J. Ojeda-Castañeda

Talbot array illuminators with binary phase gratings

We establish that, in six different cases, binary phase gratings can be applied to implement Talbot array illuminators. Three of the six cases are reported for what is to our knowledge the first time.

On-axis diffractional behavior of two-dimensional pupils

We show that, at any Fresnel number, a suitable one-dimensional Fourier transform relates the complex-amplitude distribution along the optical axis with the zero-order circular harmonic of the amplitude transmittance of a two-dimensional diffracting screen. First, our general result is applied to recognize that any rationally nonsymmetric screen generates an axial-irradiance distribution that exhibits focal shift. In this way we identify a wide set of two-dimensional screens that produce the same focal shift as that produced by the clear circular aperture. Second, we identify several apodizers for shaping the axial-amplitude distribution. We discuss some examples for achieving high-precision focusing, axial hyperresolution, or high focal depth.

Zero axial irradiance by annular screens with angular variation

For optical alignment, it may be convenient to use a three-dimensional diffraction pattern with zero irradiance along the optical axis. This pattern is created here by using annular screens in the form of a phase daisy, a daisy flower, or a pie, with an even number of slices of an equal central angle and with every other slice with a phase retardation of 180 degrees . We recognize this form of angular variation as a particular solution of a wider set of functions that are able to produce zero axial irradiance.

Noncoherent Talbot effect: Coherence theory and applications

Abstract We discuss the coherence theory of the bands generated by using an incoherently illuminated grating at infinity, and other gratings at finite distances. Our discussion is applied to the design of a noncoherent technique for spatial frequency enhancement, and a novel interferometer. Experimental results are included.

Supergaussian beams of continuous order as GRIN modes

Abstract It is recognized that for certain planar waveguides, and for certain cylindrical GRIN fibers, some diffraction modes are supergaussian beams of continuous order.

LENSLESS THETA DECODER WITH HIGH LIGHT THROUGHPUT

Abstract We describe a lensless method for obtaining Lau interference bands, at finite distances, with high light throughput, and with a rich distribution of colors. Our result is applied to implement a lensless, theta modulation decoder, which has the following features: it can decode phase modulated structures with high signal-to-noise ratio, and with high light gathering power.

Lensless theta decoder

Abstract The Lau effect at Frensel distances is discussed in terms of the virtual Fourier transform, with the purpose of implementing a theta-modulation decoder, which does not require either any lens or any spatial filter, and works with spatially incoherent light. Experimental results are included.

Strehl ratio versus defocus for noncentrally obscured pupils

We discuss from the viewpoint of the Strehl ratio versus defocus, or the normalized axial-irradiance distribution, the influence of decentering the dark mask of an annular pupil. Our treatment, which is valid for pupil apertures with any Fresnel number, permits us to infer that the axial behavior of a noncentrally obscured pupil is equivalent to that of an apodizer with continuous amplitude variations. Hence the Strehl ratio versus defocus of an optical system can be shaped by use of noncentered dark masks that act as continuous gray apodizers. Several numerically evaluated examples are presented.

Degree of coherence: a lensless measuring technique.

We present a technique for measuring the degree of coherence that is based on the self-imaging phenomenon. The technique is lensless, has multiplexing capabilities, and can work with high light throughput. Experimental verifications are given.

Schardin-Lau interferometer

Abstract We describe a novel interferometer that uses two gratings, and works with spatially incoherent light. The optical setup resemblances the interferometer designed by Schardin. However, our device exploits the formation of lensless Lau bands, at finite distances; which are obtained by using certain quasihomogeneous sources (created by the object under test), and either an amplitude, or a phase grating. Experimental results are included.