Patent Application
20240167966
The present invention relates to a method for mapping an internal structure of a sample. More particularly, although not exclusively, the present invention relates to a method for obtaining a three-dimensional map of an internal structure of a material having a high refractive index such as a gemstone.
Optical projection tomography (OPT) is a method to obtain a volumetric image of an optically transmissive sample material by recording two-dimensional images (projections) of light that has been transmitted through the object from multiple angles. Electromagnetic radiation in a range of optical wavelengths between approximately 400 and 1600 nm may be used to produce the light projections. Regions of a sample material that absorb or scatter light will cast shadows on the imaging detector. The three-dimensional structure of the sample material is then computationally reconstructed from the shape and relative darkness of the shadows cast, as the sample material is viewed from many different angles.
Some related optical tomography techniques, such as for example optical emission tomography also known as optical emission computed tomography, may use images formed by light that is emitted or scattered from a side- or front-illuminated object, instead of shadows cast by transmitted light, to reconstruct a three-dimensional volume of an object using a similar computational approach.
Operating at optical wavelengths in the visible and infrared range however has the detrimental effect of introducing complexity in the interaction between the sample material and optical light. In standard OPT applications including imaging of a gemstone, such as diamond having a rough external surface, the gemstone is submerged in a refractive index matching fluid or embedded in a refractive index matching solid to reduce scattering and make light paths entering the gemstone approximately straight lines, i.e. reduce reflection and refraction effects to a level where they become negligible for the reconstruction process. This submersion of the gemstone or other transparent material in a refractive index matching fluid or solid adds complexity to the process of obtaining a volumetric image of the material and, in the case of materials having high refractive indices (such as gemstones) may require toxic fluids or solids.
Due to the high refractive index and dispersion within the gemstone, it is not possible to use a single refractive index matching fluid or solid that has the same refractive index at different wavelengths, such as all wavelengths in the visible range. As a result, to achieve refractive index matching at multiple different wavelengths, multiple submersion materials (fluid or solid) need to be used, however it may not be possible to achieve sufficiently accurate index matching at all wavelengths. A determination of chromatic properties of a gemstone or other material, resulting in, for example, a bulk colour of a gemstone or other material, and/or a colour of an inclusion/defect within the gemstone or other material, demands probing the sample with different wavelengths of the incident light. Thus, in light of the experimental challenge faced when performing measurements at different wavelengths, available techniques present a limitation for a determination of chromatic properties in a gemstone.
In accordance with a first aspect of the present invention, there is provided a method for determining one or more features associated with an internal structure of a gemstone, the gemstone being at least partially transmissive to electromagnetic radiation, the method comprising:
In one embodiment, the method further comprises determining the external surface geometry of the gemstone. In one embodiment, processing the detected electromagnetic radiation comprises determining the external surface geometry of the gemstone using the detected electromagnetic radiation.
In one embodiment, directing electromagnetic radiation towards the gemstone comprises directing electromagnetic radiation towards the gemstone from a plurality of different incident directions relative to the external surface geometry of the gemstone.
In this embodiment, detecting electromagnetic radiation may comprise detecting electromagnetic radiation for each incident direction.
In one embodiment, processing the detected electromagnetic radiation comprises generating an output associated with a three-dimensional distribution of an optical property within the gemstone, the three-dimensional distribution of the optical property being indicative of a three-dimensional distribution of the one or more features associated with the internal structure of the gemstone.
Generating the output may comprise applying an iterative algorithm.
In one embodiment, the method further comprises using the output to generate a three-dimensional graphical representation of the three-dimensional distribution of the one or more features associated with the internal structure of the gemstone.
In one embodiment, processing the detected electromagnetic radiation comprises generating, based on the determined external surface geometry, a model of a simulated propagation of simulated electromagnetic radiation between the source of incident electromagnetic radiation and the optical detecting means and via a simulated homogeneous sample, wherein interaction between the simulated electromagnetic radiation and the simulated homogeneous sample is accounted for, the simulated homogenous sample comprising a simulated external surface having the determined external surface geometry of the gemstone and wherein the simulated homogeneous sample has a homogeneous refractive index. In the embodiment for which the method comprises directing electromagnetic radiation towards the gemstone from a plurality of different incident directions relative to the external surface geometry of the gemstone, the model of simulated propagation of the simulated electromagnetic radiation may be generated for each incident direction.
Further, the method may comprise modelling simulated refraction and attenuation of the simulated electromagnetic radiation at a plurality of virtual surface boundaries of the simulated homogenous sample. The method may further comprise modelling simulated reflection of the simulated electromagnetic radiation at a plurality of virtual surface boundaries of the simulated homogenous sample. The method may further comprise modelling, based on the model of the simulated propagation, a simulated polarisation state of the simulated electromagnetic radiation propagating between the source of incident electromagnetic radiation and the optical detecting means and via the simulated homogeneous sample, wherein modelling the simulated polarisation state accounts for an interaction between the simulated electromagnetic radiation and respective virtual surface boundaries at the external surface of the simulated homogeneous sample.
The method may further comprise modelling a shape and an intensity of a simulated beam of incident electromagnetic radiation. In this embodiment, the method may comprise using the modelled shape and intensity of the simulated beam of incident electromagnetic radiation to determine a size of a region of interaction of the simulated beam of incident electromagnetic radiation with a virtual external surface boundary of the simulated homogeneous sample.
In one embodiment, processing the detected electromagnetic radiation comprises using a computed tomography process.
The one or more features may include at least one or more of the following: a defect; an inclusion; an impurity; a chromatic property; a polarisation property.
In one embodiment, the method comprises directing electromagnetic radiation towards the gemstone at a minimum of two different wavelengths.
Detecting electromagnetic radiation may comprise detecting electromagnetic radiation for each wavelength. Processing the detected electromagnetic radiation may comprise processing the detected electromagnetic radiation for at least two wavelengths, wherein information indicative of one or more chromatic properties associated with the internal structure of the gemstone can be obtained.
