 3-D imaging for each of a plurality of values of a surface characterization parameter which is the period of the respective periodic test areas.

The value of R falls to a low value for a spacing value of less than about 0.2mm, so this is the “optical resolution” of the 3-D imaging equipment. Optical resolution is another example of a numerical characterization parameter which may be produced by the method. Optical resolution may be defined as the spacing value for which R is below a predetermined value, such as 50% or 30%.

Note that a first graph as shown in Fig. 4(b) can be plotted for the periodic test areas 22a, 23a, 24a, 25a, 26a, 27a, 28a and 29a, and a second graph as shown in Fig. 4(b) can be plotted for the periodic test areas 22b, 23b, 24b, 26b, 27b, 28b, 29b. For some 3-D imaging equipment - particularly equipment using stereoscopy - the line 31 will be significantly different when the test direction is parallel to the spacing direction of the cameras, and when it is perpendicular to the direction. One reason for this is that in such systems there is typically a step of finding “features” in an image captured by one camera which correspond to features in an image captured by the other camera, and this feature matching process is typically carried out separately for respective lines of the images, where the lines are parallel to the spacing direction of the cameras.

Alternatively, the two values of R for each spacing value can be combined (e.g. by taking their average), and used to produce a single numerical characterization value for each respective spacing value. This may be more appropriate for some imaging equipment.

Note that the optical resolution of the 3-D imaging equipment may be different at different positions in the visual field. For that reason it may be valuable to provide the test unit 20 with a plurality of identical test areas (that is, having in particular the same test direction and same spacing value) at multiple locations on the test surface 21. This would allow the optical resolution, for a given test direction, to be measured at multiple positions in the visual field. For example, one such test area may be provided at a central portion in the test surface 21, and at least one such test area at a peripheral portion of the test surface 21, so permit a comparison of the optical resolution in the centre of the visual field and the periphery of the visual field.

Another way of obtaining a numerical characterization parameter for a given periodic test area is to perform a spatial Fourier transform in the test direction. Fig. 5(a) shows the ground-truth spatial Fourier transform which would be obtained if the ridges/grooves in the periodic test area were sinusoidal. The horizontal axis shows differing spatial frequencies in the test direction. The transform contains a single non-zero value 32, corresponding to the spacing value. Note that if the ridges/grooves are not sinusoidal, the graph of Fig. 5(a) would be more complex containing non-zero values at additional spatial frequencies.

Fig. 5(b) shows the spatial Fourier transform of a 3-D image of the portion of a 3-D image produced by 3-D imaging equipment corresponding to the periodic test area. It contains not only a peak 32 at the spatial frequency corresponding to the spacing value, but other peaks. These may include peaks at low frequencies 33 due to aliasing, and peaks 34 at multiples of the peak 32 due to harmonics. It is possible to form a numerical measure of the amplitudes of the peaks 33 and/or the peaks 34, and thus quantify their effects as a numerical characterization parameter of the 3-D imaging equipment.

For lower spacing values, the height of the peak 32 in Fig. 5(b) will tend to become smaller relative to the other peaks, and at a spacing value below the optical resolution the peak 32 will tend to disappear into background noise. This provides an alternative method for finding the optical resolution for a given test direction and position in the visual field of the 3-D imaging equipment. A plot of the height of the peak 32 against the spacing value would give a modulation transfer function similar to that of Fig. 4(b). The y-axis could measure the ratio of the height of the peak 32 in the 3-D image, and the height of the peak 32 in the ground truth transform of Fig. 5(a). For a low spacing value, this may again be close to 100%. Thus, again the result would be a measure of the respective accuracy of the 3-D imaging for each of a plurality of values of a surface characterization parameter which is the period of the respective periodic test areas.

Note however that an advantage of employing the parameter R shown in Fig. 4(b) over the spatial frequency transform approach is that, since R only measures heights, calculating it does not require the test direction to be accurately known. By contrast, the measurements in Figs. 5(b) would be significantly affected if the spatial transform is carried out in a direction which is misaligned with the test direction.

