Using measurements of the spatial SNR to optimize phase contrast X-ray imaging

X-ray phase contrast imaging is a measurement task which is challenging to optimize, because many physical effects determine signal and noise. If we describe the detail visibility by the spatial signal to noise ratio, SNR($u$), we can optimize an imaging setup by maximizing its SNR($u$). We propose a measurement method for the spatial SNR which is suitable for this purpose. It consists of measuring a series of images from which the spatial SNR is calculated. This allows a convenient and exact optimization of the SNR that does not rely on theoretical simplifications and is not specific to X-ray imaging. We demonstrate the measurement method for the example of choosing the optimal geometrical magnification for cone-beam inline X-ray phase contrast. Additionally, we propose the use of a known signal reconstruction method – the Wiener Deconvolution – to improve the detail visibility by post-processing images within the limits given by the measured SNR($u$). As the SNR($u$) gives the degree of this improvement, we derive a measure for the effective spatial resolution from the SNR($u$).