Apodization of imaging systems by means of a random spatially nonstationary absorbing screen

The amplitude impulse response (AIR) of coherent imaging systems with random binary apodizers is analyzed. Formulas for the mean value and the variance of the AIR are derived for two statistical one-dimensional models of apodizers: (1) nonuniform low-density shot noise and (2) a nonuniform unipolar synchronous random process. We show that for both models a high signal-to-noise ratio is achieved within the central peak and the low-order sidelobes of the AIR. Apodizers based on the second model permit higher values of the signal-to-noise ratio than those based on the first one.

Compact all-diffractive setup for spectral synthesis with non-uniform illumination

Optical filters based on diffractive optical elements (DOE) have received increased attention since the development of the first synthetic spectrum as a tool for correlation spectroscopy [1]. The production of a synthetic spectrum requires the design of a DOE that transforms the spectrum associated with the incident light into the spectrum of interest. Based on this procedure, several approaches have been reported in the literature [1–4]. In general, these configurations employ angular dispersion elements for spectrum tailoring, so they are restricted to working off-axis, and most of them need an extra focusing refractive lens.

Application Of Anamorphic Systems To Directional Pseudocolor Encoding

An optical nonsymmetrical imaging system composed of two anamorphic spectrum analyzers in cascade is implemented. This system can provide an undistorted final image in spite of the geometrical distortion effects in the intermediate Fourier plane. The introduction of chromatic sector filters in this plane provides a real-time technique to pseudocolor encode the spatial frequency information of a black-and-white transparency. In this way, greater discrimination is achieved in the angular orientation of object details that generate the same spatial frequencies. Experimental pseudocolored images, obtained with a symmetrical system and a nonsymmetrical system, of a black-and-white transparency a…

Non-Conventional Tunable Spatial Filtering

A virtual display of the Fraunhofer diffraction pattern of any object is formed in the transverse source plane by theyirtual diffracted rays extqn0ing in the region to the left of the screen containing the transparencyl),2). Except for a few cases '')"°), the concept of virtual Fourier transform appears not to have been made use of. The main idea of this paper is, bearing in mind the property referred to in the above paragraph, to describe a novel spatial filtering technique. In this way, one can obtain different filtered images, by simply moving the point source along the optical axis. The basic theory is described below.

Compressive single-pixel multispectral Stokes polarimeter

We present a single-pixel system that performs polarimetric multispectral imaging with the aid of compressive sensing techniques. We experimentally obtain the full Stokes spatial distribution of a scene for different spectral channels.

Vector description of higher-order modes in photonic crystal fibers

We extensively study the propagation features of higher-order modes in a photonic crystal fiber (PCF). Our analysis is based on a full-vector modal technique specially adapted to accurately describe light propagation in PCF's. Unlike conventional fibers, PCF's exhibit a somewhat unusual mechanism for the generation of higher-order modes. Accordingly, PCF's are characterized by the constancy of the number of modes below a wavelength threshold. An explicit verification of this property is given through a complete analysis of the dispersion relations of higher-order modes in terms of the structural parameters of this kind of fiber. The transverse irradiance distributions for some of these high…

Achromatic diffraction of femtosecond light pulses

Diffraction of electromagnetic waves in free space is a physical phenomenon that explicitly depends on the wavelength of light radiation. As an ultrashort-pulsed waveform consists of many frequency components that are coherently superposed, diffraction of a femtosecond pulse passing through an aperture radically differs from that under continuous wave (CW) monochromatic illumination. Note that the spectral width of a 5 fs pulsed beam is approximately 400 nm, which roughly corresponds to the entire visible spectrum bandwidth. The spectral distribution of the source results in the chromatic distortion, both lateral and axial, of the optical field diffracted by the aperture. This detrimental e…

Real-time acquisition of complex optical fields by binary amplitude modulation

We describe, through simulations and experiments, a real-time wavefront acquisition technique using random binary amplitude masks and an iterative phase retrieval algorithm based on the Fresnel propagator. By using a digital micromirror device, it is possible to recover an unknown complex object by illuminating with this set of masks and simultaneously recording the resulting intensity patterns with a high-speed camera, making this technique suitable for dynamic applications.

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.

Parallel laser micromachining based on diffractive optical elements with dispersion compensated femtosecond pulses

We experimentally demonstrate multi-beam high spatial resolution laser micromachining with femtosecond pulses. The effects of chromatic aberrations as well as pulse stretching on the material processed due to diffraction were significantly mitigated by using a suited dispersion compensated module (DCM). This permits to increase the area of processing in a factor 3 in comparison with a conventional setup. Specifically, 52 blind holes have been drilled simultaneously onto a stainless steel sample with a 30 fs laser pulse in a parallel processing configuration.

Three-dimensional superresolution by annular binary filters

We present a new family of annular binary filters for improving the three-dimensional resolving power of optical systems. The filters, whose most important feature is their simplicity, permit to achieve a significant reduction, both in the transverse and in the axial direction, of the central lobe width of the irradiance point spread function of the system. The filters can be used for applications such as optical data storage or confocal scanning microscopy.

Tunable optical sectioning in confocal microscopy by use of symmetrical defocusing and apodization

We present two novel optical methods to achieve a significative improvement in the optical-sectioning capacity of confocal scanning microscopes. The techniques, whose real power is the simplicity with which they can be implemented, consist of a suitable combination of symmetrical defocusing with two different manners of apodizing both parts of the confocal architecture. It is shown that the proposed techniques are useful in both the bright-field and the fluorescence modes and for reflection and transmission geometries.

Photonically assisted RF generator with incoherent sources

An RF waveform generator operating with incoherent broadband light is successfully implemented. Complex RF ~10 GHz bandwidth waveforms are generated by means of incoherent wavelength-to-time mapping. Our technique can be scaled to the mm-wave range.

Annular binary filters for controlling the axial behaviour of optical systems

The one-dimensional (1D) version of the iterative Fourier transform algorithm (IFTA) and a modified error diffusion algorithm are proposed for binarizing rotationally symmetric pupil filters designed to shape the axial impulse response of optical system. The resulting binary masks consist of a set of transparent and opaque annular zones of equal area or equal width. A numerical experiment in which we examine the performance of the binarization methods is carried out. In this experiment the resemblance between the axial diffractive behaviour of the binary version of an axially superresolving pupil filter, and that of the original continuous-tone filter is evaluated. It is shown that the perf…

Broadband space-variant Fresnel processor

We present a radically new class of optical setup working with white-light illumination, namely, a chromatically compensated processor operating in the Fresnel domain. The optical configuration is a hybrid (diffractive-refractive) three-lens system that exhibits an intermediate achromatic Fresnel plane and an output image plane without chromatic distortion. As a first application of this optical arrangement we develop a parallel space-variant color pattern-recognition experiment with white light.

High spatiotemporal resolution in multifocal processing with femtosecond laser pulses.

We report spatial and temporal dispersion compensation for fan-out of femtosecond pulses with a low-frequency diffraction grating by means of a hybrid diffractive-refractive lens triplet. In this way, we achieve a multifocal light structure with nearly diffraction-limited light spots even for 20 fs pulse duration. The spatial chromatic compensation, which drastically reduces the lateral walk-off of the various spectral components, also allows us to improve the available bandwidth at the dispersion-compensated diffraction orders. In fact, the temporal width of the output pulse is essentially limited by the group-delay dispersion term, which is shown to be small. The high spatiotemporal resol…

Spectral imaging system for scaling the power spectrum of optical waveforms.

We propose and analyze a new photonic system to change the scale of the optical power spectrum of an ultrashort pulse. Our device corresponds to the dual (spectral domain) configuration of a temporal imaging system. It is configured with two time lenses separated by a linear first-order dispersive medium. The specific relation between the chirp rates and the first-order dispersion coefficient is obtained. The main practical constraints are discussed, and the system performance is tested by means of a numerical simulation.