Similarly, the imaging equipment may image each of the step-change test areas 231,232, 233, 234, 235, 236, 237, 238, and the results can be used to produce at least one respective numerical characterization parameter which is a measure of the accuracy of the 3-D image in that test area. When the imaging equipment is used to image each step-change test area 231,232, 233, 234, 235, 236, 237, 238, the symmetry direction of the step-change test area may be transverse to the test direction, but the test direction may not be parallel to the normal direction to the test surface 21 in the step-change test area. Specifically, the normal direction to the test surface 21 may be at angle of approximately 5 degrees to the test direction of the scanner, such that the surface in the step-change test area normal to the test surface 21 faces slightly towards the imaging equipment.

The numerical characterization parameter could be the ratio of the height of the step in the 3-D image, compared to the height in the ground truth. Alternatively, the numerical characterization parameter could be a measure of the rounding of the step in the corresponding portion of the 3-D image. In either case, the result would be a numerical characterization parameter which indicates the accuracy of the 3-D image for each of the respective values of a surface characterization parameter which, in the case of the stepchange test areas, is the height of the respective step.

Note that step 103 may optionally include an initial, and typically automatic, step of registering one or more directions and/or positions in the 3-D image formed in step 102, with respective directions and/or positions in the ground truth 3-D model.

For example, the 3-D image formed in step 102 will typically be a cloud of points in a 3-D space, and the axes in this space may be rotated and/or translated with respect to axes of the ground truth 3-D model, such that a plane in the 3-D image corresponding to the test surface 21 is in register with the test surface 21 of the ground truth model. The plane in the 3-D image corresponding to the test surface 21 may be found by considering a region of interest in the 3-D image which is away from the portions of the 3-D image corresponding to the test areas, and deriving the best fit plane for that region of interest. “Height” may then be defined as the distance from that plane in one transverse direction.

Altenatively or additionally, the axes of the space in which the 3-D image is defined may be rotated to align a derived symmetry direction of one or more of the test areas in the 3-D image, with a corresponding symmetry direction in the ground truth 3-D model. The symmetry direction in the 3-D image may be found by finding the direction with the lowest Fourier frequency transform values.

As noted above, the known 3-D imaging equipment of Fig. 1 includes two imaging modalities: stereoscopy for low spatial frequencies and photometry for high spatial frequencies. If steps 101 and 102 are performed for each of these modalities, then a respective modulation transfer function may be derived for each (e.g. for a given test direction). Fig. 6 illustrates how the results may appear, with line 41 being the modulation transfer function for stereoscopy and line 42 being the modulation transfer function for photometry. For convenience the modulation transfer function in Fig. 6 is measured using the parameter R, but it could also be obtained by a spatial transform approach as noted above. Note that at low spacing values, the modulation transfer function 42 for photometry may be greater than 100%, indicating that the photometry may over-estimate the heights of the surface structure of the test unit 20 for low spatial frequencies.

Optionally method 100 includes, in step 104, deriving a transition spacing value using data such as that given in Fig. 6. A possible transition spacing value is shown in Fig. 6 by the dashed line. The transition spacing value may be chosen, for example, as the spacing value below which line 42 is closer to 100% than line 41, i.e. such that the 3-D imaging equipment measures spatial frequencies below that corresponding to the cut-off spacing value more accurately using spectroscopy, and spatial frequencies above that corresponding to the cutoff spacing value more accurately using photometry. Another way of setting the transition spacing value is such that it is the lowest spacing value such that line 41 is above a predetermined value. Note that the transition spacing value may be different for different test directions.

The transition spacing value may be used in step 104 as an operating parameter of the 3-D imaging equipment. For example, a computer processor of the 3-D imaging equipment may be programmed to generate 3-D images of future test subjects by measuring spatial frequencies below that corresponding to the transition spacing value using spectroscopy, and by measuring spatial frequencies above that corresponding to the transition spacing value using photometry. In some cases it may be beneficial if the modulation transfer function is slightly above 100% for a spacing value just below the transition spacing value, since this may give a 3-D image with an improved visual appearance (a similar phenomenon is known in 2-D imaging as the “sharpening effect”).

