  In theory of optical aberrations, an aberrated wavefront is represented by
its coefficients in some orthogonal basis, for instance by Zernike polynomials.
However, many wavefront measurement techniques implicitly approximate the
gradient of the wavefront by the gradients of the basis functions. For a finite
number of approximation terms, the transition from a basis to its gradient
might introduce an aliasing error. To simplify the measurements, another set of
functions, an "optimal basis" with orthogonal gradients, is often introduced,
for instance Lukosz-Braat polynomials. The article first shows that such bases
do not necessarily eliminate the aliasing error and secondly considers the
problem of finding an alias-free basis on example of second-moment based
indirect wavefront sensing methods. It demonstrates that for these methods any
alias-free basis should be formed by functions simultaneously orthogonal in two
dot-products and be composed of the eigenfunctions of the Laplace operator. The
fitness of such alias-free basis for optical applications is analysed by means
of numerical simulations on typical aberrations occurring in microscopy and
astronomy.
