Spread spectrum phase modulation for coherent X-ray diffraction imaging

Abstract

High dynamic range, phase ambiguity and radiation limited resolution are three challenging issues in coherent X-ray diffraction imaging (CXDI), which limit the achievable imaging resolution. This paper proposes a spread spectrum phase modulation (SSPM) method to address the aforementioned problems in a single strobe. The requirements on phase modulator parameters are presented, and a practical implementation of SSPM is discussed via ray optics analysis. Numerical experiments demonstrate the performance of SSPM under the constraint of available X-ray optics fabrication accuracy, showing its potential to real CXDI applications.

Blind ptychography: uniqueness and ambiguities

“…In other words, each θ(n) is independently distributed with a probability density function p γ supported on (−γπ, γπ] with a constant γ ∈ [0, 1]. Continuous phase modulation can be experimentally realized with various techniques such as spread spectrum phase modulation [64].…”

“…Regardless of τ and the condition (67), the quantities a j have a common factor τ so (65) with (64) can not be satisfied unless τ = 1. It is well known that ambiguities known as raster grid pathology are present in blind ptychography with the raster scan of τ > 1 [56].…”

On relaxed averaged alternating reflections (RAAR) algorithm for phase retrieval with structured illumination

“…If the diffraction is in the regime of Fraunhofer, the phase shift can be result from optical instruments, such as optical grating, ptychography and oblique illuminations (see [20] and references therein), Some application of those structured illumination can be found in [28][29][30][31]. If we record the magnitude of the diffraction patterns in the Fresnel regime, the phase shift is automatically introduced in the original signal/image.…”

Coded aperture ptychography: uniqueness and reconstruction

“…Continuous phase modulation can be experimentally realized with various techniques depending on the wavelength. See [17,19,23,28,30,31] for recent innovation and development of random phase modulation techniques.…”

“…By Theorem 2.3 and Corollary 2.4,(29) implies that x = e iθ f for some constant θ ∈ R. To complete the proof, we only need to show e iθ f = x * . By(30) and the identity x = e iθ f , we have e iθ sgn(A * f ) = sgn(y * ) u on supp(b) (31).…”