In one embodiment, the source of incident electromagnetic radiation comprises a diffuse source of electromagnetic radiation.
In one embodiment, the method further comprises moving the gemstone, the source of incident electromagnetic radiation and the optical detecting means relative to each other.
In one embodiment, detecting electromagnetic radiation comprises detecting electromagnetic radiation transmitted from the gemstone.
In another embodiment, detecting electromagnetic radiation comprises detecting electromagnetic radiation scattered and/or reflected and/or caused by fluorescence from within the gemstone.
In accordance with a second aspect of the present invention, there is provided a system for determining one or more features associated with an internal structure of a gemstone, the gemstone being at least partially transmissive to electromagnetic radiation, the system comprising:
In one embodiment, the system is configured such that the source of electromagnetic radiation emits electromagnetic radiation towards the gemstone from a plurality of different incident directions relative to the external surface geometry of the gemstone.
In one embodiment, the processor is further configured to generate, using the output, a three-dimensional graphical representation of the one or more features associated with the internal structure of the gemstone.
In one embodiment, the processor is further configured to:
In accordance with a third aspect of the present invention, there is provided a computer program comprising executable code configured to cause the process of the system of the second aspect to execute the steps of:
In accordance with a fourth aspect of the present invention, there is provided a method for determining one or more features associated with an internal structure of a test sample, the method comprising:
In accordance with a fifth aspect of the present invention, there is provided a system for determining one or more features associated with an internal structure of a test sample, the system comprising:
In one embodiment, the test sample comprises a material having a high refractive index.
Notwithstanding any other forms which may fall within the scope of the disclosure as set forth in the Summary, specific embodiments will now be described, by way of example only, with reference to the accompanying drawings in which:
Where reference is made in any one or more of the accompanying drawings to steps and/or features that have the same reference numerals, those steps and/or features have for the purposes of this description the same function(s) or operation(s), unless the contrary intention appears.
In the context of this application, “defect” is intended to mean a naturally or manmade irregularity. A defect may include but is not exclusive to: voids, cracks, mineral inclusions, natural formations, growth patterns, etc.
Embodiments of the present invention aim at providing a method and a system for a refraction-corrected reconstruction of a distribution of one or more features associated with an internal structure of a sample. The sample may be referred to as a test sample, the terms “test sample” being used in the context of this application to refer to a sample that is being under investigation to determine one or more features, such as, however not limited to, inclusions or other defects, associated with its internal structure.
In one specific embodiment, the test sample is a gemstone, and may be a whole gemstone or a cut gemstone. The gemstone may have a complex irregularly shaped external surface geometry and may for example be a non-polished gemstone, such as a non-polished diamond or the like. However, it will be understood that embodiments of the present invention are not limited to the test sample being a gemstone and is also not limited to a sample having a complex irregularly shaped external surface geometry. The test sample may be any object or sample of a transparent or semi-transparent material. The test sample may be any sample comprising a material that is at least partially transmissive to electromagnetic radiation, and may for example, however not limited to, be a sample comprising a crystalline material having a high average refractive index, i.e. an average refractive index above 1.50.
In the context of this application, the “internal structure of the test sample” or “internal structure of the gemstone” is intended to refer to the inside or interior of the test sample or gemstone, i.e. the part of the test sample or gemstone within its envelope beneath the outer surface of the test sample or gemstone. The terms “feature(s) associated with the internal structure of the test sample” are intended to refer to any feature contained within or forming part of the test sample (e.g., gemstone) within the envelope of the test sample (e.g., gemstone) that is indicative of some inhomogeneity inside the test sample. Feature(s) associated with the internal structure or interior of the test sample or gemstone are intended to include structural features contained within or forming part of the test sample within the envelope of the test sample, such as defects, flaws, or inclusions contained within or forming part of the test sample within the envelope of the test sample, as well as other features contained within or forming part of the test sample within the envelope of the test sample such as chromatic features/properties, and polarisation features/properties. The features may be localised elements and/or may be broadly distributed through the interior of the test sample. Further, the features may comprise features with sharp or abrupt boundaries, and/or may comprise a continuous variation of features/properties.
The features may include those that are visible to the naked eye, as well as those that are only visible under levels of magnification.
The terms “inclusion”, “flaw” and “defect” are used in the following interchangeably to indicate an individual discernible irregularity inside the test sample.
Further, in the context of this application, a chromatic property is meant to relate to a wavelength dependence of optical properties of the internal structure of the test sample and is meant to include, however is not limited to, features such as: a colour of an inclusion or other defect; an average colour within the internal structure of the test sample; a continuous variation in colour in the internal structure of the test sample; an abrupt variation in colour in the internal structure of the test sample; a colour or average colour of an inclusion or other defect in the internal structure of the test sample; a colour and/or intensity of light reflected or scattered from, or emitted by, an inclusion or other defect; an average colour and/or intensity associated with absorption or fluorescence from the internal structure of the test sample; a fluorescence of an inclusion or other defect; and/or an average fluorescence associated with the internal structure of the test sample.
In the context of this application, “a polarisation property” is intended to refer to an optical property of the test sample (such as for example however not limited to, a partially transparent material) that depends on, is associated with, or relates to, a polarisation state of a beam of electromagnetic radiation interacting with the test sample. For example (however not limited to), a polarisation property of the test sample may in the context of this application refer to a birefringence of the test sample; a variation in birefringence due to the internal structure of the test sample; a polarisation dependence in scattering or fluorescence from a defect, inclusion, or impurity in the test sample.
The expressions “non-refractive internal structure”, “homogeneous refractive index”, and “homogenous internal structure” are used in the context of this application to indicate an internal structure of a sample that comprises substantially no impurities or flaws that would cause a further refraction of the electromagnetic radiation after it enters the sample, besides a first refraction that occurs at the physical boundary between the air and the sample at the sample surface or envelope. It is noted that a “homogenous internal structure” may cause attenuation, scattering, reflection and/or other optical effects.
