A fast-Fourier-transform method of topography and interferometry is proposed. By computer processing of a noncontour type of fringe pattern, automatic discrimination is achieved between elevation and depression of the object or wave-front form, which has not been possible by the fringe-contour-generation techniques. The method has advantages over moire topography and conventional fringe-contour interferometry in both accuracy and sensitivity. Unlike fringe-scanning techniques, the method is easy to apply because it uses no moving components.

Fourier-transform method of fringe-pattern analysis for computer-based topography and interferometry

A self-scanned 1024 element photodiode array and minicomputer are used to measure the phase (wavefront) in the interference pattern of an interferometer to lambda/100. The photodiode array samples intensities over a 32 x 32 matrix in the interference pattern as the length of the reference arm is varied piezoelectrically. Using these data the minicomputer synchronously detects the phase at each of the 1024 points by a Fourier series method and displays the wavefront in contour and perspective plot on a storage oscilloscope in less than 1 min (Bruning et al. Paper WE16, OSA Annual Meeting, Oct. 1972). The array of intensities is sampled and averaged many times in a random fashion so that the effects of air turbulence, vibrations, and thermal drifts are minimized. Very significant is the fact that wavefront errors in the interferometer are easily determined and may be automatically subtracted from current or subsequent wavefrots. Various programs supporting the measurement system include software for determining the aperture boundary, sum and difference of wavefronts, removal or insertion of tilt and focus errors, and routines for spatial manipulation of wavefronts. FFT programs transform wavefront data into point spread function and modulus and phase of the optical transfer function of lenses. Display programs plot these functions in contour and perspective. The system has been designed to optimize the collection of data to give higher than usual accuracy in measuring the individual elements and final performance of assembled diffraction limited optical systems, and furthermore, the short loop time of a few minutes makes the system an attractive alternative to constraints imposed by test glasses in the optical shop.

Digital wavefront measuring interferometer for testing optical surfaces and lenses

Magnetic susceptibility describes the magnetizability of a material to an applied magnetic field and represents an important parameter in the field of MRI. With the recently introduced method of quantitative susceptibility mapping (QSM) and its conceptual extension to susceptibility tensor imaging (STI), the non-invasive assessment of this important physical quantity has become possible with MRI. Both methods solve the ill-posed inverse problem to determine the magnetic susceptibility from local magnetic fields. Whilst QSM allows the extraction of the spatial distribution of the bulk magnetic susceptibility from a single measurement, STI enables the quantification of magnetic susceptibility anisotropy, but requires multiple measurements with different orientations of the object relative to the main static magnetic field. In this review, we briefly recapitulate the fundamental theoretical foundation of QSM and STI, as well as computational strategies for the characterization of magnetic susceptibility with MRI phase data. In the second part, we provide an overview of current methodological and clinical applications of QSM with a focus on brain imaging. Copyright © 2016 John Wiley & Sons, Ltd.

Overview of quantitative susceptibility mapping.

This letter presents a computationally efficient and robust LiDAR-inertial odometry framework. We fuse LiDAR feature points with IMU data using a tightly-coupled iterated extended Kalman filter to allow robust navigation in fast-motion, noisy or cluttered environments where degeneration occurs. To lower the computation load in the presence of a large number of measurements, we present a new formula to compute the Kalman gain. The new formula has computation load depending on the state dimension instead of the measurement dimension. The proposed method and its implementation are tested in various indoor and outdoor environments. In all tests, our method produces reliable navigation results in real-time: running on a quadrotor onboard computer, it fuses more than 1200 effective feature points in a scan and completes all iterations of an iEKF step within 25 ms. Our codes are open-sourced on Github. 1

FAST-LIO: A Fast, Robust LiDAR-Inertial Odometry Package by Tightly-Coupled Iterated Kalman Filter

• Rayleigh scattering is an approximation used to predict scattering from particles much smaller than an electromagnetic wavelength • The approximation is based on quasi-static ideas: in regions of space much smaller than a wavelength, fields act approximately like static fields • Basic procedure: solve statics problem to determine field inside scatterer when a uniform field (plane wave) impinges from outside • This determines field inside particle so we can then compute scattering cross sections, etc, using our previous equations • This is a nice method because we have lots of analytical techniques for solving the Laplace equation, also usually will predict constant fields inside scatterer

「レイリー散乱」(Rayleigh Scattering)

A phase unwrapping algorithm for interferometric fringes based on the unscented Kalman filter (UKF) technique is proposed. The algorithm can bring about accurate phase unwrapping and good noise suppression simultaneously by incorporating the true phase and its derivative in the state vector estimation through the UKF process. Simulations indicate that the proposed algorithm has better accuracy than some widely employed phase unwrapping approaches in the same noise condition. Also, the time consumption of the algorithm is reasonably acceptable. Applications of the algorithm in our different optical interferometer systems are provided to demonstrate its practicability with good performance. We hope this algorithm can be a practical approach that can help to reduce the systematic errors significantly induced by phase unwrapping process for interferometric measurements such as wavefront distortion testing, surface figure testing of optics, etc.

