PMC

(a) Schematic of the two-degree-of-freedom fiber-coupled heterodyne grating interferometer (AOM: acousto-optical modulators, G: diffraction grating); (b) The optical configuration of the encoder (BS: beam splitter, P: polarizer, PBS: polarizing beam splitter, PM: prism mirror, QWP: quarter-wave plate, TP: trapezoidal prism).

Definition of coordinate systems. The CS fixed to the CS represents the grating of the grating interferometer #i, and the CS fixed to the CS represents encoder #i. The Euler angles (z-y-x extrinsic) between the CS and the CS is . The red arrows represent the typical internal and external effective optical path of the encoder. Points A and C represent the refraction points of the measuring beams, and point B represent the diffraction spot.

a Sketch of the grating interferometer installed in a Philips MicroDose mammography system. The gratings are thin diffraction elements placed in the beam perpendicular to the optical axis, containing periodical line structures that absorb x-rays and/or shift their phase. A source grating (G0), a beam splitter grating (G1), and an analyser grating (G2) contribute at different steps to the recording of the phase and dark-field signals. b Photo of the grating interferometry mammography investigational device used in the study

Oblique-incidence x-ray interferometer suitable for multilayer gratings. In this three-grating interferometer, the three multilayer gratings are arranged in parallel, tilted planes and equidistant from each other. The source grating G₀ and analyzer grating G₂ are absorption gratings (e.g. W/Si multilayer grating), and the middle G₁ is a phase grating (e.g. Ni/Si multilayer grating). The diffraction beams that coherently interfere with each other are represented by the red lines. Such oblique-incidence interferometers have their equivalent normal incidence forms as explained in the text. The imaged object can be placed either in front of or behind the G₁ grating as in normal incidence setups.