The present invention relates to a method and apparatus for polarimetry and polarisation imaging.
Polarisation sensing is vital in many areas of research, with applications spanning from microscopy to aerospace technology. The improvement of measurement precision and system sensitivity always has wide importance. Traditional approaches for polarimetry may be cumbersome.
Polarisation sensing methods can be divided into two categories: time-resolved, where measurements are taken using a sequence of analysers in a time multiplexed manner, or snapshot, where different analysers are spatially multiplexed. Time resolved measurements can be easier to implement, but snapshot methods are crucial for applications with rapidly changing inputs. The standard approaches in both methods are directly or indirectly related to a core measurement equation: S=inv(A)·I, where S is the Stokes vector to be measured, and I is the vector of intensities recorded at the detector. Matrix A is known as the instrument matrix, which is determined by the system configuration. In order to enhance precision and sensitivity, numerous attempts have been made to push A towards an optimal matrix as it determines the properties of the error propagation and hence affects the measurement precision. An evaluation of systematic error amplification can be performed using the condition number (CN) of A. The theoretical minimum value CN=√{square root over (3)} for polarisation sensing has been widely studied and utilised both theoretically and experimentally.
Improvements in polarisation sensing are desirable.
According to a first aspect, there is provided a polarimeter, comprising:
The full Poincaré generator may comprise a graded refractive index, GRIN, lens.
The detector may comprise an array of detector elements configured to measure the transverse distribution of intensity of a beam from the polariser. For example the array of detector elements may be a camera that determines an image (comprising a 2D array of pixels at which intensity is sampled).
The processor may be configured to determine one or more positions of maximum intensity in the transverse distribution of intensity.
The processor may be configured to implement a machine learning algorithm that has been trained to estimate the one or more positions of maximum intensity.
The machine learning algorithm may comprise a convolutional neural network.
There may be more than one position of maximum intensity, and the processor may be configured to refine the estimate of the positions of maximum intensity based on a centrosymmetric constraint.
The processor may be configured to determine a polarisation state of the incident light from the one or more positions of maximum intensity.
Determining the polarisation state from the one or more positions of maximum intensity may comprise using a predetermined lookup table (or equivalent) that relates the position of the one or more positions of maximum intensity with a state of polarisation of the input beam.
The processor may be configured to determine an amount of depolarisation from a level of contrast in the spatial distribution of intensity determined by the detector.
According to a second aspect, there is provided a polarisation imager, comprising:
Each full Poincaré generator may comprise a graded refractive index lens.
The detector may comprise an array of detector elements configured to measure the transverse distribution of intensity of a beam from the polariser.
The processor may be configured to determine one or more positions of maximum intensity in each eigenstate from the measured transverse distribution of intensity.
The processor may be configured to implement a machine learning algorithm that has been trained to determine the one or more positions of maximum intensity in each eigenstate.
The machine learning algorithm may comprise a convolutional neural network.
There may be more than one position of maximum intensity in each eigenstate, and the processor may be configured to refine the estimate of the positions of maximum intensity based on a centrosymmetric constraint.
The processor may be configured to determine a polarisation state of the incident light at each of the plurality of different transverse positions from the one or more positions of maximum intensity in each eigenstate.
Determining the polarisation state from the one or more positions of maximum intensity may comprise using a predetermined lookup table that relates the position of the one or more positions of maximum intensity in each eigenstate with a state of polarisation.
The processor may be configured to determine an amount of depolarisation from a level of contrast in the spatial distribution of intensity determined by the detector.
According to a third aspect, there is provided a method of determining a polarisation state of a light beam, comprising:
a detector configured to determine a spatial distribution of intensity of the eigenstate selected by the polariser; and
According to a fourth aspect, there is provided a method of performing polarisation imaging, comprising:
selecting an eigenstate from each full Poincaré beam in the array of full Poincaré beams generated by the array of full Poincaré generators;
Each full Poincaré generator may comprise a graded refractive index lens.
Determining a polarisation state of the incident light beam at each of the sampled transverse positions may comprise using a processor to determine one or more positions of maximum intensity in the or each eigenstate from the measured transverse distribution of intensity.
The processor may be configured to implement a machine learning algorithm that has been trained to determine the one or more positions of maximum intensity in the or each eigenstate.
The features of each aspect (including optional features) may be combined with those of any other aspect. For example, features described with reference to the first and second aspects may be used in the methods according to the third or fourth aspects.
