###### Abstract  
In-line digital holography is a powerful tool widely used for microscopic object imaging. Usually, in-line and out-line configurations are used to implement holographic systems, but in-line-based set-ups are preferable as they are less sensitive to mechanical vibrations and refraction index variations. However, non-desired blurred conjugate images are superposed to the reconstructed object image by using in-line systems. One strategy to remove the conjugate image contribution is to include a double-sideband filter at the Fourier plane of the system. After using the filter, data obtained at the CCD are processed to retrieve the magnitude and phase (hologram) of the diffracted wavefront while removing the conjugated image. Afterwards, a diffraction integral equation is used to digitally propagate the hologram. Despite the above-mentioned factors, there is not a thorough analysis in the literature of magnification parameters associated with the final reconstructed image, this aspect being crucial for the experimental application of the above-stated approach. Under this scenario, a theoretical analysis of the longitudinal and transverse magnifications of the reconstructed images is provided in this work. The method is validated through the simulation and experimental results of different microscopic objects: glass microspheres, a micrometric reticle, and a resolution test chart USAF 1951. The obtained results provide that the combination of magnification relations with methods for hologram propagation and optimal focused image identification is effective for object position determination. This approach could be useful for 3D microparticle localization and monitoring with optimized magnification within real-time applications. digital holography; in-line interferometer; double-sideband filter; image reconstruction; transverse magnification; longitudinal magnification Article Analysis of the Image Magnification Produced by Inline Holographic Systems Based on the Double-Sideband Filter  
[PERSON], [PERSON], L.  
However, these interferometers are more sensible to changes in the refractive index of the medium and to component vibrations. The off-axis interferometers commonly used in digital holography are the Mach-Zehnder [11, 12], and Twyman-Green [13] configurations. In in-line interferometry, digital image processing methods are employed to minimize the influence of the superimposed conjugated image [14, 15, 16, 17]. Other techniques involve blocking specific parts of the spatial frequency spectrum of the superposition of the object and reference wavefronts to eliminate one of the conjugated images [18, 19]. A more recent approach presents an in-line interferometer that removes the degrading effect of conjugated images by implementing a polarization-based double-sideband filter (DSB) at the Fourier domain [20, 21, 22], arising as a useful tool for in-line holography. However, there is no analysis in the literature of the consequent magnification of the resulting images, and this information is crucial to provide the method with the necessary potential to be used in real applications for metrology or the characterization of microparticles. In this framework, the current work aims to address this lack of information and complete previous studies by presenting a thorough analysis of the image magnification associated with the in-line interferometer presented in [20, 21, 22]. The outline of this manuscript is as follows: in Section 2, we reveal the mathematical formulation related to the transverse and longitudinal magnification of the reconstructed images obtained using an in-line interferometer with the DSB filter and a convergent lens. Next, in Section 3, we numerically simulate the imaging of microscopic objects with the in-line interferometer and the DSB filter. Furthermore, we introduce the evaluation criteria employed to achieve the best-focused reconstructed image. Afterwards, we present the numerical results of the transverse and longitudinal magnifications.