Focusing of an elliptical mirror based system with aberrations

Abstract

The effect of primary aberrations on the focusing of an elliptical mirror based system is studied by using the Debye integral. Specifically, the apodization function for elliptical mirror is derived and expressed by the eccentricity of the elliptical mirror. For the elliptical mirror with low aperture, intensity distributions in the presence of aberrations near focus are presented based on the derived scalar theory, while for the high-aperture condition, vectorial theory is used to describe the electric field in the focal region. In particular, the effect of aberrations is studied under radially polarized illumination. Moreover, tolerance conditions are given based on the knowledge of focusing with aberrations. It is found that the elliptical mirror based system shares a similar level of tolerance conditions with that of the single lens, while both of them are more sensitive to the presence of astigmatism than other aberrations. It is believed that the results will theoretically support the application of the high-aperture elliptical mirror in scanning microscopy.

Engineering arrays of diffraction-limited hollow tubes and doughnut spots with prescribed distributions

“…They have been widely investigated due to their potential applications in many fields, such as particle trapping and micromanipulation, lithography, and optical microscopy [1][2][3][4][5]. Many methods for generating and operating hollow beams have been proposed, both theoretical and experimental [6][7][8][9][10][11][12]. For example, an 8λ-long azimuthally polarized optical tube with a transverse full width at half-maximum (FWHM) of 0.32λ was created through backward-focusing the field radiated from an array consisting of six magnetic dipoles with different amplitudes obtained by optimization [6].…”

“…For example, an 8λ-long azimuthally polarized optical tube with a transverse full width at half-maximum (FWHM) of 0.32λ was created through backward-focusing the field radiated from an array consisting of six magnetic dipoles with different amplitudes obtained by optimization [6]. A uniform light tunnel of variable length and narrow dark channel was obtained by modulating an azimuthally polarized Bessel-Gaussian beam using an amplitude apodization filter under a high-NA lens system [7]. An azimuthally polarized optical hollow needle, with a super-oscillatory (a) E-mail: yuyanzhong059368@163.com transverse size from 0.34λ to 0.42λ and a large depth of focus of 6.5λ, was experimentally demonstrated by focusing an azimuthally polarized wave using a single planar binary-phase lens with an NA of 0.908 [8].…”

“…The array of hollow tubes with variable lengths and controllable intervals in the focal volume can be produced by combining eqs. ( 3), ( 6), (7), and ( 8), as depicted in fig. 2(a) for the following cases: i) same lengths and same intervals; ii) same lengths and different intervals; iii) different lengths and same intervals; and iv) different lengths and different intervals.…”

Design of Scattering Scanning Near-Field Optical Microscope

“…In the case of the visible light an Al2O3 window is used, and a ZnSe window is used for the MIR light. The wavelength dependence on transparency is plotted below for each window in figures 2.4a and 2.4b.Elliptical mirrors have two focal points, and a key feature is that any light passing through one focal point on the way to the mirror will always focus to the second focal point[18]. The sample is placed at the lower focal point of the elliptical mirror.…”