KEYWORDS: Holograms, Holographic displays, Spatial light modulators, RGB color model, Near eye displays, 3D image reconstruction, Multiplexing, Light sources and illumination, Lenses, 3D displays
Near-eye displays (NED) are devices that are intended to project three dimensional images with wide-angle view. However, at present most of the 3D displays are based on stereoscopic principle, which does not satisfy the required parameters of human vision. This limitation can be overcome by implementing digital holograms within the NED. This is because a digital hologram contains the whole wavefront information of the scene. Thus, a holographic NED (HNED) is capable to reconstruct any three-dimensional scene while matching all the physiological cues of human vision. Nevertheless, truly immersion experience in HNED requires wide angle view and full colour reconstruction as well. In this work, we study HNED for pupil and non-pupil configuration that reconstructs large 3D colour scenes. The colour reconstruction is made by using RGB illumination and time multiplexing. Numerical analysis is carried out to test the FOV and the quality of reconstructions. Moreover, experimental colour reconstructions are made by employing laser for the pupil configuration and LED for non-pupil configuration. This is done to compare reconstruction quality and FOV of the displayed 3D scene.
Methods for manipulating the geometry of 3D image by linear transforming of hologram data are very efficient. Such techniques are desirable also for wide-angle viewing holographic display. Especially when there is no direct access to the reconstructed image due to lack of numerical hologram reconstruction techniques. Hence, methods based on directly manipulating the holographic image cannot be applied. In this paper, we investigate theoretically, numerically, and experimentally the image manipulations based on hologram stretching for the case of wide-angle near eye holographic display. We show that for wide-angle display the significant Petzval curvature and astigmatism errors are obtained in image reconstruction. Finally, applicability of the investigated image manipulation methods is shown with experiments of hologram reconstructions in a wide-angle holographic display.
Digital holographic microscopy (DHM) is a non-contact, profilometric tool that allows obtaining microscopic object topography from captured holograms. However, the use of DHM is limited when the object under observation has a high gradient or is discontinuous. Multi-angle digital holographic profilometry (MIDHP) is an alternative solution for overcoming this limitation for measuring the topography with discontinuities. This method combines digital holography and multi-angle interferometry. The method requires a certain number of holograms that are processed into longitudinal scanning function (LSF). The topography of the object is recovered by finding the maxima of the LSF. MIDHP enables to enlarge the measurement range and provides a high axial resolution. This paper investigates MIDHP to measure surfaces with various (low and high) surface gradients. The calculations of LSF requires many Fourier Transforms (FT) and the computations are slow. In this paper, we improve LSF calculations by introducing two algorithms. The first algorithm reduces number of FT needed by applying summation in frequency domain. Second approach applies the method of 3D filtering, which improves the quality of the reconstructed shape. The introduced approaches are verified both numerically and experimentally.
Fourier lensless holograms of large size and large viewing angle are investigated. The investigated hologram is non paraxial and has large size in horizontal direction and small in the vertical one. This paper focuses on the problem of efficiency and quality of numerical reconstruction of such large holograms. Three wavefront propagation methods are analyzed for this task: (i) Fresnel propagation, (ii) classical Angular Spectrum and (iii) Angular Spectrum with optimized zero padding. All the numerical approaches are investigated theoretically and experimentally for its numerical efficiency and reconstruction errors. Experimental verification is provided.
In this work we propose a holographic approach for accurate characterization of thickness of transparent objects. The proposed method is based on recording a series of fully-coherent holograms, which are generated with varying tilt of object plane wave illumination. The captured holograms are numerically processed to obtain the corresponding complex fields, which are used to produce the longitudinal coherence function. This function allows to measure the absolute thickness of transparent parallel plates using highly monochromatic light source. The conclusions of this work are supported with results of numerical simulations.
