Predicting the noise in hybrid (phase and attenuation) x-ray images acquired with the edge illumination technique

To analyze the noise performance of the edge illumination phase-based x-ray imaging technique when applying "single-shot" phase retrieval. The latter consists in applying a sample-specific low-pass filter to the raw data, leading to "hybrid" images in which phase and attenuation contrast are merged with each other. The second objective is to compare the hybrid images with attenuation-only images based on their respective signal-to-noise ratio (SNR).

Noise is propagated from the raw images into the retrieved hybrid images, yielding analytic expressions for the variances and noise power spectra of the latter. An expression for the relative SNR between hybrid and attenuation images is derived. A comparison with simulated data is performed. Experimental data are also shown and discussed in the context of the theory.

The noise transfer into the retrieved hybrid images is strongly related to the setup and acquisition parameters, as well as the imaged sample itself. Consequently, the relative merit between hybrid and attenuation images also depends on these criteria. Generally, the hybrid approach tends to perform worse for highly attenuating samples, as the availability of phase contrast is outweighed by the loss of photons that is necessarily encountered in hybrid acquisitions. On the contrary, the hybrid approach can lead to a much better SNR for weakly attenuating samples, as here phase effects lead to much stronger contrast, outweighing the reduction in photon numbers.

The analytic expressions inform the design of edge illumination setups that lead to minimum noise transfer into the retrieved hybrid images. We also anticipate our theory to guide the decision as to which imaging mode (hybrid or attenuation) to use in order to maximize SNR for a specific sample.