Resolution improvements in integral microscopy with Fourier plane recording.

Integral microscopes (IMic) have been recently developed in order to capture the spatial and the angular information of 3D microscopic samples with a single exposure. Computational post-processing of this information permits to carry out a 3D reconstruction of the sample. By applying conventional algorithms, both depth and also view reconstructions are possible. However, the main drawback of IMic is that the resolution of the reconstructed images is low and axially heterogeneous. In this paper, we propose a new configuration of the IMic by placing the lens array not at the image plane, but at the pupil (or Fourier) plane of the microscope objective. With this novel system, the spatial resolution is increased by factor 1.4, and the depth of field is substantially enlarged. Our experiments show the feasibility of the proposed method.

Free-depths reconstruction with synthetic impulse response in integral imaging.

Integral Imaging provides spatial and angular information of three-dimensional (3D) objects, which can be used both for 3D display and for computational post-processing purposes. In order to recover the depth information from an integral image, several algorithms have been developed. In this paper, we propose a new free depth synthesis and reconstruction method based on the two-dimensional (2D) deconvolution between the integral image and a simplified version of the periodic impulse response function (IRF) of the system. The period of the IRF depends directly on the axial position within the object space. Then, we can retrieve the depth information by performing the deconvolution with computed impulse responses with different periods. In addition, alternative reconstructions can be obtained by deconvolving with non-conventional synthetic impulse responses. Our experiments show the feasibility of the proposed method as well as its potential applications.

Random resampling masks: a non-Bayesian one-shot strategy for noise reduction in digital holography.

Holographic imaging may become severely degraded by a mixture of speckle and incoherent additive noise. Bayesian approaches reduce the incoherent noise, but prior information is needed on the noise statistics. With no prior knowledge, one-shot reduction of noise is a highly desirable goal, as the recording process is simplified and made faster. Indeed, neither multiple acquisitions nor a complex setup are needed. So far, this result has been achieved at the cost of a deterministic resolution loss. Here we propose a fast non-Bayesian denoising method that avoids this trade-off by means of a numerical synthesis of a moving diffuser. In this way, only one single hologram is required as multiple uncorrelated reconstructions are provided by random complementary resampling masks. Experiments show a significant incoherent noise reduction, close to the theoretical improvement bound, resulting in image-contrast improvement. At the same time, we preserve the resolution of the unprocessed image.

Digital holographic testing of biconvex lenses.

Lenses are one of the most important optical elements for manipulation of wavefronts. For their proper selection, the wavefronts produced by the lenses should be analyzed. Digital holography is a tool which provides whole-field reconstructions of wavefronts, and here the use of digital holographic interferometry in complete characterization of wavefronts from lenses is investigated. Digital holograms of the wavefront from the test lens are recorded for various positions of the test lens from a point source. The reconstructed phase of the wavefront from the test lens is compared with a digitally inputted wavefront for measurement of parallelism as well as curvature. The focal length of the test lens is computed by measuring the change in curvature of the wavefront for two positions of the test lens. The radius of curvature of the test lens is determined by using the test lens in the reflection mode. Refractive index of the lens material is also determined using this method. Detailed theoretical and experimental analysis is provided.

Multi-wavelengths digital holography: reconstruction, synthesis and display of holograms using adaptive transformation.

A method based on spatial transformations of multiwavelength digital holograms and the correlation matching of their numerical reconstructions is proposed, with the aim to improve superimposition of different color reconstructed images. This method is based on an adaptive affine transform of the hologram that permits management of the physical parameters of numerical reconstruction. In addition, we present a procedure to synthesize a single digital hologram in which three different colors are multiplexed. The optical reconstruction of the synthetic hologram by a spatial light modulator at one wavelength allows us to display all color features of the object, avoiding loss of details.

High-resolution far-field integral-imaging camera by double snapshot.

In multi-view three-dimensional imaging, to capture the elemental images of distant objects, the use of a field-like lens that projects the reference plane onto the microlens array is necessary. In this case, the spatial resolution of reconstructed images is equal to the spatial density of microlenses in the array. In this paper we report a simple method, based on the realization of double snapshots, to double the 2D pixel density of reconstructed scenes. Experiments are reported to support the proposed approach.

Automatic focusing in digital holography and its application to stretched holograms.

