Extended depth of field through an axicon

One of the main disadvantages of imaging systems is the limited depth of field. We present the ability of a refractive axicon for imaging with an extended depth of field. We design an imaging system with a two-step imaging approach that uses a CCD camera to capture intermediate images and uses a digital process to obtain the final images. The depth of field is analyzed based on the condition of the focal segment. In particular, the point spread functions (PSFs) are discussed in simulation in detail. The performed experiments validate the effect and feasibility of the axicon for imaging with an extending depth of field.     

Control of chromatic focal shift through wave-front coding

Control of chromatic aberration through purely optical means is well known. We present a novel, to our knowledge, optical-digital method of controlling chromatic aberration. The optical-digital system, which incorporates a cubic phase-modulation (CPM) plate in the optical system and postprocessing of the detected image, effectively reduces a system's sensitivity to misfocus in general or axial (longitudinal) chromatic aberration, in particular. A fully achromatic imaging system (one that is corrected for a continuous range of wavelengths) can be achieved by initial optimization of the optical system for all aberrations except chromatic aberration. The chromatic aberration is corrected by the inclusion of the CPM plate and postprocessing.     

Passive ranging through wave-front coding: information and application

Passive-ranging systems based on wave-front coding are introduced. These single-aperture hybrid optical-digital systems are analyzed by use of linear models and the Fisher information matrix. Two schemes for passive ranging by use of a single aperture and a single image are investigated: (i) estimating the range to an object and (ii) detecting objects over a set of ranges. Theoretical limitations on estimator-error variances are given by use of the Cramer-Rao bounds. Evaluations show that range estimates with less than 0.1% error can be obtained from a single wave-front coded image. An experimental system was also built, and example results are given.     

Extended depth of field using shapelet-based image analysis

One way to extend depth of field of any optical system is to take several images with different focus positions and combine them into a single composite image, which contains all regions fully focused. The challenge then becomes to select from each image the pixels that are in focus. We describe a new focus measure based on the shapelet decomposition. Results using simulated images with high noise content show that the shapelet-based focus measure is the most performance that traditional neighborhood-based focus approaches. Similarly shapelet focus measure provides significant improvement compared to traditional methods when objects have nontextured or homogeneous regions.     

Extended depth of field with a nonlinear silver-halide emulsion detector

Presented here are experimental results of an extended depth-of-field (EDF) system using film to record the image. The EDF system used is an application of wave-front coding. A phase mask is placed in the aperture stop of the lens to code the image data; then digital signal processing is used to decode the image. Wave-front coding is based on linear systems theory, but film is not a linear medium. An extra step of linearization is then needed to apply the technique. Both nonlinear and linearized results are shown, as is a test image that demonstrates the success of the technique for nonlinear media.     

Extended depth of field in hybrid imaging systems: Circular aperture

Abstract

A hybrid imaging system combines a modified optical imaging system and a digital post-processing step. A spatial-domain method is described to design a pupil phase plate to extend the depth of field of an incoherent hybrid imaging system with a circular aperture. This method is used to obtain a pupil phase plate to extend the depth of field, and is referred to as the EDF circular phase plate. By introducing an EDF circular phase plate at the exit pupil of a simulated diffraction-limited system and digitally processing the output of the detector, the depth of field is extended by approximately an order of magnitude more than the Hopkins defocus criterion.     

Realizations of focus invariance in optical-digital systems with wave-front coding

We report experimental verification of an extended depth of focus (EDF) system with near-diffraction-limited performance capabilities. Dowski and Cathey [Appl. Opt. 34, 1859-1866 (1995)] described the theory of this system in detail. We can create an EDF system by modifying a standard incoherent optical system with a special cubic phase plate placed at the aperture stop. We briefly review the theory and present the first optical experimental verification of this EDF system. The phase plate codes the wave front, producing a modified optical transfer function. Once the image is transformed into digital form, a signal-processing step decodes the image and produces the final in-focus image. We have produced a number of images from various optical systems using the phase plate, thus demonstrating the success of this EDF system.     

Extended coding for optical array logic

We present extended coding for optical array logic (OAL) to avoid the marginal effect. The marginal effect is defined as an effect caused by the finite size of the image region, and it is a problem in massively parallel processing by OAL. OAL is a paradigm of optical computing suitable for optical implementation utilizing image coding and discrete correlation. To avoid the marginal effect in the context of OAL, we propose a new coding rule and consider possible operations with this coding. With extended coding, binary data can be identified from background with the same number of pixels as that used in the original OAL. Simulation results of the operations verify the correctness of the proposed technique.     

Ensemble-averaged Shack-Hartmann wave-front sensing for imaging through turbid media

A technique is described for ensemble-averaging the light wave emerging from a turbid medium, enabling the recovery of optical information that is otherwise lost in a speckle pattern. The technique recovers both an amplitude and a phase function for a wave that has been corrupted by severe scattering, without the use of holography. With the phase estimated, an ensemble-averaged field is constructed that can be backprojected to form an image of the object obscured by the scattering medium. Experimental results suggest that the technique can resolve two object points whose signals are unresolved on the exit surface of a diffuser.     

Extended phase modulation depth in twisted nematic liquid crystal displays

We show how the phase modulation depth in twisted nematic liquid crystal displays (TNLCDs) can be increased dramatically by selecting a polarization configuration with a reduced mean intensity transmission. This phenomenon, which we have validated with various devices, is shown here for a device that presents a phase-only modulation only slightly over π radians in our classical rotated eigenvector configuration, but it is capable of producing close to a 2π phase depth for a configuration with 5% mean intensity transmission. A quantitative explanation is presented by means of a phasor analysis of the TNLCD eigenvector projections over input and output polarization states. The proposed technique can be a very useful solution in modern TNLCDs that have a very thin liquid crystal layer and a reduced maximum achievable phase modulation.     