Further, the expression “homogeneous sample” is used in the context of this application to mean a sample having a homogenous internal structure.
Embodiments of the present invention generally combine an optical tomography technique with a detailed modelling of reflection and refraction of light rays at the surface of a potentially complex-shaped test sample to obtain information associated with an internal structure of the sample without the need for immersing the test sample in a refractive index matching fluid or solid. More specifically, embodiments of the present invention aim at providing a refraction/reflection-corrected method and a refraction/reflection-corrected system for obtaining information regarding features internal to the test sample, i.e. features associated with an internal structure of a test sample, including three-dimensional (3D) structural features such as inclusions or other defects as well as other features, such as chromatic properties and polarisation properties. The information obtained enabling characterisation of the sample. The information obtained can also enable accurate modelling of the sample. Such modelling can be advantageous to analyse the sample, for example for a purpose such as to assess quality, determine suitability of a gem stone for an intended purpose, and/or options for cutting the stone.
In contrast, in the case without immersion in a refractive index matching material, rays of electromagnetic radiation travelling between the source of incident electromagnetic radiation 104 and the optical detecting means 106 may be reflected and/or refracted at the external surface of the gemstone 108. These reflections and refractions at the surface of the gemstone 108 may alter one or more of the direction and intensity of the incident electromagnetic radiation on the features within the gemstone, thereby, influencing the detected electromagnetic radiation. The detected electromagnetic radiation alone cannot provide an accurate characterisation of the gemstone interior due to the reflections and refractions at the surface of the gemstone. However, these reflections and refractions can be accounted for with the detected electromagnetic radiation for building a 3D model of the gemstone interior that is reflection-corrected and refraction-corrected.
It is noted that the sets of parallel incident rays of electromagnetic radiation 110 shown in
The following description will be provided in relation to the test sample being a gemstone. It will however be understood that the following description may be applied to any other type of test sample including any object or sample of a transparent or semi-transparent material, and including any sample comprising a material that is at least partially transmissive to electromagnetic radiation.
At step 202, electromagnetic radiation is directed towards the gemstone using a source of incident electromagnetic radiation.
At step 204, in response to directing the electromagnetic radiation, electromagnetic radiation is detected, using an optical detecting means such as an optical detector or an electro-optical sensor, wherein the detected electromagnetic radiation includes electromagnetic radiation detected following an interaction between the gemstone and the incident electromagnetic radiation.
At step 206, the detected electromagnetic radiation is processed, wherein the processing (i) accounts for a determination of an external surface geometry of the gemstone and for refraction and reflection effects due to the external surface geometry of the gemstone, and (ii) obtains information indicative of the one or more features associated with the internal structure of the gemstone.
The steps of method 200 may be performed simultaneously or may be performed separately.
In one embodiment, the detected electromagnetic radiation is associated with electromagnetic radiation data characteristic of the detected electromagnetic radiation, typically the intensity of the detected electromagnetic radiation, for a given orientation and position of the gemstone.
The terms “electromagnetic radiation” will now be referred to as “EM radiation”.
The data acquisition involves directing EM radiation towards the gemstone from a plurality of different incident directions.
Different optical systems may be used for the acquisition of information (e.g., signals, data, images):
In one embodiment with reference to
In another embodiment with reference to
It will further be understood that embodiments of the present invention are not limited to the use of wavelengths in the visible wavelength range and that other wavelengths such as wavelengths in the infrared wavelength range or the ultraviolet wavelength range may be envisaged.
In accordance with embodiments of the present invention, the source of incident EM radiation and the optical detecting means will in the following be referred to as being parts of an optical system.
For acquisition of information (e.g., signals, data, images) for a plurality of directions relative to the gemstone, a motion control of the gemstone may in one embodiment be provided as part of the optical system arrangement, wherein the gemstone is moved relative to the source of incident EM radiation and the optical detecting means (i.e. detector or sensor).
For example, the gemstone may be positioned on a rotation stage, or on two orthogonal rotation stages, to change the relative alignment of the optical system (source of EM radiation and optical detecting means) and gemstone to acquire views from different directions. In particular, by positioning the gemstone on two orthogonal rotation stages, the gemstone is arranged to rotate through two orthogonal rotation axes relative to the source and detector/sensor, whereby the location of the source and detector/sensor relative to the gemstone changes as the gemstone is rotated. The various locations of the source and detector/sensor as a result correspond to points on an imaginary sphere around the gemstone. Such arrangement allows scanning EM radiation through the gemstone for a relatively large number of directions, wherein a large set of data can be achieved to contribute to an accurate characterisation of the one or more features within the internal structure of the gemstone. Alternatively, the source of EM radiation and/or the detector/sensor may be arranged to controllably move relative to the gemstone, or a plurality of sources of EM radiation and/or of optical detecting means (detectors/sensors) may be used to direct EM radiation towards the gemstone from a plurality of different directions and detect EM radiation in response to directing the EM radiation. In another alternative embodiment, one or more stationary sources of EM radiation may be provided but there being an optical device which changes the ray path from the stationary source/s towards the gemstone.
In one embodiment, processing the detected EM radiation comprises using a computed tomography process.
An optical projection tomography system may be used wherein the detected EM radiation is EM radiation that transmitted from the gemstone. With reference to
Alternatively, an optical tomography system may be used wherein the optical detecting means is arranged to detect EM radiation scattered and/or reflected, and/or caused by fluorescence from within the gemstone. In this embodiment, the detected EM radiation does not include transmitted EM radiation but includes any one of scattered EM radiation, reflected EM radiation or fluorescence. The source 302, 314 may not be in line with the optical detecting means 310, 320, and may for example be placed off to the side relative to the optical detecting means or may be placed off in any transversal position relative to the optical detecting means.
The different arrangements according to embodiments of the present invention may be used for the determination of the one or more features (including inclusions and other defects, chromatic properties, etc.) associated with an internal structure of a gemstone or test sample, and the respective acquired information (e.g., signals, data, images) using the different arrangements may be combined into a merged dataset and/or used in a complementary manner.
