Purpose The use of monofocal, bifocal, or multifocal intraocular lenses (IOLs) is a common option to restore the refractive power of the eye in aphakic patients after cataract surgery. In this article, we study the predicted performance of two new designs of IOL, both with extended depth of focus: the quartic axicon and the light sword optical element (LSOE). These elements provide continuous focal segments spanning the range of dioptric power required for presbyopia compensation. Methods The performance analysis is based on the visual Strehl ratio (SR) computed in the spatial frequency domain, a neuro-optical quality metric that takes into account the effects of both the optical transfer function and the neural contrast sensitivity function. Furthermore, the classical SR and compound modulation transfer function were calculated. Some conventional transmittances of commercially available IOLs are also analyzed. Results The LSOE design has a more homogeneous behavior than other available solutions, providing a more uniform image quality over a significant fraction of the required addition range. Conclusions The angular average of the visual SR computed in the spatial frequency domain and compound modulation transfer function indicate that both designs of extended depth of focus elements provide better optical quality on the whole addition range, except at the end points, than the discrete focus designs. The LSOE performed better than the quartic axicon in terms of uniformity of image quality within the same range.