SYSTEM AND METHOD FOR CONDITION DETECTION

The present invention relates to systems and methods for condition detection, for example for detecting a condition of a plurality of regions of a material.

The current global drive towards renewable energy solutions has led to a boom in the development of photovoltaic (PV) devices. Organic photovoltaics, for example, are thin film solar cells which can be cheaply mass produced using roll to roll printing techniques. The ability to create photovoltaic elements rapidly at low cost is leading to a sharp rise in their commercialisation and availability. However, it is important to ensure that the produced photovoltaic elements show adequate performance.

Conventionally, the spatial response function of PV materials is measured through the raster scanning of a focussed laser beam across the surface of the PV element. This technique, known as Laser Beam Induced Current Scanning (LBIC) is an accepted and widely used method, however contains inherent speed restrictions in its realisation. In order to scan the test piece, the PV needs to be translated laterally using a piezo / mechanical stage, the travel time of which sets scanning speed limitations on the process. One method to increase the scanning speed of the LBIC technique is to use a digital micromirror device (DMD) to selectively redirect the illumination spot onto the PV surface rather than physically translating the element itself (Yoo. J, 2012). EP 2755 327 discloses a time-resolved single-photon or ultra-weak light multidimensional imaging spectrum system and method.

The present invention seeks to provide an improved method and system for detecting a condition of a plurality of regions of material. According to an aspect of the invention, there is provided a method of detecting a deviation of a condition of a plurality of regions of a substrate or device from a desired condition, including:

applying light to the plurality of regions;

detecting an interaction of the light with the plurality of regions;

from the interaction, detecting a deviation of a condition of the plurality of regions from the desired condition, the method using compressive sensing.

The term 'sample' is used below to refer to the substrate or device being investigated.

In embodiments, the desired condition is uniformity or a uniform or predefined spatially-varying performance of the sample. The desired condition can be the conformance of the measured sample with the design or it can be a lack of manufacturing or material defects, including but not limited to: occlusions, holes, cracks, in a sample, in the substrate or device.

In embodiments, detecting a deviation of a condition of a plurality of regions of a substrate or device from a desired condition includes detecting spatial defects in the plurality of regions.

The substrate or device may be or include an optical element.

In some embodiments, the substrate or device is optically responsive, an optically responsive element being an element which provides a response to incident light.

According to an aspect of the invention, there is provided a method of detecting a condition of a plurality of regions of an optically responsive substrate or device, including:

applying light to the plurality of regions;

detecting an interaction of the light with the plurality of regions; detecting a condition of the plurality of regions from the interaction, the method using compressive sensing.

In some embodiments, detecting an interaction of the light with the plurality of regions includes detecting, preferably measuring, a response of the optically responsive substrate or device to illumination of the plurality of regions.

In some embodiments, a response of the optically responsive substrate or device is variable in dependence on incident light.

Preferably, applying light to the plurality of regions includes applying light to the plurality of regions using an array of adjustable mirrors or an array spatial light modulator in general. According to an aspect of the invention, there is provided a method of detecting a condition of a plurality of regions of a substrate or device, including:

applying light to the plurality of regions using an array of adjustable mirrors; detecting an interaction of the light with the plurality of regions;

detecting a condition of the plurality of regions from the interaction, the method using compressive sensing.

In embodiments, one or more of the following is performed in accordance with a compressive sensing technique: applying light to the plurality of regions; detecting a condition of the plurality of regions; detecting a deviation of a condition of the plurality of regions from the desired condition.

Compressive sensing is a technique which is mainly applied in the reconstruction of images with relatively few measurements. Embodiments of the invention use this technique in a different way (Compressed Mapping) to probe the spatial variation of a photovoltaic (or other substrate or device or optically sensitive device) so that malfunctioning areas can be identified and the manufacturing process improved.

Conventional Shannon/Nyquist sampling theory requires that to avoid loss of information when recording a signal, the information must be sampled at a rate twice as fast as the signal bandwidth. This can mean that a huge amount of data needs to be acquired in order to characterise a signal well enough to analyse it. Compressive sensing allows sampling at a rate well below the Nyquist rate by using non-adaptive linear mapping to maintain the shape of the signal. This apparent something for nothing methodology really uses implicit prior knowledge about the types of defects expected in the photovoltaic (or other material).

Embodiments of the invention use a mirror array, spatial light modulator, or other similar spatially distributed array method of light modulation to project light patterns onto the substrate or device, which may be optically active, and map the surface properties by monitoring the electrical output or difference in reflected or scattered light of the substrate or device. Reconstruction of surface properties is achieved through the use of compressive sensing techniques, such as convex numerical optimisation of 11 norm and Total Variation minimisation methods.

This use of compressive sensing is effectively the reverse of the imaging use of this technique. Instead of the comparatively slow row by row scanning of a photovoltaic with a laser beam, in embodiments of the invention, computer generated patterns are projected onto the photovoltaic and the current supplied in response is detected. This allows us to make a map of the photovoltaic cell response much faster than the row by row scanning method.

Whilst the speed of LBIC techniques can be increased through using a digital mirror device (DMD) or increasing the speed of travel of the translation mechanics as discussed above, embodiments of the present invention are able to greatly increase the measurement speed as compared with raster scanning methods. In order to measure the spatial response of a PV, LBIC requires each point to be measured individually for a total of N data points. Through the incorporation of techniques developed in Compressive Sensing, embodiments of the invention can create a map of the PV response in significantly less than N measurements and thus greatly reduce measurement speed.

Compressive sensing is based in the notion that a signal that is compressible can be measured in its compressed state, where a compressible signal is one that can be described in fewer bits than its original representation. If we can represent the spatial response function of a photovoltaic in terms of a signal with a lower number of significant coefficients than its length N, then it should be possible to directly sample this signal in less than N measurements. This theory is discussed in more depth below. In other words, compressive sensing allows the method to produce a complete map of the conditions or deviations of the conditions of all of the plurality of regions without needing to scan each region individually.

In embodiments, detecting a condition of the plurality of regions, or detecting a deviation of a condition of the plurality of regions, includes processing a detected interaction of the light with the plurality of regions using a compressive sensing technique.

