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Owing to the low-gravity conditions in space, space-borne laboratories enable experiments with extended free-fall times. Because Bose-Einstein condensates have an extremely low expansion energy, space-borne atom interferometers based on Bose-Einstein condensation have the potential to have much greater sensitivity to inertial forces than do similar ground-based interferometers. On 23 January 2017, as part of the sounding-rocket mission MAIUS-1, we created Bose-Einstein condensates in space and conducted 110 experiments central to matter-wave interferometry, including laser cooling and trapping of atoms in the presence of the large accelerations experienced during launch. Here we report on experiments conducted during the six minutes of in-space flight in which we studied the phase transition from a thermal ensemble to a Bose-Einstein condensate and the collective dynamics of the resulting condensate. Our results provide insights into conducting cold-atom experiments in space, such as precision interferometry, and pave the way to miniaturizing cold-atom and photon-based quantum information concepts for satellite-based implementation. In addition, space-borne Bose-Einstein condensation opens up the possibility of quantum gas experiments in low-gravity conditions.sup.1,2.A Bose-Einstein condensate is created in space that has sufficient stability to enable its characteristic dynamics to be studied., Author(s): Dennis Becker [sup.1] , Maike D. Lachmann [sup.1] , Stephan T. Seidel [sup.1] [sup.15] , Holger Ahlers [sup.1] , Aline N. Dinkelaker [sup.2] , Jens Grosse [sup.3] [sup.4] , [...]

The Sagnac effect has been shown in inertial frames as well as rotating frames. We solve the problem of the generalized Sagnac effect in the standard synchronization of clocks. The speed of a light beam that traverses an optical fiber loop is measured with respect to the proper time of the light detector, and is shown to be other than the constant c, though it appears to be c if measured by the time standard-synchronized. The fiber loop, which can have an arbitrary shape, is described by an infinite number of straight lines such that it can be handled by the general framework of Mansouri and Sexl (MS). For a complete analysis of the Sagnac effect, the motion of the laboratory should be taken into account. The MS framework is introduced to deal with its motion relative to a preferred reference frame. Though the one-way speed of light is other than c, its two-way speed is shown to be c with respect to the proper time. The theoretical analysis of the generalized Sagnac effect corresponds to the experimental results, and shows the usefulness of the standard synchronization. The introduction of the standard synchrony can make mathematical manipulation easy and can allow us to deal with relative motions between inertial frames without information on their velocities relative to the preferred frame. Key words: generalized Sagnac effect, standard synchronization, speed of light, test theory, general framework for transformation. On a vu l'effet Sagnac aussi bien dans les referentiels inertiels qu'en rotation. Nous solutionnons le probleme de l'effet Sagnac generalise dans la synchronisation standard des horloges. La vitesse d'un signal lumineux dans la fibre optique est mesuree par rapport au temps propre du detecteur de lumiere et on montre que ce n'est pas la constante c, alors qu'elle semble etre c si mesuree par le temps de la synchronisation standard. La boucle de fibre, qui peut avoir une forme quelconque, est decrite par un nombre infini de lignes droites, ce qui permet de travailler dans le cadre de Mansouri et Sexl (MS). Pour une analyse complete de l'effet Signac, on devrait tenir compte du mouvement du laboratoire. Le cadre MS est introduit pour tenir compte d'un mouvement par rapport a un referentiel prefere. Meme si la vitesse dans une direction est autre que c, la vitesse aller-retour est egale a c par rapport au temps propre. L'analyse theorique de l'effet Sagnac generalise correspond aux resultats experimentaux et montre l'utilite de la synchronisation standard. L'introduction d'une synchronie standard peut rendre les manipulations mathematiques plus faciles et permettre de tenir compte de mouvements entre referentiels inertiels sans information sur leurs vitesses par rapport a un referentiel prefere. [Traduit par la Redaction] Mots-cles: effet Sagnac generalise, synchronisation standard, vitesse de la lumiere, theorie du test, cadre general de transformation., 1. Introduction The Sagnac effect is a phenomenon of interference by two light beams propagating along a closed loop in opposite directions. It has usually been recognized to occur in [...]

The Sagnac experiment is analysed in terms of the Ritz hypothesis, after first setting out the principles and ideas that underpin the analysis. One is the concept of an extinction distance, the distance over which all memory of the source velocity is lost as a result of absorption and re-emission by the atoms and molecules in the medium. It is shown that no fringe shift should occur on rotation of a Sagnac type interferometer in high vacuum, but the expected shift should occur in laboratory air where the extinction distance is much shorter than the dimensions of the apparatus. An outline is given of a proposed experiment that will provide a comparative test in vacuum and in air, thereby acting as a decisive test of the Ritz hypothesis.Keywords: Interferometry, Light propagation, Relativity, Ritz hypothesis, Sagnac effectPACS: 03.30.+p, 42.25.Hz, 1. IntroductionIt is over one hundred years since Albert Einstein [1] proposed his Special Theory of Relativity to explain the null result of the Michelson-Morley experiment [2]. In that time [...]

