Nonparaxial design of generalized axicons

Abstract

The geometric law of energy conservation is utilized in evaluating the phase transmittance function for axicons with arbitrary distribution of the on-axis intensity. Several simple analytical solutions are presented, and a computer-generated holographic version of the uniform-intensity axicon is examined.

Pseudo-nondiffracting beams generated by radial harmonic functions

“…However, since each of them is basically a single-lens imaging system, the size of the in-focus image changes along the depth of the field. 15 The simulation results of a spatially incoherent monochromatic imaging system are presented in Fig. 8.…”

Three dimensional analysis of chromatic aberration in diffractive elements with extended depth of focus

“…The element capable of such transformation is called a linear axicon [1]. If the structure of the element is in the form that the optical power (1/ f ) decreases inversely with the radial coordinate ( ρ ), the element is called direct axicon.…”

“…Several configurations are proposed in the bibliography [1][2][3][4][5][6][7][8][9][10]. Some of them are based on single elements [1,2,4,[6][7][8][9]10] while others are based on convenient association of several elements [3,5,8]. Extended depth of focus in a single element is usually achieved by spatial multiplexing of phase information.…”

“…All these elements share the common property that they produce a long and narrow focal segment which allows imaging in a continuous region in the image domain. The effect can be achieved by multiplexing a continuous range of focalization distances in the element, which can be done either with refractive media [1,3,4,10] or by diffractive optical elements (DOEs) [2,6,7,9,12,13]. Among these systems, we are most interested in single diffractive structures, which can be easily implemented in a spatial light modulator (SLM).…”

“…Among these systems, we are most interested in single diffractive structures, which can be easily implemented in a spatial light modulator (SLM). In particular we will focus our work on two particular elements: Light Sword Optical Elements (LSOE) and Fresnel Axicons (FA) Optical properties of these elements are widely known [1][2][3]11,15] and their performance has been optimized in several ways [16][17][18][19].…”