In embodiments, applying light to the plurality of regions includes applying a sequence of patterns of light, each pattern of light illuminating a subset of the plurality of regions. Some regions can be illuminated by multiple patterns in the sequence; some regions may be illuminated by only one of the patterns, but all of the regions of the plurality of regions are in these embodiments preferably illuminated by at least one of the patterns. The method can include applying patterns of light, determined using mathematical methods derived from compressed sensing theory, to the plurality of regions.

In embodiments, when a pattern is applied, the regions of the respective subset are illuminated simultaneously.

The patterns can overlap.

The patterns of light can be predetermined using compressive sensing for example in advance of applying the light.

The patterns of light can be or include binary random matrices and/or a set series of patterns from the Hadamard set matrix. Detecting an interaction of the light with the plurality of regions can include, for each pattern of light, detecting an interaction of the light with the respective subset of regions. Detecting a condition of the plurality of regions or detecting a deviation of a condition of the plurality of regions can include processing a detected interaction of the light with each subset of regions using a compressive sensing technique.

Some embodiments include using compressive sensing and a detection of an interaction of the light with the respective subset of regions to determine the next pattern in the sequence.

In embodiments, detecting an interaction of the light with the plurality of regions or with a subset includes detecting, preferably measuring, a reflectivity and/or transmittance of the plurality of regions or subset. This can include detecting light reflected from and/or transmitted through the plurality of regions or subset. This can be useful where the substrate or device is not optically responsive as it enables a uniformity or defect to be nevertheless detected. Where the substrate or device is optically responsive, applying light can include applying light at an active wavelength of the substrate or device. A correctly functioning optically responsive substrate or device will tend to absorb more light at its active wavelength and therefore there is a greater difference in

reflectivity/transmittance between correctly functioning and defective regions at an active wavelength.

In embodiments, detecting an interaction can include measuring an interaction and/or detecting a condition or deviation can include determining a condition or deviation.

According to an aspect of the invention, there is provided a computer program for performing the method when executed on a computing device, for example a computing device configured to operate a system as described herein.

According to an aspect of the invention, there is provided a computer program for a control unit for a system for detecting a deviation of a condition of a plurality of regions of a device or substrate from a desired condition, the program using compressive sensing and being operable to:

operate a pattern generator to generate a sequence of patterns to be applied to light projected by a light projector;

detect, from a detected interaction of light from the light projector with a plurality of regions of a device or substrate, a deviation of condition of a plurality of regions of a device or substrate from a desired condition.

The program can be operable to perform any of the operations which the control unit herein is configured or operable to perform. According to an aspect of the invention, there is provided a system for detecting a deviation of a condition of a plurality of regions of a substrate or device from a desired condition, including:

a receiving zone for receiving a substrate or device including a plurality of regions;

a light projector for projecting light onto the receiving zone;

a detector for detecting an interaction of light with a plurality of regions of a substrate or device in the receiving zone; and

a control unit configured to use compressive sensing and a detected interaction from the detector to detect a deviation of a condition of a plurality of regions of a substrate or device in the receiving zone from the desired condition.

According to an aspect of the invention, there is provided a system for detecting a condition of a plurality of regions of an optically responsive substrate or device, including:

a receiving zone for receiving a substrate or device including a plurality of regions;

a light projector for projecting light onto the receiving zone;

a detector for detecting an interaction of light with a plurality of regions of a substrate or device in the receiving zone; and

a control unit configured to use compressive sensing and a detected interaction from the detector to detect a condition of a plurality of regions of a substrate or device in the receiving zone. In embodiments, the detector includes a coupling element to couple the detector to a response output of an optically responsive substrate or device in the receiving zone, whereby the detector can detect a response of a coupled optically responsive substrate or device. Preferably, the light projector includes an array of adjustable mirrors or an array spatial light modulator. According to an aspect of the invention, there is provided a system for detecting a condition of a plurality of regions of a substrate or device, including:

a receiving zone for receiving a substrate or device including a plurality of regions;

a light projector for projecting light onto the receiving zone, the light projector including an array of adjustable mirrors;

a detector for detecting an interaction of light with a plurality of regions of a substrate or device in the receiving zone; and

a control unit configured to use compressive sensing and a detected interaction from the detector to detect a condition of a plurality of regions of a substrate or device in the receiving zone.

The control unit can include the detector or the detector and the control unit can be separate units coupled together.

In embodiments, the detector is configured to provide data relating to detected interactions to the control unit. In embodiments, the control unit is coupled to the light projector and configured to control the light projector to apply light onto the receiving zone in accordance with a compressive sensing technique.

In embodiments, the control unit is configured to detect a condition of a plurality of regions of a substrate or device in the receiving zone, or a deviation of a condition of a plurality of regions of a substrate or device in the receiving zone, using a compressive sensing technique.

In embodiments, the control unit is configured to process data from the detector relating to a detected interaction using a compressive sensing technique to detect a condition or deviation of a condition of a plurality of regions of a substrate or device in the receiving zone.

In embodiments, the light projector includes an adjustable pattern generator for selectively applying a pattern to light projected by the light projector. Each pattern that the pattern generator can generate is to enable the light projector to illuminate a subset of regions of a substrate or device in the receiving zone.

In embodiments, the detector is configured to detect an interaction of light with each subset of regions of a substrate or device in the receiving zone. The control unit is in embodiments configured to process data from the detector relating to each detected interaction of light with a substrate or device in the receiving zone, using a compressive sensing technique, to detect a condition or deviation of a condition of a plurality of regions of a substrate or device in the receiving zone.

In embodiments, to enable the projection of patterns produced by a computer program an active Microelectromechanical system (MEMS) mirror array can be used, such as those present in many computer projectors used in meeting rooms. This includes an array of tiny mirrors which can be individually addressed and switched into one of two positions. This allows each of these mirror 'pixels' to project light onto the substrate or device or to dump it elsewhere. In this way any desired pattern can be produced.

In embodiments, the control unit is configured to operate the pattern generator to generate a sequence of patterns, preferably in accordance with a compressive sensing technique. In embodiments, the control unit is configured to determine the patterns to be generated by the pattern generator.

In some embodiments, for each pattern of light, the detector is configured to detect an interaction of light with the respective subset of regions of a substrate or device in the receiving zone and the control unit is configured to process data from the detector relating to each detected interaction of light with a substrate or device in the receiving zone, using a compressive sensing technique, to determine the next pattern in the sequence. In embodiments, the adjustable pattern generator includes an array of pattern elements, each pattern element having an adjustable reflectivity and/or transmittance which is adjustable by the control unit.