AEgIS (Antimatter experiment: gravity, interferometry, spectroscopy) is an experiment approved by CERN with the goal of studying antihydrogen physics. In AEgIS, antihydrogen will be produced by charge exchange reactions of cold antiprotons with positronium atoms excited in a Rydberg state (n > 20). In the first phase of the experiment, controlled acceleration by an electric field gradient (Stark effect) and subsequent measurement of free fall in a Moire deflectometer will allow a test of the weak equivalence principle. In a second phase, the antihydrogen will be slowed, confined, and laser-cooled to perform CPT studies and detailed spectroscopy. In the present work, after a general description of the experiment, the present status of advancement will be reviewed, with special attention to the production and excitation of positronium atoms. PACS Nos: 03.75.Dg, 06.30.Gv, 25.43.+t, 34.80.Lx AEgIS (Experience sur l'Antimatiere: Gravite;, Interfeerometrie, Spectromeetrie) est une experience approuvee par le CERN qui vise une etude globale de la physique de l'anti-hydrogene. Dans AEgIS, l'anti-hydrogene sera produit par des reactions d'echange de charges d'anti-protons froids avec des atomes de positronium excitees dans un etat de Rydberg (n > 20). Dans la premiere phase de l'experience, l'acceileration est controlee par un gradient de champ electrique (effet Stark); une mesure subsequente en chute libre dans un deflectometre de Moire nous fournira un test du principe d'equivalence faible. Dans une deuxieme phase, l'anti-hydrogene sera ralenti, confine et refroidi par laser pour des etudes de CPT et de spectroscopie de precision. Apres une description geenerale de l'experience, nous passons ici en revue l'etat d'avancement des travaux en accordant une attention particuliere a la production et l'excitation des atomes de positronium. [Traduit par la Redaction], 1. Introduction A new generation of antimatter experiments has been opened after the first experiments of antihydrogen production in laboratory conditions at the CERN laboratory [1] and at Fermilab [2]. [...]

A real-time method for heterodyne speckle pattern interferometry using the correlation image sensor (CIS) is proposed. The CIS demodulates the interference phase of heterodyned speckle wavefronts pixelwise at an ordinary video frame rate. The proposed method neither suffers loss of spatial resolution nor requires a high frame rate. Interferometers for out-of-plane and in-plane deformation are developed with a 200 x 200 pixel CIS camera. Experimental results confirm that the proposed method realizes real-time imaging of a rough-surfaced object under deformation. The average standard deviations of demodulated phase-difference images for the out-of-plane and in-plane interferometers are 0.33 and 0.13 rad, respectively. [c] 2010 Optical Society of America OCIS codes: 100.2550, 100.3175, 120.5050, 120.6165, 040.2840.

In this paper, we experimentally demonstrate and compare single-exposure multiple-beam interference lithography based on conventional laser interference, evanescent wave interference, and surface plasmon interference. The proposed two-beam and four-beam interference approaches are carried out theoretically and verified experimentally, employing the proposed configurations so as to realize the patterning of one- and two-dimensional periodic features on photoresists. A custom-fabricated grating is employed in the configuration in order to achieve two- and four-beam interference. [c] 2010 Optical Society of America OCIS codes: 220.3740, 240.6680, 260.3910.

Integrated optic beam combiners offer many advantages over conventional bulk optic implementations for astronomical imaging. To our knowledge, integrated optic beam combiners have only been demonstrated at operating wavelengths below 4 [micro]m Operation in the midinfrared wavelength region, however, is highly desirable. In this paper, a theoretical design technique based on three coupled waveguides is developed to achieve fully achromatic, broadband, polarization-insensitive, lossless beam combining. This design may make it possible to achieve the very deep broadband nulls needed for exoplanet searching. [c]2010 Optical Society of America OCIS codes: 110.3175, 350.1260, 130.3120, 120.6168, 130.3060.

In this paper, we present a new scheme for parallel phase-shifting interferometry that employs a Michelson-like architecture and a simple polarization unit to generate two phase-shifting interferograms with phase shift of [pi]/2 at a single camera exposure. The parallel phase-shifting unit is built with simple optical components, and the distance between the parallel interferograms can be adjusted conveniently. Phase reconstruction is performed by using an algorithm developed for two-step phase-shifting interferometry. The practicability of the proposed configuration and the reconstruction method is demonstrated by experiments. [c] 2010 Optical Society of America OCIS codes: 050.5080, 090.2880, 260.5430, 180.3170.

We present a measurement technique to determine the thickness of a transparent glass plate (GP) by using a lateral shearing cyclic path optical configuration (CPOC) setup and polarization phase shifting interferometry (PPSI). In the technique, the GP introduces a longitudinal shift in the focus of the beam and, as a result, a spherical wavefront emerges from the lens, which is otherwise set for producing a collimated beam. Using CPOC, two laterally sheared orthogonally polarized beams are generated from the incident spherical wavefront. By applying PPSI, the slope of the optical path difference variation between the laterally sheared interfering beams is evaluated, and the radius of the spherical wavefront and the longitudinal shift of the beam focus are calculated. The thickness of the GP is determined from the standard relation between the longitudinal shift of the focus introduced by the GP and the thickness of the GP. Results obtained for a GP of 9.810 mm thickness are presented. OCIS codes: 080.3630, 120.0120, 120.3180, 120.1680.