With further references to
Steps 404 to 412 describe a specific embodiment of the processing step 206 of method 200.
At step 404, a model of an external surface geometry of the gemstone is determined.
At step 406, a model of a simulated homogeneous sample is generated, the simulated homogenous sample comprising a simulated external surface having the determined external surface geometry of the gemstone and wherein the simulated homogeneous sample has a homogeneous refractive index.
At step 408, a model is generated of a simulated propagation of simulated EM radiation between the source of incident EM radiation and the optical detecting means and via the simulated homogeneous sample, wherein a model of interaction of the simulated EM radiation with a plurality of virtual surface boundaries of the simulated homogeneous sample is generated. In one embodiment as described in the following, each virtual surface boundary will be understood to refer to a virtual surface boundary at the simulated external surface of the simulated homogeneous sample.
At step 410, an attenuation of simulated EM radiation is modelled using the model of simulated propagation including the model of interaction of the simulated EM radiation with the plurality of virtual surface boundaries of the simulated homogeneous sample.
At step 412, a 3D distribution of an optical property within the interior of the gemstone is reconstructed, the 3D distribution of the optical property being indicative of a 3D distribution of the one or more features in the internal structure of the gemstone.
With reference to
It may further contribute to improving the efficiency of the data acquisition as rays of EM radiation that miss the detector cannot be used to measure the amount of loss or scattering encountered along that path.
A computer is typically used to control the galvanometer scanner 810 inputs and thus the current scan direction, while simultaneously sampling the reference photodetector 808 and measurement photodetector 818. By computing the ratio of the respective measured EM radiation power of these two detectors 808 and 818, and correlating it with the corresponding scan position, a 3D map of the resulting transmissivity can be produced. This map is then stored for each view, i.e. each incident direction of the EM radiation and each laser wavelength, either independently or in a combined measurement file, which is later used for the reconstruction, using the processor, of the 3D distribution of one or more features associated with the internal structure of the gemstone.
In one embodiment, with reference to
In
The process is then repeated for different relative orientations of the gemstone and the source of incident EM radiation, i.e. the laser source. In a specific embodiment, the gemstone is rotated about one or more rotation axes that are centred on, and perpendicular to, the incident direction of the EM radiation from the laser source. Typically, 2D projection views are obtained and recorded for a large number of rotation steps, for example, however not limited to, more than 360 rotation steps.
In one embodiment, the detected EM radiation and obtained 2D projection views may be corrected for intensity fluctuations of the incident laser radiation. To do so, in one example, the separate reference photodetector 808 positioned in front of the galvanometer scanner 810 may be used to record intensity of EM radiation reflected by the uncoated glass plate beam sampler 806 positioned on the laser beams path, and the intensity of the reflected EM radiation may be used to correct for the intensity fluctuations of the incident laser radiation. Further, any variations in the spatial and angular sensitivity of the detector, as well as any temporal variations in the power of the lasers may be characterised and measured so as to correct the detected EM radiation and obtained 2D projection views for these variations. For example, to characterize variations in the spatial sensitivity of the detector and in the intensity of the incident laser radiation, an intensity of detected EM radiation may be recorded for an arrangement without a gemstone in the beam path (bright field) and be used at a later stage to correct the experimental data (i.e. data obtained with the gemstone in the beam path) for the mentioned variations.
It will be understood that the provided example implementation of the data acquisition is only one potential implementation and that embodiments of the present invention are not limited to this implementation, which is only used as an example.
The shape, i.e. geometry, of the external surface of the gemstone accounted for in the processing step 206 may be determined using different techniques.
In one embodiment, data associated with the external surface geometry of the gemstone is determined using the EM radiation detected at step 204, i.e. the data characteristic of the detected EM radiation such as the intensity of the detected EM radiation. In this embodiment, with reference to
In another embodiment, data associated with the external surface geometry of the gemstone is determined separately using one or more of a variety of known techniques such as, for example, X-ray computed tomography (XCT), optical surface tomography such as optical coherence tomography (OCT), or optical surface scanning. The determined data associated with the external surface geometry of the gemstone may then be used to process the EM radiation detected at step 204 and obtain information indicative of the one or more features associated with the internal structure of the gemstone. Using an XCT technique, a scan of the gemstone is acquired that allows obtaining a high-resolution 3D grayscale map of the entire gemstone, and from which a model of the external surface geometry can be extracted, e.g., using a computer graphics algorithm such as “Marching cubes”. Using an OCT technique, a plurality of scans of the gemstone are acquired for multiple viewing directions so as to capture scans substantially representative of the entire external surface of the gemstone. Like XCT, OCT generates a 3D grayscale dataset from which a surface model can be extracted, e.g., using a computer graphics algorithm such as, however not limited to, “Marching cubes”. Using an optical surface scanning technique, a 3D surface scanner is used to obtain the data associated with the external surface geometry of the gemstone such as a structured light 3D scanner or any scanning laser as considered appropriate by the person skilled in the art.
In a further embodiment, a consolidated determination of the external surface geometry of the gemstone is carried out by combining, using an algorithm, the visual hull data and the data obtained using a separate technique as mentioned above. Examples of such as techniques include (but are not limited to) XCT, optical surface tomography such as OCT, or optical surface scanning.
This embodiment may be particularly suitable for a gemstone having a rough irregular external surface. The processing of the visual hull data and the separate technique data in combination contributes to improving an accuracy of the determination of the gemstone's external surface geometry.
Subsequently, the determined external surface geometry of the gemstone is used for further processing of the detected EM radiation data so as to obtain information indicative of the one or more features associated with the internal structure of the gemstone.
The gemstone may not have the same orientation and position for each acquisition of, respectively, the data characteristic of the detected EM radiation (at step 204 of the method 200) and the separate technique data (for example using XCT, OCT or optical surface scanning as mentioned above).
