Wave-front propagation: design code for synchrotron radiation beam lines

Abstract

Third-generation synchrotron radiation light sources provide partially coherent radiation. Certain topics in the optical design of beam lines and monochromators can be studied with electric-field distributions only rather than with intensity distributions of the light source. The radiation characteristics of a dipole or an undulator can be represented by a two-dimensional complex-electric-field distribution at a distance of several meters from the insertion device center. A method is described that transforms this field distribution through a complete beam line (consisting of mirrors and gratings) to the sample plane. Diffraction at apertures can be modeled and Stokes parameters can be evaluated. The derivation of the equations was performed with the algebraic code REDUCE. A comparison with the brightness formalism is provided.

Short-pulse limits in optical instrumentation design for the SLAC Linac Coherent Light Source (LCLS)

“…For example, although in the present work we conducted our assessments of short-pulse effects primarily in spatio-temporal terms, an equivalent discussion could have been carried out equally well in the spectral-angular domain. Existing physical-optics-based treatments of radiation interacting with optical elements tend to formulate their analyses using superpositions of plane waves [34,35]; a more appropriate approach might be to include the temporal dependence explicitly [36,37] into the basis functions utilized in formulating the integrals of quasi-monochromatic propagation theory [28,38,39]. In view of the high field strengths generated by LCLS pulses, as well as to their full transverse coherence, formalisms of this type.…”

Propagation of coherent light pulses with PHASE

“…Some recent extensions in the physical optics mode are: (a) Considering the phase shift due to slope errors of real optics, given by a 2d height error file, in the past we considered only ideal optics and some waviness. The PHASE package contains a selection of scripts for IDL 8 . The functionality is integrated in an IDL class which allows an object-oriented access.…”

A hybrid method for X-ray optics simulation: combining geometric ray-tracing and wavefront propagation

“…PHASE, a wavefront-propagation code written by J. Bahrdt (Bahrdt, 1997;Bahrdt & Flechsig, 1997), is not limited to the small-angles approximation. PHASE is based on the stationary phase method and initially used a fourth-order Taylor series expansion to describe the image coordinates with respect to the source coordinates.…”

“…Based on equation (1), these state-of-the-art mirrors should be treated using the waveoptics approach even for low spatial frequencies. Among the available wave-optics codes, mirror figure errors can be simulated on programs based on the stationary phase approximation up to a certain frequency (Bahrdt, 1997;Bahrdt et al, 2011), over a broad spatial frequency range (Reininger et al, 2001) used to simulate figure errors in ideal optics (De Andrade et al, 2011) and could also potentially cover the simulation of figure errors in its recent extension that includes grazingincidence mirrors (Canestrari et al, 2014).…”