The adjustable pattern generator can include a liquid crystal display, a DMD and/or a spatial light modulator.

In embodiments, the light projector includes a light emitter for illuminating the pattern generator to project a pattern of light onto the receiving zone. In some embodiments, the detector includes a light detecting element arranged to detect light which has been transmitted through and/or reflected from a substrate or device in the receiving zone.

In embodiments, the detector includes a light detecting element disposed behind the receiving zone, wherein behind is intended to mean opposite the side of the receiving zone which is designed to be illuminated, and/or the detector includes a light detecting element in front of the receiving zone to detect light reflected from a substrate or device in the receiving zone. The detector can include a current amplifier.

The light projector can be configured to project light at an active wavelength of a substrate or device in the receiving zone. In embodiments, the detector is configured to measure an interaction of light with a plurality of regions of a substrate or device in the receiving zone or a subset thereof. The control unit can be incorporated in a computer program to be run on an external computer. The control unit can in embodiments be or include a processor.

The functions and operations described with respect to, for example, the control unit may be implemented as a computer program or computer-readable storage medium containing instructions to be executed by a processor and stored in a memory. The processor may represent generally any instruction execution system, such as a computer/processor based system or an ASIC (Application Specific Integrated Circuit), a Field Programmable Gate Array (FPGA), a computer, or other system that can fetch or obtain instructions or logic stored in memory and execute the instructions or logic contained therein. Memory represents generally any memory configured to store program instructions and other data.

Embodiments of the invention are able to scan samples with a fifth of the data points required by LBIC, with a consequent speed increase. In addition,

embodiments of the invention have a much better signal-to-noise ratio than LBIC and do not generally require noise reduction techniques such as lock-in detection.

Furthermore, in LBIC, there is generally not much current generated because of the small spot size, and the current level might change as a result of

environmental conditions. However, embodiments of the invention are able to avoid these disadvantages. By illuminating multiple regions simultaneously, embodiments are able to generate a more easily detectable interaction. Embodiments use a low-cost projection system which reduces or eliminates moving parts such as stepper movement stages and provides low cost electrical measurement with no lock-in amplifier. Embodiments provide a compressed sensing method for the detection of spatial defects in materials, in some embodiments in photovoltaic materials.

Embodiments provide, fast, large area metrology techniques to maintain quality control and reduce wastage during production for example of optically responsive elements such as photovoltaic elements.

Embodiments provide an advantageous approach to measuring the surface response profile of a photovoltaic cell using techniques developed in signal processing theory. Embodiments are able to identify the presence of defects and areas of aberrant surface response significantly faster than can be seen using a conventional raster scanning technique.

Some embodiments use a compressive mapping technique where binary, orthogonal, structured illumination patterns are projected onto the device before a convex minimisation procedure is performed to recover the response map from an incomplete measurement series. Other embodiments more fully incorporate compressed sensing theory and show a vast improvement in the time needed to observe strong features in the response map compared with both the previous technique, and the raster method. Advantageous to this technique is the concept that it will always require a fewer number of measurements than a raster scan method, with no significant differences in implementation between the two that would result in an increased time per measurement.

Embodiments apply techniques developed in compressive sensing theory to the measurement of the spatial response of a photovoltaic element. Embodiments include projecting both orthogonal illumination patterns, and random intensity patterns and in both cases embodiments can recover a feature map using less measurements than is necessary through conventional raster scanning.

Although embodiments herein are primarily described for testing a photovoltaic device, embodiments can be used for testing other substrates, both optically responsive and not optically responsive. For example, in some embodiments, the substrate or device includes an array of LEDs such as OLEDs that might be used in a television. Each LED can be considered a region of the substrate or device, and each LED will contribute to a response of the substrate or device when illuminated with light, enabling a determination to be made as to faulty LEDs in the array. In other embodiments, the substrate or device can include foil for example for blister packs for pharmaceutical tablets. The foil substrate is not optically responsive, but embodiments can be used to detect the transmittance and/or reflectivity of the foil substrate and thereby determine the presence of holes in the foil. In other embodiments, the substrate can include a film, such as a structured film for example made of plastic. The film may be structured in that it includes patterns, has a topology or surface structure, in which case it can be opaque or transparent, or the film may be structured in that it has a variation in its

transparency. Embodiments can be used to detect a conformance of the structured film to a desired structure for the film. This can be useful for example for testing optical concentrators.

Advantageously, because embodiments of the invention are able to test substrates so quickly, where substrates are being produced on an assembly line, it is possible to detect a systematic error in the assembly line quickly, and adjust the assembly line before too many substrates are produced that might otherwise be wasted or require repair.

Embodiments measure the response of a PV to applied illumination by measuring current. Embodiments can be advantageous since they are only limited by the response of PV. Embodiments of the invention can provide compressed sensing for photovoltaic characterisation. Traditional PV Spatial Response Fault Detection has used Laser Beam Induced Current (LBIC) measurements, which can be slow, requires full raster scan of sample, or Electroluminescence, which heats sample and needs a good camera.

Instead, embodiments of the invention make use of compressed sensing to replicate raster scan results, using less measurements.

Compressed sensing can use concept of sparse matrices:

• Consider a signal length N

• Now sample to observe: γ=φχ

• Solve the resulting incomplete series of linear equations using convex minimisation techniques.

In embodiments with compressed mapping

· DMD projects Hadamard Matrices onto the PV

• Transimpedence amp

Nl ADC

Measure V Embodiments can use norm for solving incomplete measurements:

^■ We now have (some) freedom of dictionary with which to describe s

^■ Incomplete so for any solution s, there exists:

r = s + r

infinite series of solutions for rin N(0)

^■ Define our l _p norm as: Ipuorm = f + xf + χζ ...

In embodiments, compressed sensing theory can be applied towards feature detection in PV characterisation. In embodiments results show a high degree of correlation between Compressed Sensing and Raster scan measurements.

In embodiments, the technique is scalable to coarser resolutions and larger PV modules.

