A new method is proposed by which the time integral of time-varying magnetic fields in different voxels can be determined by MRI. A further processing step is employed which enables the integral of the magnetic field gradients experienced by groups of voxels to be deduced. Analysis of the theoretical background and complete simulations have been used to assess the limitations of the technique and the method is applied to the measurement of a 2D spiral k-space trajectory and also of its 1D components. These measured trajectories have been used to reconstruct images from experimental spiral-scan raw data of a phantom acquired using the 2D spiral k-space trajectory. Comparisons of the resulting images are made with the image reconstructed using the corresponding theoretical trajectory. The importance of the repeatability, reliability and accuracy of the technique is demonstrated.