Example embodiments will be described, by way of example only, with reference to the drawings, in which:
Referring to
The polarimeter 10 receives an incident light beam 100 with an unknown state of polarisation (SOP). The full Poincaré generator (FPG) 110, according to the definition used herein, will produce a full Poincaré beam from any uniform input polarisation state, so the output of the FPG 110 is a full Poincaré beam (FPB) 120, which will include all polarisation states. As described in WO2020/120943, a GRIN lens can be used as a FPG 110, but other types of FPG may also be used. The specific distribution of polarisation states in the full Poincaré beam 120 (from a particular FPG) will depend on the polarisation state of the incident light beam 100.
The polariser 130 selects a polarisation state from the full Poincaré beam 120, which may be termed an eigenstate of the full Poincaré beam. Since the distribution of polarisation states in the full Poincaré beam 120 depends on the polarisation state of the incident light beam 100, this effectively maps the spatial variation in polarisation state in the full Poincaré beam 120 to a spatial variation in intensity in the beam 135 following the polariser 130.
The detector 170 is configured to detect and output the spatial distribution of intensity 140 in the beam 135 after the polariser 130. This spatial distribution of intensity 140 encodes the input polarisation state of the incident light beam 100.
The processor 250 receives the spatial distribution of intensity 140 from the detector 170 and determines the polarisation state of the input beam 100 therefrom. Examples of how this can be achieved will be explained more fully below.
The polarisation imager 20 works on similar principles to the polarimeter 10, except there is an array 118 of FPGs 110 (in this example, a 2D array). The detector 170 is configured to detect a distribution of intensity of an eigenstate from each FPG 110 (selected by the polariser 130). One way to do this is to use superpixels comprising a 2D sub-array of pixels, so that each superpixel determines a polarisation state for a FPG in the array corresponding to a different spatial location in the image. The example embodiment is shown with a light source 261 illuminating a sample 280 in transmission mode via a polarisation state generator 260 (e.g. as shown hereinbelow), but this is not essential.
There are two types of existing systems that can generate a full Poincaré beam (FPB). The first type has the functionality of transferring a specific SOP (or a limited range of SOPs) into an FPB. A typical system configuration is based on two liquid crystal spatial light modulators (SLMs) or a system using multiple passes from a single SLM. Under such a geometry, due to the SLM having a uniformly distributed slow/fast axis orientation, it is strongly polarisation dependent. It can be used to generate an FPB but is not a FPG according to the definition used herein, since it cannot generate an FPB from an arbitrary incident SOP. For example, if the incident SOP is linear and aligned in the same direction as the fast axis orientation of the first SLM, then the modulation of such a pass would lose all functionality. Hence with only one degree of freedom introduced by the second SLM (or the second pass) an arbitrary SOP cannot be generated.
A FPG according to the definition used herein may comprise a linear retarder assembly that contains all combinations of fast axis orientations (θ from 0° to 180°) and retardance values (δ from 0° to 180°) as shown in
An alternative type of FPG comprises a mixed diattenuator array as shown in
FPGs herein are not limited to these two broad types but could also in principle be generated by other mechanisms.
In some embodiments an image processing algorithm may be used to directly relate a detected intensity distribution 141, 142 to a SOP of the incident light 100.
For an FPB with order 2 (such as a GRIN lens, used in this example), there will be two positions of maximum intensity 150. For an FPB with order 1 there would be a single position of maximum intensity (and so on). Where there is more than one position of maximum intensity in the intensity distribution 140, in principle a single position is enough to determine the SOP of the input, but determining more than one position of maximum intensity 150 may be used to reduce error (which may otherwise result from noise and other measurement uncertainties).
As schematically illustrated in
In certain embodiments, all points of the intensity distribution 140 may be used to determine an accurate location for the at least one point of maximum intensity 150. A range of techniques can be used to determine the position of the point of maximum intensity 150. In a very simple example, the intensity distribution 140 may be smoothed using a moving average, and a maximum value of the intensity distribution 140 determined as the position of the point of maximum intensity 150.
A more robust approach for determining at least one position of maximum intensity 150 is to use an image processing machine learning algorithm. A convolutional neural network (CNN) is a suitable type of machine learning algorithm. The intensity distribution 140 may be provided to a CNN that determines a probability map defining the probability (e.g. from 0-1) that each location comprises a position of maximum intensity 150. The probability map can be used by a further algorithm to determine the at least one position of maximum intensity 150 (for example, in the case of a GRIN lens FPG, based a centrosymmetric constraint).
The output probability map 255 (which may also referred to as a heat map) may be further processed to refine the positions of the at least one position of maximum intensity 150 (e.g. by imposing a centrosymmetric constraint). The positions of maximum intensity 150 may be used with a lookup table 125 (or similar) to determine the input SOP therefrom.