Embodiments of the invention are described below, by way of example only, with reference to the accompanying drawings, in which:

Figure 1 a shows a raster scan in which each measurement is taken under illumination of a single point only and successive measurements follow the signal as the illuminated spot is scanned methodically over the surface of the PV, one dataset at a time;

Figure 1 b demonstrates how multiple points are illuminated simultaneously for each measurement in embodiments of the invention, so that each datum covers a much greater surface area of a substrate or device than for a raster scan;

Figure 2 shows a schematic diagram of a system according to an embodiment of the invention;

Figure 3 shows recorded voltage responses from a photovoltaic in an embodiment of the invention as successive Hadamard patterns are projected onto the surface; Figure 4a and b show a comparison of the growth of the correlations between the raster scan of a PV test piece, and the recovered map obtained through the compressed sensing algorithm, as a function of increasing numbers of Hadamard patterns; Figure 4a shows this growth for the l_i norm minimisation algorithm; Figure 4b shows this behaviour for the TV technique

Figure 5 shows a comparison of the reconstruction of the spatial response of a photovoltaic in an embodiment of the invention when defined using only the Left: 1 % and Middle: 0.5%, most significant coefficients in the Discrete Cosine

Transform domain; For comparison purposes on the Right we see the recovered spatial response map of the PV when measured using a raster technique with the same configuration;

Figure 6 shows a comparison of the measurement of the PV response function in an embodiment of the invention using only Left: 190 and Right: 350, randomly projected binary patterns, both reconstructions being performed by recovering the signal in the DCT domain;

Figure 7 shows the growth of measured correlation coefficients for the comparison of the reconstructed spatial response function as obtained in the DCT domain against the LBIC raster scan of photovoltaic;

Figure 8 shows growth of the recovered correlation coefficients using a discrete sine transform dictionary;

Figure 9 is a schematic diagram showing the projection of a light pattern onto a substrate or device in accordance with an embodiment of the invention;

Figure 10 is a diagram showing in pictorial form some results of an embodiment of the invention; Figure 1 1 shows the growth of the linear correction coefficient for a cracked, spotted sample using three different dictionary types;

Figure 12 shows a PV response to binary Hadamard patterns; and

Figures 13 to 20 are explanatory figures showing and describing features of embodiments of the invention.

The embodiment shown in the figures is for the detection of spatial defects in photovoltaic materials (inorganic, organic, dye sensitised or others) and the description below is primarily concerned with an example using a particular test photovoltaic. However, other embodiments can be used to detect spatial defects or other conditions in other materials as described elsewhere. The description below outlines some examples of compressive sensing. However, the skilled person can select a number of different methods from the known discipline of compressive sensing as appropriate to any given application.

Glossary/Abbreviations

CS: Compressed Sensing / Compressive Sensing

DMD: Digital Micromirror Device

DCT: Discrete Cosine Transform

DST: Discrete Sine Transform

LBIC: Laser Beam Induced Current

PV: Photovoltaic

RIP: Restricted Isometry Property

SNR: Signal to noise ratio

TV: Total Variation

ADC: analogue to digital converter

Definitions Signal: Throughout this description the term "signal" is used in a theoretical capacity rather than the conventional experimental use referring to an electrical impulse associated with a measurement. Here we define "signal" as: A function which conveys information regarding the behaviour or attributes of a phenomenon.

Compressed Mapping

Technique overview

An important concept in the technique of compressed mapping is the notion that a signal can be alternately represented in a different basis set to the ordinary

Cartesian identity matrix. LBIC scanning of a PV surface is a measurement of the final spatial response function as a signal, using a series of contiguous identity measurement matrices. As a result of this, information contained at the end of the signal is only obtained through complete scanning due to the point by point nature of the scan.

Embodiments of the invention utilise a digital micromirror device (DMD) element as incorporated into fast LBIC scanning systems (Donoho. D, 2006) (Gupta, 2007) to display a series of binary, orthogonal measurement matrices as an alternative to the identity matrix, see Figure 1 .

Figure 1 a shows how, with a raster scan, each measurement is taken under illumination of a single point only. Successive measurements follow the signal as the illuminated spot is scanned methodically over the surface of the PV, one dataset at a time. Figure 1 b demonstrates how in embodiments of the invention multiple points are illuminated simultaneously for each measurement, so that each datum covers a much greater surface area of the PV than for a raster scan. The significance of this is that it allows for multiple points on the signal to contribute to a single measurement result, and crucially an incomplete series of measurements nevertheless may contain information from every point on the surface of the PV. The word incomplete here is used to be consistent with the mathematical techniques for solving an incomplete series of linear simultaneous equations, and corresponds to a series of K measurements where K<N .

As a result of this it is possible to reconstruct the spatial response profile of the PV surface through a smaller number of measurements than is required in the conventional raster scanning technique. The primary difficulty associated with this lies in the reconstruction process itself, necessitating the solution of a highly underspecified series of simultaneous equations. Here two algorithms are utilised common in the field of compressed sensing, the l_i norm (Candes E. , 2006) and total variation (TV) (Candes E. R., 2005), methods which are described more comprehensively below. The l_i norm method is most suited to recovery of signals where a large number of the coefficients are zero, and the TV method is optimised for the recovery of signals which have a low degree of spatial variability. It can be seen that due to the nature of the response of the test photovoltaic the TV algorithm performs better than the l_i norm algorithm, as there is less spatial variability in the response map than there is spatial sparsity. This is not necessarily true for all photovoltaics, an example to the contrary could be a perfectly uniform response map with only a single small defective area.

Measurement matrices

The measurement matrices used in compressed mapping are taken from

successive lines of the Hadamard matrix, a binary orthogonal matrix with elements of +1 and -1 only. This can therefore be easily implemented using a conventional DMD as an alternative to the raster scan of identity matrices whilst also retaining the orthogonality condition they possess. A significant advantage associated with using these patterns for data acquisition is that since they illuminate on average half of the PV in one exposure, the signal to noise ratio (SNR) is significantly improved over the single pixel illumination method without the need for a bias light. It is important to ensure that whilst the Hadamard transmission coefficients are 0 and 1 , they are re-scaled to +1 and -1 in data analysis otherwise the reconstruction algorithm can fail to converge.

System

Figure 2 shows a schematic diagram of a system according to an embodiment of the invention, showing the layout used for the example described herein.

The system 10 includes a light emitter 12, in this case a 636.2nm pigtailed fibre coupled laser. However, in other embodiments, other types of light emitters can be used or lasers configured to emit at other wavelengths of light can be used.

Furthermore, although in this embodiment the light emitter includes a light source, in other embodiments the light emitter can emit light which it has redirected from a remote source; for example, the light emitter can be an end of an optical fibre, the other end of which receives light from a light source.

