Extended axial irradiances: Barker rings.

For extending focal depth we employ a set of transparent concentric rings, which are coded with the Barker sequences of length L. At the neighborhood of the paraxial focal plane, these transparent masks generate an axial uniform distribution, which is modulated with sinusoidal variations. For imaging applications, one can extend focal depth if the Barker length is congruent to unity modulo 4. And, for optical trapping, a bottle neck irradiance distribution is generated if the Barker length is congruent to three modulo 4.

Two-conjugate zoom system: the zero-throw advantage.

We present the Gaussian design of a two-conjugate zoom system, which does not require any mechanical compensation. The device works in two stages. First, with fixed optical power, a lens images the pupil aperture, forming a pair of conjugate planes. Then, we invert the conjugate planes for setting the two-conjugate condition. At the second stage, two varifocal lenses generate a tunable magnified virtual image, at the fixed object plane. The varifocal lenses have fixed interlens separation, and they work with zero-throw. We specify the optical powers of the composing elements and the equivalent optical power as functions of the variable magnification.

Reducing field depth: annular Hadamard masks.

For optically narrowing field depth, we explore the use of annular masks that are coded with the elements of Hadamard matrices. We show that with no further reduction of light throughput, these annular masks can enhance the influence of focus error on the modulation transfer functions (MTF). We report numerical evaluations of the irradiance point spread functions (PSFs), their associated MTFs, and of some digitally generated images. For complementing our assessments, we evaluate the Fisher information of these Walsh-Hadamard, annular masks. We suggest an optical technique for breaking 3-D scenes into several 2-D sliced frames by translating out-of-focus images into background noise.

Schlieren masks: square root monomials, sigmoidal functions, and off-axis Gaussians.

By using an effective transfer function, one can describe conveniently the nonlinear mapping between an input thin transparent structure and its image irradiance distribution. This effective transfer function is useful for making sound comparisons between several spatial filters employed for phase rendering. Here, we unveil three nonconventional Schlieren techniques, which employ absorption masks whose amplitude distributions are described by square root monomials, by sigmoidal functions, or by off-axis Gaussian functions. We apply the effective transfer function for analyzing the similarities between the proposed masks and other Schlieren techniques.

Hopkins procedure for tunable magnification: surgical spectacles.

We analyze the use of two varifocal lenses, with fixed interlens separation, for achieving tunable magnification at a specific throw. Our discussion extends the Hopkins procedure circumscribed to the determination of fixed optical powers in a multilens system. We illustrate our results by presenting the Gaussian optics design of surgical spectacles, which have tunable magnification while generating virtual images with zero throw. We also report novel formulas describing this type of two-lens zoom system, which works without any mechanical compensation.

Pseudo-random masks for angular alignment.

We present an alignment technique that exploits angular correlations by employing a pair of masks, which encode in an angular format pseudo-random sequences. The angular correlator generates peaked irradiance distributions on-axis, provided that the elements of the pair are aligned. Otherwise, the on-axis irradiance distribution decreases to a minimum value. Since the proposed angular correlator is independent of the lateral magnification, it is useful for testing the performance of varifocal lenses. A merit function describes the tolerance to focus errors associated with the location of a small size detector. We use linearly polarized films for showing that the technique also works well with broad band light.

Multiple-frame photography for extended depth of field.

For extending the depth of field, we analyze the result of superimposing several snapshots, which are taken while changing the amount of focus error, at full pupil aperture. We unveil the use of a varifocal lens for controlling the amount of focus error, without modifying either the lateral magnification or light throughput. After recording a set of snapshots, we use suitable acquisition factors for shaping an optical transfer function, which has reduced sensitivity to focus errors.

Conjugate phase plate use in analysis of the frequency response of imaging systems designed for extended depth of field.

We unveil a relationship between generating a point spread function with a pair of conjugate phase elements and visualizing the modulation transfer function (MTF) of a single phase element for a variable focus error, at a tunable spatial frequency. We show that the defocused MTF of a pair of conjugate phase elements can be expressed as the modulus of the second order ambiguity function of a single phase element. Finally, we propose a tunable wavefront coding technique with a pair of quartic (4th power) conjugate phase elements.

Ambiguity function analysis of pulse train propagation: applications to temporal Lau filtering.

We use the periodic-signal ambiguity function for visualizing the intensity-spectrum evolution through propagation in a first-order dispersive medium. We show that the degree of temporal coherence of the optical source plays the role of a low-pass filter on the signal's ambiguity function. Based on this, we present a condition on the temporal Lau effect for filtering harmonics at fractions of the Talbot length. This result allows one to increase the repetition rate of a pulse train obtained from a sinusoidally phase-modulated CW signal.

Bow-tie effect: differential operator.

We propose to use a differential operator for representing the influence of phase-only filters on the defocused modulation transfer function of the clear pupil aperture. We present a phase-only filter that implements optically Taylor's theorem in phase space. We show numerical simulations of the modulation transfer functions and the images that can be obtained by using the proposed filter.

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.

High focal depth with fractional-power wave fronts.

We explore the use of phase profiles with fractional power for tailoring modulation transfer functions with high focal depth at high pupil apertures. We present numerical simulations of the images that can be obtained with certain fractional-power profiles.