To proceed with the reconstruction process and determine the one or more features associated with the internal structure of the gemstone, an orientation and position of the gemstone during acquisition of the data for determining the external surface geometry of the gemstone and an orientation and position of the gemstone during acquisition of the data characteristic of the detected EM radiation at step 204 of the method 200 must be taken into account. Coordinates indicative of the orientation and position of the gemstone 502 relative to the scanning optical system 300 when acquiring the data characteristic of the EM radiation detected at step 204 (referred to in the following as “projection data”) need to be “aligned” with coordinates indicative of the orientation and position of the gemstone 502 relative to the data acquisition system of the separate technique (referred to in the following as ‘external surface geometry data’). The external surface geometry data and the projection data may be aligned by several approaches: (a) physical alignment of the two optical scanning systems used for the acquisition of, respectively, the external surface geometry data and the projection data (e.g. by integrating both scanning systems into a single apparatus); (b) using registration marks on the gemstone; or (c) creating an approximate external surface geometry model from the projection data using the visual hull reconstruction technique as described above, and then use a 3D registration method to align the obtained visual hull to the external surface geometry model obtained separately (referred to in the following as “separate external surface geometry model”) using one of the techniques such as, however not limited to, XCT, optical surface tomography such as OCT, or optical surface scanning. This latter aligning approach (c) will now be further described.
The orientation of the separate external surface geometry model relative to the visual hull model is determined by determining the relative translation, scale and rotation of one of the models (i.e. the separate external surface geometry model or the visual hull model) that aligns the one model most closely with the other one of the models (i.e. the other one of the separate external surface geometry model and the visual hull model). Such determination may be performed, in a standard case, using a technique known as mesh registration where both models are represented as a surface mesh. Any known mesh registration technique as considered appropriate by the person skilled in the art may be used.
Using the determined external surface geometry of the gemstone, reflection and refraction of rays of EM radiation at the external surface of the gemstone can then be modelled, whereby refraction and reflection effects due to the gemstone external surface geometry can be accounted for to process the detected EM radiation. Modelling the refraction and reflection effects due to the external surface geometry of the gemstone enables a compensation for these effects during the analysis/processing of the detected EM radiation to determine features internal to the gemstone. Thus, avoiding the need to envelop the gemstone in a refractive index matching material.
Modelling of a simulated propagation of simulated electromagnetic radiation between the source of incident electromagnetic radiation and the optical detecting means and via a simulated homogeneous sample will now be described, with reference to steps 406 and 408 of flow chart 400.
In one embodiment, an assumption is made that the source of simulated EM radiation is quasi-monochromatic (or may consist of multiple independent quasi-monochromatic components), where quasi-monochromatic means that the EM radiation has a sufficiently narrow spectrum such that gemstone properties do not vary significantly within that spectrum. Further, another assumption is made that after simulated refraction of the simulated EM radiation at one or more virtual boundaries of the simulated homogeneous sample, the simulated EM radiation propagates within the simulated homogenous sample without refraction.
With reference to
In order to model propagation of EM radiation within a highly-refracting gemstone, both the following elements are calculated: (i) the geometry of the path that each incident ray of EM radiation follows within a simulated interior 606 of the simulated homogeneous sample 600, and (ii) an intensity loss in the EM radiation as the EM radiation is transmitted through and reflected from the virtual surface boundaries 608 and 610 at the simulated external surface of the simulated homogeneous sample 600. For elements (i) and (ii), the following mathematical notations are introduced:
The parentheses/brackets after s and R in the above denote a functional dependence: intensity loss at the surface depends on the ray-path and the initial polarisation state, which in turn depend on the direction and origin-point of the beam of simulated EM radiation. If the incident polarisation state p is not uniform, the function s would depend on the ray direction and origin and be written as P(v, w). It is noted that the term s[R(v, w), p] for modelling interactions with surface boundaries of the sample is only well defined if the initial polarisation state p of the light beam is known.
Further, it is noted that R and s model the paths and the intensities of the simulated EM radiation in the case of a simulated homogeneous sample 600 that is transparent and has a homogeneous refractive index. In one embodiment, it is assumed that any structure within the simulated homogeneous sample 600 affects the ray's intensity but not its path, and accordingly the modelled ray paths of the simulated EM radiation, the simulated polarisation state and the simulated surface attenuation do not change in the presence of an attenuating internal structure in the simulated homogeneous sample 600.
Both R and s can be calculated for each ray (defined by v and w) as long as the simulated polarisation state p is known, using the external surface geometry model determined at step 404, ray tracing, Snell's law and Fresnel equations (reproduced in equations (1) and (2) below) along with the simulated homogeneous sample's homogeneous refractive index.
In a more general case where a sample would alternatively be simulated as being in-homogeneously birefringent, surface attenuation would not be known directly from the measured projection data but would depend on the simulated internal structure of the simulated sample. This case requires a more complex processing formulation where surface attenuation is included in the modelling for the reconstruction step 408.
In one embodiment, the transverse beam shape (profile) is also modelled to better capture the simulated interactions of simulated EM radiation with virtual surface boundaries of the simulated homogeneous sample. An accurate model of the beam shape can be used to model depth-of-field effects. Once this model is incorporated into the simulation, features outside the depth-of-field may appear diffuse (or entirely absent). These diffuse features may be down-weighted (or ignored entirely) in a correction step. These weights may be hard-coded. For example, the features outside the depth-of-field may be ignored entirely, or they may be calculated.
Propagation of the simulated EM radiation is in one embodiment simulated using a simplified ray-optics model.
A path of each simulated beam of simulated EM radiation is traced in segments. First, the simulated beam is traced from the position v in the direction w until the simulated beam either: (i) intersects the detector (not shown) and is recorded without losing intensity; (ii) misses the simulated homogeneous sample and detector, in which case the corresponding intensity measurement contains no information and is removed from the data set; or (iii) intersects the simulated external surface of the simulated homogeneous sample (where it may or may not ultimately intersect the detector). Where the simulated beam intersects the simulated external surface of the simulated homogeneous sample, a simulated refraction of the simulated EM radiation as well as a simulated reflection of the simulated EM radiation at one or more virtual surface boundaries of the simulated homogeneous sample are then modelled.
