Stability improvements for an interferometer through study of spectral interference patterns

Conventional Mach-Zehnder interferometer configuration is modified to enhance its stability from the vibrations. To study the effects of vibrations on the Mach-Zehnder interferometer, we used spectral interference fringes from a broadband nanosecond dye laser source. We observed an improvement in the stability of the interferometer by a factor of 3.     

Observation of the Gouy phase anomaly in astigmatic beams

The Gouy phase anomaly, well established for stigmatic beams, is validated here for astigmatic beams. We simulate the predicted Gouy phase anomaly near astigmatic foci using a beam propagation algorithm integrated within lens design software. We then compare computational results with experimental data acquired using a modified Mertz-Sagnac interferometer. Both in simulation and in experiment, results show that a π/2-phase change occurs as the beam passes through each of the astigmatic foci, experimentally validating results derived in a recent paper by Visser and Wolf [Opt. Commun. 283, 3371-3375 (2010)].     

Removal of bias and the conjugate image in incoherent on-axis triangular holography and real-time reconstruction of the complex hologram

We present and experimentally test a new passive-device incoherent holographic system that removes the bias and the conjugate image. The system is based on the triangular interferometer with the modification of insertion of simple passive devices and can easily be extended for obtaining real-time complex holograms without bias and conjugate images for moving objects. A scheme for real-time reconstruction of the complex hologram is also presented and experimentally tested.     

Alternative method for measuring the full-field refractive index of a gradient-index lens with normal incidence heterodyne interferometry

A linearly/circularly polarized heterodyne light beam coming from a heterodyne light source with an electro-optic modulator in turn enters a modified Twyman-Green interferometer to measure the surface plane of a GRIN lens. Two groups of periodic sinusoidal segments recorded by a fast complementary metal-oxide semiconductor camera are modified, and their associated phases are derived with the unique technique. The data are substituted into the special equations derived from the Fresnel equations, and the refractive index can be obtained. When the processes are applied to other pixels, the full-field refractive-index distribution can be obtained similarly. Its validity is demonstrated.     

High-visibility interferometric measurement of the diffraction phase

We obtain the absolute phase in Fresnel diffraction for Gaussian beams by using a modified polarization Sagnac interferometer in which counterpropagating paths are spatially separated and labeled according to polarization. By erasing the polarization "which-path" information with an analyzing polarizer situated after the modified interferometer, we are able to regain interference and to precisely control the relative intensities of the diffracted and the reference beams. The resulting optimized visibility allows for a precise phase determination. This setup is very stable, requiring no active elements.     

Improved angle interferometer based on total internal reflection

We describe an improved interferometer for angle measurement based on the internal reflection effect. The improvement is achieved by eliminating the influence of wave-plate rotation on the measurement. In the proposed angle interferometer the wave plate is fixed and placed between a rhomb assembly and a retroreflector. This scheme not only allows the angle interferometer to keep the optical configuration compact but also doubles the resolution and can measure the pitch and yaw of moving objects. Both a theoretical analysis and an experimental verification have been conducted on the interferometer. The results indicate that the performance of the modified angle interferometer is greatly improved, especially when the rotation angle is large. The nonlinearity error of the measurement equation is also addressed.     

Experimental study of a shearing interferometer concept for at-wavelength characterization of extreme-ultraviolet optics

We describe the experimental evaluation of a shearing interferometer concept for at-wavelength testing of extreme-ultraviolet optics. The concept is based on the Ronchi test, which has been modified by a new design for entrance and exit gratings to suppress disturbing higher-order interference patterns. The interferometer concept has been tested on an experimental setup, of which all relevant parameters have been scaled from extreme-ultraviolet to visible-light wavelengths. A Twyman-Green interferometer has been integrated into the setup for comparison with the improved Ronchi test. A systematic difference of 7-12 mlambda rms has been found between wave fronts measured with the improved Ronchi test and with the Twyman-Green interferometer. Possible error sources have been analyzed. The accuracy of the interferometer is estimated to be 10 mlambda rms.     

Modified white-light Mach-Zehnder interferometer for direct group-delay measurements

A modified white-light Mach-Zehnder interferometer based on a single beam splitter is described for direct group-delay measurements. The arms of the interferometer are folded in such a manner that a single beam splitter can be used to split the incoming beam and combine the outgoing beams. This method offers a twofold advantage: The measuring range of the interferometer is twice as large as that of the Michelson interferometer, and the systematic error that is associated with the beam splitter is minimized because of the configuration. We report the results of measurements on various optical components performed in the 555-630-nm spectral region and propose a scheme for the processing of the experimental data. We present a comparison of the data analyzed by the proposed processing scheme along with the theoretical calculations.     