Transillumination imaging through biological tissue by single-pixel detection

One challenge that has long held the attention of scientists is that of clearly seeing objects hidden by turbid media, as smoke, fog or biological tissue, which has major implications in fields such as remote sensing or early diagnosis of diseases. Here, we combine structured incoherent illumination and bucket detection for imaging an absorbing object completely embedded in a scattering medium. A sequence of low-intensity microstructured light patterns is launched onto the object, whose image is accurately reconstructed through the light fluctuations measured by a single-pixel detector. Our technique is noninvasive, does not require coherent sources, raster scanning nor time-gated detection…

Diffractive pulse-front tilt for low-coherence digital holography

We use a diffractive lens to generate the proper pulse-front-tilt to record full-field off-axis holograms with a 10fs laser source. We experimentally demonstrate optical sectioning of three-dimensional samples with a resolution of about 5 microns.

Achromatic fan-out diffractive system for white-light free-space optical interconnects

Abstract A simple and versatile white-light fan-out diffractive system based on the achromatization of the fractional Talbot effect is proposed. This achromatic configuration is able to interconnect a single polychromatic point source with a 2-D array of optoelectronic microdevices with low residual chromatic aberration even for white light. The whole broadband beamsplitter system is formed by two simple diffractive optical elements, a periodic diffractive lenslet array and a diffractive lens, that are made with a direct laser writing technique giving high light efficiency. The focal amplitude distribution corresponding to the lenslet array produces, by free-space propagation, self-replicas…

Axial resolution in two-color excitation fluorescence microscopy by phase-only binary apodization

We study the effect of a kind of binary phase-only filters, the Toraldo filters, in two-color excitation fluorescence microscopy. We show that by simple insertion of a properly designed Toraldo filter in one of the illumination arms the axial resolution of the system is significantly improved. Specifically, the main peak of the point spread function is narrowed by 22% along the axial direction.

Axial behavior of diffractive lenses under Gaussian illumination: complex-argument spectral analysis

We present a general procedure to analyze the axial-irradiance distribution generated by an unlimited diffractive lens under coherent, Gaussian illumination. The resulting on-axis diffraction pattern, which is evaluated in terms of the power complex spectrum of the Fresnel-zone transmittance, explicitly depends on the truncation parameter that we define, which evaluates the effective number of zones illuminated by the Gaussian beam. Depending on the value of this parameter, different kinds of axial behavior are observed. In particular, for moderate values a multiple-focal-shift phenomenon appears, and a simple formula for its evaluation is presented. Additionally, for low values of the trun…

Inverse focal shift: A new effect in truncated cylindrical waves

We report on a general analytical procedure to analyse the axial focusing properties of uniform cylindrical waves truncated by a rectangular window. The resulting on-axis diffraction pattern explicitly depends on the square of the window height-to-width ratio. Depending on the value of this parameter, different kinds of axial behaviour are observed. In particular, it is found that for low values of this parameter and low Fresnel number, instead of the expected focal-shift effect, an inverse focal-shift phenomenon can appear, i.e. the maximum of the axial-irradiance distribution is displaced further away from the window.

Free-motion beam propagation factor measurement by means of a liquid crystal SLM

We propose a compact and robust method to measure beam propagation factor (M2) of continuous wave (cw) laser beams. In contrast to the conventional scanning procedure described in the ISO/DIS 11146 standard, our proposal takes advantage of the features of programmable liquid crystal spatial light modulators (SLMs) where a lens is codified. Then, by using a CCD at a fixed position, the beam width according to the second order moment of the irradiance is determined for each focal length of the codified lenses. After adjusting the measured data to the theoretical focusing behavior of a real laser beam, the beam propagation factor is obtained. The proposed method was successfully validated in t…

Diffractive optics for processing ultrashort light pulses

In this work we combine, in principle, two disjoint optical fields, diffractive optics and ultrashort light radiation. This combination allows us to manipulate in a very unconventional manner femtosecond pulses and, on the other hand, to implement a set of novel applications. In our case we have focused our attention on material processing and biophotonics applications.

20 GHz arbitrary radio-frequency waveform generator based on incoherent pulse shaping

We demonstrate a new approach of photonically assisted radiofrequency (RF) waveform generation using a spectrally incoherent light source. The system is based on the so-called generalized frequency-to-time mapping operation. In this work, external modulation of the source is done by concatenating two electro-optic Mach-Zehnder modulators properly biased to achieve short pulse gates which allow for broad bandwidth electrical signals. Also, the spectral shaping stage is performed prior to O/E conversion. A detailed theoretical analysis demonstrates that even in this case the frequency-to-time mapping is preserved. The key is that the noise level is greatly reduced because the amplitude filter…

Experimental generation of high-contrast Talbot images with an ultrashort laser pulse

A femtosecond Ti:sapphire laser oscillator emitting pulses with 800 nm central wavelength, 10.9 fs pulse width, and 75 MHz repetition rate, combined with a dispersion-compensated diffractive system, was used to implement a large-area, high-contrast, broadband optical interference technique based on the Talbot effect. Chromatic artifacts associated with the huge spectrum of the optical source (approximately 150 nm) are compensated for with an air-separated hybrid diffractive-refractive lens doublet. The spatial resolution of the chromatically compensated Talbot images under femtosecond illumination is nearly identical to that achieved under continuous wave monochromatic illumination. Further…

Hybrid (diffractive-refractive) optical processor for space-variant color pattern recognition

Space-variant optical processing constitutes an interesting approach in information processing techniques when the location of the reference object is of as much importance as its identification. Applications range from machine vision, optical logic, or neural network systems, to cryptography. First results of positional sensitivity were obtained in the past few years by Fresnel transform correlators with coherent light [1,2]. On the other hand, optical Fresnel cor-relators working under broadband point-source illumination allow us to exploit color information of input scenes and present a discrimination ability higher than its monochromatic counterparts. However, the use of the wavelength …

Analytical formula for calculating the focal shift in apodized systems

We report a quite simple analytical formula for the evaluation of the focal shift in apodized systems, with or without rotational invariance. Specifically it is shown that the magnitude of the focal shift is determined by the product of the Fresnel number of the focusing geometry and the standard deviation of a mapped version of the azimuthal average of the pupil transmittance. To illustrate our approach, several examples are examined.

Compressive holography with a single-pixel detector.

This Letter develops a framework for digital holography at optical wavelengths by merging phase-shifting interferometry with single-pixel optical imaging based on compressive sensing. The field diffracted by an input object is sampled by Hadamard patterns with a liquid crystal spatial light modulator. The concept of a single-pixel camera is then adapted to perform interferometric imaging of the sampled diffraction pattern by using a Mach-Zehnder interferometer. Phase-shifting techniques together with the application of a backward light propagation algorithm allow the complex amplitude of the object under scrutiny to be resolved. A proof-of-concept experiment evaluating the phase distributio…

All-incoherent dispersion-compensated optical correlator

We report on a simple, spatially incoherent, wavelength-independent imaging system that, in contrast to the conventional case, exhibits a dispersion-compensated point-spread function. Our hybrid (diffractive-refractive) three-lens imaging configuration thus acts as an all-incoherent dispersion-compensated optical irradiance correlator. So the optical arrangement is well adapted to processing color information (both spatially and temporally incoherent) under natural illumination.

Dispersion-to-spectrum mapping in nonlinear fibers based on optical wave-breaking

In this work we recognize new strategies involving optical wave-breaking for controlling the output pulse spectrum in nonlinear fibers. To this end, first we obtain a constant of motion for nonlinear pulse propagation in waveguides derived from the generalized nonlinear Schrödinger equation. In a second phase, using the above conservation law we theoretically analyze how to transfer in a simple manner the group-velocity-dispersion curve of the waveguide to the output spectral profile of pulsed light. Finally, the computation of several output spectra corroborates our proposition.

New photonic devices for ultrafast pulse processing operating on the basis of the diffraction-dispersion analogy

The space-time analogy is a well-known topic within wave optics that brings together some results from beam diffraction and pulse dispersion. On the above basis, and taking as starting point some classical concepts in Optics, several photonic devices have been proposed during the last few years with application in rapidly evolving fields such as ultrafast (femtosecond) optics or RF and microwave signal processing. In this contribution, we briefly review the above ideas with particular emphasis in the generation of trains of ultrafast pulses from periodic modulation of the phase of a CW laser source. This is the temporal analogue of Fresnel diffraction by a pure phase grating. Finally, we ex…

Diffractive optics for high-resolution low-coherence digital holography

We study the properties of the recording of off-axis holograms when a 10 fs pulsed laser is used as illumination source. A proper optical design involving one diffractive lens outside a Michelson interferometer enables the recording of full-field off-axis holograms with high resolution and optical sectioning. We demonstrate our approach with some experimental results that show optical sectioning with a maximum resolution of 3.5 µm. We note that the axial resolution of the technique is reduced up to 9 µm when the object beam travels through a few millimeters of glass due to the pulse broadening along dispersive media.