The light emitter is configured to emit light via a collimating element 14, in this case a collimating lens, to a beamsplitter 16. The collimating element is configured to collimate light emitted from the light emitter. While the collimating element 14 is advantageous in ensuring the use of collimated light, it is not necessary in every embodiment.

The beamsplitter 16 is in this embodiment a 50:50 beamsplitter cube and is arranged to transmit light received from the light emitter through it to allow it to travel to a pattern generator 18. The beamsplitter 16 is also arranged to direct light received from the pattern generator towards a receiving zone 20. In this example, the beamsplitter includes a mirror element 22 arranged at 45° to the direction of light received from the pattern generator 18 and configured to be substantially transparent to light from the direction of the light emitter 12 but reflective to light from the direction of the pattern generator 18, the light emitter, beamsplitter and pattern generator being optically aligned. In this embodiment, to be optically aligned, the components are arranged in a straight line. However, it is not excluded that optical fibres or other optical directors could be placed in an optical path to allow components to deviate from a straight-line arrangement but remain optically aligned. The pattern generator is an optical element configurable to reflect back to the beamsplitter part of the light received from the beamsplitter, the part of the light reflected being selected so as to form a pattern of light. The pattern generator includes an array of elements which can selectively be configured to cause light to be reflected to the beamsplitter or not, thereby allowing the configuration to select a particular light pattern. In this embodiment, the pattern generator is a DMD which contains a pixelated array of mirrors, each of which can be selectively orientated in either of two directions, to a beam dump 24 outside the system, or to the beamsplitter to be used as the intensity modulated illumination source. However, in other embodiments, the pattern generator can include other devices which include an array of adjustable reflective elements which can selectively adjust the direction or amount of reflection, or devices which include an array of elements of adjustable transmittance together with a reflective element, whereby each element can selectively allow or prevent light from passing through the device and being reflected to the beamsplitter by the reflective element. The pattern generator can in some embodiments include a liquid crystal display and/or a spatial light modulator. However, a DMD is preferred as it does not lose much light and it is able to provide light in a substantially uniform way, which is advantageous when a particular condition or departure from a particular condition is to be detected. In this embodiment, optically aligned between the beamsplitter 16 and the receiving zone 20 is a filtering device 26. The filtering device 26 can spatially filter the light to reduce diffraction artefacts, but is not necessary in all embodiments. In this embodiment, the filtering device includes a first filtering device lens 28, a filtering element 30 and a second filtering device lens 32. The first and second filtering device lenses are collimating lenses and the filtering element 30 is disposed between the first and second filtering device lenses at the focal point of both lenses. The filtering device 26 is disposed so that the second filtering device lens 32, which is the filtering device lens closer to the receiving zone 20, is distanced from the receiving zone by one focal length of the second filtering device lens.

The system includes a control unit 34 in communication with the pattern generator to control the pattern produced by the pattern generator, and optionally also in communication with the light emitter to control emission of light by the light emitter. The control unit may be a single computer, or may comprise multiple modules, parts or components, each configured to perform a different operation. The different modules, parts or components may be in the same or different location.

In use, a substrate or device to be tested 36 is placed at the receiving zone, the substrate or device having a plurality of regions. The plane containing the plurality of regions is disposed in a plane conjugate to the pattern generator. In this case, the substrate or device to be tested is a photovoltaic device and the regions can be considered 'pixels', however other substrates can be tested in embodiments of the invention. The system is to detect a condition or deviation from a desired condition. In this case, the condition to be detected is the presence of defective regions or a deviation of performance of regions from a desired or threshold performance. In this embodiment, a response output of the substrate or device is coupled to a detector. In this embodiment, the detector is the control unit 34 and the control unit is configured to perform the processing described herein to process the detected interaction of light with the substrate or device; however in other embodiments the detector can be a separate component. In this

embodiment, the response output is an electrical output from the photovoltaic device which provides electricity via the electrical output in response to incident light on the photovoltaic device. In this embodiment, measurement output from the photovoltaic is amplified using a Vinculum transimpedence amplifier, and read in as a voltage output through a National Instruments analogue to digital converter (ADC). The light emitter emits light which is collimated by the collimating lens 14, passes through the beamsplitter 16, and to the pattern generator 18. The pattern generator selectively retroreflects a pattern of light to the beamsplitter under the control of the control unit 34. The retroreflected pattern of light is reflected by the reflective element 22 of the beamsplitter, passes through the filtering device and falls on the substrate or device in the receiving zone, thereby illuminating a subset of the plurality of regions of the substrate or device. In response to the pattern of light falling on the subset of regions the substrate or device, the substrate or device generates a response which is detected by the detector.

This process continues with a sequence of different patterns being generated by the pattern generator to illuminate different sets of regions of the substrate or device and the response of the substrate or device being detected. The selection of patterns to be used and analysis of the response of the substrate or device are discussed elsewhere herein. In other words, the embodiment shown in Figure 2 allows for the retroreflection of light onto a DMD array which is then redirected through a lens, spatially filtered to reduce diffraction artefacts, and recollimated onto a photovoltaic sample placed in a plane conjugate to the DMD. A collimated laser source is partially reflected off the DMD, containing a structured intensity pattern formed through the selective beam dumping of encoded pixels of the DMD. This is then spatially filtered and re- conjugated onto the surface of the photovoltaic under test.

Signal reconstruction

In order to reconstruct the signal corresponding to the spatial response function of the PV, a series of voltage measurements is obtained corresponding to each

Hadamard map projected onto the active surface of the substrate or device. In one embodiment, the mean of 1000 voltage readings is taken at 1 KHz per Hadamard map, and subtracted from this is the mean voltage corresponding to the projection of the inverse Hadamard projection in order to eliminate dark current. However, the precise number of readings and frequency of readings can be varied in other embodiments. Each Hadamard matrix is reshaped to form a 1 D sampling vector, which forms successive rows of a measurement matrix A, allowing us to pose the reconstruction in the form of solving the linear equation:

y = Ax

where y is the series of voltage measurements taken and x the spatial response function of the PV itself. For a complete measurement set this is a fully specified series of simultaneous equations in an orthogonal basis set, and thus easily solvable. An underspecified, incomplete measurement set will nevertheless contain information from all points of the signal x, and can be reconstructed using the l_i norm minimisation and TV algorithms, which is further explained later, into an approximation of the original signal.