In order to train the example CNN 251, 57877 pairs of simulated/experimental images were used to generate a training set. The simulated images were calculated via a GRIN lens retardance model as ground truth. The experimental images were acquired with known SOP input using the system shown in
The example CNN 251 was trained with a stochastic gradient descent (SGD) optimizer using gradients computed with backpropagation, with batch size set to 4, learning rate 0.001, momentum 0.9. A weighted L-2 loss function (Eq. 1)) was adopted to deal with the “imbalanced classification” problem, since the bright area only takes up a small part of the image:
where N is the total number of pixels, vi the predicted value of the i th pixel, and vi* the ground truth value of the i th pixel. wi is the weight of the i th pixel, which was set to 50 if vi*>0, otherwise 1. λ=0.0005 is the coefficient of the regulariser A, where A=[a0, a1, a2, . . . , ak] is the set of all parameters in the network. The network was trained over 5 epochs and converged in one hour on a PC (OS: Ubuntu 16.04; CPU: i7-4770; GPU: NVIDA GTX 1080 Ti).
There are several advantages of using machine learning to identify positions of maximum intensity in the intensity distribution: i) preparation of the training set is straightforward and it is easy to cover an adequate domain; ii) finding the SOP takes only 30 ms on a normal desktop GPU, enabling real-time online SOP detection; iii) the network is robust to temporal/spatial noise from the image acquisition system.
According to the example approach in which a probability map 255 of the position(s) of maximum intensity is determined, there is an intrinsic link between the image resolution (with pixel number n×n) and the polarisation resolution (sensitivity Sp) of the system.
This hardware parameter could be used to indicate the maximum sensitivity of the system (defined as the minimum SOP change that can be detected), assuming other noise sources are minimised, which can guide the training process of the CNN with respect to the best effective dataset. This sensitivity can be calculated as
where Ds is the dimension of the Stokes vector,
represents the effective pixel number (for a GRIN lens based FPG, there is a circular area). K is a constant parameter. As the topological order η of the GRIN lens is 2, there would in effect be half the number of pixels to determine Sp. Here it is assumed the sampling depth is sufficient and the non-linearity of the system is low. Following the above equation, it is possible to plot the theoretical relationship between Sp and intensity image with resolution n×n, if systematic and random errors are minimised, as shown in
In other embodiments, rather than the CNN determining a probability map 255 that is useful for determining at least one position of maximum intensity 150, a CNN may be trained to simply determine the input SOP directly from the input intensity distribution 140. This may be a less flexible approach, in that the CNN will encode the mapping 125 of the intensity distribution 140 of the selected eigenstate to input SOP (so the CNN will be tailored for a specific PBG 110 and polariser 130), but may be more accurate.
A polarisation state analyser (PSA) 15, receives light with an arbitrary SOP from the PSG 260 and detects an intensity distribution 140 suitable for processing to determine the input SOP in accordance with embodiments,. The PSA 15 comprises an FPG 110 in the form of a GRIN lens (e.g. Femto Technology Co. Ltd., G-B161157-S1484, NA=0.1, Pitch=2) followed by a fixed circular polariser 130 (e.g. Thorlabs, CP1L633) and detector (e.g. Thorlabs, DCC3240N).
The SOPs in the output 183 was analysed according to the example embodiment described herein, sampling along 200 points on the arrow 185 (along the y axis) in the sample region 186. The results are depicted in
The SOP of the polarised parts of the input light field corresponding with each Poincaré sphere remains the same. The level of contrast in the intensity distribution 140 image is proportional to the level of depolarisation of the target beam. The DOP (degree of polarisation, which is the inverse of the degree of depolarisation) of the input light field can be therefore be calculated from a normalised intensity value of the brightest and darkest points (Imax and Imin) on the intensity distribution 140 according to a simple calculation, DOP=(Imax−Imin)/(Imax+Imin) This is another advantage of polarimeters according to embodiments, which may enable the depolarisation to be determined in a simple way.
Although the appended claims are directed to particular combinations of features, it should be understood that the scope of the disclosure of the present invention also includes any novel feature or any novel combination of features disclosed herein either explicitly or implicitly or any generalisation thereof, whether or not it relates to the same invention as presently claimed in any claim and whether or not it mitigates any or all of the same technical problems as does the present invention.
Features which are described in the context of separate embodiments may also be provided in combination in a single embodiment. Conversely, various features which are, for brevity, described in the context of a single embodiment, may also be provided separately or in any suitable sub combination.
The examples provided in the detailed description are intended to provide examples of the invention, not to limit its scope, which should be determined with reference to the accompanying claims.
Number | Date | Country | Kind |
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2020334.5 | Dec 2020 | GB | national |
Filing Document | Filing Date | Country | Kind |
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PCT/GB2021/053293 | 12/14/2021 | WO |