Arbitrary Waveform Generator Based on All-Incoherent Pulse Shaping

An all-incoherent technique for the generation of arbitrary electromagnetic intensity profiles is presented. It is based on spectral filtering of a broadband continuous-wave light source so that the filtered spectral density function (SDF) becomes the user-defined waveform. After large temporal modulation and subsequent distortion in a first-order dispersive medium, the incoherent mapping of the filtered SDF to the time domain occurs. Finally, optical-to-electrical conversion in a fast photodiode allows the optical intensity to be mapped into the electrical domain

Scale-tunable optical correlation with natural light

We describe two different scale-tunable optical correlators working under totally incoherent light. They behave as spatially incoherent wavelength-independent imaging systems with an achromatic point-spread function (PSF). In both cases it is possible to adapt the scale of the achromatic PSF, i.e., to modify the scaling factor of the PSF and preserve the chromatic compensation, by one's shifting the input along the optical axis. The remarkable properties of these systems allow us to carry out a scale-tunable color pattern-recognition experiment with natural light.

Quasi-wavelength-independent broadband optical Fourier transformer

The chromatic behaviour associated with diffractive optical elements is exploited herein to design a hybrid (diffractive-refractive) lens triplet showing very great wavelength-compensation capabilities for the Fraunhofer diffraction pattern of any diffracting screen under broadband point-source illumination. Within the paraxial Fresnel diffraction theory, we show that perfect compensation for the axial position of the Fourier transform of the input can be accomplished if we neglect the secondary spectrum of the refractive objective. Simultaneously, an achromatic correction for the scale of the Fraunhofer pattern is achieved. In this way, even for white light, only a low residual transversal…

Wavelength tuning of femtosecond pulses generated in nonlinear crystals by using diffractive lenses

We demonstrate that diffractive lenses (DLs) can be used as a simple method to tune the central wavelength of femtosecond pulses generated from second-order nonlinear optical processes in birefringent crystals. The wavelength tunability is achieved by changing the relative distance between the nonlinear crystal and the DL, which acts in a focusing configuration. Besides the many practical applications of the so-generated pulses, the proposed method might be extended to other wavelength ranges by demonstrated similar effects on other nonlinear processes, such as high-order harmonic generation.

Dispersion-compensated Lau-like processor

We present a diffractive lens-based optical assembly with which to achieve high-contrast Lau-like interferential fringes with totally incoherent illumination.

Achromatic Fourier transforming properties of a separated diffractive lens doublet: Theory and experiment

The strong chromatic distortion associated with diffractive optical elements is fully exploited to achieve an achromatic optical Fourier transformation under broadband point-source illumination by means of an air-spaced diffractive lens doublet. An analysis of the system is carried out by use of the Fresnel diffraction theory, and the residual secondary spectrum (both axial and transversal) is evaluated. We recognize that the proposed optical architecture allows us to tune the scale factor of the achromatic Fraunhofer diffraction pattern of the input by simply moving the diffracting screen along the optical axis of the system. The performance of our proposed optical setup is verified by sev…

Imaging through scattering media by microstructured illumination

We describe a method to image objects through scattering media based on microstructured illumination. A spatial light modulator is used to project a set of microstructured light patterns onto the sample. The image is retrieved computationally from the photocurrent fluctuations provided by a detector with no spatial structure. We review several optical setups developed in the last years with different illumination strategies and applied to different turbid media. In particular we introduce a new non-invasive optical system based on a reflection configuration. Our technique does not require coherent light, raster scanning, time-gated detection or a-priori calibration processes. Furthermore it…

Structured-light imaging through scattering

We present a structured illumination technique to image objects hidden beneath scattering. The sample is computationally retrieved from a known ensemble of light patterns codified onto a digital micromirror device and photocurrent fluctuations provided by a detector with no spatial resolution. Results of laboratory experiments will be shown. Article not available.

Incoherent optical correlator

A nonconventional setup based on the Lau effect is employed for implementing a lensless incoherent correlator of 2-D signals with compact support.

Broadband dispersion compensation using inner cladding modes in photonic crystal fibers.

A photonic crystal fiber is optimized for chromatic dispersion compensation by using inner cladding modes. To this end, a photonic-oriented version of the downhill-simplex algorithm is employed. The numerical results show a dispersion profile that accurately compensates the targeted dispersion curve, as well as its dispersion slope. The presented fiber has a simple structure, while radiation losses can be reduced simply by adding a few more air-hole rings. Fabrication tolerances are also considered showing how fabrication inaccuracies effects can be overridden by just adjusting the compensation length.

Fraunhofer diffraction patterns from apertures illuminated with nonparallel light in nonsymmetrical Fourier transformers.

In a recent paper, a 2-D axially nonsymmetrical Fourier transforming with an anamorphic system was presented. This work extends its performances with the use of spherical illumination. The results provide the conditions to obtain an exact Fourier transform and a greater angular magnification coefficient than with parallel illumination. Experimental results of the latter are shown.

Spatio-temporal control of ultra-short pulses by using diffractive optical elements

Diffractive optical elements (DOEs) have shown their applicability to control the spatio-temporal characteristics of ultra-short laser pulses. DOEs can provide high efficiency, compactness, very low material dispersion and, when implemented with spatial light modulators, real-time pulse engineering. In this communication, we report management of temporal and spectral profiles of ultra-short pulses by means of a quasi-direct space-to-time (QDST) pulse shaper. Moreover, we present spatio-temporal control, including dispersion compensation, by DOEs, and applications for activating nonlinear processes. On the other hand, we have achieved complete spatial control of ultra-short pulses, overcomin…

Femtosecond digital lensless holographic microscopy to image biological samples

The use of femtosecond laser radiation in digital lensless holographic microscopy (DLHM) to image biological samples is presented. A mode-locked Ti:Sa laser that emits ultrashort pulses of 12 fs intensity FWHM, with 800 nm mean wavelength, at 75 MHz repetition rate is used as a light source. For comparison purposes, the light from a light-emitting diode is also used. A section of the head of a drosophila melanogaster fly is studied with both light sources. The experimental results show very different effects of the pinhole size on the spatial resolution with DLHM. Unaware phenomena on the field of the DLHM are analyzed.

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…

Incoherent photonic techniques for RF-AWG

The capabilities for RF-AWG in terms of waveform fidelity for three different incoherent photonic methods are revised and discussed: incoherent frequency-to-time mapping, incoherent MWP filtering with N discrete taps, and multi-wavelength pulse compression.

Dispersion management in two-photon microscopy by using diffractive optical elements.

We demonstrate efficient generation of wide-field fluorescence signals in two-photon microscopy exploiting diffractive optical elements and short pulses by using a dispersion-compensated beam delivery optics module. Computer-generated holograms are codified onto a phase-only spatial light modulator, which allows for arbitrary single-shot patterning of the sample. Spatiotemporal shaping of the pulse is mandatory to overcome spatial chirp and pulse-front tilt effects that spread both in space and time the irradiance patterns, thus limiting not only the spatial resolution but also the signal-to-noise ratio in two-photon microscopy. By using a multipass amplifier delivering 30 fs, 0.8 mJ pulses…

Space-Time Analogies in Optics

Abstract The so-called space-time analogy constitutes a source of inspiration to understand, engineer, and implement new systems for ultrafast optical signal processing based on concepts borrowed from the well-established field of Fourier Optics. In this review, we start by describing in a comprehensive manner the most basic notions of this analogy and discuss some recent developments with state-of-the-art technology, including the silicon-chip-based time lens and ultra-dispersive Raman devices, among others. Apart from the applications in optical communications, special emphasis is paid on the collateral benefits that the “ultra” appellative brings in fields as diverse as optical frequency…

Source linewidth effects in temporal imaging of Gaussian Schell-model pulses

A transform-limited Gaussian pulse generated from an externally modulated stationary source is launched within a temporal imaging system composed of a second-order dispersion followed by a time lens and a subsequent quadratic dispersion. We consider the effect of the statistical properties of the emitted light for temporal imaging. In particular, it is shown that the design parameters that ensure a received signal with the minimum root-mean-square (rms) width achievable, which is called the temporal image of the incident pulse, are strongly dependent on the coherence properties of the input waveform. Finally, limitations on the temporal resolution of the setup are highlighted and a realisti…

Image transmission through dynamic scattering media by single-pixel photodetection

Smart control of light propagation through highly scattering media is a much desired goal with major technological implications. Since interaction of light with highly scattering media results in partial or complete depletion of ballistic photons, it is in principle impossible to transmit images through distances longer than the extinction length. Nevertheless, different methods for image transmission, focusing, and imaging through scattering media by means of wavefront control have been published over the past few years. In this paper we show that single-pixel optical systems, based on compressive detection, can also overcome the fundamental limitation imposed by multiple scattering to suc…

Compressive imaging in scattering media.

