Optical imaging

1 . A computer implemented method of generating training data for use in training a trainable image processing algorithm implemented on an image processor to be used in optical imaging, the method comprising:

for each spatial mode of a plurality of different spatial modes of light, detecting a component of light reflected or emitted by a first training object in that mode;

simulating an expected output of the image processor when imaging the first training object by:

for each spatial mode of the plurality of different spatial modes of light, determining a theoretically expected signal that is measured by detecting the component of light reflected or emitted by the training object in that mode; and

generating an image based on the determined theoretically expected signals in the plurality of different spatial modes of light; and

associating the detected components of light with the generated image, the generated image being a label for the training object, wherein a variance between the label and an image constructed by using the trainable image processing algorithm to process the detected components of light suitable is used in training the trainable image processing algorithm.

2 . The method of claim 1 , wherein, the components of the light corresponding to the plurality of different spatial modes of light reflected or emitted by the training object are detected by heterodyne detection, the method comprising:

using a coherent or incoherent monochromatic light source to illuminate the training object; and

mixing light from the light source reflected by the training object with a local oscillator, the local oscillator in the spatial mode of light.

3 . The method of claim 2 , comprising:

splitting an output of the light source to provide the local oscillator and the light for illuminating the training object.

4 . The method of claim 1 , wherein the components of the light corresponding to the plurality of different spatial modes of light reflected or emitted by the training object are detected by spatial demultiplexing of the light reflected or emitted by the training object into the plurality of different spatial modes of light.

5 . The method of claim 1 , wherein:

the components of the light corresponding to the plurality of different spatial modes of light reflected or emitted by the training object are detected by spatial demultiplexing of the light reflected or emitted by the training object; and

the determining of the theoretically expected signals includes modelling use of spatial demultiplexing for detecting the components of the light corresponding to the plurality of different spatial modes of light reflected or emitted by the training object.

6 . The method of claim 1 , wherein the different spatial modes of light are transverse modes.

7 . The method of claim 6 , wherein the spatial modes of light are Hermite-Gaussian modes or Zernike modes.

8 . The method of claim 1 wherein the different spatial modes of light form an orthogonal set of modes of light.

9 . The method of claim 1 , wherein the plurality of different spatial modes of light includes at least 25 modes of light.

10 . The method of claim 1 , wherein the training object comprises an image of an article having nanoscale features and predefined structure, and the method comprises generating a plurality of different training objects using images of the same article in different positions and/or orientations.

11 . The method of claim 1 , wherein the training object comprises a bitmap image comprising a random pattern or combination of simple geometric shapes.

12 . A non-transitory machine-readable computer medium containing instructions, when executed by a machine, cause the machine to perform the method of claim 1 .

13 . The method of claim 1 , wherein:

detecting the component of light reflected by the first training object in a first spatial mode of the plurality of different spatial modes of light comprises:

detecting light reflected by the first training object;

providing a reference signal shaped into the first spatial mode of light, the detected light and reference signal being frequency shifted;

combining the light reflected by the first training object and the reference signal at a beam splitter;

detecting the signals from both outputs of the beamsplitter; and

determining a difference between the signals from both outputs of the beamsplitter to determine the component of light reflected by the first training object in the first spatial mode of the plurality of different spatial modes of light;

determining of the theoretically expected signal in the first mode includes modelling the steps used to detect the component of the light corresponding to the first mode of the plurality of different spatial modes of light.

14 . A method of training an image processor for use in optical imaging, the image processor configured to use a trainable image processing algorithm to process light reflected or emitted by an object in each spatial mode of a plurality of different spatial modes of light to generate an image of the object, the method comprising:

generating a set of training data by

providing a plurality of training objects, and

for each training object,

detecting the component of light reflected or emitted by the training object in each spatial mode of the plurality of different spatial modes of light;

for each spatial mode of the plurality of different spatial modes of light, determining a theoretically expected signal that is measured by detecting the component of light reflected or emitted by the training object; and

generating an image based on the determined theoretically expected signals in the plurality of different spatial modes of light;

and

associating the detected components of light with the generated image, the generated image being a label for the training object;

using the image processor to construct detected images of the plurality of training objects by using the trainable image processing algorithm to process the detected components of light;

comparing the images constructed by the image processor to the associated label for each training object to determine a variance between the image constructed by the image processor and the associated label; and

updating the trainable image processing algorithm based on the determined variance between the image constructed by the image processor and the associated label.

15 . The method of any of claim 14 , wherein amplitudes of the detected components are provided as inputs to the image processing algorithm.

16 . The method of claim 15 , further comprising: determining phases of the detected components and providing the phase as an input to the image processing algorithm with the amplitudes.

17 . The method of claim 14 , wherein the image processor comprises a neural network configured to implement the trainable image processing algorithm, the neural network having:

an input layer arranged to receive the detected components;

an output layer arranged to provide the image constructed from the detected components;

one or more hidden layers between the input layer and output layer; and

couplings to provide signals between adjacent layers,

wherein the image processing unit algorithm comprises weights applied to signals sent from one layer to a next layer and activation functions applied to the detected components, at the units within the layers, to construct an image as an output; and

wherein updating the trainable image processing algorithm comprises updating the weights and activation functions based on the variance between the images constructed by the image processor and the label.

18 . A method of optical imaging comprising:

for each spatial mode of a plurality of different spatial modes of light, detecting a component of light reflected or emitted by an object, the detected component corresponding to the mode; and

generating an image using an image processor trained in accordance with the method of claim 14 .

19 . The method of optical imaging as claimed in claim 18 , wherein the component of light arriving from the object in each of the plurality of different spatial modes of light is detected by

spatial demultiplexing of the light reflected or emitted by the object.

20 . The method of claim 18 , wherein:

detecting the component of light reflected by the object in a first spatial mode of the plurality of different spatial modes of light comprises:

detecting light reflected by the object;

providing a reference signal shaped into the first spatial mode of light, the detected light and reference signal being frequency shifted;

combining the light reflected by the object and the reference signal at a beam splitter;

detecting the signals from both outputs of the beamsplitter; and

determining a difference between the signals from both outputs of the beamsplitter to determine the component of light reflected by the object in the first spatial mode of the plurality of different spatial modes of light.