In this work, we have developed a different algorithm than the classical one on phase-shifting interferometry. These algorithms typically use constant or homogeneous phase displacements and they can be quite accurate and insensitive to detuning, taking appropriate weight factors in the formula to recover the wrapped phase. However, these algorithms have not been considered with variable or inhomogeneous displacements. We have generalized these formulas and obtained some expressions for an implementation with variable displacements and ways to get partially insensitive algorithms with respect to these arbitrary error shifts. OCIS codes: 120.0120, 120.3180.

Two-dimensional refractive index profiles of ion exchanged channel waveguides in glass have been obtained from the analysis of interferometer data. To obtain depth data, a shallow bevel is produced in the glass by polishing. The refractive index profile information that is contained within the derivative of the phase data is extracted directly using a continuous wavelet transform algorithm. The algorithm used to characterize and smooth the wavelet ridge is discussed in detail. OCIS codes: 100.5070, 100.7410, 180.3170, 230.7380.

Laser scanning surveys were performed on the primary mirror of the very long baseline interferometry (VLBI) telescopes situated at Medicina and Noto observatories, with the specific purpose of investigating (1) gravity deformation patterns of the radio telescopes' primary reflector and (2) the magnitude and relative variations of focal length as the antennas are steered in elevation. Both instruments have Azimuth-Elevation mounts and have 32 m parabolic mirrors which were surveyed in steps of 15[degrees] spanning the 90-15[degrees] elevation range. The scanning sessions were performed from two standpoints using a GS200 Trimble-Mensi; the sampling interval was set to 2 cm at a distance of 15 m. The complete surface of the main reflector at every elevation position was obtained by merging the two separate point clouds acquired from the two standpoints; each elevation is represented by at least 1.3 millions points. The merged clouds were compared for determining relative deformation patterns and magnitude. As the elevation decreases from 90-15[degrees], the edges of the primary mirror of both telescopes fold in by a couple of cm. A least-squares adjustment was applied to point clouds corresponding to different elevations aimed at estimating the parameters of the rotational paraboloids that better fit the experimental data. This led to estimate the focal length variations induced by the structure deformative behavior. The focal lengths of the best-fit surfaces were compared. Their largest variation is found to be 2.5 cm at Medicina, between the 90[degrees] and the 15[degrees] positions. The clouds were also used to attempt a direct computation of the incoming radio signal's path length variation due to primary reflectors' deformations. Finally, two Leica total stations, a TDA5005 and a TC2003, were used to perform a survey of the local ground control network and of some selected targets placed on the edge of the dish. The comparison of the distances determined with the two terrestrial surveying methods (laser scanner versus triangulation and trilateration) highlights a statistically significant scale factor of about 1.0005 [+ or -] 0.0002, being the laser estimates smaller than those obtained with total stations. This study proves that laser scanners can be efficiently used to determine gravitational influences on large VLBI telescopes' primary reflectors: deformation patterns are clearly and reliably depicted, focal length and incoming radio signal path variations are precisely quantified. DOI: 10.1061/(ASCE)SU.1943-5428.0000008 CE Database subject headings: Lasers; Telescopes; Deformation; Surveys.

Experimental results from a video-rate terahertz interferometric imaging system are presented. The source emits continuous narrow bandwidth radiation at 0.1 THz. The 2D image of a point source is reconstructed at a rate of 16 ms per frame with a four-element detector array. The image resolution and quality are affected by the number of detectors, the configuration of the detection array, and how well the baselines are calibrated. Details of the hardware system and video-rate terahertz image are presented. OCIS codes: 110.3175, 100.3010.

The manufacturing of toric mirrors for the Very Large Telescope-Spectro-Polarimetric High-Contrast Exoplanet Research instrument (SPHERE) is based on Active Optics and stress polishing. This figuring technique allows minimizing mid and high spatial frequency errors on an aspherical surface by using spherical polishing with full size tools. In order to reach the tight precision required, the manufacturing error budget is described to optimize each parameter. Analytical calculations based on elasticity theory and finite element analysis lead to the mechanical design of the Zerodur blank to be warped during the stress polishing phase. Results on the larger (366 mm diameter) toric mirror are evaluated by interferometry. We obtain, as expected, a toric surface within specification at low, middle, and high spatial frequencies ranges. OCIS codes: 220.1080, 220.5450, 220.1250, 220.1000, 220.4610.

SIM PlanetQuest will perform narrow-angle astrometry with microarcsecond accuracy using starlight interferometry requiring tens of picometers accuracy in estimating the optical path difference change between observing two stars. One challenge is to accurately model the white-light fringes and calibrate the required model parameters. Previous studies have developed algorithms based on a CCD-pixel-level calibration scheme assuming slowly varying phase-dispersion functions. However, recent measurements from the SIM PlanetQuest Spectral Calibration Development Unit (SCDU) showed that wavefront aberrations caused the phase-dispersion functions to vary by tens of nanometers across the bandwidth of a CCD pixel, making the previous CCD-pixel-based calibration scheme inadequate. We present a white-light fringe model including the extra phase dispersions caused by the wavefront aberrations together with a calibration and estimation scheme using long-stroke fringe measurements to resolve the bandwidth of pixels. Using simulated data, we show that the total systematic errors in the calibration and estimation scheme are less than a picometer. With SCDU experimental data, we demonstrate that the end-to-end accuracy of the calibration and estimation algorithm is better than 20 pm, achieving the SIM PlanetQuest Engineering Milestone 4. OCIS codes: 100.2650, 120.3180, 120.5050, 120.5060.

