Tensor field mapping

A non-transitory computer-readable storage medium for use in conjunction with a computer, the computer-readable storage medium configured to store program instructions that, when executed by the computer, cause the computer to perform operations comprising:

• applying, to a sample, an excitation using a source, wherein the excitation has at least a wavelength and an intensity or a flux, wherein the excitation comprises one of:
• electromagnetic radiation in a band of wavelengths different from an x-ray band of wavelengths, a particle beam, a sound wave, a magnetic field, or an electric field, and wherein the excitation excludes electromagnetic radiation in the x-ray band of wavelengths;
• measuring, using a measurement device, a response associated with the sample to the excitation;
• calculating, with the computer that initiates a forward model with multiple voxels that represent the sample, at least a predicted value of the response that was measured in the measuring operation, wherein the forward model simulates response physics occurring within the sample to a given excitation with a given wavelength and a given intensity of a given flux, that are selected from a range of measurement conditions that includes the excitation, the wavelength, and the intensity or the flux, and at least a different wavelength and at least a different intensity or a different flux, and
• wherein the forward model is a function of the excitation, the wavelength, the intensity or the flux, model parameters of the multiple voxels, and differential or phenomenological equations that approximate the response physics of the sample and are solved in the calculating;
• computing, with the computer, a difference between at least the measured response and at least the calculated predicted value of the response;
• solving, with the computer, an inverse problem as a function of the computed difference in order to determine revisions to the model parameters on a voxel-by-voxel basis;
• iteratively repeating instances of a group of operations comprising the operations of applying, measuring, calculating, computing and solving until the computed difference is less than a predefined value, wherein the excitation is modified in at least one of the instances of the applying based at least in part on the computed difference in a prior instance of the group of operations, wherein the model parameters are determined sequentially in the instances of the group of operations based on time scales associated with the model parameters, and wherein a model parameter that has a shortest time scale is determined first;
• and
• providing the model parameters as an output to a user, another electronic device, a display or memory when the computed difference is less than the predefined value, wherein the providing of the model parameters comprises storing the model parameters in the memory;
• and
• wherein a state of the sample either has not relaxed to a predefined state or is not reset to the predefined state between the instances of the group of operations, so that the sample has a dynamic state between at least some adjacent instances of the group of operations.

A system configured to determine model parameters of multiple voxels, comprising:

• a source configured to provide an excitation, wherein the excitation comprises at least one of:
• a neutron beam, an electron beam, an electromagnetic beam in an optical band of wavelengths, an electromagnetic beam in an infrared band of wavelengths, a sound wave in an ultrasound band of wavelengths, a proton beam, an electric field associated with an impedance measurement device, or an magnetic field associated with a susceptibility measurement device;
• a measurement device configured to perform measurements, wherein the measurement device comprises at least one of:
• a neutron detector, an electron detector, an optical detector, an infrared detector, an ultrasound detector, a proton detector, the impedance measurement device or the susceptibility measurement device;
• a processor, coupled to the source, the measurement device and memory, configured to execute program instructions;
• and
• the memory, coupled to the processor, configured to store the program instructions that, when executed by the processor, cause the system to perform operations comprising:
• applying, to a sample, the excitation using the source, wherein the excitation has at least a wavelength and an intensity or a flux, wherein the excitation comprises one of:
• electromagnetic radiation in a band of wavelengths different from an x-ray band of wavelengths, a particle beam, the sound wave, the magnetic field, or the electric field, and wherein the excitation excludes electromagnetic radiation in the x-ray band of wavelengths;
• measuring, using the measurement device, a response associated with the sample to the excitation;
• calculating, with a computer that initiates a forward model with the multiple voxels that represent the sample, at least a predicted value of the response that was measured in the measuring operation, wherein the forward model simulates response physics occurring within the sample to a given excitation with a given wavelength and a given intensity of a given flux, that are selected from a range of measurement conditions that includes the excitation, the wavelength, and the intensity or the flux, and at least a different wavelength and at least a different intensity or a different flux, and
• wherein the forward model is a function of the excitation, the wavelength, the intensity or the flux, the model parameters of the multiple voxels, and differential or phenomenological equations that approximate the response physics of the sample and are solved in the calculating;
• computing, with the computer, a difference between at least the measured response and at least the calculated predicted value of the response;
• solving, with the computer, an inverse problem as a function of the computed difference in order to determine revisions to the model parameters on a voxel-by-voxel basis;
• iteratively repeating instances of a group of operations comprising the operations of applying, measuring, calculating, computing and solving until the computed difference is less than a predefined value, wherein the excitation is modified in at least one of the instances of the applying based at least in part on the computed difference in a prior instance of the group of operations, wherein the model parameters are determined sequentially in the instances of the group of operations based on time scales associated with the model parameters, and wherein a model parameter that has a shortest time scale is determined first;
• and
• providing the model parameters as an output to a user, another electronic device, a display or memory when the computed difference is less than the predefined value, wherein the providing of the model parameters comprises storing the model parameters in the memory;
• and
• wherein a state of the sample either has not relaxed to a predefined state or is not reset to the predefined state between the instances of the group of operations, so that the sample has a dynamic state between at least some adjacent instances of the group of operations.