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.

Broadband behavior of an optical-digital focus-invariant system.

We present experimental evidence that demonstrates a greatly increased depth of field in a broadbandilluminated imaging system through the use of a special-purpose phase mask and digital filtering. The phase mask is of a simple rectangularly separable cubic-phase design, whereas the digital filtering used was a simple object-independent least-squares inverse filter. We demonstrate successful operation of the system over a range corresponding to 30 times the Hopkins criterion for allowable misfocus.

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.

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.