Apparatus and method for spatial light modulation

A computer-implemented method of transmitting through a disordered medium from a transmitter to a receiver an image represented as input coherent electromagnetic radiation, the disordered medium represented by a transmission matrix comprising a plurality of complex-valued transmission constants that relate said input coherent electromagnetic radiation to output electromagnetic radiation at said receiver, which method comprises the steps of:

• performing a characterising process on said disordered medium to determine said transmission matrix;
• using said transmitter to transmit said image through said disordered medium;
• performing a reconstruction process using said transmission matrix to generate a reconstructed image from the output electromagnetic radiation at said receiver;
• wherein in said characterisation process the step of determining said transmission matrix comprises:
• determining said complex-valued transmission constants as real-valued transmission constants by using an approximately linear relationship between said input electromagnetic radiation and said output electromagnetic radiation;
• and
• using said real-valued transmission constants to generate and store a version of the transmission matrix;
• and said reconstruction process comprises the steps of:
• generating a plurality of output images comprising intensity or amplitude values of said output electromagnetic radiation;
• generating said reconstructed image by combining said plurality of output images and said version of the transmission matrix in a way that effects a matrix multiplication of an inverse of said transmission matrix and said plurality of output images;
• and
• outputting said reconstructed image from said receiver;
• wherein said step of determining said transmission matrix comprises the step of using data processing technique having a forward model that links the image to the plurality of output images with a series of linear equations, and using an algorithm to obtain the real-valued transmission constants of the transmission matrix by solving the series of linear of equations;
• wherein said characterising process comprises the steps of:
• at said transmitter:
• providing a plurality of controllable electromagnetic radiation sources for transmitting said image and/or
• at said receiver:
• providing a plurality of electromagnetic radiation detectors;
• receiving said plurality of output images from said disordered medium with said plurality of electromagnetic radiation detectors, each output image of said plurality of output images comprising said output electromagnetic radiation field in the form of an intensity speckle pattern corresponding to one of said plurality of known input images;
• and
• processing said known input images and said output images to determine said real-valued transmission constants;
• wherein the step of determining said real-valued transmission constants comprises:
• for a first pair, mn, of electromagnetic radiation detector m (m=1, 2, . . . m) and electromagnetic radiation source n (n=1, 2, . . . , N):
• (a) take the first input and output image pair (p=1) and determine the product of (i) the measured output electromagnetic intensity or amplitude at electromagnetic radiation detector m, (Im p), and (ii) a binary value, (hn p), indicating whether the corresponding electromagnetic radiation source n of the pair mn was on or off for that input and output image pair p (p=1);
• (b) repeat step (a) for each input and output image pair p (p=2, 3, . . . , P);
• (c) sum the products obtained in steps (a) and (b);
• and
• (d) divide said sum by the number of electromagnetic radiation sources N and store the result as the mnth real-valued transmission constant in said transmission matrix;
• and
• repeat steps (a) to (d) for each other pair of electromagnetic radiation detector m and electromagnetic radiation source n to generate m×n real-valued transmission constants and store as the transmission matrix.