Study the effect of aberrations on Point spread function and encircled energy of annular aperture

In this work, the encircled energy of point spread function (PSF(for annular aperture have been studied. This study is done for the case of diffraction limited system and for different kinds of first and third order aberrations were occurred, like tilt error, focus error, spherical aberration, and coma aberration. The study showed that the spherical aberration (third order aberration) can be balanced with focus error (first order aberration) to reduce the effect of these errors on encircled energy. The same thing occurs with coma aberration (third order aberration) which balanced with tilt error (first order aberration).