When a traced ray intersects the simulated external surface of the simulated homogeneous sample, it will do so at a point. However, the beam of EM radiation is of a finite width (transverse size), and so will interact with the simulated external surface of the simulated homogeneous sample in a finite-sized patch around this point. Known properties of the EM radiation are used to determine the size of this region of interaction (RoI). In one embodiment, the transverse profile of the simulated beam of simulated EM radiation is modelled as a Gaussian beam and the known properties may be the width and position of the beam waist of the Gaussian beam. However, it will be understood that embodiments of the present invention are not limited to the simulated beam being a Gaussian beam and other numerical models of beam propagation may be used, such as for example a Bessel beam.
To simulate the interaction between simulated EM radiation and the simulated external surface of the simulated homogeneous sample within this RoI, the simulated beam of simulated EM radiation is temporarily split into a plurality of simulated rays of simulated EM radiation, each ray obeying the ray-optics approximation, and each ray being incident on a different part of the RoI. It is to be noted that if the simulated beam isn't considered to have a finite -width then the simulation of the interaction between simulated EM radiation and the simulated external surface of the simulated homogeneous sample within the RoI is applied with just a single ray of simulated EM radiation.
Ray-tracing is then performed for each simulated ray to calculate the angle-of-incidence and point-of-interaction at virtual surface boundaries at the simulated external surface of the simulated homogeneous sample. For each simulated ray within the simulated beam of simulated EM radiation, Snell's law is used to calculate the angle of refraction, while the Fresnel equations are used to calculate the intensity of reflection and refraction for the “s” and “p” simulated polarisation components.
Information obtained from the Fresnel equations can be summarised in a Mueller matrix, which allows the polarisation state and intensity of the EM radiation detected at the detector to be simulated following surface interactions at the virtual surface boundaries of the simulated homogeneous sample.
With reference to
If the Mueller matrices and angles-of-refraction for all simulated rays within a simulated beam (v, w) of simulated EM radiation are sufficiently similar, a simulation of the beam of simulated EM radiation can further be conducted. To do so, a weighted average is calculated of the Mueller matrices and angles-of-refraction for each simulated ray within the simulated beam of EM radiation. Weightings are determined according to the transverse intensity profile of the simulated beam of simulated EM radiation. If Mueller matrices and angles-of-refraction for all simulated rays within a simulated beam of simulated EM radiation are not sufficiently similar and further simulation of the beam of simulated EM radiation cannot be conducted, a measurement of the detected simulated EM radiation corresponding to the traced simulated beam of simulated EM radiation is considered to not contain useful information and is removed from the dataset.
Thus, an averaged angle-of-refraction determined for the simulated ray 604 of simulated EM radiation as it enters the gemstone 600, in combination with the location where it intersects the surface of the gemstone 600 at 608, provides information for ray-tracing along a new ray-path segment beyond the surface of the gemstone 600. If that new segment is within the gemstone 600, then it is added to the set R(v, w). The resulting average Mueller matrix describes changes to the beam polarisation state and intensity and is generated for each ray-surface interaction. The intensity change is recorded to s[R(v, w), p] and the new polarisation state of the beam recorded.
The above-described test for uniformity of all simulated rays within a beam (v, w) is applied at each location where the beam interacts with the surface—i.e. at the exit location and at any locations of partial or total internal reflection along the beam path. If the Mueller matrices and angles-of-refraction for all simulated rays within a simulated beam of simulated EM radiation are not sufficiently similar at any of these locations, then the data for this beam is removed from the dataset.
Using the new direction of propagation and the aforementioned beam properties, the process is repeated to determine a second region-of-interaction (RoI) between the surface of the gemstone 600 and the simulated beam of simulated EM radiation. This time, the simulated beam is striking a virtual surface boundary of the gemstone 600 from the interior. For the modelling, i.e. ray tracing model, virtual surface boundaries are virtual surface boundaries at the simulated external surface (corresponding to the determined external surface geometry of the gemstone) of the simulated homogeneous sample. The second region-of-interaction is modelled in the same manner as the first interaction, however there are two distinct cases to consider which is illustrated in
It is noted that it is also envisaged to further model the paths of reflected portions of each simulated ray of simulated EM radiation to see whether the reflected portions eventually hit the detector, in which case the simulated intensity of simulated EM radiation reaching the detector would be the result of multiple interactions.
It is noted that iterative analysis may be used to map the simulated ray paths attributable to each internal boundary of the gemstone. For ray-tracing modelling within the interior of the gemstone, a threshold number of total simulated internal reflections, e.g. 1 or 2, may be considered to minimise uncertainties with each ray direction change. It should be appreciated that the accuracy of the ray tracing modelling may degrade where multiple virtual surface boundaries are encountered by the simulated beam of EM radiation, and the ray tracing modelling may be less reliable the more virtual surface boundaries are encountered.
Following the data acquisition steps 402 and 404 and as a result of the above simulations 406 and 408, for each simulated ray (v, w) in the scan, the following elements of input information are obtained for further processing by a processor:
As shall be described in the following, it is possible, using standard methods of computed tomography, to configure the processor to process the above elements of input information to generate an output associated with a linear attenuation coefficient of the internal structure of the test sample.
Comparison with Conventional Tomography
In conventional tomographic imaging or computed tomography, measurements are collected that correspond to sums over straight rays (i.e. line integrals) through some 3D quantity of interest. In other words, rays of EM radiation move through the sample in straight lines and accumulate changes (e.g. attenuation) as they go. In a conventional tomographic imaging setup, it is assumed that refraction is negligible and that the ray paths are straight lines.
