0000000000148164
AUTHOR
Jorge Ojeda-castaneda
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.
Image synthesis using the Lau effect
Abstract Based on the Lau effect at finite distances, we describe a lensless optical setup for synthesizing laterally periodic images; which are composed of several, incoherently superimposed, object substructures. Some experimental verifications are also reported.
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.
Holographic interferometer with tunable radial and lateral displacement
The hologram of a point source, together with the real point source, is used to implement a simple holographic interferometer that can be tuned in its radial and/or lateral displacements. We show that our device is easy to use for creating cosinusoidal gratings and zone plates and for optical testing.
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-precisio…
Bidirectional Nonorthogonal Schardin-Lau Interferometer
We discuss the formation of self-images of a 2-D grating composed by two rulings of equal period, but in-plane rotated. We describe the in-register condition for setting the lensless Lau effect, with this type of gratings; and we propose to use the above configuration for interferometrically visualizing, in noncoherent light, phase structures, in two nonorthogonal directions.
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.
Moiré with zone plates pseudo-randomly encoded
Abstract Moire patterns are a convenient method for optically sensing lateral displacements, or in-plane rotations. Sharp moire fringes are here created by using two zone plates, pseudo-randomly encoded. Our results may be useful in metrology, optical testing, and robotics. Experimental results are reported.
Talbot interferometry: a new geometry
Abstract With the Talbot effect, planes are found where the Fresnel diffraction pattern, of a Ronchi ruling, exhibits zero visibility. These planes are exploited to propose a novel geometry for Talbot interferometry, which has high sensitivity. Experimental verifications are included.
Electro-optic time lens with an extended time aperture
We propose what we believe to be a new approach to correct the residual aberrations of time lenses implemented through electro-optic sinusoidal phase modulation. The method is based on a single modulator driven with various harmonic channels coming from the same clock signal. Proper weighting of the amplitude and phase of the channels allows us to achieve nearly perfect parabolic phase modulation over a fraction of the clock period. We show numerically that our proposal only requires three harmonics of the clock frequency to achieve truly parabolic modulation over a time window that extends across 70% of the period. We illustrate the benefits of this aberration-free scheme in a pulse compre…
Off-axis focal shift for rotationally nonsymmetric screens
We report on an analytical formulation for evaluating the amplitude distribution along any line directed toward the geometrical focus of a spherical wave front that passes through a rotationally nonsymmetric diffracting screen. Our formula consists of two factors. The first factor involves the one-dimensional Fourier transform of the projection of the screen function onto the off-axis line. The second factor depends on the inverse distance to the screen and permits us to recognize the existence of focal shift along off-axis lines.
Zone plates with cells apodized by Legendre profiles
By apodizing the cells of a zone plate and changing the opening ratio, it is possible to shape the relative power spectrum of its foci. We describe a novel procedure that leads to an analytical formula for shaping the focus power spectrum by using apodizers expressible as the Legendre series; these act on cells of arbitrary opening ratio. Our general result is used to design zone plates that have missing foci and to discuss a synthesis procedure using apodizers with various opening ratios. Our applications can also be used for shaping the power spectrum of 1-D gratings.
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.
Lau rings: In-register incoherent superposition of radial self-images
Abstract We describe an optical method for obtaining in-register, incoherent superposition of self-images, with radial symmetry. That is, the Lau effect is implemented, either at infinity or at finite distances, in the form of bright and dark rings of high visibility. This is applied for visualizing radially phase structures, with good-signal-to-noise ratio.
Tunable axial superresolution by annular binary filters. Application to confocal microscopy
We present a set of annular binary pupil filters for increasing the axial resolving capacity of imaging systems. The filters consist of two transparent annuli of the same area. It is shown that by changing the area of the transparent regions it is possible to obtain a tunable reduction of the width of the central lobe of the axial point spread function of the imaging system. However, this reduction is accompanied by a severe increase of the strength of secondary lobes, what can make these filters not very useful when used in conventional imaging systems. That is why we propose to use these filters for apodizing confocal microscopy systems. It is shown that in this case an important reductio…
Multiple incoherent 2D optical correlator
Abstract A nonconventional setup, based on the Lau effect, is employed for implementing a lensless version of an incoherent object-space correlator of 2D signals with compact support. Experimental results are also shown.
<title>Fibers supporting super-Gaussian beams: cladding effects</title>
We define a matching function that describes the amplitude variations produced over supergaussian beams, by cladding optical fibers that, if uncladded, can sustain this type of beams as Eigenmodes.
Side-lobe suppression in electro-optic pulse generation
A simple method is presented for rejecting undesirable tails and wings, around the main pulses of a periodic train, which is generated by electro-optical, sinusoidal phase modulation. It is shown that, by using a broadband optical carrier, the nonlinear chirp components generated by sinusoidal phase modulation can be filtered out. Thus, nearly apodised picosecond pulsation can be generated.
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.
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.