We report novel approaches to the design of halftone masks for analog lithography. The approaches are derived from interferometric phase contrast. In a first step we show that the interferometric phase-contrast method with detour holograms can be reduced into a single binary mask. In a second step we introduce the interferometric phase-contrast method by interference of the object wavefront with the conjugate object wavefront. This method also allows for a design of a halftone mask. To use kinoform holograms as halftone phase masks, we show in a third step the combination of the zeroth-order phase-contrast technique with the interferometric phase-contrast method. OCIS codes: 220.3740, 100.5070, 220.4000.

An electronic speckle pattern interferometer is introduced that can produce time-averaged interferograms of harmonically vibrating objects in instances where it is impractical to isolate the object from ambient vibrations. By subtracting two images of the oscillating object, rather than the more common technique of subtracting an image of the oscillating object from one of the static objects, interferograms are produced with excellent visibility even when the object is moving relative to the interferometer. This interferometer is analyzed theoretically and the theory is validated experimentally. OCIS codes: 120.6160, 120.7280, 330.4150.

I describe an improved implementation of a previously reported interferometric device, the sampling field sensor (SFS) [Appl. Opt. 47, B32-B43 (2008)]. It provides X, Y, and XY shearing interferometric information simultaneously (space multiplexed) with amplitude and polarization information while using time-multiplexed phase shifting. Its simple common-path configuration makes it compact and vibration insensitive, as demonstrated by the ~ [lambda]/125 phase estimation repeatability that was below the coherent noise floor (estimated at ~ [lambda]/50). The SFS may be viewed as an efficient, robust and accurate full-field optical-digital interface, easy to integrate with traditional imaging systems. This is demonstrated by using the sensor as the focal plane array of a transmitted-light microscope in a straightforward setup using an illumination path polarization phase shifter. This work is focused on a qualitative demonstration and presents phase, amplitude, and polarization images of different types of human cheek cells and Caenorhabditis elegans larvae. OCIS codes: 090.1995, 120.3180, 120.5050, 170.0180, 180.3170, 350.5030.

A simple but reliable method, namely the working-point control by tuning the laser frequency, for the dynamic phase shift measurement in a passive homodyne interferometric fiber-optic sensor is proposed. A dc voltage calculated from the photodetector output is applied to the light source to control the interferometer at the condition of maximum sensitivity. Then the signal's phase shift can be obtained from the components of zero and fundamental frequencies. To test the method, an all polarization-maintaining Mach-Zehnder interferometer with a piezoelectric ceramic (PbZrTi[O.sub.3], or PZT) cylinder in one arm is constructed. The experimental results show that the simulation signal's phase shift generated by the PZT cylinder can be read out correctly with the method. It has the advantages of simplicities of operation, no-active element in the sensing head, and large operating bandwidth. It can be used for readout of dynamic phase shifts in various interferometric fiber-optic sensors. OCIS codes: 060.2370, 060.2920, 070.6020, 120.3180, 120.5050, 120.5060.

The problem of imaging through turbulent media has been studied frequently in connection with astronomical imaging and airborne radars. Therefore most image restoration methods encountered in the literature assume a stationary object, e.g., a star or a piece of land. In this paper the problem of interferometric measurements of slowly moving or deforming objects in the presence of air disturbances and vibrations is discussed. Measurement noise is reduced by postprocessing the data with a digital noise suppression filter that uses a reference noise signal measured on a small stationary plate inserted in the field of view. The method has proven successful in reducing noise in the vicinity of the reference point where the size of the usable area depends on the degree of spatial correlation in the noise, which in turn depends on the spatial scales present in the air turbulence. Vibrations among the optical components in the setup tend to produce noise that is highly correlated across the field of view and is thus efficiently reduced by the filter. OCIS codes: 090.2880, 010.7060, 110.0115.

We describe an interferometric ellipsometer that, in contrast to previous designs, requires a single reflection from a sample surface so that tan [psi], and A are measured directly. A reference beam is created in one arm of a modified Mach-Zehnder interferometer such that the p and s polarizations have a common phase and fixed relative amplitude, irrespective of the sample. This beam is combined interferometrically with the measurement beam. The output beam is spatially separated into its polarization components and temporal fringes created at the photodetectors via mechanical scanning of one of the mirrors. Measurements made on a reference Si[O.sub.2] film are in excellent agreement with the calibration certificate while those made on a glass surface demonstrate measurement capabilities for low reflectivity samples. Estimates of the noise performance indicate a precision, in air, of ~41 pm. OCIS codes: 120.0120, 120.2130, 120.3180.

White-light interferometry measuring an optically rough surface commonly does not resolve the lateral structure of the surface. This means that there are height differences within one resolution cell that exceed one-fourth of the wavelength of the light used. Thus the following questions arise: Which height is measured by white-light interferometry? How does the surface roughness affect the measurement uncertainty? The goal of the presented paper is to answer these questions by means of numerical simulations. Before the aforementioned questions can be answered, the distribution of the intensity of individual speckles, the influence of surface roughness, and the spectral width of the light source used are discussed. OCIS codes: 030.6140, 030.6600, 120.3180, 120.6650.