One challenge that has long held the attention of scientists is that of clearly seeing objects hidden by turbid media, as smoke, fog or biological tissue, which has major implications in fields such as remote sensing or early diagnosis of diseases. Here, we combine structured incoherent illumination and bucket detection for imaging an absorbing object completely embedded in a scattering medium. A sequence of low-intensity microstructured light patterns is launched onto the object, whose image is accurately reconstructed through the light fluctuations measured by a single-pixel detector. Our technique is noninvasive, does not require coherent sources, raster scanning nor time-gated detection…

White-light optical implementation of the fractional fourier transform with adjustable order control.

An optical implementation of the fractional Fourier transform (FRT) with broadband illumination is proposed by use of a single imaging element, namely, a blazed diffractive lens. The setup displays an achromatized version of the FRT of order P of any two-dimensional input function. This fractional order can be tuned continuously by shifting of the input along the optical axis. Our compact and flexible configuration is tested with a chirplike input signal, and the good experimental results obtained support the theory.

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.

Dynamical binary modulation of ultrabroadband light beams by using principal states of polarization of liquid crystal devices

Dynamical modulation of ultrabroadband beams, such as those produced by femtosecond laser or incoherent sources, is not an easy task due to the dispersive nature of the devices commonly employed. Phase modulation has been performed by means of deformable micromirror arrays. These devices are expensive and do not permit amplitude modulation. For micro- and nano-structuring of materials with femtosecond lasers is common to pattern the surface with the light irradiance produced by a computer generated hologram implemented onto a liquid crystal (LC) type spatial light modulator. This enables dynamical patterning [1,2]. Reduced spectral bandwidths, of the order of tens of nanometers, have been u…

Gaussian imaging transformation for the paraxial Debye formulation of the focal region in a low-Fresnel-number optical system

The Debye formulation of focused fields has been systematically used to evaluate, for example, the point-spread function of an optical imaging system. According to this approximation, the focal wave field exhibits some symmetries about the geometrical focus. However, certain discrepancies arise when the Fresnel number, as viewed from focus, is close to unity. In that case, we should use the Kirchhoff formulation to evaluate accurately the three-dimensional amplitude distribution of the field in the focal region. We make some important remarks regarding both diffraction theories. In the end we demonstrate that, in the paraxial regime, given a defocused transverse pattern in the Debye approxi…

Totally incoherent optical processing operations with achromatic diffraction-based setups

We report on a novel family of totally incoherent, chromatic-dispersion compensated hybrid (refractive-diffractive) lens setups for implementing, in the Fraunhofer or in the Fresnel diffraction region, different achromatic diffraction-based processing operations.

Sidelobe decline in single-photon 4Pi microscopy by Toraldo rings.

We demonstrate theoretically the feasibility of single-photon 4Pi-confocal microscopy. By inserting a pair of properly designed multi-ring phase-only pupil filters in the illumination path of a 4Pi microscope the height of the sidelobes of the point spread function substantially reduced, so that there is no ambiguity in the 3D image. Then, an axial resolution up to four times higher than that of single-photon confocal microscope can be effectively achieved.

Analytical Evaluation of the Temporal Focal Shift for Arbitrary Pulse Shapes

In this letter, we analyze the propagation of linearly chirped arbitrary-shaped light pulses through a parabolic dispersive medium to derive an analytical formula of assessing the location of the transverse plane where the pulse root-mean-square width is minimum. Closed form expressions for compressed pulses, which are independent of the input pulse shape, are demonstrated. In this way, we demonstrate that both the relative temporal focal shift and the minimum pulsewidth are solely determined by two factors, the temporal equivalent of the Fresnel number of the geometry and the pulse quality factor, i.e., the temporal analogue of the spatial M/sup 2/ beam quality factor. Some examples are di…

Digital Holographic Microscopy: A New Imaging Technique to Quantitatively Explore Cell Dynamics with Nanometer Sensitivity

In the first part of this chapter, we describe how the new concept of digital optics applied to the field of holographic microscopy has made it possible to quantitatively and accurately measure the phase retardation induced on the transmitted wavefront by the observed transparent specimen, allowing thus to develop a reliable and flexible digital holographic quantitative phase microscopy (DH-QPM). In the second part the most relevant DH-QPM applications in the field of cell biology are presented. Particularly, applications taking directly advantage of benefits provided by digital optics particularly off-line autofocusing and extended depth of focus, are outlined. Otherwise, special emphasis …

White-light Fourier transformer with low chromatic aberration.

A simple Fourier transformation system working with broadband parallel illumination is presented. The proposed setup, consisting of two on-axis zone plates and an achromatic objective, allows us to obtain the achromatic Fourier transform representation of the input at a finite distance with a low chromatic aberration. The discussion of the system, using the Fresnel diffraction theory, leads to an analytical expression to evaluate the transversal and longitudinal chromatic aberrations. It is shown that the resulting chromatic aberrations for typical values of the involved parameters are less than 1% over the entire visible spectrum.

Dispersion properties and spatial solitons in photonic crystal fibres

Optical security and encryption with totally incoherent light

We present a method for securing and encrypting information optically by use of totally incoherent illumination. Encryption is performed with a multichannel optical processor working under natural (both temporal and spatially incoherent) light. In this way, the information that is to be secured can be codified by use of color signals and self-luminous displays. The encryption key is a phase-only mask, providing high security from counterfeiting. Output encrypted information is recorded as an intensity image that can be easily stored and transmitted optically or electrically. Decryption or authentication can also be performed optically or digitally. Experimental results are presented.

High-contrast white-light Lau fringes

We present a new optical assembly with which to achieve Lau fringes with totally incoherent illumination. Gratinglike codification of the spatially incoherent source combined with an achromatic Fresnel diffraction setup allows us to achieve Lau fringe-pattern visibility of almost 100% with broadband light. The white-light character to our proposed setup is in stark contrast to previous monochromatic implementations. Potential implications of this fact are identified.

Sloped-wall thin-film photonic crystal waveguides

The effect of the slope of the groove walls in the behavior of thin-film one-dimensional photonic crystal waveguides is extensively studied. In this respect, we point out its influence on the modal dispersion relations and then on the bandgap structure in general. Likewise, we also prove the lack of accuracy in the evaluation of the bandgap edges when material dispersion is ignored. The extreme importance of both facts, the wall slope and the material dispersion, in the analysis and design of realistic photonic crystal devices is emphasized. In particular, we exploit the wall slope as a new design parameter. By suitably choosing the value of the above parameter, sloped-wall photonic crystal…

Differential toolbox to shape dispersion behavior in photonic crystal fibers.

We present an analytical procedure to compute the first derivatives of the propagation constants with respect to several structural parameters in photonic crystal fibers (PCFs). From them we can easily evaluate the same derivatives of other directly related magnitudes. The above derivatives provide the trend of the magnitude at issue, which allows us to take advantage of a gradient-based algorithm to shape the properties of the guiding structure. In this way we implement an optimization process to carry out real inverse design in PCFs. We focus our attention on designing PCFs with a specific chromatic dispersion behavior. Likewise, the same approach makes it possible to analyze their fabric…

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…

Zero permeability and zero permittivity band gaps in 1D metamaterial photonic crystals

We consider layered heterostructures combining ordinary positive index materials and dispersive metamaterials. We show that these structures can exhibit a new type of photonic gap around frequencies where either the magnetic permeability \mu or the electric permittivity \epsilon of the metamaterial is zero. Although the interface of a semi-infinite medium with zero refractive index (a condition attained either when \mu= 0 or when \epsilon= 0) is known to give full reflectivity for all incident polarizations, here we show that a gap corresponding to \mu = 0 occurs only for TE polarized waves, whereas a gap corresponding to \epsilon = 0 occurs only for TM polarized waves. These band gaps are …

White-light-modified Talbot array illuminator with a variable density of light spots.

