  The development of new techniques for characterizing atmospheric optical
turbulence (OT) has become an active topic of research again in recent years.
In order to facilitate these studies, we reconsidered known theoretical results
and obtained some new practically useful conclusions. We introduce a
dimensionless Fresnel filter, which allows us to approximate a polychromatic
weighting function (WF) by a monochromatic one with a typical precision of
several percent. A so-called dimensionless WF can be easily scaled for a
receiving aperture of any size. For the case of a circular aperture and
monochromatic radiation, an analytical expression for the WF was found. The WFs
for a square aperture and for a circular aperture match with relative
difference less than 0.01 if the circular aperture diameter is 1.15 times
larger than the square aperture side.
  A linear digital filter can be applied to the scintillation signal from an
image detector. As an example of digital filtering, we considered the power law
filter $\propto f^{5/3}$ with the WF being constant in a wide range of
altitudes. We discuss the main limitations of this approach for measuring OT
integral: finite pixel size, aliasing, and finite image detector size.

Instrumentation and Methods for Astrophysics;Optics