We observe power coupling from the fundamental mode to frequency-degenerate higher-order spatial modes in optical resonators illuminated with a 30 W laser. Thermally-induced modal frequency degeneracy facilitates power transfer from the fundamental mode to higher-order modes, reduces power coupling into the cavity, and triggers power fluctuations. Modeling thermoelastic deformation of a mirror's surface shows predicted modal frequency degeneracy to be in reasonable agreement with experimental observations. Predictions for the Laser Interferometer Gravitational-wave Observatory (LIGO) show that the circulating fundamental-mode power necessary for gravitational-wave detection is compromised at coating absorptions of 3.8 and 0.44ppm for Enhanced and Advanced LIGO Fabry-Perot cavities, respectively. OCIS codes: 140.0140, 140.4780, 140.6810, 230.5750, 260.5740.

A rapid algorithm for phase and amplitude reconstruction from a single spatial-carrier interferogram is proposed by bringing a phase-shifting mechanism into reconstruction of a carrier-frequency interferogram. The algorithm reconstructs phase through directly obtaining and integrating its real-value derivatives, avoiding a phase unwrapping process. The proposed method is rapid and easy to implement and is made insensitive to the profile of the interferogram boundaries by choosing a suitable integrating path. Moreover, the algorithm can also be used to reconstruct the amplitude of the object wave expediently without retrieving the phase profile in advance. The feasibility of this algorithm is demonstrated by both numerical simulation and experiment. OCIS codes: 100.5070, 100.2650, 120.3180, 120.5050.

We present a simple and novel algorithm for the phase extraction from a single interferogram based on the spatial processing of interference patterns. This new evaluation procedure is suitable for application in environments where the presence of vibrations impedes the use of a classical phase-shifting interferometry scheme with multiple exposures. The algorithm does not require the introduction of a linear carrier as required in Fourier transform techniques. The addition of a carrier can be a significant drawback, e.g. in the case of wavefronts with strong aberrations where the minimum required linear carrier is not even resolved by the detector. The basic idea relies on the spatial application of a temporal phase-shifting algorithm and an iterative correction process to obtain an accurate reconstruction of the wavefront. The validity and performance of the proposed method is shown with numerical and experimental results. OCIS codes: 120.3180, 120.5050, 120.3940.

An improved peak-to-peak method is developed for interrogating the absolute cavity length of fiber optic extrinsic Fabry--Perot interferometric (EFPI) sensors with high resolution. A fiber Fabry--Perot tunable filter (FFP-TF) is used to scan the optical spectrum of an EFPI, and the problems caused by the nonlinear performance and poor repeatability of the FFP-TF are removed by using a wavelength calibration technique. A linear fitting is used to calculate the wavelength spacing between two adjacent apexes in the optical spectrum, and the cavity length can be retrieved using this wavelength spacing. The experimental results show that the measuring resolution is improved from 25 to 1 [micro]m, and a linear output is also obtained. OCIS codes: 060.2370, 120.3930.

What we believe to be a new technique for the measurement of two-dimensional retardation distributions of a wave plate (WP) is presented. Phase-shifting interferometry has been applied for determining the relative retardation distribution using a Nomarski prism (NP) as a phase shitter. Absolute retardation distribution is obtained by accurately determining the position of zero retardation in the interference field using white light interference fringes and adjusting the phase distribution with respect to the zero retardation position. The measured absolute retardation distribution of the NP is subtracted from that obtained for the combination of the WP and NP, to get the desired retardation distributions for the WP. The technique is suitable for the measurement of phase retardation of both single and multiple order WPs, as the actual phase retardation distributions are obtained. Results obtained for WPs are presented. OCIS codes: 260.1180, 260.1440, 260.3160, 269.5430

An advanced iterative algorithm is presented to extract phase distribution from randomly and spatially nonuniform phase-shifted interferograms. The proposed algorithm divides the interferograms into small blocks and retrieves local phase shifts accurately by iterations. Therefore, the phase distribution can be calculated with high precision by eliminating the effect of tilts occurring during phase shifting. Simulated results and experiments demonstrate that the proposed algorithm exhibits high precision and converges faster than previous algorithms even when the tilt errors are up to 27.6% of the normal phase step. OCIS codes: 120.0120, 120.3180, 120.5050, 120.2650, 050.5080.

This paper introduces the innovative concept of multidimensional waveform encoding for spaceborne synthetic aperture radar (SAR). The combination of this technique with digital beamforming on receive enables a new generation of SAR systems with improved performance and flexible imaging capabilities. Examples are high-resolution wide-swath radar imaging with compact antennas, enhanced sensitivity for applications like along-track interferometry and moving object indication, and the implementation of hybrid SAR imaging modes that are well suited to satisfy hitherto incompatible user requirements. Implementation-specific issues are discussed and performance examples demonstrate the potential of the new technique for different remote sensing applications. Index Terms--Adaptive radar, along-track interferometry (ATI), ambiguity reduction, digital beamforming, displaced phase centre antenna (DPCA), ground moving target indication (GMTI), high-resolution wide-swath SAR imaging, hybrid SAR, MIMO SAR, synthetic aperture radar (SAR), waveform diversity.

