Transverse and longitudinal magnification of reconstructed images using inline digital holography with the double-sideband filter

Inline digital holography is useful to reconstruct focused images of microscopic objects. This configuration is less sensitive to mechanical vibrations and refraction index variations. However, the blurred conjugate image is formed over the focused image. To remove the conjugate image a double-sideband (DSB) filter was proposed. The main sketch proposed to constitute the filter is as follows: first a collimated and linearly polarized wavefront illuminates microscopic objects to be studied. A convergent lens is placed in the overlap between the diffracted wavefront and illumination wavefront. Afterwards, at the focal plane of this lens a Liquid Crystal Spatial Light Modulator (SLM-LC) is positioned, followed by a linear polarizer. Finally, the resulting fringe patterns are recorded with a CCD. Under this scenario, two phase retardation values (0° and π) are addressed to each half of the SLM-LC screen. In this form, the half of spatial frequency spectrum is blocked. Next, the values of the phase retardation on each half of SLM-LC screen are digitally exchanged, and the other half of the spatial frequency spectrum is blocked. In the computer, both fringe patterns are processed to retrieve the complex amplitude with magnitude and phase (hologram) of the diffracted wavefront, and thus, one of the conjugated images is removed. A diffraction integral equation is used to propagate digitally the hologram. Sparsity metric is applied to determine the best focused image. In this work, we provide a theoretical analysis of the longitudinal and transverse magnifications of the reconstructed images. We demonstrate that transverse and longitudinal magnification depend on the focal length of the lens as well as the length from the lens to the CCD. If the object position changes, the reconstruction length is proportional to longitudinal magnification of the system, while the transverse magnification of the reconstructed image does not vary. This is desirable for the displacement trace of moving particles, or for reconstruction of microscopic objects in different planes, in a 3D volume. Finally, we present the experimental results obtained in the reconstruction of the images of microscopic objects. We reconstruct the image of glass microspheres (diameter: 14.5 μm ± 1 μm), a micrometric reticle (100 μm), and a resolution test chart 1951 USAF, to verify longitudinal and transverse magnifications. The proposed study is useful for the study and tracking of quasi-transparent microscopic samples with optimized magnification.