Arbitrarily high focal depth with finite apertures

We modify the concept of superresolution for achieving arbitrarily extended focal depth with a finite aperture. The Legendre polynomials are used for designing a novel apodizer that produces arbitrarily high depth of focus. This kind of apodizer can also arbitrarily reduce the sensitivity to spherical aberration. Since these benefits are achieved at the expense of light throughput, we report on a formula for evaluating light throughput of this kind of filter.