An aspherical lens is fabricated from an ultraviolet (UV) curable polymer and is characterized by measuring its focal spot. Electrostatic force is employed to manipulate the shape of the liquid polymer lens. Experiment results show that a liquid lens in a strong electrostatic field can be distorted from initial spherical shape to parabolic to even near cone shape. With in situ measurement of the surface profile and focal spot, an aspherical liquid lens with good performance can be cured to a solid aspherical lens by UV light. A probe scanning microscope is employed to accurately measure the focal spot of the aspherical lens, and the modulation transfer function (MTF) of the aspherical lens is calculated to characterize it. A focal spot of 1.825 microm diameter, an MTF of 800 line pairs/mm cutoff spatial frequency, and a Strehl ratio of 0.742 are achieved. These demonstrate the feasibility of fabricating an aspherical lens with small aberrations by using this method.
A compound eye has the advantages of a large field of view, high sensitivity, and compact structure, showing that it can be applicable for 3D object detection. In this work, an artificial compound eye system is developed for 3D object detection, consisting of a layer of lenslets and a prism-like beam-steering lens. A calibration method is developed for this system, with which the correspondences between incident light rays and the relevant image points can be obtained precisely using an active calibration pattern at multiple positions. Theoretically, calibration patterns at two positions are sufficient for system calibration, although more positions will increase the accuracy of the result. 3D positions of point objects are calculated to evaluate the system, which are obtained by the intersection of multiple incident light rays in the least-squares sense. Experimental results show that the system can detect an object with angular accuracy of better than 1 mrad, demonstrating the feasibility of the proposed compound eye system. With a 2D scanning device, the system can be extended for general object detection in 3D space.
Bessel beams have been increasingly used for their advantages of non-diffraction and long focal depth. In this paper, we studied the propagation of on-axis and off-axis Bessel beams in a gradient-index medium. By expressing a Bessel beam in integral form, the analytical expression of an on-axis, decentered, and tilted Bessel beam through a paraxial optical system is derived with the ABCD matrix method and Collins diffraction integral formula. Main lobe size and trajectory of the zeroth- and second-order Bessel beam are obtained, demonstrating that the Bessel beam is focused by the gradient-index medium and its main lobe trajectory is exactly the same as the corresponding geometrical ray for both the decentered and tilted Bessel beam. Effects of beam apodization are finally studied by the Fourier beam propagation method, showing that the side lobes of the Bessel beam vanish when the beam is focused inside the medium as only part of the beam enters the lens.
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