The aim of this work is to develop a holographic method that provides the shape reconstruction with an extended measurement range and preserved high accuracy. The method requires recording of series of fully-coherent holograms generated with varying tilt of plane wave illumination. The captured holograms are numerically processed to obtain the corresponding complex fields. The complex fields are used to produce a new set of holograms, which are used for calculating the longitudinal coherence function. This function allows observing fringes of high contrast at specific heights similar to white light interferometry, and thus, shape reconstruction of the three-dimensional object is carried out. The conclusions of this work are supported with results of numerical simulations.
The aim of this work is to develop a holographic method that provides the shape reconstruction with high, interferometric accuracy and an extended measurement range. The method requires recording of a set of n holograms obtained for selected combination of illumination angles θ𝑛. The difference between the optical phases corresponding to on-axis φ0 and offaxis φ𝑛 fields allows calculating the object height. To maintain high-accuracy evaluation of height the dedicated shape reconstruction algorithm is proposed. The algorithm consists of n steps, each with several substeps. Each substep is divided into: (1) calculation of the height from φ0 and φ𝑛 ; (2) propagation of the optical fields. In this paper, the proposed algorithm is numerically validated using three types of objects.
Recovering phase information with Deterministic approaches as the Transport of Intensity Equation (TIE) has recently
emerged as an alternative tool to the interferometric techniques because it is experimentally easy to implement and
provides fast and accurate results. Moreover, the potential of employing partially coherent illumination (PCI) in such
techniques allow obtaining high quality phase reconstructions providing that the estimation of the corresponding Phase
Transfer Function (PTF) is carried out correctly. Hence, accurate estimation of the PTF requires that the physical
properties of the optical system are well known. Typically, these parameters are assumed constant in all the set of
measurements, which might not be optimal. In this work, we proposed the use of an amplitude Spatial Light Modulator
(aSLM) for tuning the degree of coherence of the optical system. The aSLM will be placed at the Fourier plane of the
optical system, and then, band pass filters will be displayed. This methodology will perform amplitude modulation of the
propagated field and as a result, the state of coherence of the optical system can be modified. Theoretical and
experimental results that validate our proposed technique will be shown.
The paper presents modifications of full-field optical methods commonly used to test the surface quality of optical components used for forming a high power laser beam and tests of a final wavefront. The modifications in reference to surface measurements rely on implementation of the novel fringe pattern processing methods including the quality improvement of initial interferogram and analysis of a reconstructed phase based on Hilbert-Huang transform aided by the principal component analysis. Also the Point Diffraction Interferometer as the efficient tool for high quality measurements of elements with high NA is introduced. In reference to a wavefront quality measurements two solutions are discussed: the use of a lateral shear interferometer and the system employing Transport of Intensity Equation method. The pros and cons for both methods are discussed.
Quantitative Phase Imaging based on the Transport of Intensity Equation (TIE) has shown to be a practical tool for retrieving the phase information of biological and technical samples. When recovering the phase information with the TIE, the maximum lateral resolution that can be obtained is limited by the numerical aperture (NA) of the optical system. In order to overcome this limitation, a system that combines structured illumination and TIE-like techniques have been proposed. These methodologies enlarge synthetically the NA of the optical system, and thus, the lateral resolution of the retrieved phase can be improved. However, the employment of structured illumination may bring error amplifications in the retrieved phase due to its sensitiveness to phase discontinuities and shot noise. In this work, we propose a new methodology that improves the lateral resolution of the retrieved phase beyond the diffraction limit avoiding the problems related with the structured illumination. The methodology presented here uses tilted illumination and a TIE solver. We show that when using this configuration, we can extend the set of recovered frequencies by adjusting the angle of the tilted wave-front. Further, our methodology is designed to extend the NA by employing less tilted angles than other similar techniques. Hence, the final retrieved phase will have an enhanced lateral resolution without amplifying the numerical errors and employing a few tilted angles. Moreover, we show that the algorithm presented here can be combined with other TIE algorithms that are used for suppressing the Low Frequency Artifacts (LFAs) usually present when using TIE based techniques.
