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.

Channel reduction and applications to image processing.

Oftentimes when one is dealing with digital color images it is desired that some sort of image processing be performed on the spatial information. Current methods require that one process each of the channels (also called planes or colors) of an image separately, which increases the number of computations significantly. A novel, to our knowledge, approach to reducing the number of channels in a color image is presented. The channel-reduction process is intended to facilitate such color image-processing situations essentially by the separation of the spectral information from the spatial information, as in a paint-by-numbers picture. In this case the image processing need be applied only to a single channel of data and the color added afterward. With a compression ratio of slightly less than 3:1 the method is not intended to compete with existing compression methods but rather to permit the processing of images in a compressed state.

Extended depth of field and aberration control for inexpensive digital microscope systems.

We present a new application and current results for extending depth of field using wave front coding. A cubic phase plate is used to code wave fronts in microscopy resulting in extended depths of field and inexpensive chromatic aberration control. A review of the theory behind cubic phase plate extended depth of field systems is given along with the challenges that are face when applying the theory to microscopy. Current results from the new extended depth of field microscope systems are shown.

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.

Defocus transfer function for circularly symmetric pupils.

We present a two-dimensional function that graphically illustrates the effects of defocus on the optical transfer function (OTF) associated with a circularly symmetric pupil function. We call it the defocus transfer function (DTF). The function is similar in application to the ambiguity function, which can be used to display the OTF associated with a defocused rectangularly separable pupil function. The properties of the DTF make it useful for analyzing optical systems with circularly symmetric pupils when one is interested in the OTF as a function of defocus. In addition to presenting these properties, we give examples of the DTF for systems with clear, bifocal, and annular pupil functions.

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 depth of field through wave-front coding.

We designed an optical-digital system that delivers near-diffraction-limited imaging performance with a large depth of field. This system is the standard incoherent optical system modified by a phase mask with digital processing of the resulting intermediate image. The phase mask alters or codes the received incoherent wave front in such a way that the point-spread function and the optical transfer function do not change appreciably as a function of misfocus. Focus-independent digital filtering of the intermediate image is used to produce a combined optical-digital system that has a nearly diffraction limited point-spread function. This high-resolution extended depth of field is obtained through the expense of an increased dynamic range of the incoherent system. We use both the ambiguity function and the stationary-phase method to design these phase masks.

Practical speed limits of free-space global holographic interconnects: time skew, jitter and turn-on delay.

The speed limits imposed on free-space global interconnects are affected by factors that can be divided into three groups: geometric parameters of the optical system that determine the propagation time and time skew, emitter parameters (turn-on delay and timing jitter), and system requirements (fan-in in the detector and bit error rate). For 32 × 32 global interconnects, numerical estimations of light propagation time and timing skew are presented. Time delay and jitter in a diode laser are calculated. After evaluation of these parameters, the timing and synchronization methods (gate and strobe or time of flight) can be selected, and the ultimate clock frequency of the overall system can be determined. The decisive role of contrast ratio and fan-in in the detector plane in determining the practical modulation rate of the diode laser is discussed.

Single-lens single-image incoherent passive-ranging systems.

We introduce a new system for single-lens single-image incoherent passive ranging. The only a priori object information this system requires is that the objects to be ranged must possess a low-pass spatial frequency spectrum. Physically, this system for passive ranging is a standard optical imaging system that is customized with a special-purpose optical mask or filter. Analytically, this optical mask customizes the transfer function of the optical system in such a way that objects form images that contain range-dependent information. This range-dependent information lies in the spatial spectrum nulls or zeros of the image.

Ferroelectric liquid-crystal-based binary optical memory employing feedback.

A two-dimensional bit-oriented refreshing optical memory that is loosely based on the design of an electronic flip-flop is presented. The test system consisted of two amorphous-silicon liquid-crystal optically addressed spatial light modulators placed into an inverting configuration to provide a stable refreshable memory element. A description of the optically addressed spatial light modulator device and its operation is presented. The optical design of the memory with the optically addressed spatial light modulator is described, and timing and component requirements are delineated. The results and analysis of testing for a one-pixel memory system are reported. The expected requirements and limitations of a multipixel system are discussed.

Optical database/knowledgebase machines.

In this paper we discuss various aspects of databases and knowledgebases and indicate how optics can play an important role in the solution of many of the previously unsolved problems in this field.

Superresolving phase conjugate scanning microscope.

Analytical and experimental results of a new type of optical scanning microscope, which uses a phase conjugate mirror and pinholes to achieve superresolution, are presented. The phase conjugate scanning microscope has a higher Rayleigh resolution limit and better sectioning discrimination than conventional, single pass, and double pass scanning microscopes. It also can reduce the effect of static and dynamic aberrations on the imaging process, is very easy to align, and has the potential of introducing optical power gain into the system.

Polarization-based optical parallel logic gate utilizing ferroelectric liquid crystals.

We describe parallel optical XOR and XNOR logic gates implemented with ferroelectric liquid-crystal (FLC) electro-optic elements to yield naturally a logic in which the binary gate outputs are indicated by two orthogonal polarizations of transmitted light. These gates absorb no power from the incident light beam and hence can be cascaded without the need to regenerate NOT inputs. The FLC elements also confer the advantages of low-voltage, low-power, submicrosecond switching and intrinsic two-state memory. Experimental results demonstrating the XOR and XNOR function are presented, along with measurements of the percentage of polarized light rotated into the two binary states.

Optical implementations of mathematical resolution.

Mathematical resolution is an algorithmic technique for reasoning from facts expressed in clause form to a conclusion. The technique is normally implemented on electronic computers with list-processing languages. This paper presents data representation and processing techniques for a parallel implementation using array-based optical logic. Implementations up through the quantified propositional calculus are presented, and the operations of resolvent formation, unification, and search are discussed. It is shown that a largely parallel formulation of resolution is possible, and optical technologies are suggested to implement this formulation.

Imaging through turbulent water using speckle reference holography.

A dramatic reduction in image distortion resulting from turbulent water has been demonstrated using speckle reference holography. Conventional photographs taken simultaneously over the same path clearly show that the holographic technique eliminates most image distortion.

Compensation for Atmospheric Phase Effects at 10.6 micro.

A holographic technique to compensate for atmospherically induced phase distortion of a 10.6-micro laser beam is presented. After a brief outline of the principle of adaptive phase-distortion compensation, the experimental setup to demonstrate feasibility is described. Results obtained for a reflecting target at distances of 150 m and 4600 m are presented and discussed in detail. It is shown that the power delivered onto a target and thus the return signal can be significantly increased by the principle of adaptive phase-distortion compensation. By compensating for phase distortions in both the transmitted and received beams, the signal-to-noise ratio of the received signal can be improved by a factor of N(2), N being the number of apertures used, if the phase relation was completely random beforehand. The results of these tests demonstrate that large arrays can be utilized in spite of the distorting effects which are normally produced by the atmosphere.