Locating acoustic emission with an amplitude-multiplexed acoustic sensor array based on a modified mach-zehnder interferometer

We report on an amplitude-division-multiplexed interferometric sensor array for locating acoustic emission. Preliminary experiments were carried out with a modified Mach-Zehnder interferometer consisting of two sensing arms and a reference arm and demonstrated a one-dimensional location accuracy of a few centimeters. The system can be extended for two- and three-dimensional location of acoustic emissions by the addition of one or two more sensing arms, respectively, in the interferometer.     

原子干涉仪灵敏度的阿伦方差分析

针对分析原子干涉仪灵敏度时,采用哪种阿伦方差容易出现混淆的问题,系统地给出了阿伦方差、重叠阿伦方差和修正阿伦方差三种形式在时域和频域中的详细推导,分析了它们对五类典型噪声的分辨能力,指出修正阿伦方差具有更加适合评估原子干涉仪长期稳定性的特点。基于修正阿伦方差在频域中的表达式,文中还首次给出了存在测量死区的原子干涉仪灵敏度与噪声功率谱之间的传递函数,通过分析其特点,指出了提高原子干涉仪灵敏度的两条具体途径,为原子干涉仪技术的进一步发展和评价奠定了更加扎实的理论基础。     

In situ optical testing of infrared lenses for high-performance cameras

We propose to evaluate infrared lenses with a dedicated analyzer having the same mechanical interface as the usual cameras. The proposed analysis is based on a wavefront measurement and allows a diagnostic of possible internal defects of the analyzed lens. The infrared lens analyzer described is constituted with a quadriwave lateral shearing interferometer and works with a blackbody light. We describe the response of this interferometer and an innovative method to obtain the wavefront under test. We finally present the experimental analysis of long-wavelength infrared lenses and the particular case of a modified lens that generates a large spherical aberration.     

Measurement of the Sensitivity Function in a Time-Domain Atomic Interferometer

We present here an analysis of the sensitivity of a time-domain atomic interferometer to the phase noise of the lasers used to manipulate the atomic wave packets. The sensitivity function is calculated in the case of a three-pulse Mach-Zehnder interferometer, which is the configuration of the two inertial sensors we are building at the Laboratoire National de Metrologie et d'Essais-Systeme de References Temps-Espace. We successfully compare this calculation to experimental measurements. The sensitivity of the interferometer is limited by the phase noise of the lasers as well as by residual vibrations. We evaluate the performance that could be obtained with state-of-the-art quartz oscillators, as well as the impact of the residual phase noise of the phase-locked loop. Requirements on the level of vibrations are derived from the same formalism.     

Phase Shifting Scatter Plate Interferometer Using a Polarization Technique

Abstract

The structure of a conventional scatter plate interferometer is modified by a polarization technique, and a new type of phase shifting scatter plate interferometer is presented. It has both the merits of a conventional scatter plate interferometer and the phase shifting interferometric technique. The working of this interferometer is demonstrated.     

Design of a Triangular Active Ring Laser 13 m on a Side

The design and testing of a proof-of-principle triangular active ring laser interferometer ~13 m on a side is discussed. Issues such as lock in, multimode interference, mode hopping, and neon isotope mixtures are examined as they relate to large He-Ne ring lasers. Responses of the ring laser to Earth's rotation and perturbations that change its tilt or area are presented. Some potential applications are suggested for large interferometers.     

Interferometric distributed optical-fiber sensor

An interferometric technique is described for detecting and locating perturbations along an optical fiber. This distributed sensor, based on a modified fiber-ring interferometer, has a position-dependent response to time-varying disturbances such as strain or temperature. These disturbances cause a phase shift that is detected and converted to spatial information. The sensor consists of two parts, namely, a reflecting-fiber-ring interferometer and a differentiating-ring interferometer. The reflecting ring consists of a fiber ring with one port of the coupler connected to a reflector. Consequently the output port of the reflecting-ring interferometer is the same as the input port. Because it is an inherent zero-path-imbalanced system, a short-coherence-length source such as a light-emitting diode can be used. Any time-varying perturbation on the fiber in the ring results in a detector signal proportional to the product of the rate-of-phase change caused by the perturbation and the distance of the perturbation relative to the center of the fiber ring. The second part of the system, a differentiating-ring interferometer, consists of the same fiber-ring interferometer modified only slightly. The output of this part of the sensor is proportional only to the rate of phase change as a result of the unknown perturbation and contains no distance information. By dividing the output of the reflecting-ring interferometer by the output of the differentiating-ring interferometer, we determine disturbance location. Results obtained with a 155-m distributed fiber sensor are discussed.     

