This repo implements a Fourier transform inversion of the 2D Biot-Savart law to reconstruct a 2D current density distribution from an image of the out-of-plane magnetic field B_z, or a magnetic flux signal given by B_z convolved with a magnetic sensor's point spread function (PSF) or imaging kernel.
The method is based the following reference:
"Using a magnetometer to image a two‐dimensional current distribution," J. Appl. Phys. 65, 361–372 (1989) https://doi.org/10.1063/1.342549.
A free PDF of the paper is available at https://www.vanderbilt.edu/lsp/documents/jap-roth-using-89.pdf.
A sample dataset from a scanning SQUID current imaging experiment is provided in ./sample_data/. The dataset includes the point spread function of the SQUID magnetometer (psf.npz) obtained by imaging a small magnetic dipole oriented out of the plane. The current imaging data (mag.npz) was obtained by sourcing a ~600 Hz 1 µA AC current through a small device and measuring the AC flux picked up by the SQUID using a lockin amplifier. The reconstructed current density is in arbitrary units because the magnetic moment of the dipole used to calibrate the SQUID point spread function is unknown.
The Image class represents a magnetometry image from which to reconstruct a 2D current density. The reconstruct_current() function performs the Fourier transform inversion of the 2D Biot-Savart law.
Basic usage:
from current_reconstruction import Image, reconstruct_current
from current_reconstruction.test import load_psf_data, load_mag_data
psf_data = load_psf_data()
mag_data = load_mag_data()
psf = Image(
psf_data["xs"], # shape (m, ) array of x coordinates
psf_data["ys"], # shape (n, ) array of y coordinates
psf_data["data"], # shape (n, m) array of values
)
mag = Image(mag_data["xs"], mag_data["ys"], mag_data["data"])
# Sensor-sample standoff in the same units as
# psf.xs, psf.ys, mag.xs, and mag.ys
standoff = mag_data["standoff"]
# Cutoff frequencies for Hanning filter.
# These are determined empirically.
kx_max, ky_max = 1.0, 1.0
jx, jy = reconstruct_current(mag, standoff, psf=psf, kx_max=kx_max, ky_max=ky_max)