Computer-generated holograms of three-dimensional realistic objects recorded without wave interference

We propose a method of synthesizing computer-generated holograms of real-life three-dimensional (3-D) objects. An ordinary digital camera illuminated by incoherent white light records several projections of the 3-D object from different points of view. The recorded data are numerically processed to yield a two-dimensional complex function, which is then encoded as a computer-generated hologram. When this hologram is illuminated by a plane wave, a 3-D real image of the object is reconstructed.     

Signal-to-noise ratio development for quality engineering

Dr. Taguchi developed the concept of signal-to-noise (SN) ratio in quality engineering to evaluate the performance of a system. The objective is to develop systems which are robust against noise factors. The SN ratio indicates the degree of the predictable performance of a product or process in the presence of noise factors. Parameter design of the Taguchi method optimizes the SN ratio in the domain of control factors, so that performance could be made insensitive to the noise factors in order to improve product quality. If the domain of the control factors is a continuous space, the problem is a non-linear programming problem. Usually, in practice, there are only a few available levels for the control factors. Thus, experimental design methods can be useful for such problems. The SN ratio for four cases of dynamic characteristic problems is developed in this paper. This paper also gives the method to compute SN ratios for both equispaced and non-equispaced intervals for levels of signal factors. Two examples are presented to illustrate the method.     

Signal-to-noise ratio in microelectrode-array-based electrochemical detectors

The signal-to-noise ratio at an electrode array depends on the electrode area, the perimeter-to-area ratio of the electroactive portion of the surface, the mass transfer coefficient of the analyte-electrode combination, the measurement bandwidth, and the sources and magnitudes of the noises. Simple models for chronoamperometry with an array in quiescent solution and for hydrodynamic current at an array in one wall of a rectangular conduit through which analyte-containing solution is following are given. Noises from seven sources, including environmental noises, are considered in a noise model. The signal and noise models are combined to yield a model for signal-to-noise ratio at array-based electrochemical detectors. There exists an optimum array density for a given area that depends on the noise power, noise resistance, the current density at a sparse array, and the current density at a solid electrode of the same area. Approximations that lead to simple expressions for the optimum electroactive area fraction and noise resistance lead to results that are in good agreement with more complex and less approximate calculations. Electrodes of millimeter dimensions consisting of about 1% active surface with electroactive "pieces" of micrometer dimensions are anticipated to yield detection limits of about 1 fmol injected into a typical packed-column liquid chromatograph. This corresponds to about 10(-10) M analyte in the detector and about an order of magnitude improvement over solid electrodes.     

Reconstruction dynamics of recorded holograms in photochromic glass

We have investigated the dynamics of the record-erase process of holograms in photochromic glass using continuum Nd:YVO? laser radiation (λ=532 nm). A bidimensional microgrid pattern was formed and visualized in photochromic glass, and its diffraction efficiency decay versus time (during reconstruction step) gave us information (D, Δn) about the diffusion process inside the material. The recording and reconstruction processes were carried out in an off-axis setup, and the images of the reconstructed object were recorded by a CCD camera. Measurements realized on reconstructed object images using holograms recorded at a different incident power laser have shown a two-stage process involved in silver atom kinetics.     

Signal-to-noise ratio of phase sensing telescope interferometers

The paper described is the third part of a trilogy dealing with the principles, performance, and limitations of what the author named "telescope-interferometers" (TIs). The basic idea consists in transforming one telescope into a wavefront error (WFE) sensing device. This can be achieved in two different ways, namely, off-axis and phase-shifting TIs. In both cases the point-spread function measured in the focal plane of the telescope carries information about the transmitted WFE, which is retrieved by fast and simple algorithms suitable to an adaptive optics (AO) regime. The uncertainties of both types of TIs are evaluated in terms of noise and systematic errors. Numerical models are developed to establish the dependence of driving parameters such as useful spectral range, angular size of the observed star, or detector noise on the total WFE measurement error. The latter is found particularly sensitive to photon noise, which rapidly governs the achieved accuracy for telescope diameters higher than 10 m. A few practical examples are studied, showing that the TI method is applicable to AO systems for telescope diameters ranging from 10 to 50 m, depending on seeing conditions and magnitude of the observed stars. Also discussed is the case of a space-borne coronagraph, where the TI technique provides high sampling of the input WFE map.     