Performance Metric

This technique does not offer a perfect reproduction of the spatial sensitivity of a photovoltaic, but it does allow the identification of defects in an extremely short time period. Ideally the reconstructed response map should match the map obtained through a raster scan in the same set up, and hence we compare the normalised signals corresponding to each for their correlation. A perfectly reconstructed map should have a Pearson's linear correlation coefficient of 1 , as there will be a 1 -to-1 match between all data points. As a result of the increased SNR that comes as a benefit of illuminating approximately half of the PV surface at any one time, we would expect a perfect reconstruction to be slightly below 1 , taking into account a diminished contribution from the dark noise with respect to the raster map acquired using the same configuration. This is due to the

comparatively low light levels used in the raster scan, with illumination being incident on one virtual pixel only. Initial Results

Figure 3 shows a chart of the recorded voltages corresponding to the display of successive rows of the Hadamard matrix on the DMD, using N = 768 and reshaped to form a 32 x 24 element array. In Fig 3 the black line, which is the series of voltage measurements, should be compared with the red line

corresponding to the sum of the specific Hadamard pattern used. As we can see, with the exception of roughly the first 25 patterns displayed, this sum value is equal to zero indicating that the number of "on" pixels is exactly equal to the number of "off" pixels, i.e. exactly half of the area under test is illuminated for the vast majority of the data acquisition process. Despite this there is a very clear structure to the output voltage measurements, in particular it can be seen that behaviour of the PV output between N=55 and N=90 is somewhat echoed twice more as the full matrix is scanned. As these evidently do not correspond to an increase in the intensity of light projected onto the PV they must instead correspond to stimulation of regions of increased or decreased sensitivity and thus provide key structural information on the spatial responsivity map.

It is instructive to look at how well the spatial response map produced through compressed sensing compares with that obtained through a raster scanning technique as the number of measurements increases. Figure 4 shows how using increasing numbers of Hadamard patterns affects the correlation between these two measurements for both the l_i norm and TV algorithms. As mentioned above, we see that the correlation from the TV algorithm rises and plateaus more rapidly than the l_i norm minimisation technique does. This is a consequence of the fact that our spatial response map varies more sparsely than it can be mathematically described. Noteworthy in Figure 4 are the sudden jumps in correlation we see in the behaviour of both reconstruction techniques. These rapid increases in reconstruction accuracy correspond strongly to the presence of the repetitive behaviour seen in Figure 3. By including these larger magnitude measurement values, we include data which contains more spatial significance to the description of our response map. Limitations

It can be seen from Figure 4 that for the TV reconstruction algorithm, a 90% correlation is achieved to the raster scanned image when we supply just over half the total number of required measurements for that technique. For better than 95% accuracy we observe that we must provide roughly 600 out of a total 768 data points, which when combined with the time required to perform the signal reconstruction does not represent an increase in overall measurement speed due to the time necessary to perform the computation. The display of Hadamard patterns for data acquisition imposes two severe limitations into the compressed mapping technique.

The first of these is that the signal we are trying to reconstruct is that of our response map when it is described spatially, that is using an identity matrix as our basis set. As we see however the map we are trying to measure is not one which is sparse when described in such a manner, hence the very limited success of the l_i norm algorithm. Sparsity refers to the amount of coefficients in a signal which are significant/non-zero, and is discussed further below. Other embodiments, such as described below, have the ability to recover a signal in an already compressed state, which is sufficiently sparse to require significantly fewer measurements.

The second and more restrictive of the limitations is that when we consider only the first N measurements, what we are considering is the effect of probing our test piece in N specific ways. Once again consider Figure 3 and the behaviour of the measurement values for varying Hadamard patterns. Large magnitude voltages here represent a significant coefficient in the description of our signal using a Hadamard basis. By considering a limited number of these patterns, which may not include one of these, we limit ourselves to a reconstruction based on a series of less significant measurements. We cannot guarantee a priori knowledge of which Hadamard patterns will be the most significant for an unknown sample, and as a result a non-complete measurement set will have a high probability of omitting these valuable individual measurements from our reconstruction. It is desirable to separate the concepts of the matrix we project, and the matrix that we wish to describe our system as a function of. This leads us to the basis of true compressed sensing.

From compressed mapping to compressed sensing Compressed sensing theory

The use of compressed sensing techniques requires an understanding of some of the theoretical background to the field.

Important to the concept of compressed sensing is the notion of signal being sparse. Any signal, x, of length, N can be described as: where q is a N length column vector of coefficients and is a NxN orthonormal matrix that forms the basis set of the signal description. The basis set i i is referred to as the dictionary we use to define our signal x. A signal is called K- sparse if there are N-K values of q which are zero, that is the signal can be described in only K coefficients, and can be called compressible if there are K large coefficients and N-K small ones that can well approximate the signal in question. Compressive sensing theory is rooted in the notion that for a known signal x there exists some dictionary such that a sparse representation is possible. We desire the case where K is as small as possible so that the minimum number of measurements possible can be made to reconstruct our signal.

This theory is sufficient for the compressibility of signals that are known; all that is necessary is the dictionary in which the signal is represented, the magnitude of the significant coefficients and their location within that dictionary. When we are measuring an unknown signal however we lack the knowledge of the location of our K significant values, and it is important to overcome this limitation in order to use this branch of signal processing theory for fast measurement processes.

Consider the example of making a measurement of our signal x, which we assume is -sparse in a known dictionary. If we do not know where the important coefficients are we cannot identify the rows in our dictionary to sample from, and thus have no way of using its sparsity to our advantage in measurement. To get round this we separate the measurement matrix used from the concept of the basis set which forms our dictionary. For an incomplete series of measurements yielding a results vector y, with an arbitrary sampling matrix φ, acting on signal x, we naturally have: y = φχ. From earlier we know x = ipc and can now rewrite:

giving us a description of our measurements as a function of our sparse signal coefficients and a measurement matrix Θ. Crucially here Θ is the matrix

multiplication of φ and ψ so that our MxN measurement matrix nevertheless fully addresses the NxN dictionary in which our signal is sparse. This allows us to measure an unknown signal in K<N measurements provided we use a suitable measurement matrix. Advantageously, the rows of our measurement matrix do not sparsely represent the columns of our dictionary, known as the incoherence condition, and that for any 3K-Sparse vector, v.

