Imaging with extended focal depth by means of lenses with radial and angular modulation

Abstract

The paper presents imaging properties of modified lenses with the radial and the angular modulation. We analyze three following optical elements with moderate numerical apertures: the forward logarithmic axicon and the axilens representing the radial modulation as well as the light sword optical element being a counterpart of the axilens with the angular modulation. The abilities of the elements for imaging with extended depth of focus are discussed in detail with the help of structures of output images and modulation transfer functions corresponding to them. According to the obtained results only the angular modulation of the lens makes possible to maintain the acceptable resolution, contrast and brightness of the output images for a wide range of defocusing. Therefore optical elements with angular modulations and moderate numerical apertures seem to be especially suitable for imaging with extended focal depth.

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

“…Coincidence of MTFs means that using the three colored spots for signal processing is achievable without distorting any channel with respect to other. In [27], the authors present imaging properties of LSOEs, with similar MTFs that the ones calculated here. Thus, it is possible to obtain simultaneously three different chromatic channels that can be processed together or separately.…”

Assessment of imaging with extended depth-of-field by means of the light sword lens in terms of visual acuity scale

“…According to previously reported theoretical studies, numerical simulations, and qualitative experiments [12][13][14][15][16][17][18], an element of this kind can form recognizable images of acceptable quality in the presence of a defocus of 0-4 diopters. The LSL demonstrated its superiority over other solutions designed especially for multifocal and EDF imaging.…”

“…In general, they can be divided into three main families: accommodative proposals, multifocal proposals, and proposals with Extended Depth of Field (EDF). Between the members of the second group, there can be found bifocal or multifocal lenses [1,2], whereas in the last group one can find rotationally symmetric phase masks [3][4][5], axicons [6][7][8], lenses with negative spherical aberration [9,10], and light sword optical elements (LSOEs) [11][12][13]. In contrast to other elements, the LSOEs are distinguished by angular variation of the optical power.…”

“…7 that, because of the partly off-axis character of the LSL imaging capability, a small waving of the image takes place with displacements of less than 3 arcmin (0.087 prism diopter). It is a natural consequence of the lack of rotational symmetry in the LSL shape, which causes the focusing of light into the off-axis direction perpendicular to the actual focusing angular segment [12]. The ability of the human visual system to adapt to this situation remains to be investigated, with some studies indicating high flexibility [27,28].…”

Tunable apodizers and tunable focalizers using helical pairs

“…Other phase masks are able to reduce the influence of focus errors on the Modulation Transfer Function (MTF) [4][5][6][7][8][9]. However, these phase masks generate unwanted oscillation around a tendency curve.…”