Distribution analyzing device and distribution analyzing method

A distribution analyzing device for analyzing a distribution of a field having a property satisfying a Laplace equation, the distribution analyzing device comprising:

• a processor;
• and
• a non-transitory computer-readable recording medium having stored thereon executable instructions, which when executed by the processor, cause the distribution analyzing device to function as:
• an obtaining unit configured to obtain measurement data of the field measured, when a sensor sensing area of a sensor passes over the field, independently at each of rotation angles of the sensor sensing area and at each of grid coordinate positions of the sensor sensing area on a measurement plane where the field is measured, the sensor sensing area being (i) a finite area which relatively rotates about an axis perpendicular to the measurement plane, (ii) an area which relatively moves such that a predetermined position in the area is brought to each of the grid coordinate positions in a state where the area has relatively rotated, and (iii) an area in which the field is sensed as an aggregate;
• and
• a calculation unit configured to calculate the distribution of the field from the measurement data of the field, using an arithmetic expression obtained by deriving a target harmonic function, which indicates the distribution of the field, using a condition that a convolution of the target harmonic function and a shape function, which indicates a shape of a cross section of the finite sensor sensing area along a plane parallel to the measurement plane, is equal to a provisional harmonic function derived by solving the Laplace equation using the measurement data of the field and a size of the sensor sensing area in a direction perpendicular to the measurement plane,
• wherein:
• information on the shape of the cross section of the finite sensor sensing area along the plane parallel to the measurement plane is reflected in the calculation of the distribution of the field such that the distribution of the field is able to be analyzed using both the rotation angles of the sensor sensing area and the grid coordinate positions of the sensor sensing area, regardless of a size of the sensor,
• the arithmetic expression used by the calculation unit to calculate the distribution of the field from the measurement data of the field includes division of an expression obtained by integrating, over the rotation angles, an expression including multiplication of the shape function and the provisional harmonic function, by an expression obtained by integrating, over the rotation angles, an expression including a square of an absolute value of the shape function, the shape function and the provisional harmonic function each having been subjected to a Fourier transform, and
• the shape function indicating the shape of the cross section of the finite sensor sensing area along the plane parallel to the measurement plane is a function which returns 1 when a position included in the shape is given as a parameter, and returns 0 when a position not included in the shape is given as a parameter.