A flexible array illuminator, comprising only two conventional optical elements, with a variable density of bright white-light spots is presented. The key to our method is to obtain with a single diffractive lens an achromatic version of different fractional Talbot images, produced by free-space propagation, of the amplitude distribution at the back focal plane of a periodic refractive microlens array under a broadband point-source illumination. Some experimental results of our optical procedure are also shown.

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.

Analytical formulation of the axial behavior of apodized general Bessel beams

We present an analytical formula for the evaluation of the axial-irradiance distribution of general Bessel beams apodized by a radially-nonsymmetric window. Our approach is based on the similarity between the axial behavior of such beams and the propagation properties of a properly modified version of the window transmittance. To illustrate our formalism, we analyze the axial behavior of some complex beams.

Achromatic Fresnel diffraction patterns

Abstract A novel method for obtaining a single, but arbitrary, achromatic Fresnel diffraction pattern of any pupil with broadband parallel illumination is presented. The optical device simply consists of an achromatic objective and an on-axis zone plate. A criterion for selecting the system parameters in order to minimize the residual chromatic aberrations is given. The recording of the selected diffraction field is obtained with low chromatic aberrations even for white-light illumination. An experimental verification is shown to illustrate this approach.

Computational imaging with single-pixel detection: Applications in scattering media

We describe computational imaging techniques based on single-pixel detection providing multidimensional information of an input scene. The key element of the optical recording stage is a spatial light modulator which sequentially generates a set of intensity light patterns to sample the scene. In this way, it is possible to use single-pixel detectors to measure different optical parameters such as the light intensity, the spectral content, the polarization state, or the phase. The spatial distribution of these parameters is then computed by applying the theory of compressive sampling. In particular, in this contribution we present a new method to transmit images through scattering media. We…

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.

OPCPA using beams shaped by diffractive optical elements

Optical parametric chirped pulse amplification (OPCPA) is becoming a widely accepted technique for the generation of high energy ultrashort laser pulses. Flat-top spatial profile pump beams can improve the efficiency of OPCPA, however such beams can be energetically costly to generate and are difficult to implement for low pump energy systems. An elegant and efficient solution to the generation of flat-top spatial profiles is the use of a diffractive optical element (DOE), however these devices distort the geometric phase of the pulses, possibly making them unsuitable for phase coherent interactions such as OPCPA.

Temporal self-imaging effect for chirped laser pulse sequences: Repetition rate and duty cycle tunability

We express parabolic-dispersion-induced transformations of a linearly chirped signal in terms of those suffered by the unchirped version of the same input signal. Specifically, we unveil that any amount of chirping and dispersion produces, aside from a scale factor, the same pulse-distortion effect as a certain parabolic dispersion in the unchirped input. This relevant result allows us to derive, as a particular case, the dispersion condition that leads to the temporal self-imaging phenomenon for laser pulse sequences globally affected by a quadratic-phase modulation. This combined action of chirping and dispersion is proposed as a technique for generating laser pulse sequences with customi…

Incoherent frequency-to-time mapping: application to incoherent pulse shaping

After temporal amplitude modulation of a spectrally incoherent optical source the averaged intensity profile at the so-called temporal far-zone regime coalesces with a magnified replica of the spectral density function of the source. This has provided the basis for the generalization of the frequency-to-time mapping technique in the partially coherent case. Based on this fact, temporal intensity waveform generation is demonstrated by spectral filtering the incoherent source before the temporal modulation stage. We refer to this technique as full incoherent pulse shaping. Although only the average intensity of the output signal is properly shaped, intensity fluctuations between the different…

White-light array generation with a diffractive lenslet array

Abstract In this paper we present two different optical configurations providing a white-light array generator based on a diffractive lenslet array (DLA). In both cases, starting from a white-light point source we achieve a regularly spaced set of sharp light spots by use of a single DLA and a small number of extra lenses (only one or two). The first optical system permits us to change the separation between the intensity peaks in a tunable way. The second is very compact and consists only of diffractive lens elements. The key question in both set-ups is the use of achromatic Fourier-transform methods. In this way, we achieve, in a first-order approximation, the superposition of the chromat…

Smooth and stable supercontinuum generation with standard photonic crystal fibers

We identify some simple-to-fabricate photonic crystal fibers, with only two families of air-hole sizes, which provide a wide, smooth and highly-coherent supercontinuum.

Analytical evaluation of chromatic dispersion in photonic crystal fibers

We present a two-dimensional modal approach for the evaluation, in an analytical manner, of chromatic dispersion in any kind of optical fiber. It combines an iterative Fourier technique to compute the propagation constant at any fixed wavelength and an analytical procedure to calculate its derivatives. The proposed formulation takes into account the effective anisotropy of the interfaces and allows us to deal with microstructured fibers, in general, and specifically with realistic photonic crystal fibers (PCFs), including arbitrary spatial refractive-index distributions of dispersive and absorbing materials. This fast and accurate numerical technique is extremely useful for both analysis an…

Real-time optical spectrum analyzers operating with spectrally incoherent broadband continuous-wave light source

On the framework of coherence theory we discuss the averaged temporal intensity output provided by real-time optical Fourier transformers when the spectral line shape of the stationary source is considered. Some numerical examples are given and the deviations from perfectly monochromatic sources are pointed out.

Chromatic compensation in the near-field region: shape and size tunability

We report a diffractive-lens triplet with which to achieve wavelength compensation in the near field diffracted by any aperture. On the one hand, the all-diffractive triplet allows us to tune, in a sequential way, the Fresnel-irradiance shape to be achromatized by changing the focal length of one diffractive lens. On the other hand, we can adjust the scale of the chromatically compensated Fresnel diffraction field by shifting the aperture along the optical axis. Within this framework, we present an extremely flexible white-light Fresnel-plane array illuminator based on the kinoform sampling filter. A variable compression ratio and continuous selection of the output pitch are the most appeal…

Spectral broadening enhancement in silicon waveguides through pulse shaping

Spectral broadening in silicon waveguides is usually inhibited at telecom wavelengths due to some adverse effects related to semiconductor dynamics, namely, two-photon and free-carrier absorption (FCA). In this Letter, our numerical simulations show that it is possible to achieve a significant enhancement in spectral broadening when we properly preshape the input pulse to reduce the impact of FCA on spectral broadening. Our analysis suggests that the use of input pulses with the correct skewness and power level is crucial for this achievemen This work was financially supported by the Plan Nacional Investigación, Desarrollo e Innovación (I+D +I) under the research project TEC2008-05490, by…

Variable fractional Fourier processor: a simple implementation

A new set of optical implementations of the fractional Fourier transform (FRT) is developed by use of Wigner matrix algebra. The reinterpretation of some elementary operations that synthesize a rotation in the phase-space domain allows us to propose a lensless setup for obtaining the FRT. This compact configuration is also very flexible, because the fractional degree of the transformation can be varied continuously by shifting the input and the output planes along the optical axis by proper amounts. The above results permit one to build an optical FRT processor formed by two FRT systems in cascade, with a spatial filter between them. We present the design of such a variable FRT processor, w…

White-light implementation of the Wigner-distribution function with an achromatic processor.

A temporally incoherent optical processor that combines diffractive and refractive components is proposed for performing two different operations simultaneously: an achromatic image along an axis and an achromatic one-dimensional Fourier transformation along the orthogonal axis. These properties are properly employed to achieve the achromatic white-light display of the Wigner-distribution function associated with a one-dimensional real signal, with high redundancy and variable scale.

