Electronic imaging using a logarithmic asphere

Abstract

Transmission functions are derived that are valid in the nonparaxial case for a class of lenses that will image a continuum of points along an optical axis to a single image point. This lens, which we call a logarithmic asphere, is then used in a digital camera. The resolution of the camera is limited by the pixel size of the CCD; i.e., it is not diffraction limited. Digital processing is used to recover the image, and image-plane processing is used for speed. We find a tenfold increase in the depth of field over that for the diffraction-limited case.

Wavefront Coding Fluorescence Microscopy Using High Aperture Lenses

“…Two specific functions that have been successful are the cubic [3,6] and logarithmic [5] phase masks, where the phase is a cubic or logarithmic function of distance from the centre of the pupil, in either radial or rectangular co-ordinates. The logarithmic design is investigated in detail in Chap.…”

Phase pupil functions for reduction of defocus and spherical aberrations

“…As discussed below, there is an increase in the width of the PSF with a consequent reduction in axial intensity, as indicated by the scaling parameters in the f igure. Logarithmic f ilters (LFs) were previously reported 8,13 ; however, contrary to our approach, the derivation of such filters was mainly achieved from geometric-optics considerations without including diffraction effects.…”

“…More recently, a novel approach that combines phase filters with digital processing to alleviate optical aberrations was reported. 9,12,13 In this Letter we describe the design of such a phase f ilter, obtained from the evaluation of the Strehl ratio of circularly symmetric optical systems, the intensity distribution along the optical axis of which is evaluated by use of the stationary phase approximation. 12 The performance of this phase f ilter in combination with an ideal lens is compared with that of an ideal lens without the phase filter and with previously reported phase filters that exhibited rectangular symmetry.…”

A compact Airy beam light sheet microscope with a tilted cylindrical lens

“…Note however that this does not necessarily prevent high resolution imaging. In fact, the introduction of various higher-order aberrations has proven useful for imaging in the presence of aberrations [18][19][20][21]. Residual higher order terms may thus be of less importance to the final image quality, though the microscope may require additional calibration before use.…”