Optionally, to reduce computational effort, the stereoscopic imaging may not be carried out to produce a depth value for each pixel of the two images. Rather, it may be done only for a selected proportion of the pixels within the images (e.g. every k-th pixel, where k is an integer greater than one), and then depth values for pixels between the selected pixels may be found by interpolation using the depth values for the selected pixels, to give a low resolution image to which higher spatial frequency data derived from photometry can be added. The value of kcan be chosen in dependence on the transition spacing value, e.g. such that consecutive selected pixels in each direction have a pairwise spacing corresponding to the transition spacing value in the corresponding test direction. This saving in computational effort is possible because it is known in advance that spatial frequencies of the 3-D image higher than the transition spatial frequency will not be derived via stereoscopy.

If the optional step 104 of the method 100 is performed, it may be followed by a step 105 of imaging a new test subject, using the operating parameter(s) derived in step 104.

Fig. 7 is a schematic view of another test unit 20’ which can be used in the method of Fig. 1. Like the test unit 20, the test unit 20’ has a test surface 21 ’ which is generally flat, but with periodic test areas 22a’, 22b’and 22c’. In contrast to the test unit 20, the periodic test areas 22a’, 22b’ and 22c’ have respective test directions 23a’, 23b’, 23c’ which are mutually spaced apart by 60 degrees. (Note however that since, for a given test area, it is arbitrary whether one considers the test direction as a first direction transverse to the symmetry direction in the plane of the test surface 21’, or in the opposite direction, saying that the test directions are spaced by 60 degrees is equivalent to saying that they are spaced by 120 degrees.). Although for simplicity Fig. 7 shows three periodic test areas 22a’, 22b’, 22c’ having the same spacing value, more generally test unit 20’ may include, for each of the test directions 23a’, 23b’, 23c’ multiple corresponding periodic test areas having different respective spacing values.

Fig. 8 shows a schematic cross-sectional view of a portion of another test unit which can be used in the method 100. The portion includes periodic test areas 22a”, 22b” having the same spacing value and the same test direction (left-to-right in Fig. 8), but in which the ridges/grooves have different respective heights. The ridges/grooves in periodic test area 22a’ have a lower height than in periodic test area 22b’. In other words, the amplitude of the variation of the height in periodic test area 22a’ is less than in periodic test area 22b’. The arrows 45 indicate the direction from a camera of the 3-D imaging equipment, or the propagation direction of light from a light source. The dashed line 46 is parallel to the arrows 45 and a tangent to one of the ridges in the area 22b”. It will be noted that in the portion 47 of the periodic test area 22b’, which is the portion between the respective positions where the line 46 intercepts a ridge and a groove, the top of the ridge occludes the groove. This does not occur in periodic test area 22a’. In other words, the 3-D imaging equipment will image periodic test area 22b’ less accurately than periodic test area 22a’. A numerical parameter quantifying this difference can be obtained in step 103. Thus, by including both periodic test areas 22a’ and 22b’ in the test unit 20”, the test unit 20’ can be used to provide a numerical measure of the degree to which, for certain 3-D imaging equipment the grooves are occluded by the ridges. This parameter is referred to as “visibility”. Note that for simplicity Fig. 8 only shows periodic test areas for a single test direction and a single spacing value, but it is to be understood that the test unit may include, for each of multiple test directions and/or multiple spacing values, multiple periodic test areas in which the surface structures have different respective amplitudes.

Fig. 9 illustrates a method 200 which is a variant of the method 100. Steps 201-203 are identical to steps 101-103 respectively. In step 204, a numerical model of the 3-D imaging equipment is formed using the numerical characterization parameter(s) obtained in step 203. In step 205, this numerical model is used to predict numerical characterization parameter(s) for a number of 3-D imaging configurations which were not used in step 202, for example different lighting conditions, different test subjects, etc. These imaging configurations may include different settings of operating parameters of the 3-D imaging equipment.

In step 206, using the predictions of the numerical characterization parameters obtained in step 205, operating parameters of the 3-D imaging equipment are chosen, e.g. to achieve the best trade off in a range of 3-D imaging configurations. In step 207, the 3-D imaging equipment is set according to these operating parameters, and a new test subject is imaged.

Fig. 10 is a block diagram showing a technical architecture of a system 300 for performing the computational steps of the methods 100, 200.

The technical architecture includes a processor 322 (which may be referred to as a central processor unit or CPU) that is in communication with a 3-D imaging equipment 310. The processor 322 is also in communication with memory devices including secondary storage 324 (such as disk drives or memory cards), read only memory (ROM) 326, and random access memory (RAM) 328. The processor 322 may be implemented as one or more CPU chips.