Practical phase unwrapping of interferometric fringes based on unscented Kalman filter technique

Taking advantage of the broad spectrum of the Cabannes-Brillouin scatter from atmospheric molecules, the high spectral resolution lidar (HSRL) technique employs a narrow spectral filter to separate the aerosol and molecular scattering components in the lidar return signals and therefore can obtain the aerosol optical properties as well as the lidar ratio (i.e., the extinction-to-backscatter ratio) which is normally selected or modeled in traditional backscatter lidars. A polarized HSRL instrument, which employs an interferometric spectral filter, is under development at the Zhejiang University (ZJU), China. In this paper, the theoretical basis to retrieve the aerosol lidar ratio, depolarization ratio and extinction and backscatter coefficients, is presented. Error analyses and sensitivity studies have been carried out on the spectral transmittance characteristics of the spectral filter. The result shows that a filter that has as small aerosol transmittance (i.e., large aerosol rejection rate) and large molecular transmittance as possible is desirable. To achieve accurate retrieval, the transmittance of the spectral filter for molecular and aerosol scattering signals should be well characterized.

Retrieval and analysis of a polarized high-spectral-resolution lidar for profiling aerosol optical properties

A compact quadriwave lateral shearing interferometer (QWLSI) with strong adaptability and high precision is proposed based on a novel randomly encoded hybrid grating (REHG). By performing the inverse Fourier transform of the desired ±1 Fraunhofer diffraction orders, the amplitude and phase distributions of the ideally calculated quadriwave grating can be obtained. Then a phase chessboard is introduced to generate the same phase distribution, while the amplitude distribution can be achieved using the randomly encoding method by quantizing the radiant flux on the ideal quadriwave grating. As the Faunhofer diffraction of the REHG only contains the ±1 orders, no order selection mask is ever needed for the REHG-LSI. The simulations and the experiments show that the REHG-LSI exhibits strong adaptability, nice repeatability, and high precision.

Quadriwave lateral shearing interferometer based on a randomly encoded hybrid grating.

Calibration for misalignment aberrations is one of the challenges in non-null interferometric aspheric testing. The high-order misalignment aberrations are especially difficult to distinguish from the rest of the testing system. The traditional calibration method removing the first four terms from the Zernike coefficients of the test wavefront is obviously inaccurate. Computer-aided alignment is considered to be an effective method; however, it is less practical due to its dependency on mechanical or manual adjustment, as are other common methods. A practical and accurate calibration method based on system modeling is proposed in this paper for misalignment aberrations’ removal. In this work, actual misalignments, which are calculated from five selected low-order aberrations of the test wavefront in the experiment, are simulated in the model to predict all misalignment aberrations by ray tracing. These aberrations then are removed by a simple wavefront data subtraction. The method depends on neither a precise adjusting mechanism nor a troublesome manual adjustment. Experimental results showing feasibility and repeatability of the proposed method are presented.

Practical and accurate method for aspheric misalignment aberrations calibration in non-null interferometric testing

A non-null annular subaperture stitching interferometry (NASSI), combining the subaperture stitching ideal and non-null test method, is proposed for steep aspheric testing. Compared with standard annular subaperture stitching interferometry (ASSI), a partial null lens (PNL) is employed as an alternative to the transmission sphere, to generate different aspherical wavefronts as the references. The coverage subaperture number would be reduced greatly for the better performance of aspherical wavefronts in matching the local slope of aspheric surfaces. In this way, relatively large overlapping areas can be obtained for adjustment errors correction while the error accumulation would be decreased. With the reverse optimization reconstruction (ROR) method for retrace error correction, the figure error of each subaperture can be retrieved accurately. Therefore, the testing accuracy and efficiency are thus increased. The dynamic test range is extended as well. A numerical simulation exhibits the comparison of the performance of the NASSI and standard ASSI, which demonstrates the high accuracy of the NASSI in testing steep aspheric. Experimental results of NASSI are shown to be in good agreement with those of the Zygo interferometer.

Yibing Shen

Papers

Practical phase unwrapping of interferometric fringes based on unscented Kalman filter technique

Retrieval and analysis of a polarized high-spectral-resolution lidar for profiling aerosol optical properties

Quadriwave lateral shearing interferometer based on a randomly encoded hybrid grating.

Practical and accurate method for aspheric misalignment aberrations calibration in non-null interferometric testing

Non-null annular subaperture stitching interferometry for steep aspheric measurement