Deterministic Phase Retrieval techniques (DPRTs) employ a series of paraxial beam intensities in order to recover the phase of a complex field. These paraxial intensities are usually generated in systems that employ plane-wave illumination. This type of illumination allows a direct processing of the captured intensities with DPRTs for recovering the phase. Furthermore, it has been shown that intensities for DPRTs can be acquired from systems that use spherical illumination as well. However, this type of illumination presents a major setback for DPRTs: the captured intensities change their size for each position of the detector on the propagation axis. In order to apply the DPRTs, reescalation of the captured intensities has to be applied. This condition can increase the error sensitivity of the final phase result if it is not carried out properly. In this work, we introduce a novel system based on a Phase Light Modulator (PLM) for capturing the intensities when employing spherical illumination. The proposed optical system enables us to capture the diffraction pattern of under, in, and over-focus intensities. The employment of the PLM allows capturing the corresponding intensities without displacing the detector. Moreover, with the proposed optical system we can control accurately the magnification of the captured intensities. Thus, the stack of captured intensities can be used in DPRTs, overcoming the problems related with the resizing of the images. In order to prove our claims, the corresponding numerical experiments will be carried out. These simulations will show that the retrieved phases with spherical illumination are accurate and can be compared with those that employ plane wave illumination. We demonstrate that with the employment of the PLM, the proposed optical system has several advantages as: the optical system is compact, the beam size on the detector plane is controlled accurately, and the errors coming from mechanical motion can be suppressed easily.
Phase retrieval techniques based on the Transport of Intensity Equation (TIE) use a sequence of through-focus intensity
images in order to recover the phase information. Classically, the capturing of these images have been made using
equally spaced plane separations. Recently, it has been shown that the phase retrieval techniques based on TIE can be
carried out using unequally plane separations. In this work we compare quantitatively the phase reconstruction of various
TIE solvers using the equal and unequal plane separation strategy.
KEYWORDS: Signal to noise ratio, Phase retrieval, Neodymium, Error analysis, Solids, Computer simulations, Ions, Linear filtering, Chemical elements, Numerical analysis
The Transport of Intensity Equation (TIE) relates linearly the phase of an object to the intensity distribution in the Fresnel region and can be used as a phase retrieval technique. The key element in a TIE based solver is the calculation of the axial intensity derivative. This parameter is calculated from a series of captured intensities but its accuracy is subject to several parameters, such as e.g. the separation between the measurement planes, the Signal to Noise Ratio (SNR) in the captured intensities, the actual object phase distribution. Despite the importance of the estimation of this parameter, there is no general discussion how to optimize the axial intensity derivative. In this work, we developed the mathematical framework in which the retrieved phase can be obtained. An optimal separation is derived, which minimizes the error in the calculation of the axial derivative. Besides this, we study using a numerical analysis how the accuracy of the axial derivative influence the accuracy of the retrieved phase. Hence, we present a numerical procedure based in the Root Square Mean Error, which is able to minimized the error in the retrieved phase. It is later shown that this analysis is significant more accurate than available methods proposed in the literature. It is further shown, that the plane separation that minimizes the error in the axial intensity derivative is different to the plane separation that minimizes the error in the retrieved phase.
The transport of intensity equation (TIE) describes the relation between the object phase and the intensity distribution in
the Fresnel region and can be used as a non-interferometric technique to estimate the phase distribution of an object. A
number of techniques have been developed to solve the TIE. In this work we focus on one popular class of Poisson
solvers that are based on Fourier and the Multigrid techniques. The aim of this paper is to present an analysis of these
types of TIE solvers taking into account the effect of the boundary condition, i.e. the Neumann Boundary Condition
(NBC), the Dirichlet Boundary Condition (DBC), and the Periodic Boundary Condition (PBC). This analysis, which
depends on the location of an object wave-front in the detector plane, aims to identify the advantages and disadvantage
of these kinds of solvers and to provide the rules for choice of the best fitted boundary condition.
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