The system 300 includes a user interface (Ul) 330 for controlling the processor 322. The Ul 330 may comprise a touch screen, keyboard, keypad or other known input device. If the Ul 330 comprises a touch screen, the processor 322 is operative to generate an image on the touch screen. Alternatively, the system may include a separate screen (not shown) for displaying images under the control of the processor 322.

The secondary storage 324 typically comprises a memory card 324a or other storage device and is used for non-volatile storage of data and as an over-flow data storage device if RAM 328 is not large enough to hold all working data. Secondary storage 324 may be used to store programs which are loaded into RAM 328 when such programs are selected for execution.

The ROM 326 is used to store instructions and perhaps data which are read during program execution. The secondary storage 324, the RAM 328, and/or the ROM 326 may be referred to in some contexts as computer readable storage media and/or non-transitory computer readable media.

The processor 322 executes instructions, codes, computer programs, scripts which it accesses from hard disk, floppy disk, optical disk (these various disk based systems may all be considered secondary storage 324), flash drive, ROM 326, or RAM 328. While only one processor 322 is shown, multiple processors may be present. Thus, while instructions may be discussed as executed by a processor, the instructions may be executed simultaneously, serially, or otherwise executed by one or multiple processors. The ROM 326 or RAM 328 may store data characterizing the shape of the test surface of the test unit, such as a ground truth 3-D image of the test surface.

The processor 322 may be operative to trigger the 3-D imaging equipment 310 to perform imaging of a test unit. It is also operative to receive a 3-D image generated by the 3-D imaging equipment 310, and analyse it by comparing the received image with the ground truth 3-D image in the manner explained above to generate numerical characterization parameters characterizing the 3-D imaging equipment 310 and optionally operating parameters for the 3-D imaging equipment 310. The processor 322 may be operative to send the operating parameters to the 3-D imaging equipment 310, to use in future imaging.

Whilst the foregoing description has described exemplary embodiments, it will be understood by those skilled in the art that many variations of the embodiment can be made within the scope of the attached claims.

For example, although in the test unit 20 of Fig. 2, the groove/ridges of different periodic test areas are spaced apart from each other, in a variation grooves/ridges may extend continuously from one periodic test area to another. For example, the grooves/ridges may be formed as elongated loops on the test surface, such that the different periodic test areas are respective portions of the test surface where the grooves/ridges have different spacings and/or curvatures.

Claims

1. A method of obtaining a plurality of numerical characterization parameters characterizing three dimensional imaging equipment, the method comprising:

(a) using the three dimensional imaging equipment to form a three-dimensional image of a test unit having a test surface having a known three-dimensional surface structure, the test surface comprising a plurality of test areas, and the three-dimensional surface structure of different ones of the test areas having different respective spatial characteristics; and (b) comparing the three-dimensional image with the known three-dimensional surface structure to obtain the at least one numerical characterization parameter; wherein the numerical characterization parameters include a respective measure of the accuracy of the three-dimensional image for each of a plurality of values of a surface characterization parameter which characterizes a plurality of the test areas.

2. A method according to claim 1 in which the test surface is formed as a low-spatialfrequency surface having no spatial frequency components below a predetermined spatial wavelength, and containing surface structures in each of the test areas with spatial frequency components at or below the predetermined spatial wavelength, the low-spatialfrequency surface being substantially flat in at least one test area.

3. A method according to claim 1 or claim 2 in which in at least one test area the surface structure has longitudinal symmetry in a corresponding symmetry direction.

4. A method according to claim 3 in which, for at least one symmetry direction, there are a corresponding plurality of test areas which are longitudinally symmetric in this symmetry direction, the plurality of test areas having different spatial frequency characteristics transverse to the symmetry direction.

5. A method according to claim 4, in which the surface structure in a plurality of the test areas corresponding to a given symmetry direction has a different respective spatial frequency.

6. A method according to claim 4 or claim 5, in which the plurality of test areas corresponding to a given symmetry direction include test areas in which the spatial structure transverse to the symmetry direction has different respective amplitudes.