Fiber-based single-channel polarization-sensitive spectral interferometry

We present a novel, to our knowledge, fiber-based single-channel polarization-sensitive spectral interferometry system that provides depth-resolved measurement of polarization transformations of light reflected from a sample. Algebraic expressions for the Stokes parameters at the output of the interferometer are derived for light reflected from a birefringent sample by using the cross-spectral density function. By insertion of a fiber-optic spectral polarimetry instrument into the detection path of a common-path spectral interferometer, the full set of Stokes parameters of light reflected from a sample can be obtained with a single optical frequency scan. The methodology requires neither polarization-control components nor prior knowledge of the polarization state of light incident on the sample. The fiber-based single-channel polarization-sensitive spectral interferometer and analysis are demonstrated by measurement of phase retardation and fast-axis angle of a birefringent mica plate.     

Dove prism with increased throughput for implementation in a rotational-shearing interferometer

An analytical expression is derived for the tilt introduced into a wave front by a Dove prism with manufacturing errors in the prism's base angles and pyramidal angle. We found that the tilt decreases when the base angles are increased above the values of traditional design. The increase in the length-aperture ratio of a prism is detrimental to the prism's performance. However, a Dove prism with a widened aperture increases throughput and maintains a manageable prism weight for implementation in a rotational shearing interferometer. Thus we propose a Dove prism designed with a widened aperture to increase throughput in a rotational shearing interferometer and with larger base angles to minimize the wave-front tilt introduced by manufacturing errors. Experimental results implemented in a rotational shearing interferometer demonstrate the feasibility of this design.     

Generation of inhomogeneously polarized laser beams by use of a Sagnac interferometer

A principal scheme for an external cavity technique for changing the polarization of a laser beam based on a modified Sagnac interferometer is proposed. The modified Sagnac interferometer includes standard optical components: a displacement polarizing beam splitter, an angle reflector, and a Dove prism. The radially polarized beams, obtained with the help of the developed scheme, allow the generation of a longitudinally polarized electric field by sharp focusing. The phase correction of radially polarized modes of higher orders leads to increasing the longitudinal field in the focus of the beam.     

Interferometric seeing measurements on Mt. Wilson: power spectra and outer scales

We have measured power spectra of atmospheric phase fluctuations with the Mark III stellar interferometer on Mt. Wilson under a wide variety of seeing conditions. On almost all nights, the high-frequency portions of the temporal power spectra closely follow the form predicted by the standard Kolmogorov-Tatarski model. At lower frequencies, a variety of behavior is observed. On a few nights, the spectra clearly exhibit the low-frequency flattening characteristic of turbulence with an outer-scale length of the order of 30 m. On other nights, examination of individual spectra yields no strong evidence of an outer scale less than a few kilometers in size, but comparison of the spectra on different interferometer baselines shows a saturation of the spatial structure function on long baselines. This saturation is consistent with the assumption of an outer-scale length similar to that derived for the nights when low-frequency flattening of the spectra is clearly seen. We discuss possible explanations of this behavior and conclude that power spectra from a single interferometer baseline are a poor diagnostic for the effective outer scale compared with multiple-baseline spectra.     

Window function influence on phase error in phase-shifting algorithms

We present five different eight-point phase-shifting algorithms, each with a different window function. The window function plays a crucial role in determining the phase (wavefront) because it significantly influences phase error. We begin with a simple eight-point algorithm that uses a rectangular window function. We then present alternative algorithms with triangular and bell-shaped window functions that were derived from a new error-reducing multiple-averaging technique. The algorithms with simple (rectangular and triangular) window functions show a large phase error, whereas the algorithms with bell-shaped window functions are considerably less sensitive to different phase-error sources. We demonstrate that the shape of the window function significantly influences phase error.