\\θν\\ ₂

\\v\\ ₂

for€ > 0, known as the Restricted Isometry Property (RIP) (Candes E. , 2006). It happens that these properties can both be met through forcing the measurement matrix φ to contain random entries with a Gaussian probability distribution.

Compressive sensing can depend on sparsity and compressibility. Consider x is an arbitrary signal, which may be length N, and s is a sparse vector. We posit that there will exist some set of basis functions \psi in which this signal is sparse (x = ips). Now if we sample using \phi we recover measurements y ( y = φχ), substitute to see that we can use a series of measurements to recover our sparse coefficients, even when we don't know the original signal provided we know the basis set in which it is sparse, y = -ψε = 0s. In embodiments, the resulting incomplete series of linear equations can be solved using convex minimisation techniques.

Li norm minimisation

Whilst we now have an understanding of the formation of the measurement matrix, we still need to consider how to reconstruct our set of measurements y into our desired signal x. Previously we saw that for the case of compressed mapping the TV algorithm returns more accurate signal reconstructions than the l_i norm minimisation method, primarily because the variational sparsity of our desired signal was greater than the sparsity of the signal itself. Using the knowledge from above we are no longer limited to using Hadamard projections, but can now project binary random matrices onto the photovoltaic and explore different dictionaries in which we describe our signal. Li norm, by its very nature, was an ill- suited method for the reconstruction of our signal in the Hadamard dictionary as it was roughly as -sparse as it is in the Identity matrix basis set. Now we have more flexibility in our dictionary we can attempt to significantly reduce the sparsity of our representation through considering transform functions, as described in the next section, and therefore vastly increase the suitability of l_i norm for

reconstruction.

The reason it is non-trivial to solve an underspecified series of linear equations is that for every vector of coefficients c that is a valid solution to = 6c, there are infinitely many other solutions of the form c' = c + r where r is any vector in the kernel of the reconstruction matrix Θ. By definition the null space of the matrix Θ will always contain the zero vector, 0, ensuring that the combination vector subspace of all c + r will contain the desired sparse coefficient vector. This compound vector c' is therefore a translation of the desired sparse coefficient vector in the space M. ^N . To understand why l_i norm minimisation is ideal for sparse signal reconstruction we need look at fundamental geometry. The "traditional" magnitude of a vector is the square root of the sum of the squares of each vector coefficient, i.e.:

This is more generally known as the L ₂ norm of the vector X. In general, we can express the L _p norm as:

1

L _p norm = ||x|L = (| JP + \X ₂ + - . |X _W |P)P .

For convenience, let us consider the unit "circle" of various L _p norms in the real space E ² in which also lies the translated sparse vector, c' . The distribution in space of all values of the unit L ₂ norm is spread homogenously in a circle around the origin point. For the l_i norm however we observe that the distribution extends further out along co-ordinate axes. This neatly demonstrates why we use the l_i norm minimisation technique rather than the L ₂ norm, as the intersection of the l_i norm with the vector subspace c' will occur in a region close to a co-ordinate axis with a higher probability, and of course a vector which lies along co-ordinate axes is by definition sparse.

Transform dictionaries

In order to both enhance the probability of the l_i norm minimisation recovering our sparse vector, as well as to speed up measurement, we want to make our vector c as sparse as possible. Using a projection matrix, ø, containing random entries will preserve the restricted isometry property (RIP) of our measurement matrix Θ (Baranuik, 2007), and allow us to explore using various dictionaries, ip _u to describe the photovoltaic spatial response function. For the measurements described above using a N = 768 signal, we see that after normalising the measurement values 680 coefficients have magnitudes greater than 1 % of the maximum. This by no means constitutes a sparse signal, and the observation of the l_i norm algorithm failing to reproduce this to the same ability of the TV algorithm is hardly surprising. This however is for when we describe our signal simply using the identity matrix as a basis set. Being able to use a random binary projection matrix now allows us to consider reconstructing our signal as described in a different basis set. Calculating the discrete cosine transform (DCT)

coefficients allows us to see that there are only 1 13 entries with absolute magnitudes above 1 % of the maximum signal value, and 317 above 0.5%.

Similarly for the discrete sine transform we see 107 and 321 coefficients respectively. This is a significant increase in the sparsity of our signal and therefore increases the likelihood of the l_i norm algorithm recovering a vector which well describes our surface response profile. We can see in Figure 5 that the reconstruction of our spatial response map using only the most significant signal coefficients in the DCT doman produces a result which reproduces the features of the overall response, described in less than half of the number of terms. Figure 5 shows a comparison of the reconstruction of the spatial response of the

photovoltaic when defined using only the Left: 1 % and Middle: 0.5%, most significant coefficients in the Discrete Cosine Transform domain. For comparison purposes on the Right we see the recovered spatial response map of the PV when measured using a raster technique with the same configuration.

Measurement procedure

The data acquisition procedure used for the more flexible compressed sensing analysis is very similar to that of the previously described compressed mapping technique. Instead of projecting binary Hadamard patterns onto the photovoltaic surface however, we project a binary random matrix as determined through:

The output voltage was sampled for 1 second at 1 kHz, taking the measurement voltage as the difference in means of the recorded voltages for the binary mask from the corresponding inverse. The l_i norm algorithm of the series of voltage measurements is supplied along with the matrix multiplication of our random binary projection matrix with the dictionary function under consideration at the time.

Results

Figure 6 shows a comparison of the measurement of the PV response function using only Left: 190 and Right: 350, randomly projected binary patterns. Both reconstructions were performed by recovering the signal in the DCT domain. It is immediately apparent that using an alternate dictionary to the identity matrix, and hence attempting the recovery of a more sparse signal, drastically reduces the number of measurements necessary to produce a map of the PV spatial response function. Features recognisable from the map produced using a conventional raster scan began to emerge upon utilisation of less than a quarter of the measurements, as seen in Figure 6, and rapidly became more defined with increasing numbers of measurements. Using less than half of the required number of measurements for a raster measurement clearly shows the behaviour of the spatial response map when considering a DCT dictionary closely resembles the raster scan result seen in Figure 5.

This behaviour was also observed when transforming the signal into the sine domain using DSTs. The transform coding in these cases was taking the

DCT/DST of successive rows from the standard identity matrix before multiplying with the projection matrix, with no a priori attempt at optimising either the order of the projection matrix voltages or the dictionary itself in an attempt to enhance reconstruction speed.