Magnified reconstruction of digitally recorded holograms by Fresnel-Bluestein transform

A method for numerical reconstruction of digitally recorded holograms with variable magnification is presented. The proposed strategy allows for smaller, equal, or larger magnification than that achieved with Fresnel transform by introducing the Bluestein substitution into the Fresnel kernel. The magnification is obtained independent of distance, wavelength, and number of pixels, which enables the method to be applied in color digital holography and metrological applications. The approach is supported by experimental and simulation results in digital holography of objects of comparable dimensions with the recording device and in the reconstruction of holograms from digital in-line holographic microscopy.     

Twin-sensitivity measurement by spatial multiplexing of digitally recorded holograms

We present an all-numeric multiplexing/demultiplexing technique for digitally recorded holograms that allow the simultaneous determination of the in-plane and the out-of-plane components of the displacement vector of an object submitted to some loading. The twin-sensitivity measurement is obtained from two different illumination directions that give two sensitivity vectors. The spatial multiplexing is achieved by an incoherent mixing of two duplets of coherent waves that produce holograms carried with orthogonal polarized reference waves. The spatial demultiplexing uses the autocorrelation function of the multiplexed holograms as a position estimator. The estimator then enables the determination of the pixel-to-pixel correspondence between the holograms for the double component determination. Results of the experiment are presented.     

Compressive holography of diffuse objects

We propose an estimation-theoretic approach to the inference of an incoherent 3D scattering density from 2D scattered speckle field measurements. The object density is derived from the covariance of the speckle field. The inference is performed by a constrained optimization technique inspired by compressive sensing theory. Experimental results demonstrate and verify the performance of our estimates.     

Signal-to-noise ratio analysis of all-fiber common-path optical coherence tomography

We present theoretical analysis and experimental verification of the signal to noise ratio (SNR) of a common-path interferometer-based optical coherence tomography (OCT) system. Based on fully integrated all-fiber implementation of a common-path time-domain OCT system, we derived the SNR of the system including the effect of beat noise, which turns out to be twice as large as the excess noise term. We verified the theoretical SNR through a series of experiments, utilizing both controlled phantom and biological samples such as a rat brain with tumor and a frog retina. The results showed that the source power and the reference reflectivity can be easily controlled to optimize the SNR of OCT imaging. We have also analyzed the effect of the fiber delays and the offset in the fiber autocorrelator of the common-path OCT system on the overall SNR.     

Sidelobeless multiple-object discriminant filters recorded as discrete-type computer-generated holograms

The computer generation of sidelobeless multiple-object discriminant correlation filters has been stressed. We propose to synthesize the filter functions by use of the simulated-annealing algorithm. By this method the filters can be obtained as discrete-type computer-generated holograms. The filters can suppress the sidelobes and provide sharp correlation peaks. A computer simulation and an optical experiment were performed, and the expected correlation responses were obtained.     

Signal-to-noise ratio study of full-field fourier-domain optical coherence tomography

We report a new approach in optical coherence tomography (OCT) called full-field Fourier-domain OCT (3F-OCT). A three-dimensional image of a sample is obtained by digital reconstruction of a three-dimensional data cube, acquired with a Fourier holography recording system, illuminated with a swept source. We present a theoretical and experimental study of the signal-to-noise ratio of the 3F-OCT approach versus serial image acquisition (flying-spot OCT) approach.     

Signal-to-noise ratio threshold effect in track before detect

Track before detect (TBD) refers to simultaneous detection and tracking using unthresholded sensor responses over time. The motivation for TBD is its capacity to deal with low signal-to-noise ratio (SNR) targets. Previously, the achievable error for TBD has been established using Cramer?Rao analysis. Although computationally simple the Cramer?Rao bound is not useful at low SNR as it does not predict the threshold effect. A more accurate notion of the achievable performance at low SNRs is provided by the computationally more complicated Barankin bound. The computational complexity of the Barankin bound arises from the need to optimise over a number of test points, with the tightness of bound increasing with the number of test points. An approximation to the Barankin bound is proposed which permits the use of multiple test points with reasonable computational expense. The improvements in threshold SNR prediction offered by the proposed bound are demonstrated in numerical examples.     