Signal processing methods based on maximum-likelihood theory, discrete chirp Fourier transform, and spectral estimation methods have enabled accurate measurement of phase in phase-shifting interferometry in the presence of nonlinear response of the piezoelectric transducer to the applied voltage. We present the statistical study of these generalized nonlinear phase step estimation methods to identify the best method by deriving the Cramer-Rao bound. We also address important aspects of these methods for implementation in practical applications and compare the performance of the best-identified method with other bench marking algorithms in the presence of harmonics and noise. OCIS codes: 120.0120, 120.2880, 120.5050.

We present a technique for measuring the modal filtering ability of single mode fibers. The ideal modal filter rejects all input field components that have no overlap with the fundamental mode of the filter and does not attenuate the fundamental mode. We define the quality of a nonideal modal filter [Q.sub.f] as the ratio of transmittance for the fundamental mode to the transmittance for an input field that has no overlap with the fundamental mode. We demonstrate the technique on a 20 cm long mid-infrared fiber that was produced by the U.S. Naval Research Laboratory. The filter quality [Q.sub.f] for this fiber at 10.5 gm wavelength is 1000 [+ or -] 300. The absorption and scattering losses in the fundamental mode are approximately 8 dB/m. The total transmittance for the fundamental mode, including Fresnel reflections, is 0.428 [+ or -] 0.002. The application of interest is the search for extrasolar Earthlike planets using nulling interferometry. It requires high rejection ratios to suppress the light of a bright star, so that the faint planet becomes visible. The use of modal filters increases the rejection ratio (or, equivalently, relaxes requirements on the wavefront quality) by reducing the sensitivity to small wavefront errors. We show theoretically that, exclusive of coupling losses, the use of a modal filter leads to the improvement of the rejection ratio in a two-beam interferometer by a factor of [Q.sub.f]. OCIS codes: 060.2390, 060.2430, 060.2270.

The bio-optical compact disk (BioCD) is an optical biosensor that performs common-path molecular interferometry of patterned proteins on a disk spinning at high speed. The common-path configuration makes it ultrastable and allows surface height precision below 10 pm. In this paper we show that two complementary interferometric quadrature conditions exist simultaneously that convert the modulus and phase of the reflection coefficient, modulated by protein patterns on the disk surface, into intensity modulation at the detector. In the far field they separate into spatially symmetric and antisymmetric intensity modulation in response to the local distribution of protein. The antisymmetric response is equivalent to differential phase-contrast detection, and the symmetric response is equivalent to in-line (IL) common-path interferometry. We measure the relative sensitivities of these orthogonal channels to printed protein patterns on disk structures that include thermal oxide on silicon and Bragg dielectric stacks. The scaling mass sensitivity of the IL channel on oxide on silicon was measured to be 0.17 pg/mm. OCIS codes: 110.4190, 120.3180, 310.0860, 180.5810.

In this paper, we show that polarimetric and interferometric SAR (PolInSAR) images can be efficiently partitioned into homogeneous regions with a statistical technique based on minimization of a parameter-free criterion. This technique consists of finding a polygonal partition of the image that minimizes the stochastic complexity, assuming that the image is made of a tessellation of statistically homogeneous regions. The obtained results demonstrate that a global partition in statistically homogeneous regions of PolInSAR images can provide better results than a partition based on a single characteristic such as polarimetry or interferometry only. Index Terms--Image segmentation, polarimetric interferometry, SAR interferometry, SAR polarimetry, synthetic aperture radar (SAR).

We characterize the optical modulation properties of a polyvinyl alcohol/acrylamide (PVA/AA) photopolymer at the lowest end of recorded spatial frequencies. To achieve this goal we have constructed a double beam interferometer in combination with the setup to expose the recording material. This is a novel approach since usually holographic recording materials are only characterized at high spatial frequencies. Some benefits are provided by the approach we propose: a direct calculation of the properties of the material is possible, and on the other hand additional information can be obtained since the results are not influenced by diffusion processes. Furthermore, this characterization is needed to optimize the PVA/AA photopolymers for another range of applications, such as recording of diffractive optical elements, where very low spatial frequencies are recorded. Different PVA/AA compositions and layer thicknesses have been analyzed. We have found that, depending on the layer characteristics, we can achieve high values of the phase-shift modulation depth and enhance the sensitivity of the material. OCIS codes: 160.0160, 160.5470, 160.4670.

Astrometric measurements using stellar interferometry rely on the precise measurement of the central white-light fringe to accurately obtain the optical path-length difference of incoming starlight to the two arms of the interferometer. Because of dispersion in the optical system the optical path-length difference is a function of the wavelength of the light and extracting the proper astrometric signatures requires accommodating these effects. One standard approach to stellar interferometry uses a channeled spectrum to determine phases at a number of different wavelengths that are then converted to the path-length delay. Because of throughput considerations these channels are made sufficiently broad so that monochromatic models are inadequate for retrieving the phase/delay information. The presence of dispersion makes the polychromatic modeling problem for phase estimation even more difficult because of its effect on the complex visibility function. We introduce a class of models that rely on just a few spectral and dispersion parameters. A phase-shilLing interferometry algorithm is derived that exploits the model structure. Numerical examples are given to illustrate the robustness and precision of the approach. OCIS codes: 120.3180, 120.5050, 120.5060.

