In this paper, the Transport of Intensity Equation (TIE) for testing of an aspheric surface is verified experimentally. Using simulation, a proper defocus distance Δ𝑧 that leads to an accurate solution of TIE is estimated whenever the conic constant and configuration of the experiment are known. To verify this procedure a non-nulled experiment for testing an aspheric is used. For verification of the solution, the results are compared with the Shack-Hartmann sensor. The theoretical method and experimental results are compared to validate the results.
Interferometric based techniques are often used for 3D quantitative phase imaging. While these techniques are sensitive to vibrations, non-interferometric intensity based techniques such as the transport of intensity equation (TIE) do not suffer from such a drawback. Phase reconstruction of phase objects using TIE technique is accomplished by recording several diffraction patterns at different observation planes through axially translating the CCD. In this paper, we purpose to use a spatial light modulator (SLM) in a modified 4f TIE optical setup to acquire 3D tomographic images of phase objects. This modified setup will reduce the acquisition time dramatically making the TIE technique useful for dynamic events such as biological samples. We illustrate how 3D phase objects can be reconstructed tomographically by constructing a rotating mechanism for the sample. At each angle of rotation, two diffraction patterns are captured by the CCD either sequentially or instantaneously with the help of a reference mirror. The reconstructed optical fields are tomographically recomposed to yield the final 3D shape using a tomographic backprojection technique. Finally, a reconfigurable hardware controlled by a GUI is employed to synchronize the CCD, the SLM and the rotating stage.
In this work we will extend the traditional TIE setup of phase retrieval of a phase object through axial translation of the CCD by employing a tunable lens (TL-TIE). This setup is also extended to a 360° tomographic 3D reconstruction through multiple illuminations from different angles by rotating the phase object. Finally, synchronization between the CCD, and the tunable lens is employed using a reconfigurable hardware to automate the 3D 360° tomographic reconstruction process.
Recently the transport–of–intensity equation (TIE) has extended from one wave to two waves and then applied to calculate the phase of the interference field. In this work we will present the experimental verification of the application of TIE in the reconstruction of two interfering wavefronts. A Fizeau interferometer with phase shift capability is used for testing a flat surface. An error analysis is performed on the difference between the reconstructed wavefronts using TIE and the one measured wavefronts using phase shifting method. The error analysis shows some systematic errors with RMS value less than 0.5rad or λ/10. The issues such as computation time and spatial resolution of the reconstructed waves are discussed and possible applications of the presented method are given.
Phase distribution may be determined by measuring only the intensity distributions along the optical axis via the Transport of Intensity Equation (TIE). TIE has been a viable alternative to interferometry techniques for experimental conditions where those techniques perform poorly. These conditions are either because of the requirement one applies on the spatial and temporal coherence of the optical source or because of sensitivity and resolution issues. Optical testing is crucial in applications using manufactured optical elements. In this paper, we developed a method and experimental realizations capable to use both Shake-Hartman wavefront sensing (SHWS) and TIE method for testing transparent and reflective optical surfaces. The integration of TIE and SHWS has the advantage for obtaining high spatial resolution and wide dynamic range which cannot be obtained using only one of those methods. We showed that the retrieved phase profile and quantified surface variations of unknown samples from both methods are in very good agreement with each other.
Digital holographic microscopy (DHM) is an effective and non-destructive technique for quantitative phase contrast imaging of biological samples and living organelles. In this paper, using a simple and stable common-path DHM setup we study lipid bilayer dynamics and detect their morphological changes. Stacks of lipid amphiphilic molecules in excess water and at the presence of an external stimulus, stress, or force have great capability for the formation of multilamellar cylindrical tubes that are called myelin figures(MFs). MFs can be found in various healthy and diseased living cells and their formation and dynamics in various conditions involve mysterious configurations that have been of high interest. We utilized nanoparticles solved in water with different concentrations as an external stimulus for MFs of POPC lipid. The nanoparticles are injected into the sample container via a microinjection pump in a constant rate and MFs growth rate and their volume changes are measured by a compact digital holographic system. The setup is based on a binocular conventional microscope making the setup very stable against vibrations and noises. The recorded holograms are then computationally reconstructed. The measurements and investigations are performed by analyzing the reconstruction process. We showed that nanoparticles increase the growth rate of MFs during the first few seconds. However, after few seconds, the growth rate does not alter significantly comparing to the absence of nanoparticles.
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