Dispersion-compensated beam-splitting of femtosecond light pulses: Wave optics analysis

Recently, using parageometrical optics concepts, a hybrid, diffractive-refractive, lens triplet has been suggested to significantly improve the spatiotemporal resolution of light spots in multifocal processing with femtosecond laser pulses. Here, we carry out a rigorous wave-optics analysis, including the spatiotemporal nature of the wave equation, to elucidate both the spatial extent of the diffractive spots and the temporal duration of the pulse at the output plane. Specifically, we show nearly transform-limited behavior of diffraction maxima. Moreover, the temporal broadening of the pulse is related to the group velocity dispersion, which can be pre-compensated for in practical applicati…

Dynamic wavefront sensing and correction with low-cost twisted nematic spatial light modulators

Off-the-shelf spatial light modulators (SLMs), like twisted nematic liquid crystal displays (TNLCDs) used in projection systems, show some interesting features such as high spatial resolution, easy handling, wide availability, and low cost. We describe a compact adaptive optical system using just one TNLCD to measure and compensate optical aberrations. The current system operates at a frame rate of the order of 10 Hz with a four-level codification scheme. Wavefront estimation is performed through conventional Hartmann–Shack sensing architecture. The system has proved to work properly with a maximum rms aberration of 0. 76 μm and wavefront gradient of 50 rad/mm at a wavelength of 514 nm. The…

Designing the properties of dispersion-flattened photonic crystal fibers

We present a systematic study of group-velocity-dispersion properties in photonic crystal fibers (PCF's). This analysis includes a thorough description of the dependence of the fiber geometrical dispersion on the structural parameters of a PCF. The interplay between material dispersion and geometrical dispersion allows us to established a well-defined procedure to design specific predetermined dispersion profiles. We focus on flattened, or even ultraflattened, dispersion behaviors both in the telecommunication window (around 1.55 microm) and in the Ti-Za laser wavelength range (around 0.8 microm}. We show the different possibilities of obtaining normal, anomalous, and zero dispersion curves…

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.

Limits for the Generation of Ultra-Wideband Signals with the Incoherent-Pulse-Shaping Technique

Recently, an nil-optical technique to generate arbitrary RF waveforms through Altering of the spectral density function of a broadband spectrally incoherent optical source has been introduced. The spectrum is tailored so that the output averaged intensity after large temporal modulation and subsequent distortion in a group-delay-dispersion circuit becomes the user-defined waveform. In general, there is a tradeoff between the spectral width and the signal-to-noise ratio of the output signal. Here, we provide an analytical treatment of the problem based on the optical coherence theory. In particular, we analyze the possibility to employ this technique for ultra-wideband (UWB) applications.

Space-time analogy for partially coherent plane-wave-type pulses.

In this Letter we extend the well-known space-time duality to partially coherent wave fields and, as a limit case, to incoherent sources. We show that there is a general analogy between the paraxial diffraction of quasi-monochromatic beams of limited spatial coherence and the temporal distortion of partially coherent plane-wave pulses in parabolic dispersive media. Next, coherence-dependent effects in the propagation of Gaussian Schell-model pulses are retrieved from that of their spatial counterpart, the Gaussian Schell-model beam. Finally, the last result allows us to present a source linewidth analysis in an optical fiber communication system operating around the 1.55 microm wavelength w…

Extremely efficient evaluation of chromatic dispersion in realistic photonic crystal fibers

We present a fast and accurate procedure for the evaluation of chromatic dispersion in photonic crystal fibers. It combines an iterative Fourier technique to compute the propagation constant at any fixed wavelength and an analytical approach to calculate its derivatives.

Effective Fresnel-number concept for evaluating the relative focal shift in focused beams

We report on an analytical formulation, based on the concept of effective Fresnel number, to evaluate in a simple way the relative focal shift of rotationally nonsymmetric scalar fields that have geometrical focus and moderate Fresnel number. To illustrate our approach, certain previously known results and also some new focusing setups are analytically examined.

Self-imaging properties of a periodic microlens array: versatile array illuminator realization

Abstract The general features of the wavefield diffracted by a microlens array are described. The transversal periodicity of both a refractive and a diffractive periodic microlens array allows to obtain a set of replicas of the focal intensity distribution along the optical axis of the system, with different multiplicity. The result is applied for implementing a versatile optical array illuminator, with a variable density of bright spots at the output plane. Some experimental results of the procedure are shown.

Passive Polarimetric Imaging

Passive electro-optical polarimetric imaging is a form of remote sensing in which the properties associated with electromagnetic field orientation are exploited as a means to discriminate between objects in an extended scene. The purpose of this chapter is to introduce some fundamental concepts in the science of imaging polarimetry. These concepts include the Stokes-Mueller description of polarized light, the physical mechanisms that contribute to polarimetric image contrast, a mathematical description of several polarimetric imaging systems, and an example target detection algorithm. Polarimetric image contrast is discussed in terms of reflected, emitted, and scattered light. Special empha…

Geometrical Transformations In The Fraunhofer Plane

A virtual display of the Fraunhofer diffraction pattern is generated solely by illuminating the object with a point source. If this pattern is imaged with an anamorphic system, several linear geometrical transformations can be achieved. Furthermore, a nonsymmetrical Fourier transformer with a variable degree of anamorphic magnification on the Fraunhofer pattern can be implemented.

Wavelength compensation of broadband light diffraction

m-bonacci metamaterial multilayers: location of the zero-average index bandgap edges

We examine quasiperiodic multilayers arranged in m-bonacci sequences, which combine ordinary positiveindex materials and dispersive metamaterials with negative index in a certain frequency range. When the volume-averaged refractive index of the nonperiodic multilayer equals zero, the structure does not propagate light radiation and exhibits a forbidden band. We identify some analytical expressions to determine the upper and lower limits of the above zero-average refractive-index bandgap. We recognize that these limits are not explicitly dependent on the geometrical parameters of the stack of layers. © 2009 Optical Society of America. Fil: Monsoriu, J.A.. Universidad Politécnica de Valencia;…

All-fiber incoherent frequency-to-time mapping method for microwave signal generation with baseband transmission and multicasting support

We present a proof-of-principle experiment for achieving simultaneous distribution of baseband radio-frequency data and up-conversion with broadcasting support over a passive optical network. The technique is based on an incoherent frequency-to-time mapping method for pulse shaping. Specifically, we synthesize the spectral density function of sliced ASE noise from an EDFA with a periodic Mach-Zehnder fiber interferometer optical filter. By using external intensity modulation combined with propagation in an optical fiber, after photodetection, the resultant averaged temporal pulse profile resembles the shape of the incoherent source. The photodetected signal contains both the baseband data a…

Optoelectronic Information Encryption with Incoherent Light

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…

Focal-shift formula in apodized nontelecentric focusing systems

A single analytical formulation for evaluating the focal shift in any apodized nontelecentric focusing setup is reported. The formulation is also useful in the case of imaged paraxial beams. We show explicitly that the magnitude of the focal shift is determined by only one parameter that depends on the effective width of the pupil filter and its axial position. To illustrate our approach we examine different focusing setups.

All-diffractive achromatic Fourier-transform setup

An achromatic Fourier transformation under broadband converging spherical-wave illumination is optically achieved by use of only two on-axis blazed zone plates. The novel optical configuration provides the achromatic Fraunhofer diffraction pattern of an arbitrary input signal with adjustable magnification. Further analysis of the system permits us to obtain a simple analytical expression to evaluate both the longitudinal and the transversal residual chromatic aberration, resulting in a compact achromatic Fourier transformer with low chromatic errors, even for a wide spectral content of the point source.

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.

Radon–Wigner display: a compact optical implementation with a single varifocal lens

A new optical implementation of the Radon‐Wigner display for one-dimensional objects is presented, making use of the fractional Fourier transform approach. The proposed setup makes use of only two conventional refractive elements: a cylindrical lens and a varifocal lens. Although the exact magnifications cannot be achieved simultaneously for all the fractional transforms, an optimum design can be obtained through balancing the conflicting magnification requirements. Experimental results are obtained with a commercially available progressive addition lens. For comparison, computer simulations are also provided. © 1997 Optical Society of America

Broadband focused waves with compensated spatial dispersion: transverse versus axial balance.

We determine the constraints an ABCD optical system must verify to achieve, at the focal region, broadband waves with compensated spatial dispersion either along the optical axis, called on-axis isodiffracting fields, or in the lateral direction, here named in-plane isodiffracting beams. An optical configuration is identified for generating both types of achromatic broadband focused wave fields. An experimental verification is also provided.