The modelling of propagation of the EM radiation in accordance with embodiments of the present invention differ from conventional computed tomography in several important ways:
In conventional tomography of non-refracting test samples, the model of propagation of EM radiation is referred to as the “X-ray projection transform” operator that predicts the total attenuation that will be suffered by each ray (v, w) that passes through a volume with a spatial distribution of attenuation μ(x), i.e.:
[μ(x), (v, w)]=−ln[I(v, w)/I0(v, w)] (3)
Mathematically, in accordance with an embodiment of the present invention, the model of propagation of the EM radiation is defined as a counterpart to the projection operator (i.e. model of propagation) that is used in conventional computed tomography. The “generalised projection operator” in accordance with embodiments of the present invention comprises two terms:
′[μ(x), (v ,w)]≡
R[μ(x), (v, w)]+ln(s[R(v, w), p]), (4)
The quantities R[μ(x), (v, w)] and ln(s[R(v, w), p]) correspond to two parts of the model:
This generalised projection operator captures behaviours important to the optical imaging system whilst retaining important mathematical properties of the more conventional projection operator .
Using as inputs: (i) the detected EM radiation (as at step 204 of method 200) and (ii) the generalised projection operator ′ (a non-linear integral transform modelling the propagation of EM radiation, which comprises modelling attenuation of the EM radiation as it propagates between the source of incident EM radiation and the detector and via the gemstone), the processor is arranged to generate an output associated with a three-dimensional distribution of an optical property within the internal structure of the gemstone, the optical property being associated with an interaction between the gemstone and the incident electromagnetic radiation directed from the respective incident direction, the three-dimensional distribution of the optical property being indicative of a three-dimensional distribution of the one or more features (including defects, inclusions, impurities, chromatic properties, polarisation properties) in the internal structure of the gemstone. For example, using an optical projection tomography system for data acquisition, the optical property may be the transmissivity. In another embodiment where EM radiation scattered from within the gemstone is detected, the optical property may be the scattering strength. The optical property is typically related to the intensity of the EM radiation detected at the detector/sensor.
The three-dimensional distribution of the optical property is indicative of a three-dimensional distribution of the one or more features within the internal structure of the gemstone and the processor is arranged to determine the one or more features associated with the internal structure of the gemstone using the determined three-dimensional distribution of the optical property.
The conventional tomographic reconstruction problem of calculating a 3D quantity of interest, such as a 3D linear attenuation coefficient p(x), from its line integrals [μ(x), (v, w)] is equivalent to calculating an inverse to
. For sufficiently straightforward tomographic imaging experiments, this is done using “Fourier-slice” based methods, or “filtered back-projection”.
In the more general case, calculation of the inverse operator is either unfeasible or impossible. If so, a solution is iteratively approximated using algorithms such as SIRT, SART, or EMTR. These algorithms run (iterate) multiple times, each time producing a result progressively closer to the correct answer. Furthermore, these algorithms have the significant advantage that they do not require knowledge (or the existence) of the inverse operator.
Once a generalised projection operator ′ is defined and the associated modelling completed (yielding simulated ray paths R(v, w) and attenuations s[R(v, w), p], it is straightforward to use well-established algorithms to reconstruct the 3D linear attenuation coefficient μ(x) from the recorded intensities I(v, w) and I0(v, w) contained in the projection data. To do so, a generalised back projection operator
′ is defined as the adjoint of
R. This operator denotes back projection (see, for example, A. C. Kak and Malcolm Slaney, Principles of Computerized Tomographic Imaging, Society of Industrial and Applied Mathematics, 2001) along the ray-path segments R(v, w). Back projection is a term used in computed tomography, which can be described colloquially as the “smearing” of output values along the corresponding ray-path segments.
To solve for μ(x), an algorithm such as SIRT or EMTR may be used, which may be found in publications from the literature relating to tomography (e.g. for EMTR, Kenneth Lange, Richard Carson, et al., Em reconstruction algorithms for emission and transmission tomography, Journal of Computer Assisted Tomography 8(2):306-16, 1984; for SIRT, A. C. Kak and Malcolm Slaney, Principles of Computerized Tomographic Imaging, Society of Industrial and Applied Mathematics, 2001), in which the conventional projection and back projection operators are replaced with the generalised variants described above. The algorithm is then run until it converges on a result. In certain cases, e.g., where it is known that the gemstone is predominantly transparent with only isolated defects, compressed-sensing algorithms that assume spatial sparsity (such as CS-SIRT) may be particularly useful. Poisson or Gaussian noise at the detector may also be taken into account.
As mentioned previously, the term s[R(v, w), p] for modelling interactions with surface boundaries of the sample is only well defined if the initial polarisation state p of the light beam is known. If the linear attenuation coefficient μ(x) is known, the initial polarisation state of the incident EM radiation may be determined by searching for the set of parameters which best matched the input data:
p(v, w)=argmin[p′(v, w); |−ln[I(v, w)/I0(v, w)]−R[μ(x), (v, w)]+ln(s[R(v, w), p′(v, w)])|0.5], (5)
where argmin[a; b(a)] is the value of a that minimises the function b(a), and |.|0.5 is the p-norm for p=0.5. In one embodiment, the p=0.5 norm is used, which emphasises matching broad/flat features in images, but another norm may alternatively be used.
In practice, neither p(v, w) or μ(x) is known exactly. However, one of these parameters can be approximated with an estimate of the other using the following iterative procedure:
p
(t)(v, w)=argmin[p′(v, w); |−ln[I(v, w)/I0(v, w)]−PR[μ(t−1)(x), (v, w)]+ln(s[R(v, w)])|0.5]; (6)
In accordance with an embodiment of the present invention, a “polarisation state” is defined using the Stokes parameters. These parameters are properties of the probability distribution of EM field states, so the above iterative procedure may be interpreted as an expectation-maximisation algorithm.