The searching and recovering of the correct reconstruction distance in digital holography (DH) can be a cumbersome and subjective procedure. Here we report on an algorithm for automatically estimating the in-focus image and recovering the correct reconstruction distance for speckle holograms. We have tested the approach in determining the reconstruction distances of stretched digital holograms. Stretching a hologram with a variable elongation parameter makes it possible to change the in-focus distance of the reconstructed image. In this way, the proposed algorithm can be verified at different distances by dispensing the recording of different holograms. Experimental results are shown with the aim of demonstrating the usefulness of the proposed method, and a comparative analysis has been performed with respect to other existing algorithms developed for DH.

3D integral imaging display by smart pseudoscopic-to-orthoscopic conversion (SPOC).

Previously, we reported a digital technique for formation of real, non-distorted, orthoscopic integral images by direct pickup. However the technique was constrained to the case of symmetric image capture and display systems. Here, we report a more general algorithm which allows the pseudoscopic to orthoscopic transformation with full control over the display parameters so that one can generate a set of synthetic elemental images that suits the characteristics of the Integral-Imaging monitor and permits control over the depth and size of the reconstructed 3D scene.

Optical implementation of micro-zoom arrays for parallel focusing in integral imaging.

We report 3D integral imaging with an electronically tunable-focal-length lens for improved depth of field. The micro-zoom arrays are generated and implemented based on the concept of parallel apodization. To the best of our knowledge, this is the first report of parallel dynamic focusing in integral imaging based on the use of micro-zoom arrays.

Numerical multiplexing and demultiplexing of digital holographic information for remote reconstruction in amplitude and phase.

We investigate the possibility to multiplexing (Mux) and demultiplexing (de-Mux) numerically digital holograms (DHs) with the aim of optimizing their storage and/or transmission process. The DHs are multiplexed and demultiplexed thanks to the unique property of the digital holography to numerically manage the complex wavefields. We show that it is possible to retrieve correctly quantitative information about the amplitude and phase of one hundred DHs. This result can be useful to transmit efficiently, in terms of reduced amount of data, the DHs from the recording head to a remote display unit.

Digital slicing of 3D scenes by Fourier filtering of integral images.

We present a novel technique to extract depth information from 3D scenes recorded using an Integral Imaging system. The technique exploits the periodic structure of the recorded integral image to implement a Fourier-domain filtering algorithm. A proper projection of the filtered integral image permits reconstruction of different planes that constitute the 3D scene. The main feature of our method is that the Fourier-domain filtering allows the reduction of out-of-focus information, providing the InI system with real optical sectioning capacity.

Spread-space spread-spectrum technique for secure multiplexing.

A novel technique for multiplexing complex images is proposed in which each image may be demultiplexed only if a set of random encryption keys is known. The technique utilizes the ability of the double random phase encoding method to spread a signals' energy in both the space and the spatial frequency domains in a controlled manner. To multiplex, images are independently encrypted with different phase keys and then superimposed by recording sequentially on the same material. Each image is extracted by using the particular key associated with it. During decryption the energy from the other images is further spread, making it possible to minimize its effects by using suitable filters. Wigner analysis is applied to the technique, and numerical results are presented.

Facet braiding: a fundamental problem in integral imaging.

A rigorous explanation of a phenomenon that produces significant distortions in the three-dimensional images produced by integral imaging systems is provided. The phenomenon, which we refer to as the facet-braiding effect, has been recognized in some previous publications, but to our knowledge its nature has never been analyzed. We propose a technique for attenuating the facet-braiding effect. We have conducted experiments to illustrate the consequences of the facet-braiding effect on three-dimensional integral images, and we show the usefulness of the proposed technique in eliminating this effect.

Enhanced viewing-angle integral imaging by multiple-axis telecentric relay system.

One of the main limitations of integral imaging is the narrow viewing angle. This drawback comes from the limited field of view of microlenses during the pickup and display. We propose a novel all-optical technique which allows the substantial increase of the field of view of any microlens and therefore of the viewing angle of integral-imaging displays.

Image recognition in the presence of non-Gaussian noise with unknown statistics.

