Fractional Montgomery effect: a self-imaging phenomenon

Abstract

Self-imaging means image formation without the help of a lens or any other device between object and image. There are three versions of self-imaging: the classical Talbot effect (1836), the fractional Talbot effect, and the Montgomery effect (1967). Talbot required the object to be periodic; Montgomery realized that quasiperiodic suffices. Classical means that the distance from object to image is an integer multiple of the Talbot distance Z(T) = 2p2/lambda, where p is the grating period. Fractional implies a distance that is a simple fraction of Z(T): say, Z(T)/2, Z(T)/4, 3Z(T)/2.... We explore the most general case of the fractional Montgomery effect.

Characterization of imaging performance in differential phase contrast CT compared with the conventional CT: Spectrum of noise equivalent quanta NEQ( k )

“…36 G 1 and G 2 work together as a shearing interferometer [37][38][39] to detect the wavefront alteration caused by the object in x-ray beam. The x-ray tube irradiates the specimen, while the specimen stage rotates by a range satisfying the data sufficiency condition, and the CCD x-ray detector is employed for data acquisition.…”

“…The key component of the imaging chain is grating G 1 , a diffraction interferometer based on the Talbot effect. [37][38][39] Figure 1(b) shows how G 1 works by virtually decomposing it into gratings A and B. The extra optical path corresponding to grating B relative to that through grating A is half wavelength, which is equivalent to a 180…”

Imaging performance in differential phase contrast CT compared with the conventional CT-noise equivalent quanta <i>NEQ(k)</i>

“…G 1 is a phase grating and G 2 an absorption grating, which can be fabricated with photolithography, deep chemical etching and electroplating 34 . G 1 and G 2 work together as a shearing interferometer [35][36][37] to detect the wavefront alteration caused by the object in x-ray beam.…”

“…The key component of the imaging chain is grating G 1 , a diffraction interferometer based on the Talbot effect [35][36][37] . Fig.…”

“…The imaging mechanism of x-ray tube and grating based DPC-CT is elaborated in references 8,[35][36][37] , and a concise review is given here for completeness. According to Fresnel analysis 38,39 , the irradiance I(x, z) at the CCD detector is where Δx is a displacement in x-direction, and φ(x, y) is the phase corresponding to Δx, which is the projection of the refractive coeffiecient along the x-ray path Z…”