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.

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.

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.

Reduction of the spherical aberration effect in high-numerical-aperture optical scanning instruments.

In modern high-numerical-aperture (NA) optical scanning instruments, such as scanning microscopes, optical data storage systems, or laser trapping technology, the beam emerging from the high-NA objective focuses deeply through an interface between two media of different refractive index. Such a refractive index mismatch introduces an important amount of spherical aberration, which increases dynamically when scanning at increasing depths. This effect strongly degrades the instrument performance. Although in the past few years many different techniques have been reported to reduce the spherical aberration effect, no optimum solution has been found. Here we concentrate on a technique whose mai…

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.

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 …

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.

Self-referenced phase reconstruction proposal of Ghz bandwidth non-periodical optical pulses by in-fiber semi-differintegration

Abstract We propose two new techniques able to retrieve the phase profile of a given temporal optical pulse based on the use of in-fiber semi-differintegral operators, where by semi-differintegration we mean either a 0.5th-order differentiation or integration. In both cases, the signal's temporal phase can be obtained by simple dividing two temporal intensity profiles, namely the intensities of the input and output pulses of a spectrally shifted semi-differintegral operator. In both cases, we obtained simple analytical expressions for the phase profile. The techniques are self-referenced and well-suited for real-time applications. We numerically prove the viability of these proposals.

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.

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.

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…

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…

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.

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…

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.

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.

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…

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…

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…

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…

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…

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…

Resolution-enhanced optical coherence tomography based on classical intensity interferometry.

We propose a fourth-order interference scheme for optical coherence tomography operating with broadband incoherent (or quasi-incoherent) light. It is shown that using this proposal, an axial resolution improvement by a factor of 2 and a better sensitivity for weakly reflecting samples are obtained than with the standard second-order correlation scheme. From a practical perspective, we suggest the use of broadband Q-switched pulses and performing ultrafast intensity correlation with a nonlinear crystal. The global performance of our proposal is illustrated by means of numerical simulations

Wavelength compensation of broadband light diffraction

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

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.

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.

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.

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 …

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.

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.

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.

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.

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…

Reconfigurable Shack-Hartmann sensor without moving elements.

We demonstrate wavefront sensing with variable measurement sensitivity and dynamic range by means of a programmable microlens array implemented onto an off-the-shelf twisted nematic liquid crystal display operating as a phase-only spatial light modulator. Electronic control of the optical power of a liquid lens inserted at the aperture stop of a telecentric relay system allows sensing reconfigurability without moving components. Results of laboratory experiments show the ability of the setup to detect both smooth and highly aberrated wavefronts with adequate sensitivity.

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…

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.