Restoration of Vector Magnetization Image from Vector Scanning-SQUID Microscope Measurement

A generalized mathematical framework to treat image data measured by the scanning superconducting quantum interference device (SQUID) microscope using a three-dimensional vector pickup coil is presented. The blurring of the images originating from the effects of diamagnetism due to the superconductivity of the sensor, the non-zero sensor size, and the finite sensor-to-sample separation are numerically reduced. We use a lattice model of the measurement system, and singular value decomposition and the Moore-Penrose pseudo-inverse matrix are employed to handle ill-conditioned matrices we encounter in the numerical processes. Based on a numerical model, measurement of the vector magnetization distributed on a sample surface, and the image restoration using the present procedure are demonstrated.