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…
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.
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.
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…
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…
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…
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.
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.
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…
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.
Focal switch: a new effect in low-Fresnel-number systems
It is shown for the first time we believe, that when a spherical wave illuminates a certain type of diffracting screen, in addition to the expected focal-shift effect, depending on the value of the Fresnel number of the focusing system, a focal switch effect can appear, i.e., an increase in the height of the lateral lobe of the axial-intensity distribution over that of the central lobe.
Wavelength compensation of broadband light diffraction
Optoelectronic Information Encryption with Incoherent Light
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…
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.
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.
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.
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…