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Iterative algorithm for subaperture stitching test with spherical interferometers.

Recently we have proposed an iterative algorithm for subaperture stitching interferometry. It was referred to as the subaperture stitching and localization (SASL) algorithm. The limitation of the algorithm is that three-dimensional Cartesian coordinates are required, whereas the standard spherical interferometer can read out only the phase differences on the pixels. On the basis of the SASL algorithm, we propose an iterative algorithm for a spherical subaperture stitching test. It deals with data directly from the spherical interferometer. Unknown radii of best-fit spheres for a null test of subapertures are included in the optimization variables. The developed algorithm inherits the advantages of the SASL algorithm.

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Spiral interferogram analysis.

Interference microscopy using spatial Fourier filtering with a vortex phase element leads to interference fringes that are spirals rather than closed rings. Depressions and elevations in the optical thickness of the sample can be distinguished immediately by the sense of rotation of the spirals. This property allows an unambiguous reconstruction of the object's phase profile from one single interferogram. We investigate the theoretical background of "spiral interferometry" and suggest various demodulation techniques based on the processing of one single interferogram or multiple interferograms.

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Bifocal optical coherenc refractometry of turbid media.

We propose and demonstrate a novel technique, which we term bifocal optical coherence refractometry, for the rapid determination of the refractive index of a turbid medium. The technique is based on the simultaneous creation of two closely spaced confocal gates in a sample. The optical path-length difference between the gates is measured by means of low-coherence interferometry and used to determine the refractive index. We present experimental results for the refractive indices of milk solutions and of human skin in vivo. As the axial scan rate determines the acquisition time, which is potentially of the order of tens of milliseconds, the technique has potential for in vivo refractive-index measurements of turbid biological media under dynamic conditions.

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Three-dimensional tracking of small spheres in focused laser beams: influence of the detection angular aperture.

Back-focal-plane interferometry is a method capable of determining the three-dimensional position of a particle with high precision (< 3 nm) at high sampling rates (1 MHz). We investigated theoretically the performance of such a system for dielectric spheres with diameters D = 0.53-3 microm and for metallic spheres with D < or = 300 nm. Good sensitivity and linearity were achieved for a detection angular aperture sin(alpha) of no more than 0.5. A value of sin(alpha) > 0.7 should be used only for dielectric spheres with diameters approximately equal to the laser wavelength. Harmonic optical traps can be calibrated by measurement of the thermal motion of the sphere. We performed Brownian dynamics simulations and subsequent thermal noise analyses to prove that the wrong sin(alpha) incorrectly suggests an increased and nonharmonic axial trapping potential.

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Strong Bragg gratings photoinduced by 633-nm illumination in evaporated As2Se3 thin films.

Bragg gratings are used in several photonic devices to reflect, and thus to isolate, specific wavelengths of light. Gratings can be photoinduced in chalcogenide glasses by illumination of bandgap light in an interference pattern. We used holographic interferometry to create Bragg gratings in amorphous As2Se3 thin films with a period of 0.56 microm by illumination with 633-nm light. The quality of the gratings was tested in real time, and refractive-index modulations as high as 0.037 were measured. These gratings were found to be stable over a period of several months if they were kept in the dark.

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Enhancing the phase profile and contrast of an interferogram by polarization recording in bacteriorhodopsin.

Interferometry is a technique for reconstructing the profiles of phase objects. We present a novel interferometric setup for generating interferograms with doubled phase profile and enhanced contrast compared with the standard interferogram. The proposed system consists of a two-beam interferometer in which the reference and test waves are circularly polarized orthogonally to each other. They are superposed upon a bacteriorhodopsin film, creating a polarization grating that is distorted by the phase of the test object. This polarization pattern is read by a polarized He-Ne beam. We show analytically and experimentally that, when the zero diffraction order is removed, an interferogram with doubled phase profile and enhanced contrast is obtained.

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Phase-shifting windowed Fourier ridges for determination of phase derivatives.

Determination of the phase or phase derivative from interferometric fringe patterns is an important task in optical interferometry. The use of wavelet ridges was recently shown to be an effective method for phase retrieval from a single fringe pattern. One necessary requirement in this method is the need for carrier frequency. In cases when carrier frequency is not available, the novel phase-shifting windowed Fourier ridges method can be used. Phase derivatives with the proper sign can be directly retrieved even in the presence of noise. An application for curvature determination from speckle shearographic fringes demonstrates the effectiveness of the method.

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Diode-pumped 10-fs Cr3+:LiCAF laser.

We demonstrate 10-fs pulses from a diode-pumped, soft-aperture Kerr lens mode-locked Cr3+:LiCAF laser with a spectral bandwidth of 150 nm and 40 mW of output power at a repetition rate of 110 MHz. For dispersion compensation, double-chirped mirrors and prisms are used. The pulses are characterized by use of spectral shearing interferometry.

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Generation of 3.8-fs pulses from adaptive compression of a cascaded hollow fiber supercontinuum.

We demonstrate generation of 3.8-fs pulses with energies of up to 15 microJ from a supercontinuum produced in two cascaded hollow fibers. Ultrabroadband dispersion compensation was achieved through a closed-loop combination of a spatial light modulator for adaptive pulse compression and spectral-phase interferometry for direct electric-field reconstruction (SPIDER) measurements as feedback signal.