The behaviour of the correlation coefficients over iteratively more measurement voltages shows a rapid growth, plateauing to a roughly constant linear correlation coefficient much more rapidly than when considering Hadamard projections.

Figure 7 shows this behaviour when using the cosine dictionary, and can be compared to Figure 4 clearly showing a much more rapid reconstruction of the desired signal. We observe that a better than 90% correlation in reconstructed signal is achieved after only 150 measurements, down from over twice that when using Hadamard projections.

Figure 8 charts the growth of reconstruction accuracy for the l_i norm algorithm when the signal is described in the discrete sine transform dictionary. Just like for the DCT basis, we see a very rapid rise in correlation within the first quarter of the full measurement set. We see in both dictionaries a plateauing behaviour, with the sudden spikes observed in Figure 4 completely absent. This demonstrates that separating the projection matrix from the dictionary basis aids in a more rapid measurement, as we no longer omit any significant vectors coefficients in our description of the sparse signal. Embodiments of the invention provide a significant reduction in the number of measurements required to obtain a result which displays the behaviour and significant features of the desired response map.

Although the description above mentions that embodiments can test a substrate or device in half the data points as a conventional raster scan, some embodiments have been found to reduce the number of data points needed by a factor of 5.

Figure 1 1 shows the reconstruction correlation coefficient for samples containing both a spot and a crack for three transforms; the DCT, DST and the Hartley transform. As we can see, the use of a binary random sensing matrix along with sinusoidal dictionaries provides a much more rapid convergence of the correlation coefficient with respect to a raster scanned result than is observed using rows from the Hadamard matrix as the sensing matrix. The effectiveness of embodiments of the invention is demonstrated in the following paper, which is incorporated by reference in its entirety: KQUTSOURAKIS, G. ... et al, 2015. Towards current mapping of photovoltaic devices by compressed imaging. IN: Hutching, M. and Cole. A. (eds). Pr ceedings of the 11th Photovoltaic Science, Applications and Technology Conference€97 (PVSAT-11), 15th- 17th April 2015, University of Leeds,

Modifications

There are numerous features that can be modified.

Firstly, as can be seen in Figure 2, the DMD element is addressed so that the projection matrix is retroreflected back along the path of incidence. A consequence of this is that a small degree of horizontal tilt is added to orient the reflected beam in the required direction with the consequence that the conjugate plane in which we place our PV sample is no longer perpendicular to the direction of beam propagation. We instead have a tilted conjugate plane which means the projection matrix is incident on the PV sample at a skew angle, so the effective pixels are no longer square. However, it is possible to address the DMD on an angle, and to redirect the beam horizontally using a second mirror to create a horizontally propagating beam with a correctly conjugated image of the DMD.

A second potential shortcoming is from the intensity distribution of the illumination. It can be seen in Figure 5 and Figure 6 the strong Gaussian distribution in the recovered profile. The spatial response of the photovoltaic can be decoupled from variations in the illumination field in order to identify aberrant features with more confidence. In embodiments, the addition of an engineered diffuser element directly after the laser launch, that is between the light emitter and the

beamsplitter, enables a significant degree of non-uniformity to be removed by modifying the profile of the beam into an approximal top hat function. A

beamsplitter can then be used directly in front of the receiving zone to direct a portion of the light to a detector to measure the intensity distribution which is incident on the receiving zone, that is onto the PV surface, and it is thereby possible to compensate for any residual nonuniformities in the recovered signal. Some embodiments do not require the beamsplitter 16. For example, the pattern generator can be configured to selectively allow a pattern of light to be transmitted through it rather than be reflected. In that case, the receiving zone can be optically aligned with the pattern generator so that light transmitted through the pattern generator falls on the receiving zone. In such embodiments, the pattern generator can be as described above, but configured to selectively allow transmission rather than reflection. Although the system above is described as detecting a response of the substrate or device, this is not the only way of testing the substrate or device. In some embodiments, the detector includes a light detector arranged to detect light which has been transmitted through and/or reflected from the substrate or device. For example, the detector can include a light detecting element disposed behind the receiving zone, wherein behind is intended to mean opposite the side of the receiving zone which is designed to be illuminated, and/or the detector can include a light detecting element in front of the receiving zone to detect light reflected from a substrate or device in the receiving zone. These means of detection can be used in addition to or instead of detection of a response of the substrate or device. They are particularly useful where the substrate or device is not an optically responsive substrate or device and does not therefore generate a response of its own in response to incident light.

However, they can still advantageously be used with optically responsive substrates, especially if the light emitter is configured to emit light at an active wavelength of the substrate or device since at such wavelengths, the optically sensitive substrate or device will tend to absorb more light and allow less to be reflected/transmitted. Therefore, there will be a significant difference between reflections/transmissions from regions that are performing correctly and defects. Furthermore, as discussed above, embodiments are not restricted to use with photovoltaic devices, but many types of optically responsive and non-optically responsive substrates can be tested by systems according to embodiments of the invention. In each case, the system may be testing for a different condition, but typically the system is testing for uniformity or a predefined spatially varying condition of the substrate or device or conformance of the substrate or device with a design or lack of manufacturing or material defects, for example a uniform or predefined spatially varying opacity or reflectivity, or a uniform or predefined spatially varying performance of optically responsive regions.

Embodiments can be used to look at a variety of PV materials and investigate the morphology of commonly found defects seen in their production. By examining these it is possible to study their representation in different dictionaries and optimise the basis set used to recover the signal. Furthermore it is possible to use an adaptive measurement matrix, whether modifying the Gaussian probability distribution or thresholding the results so that projection matrices corresponding to a low signal strength are dismissed.

In addition to these considerations the Total Variation minimisation algorithm can be adapted so that it is compatible with arbitrary dictionaries.

The description above only considers the use of discrete sine and cosine transform dictionaries. It is possible to use the popular wavelet transform technique as a signal representation basis, and/or to use weighting of significant coefficients using a priori knowledge of likely signal shape.

All optional and preferred features and modifications of the described

embodiments and dependent claims are usable in all aspects of the invention taught herein. Furthermore, the individual features of the dependent claims, as well as all optional and preferred features and modifications of the described embodiments are combinable and interchangeable with one another. The disclosures in United Kingdom patent application number 1415393.6, from which this application claims priority, and in the abstract accompanying this application are incorporated herein by reference.

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