Single-shot color digital holography based on the fractional Talbot effect

We present a method for recording on-axis color digital holograms in a single shot. Our system performs parallel phase-shifting interferometry by using the fractional Talbot effect for every chromatic channel simultaneously. A two-dimensional binary amplitude grating is used to generate Talbot periodic phase distributions in the reference beam. The interference patterns corresponding to the three chromatic channels are captured at once at different axial distances. In this scheme, one-shot recording and digital reconstruction allow for real-time measurement. Computer simulations and experimental results confirm the validity of our method.

Single-zone-plate achromatic fresnel-transform setup: Pattern tunability

Abstract White-light point-source illumination results in the chromatic blurring of the optical field diffracted by an aperture. In this paper, broadband dispersion compensation for a continuous set of Fresnel diffraction patterns associated with an arbitrary input transparency is carried out, in a sequential way, by means of a single on-axis blazed zone plate. The input is illuminated with a white-light converging spherical wavefront and the diffractive lens is inserted at the virtual source plane. We recognize that the position of the input along the optical axis permits to achieve a different achromatic Fresnel diffraction pattern with low residual chromatic aberrations. The theory deriv…

Dispersion Compensation in Holograms Reconstructed by Femtosecond Light Pulses

This chapter describes how the spatiotemporal dispersion associated with the diffraction of broadband femtosecond light pulses through computer generated holograms (CGHs) can be compensated to a first order with a properly designed dispersion compensation module (DCM). The angular dispersion of the beam associated to CGHs leads to both spatial and temporal distortion of the pulse. Some experiments in one-shot second harmonic generation, wide-field two-photon microscopy, and parallel micromachining are shown to study the quality of the compensation performed with the DCM.

Shaping the supercontinuum spectral profile

We numerically recognize a procedure for shaping, at least to some extent, the spectral profile of the supercontinuum (SC) generated by soft-glass photonic crystal fibers (PCFs). As example, we identify a PCF geometry that provides an ultrawide (over an octave) and very flat SC when pumped with pulsed light parameters corresponding to a commercially available Er-doped femtosecond fiber laser.

Chromatic compensation of broadband light diffraction: ABCD-matrix approach

Compensation of chromatic dispersion for the optical implementation of mathematical transformations has proved to be an important tool in the design of new optical methods for full-color signal processing. A novel approach for designing dispersion-compensated, broadband optical transformers, both Fourier and Fresnel, based on the collimated Fresnel number is introduced. In a second stage, the above framework is fully exploited to achieve the optical implementation of the fractional Fourier transform (FRT) of any diffracting screen with broadband illumination. Moreover, we demonstrate that the amount of shift variance of the dispersion-compensated FRT can be tuned continuously from the spati…

Single-shot digital holography
by use of the fractional Talbot effect

We present a method for recording in-line single-shot digital holograms based on the fractional Talbot effect. In our system, an image sensor records the interference between the light field scattered by the object and a properly codified parallel reference beam. A simple binary two-dimensional periodic grating is used to codify the reference beam generating a periodic three-step phase distribution over the sensor plane by fractional Talbot effect. This provides a method to perform single-shot phase-shifting interferometry at frame rates only limited by the sensor capabilities. Our technique is well adapted for dynamic wavefront sensing applications. Images of the object are digitally recon…

Millimeter-wave and microwave signal generation by low-bandwidth electro-optic phase modulation

We propose, analyze and numerically illustrate a photonic-based technique for waveform generation of electrical signals approaching the 50 GHz bandwidth with time apertures as large as a few nanoseconds, by low-frequency, up to 2 GHz, electro-optic phase modulation of time-stretched optical pulses. Synthesis of the electrical waveform relies on phase-to-amplitude conversion of the modulated signal by a group delay dispersion circuit designed to behave as a transversal filter with N taps. Although arbitrary waveform generation capabilities are limited, a wide variety of user-defined signals are numerically demonstrated by appropriately designing the low-frequency signal driving the electro-o…

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.

Focal Length Measuring Technique Using The Talbot Effect

The Talbot effect - or self-imaging phenomenon - is applied to the measurement of focal lengths. The technique only requires axial distances to be measured and is suitable for both converging and diverging thick lenses.

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.

Hybrid (refractive-diffractive) Fourier processor: A novel optical architecture for achromatic processing with broadband point-source illumination

We report on an achromatic Fourier processor constituted basically by a quasi-wavelength-independent imaging forming system whose first half performs an achromatic Fourier transform of the colour input. The novel optical architecture, only formed by a small number of diffractive and refractive lenses, works under white-light point-source illumination and provides an intermediate achromatic real Fraunhofer plane and a final colour image without chromatic distortion. In this way, our optical processor performs simultaneously, with a single filter, the same spatial filtering operation for all the spectral components of the broadband illumination. The practical capabilities of our proposal are …

Shift-variant digital holographic microscopy: inaccuracies in quantitative phase imaging

Inaccuracies introduced in quantitative phase digital holographic microscopy by the use of nontelecentric imaging systems are analyzed. Computer modeling of the experimental result shows that even negligible errors in the radius and center of curvature of the numerical compensation needed to get rid of the remaining quadratic phase factor introduce errors in the phase measurements; these errors depend on the position of the object in the field-of-view. However, when a telecentric imaging system is utilized for the recording of the holograms, the numerical modeling and experimental results show the shift-invariant behavior of the quantitative-phase digital holographic microscope.

Nearly zero ultraflattened dispersion in photonic crystal fibers.

We present a procedure for achieving photonic crystal fibers with nearly zero ultraflattened group-velocity dispersion. Systematic knowledge of the special guiding properties of these fibers permits the achievement of qualitatively novel dispersion curves. Unlike the behavior of conventional fibers, this new type of dispersion behavior permits remarkably improved suppression of third-order dispersion, particularly in the low-dispersion domain.

Variable fractional Fourier processor: a simple implementation: erratum

One-dimensional error-diffusion technique adapted for binarization of rotationally symmetric pupil filters

Abstract Two novel algorithms for the binarization of continuous rotationally symmetric real and positive pupil filters are presented. Both algorithms are based on the one-dimensional error diffusion concept. In our numerical experiment an original gray-tone apodizer is substituted by a set of transparent and opaque concentric annular zones. Depending on the algorithm the resulting binary mask consists of either equal width or equal area zones. The diffractive behavior of binary filters is evaluated. It is shown that the filter with equal width zones gives Fraunhofer diffraction pattern more similar to that of the original gray-tone apodizer than that with equal area zones, assuming in both…

Wavelength-compensated Fourier and Fresnel transformers: a unified approach

We recognize that one can adapt any dispersion-compensated broadband optical Fourier transformer to achieve wavelength compensation in the Fresnel diffraction region just by inserting a diffractive lens at the input plane and vice versa. This unification procedure is employed in a second stage in the design of a novel hybrid (diffractive-refractive) optical setup that provides, in a sequential way, nearly wavelength-independent Fresnel diffraction patterns in the irradiance of the object transmittance.

Guiding properties of a photonic quasi-crystal fiber based on the thue-morse sequence

We present a novel microstructured optical fiber having a quasi-periodic distribution of air holes based on the Thue–Morse sequence. The transverse section of these fibers is basically a two-dimensional photonic quasi-crystal that can also provide complete photonic bandgaps without being a perfect periodic structure. Like in the conventional photonic crystal fibers, if the quasi-periodicity is broken by decreasing the size of some air holes or by introducing an extra air hole, the modified holes become defects that localize and guide light along the fiber. The guidance is attributed to the inhibition of transverse radiation produced by the photonic quasi-crystal cladding. Dispersion curves …

Vector Description of a Realistic Photonic Crystal Fiber

One-shot color digital holography based on the fractional talbot effect

We present a simple method for recording on-axis color digital holograms in a single shot. Our system performs parallel phase-shifting interferometry by using the fractional Talbot effect for every chromatic channel simultaneously. Experimental results are also shown.