7. A method according to claim 4, claim 5 or claim 6, in which the plurality of test areas corresponding to a given symmetry direction include test areas which are at different respective distances from a central portion of the visual field of the three dimensional imaging equipment.

8. A method according to any of preceding claims in which in each test area the surface structure has a spatial frequency in a corresponding test direction characterized by one or more spatial frequency peaks.

9. A method according to claim 8 in which, for at least one pair of the test areas, the respective test directions are at a non-zero angle to each other.

10. A method according to claim 8 in which, for at least one pair of the test areas, the respective test directions are orthogonal to each other.

11. A method according to claim 9 or claim 10 in which, for at least one pair of the test areas, the test directions are spaced from each other by 180/n degrees, where n is an integer higher than two.

12. A method according to any of claims 8 to 11 in which, during the formation of the three dimensional image, the test surface is arranged with the test direction of at least one test area aligned with a component transverse to the test surface of a spacing direction of a pair of cameras of the three dimensional imaging equipment.

13. A method according to any of claims 8 to 12 in which, during the formation of the three dimensional image, the test surface is arranged with the test direction of at least one of the test areas aligned with the component parallel to the test surface of the propagation direction of directional light emitted by at least one respective directional light source of the three dimensional imaging equipment.

14. A method according to any preceding claim in which at least one said numerical characterization parameter is obtained for each test area.

15. A method according to any preceding claim in which at least one said numerical characterization parameter is indicative of the ratio of the surface structure amplitude of a test area of the test unit and the surface structure amplitude of the portion of the three dimensional image corresponding to that test area.

16. A method according to any preceding claim in which the step of obtaining the at least one numerical characterization parameter includes performing a spatial frequency transform into the spatial frequency domain.

17. A method according to any preceding claim in which at least one of the test areas is a periodic test area, each periodic test area being periodic for a corresponding spatial frequency.

18. A method according to claim 17 in which at least one said numerical characterization parameter is obtained for each of a plurality of periodic test areas having respective periodicities which are different spatial frequencies, thereby obtaining a modulation transfer function relating imaging resolution to surface spatial frequency of the periodic test areas.

19. A method according to any preceding claim in which the test areas comprise stepchange test areas in which the test surface has a single transition transverse to the test surface.

20. A method according to claim 19 in which at least one said numerical characterization parameter is obtained for each of a plurality of step-change test areas having respective transitions of different respective extents transverse to the test surface, thereby obtaining a modulation transfer function relating imaging resolution to the extent of the transitions.

21. A method according to any preceding claim further comprising setting an operating parameter of the three dimensional imaging equipment based on the at least one numerical characterization parameter.

22. A method according to claim 21 in which the operating parameter is a transition spatial frequency between at least two imaging modalities, the three dimensional imaging equipment being arranged to generate three dimensional images according to a first said imaging modality for spatial frequencies below the transition frequency, and three dimensional images according to a second said imaging modality for spatial frequencies above the transition frequency.

23. A method according to any preceding claim further comprising:

using the numerical characterization parameters to derive a model of the three dimensional imaging equipment;

using the model of the three dimensional imaging equipment to estimate one or more numerical characterization parameters of the three dimensional imaging equipment in different optical conditions from those in which the three dimensional image was formed; and setting at least one operating parameter of the three dimensional imaging equipment based on the one or more estimated numerical characterization parameters.

24. An apparatus for obtaining a plurality of numerical characterization parameters characterizing three dimensional imaging equipment, the apparatus comprising:

(a) a test unit having a test surface having a known three-dimensional surface structure, the test surface comprising a plurality of test areas, and the three-dimensional surface structure of different ones of the test areas having different respective spatial characteristics; and (b) a processor arranged to:

(i) receive from the three dimensional imaging equipment a three dimensional image of the test surface; and (ii) compare the three dimensional image with the known three-dimensional surface structure to obtain the plurality of numerical characterization parameters;

wherein the numerical characterization parameters include a respective measure of the accuracy of the three-dimensional image for each of a plurality of values of a surface characterization parameter which characterizes a plurality of the test areas.

25. An apparatus according to claim 24 in which the test surface is formed as a lowspatial-frequency surface having no spatial frequency components below a predetermined spatial wavelength, and containing surface structures in each of the test areas with spatial frequency components at or below the predetermined spatial wavelength, the low-spatialfrequency surface in at least one test area being substantially flat.

