A simple strategy based on wavefront propagation in the Fresnel regime to reduce a ringing effect by using an ideal filter in off-axis digital holography (DH) is presented. In addition, we demonstrate a better focusing capacity by using this ideal filter than Butterworth and Gaussian methods. It also provides a way to increase the visibility of the refocused plane by reducing the influence of the out-of-focus planes. We also use the unique feature of the refocusing capability of DH in the reconstructed and enhanced image, which is obtained from the averaging operation between the image at the focused image plane (z=zhd0) and the first Talbot distance order (z=zhd1). This distance is determined by the periodic ringing. Reductions of 50% of these anomalies are computed in simulation and 30% is obtained experimentally (nearly 2 nm). Also a numerical simulation shows that the focusing resolution is directly related to the filter size and shows a 0.8 mm focus zone with an ideal filter. Numerical simulations and experimental results are carried out to validate the proposal.
Single particle position calculation in three dimensions (3D) with high accuracy is the very important in several branches
of science. On the other hand, the use of in-line holography to study very small objects in a dynamic volume is a
technique of importance for scientists and engineers across a variety of disciplines for obtaining information about size,
shape, trajectory and velocity of small objects such as dust particles. However, in general for in-line holography,
accurate determination of the object's position in the optical axis direction is difficult. In order to overcome this
shortcoming, we proposed to use in-line holography set up to record particle images in two orthogonal forward
configurations. In this study, we avoid digital holography reconstruction to calculate particle position. To determine
particle position, the proposed method is based on the calculation of the size and position of the central spot size (CSS) of
a particle diffraction image. The size of the CSS is calculated by using the Continuous Wavelet Transform (CWT) and
Continuous Hough Transforms (CHT), an then the size of the CSS is related to a calibration curve calculated
experimentally in order to determine the "z" particle position and centroid of the CSS render the "x-y" position of a
particle image. The procedure proposed in this work to determine the 3D particle position is so simple since it avoids a
complicated experimental set-up and several computational steps in order to obtain the 3D position of the particles. Our
approach offers the following advantages: First, the mathematical accuracy, light illumination as well as particle and
medium refractive indexes are used during the analysis. Second, it is not required to resolve the size of particle since we
calculate only the size of CSS of a diffraction particle image pattern.
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