Fast calculation method for optical diffraction on tilted planes by use of the angular spectrum of plane waves

Abstract

A novel method for simulating field propagation is presented. The method, based on the angular spectrum of plane waves and coordinate rotation in the Fourier domain, removes geometric limitations posed by conventional propagation calculation and enables us to calculate complex amplitudes of diffracted waves on a plane not parallel to the aperture. This method can be implemented by using the fast Fourier transformation twice and a spectrum interpolation. It features computation time that is comparable with that of standard calculation methods for diffraction or propagation between parallel planes. To demonstrate the method, numerical results as well as a general formulation are reported for a single-axis rotation.

Computer-generated holograms for three-dimensional surface objects with shade and texture

“…According to Ref. 13, the computation time of rotational transformation is dominated by FFTs, and FFT operation must be executed twice to rotate a planar surface. However, most of the inverse FFTs of Eq.…”

“…10,11 A similar method based on the Rayleigh-Sommerfeld integral has been reported within the context of free-space beam propagation. 12 Recently, the author reported a more precise formulation and numerical consideration 13 as an extension of an angular spectrum of plane waves 14 in which remapping the angular spectrum plays an important role. The remapping also eases the difficulty of creating object fields in wave-oriented methods.…”

“…The first technique, based on the rotational transformation of wave fields presented in Ref. 13 and on remapping of the angular spectrum, provides a method for synthesis of the object fields. This technique makes it possible to create diffusive fields of arbitrarily tilted planar surfaces that have an arbitrary shape and texture.…”

Desarrollo de un módulo experimental de difracción de la luz para un laboratorio de física controlado de forma remota/Development of an experimental module of light diffraction for a physics laboratory remotely controlled

“…Aunque este método presenta resultados interesantes, su enfoque tiene como objetivo el diseño de un sistema CCD para la medida de difracción, lo que implica la construcción del sistema haciéndolo poco viable para la implementación del proyecto. En [20] presentan un método para la simulación de la propagación de campo basado en el espectro angular de ondas planas utilizando el dominio de Fourier. Este método elimina las limitaciones geométricas que plantea el cálculo de propagación convencional y permite calcular amplitudes complejas de ondas difractadas en un plano no paralelo a la abertura.…”

X-ray metrology and performance of a 45-cm long x-ray deformable mirror

“…19 This allows us to propagate the field to the z-distance where the center of the field encounters the tilted optic. We then tilt the electric field so that it is parallel to the surface of the optic, apply any phase errors, and then tilt it back to normal.…”