Extended focused imaging for digital holograms of macroscopic three-dimensional objects

When a digital hologram is reconstructed, only points located at the reconstruction distance are in focus. We have developed a novel technique for creating an in-focus image of the macroscopic objects encoded in a digital hologram. This extended focused image is created by combining numerical reconstructions with depth information extracted by using our depth-from-focus algorithm. To our knowledge, this is the first technique that creates extended focused images of digital holograms encoding macroscopic objects. We present results for digital holograms containing low- and high-contrast macroscopic objects.     

Computer-generated holograms for three-dimensional surface objects with shade and texture

Digitally synthetic holograms of surface model objects are investigated for reconstructing three-dimensional objects with shade and texture. The objects in the proposed techniques are composed of planar surfaces, and a property function defined for each surface provides shape and texture. The field emitted from each surface is independently calculated by a method based on rotational transformation of the property function by use of a fast Fourier transform (FFT) and totaled on the hologram. This technique has led to a reduction in computational cost: FFT operation is required only once for calculating a surface. In addition, another technique based on a theoretical model of the brightness of the reconstructed surfaces enables us to shade the surface of a reconstructed object as designed. Optical reconstructions of holograms synthesized by the proposed techniques are demonstrated.     

Signal-to-noise ratio for astronomical imaging by deconvolution from wave-front sensing

One method for improving the quality of astronomical images measured through a atmospheric turbulence uses simultaneous short-exposure measurements of both an image and the output of a wave-front sensor exposed to an image of the telescope pupil. The wave-front sensor measurements are used to reconstruct an estimate of the instantaneous generalized pupil function of the telescope, which is used to compute an estimate of the instantaneous optical transfer function, which is then used in a deconvolution procedure. This imaging method has been called both deconvolution from wave-front sensor (DWFS) measurements and self-referenced speckle holography. We analyze the signal-to-noise ratio (SNR) behavior of this imaging method in the spatial frequency domain. The analysis includes effects arising from differences in the correlation properties of the incident and the estimated pupil phases and the fact that the object-spectrum estimator is a randomly filtered doubly stochastic Poisson random process. SNR resultsobtained for the DWFS method are compared with the speckle-imaging powerspectrum SNR for equivalent seeing conditions and light levels. It is shown that for unresolved stars the power-spectrum SNR is superior to the DWFS SNR. However, for extended objects the power-spectrum SNR and the DWFS SNR are similar. Since speckle imaging uses a separate Fourier phasereconstruction process not required by the DWFS method, the DWFS method provides an alternative to speckle imaging that uses simple postprocessing at the cost of a wave-front sensor measurement but with no loss of SNR performance for extended objects.     

Analytical design for computer-generated Fourier holograms of shaded multi-polygonal three-dimensional objects

We report here on design and computer simulation of computer-generated holograms for three dimensional (3D) imaging and display. Angular spectrum of general polygon patches was calculated in closed analytical form that includes angular dependence of the intensity and linear gradient of phase at each polygon. Special attention was paid to reduction of the dynamic range in the amplitude transmittance of the hologram by proper random choices of slopes and initial phases of each polygon. Numerical computer simulation results proved that our polygon-patched design demonstrates halftones of object shades and shows expected sharp focusing of different parts of the reconstructed 3D images in their different cross-sections.     

Computer-generated holograms of three-dimensional objects synthesized from their multiple angular viewpoints

Synthesizing computer-generated holograms (CGHs) of a general three-dimensional (3D) object is usually a heavy computational task. We propose and demonstrate a new algorithm for computing CGHs of 3D objects. In our scheme, many different angular projections of computer-designed 3D objects are numerically processed to yield a single two-dimensional complex matrix. This matrix is equivalent to the complex amplitude of a wave front on the rear focal plane of a spherical lens when the object is located near the front focal point and illuminated by a plane wave. Therefore the computed matrix can be used as a CGH after it is encoded to a real positive-valued transparency. When such CGH is illuminated by a plane wave, a 3D real image of the objects is constructed. The number of computer operations are equivalent to those of a two-dimensional Fourier CGH. Computer and optical constructions of 3D objects, both of which show the feasibility of the proposed approach, are described.