The simultaneous quantitative measurement of out-of-plane displacement and slope using the fast Fourier transform method with a single three-aperture digital speckle pattern interferometry (DSPI) arrangement is demonstrated. The method coherently combines two sheared object waves with a smooth reference wave at the CCD placed at the image plane of an imaging lens with a three-aperture mask placed in front of it. The apertures also introduce multiple spatial carrier fringes within the speckle. A fast Fourier transform of the image generates seven distinct diffraction halos in the spectrum. By selecting the appropriate halos, one can directly obtain two independent out-of-plane displacement phase maps and a slope phase map from the two speckle images, one before and the second aider loading the object. It is also demonstrated that by subtracting the out-of-plane displacement phase maps one can generate the same slope phase map. Experimental results are presented for a circular diaphragm clamped along the edges and loaded at the center. OCIS codes: 120.2650, 120.5050, 120.6150, 120.6160, 070.2590.

We present a method that allows the reconstruction of smooth phase distributions from their laterally sheared representation. The proposed approach is efficient in the sense that only one sheared distribution is needed to completely restore the signal. A mandatory requirement is that the phase distribution is spatially limited. The method is exemplified by means of a synthetic signal, and in addition a practical algorithm is given. Finally, experimental results are presented. The deformation of a metallic surface is investigated by both speckle shearography and electronic speckle pattern interferometry (ESPI) respectively. To give proof of the proposed technique, the phase distribution reconstructed from the shearographic measurement is shown to match the results obtained by the ESPI. OCIS codes: 070.2590, 070.6020, 100.3010, 100.5070, 120.3180, 120.4630.

A novel single-channel color-image watermarking with digital-optics means based on phase-shifting interferometry (PSI) and a neighboring pixel value subtraction algorithm in the discrete-cosine-transform (DCT) domain is proposed. The converted two-dimensional indexed image matrix from an original color image is encrypted to four interferograms by a PSI and double random-phase encoding technique. Then the interferograms are embedded in one chosen channel of an enlarged color host image in the DCT domain. The hidden color image can be retrieved by DCT, the improved neighboring pixel value subtraction algorithm, an inverse encryption process, and color image format conversion. The feasibility of this method and its robustness against some types of distortion and attacks from the superposed image with different weighting factors are verified and analyzed by computer simulations. This approach can avoid the cross-talk noise due to direct information superposition, enhance the imperceptibility of hidden data, and improve the efficiency of data transmission.

An interferometric lithographic technique and double exposure method are applied to theoretically and experimentally investigate several kinds of 2D periodic structures. The shape, lattice symmetries, and lattice constants of the 2D structures, for different substrate rotational angles, are obtained from the simulated predictions. The shape of the 2D structures can be varied by controlling the rotational angle of the substrate and the development process, and they are validated experimentally. The variation of the lattice symmetry of the 2D structure with the substrate rotational angle is discussed in detail in relation to the axial angle and lattice constant. It is found that square, circular, rectangular, and elliptical scatterers which are arranged in parallelogram, triangular, and square lattices (with different lattice constants) can be obtained. The photonic bandgaps for each condition are also investigated. When the substrate rotational angles are the same, the normalized frequency ([omega]a/2[pi]c) of photonic bandgap structures with an equal filling factor are very similar regardless of the interference angle. The results are helpful in designing the forbidden frequency when the lattice constant and the scatterer shape can be controlled by the interferometric lithographic technique. OCIS codes: 260.3160, 220.4000.

Speckle noise represents one of the major problems when synthetic aperture radar (SAR) data are considered. Despite the fact that speckle is caused by the scattering process itself, it must be considered as a noise source due to the complexity of the scattering process. The presence of speckle makes data interpretation difficult, but it also affects the quantitative retrieval of physical parameters. In the case of one-dimensional SAR systems, speckle is completely determined by a multiplicative noise component. Nevertheless, for multidimensional SAR systems, speckle results from the combination of multiplicative and additive noise components. This model has been first developed for single-look data. The objective of this paper is to extend the single-look data model to define a multiiook multidimensional speckle noise model. The asymptotic analysis of this extension, for a large number of averaged samples, is also considered to assess the model properties. Details and validation of the multilook multidimensional speckle noise model are provided both theoretically and by means of experimental SAR data acquired by the experimental synthetic aperture radar system, operated by the German Aerospace Center. Index Terms--Covariance matrix, interferometry, multidimensional signal, noise modeling, polarimetry, quantitative remote sensing, speckle noise, synthetic aperture radar (SAR).

Snow accumulation in remote regions, such as Greenland and Antarctica, is a key factor for estimating the Earth's ice mass balance. In situ data are sparse: hence, they are useful to derive snow accumulation from remote sensing observations, such as microwave thermal emission and radar brightness. These data are usually interpreted using electromagnetic models in which volume scattering is the dominant mechanism. The main limitation of this approach is that microwave brightness is not well related to backscatter if the ice sheet is layered. Because larger grain size and thicker annual layers both increase radar image brightness, with the first corresponding to lower accumulation rate and the second to higher accumulation rate, models of radar brightness alone cannot accurately reflect accumulation. Consideration of correlation measurements can also resolve this ambiguity. We introduce an interferometric ice scattering model that relates the interferometric synthetic aperture radar correlation and radar brightness to both ice grain size and hoar layer spacing in the dry-snow zone of Greenland. We use this model and the European Remote Sensing satellite radar observations to derive several parameters related to snow accumulation rates in a small area in the dry-snow zone. These parameters show agreement with four in situ core accumulation rate measurements in this area, whereas models using only radar brightness data do not match the observed variation in accumulation rates. Index Terms--Correlation, Greenland ice sheet, normalized power backscattered, radar interferometry, surface scatter, the dry-snow zone, volume scatter.