Extended pseudorandom sequences and two-dimensional coding collimators based on them

A new extensive class of one-dimensional binary sequences, called extended pseudorandom sequences, is proposed which enables a radiation-physics experiment to be optimized more completely and enables problems of planar emission tomography to be solved effectively using integral-code measuring systems. __________ Translated from Izmeritel’naya Tekhnika, No. 6, pp. 66–71, June, 2007.     

Extended ternary sequences and two-dimensional coding collimators based on them

A new extensive class of one-dimensional ternary (−1, 0, +1)-sequences, called extended ternary sequences, is proposed, which enables radiation-physics experiments to be more completely optimized and enables problems of emission planar tomography to be solved more effectively using code-based integrated measurement systems. __________ Translated from Izmeritel'naya Tekhnika, No. 8, pp. 62–68, August, 2008     

Branch-point reconstruction in laser beam projection through turbulence with finite-degree-of-freedom phase-only wave-front correction

Wave-front sensing and deformable mirror control algorithms in adaptive optics systems are designed on the premise that a continuous phase function exists in the telescope pupil that can be conjugated with a deformable mirror for the purpose of projecting a laser beam. However, recent studies of coherent wave propagation through turbulence have shown that under conditions where scintillation is not negligible, a truly continuous phase function does not in general exist as a result of the presence of branch points in the complex optical field. Because of branch points and the associated branch cuts, least-squares wave-front reconstruction paradigms can have large errors. We study the improvement that can be obtained by implementing wave-front reconstructors that can sense the presence of branch points and reconstruct a discontinuous phase function in the context of a laser beam projection system. This study was conducted by fitting a finite-degree-of-freedom deformable mirror to branch-point and least-squares reconstructions of the phase of the beacon field, propagating the corrected field to the beacon plane, and evaluating performance in the beacon plane. We find that the value of implementing branch-point reconstructors with a finite-degree-of-freedom deformable mirror is significant for optical paths that cause saturated log-amplitude fluctuations.     

Image transfer through cirrus clouds. I. Ray trace analysis and wave-front reconstruction

A new technique for modeling image transfer through cirrus clouds is presented. The technique uses a ray trace to model beam propagation through a three-dimensional volume of polydisperse, hexagonal ice crystals. Beyond the cloud, the technique makes use of standard Huygens-Fresnel propagation methods. At the air-cloud interface, each wave front is resolved into a ray distribution for input to the ray trace software. Similarly, a wave front is reconstructed from the output ray distribution at the cloud-air interface. Simulation output from the ray trace program is presented and the modulation transfer function for stars imaged through cirrus clouds of varying depths is discussed.     

Asymmetric phase masks for extended depth of field

We present a family of asymmetric phase masks that extends the depth of field of an optical system. To verify our proposal, we compute several modulation transfer functions with focus errors, and we report numerical simulations of the images that can be achieved by use of our proposed procedure.     

Improved depth map through optimal axis stereo

Feature-based stereo correspondence techniques suffer from the major limitation that it is difficult to match along epipolar lines and this often results in a sparse set of depth points. Past researchers attempted to solve this problem through trinocular stereo. In this paper, a new method has been proposed for reducing the sparsity of depth points by orienting the epipolar line of the cameras in a direction that maximizes the number of feature points. The corresponding epipolar axis has been termed as the optimal axis. Our analytical as well as simulation results have established that for a limited edge scenario, the proposed approach can lead to considerable improvement in the number of feature points that can be matched. We have introduced a figure-of-merit for the optimal axis and discussed how it is qualitatively related to the variance of the probability density function (pdf). We have also presented the results of our simulation experiment, termed as the random stick experiment. Finally, we have also shown the results of improved reconstructed surface of a synthetic image using optimal axis alignment.     

Gaussian weighting of ocular wave-front measurements

The measurement of ocular wave-front error gives insight into the optical performance of the eye and possibly a means for assessing visual performance. The visual system responds not only to the quality of the optical image formed on the retina but also to the processing that occurs in the retina and the brain. To develop a metric of visual performance based on wave-front error measurements, these latter processes must somehow be incorporated. In representing the wave-front error in terms of Zernike polynomials, it appears that terms with lower angular frequency have a greater deleterious effect on visual performance than higher-angular-frequency terms. A technique for weighting the pupil function of the eye with a Gaussian filter is demonstrated. It is further demonstrated that the variance of the Gaussian-weighted wave-front error is well correlated with visual performance.     

Wall coding for a field access bubble device

Device design and margins are given for bubble wall state coding in a field access Permalloy device. The wall states chosen to be the binary states are the S = 1 state and the S = ½, both of which have unsaturated capping layers. The 2.7 μm epitaxial (epi) garnet (YSmGdCaGe) is grown on top of a thin (0.2 μm) epi garnet (YNd GdCaGe) layer which has in-plane magnetization and is called a boot. The S = 1 state has 15 percent current margin and 20° phase margin: the S= ½ state has 45 percent current margin and 35° phase margin. The read-write bias margin is 18 Oe and is limited by the deflectometer detector.     

Measurement of wave-front aberration in soft contact lenses by use of a Shack-Hartmann wave-front sensor

Lower- and higher-order wave-front aberrations of soft contact lenses were accurately measured with a Shack-Hartmann wave-front sensor. The soft contact lenses were placed in a wet cell filled with lens solution to prevent surface deformation and desiccation during measurements. Aberration measurements of conventional toric and multifocal soft contact lenses and a customized soft contact lens have proved that this method is reliable. A Shack-Hartmann wave-front sensor can be used to assess optical quality of both conventional and customized soft contact lenses and to assist in enhancing lens quality control.