Determination of optimal laplacian estimates and optimal inter-ring distances for concentric ring electrodes

A system comprising:

• a concentric ring electrode (CRE) comprising at least an inner ring and an outer ring, and configured to measure a set of potential differences comprising at least a first potential difference corresponding to the inner ring and a second potential difference corresponding to the outer ring;
• and
• an amplification device configured to estimate a functional of an electrostatic potential by combining the measured set of potential differences based on a set of coefficients, wherein the set of coefficients is determined by a method comprising:
• receiving information specifying a geometrical configuration of the CRE;
• and
• estimating a dependence of the functional on the set of potential differences, by at least:
• determining a null space of a matrix associated with a series expansion of the electrostatic potential for the geometrical configuration;
• and
• determining, based on the null space, the set of coefficients for the dependence, the set of coefficients comprising at least a nonzero first coefficient of the first potential difference and a nonzero second coefficient of the second potential difference, wherein the first coefficient is between −10 and 10 times the second coefficient.

A non-transitory computer-readable storage medium storing instructions, that upon execution on a computer system, cause the computer system to perform a method for determining a functional of an electrostatic potential, the electrostatic potential measurable by a concentric ring electrode (CRE) comprising at least an inner ring and an outer ring, the method comprising:

• receiving information specifying a geometrical configuration of the CRE;
• and
• estimating a dependence of the functional on a set of potential differences comprising at least a first potential difference corresponding to the inner ring and a second potential difference corresponding to the outer ring, by at least:
• determining a null space of a matrix associated with a series expansion of the electrostatic potential for the geometrical configuration;
• and
• determining, based on the null space, a set of coefficients for the dependence, the set of coefficients comprising at least a nonzero first coefficient of the first potential difference and a nonzero second coefficient of the second potential difference, wherein the first coefficient is between −10 and 10 times the second coefficient.