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Distributed three-dimensional fiber Bragg grating refractometer for biochemical sensing.

We demonstrate a three-dimensional (3-D) distributed refractometer that measures refractive index in a small volume. The sensor is based on an evanescent-wave fiber Bragg grating that is interrogated by low-coherence spectral interferometry. The measurement can be performed on a short time scale without the need for a mechanical scan. The new sensor was used to simultaneously measure glucose concentration in several droplets along a single sensor and to interrogate the time-dependent evaporation process of a water droplet. The new measurement technique might enable novel 3-D distributed sensors to be developed and multiple discrete measurements to be made in a small volume.

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Inverse scattering problem for optical coherence tomography.

We deal with the imaging problem of determining the internal structure of a body from backscattered laser light and low-coherence interferometry. Specifically, using the interference fringes that result when the backscattering of low-coherence light is made to interfere with the reference beam, we obtain maps detailing the values of the refractive index within the sample. Our approach accounts fully for the statistical nature of the coherence phenomenon; the numerical experiments that we present, which show image reconstructions of high quality, were obtained under noise floors exceeding those present for various experimental setups reported in the literature.

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Optical pulse compression to 3.4 fs in the monocycle region by feedback phase compensation.

We compensated for chirp of optical pulses with an over-one-octave bandwidth (495-1090 nm; center wavelength of 655.4 nm) produced by self-phase modulation in a single argon-filled hollow fiber and generated 3.4-fs, 1.56 optical-cycle pulses (500 nJ, 1-kHz repetition rate). This was achieved with a feedback system combined with only one 4-f phase compensator with a spatial light modulator and a significantly improved phase characterizer based on modified spectral phase interferometry for direct electric-field reconstruction. To the best of our knowledge, this is the shortest pulse in the visible-to-infrared region.

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Piezo-driven deformable mirror for femtosecond pulse shaping.

We have developed a deformable, gold-coated mirror based on piezoelectric actuators with 15-micros response time. With 20 independent channels we were able to compress 72-fs pulses from a Ti:sapphire oscillator down to 45 fs in a 4f zero-dispersion compressor arrangement. Spectral interference was used to measure the mirror performance, while the spectral phase interferometry for direct electric field reconstruction (SPIDER) technique was used for the laser pulse characterization.

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Chromatic dispersion characterization by direct instantaneous frequency measurement.

A new concept for the measurement of chromatic dispersion is presented. The group delay of the device under test is directly obtained from the instantaneous frequency of a short optical pulse after propagation in the device, itself obtained with temporal and spectral interferometry. Temporal and spectral fringe encoding provide excellent accuracy and resistance to noise, and a wide variety of dispersions can be characterized even at high insertion losses.

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Zero-additional-phase SPIDER: full characterization of visible and sub-20-fs ultraviolet pulses.

We demonstrate a novel spectral-shearing interferometry setup for characterizing the temporal amplitude and phase of ultrashort optical pulses over an extremely wide wavelength region. By the mixing of two strongly chirped auxiliary pulses with the pulse to be characterized, two spectrally sheared replicas are generated, and their spectral interference is evaluated. We fully characterize 10-fs pulses in the visible region by sum-frequency mixing and 19-fs pulses in the ultraviolet region by difference-frequency mixing. The scheme is self-referencing and highly sensitive. The zero-additional-phase scheme does not alter the unknown pulses and yields the pulse shape at the interaction point of a spectroscopic experiment.

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Generalized method for wave-front analysis.

We suggest and demonstrate a new method for wave-front analysis based on common-path phase-shift interferometry. We introduce a formalism and an iterative mathematical algorithm in which the wave front is transformed, modified, and inversely transformed. The resulting intensity data are sufficient to reconstruct the entire wave front. In a more restricted case, in which the wave-front modifications are arbitrarily applied over arbitrary spatial regions of the wave front, the wave front is reconstructed semianalytically by use of a model that allows a local solution, followed by an iterative algorithm. Measurement results indicating that the suggested approach has an improved measurement accuracy with respect to existing quantitative phase measurement methods are presented.

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Controlling image size as a function of distance and wavelength in Fresnel-transform reconstruction of digital holograms.

A method for controlling the size of amplitude and phase images reconstructed from digital holograms by the Fresnel-transform method is proposed and demonstrated. The method can provide a constant reconstruction pixel width in the reconstructed image plane, independent of the recording and reconstruction distance. The proposed method makes it possible to maintain the size of an object for a sequence of digital holograms recorded at different distances and, therefore, to subtract phase maps for an object recorded at different distances. Furthermore, the method solves the problem of superimposition in multiwavelength digital holography for color display and holographic interferometry applications.

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Tunable two-dimensional femtosecond spectroscopy.

We have developed a two-dimensional (2D) Fourier-transform femtosecond spectroscopy technique for the visible spectral region. Three-pulse photon echo signals are generated in a phase-matched noncollinear four-wave mixing box geometry that employs a 3-kHz repetition-rate laser system and optical parametric amplification. Nonlinear signals are fully characterized in amplitude and phase by spectral interferometry. Unlike for previous setups, we achieve long-term phase stability by employing diffractive optics and interferometric accuracy of excitation-pulse time delays by using movable glass wedges. As an example of this technique, 2D correlation and relaxation spectra at 600 nm are shown for a solution of Nile Blue dye in acetonitrile.

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