Detection of coordinates and magnification of a reconstructed holographic image of a particle is quite difficult because of the lack of a strict geometric-optical model of digital holographic imaging. Traditional optics and microscopy usually use lenses for image magnification. In digital holography, magnified images can be generated without mechanical focusing and optical components, for example, by controlling the divergence of illuminating beams. This work discusses optimization of the optical scheme of digital holography for lensless magnification of reconstructed images; justifies the feasibility of using a geometric-optics apparatus in the design of digital holographic systems, and describes their limitations. The results of the work can be used in the design and development of digital holographic microscopy systems and for high-precision reconstruction and analysis of holographic images of particles.