Fig. 4: Spatial profiles reconstructed from magnetic measurements.

a, b \({\rho }_{1{\rm {D}}}\left(x\right)\) spatial reconstructions for configuration A/B without the wire and for three different wire positions. The signals were normalised to have the same magnitude at one position (−0.15 mm) where the wire does not obstruct the beam. The error bars were calculated from the standard deviation of repeat measurements. Note that the origin itself cannot be measured in a magnetic scan measurement due to uncertainty in the measurement background, which in a Fourier transform appears at the origin, furthermore the errors are larger in the points close to the origin due to slow drifts in the detection efficiency. c The initial beam density from a measurement without a wire (magenta markers) was multiplied by zero at the expected wire position to produce the input for the simulation (black dashed line). Precession calculations followed by a Fourier transform produced a simulated profile (blue markers) which compares very well with the profile reconstructed from a measurement (green markers). d, e Simulated reconstructions of \({\rho }_{1{\rm {D}}}\left(x\right)\) for a sharp impulse peak centred at 0.6 mm and for resolutions of 50 and 10 μm, respectively, and for varying Gaussian velocity distributions with a FWHM of 0%, 3%, 6%, 10% and 20%.