  Recently, a method for obtaining diffraction-attenuation resistant beams in
absorbing media was developed through suitable superposition of ideal
zero-order Bessel beams. In this work, we will show that such beams maintain
their resistance to diffraction and absorption even when generated by finite
apertures. Also, we shall extend the original method to allow a higher control
over the transverse intensity profile of the beams. Although the method has
been developed for scalar fields, it can be applied to paraxial vector wave
fields as well. These new beams can possess potential applications, such as
free space optics, medical apparatuses, remote sensing, optical tweezers, etc..
