In the article a theoretical basis and some practical results of treatment with the inverse task as solution of the problem of free boundary are presented. This solution originates from the hydrodynamic theory of boundaries, see Kosorin (2005; 1993). Its main product is the method for transformation of Ndimensional hydrodynamic task into N-1 dimesional one which allows to formulate and solve an inverse task, where the seepage velocity field has to be determined in the domain below the given free water surface. In this case the free surface is assumed to be given by means of contour lines. and V štúdii sú uvedené teoretické východiská a praktické ukážky riešenia inverznej úlohy ako problému voľnej hranice pri sledovaní pohybu podzemnej vody. Toto riešenie vychádza z hydrodynamickej teórie hraníc, pozri Kosorin (2005; 1993). Hlavný produkt teórie je metóda transformácie N-rozmernej hydrodynamickej hraničnej úlohy na N-1 rozmernú hranicu pôvodnej oblasti. To dovoľuje formulovať a riešiť aj tie inverzné úlohy, kde sa rýchlostné pole podzemnej vody určuje v oblasti pod zadanou voľnou hladinou na základe informácií o tejto hranici a geológii prostredia. V tomto prípade ide o voľnú hladinu, zadanú vrstevnicami.
The paper presents a detailed theoretical analysis of a rotationally symmetrical aspherical lens consisting of one spherical and one aspherical surface. That lens exhibits the corrected spherical aberration for a given position of the object. On the base of the derived mathematical relations the calculation procedure for the lens shape is described. and V práci je provedena podrobná teoretická analýza vlastností rotačně symetrické asférické čočky tvořené jednou sférickou a jednou asférickou plochou a která má pro danou polohu předmětu korigovanou sférickou aberaci. Jsou odvozeny vztahy a uveden postup výpočtu této asférické čočky.
During the design process of optical systems, it is desirable to obtain residual aberrations of designed optical systems as small as possible. By analysis of the dependence of aberrations on the numerical aperture and field of view, it is possible to find such values of the numerical aperture and field of view, where the residual aberration is zero. Such values of the numerical aperture and field of view are called correction zones. The work theoretically analyses the described problem and equations are derived for expression of wave aberration coefficients using correction zones for aberrations of the third and fifth order. Finally, there was done an analysis of optimal values of correction zones and optimal position of the centre of reference sphere using derived equations. This analysis was done for the case when we require the minimum deviation of wave aberration from zero.