Spatial spectra of strong scintillation behind a phase screen with isotropic heterogeneities have been studied. The medium forming the screen was described by the Kolmogorov 3D spectrum of heterogeneities. Calculations were performed for conditions of optical observations through the Earth's atmosphere from a satellite. The domains of applicability for three different approximations of the solution of the equations for 2D spectra have been studied; the possibility to determine medium parameters from the observed 1D spectra of strong scintillation is investigated; and the domain of measured parameters, which contains the solution for the inverse problem stable with respect to measurement errors, has been determined.