This paper reviews the relative calibration of an interferometric radiometer taking into account the experimental results of the first batch of receivers developed in the frame of the European Space Agency's Soil Moisture and Ocean Salinity mission. Measurements show state-of-the-art baseline performance as long as the system is capable of correcting the effect of orbital temperature swing. A method to validate internal calibration during in-orbit deep-sky views and to correct linearity errors is also presented. Index Terms--Calibration, interferometry, radiometer.

In spectrally resolved white-light interferometry (SRWLI), the white-light interferogram is decomposed into its monochromatic constituent. The phase of the monochromatic constituents can be determined using a phase-shifting technique over a range of wavelengths. These phase values have fringe order ambiguity. However, the variation of the phase with respect to the wavenumber is linear and its slope gives the absolute value of the optical-path difference. Since the path difference is related to the height of the test object at a point, a line profile can be determined without ambiguity. The slope value, though less precise helps us determine the fringe order. The fringe order combined with the monochromatic phase value gives the absolute profile, which has the precision of phase-shifting interferometry. The presence of noise in the phase may lead to the misidentification of fringe order, which in turn gives unnecessary jumps in the precise profile. The experimental details of measurement on standard samples with SRWLI are discussed in this paper. OCIS codes: 120.3180, 120.3940, 120.5050.

Traditional high-precision optical techniques, such as interferometry, are in ever-greater demand for noncontrolled environments. This is the case for the UPC-ZEBRA, a large-aperture interferometer that was built to measure vertical discontinuities (i.e., piston errors) in segmented mirrors. The large mechanical systems used to drive the interferometer to the different measurement positions generate perturbations that are highly incompatible with the expected piston measurements on the nanometer scale. We introduce a new system based on a line-scan CCD to track interference fringes. The error signal obtained from this fringe tracker has been used in a closed-loop control system to actively stabilize the interferometer. The perturbation has been attenuated by a factor of 1/200. OCIS codes: 120.3180, 120.3930.

We present a new method of regional identification, partition, and integral (RIPI) phase unwrapping for processing images, especially those with low quality, obtained from moire interferometry experiments. By introducing the principle of preorder traversal of a general tree in data structures and then by applying the idea of a regional integral, the proposed method makes regional partition and phase evaluation much easier and more accurate, and it also overcomes the common faults that can occur when conventional approaches, such as line defects, are used. Examples are given to demonstrate the advantage and applicability of the proposed RIPI method when processing experimental images. It is shown that the proposed method works well for global phase distribution, and, at the same time, local mutational information is preserved and limited to its vicinity without affecting other parts. OCIS codes: 100.5070, 120.3180, 120.4120.

We present a refractometer based on the principle of total internal reflection that can sensitively record, in real time, the refractive index of fluids over a wide range of refractive indices. The device uses a divergent laser beam and a linear diode array, and has no mechanical or optical moving parts, enabling us to achieve the measurement of a refractive index at a sensitivity level of [10.sup.-6]. Our refractometer does not rely on interferometry, thus enabling the device to be compact, portable, and inexpensive. To the best of our knowledge, this is the first time a noninterferometric device that performs real-time differential refractometry with a sensitivity of better than [10.sup.-5] has been demonstrated in the literature. We show that our experimental results agree very well with Fresnel theory. We establish a theoretical limit on the sensitivity of this class of refractometers. OCIS codes: 260.6970, 290.3030, 120.4640, 120.5700, 120.5710, 170.3890.

A digital speckle pattern interferometer based on a complementary metal-oxide semiconductor (CMOS) camera is described. The temporal evolution of dynamic deformation is measured using interframe phase stepping. The flexibility of the CMOS detecter is used to identify regions of interest with full-field time-averaged measurements and then to interrogate those regions with time-resolved measurements sampled at up to 70 kHz. A numerical and analytical investigation shows that the maximum surface velocity that can be reliably measured with interframe phase stepping corresponds to [+ or -] 0.3 times the surface velocity at which the interferogram is sampled at the Nyquist limit. OCIS codes: 120.6160, 120.7280, 060.2310.

Frequency changes induced by bias or temperature modulation of injection diode lasers can provide an economical and effective method of applying phase-stepping interferometry to optical metrology. However, the intrinsic frequency instability of these devices limits their use in gauge block interferometry where precise and repeatable phase steps must be maintained simultaneously on two discontinuous surfaces and over relatively long path lengths. We demonstrate a method using a visible injection diode laser, the frequency of which is locked by using a Fabry-Perot interferometer. Small changes to the length of the Fabry-Perot interferometer shift the frequency of the laser producing proportional and repeatable phase steps to the gauge block interferogram. This method has been successfully implemented with a Fizeau-type gauge block interferometer with a phase measurement resolution of 0.005[lambda]. The phase data are then processed to map the surface form of gauge blocks up to 100 mm in length and to objectively assess surface shape parameters. OCIS codes: 120.3930, 120.5050, 120.6650, 140.2020.