Use of a grating in a coherent optical-processing configuration for evaluating the refractive index of a lens: comments

La methode consiste en la determination de l'indice de refraction de la lentille d'essai a partir de la separation entre 2 ordres de diffraction successifs dans la figure de diffraction de Fraunhofer d'un reseau a 1 dimension, lorsque la lentille, qui effectue la transformation de Fourier a 2 dimensions, est immergee dans differents liquides a l'interieur d'une cellule en verre

Reconfigurable RF waveform generation using optical incoherent sources

An RF waveform generator operating with incoherent broadband light is successfully implemented. Complex RF ~10 GHz bandwidth waveforms are generated by means of incoherent wavelength-to-time mapping. Our technique can be scaled to the mm-wave range.

Octave-spanning ultraflat supercontinuum with soft-glass photonic crystal fibers

We theoretically identify some photonic-crystal-fiber structures, made up of soft glass, that generate ultrawide (over an octave) and very smooth supercontinuum spectra when illuminated with femtosecond pulsed light. The design of the fiber geometry in order to reach a nearly ultraflattened normal dispersion behavior is crucial to accomplish the above goal. Our numerical simulations reveal that these supercontinuum sources show high stability and no significant changes are detected even for fairly large variations of the incident pulse. Ministerio de Ciencia e Innovación (TEC2008-05490) and Generalitat Valenciana (GV/2007/043).

Use of balanced detection in single-pixel imaging

We introduce balanced detection in combination with simultaneous complementary illumination in a single-pixel architecture. With this novel detection scheme we are able to recover a real-time video stream in presence of ambient light.

Supercontinuum spectral control

Supercontinuum (SC) generation in photonic crystal fibers (PCFs) is a cutting-edge phenomenon extensively studied in recent years [1]. SC has found many scientific and technological applications. The control of the SC spectral characteristics is crucial in most of them. A pioneering attempt in this direction was reported in Ref. [2]. We point out that SC is typically generated by accessing the anomalous dispersion regime of the fiber, i.e., when the group velocity dispersion (GVD) coefficient is lower than zero, β 2 ≪0. The recent achievement of soft-glass PCFs, namely, PCFs made up of a transparent material that shows higher nonlinear response than the widely used fused silica, opens new p…

Computational imaging with a balanced detector

Single-pixel cameras allow to obtain images in a wide range of challenging scenarios, including broad regions of the electromagnetic spectrum and through scattering media. However, there still exist several drawbacks that single-pixel architectures must address, such as acquisition speed and imaging in the presence of ambient light. In this work we introduce balanced detection in combination with simultaneous complementary illumination in a single-pixel camera. This approach enables to acquire information even when the power of the parasite signal is higher than the signal itself. Furthermore, this novel detection scheme increases both the frame rate and the signal-to-noise ratio of the sys…

Lossless equalization of frequency combs

Frequency combs obtained by sinusoidal phase modulation of narrow-band continuous-wave lasers are widely used in the field of optical communications. However, the resulting spectral envelope of the comb is not at. In this Letter, we propose a general and eficient approach to achieve at frequency combs with tunable bandwidth. The idea is based on a two-step process. First, eficient generation of a train with temporal at-top-pulse profile is required. Second, we use large parabolic phase modulation in every train period in order to map the temporal intensity shape into the spectral domain. In this way, the resulting spectral envelope is at and the size is tunable with the chirping rate. Two d…

Diffractive optics for quasi-direct space-to-time pulse shaping.

The strong chromatic behavior associated with a conventional diffractive lens is fully exploited to propose a novel optical device for pulse shaping in the femtosecond regime. This device consists of two optical elements: a spatially patterned circularly symmetric mask and a kinoform diffractive lens, which are facing each other. The system performs a mapping between the spatial position of the masking function expressed in the squared radial coordinate and the temporal position in the output waveform. This space-to-time conversion occurs at the chromatic focus of the diffractive lens, and makes it possible to tailor the output central wavelength along the axial location of the output point…

Flat-top ultra-wideband photonic filters based on mutual coherence function synthesis

A novel all-incoherent optical circuit that allows for band-pass microwave-photonic filter design is presented and verified through numerical simulation. In contrast to conventional spectrum-sliced optical architectures that operate on the basis of a finite number of discrete taps, our proposal is based on arbitrary shaping of the spectrum of the broadband optical source in a conventional frequency encoder. This fact dramatically increases the free spectral range of the filter with respect to the conventional discrete-time optical processing. The filter transfer function is given by the mutual coherence function of the filtered source which allows, through an inverse problem, sculpting the …

Pulse-by-pulse method to characterize partially coherent pulse propagation in instantaneous nonlinear media.

We propose a numerical method for analyzing extensively the evolution of the coherence functions of nonstationary optical pulses in dispersive, instantaneous nonlinear Kerr media. Our approach deals with the individual propagation of samples from a properly selected ensemble that reproduces the coherence properties of the input pulsed light. In contrast to the usual strategy assuming Gaussian statistics, our numerical algorithm allows us to model the propagation of arbitrary partially coherent pulses in media with strong and instantaneous nonlinearities.

Diffractive optics for spectral tuning of second harmonic and supercontinuum generated in nonlinear crystals

It is shown that diffractive lenses can tune the spectrum of femtosecond pulses after nonlinear optical processes. We focus on spectra of second-order pulses generated in birefringent crystals and supercontinuum in sapphire crystals. The tunability is achieved by changing the relative distance between the nonlinear crystal and the diffractive lens.

Optical encryption with compressive ghost imaging

Ghost imaging (GI) is a novel technique where the optical information of an object is encoded in the correlation of the intensity fluctuations of a light source. Computational GI (CGI) is a variant of the standard procedure that uses a single bucket detector. Recently, we proposed to use CGI to encrypt and transmit the object information to a remote party [1]. The optical encryption scheme shows compressibility and robustness to eavesdropping attacks. The reconstruction algorithm provides a relative low quality images and requires high acquisitions times. A procedure to overcome such limitations is to combine CGI with compressive sampling (CS), an advanced signal processing theory that expl…

Biorthonormal-basis method for the vector description of optical-fiber modes

This paper gives the theoretical basis for the development of real vector modal methods to describe optical-fiber modes. To this end, the vector wave equations, which determine the electromagnetic fields, are written in terms of a pair of linear, nonself-adjoint operators, whose eigenvectors satisfy biorthogonality relations. The key of our method is to obtain a matrix representation of the vector wave equations in a basis that is defined by the modes of an auxiliary system. Our proposed technique can be applied to fibers with any profile, even those with a complex refractive index. An example is discussed to illustrate our approach.

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.

Parallel phase-shifting digital holography based on the fractional Talbot effect

A method for recording on-axis single-shot digital holograms based on the self-imaging phenomenon is reported. A simple binary two-dimensional periodic amplitude is used to codify the reference beam in a Mach-Zehnder interferometer, generating a periodic three-step phase distribution with uniform irradiance over the sensor plane by fractional Talbot effect. An image sensor records only one shot of the interference between the light field scattered by the object and the codified parallel reference beam. Images of the object are digitally reconstructed from the digital hologram through the numerical evaluation of the Fresnel diffraction integral. This scheme provides an efficient way to perfo…

Donor and acceptor guided modes in photonic crystal fibers.

We present a triangular photonic-crystal-fiber structure that exhibits guided modes simultaneously above and below the first conduction band. We achieve this configuration by decreasing the size of one of the airholes (the defect) in a specific triangular lattice. More generally, we analyze the behavior of guided modes that depends on the size of the defect. Defects generated by decreasing or increasing the size of one of the holes produce donor or acceptor guided modes, respectively, in analogy with impurity levels in solid-state crystals. We conclude that the guiding mechanism for both donor and acceptor modes is produced by a unique phenomenon of multiple interference by a periodic struc…

Phase imaging via compressive sensing

This communication develops a novel framework for phase imaging at optical wavelength by merging digital lenless phase-shifting holography with single-pixel optical imaging based on compressive sensing.

High-visibility interference fringes with femtosecond laser radiation.

We propose and experimentally demonstrate an interferometer for femtosecond pulses with spectral bandwidth about 100 nm. The scheme is based on a Michelson interferometer with a dispersion compensating module. A diffractive lens serves the purpose of equalizing the optical-path-length difference for a wide range of frequencies. In this way, it is possible to register high-contrast interference fringes with micrometric resolution over the whole area of a commercial CCD sensor for broadband femtosecond pulses.