Jorge Ojeda-Castaneda

MULTILEVEL PHASE GRATINGS FOR ARRAY ILLUMINATORS

We describe a variety of multilevel phase structures that can be used to generate Lohmanns array illuminators. We report several experimental verifications of the synthesis of such multilevel phase structures by using simple binary curves in a conventional optical processor.

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.

Irradiance at Fresnel planes of a phase grating

The Wigner distribution function is used to describe general properties of the irradiance distribution at the Fresnel diffraction planes of one-dimensional phase gratings. We report a remarkably simple, analytical expression for the irradiance distribution at one quarter of the Talbot length of any phase grating. As illustrative examples, we consider binary and triangular phase profiles.

Fresnel diffraction of substructured gratings: matrix description.

We present a matrix formalism to describe the near-field diffraction pattern, at fractions of a Talbot distance, of a grating whose unit cell is composed of a discrete substructure. We show that this formalism is useful for designing Lohmann array illuminators.

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 Taylors 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.

Numerical optimization of phase-only elements based on the fractional Talbot effect

Based on the matrix description of the fractional Talbot effect, a new and effective method to numerically optimize diffractive optical elements that work in the Fresnel diffraction regime is described. When the investigation is restricted to spatially quantized phase-only gratings, diffraction can be described in terms of the fractional Talbot effect and the diffraction amplitude is efficiently evaluated from a finite set of sampling points. As an illustrating example we numerically optimize Talbot array illuminators. Our results show that a limited number of discrete phase levels does not imply a limited compression ratio but does lead to a reduced diffraction efficiency. Experimental results obtained from lithographically fabricated surface-relief gratings are compared with our theoretical designs.

Increased depth of field with phase-only filters: ambiguity function (Invited Paper)

We discuss the symmetry properties of the Ambiguity Function. Next, we use it as a design tool for increasing the depth of field of imaging systems. We present a family of anti-symmetric phase-only masks that extend the depth of field of an optical system. We compute several Optical Transfer Functions with focus errors, and we report numerical simulations of the images that can be achieved using our proposed phase-only filters.

Phase mask for high focal depth

We present a phase mask that substantially reduces the influence of focus error of an optical system; while preserving light gathering power, and lateral resolution. Numerical simulations and first experimental results are shown.

Simultaneous Cartesian coordinate display of defocused optical transfer functions

We show that by using a binary spatial filter and a square-law detector we can display all the defocused optical transfer functions (OTFs) in a given study in a single picture. The resulting unique picture has as its horizontal coordinates the spatial frequency and as its vertical coordinates the amount of defocus. The gray-level variations are proportional to the modulus of the OTF, that is, the modulation transfer function. Numerical simulations are included.

Multiplicative noise reduction using the Lau effect

The extension of the Talbot effect to incorporate noncoherent light is known as the Lau effect. Here, we employ the Lau effect for substantially reducing the influence of binary multiplicative noise on periodic patterns. The method proposed may be lensless. The coherence theory of our proposal and experimental verifications are included.