A linear system can be represented by its eigenmodes. Thus, the response of an optical system working under coherent illumination can be described using plane wavefronts; which are the eigensolutions of the Helmholtz equation. This is the cornerstone concept in Fourier optics. Sometimes, however, it is convenient to translate the concept of plane wave to other modes; for example using prolate functions 1, or Legendre poynomi- als2'3. In particular, a 1-D plane wavefront, the kernel of the 1-D Fourier transformation, can be suitably written using Buer's formula4, as a linear superposition of Legen- dre polynomials, which constitute an orthonormal base. With this simple mathematical tool one can solve many different problems in optics.