We design receivers to detect a known pattern or a reference signal in the presence of very general and non-Gaussian types of noise. Three sources of input-noise degradation are considered: additive, multiplicative, and disjoint background. The detection process involves two steps: (1) estimation of the relevant noise parameters within the framework of hypothesis testing and (2) maximizing a certain metric that measures the likelihood of the target being at a given location. The parameter estimation portion is carried out by moment-matching techniques. Because of the number of unknown parameters and the fact that various types of input-noise processes are non-Gaussian, the methods that are used to estimate these parameters differ from the standard methods of maximizing the likelihood function. To verify the existence of the target at a certain location, we use l(p)-norm metric for p > or = 0 to measure the likelihood of the target being present at the location of interest. Computer simulations are used to show that for the images tested here, the receivers designed herein perform better than some existing receivers.

Noise robustness of nonlinear filters for image recognition.

We analyze the performance of the Fourier plane nonlinear filters in terms of signal-to-noise ratio (SNR). We obtain a range of nonlinearities for which SNR is robust to the variations in input-noise bandwidth. This is shown both by analytical estimates of the SNR for nonlinear filters and by experimental simulations. Specifically, we analyze the SNR when Fourier plane nonlinearity is applied to the input signal. Using the Karhunen-Loève series expansion of the noise process, we obtain precise analytic expressions of the SNR for Fourier plane nonlinear filters in the presence of various types of additive-noise processes. We find a range of nonlinearities that need to be applied that keep the output SNR of the filter stable relative to changes in the noise bandwidth.

Optimum receivers for pattern recognition in the presence of Gaussian noise with unknown statistics.

We develop algorithms to detect a known pattern or a reference signal in the presence of additive, disjoint background, and multiplicative white Gaussian noise with unknown statistics. The presence of three different types of noise processes with unknown statistics presents difficulties in estimating the unknown parameters. The standard methods such as expected-maximization-type algorithms are iterative, and in the framework of hypothesis testing they are time-consuming, because corresponding to each hypothesis one must estimate a set of parameters. Other standard methods such as setting the gradient of the likelihood function with respect to the unknown parameters will lead to a nonlinear system of equations that do not have a closed-form solution and require iterative methods. We develop an approach to overcome these handicaps and derive algorithms to detect a known object. We present new methods to estimate unknown parameters within the framework of hypothesis testing. The methods that we present are direct and provide closed-form estimates of the unknown parameters. Computer simulations are used to show that for the images tested, the receivers that we have designed perform better than existing receivers.

Real-time three-dimensional object recognition with multiple perspectives imaging.

A novel system for recognizing three-dimensional (3D) objects by use of multiple perspectives imaging is proposed. A 3D object under incoherent illumination is projected into an array of two-dimensional (2D) elemental images by use of a microlens array. Each elemental 2D image corresponds to a different perspective of the 3D object. Multiple perspectives imaging based on integral photography has been used for 3D display. In this way, the whole set of 2D elemental images records 3D information about the input object. After an optical incoherent-to-coherent conversion, an optical processor is employed to perform the correlation between the input and the reference 3D objects. Use of micro-optics allows us to process the 3D information in real time and with a compact optical system. To the best of our knowledge this 3D processor is the first to apply the principle of integral photography to 3D image recognition. We present experimental results obtained with both a digital and an optical implementation of the system. We also show that the system can recognize a slightly out-of-plane rotated 3D object.

Hidden images in halftone pictures.

A method of concealing an image in a different halftone image is proposed. Continuous-tone levels of the visible images are represented by the area of the halftone dots. However, the hidden image is encoded by the dots' positions inside their cells. Only a spatial correlator with a unique filter function can reveal the hidden image from the halftone picture. The technique and its robustness to noise and distortions are demonstrated.

Shift-invariant three-dimensional object recognition by means of digital holography.

We present an optoelectronic method to analyze three-dimensional (3D) scenes that is able to detect the presence, and also the position and orientation, of a reference 3D object. The data-acquisition procedure is based on digital holography. A phase-shifting interferometer records a single digital Fresnel hologram of the 3D scene with an intensity-recording device. Holographic information of the 3D reference object is also obtained with the same method. Correlation techniques are then applied to recognize the presence and position of the 3D reference object in the 3D scene. The technique also allows us to detect the 3D reference with a small out-of-plane rotation. Preliminary experimental results are presented that demonstrate the theory.