26. An apparatus according to claim 24 or claim 25 in which in at least one test area the surface structure has longitudinal symmetry in a corresponding symmetry direction.

27. An apparatus according to claim 26, in which, for at least one symmetry direction, there is a corresponding plurality of test areas which are longitudinally symmetric in this symmetry direction, the plurality of test areas having different spatial frequency characteristics transverse to the symmetry direction.

28. An apparatus according to claim 27, in which the surface structure in the plurality of test areas corresponding to a given symmetry direction has a different respective spatial frequency.

29. An apparatus according to claim 27 or claim 28, in which the plurality of test areas corresponding to a given symmetry direction include test areas in which the spatial structure transverse to the symmetry direction has different respective amplitudes

30. An apparatus according to claim 27, claim 28 or claim 29 in which the plurality of test areas corresponding to a given symmetry direction include test areas which are at different respective distances from a central portion of the visual field of the three dimensional imaging equipment.

31. An apparatus according to any of claims 24 to 30 in which in each test area the surface structure has a spatial frequency in a corresponding test direction characterized by one or more spatial frequency peaks.

32. An apparatus according to claim 31 in which, for at least one pair of the test areas, the respective test directions are at a non-zero angle to each other.

33. An apparatus according to claim 31 in which, for at least one pair of the test areas, the respective test directions are orthogonal to each other.

34. An apparatus according to claim 32 or claim 33 in which, for at least one pair of the test areas, the test directions are spaced from each other by 180/n degrees, where n is an integer higher than two.

35. An apparatus according to any of claims 24 to 34 in which the processor is arranged to obtain at least one said numerical characterization parameter for each test area.

36. An apparatus according to any of claims 24 to 35 in which the processor is arranged to obtain at least one said numerical characterization parameter which is indicative of the ratio of the surface structure amplitude of a test area of the test unit and the surface structure amplitude of the portion of the three dimensional image corresponding to that test area.

37. An apparatus according to any of claims 24 to 36 in which the processor is arranged to perform a spatial frequency transform of a portion of the three dimensional image into the spatial frequency domain.

38. An apparatus according to any of claims 24 to 37 in which at least one of the test areas is a periodic test area, each periodic test area being periodic for a corresponding spatial frequency.

39. An apparatus according to claim 38 in which the processor is arranged to obtain at least one said numerical characterization parameter for each of a plurality of periodic test areas having respective periodicities which are different spatial frequencies, thereby obtaining a modulation transfer function relating imaging resolution to surface spatial frequency of the periodic test areas.

40. An apparatus according to any of claims 24 to 39 in which the test areas comprise step-change test areas in which the test surface has a single transition transverse to the test surface.

41. An apparatus according to claim 40 in which at least one said numerical characterization parameter is obtained for each of a plurality of step-change test areas having respective transitions of different respective extents transverse to the test surface, thereby obtaining a modulation transfer function relating imaging resolution to the extent of the transitions.

42. An apparatus according to any of claims 24 to 41 in which the processor is further arranged to:

use the numerical characterization parameters to derive a model of the three dimensional imaging equipment;

use the model of the three dimensional imaging equipment to estimate one or more numerical characterization parameters of the three dimensional imaging equipment in different optical conditions from those in which the three dimensional image was formed; and select at least one operating parameter of the three dimensional imaging equipment based on the one or more estimated numerical characterization parameters.

43. A test unit for use in the apparatus of any of claims 24 to 42, the test unit defining a test surface having a plurality of periodic test areas, the three-dimensional surface structure of different ones of the periodic test areas having different respective spatial frequency characteristics, wherein:

in each periodic test area the surface structure has a longitudinal symmetry in a corresponding symmetry direction;

for at least one symmetry direction, there are a corresponding plurality of test areas which are longitudinally symmetric in this symmetry direction, the plurality of periodic test areas having different respective spatial frequency characteristics transverse to the symmetry direction; and for at least one pair of the periodic test areas, the respective symmetry directions are at a non-zero angle to each other.

Intellectual

Property

Office

Application No: GB 1621216.9 Examiner: Dr E P Plummer