It is noted that in one embodiment, to obtain information associated with chromatic properties of the internal structure of the gemstone, a source of incident EM radiation emitting at multiple wavelengths, either one or multiple wavelengths-at-a-time, is used in step 402. For example, multiple wavelengths, one or multiple wavelengths-at-a-time, may be used for embodiments aiming at obtaining: (a) a map of the average colour (wavelength dependence) of the bulk test sample and/or of individual defects, and/or (b) an improvement of the illumination coverage within the test sample by varying the refraction angles of the light. In this case where multiple wavelengths are used in step 402, then one may reconstruct multiple 3D distributions of the optical property (e.g. one for each wavelength), and the complementary information from these 3D distributions may be combined using an algorithm to derive chromatic information about the one or more features associated with the internal structure of the gemstone.
Further, it will be understood that other properties of the source and beam of incident EM radiation may be modelled and taken into account by a processor for ray-tracing modelling and processing of the detected EM radiation. For example, other properties of the source and beam of incident EM radiation may include the beam size, focal plane and depth of field (for Gaussian beams, as other beam shapes may be characterised by different information), wavelength, location and direction.
Using iterative reconstruction techniques of the types described above, it is then possible to combine the optical property data determined by the processor for the different incident directions of the electromagnetic radiation to reconstruct the three-dimensional distribution of the optical property within the internal structure of the gemstone. The three-dimensional distribution of the optical property within the internal structure of the gemstone is indicative of a three-dimensional distribution of one or more features, such as inclusions and other defects, chromatic properties associated with the internal structure of the gemstone.
In one embodiment, the method may further comprise generating a three-dimensional graphical representation indicative of the three-dimensional distribution of the determined one or more features (including any one or more of the following: defects; inclusions; impurities; chromatic properties such as average colour, continuous variation of colour within the test sample, or average colour of inclusions/defects; polarisation properties) associated with the internal structure of the gemstone. In other words, the three-dimensional graphical representation corresponds to a three-dimensional reconstruction of one or more features within the internal structure of the gemstone. In this embodiment, the processor may be arranged to use the reconstructed 3D distribution of the one or more features associated with the interior of the gemstone to generate a corresponding 3D graphical representation.
In a further embodiment, it will be understood that it is envisaged to use an imaging approach instead of a scanning approach. In such an embodiment, a telecentric imaging system with a position-sensitive 2D imaging detector may be used. Instead of each measurement being associated with the EM radiation's incident direction w and point of origin v, each measurement will be associated with a position v on the detector and a vector w parallel to the optical axis of the telecentric lens. With this re-definition, ray-tracing begins at the detector instead of the source and the generalised projection operator is otherwise identical to that discussed above. The processor may then be configured to generate a model of simulated ray paths of simulated EM radiation between each image sensor pixel and the diffuse light source, wherein the imaging approach is the optical reciprocal to the scanning approach. More specifically, for each viewing angle, which relates to each pixel on the image sensor, the processor is configured to determine the ray exit point from the simulated homogeneous sample surface.
In cases where information associated with chromatic properties of the gemstone (e.g., bulk colour, or colour of inclusions) is to be extracted, transmitted intensity of EM radiation through the gemstone is measured for several different colour (wavelengths) of quasi-monochromatic light. Each of these measurements is reconstructed separately, resulting in respective 3D attenuation maps of the gemstone for each different colour. These are then combined using an algorithm to extract the information associated with chromatic properties of the gemstone (e.g., bulk colour, or colour of inclusions). In other words, the processor is arranged to determine optical property data for each wavelength (or narrow band of wavelengths) and a corresponding reconstruction of the three-dimensional distribution of the optical property within the internal structure of the gemstone is performed independently for each wavelength. Indeed, for each wavelength, the gemstone may yield different ray paths. The processor is arranged to determine chromatic properties associated with the internal structure of the gemstone (e.g., a colour of an inclusion or other defect; an average colour within the internal structure of the test sample; a continuous variation in colour in the internal structure of the test sample; a colour or average colour of an inclusion or other defect in the internal structure of the test sample; a brightness of an inclusion or other defect; an average brightness associated with the internal structure of the test sample; a fluorescence of an inclusion or other defect; an average fluorescence associated with the internal structure of the test sample) by accounting for differences between the various optical property data determined at the different wavelengths.
Embodiments of the present invention thus provide an advantage that a refraction-corrected reconstruction of a three-dimensional map of chromatic properties within the envelope of a sample, such as a gemstone, including one or more of the following: a colour of an inclusion or other defect; an average colour within the internal structure of the test sample; a continuous variation in colour in the internal structure of the test sample; a colour or average colour of an inclusion or other defect in the internal structure of the test sample; a brightness of an inclusion or other defect; an average brightness associated with the internal structure of the test sample; a fluorescence of an inclusion or other defect; and/or an average fluorescence associated with the internal structure of the test sample, may be determined without the need for submerging the test sample in different refractive index matching fluids or embedding the test sample in different refractive index matching solids.
More comprehensive generalisations of the above models may further be required for embodiments wherein the gemstone or other test sample is either homogeneously or in-homogeneously birefringent.
When detecting and using electromagnetic radiation scattered, reflected, and/or caused by fluorescence from within the test sample to identify defects or imperfections within the test sample, the source of electromagnetic radiation and the optical detecting means, i.e. detector or sensor, may be positioned by placing the detector to one side, or adjacent to the source.
In the claims which follow and in the preceding description of the invention, except where the context requires otherwise due to express language or necessary implication, the word “comprise” or variations such as “comprises” or “comprising” is used in an inclusive sense, i.e. to specify the presence of the stated features in various embodiments of the invention.
Modifications and variations as would be apparent to a skilled addressee are determined to be within the scope of the present invention.
It is also to be understood that, if any prior art publication is referred to herein, such reference does not constitute an admission that the publication forms a part of the common general knowledge in the art, in Australia or any other country.
| Number | Date | Country | Kind |
|---|---|---|---|
| 2021900371 | Feb 2021 | AU | national |
| Filing Document | Filing Date | Country | Kind |
|---|---|---|---|
| PCT/AU2022/050102 | 2/15/2022 | WO |
