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

We present an optical metrology instrument for measuring both transmitted and reflected wavefront error (TWE and RWE) of coated or uncoated optics over a diameter of 5 inches. Depending on the coating transmittance and reflectance, the measurements have to be done at different wavelengths. Interferometer is a standard instrument to measure the TWE and RWE of uncoated optics. But in the case of coated optics (bandpass filters for example) measurement of TWE is not possible because the optics may not transmit the interferometer laser light. The chosen solution is based on a quadriwave lateral shearing interferometer (QWLSI) wavefront sensor. QWLSI is an achromatic technique, meaning that it measures OPD at any wavelength without any need for recalibration at specific wavelengths. Consequently, various sources at different wavelengths can be used with the same instrument and metrology bench. In addition, QWLSI measures the derivative of phase contrary to interferometer that measures phase. Therefore, QWLSI has by design a better WFE dynamic range for TWE and RWE measurement. Moreover accuracy (below 15nm RMS) and repeatability (below 2nm RMS) is perfectly adapted to optical metrology measurement. The optical solution is a standard double pass configuration composed of a collimator and a beam expander to adapt the size of the beam to the wavefront sensor aperture. We use LED sources to avoid any noise due to interferences within the optics, which occur with coherent light. We can use different wavelength between 400nm and 1100nm. We can optimize the longitudinal chromatic aberration by moving a lens from the beam expander. We characterized the bench according to the ISO 5725 standard for different wavelengths. Its precision was tested with different samples (filters and mirror). The precision on TWE was found to be below 2nm RMS.

Distributions of amplitude and phase for bivariate distributions

We inv estigate the problem in which a volume hologram is produced by two waves of arbitrary amplitude and phase distribution (the only restriction being that they must obey the rules of geometrical optics), and the developed hologram is illuminated by one of the waves having the same phase distribution but not necessarily the same amplitude distribution. Coupled partial differential equations are derived and solved in the form of an infinite series valid for both transmission and reflection holograms. For transmission holograms a simple approximate solution is given for the amplitude of the reconstructed wave in the immediate vicinity of the input surface.

Systematic error analysis and correction in quadriwave lateral shearing interferometer

Diffractive optical elements able to generate on-axis (zero-order) phase as well as amplitude distributions are described. The proposed elements are surface-relief plates, that is phase-only elements, that are based on concepts of computer-generated masks followed by lithographic and etching processes. The proposed encoding method assumes variable spatial partitioning of the cell and a fixed phase value allocated to each subcell. This method requires the minimal number of etching levels needed for full representation of the wave front, that is three, but can be applied with improved efficiency using more etching levels. The reconstructed amplitude and phase distributions contain some noise owing to the encoding process. Discussion of the error sources is given.

The feasibility of using a Kerr magneto-optic-effect display as the input to a coherent optical computer is discussed and experimentally verified. Simple amplitude and phase distributions were generated on a continuous ferromagnetic thin film and their Fourier transforms were displayed with a lens. An experiment was performed demonstrating spatial filtering of a magneto-optically generated amplitude distribution. Magneto-optic generation of more complicated amplitude distributions requires a matrix-type thin-film structure and this input must be treated as sampled data.

The traditional multiposition method of the M2 factor measurement system is a good method, but it is relatively time consuming, so it cannot meet the requirements of the transient test of a Gaussian beam. To solve this problem, a quadriwave lateral shearing interferometer and a wavefront construction method based on a difference Zernike polynomial are analyzed. This interferometer uses a special grating to select four replicas of the wavefront, and the interferogram generated by four replicas includes difference wavefront information. Then the difference Zernike polynomial method is used to analyze quadriwave lateral shearing interferograms. The characteristic parameters are obtained after finding the optimal terms of the Zernike polynomials. As a result, the errors of F-number, beam radius, and radius of curvature are 3.7%, 3.8%, and 0.6%, respectively, which verifies this method to calculate parameters of Gaussian beam. In addition, we also find that the shear amount has influence on the reconstructed wavefront. It is showed that as the amount of shear increases from 20 pixels to 90 pixels, the peak-to-valley (P-V) values and RMS values both gradually decrease with a nonlinear relationship, which could be used to decrease the error of wavefront reconstruction further.

A method is proposed for the reconstruction of an optical field with the aid of two transparencies. Information on the distribution of the amplitudes and phases of the optical field is recorded by directing radiation into two channels. The distribution of the field amplitudes is recorded in the usual way in one channel, whereas the other channel visualizes the phase distribution and ensures that it is recorded in a phase-sensitive material. Reconstruction involves illumination of these two transparencies used in combination with a plane monochromatic wave.

A generalized product-of-convolution model for simulation of quantitative phase microscopy of thick heterogeneous specimen under tilted plane-wave illumination is presented. Actual simulations are checked against a much more time-consuming commercial finite-difference time-domain method. Then modeled data are compared with experimental measurements that were made with a quadriwave lateral shearing interferometer.

Continuous-wave off-axis and in-line terahertz digital holography with phase unwrapping and phase autofocusing

This paper proposes a novel hybrid antenna configuration, which combines two kinds of high-performance antennas, i.e., reflectarray and transmitarray, creating a low-profile low-cost low-mass design with both amplitude and phase distribution controls. In this hybrid arrangement, a flat Cassegrain reflectarray, with compact ring focus, is implemented as the feed to illuminate the upper transmitarray. In the process of reflectarray design, the particle swarm optimization technique is utilized to synthesize the phase distribution on the reflectarray aperture to generate a desired amplitude distribution on the upper transmitarray aperture. During the transmitarray design process, the dimensions of the double-loop elements of the upper transmitarray are adjusted to compensate for the phase delay of the wave from the lower reflectarray and form a desired phase distribution on the transmitarray aperture. A detailed design procedure for a Cassegrain-reflectarray-fed transmitarray antenna with a small focus-to-diameter ratio of 0.3 is presented. The simulated and measured results demonstrate that the hybrid-configuration antenna can achieve an aperture efficiency of around 40%.

This paper presents the method of determination of the amplitude and plane distribution in antenna plane aperture. This method is based on homodyne one, where the initial microwave oscillation is heterodyne one. The mobile probe unit consists of proper antenna probe and reflecting controlled phase shifter. The initial microwave oscillation is shifted on low frequency with reflecting controlled phase shifter. The initial phase and frequency of microwave oscillations are eliminated. Low frequency feeder with arbitrary phase stability is used to carry the low frequency oscillations to mobile probe unit. The initial phase of low frequency oscillation is transferred on microwave.

The most successful holographic method so far is off-axis electron holography, which uses the Moellenstedt electron biprism [1] as a beam splitter. It superposes an offaxis reference wave to the image wave hence gives rise to a cosinoidal interference pattern (“hologram”), which contains both amplitude and phase in the contrast and position of the interference fringes, respectively. By means of a reconstruction procedure, the distribution of amplitude and phase are determined quantitatively, i.e. the image wave is revived completely in the computer. Details and further references can be found in review [2].

Equatorial deep jets (EDJ) are zonal currents along the equator in all three ocean basins that alternate in direction with depth and time. In the Atlantic below the thermocline, they are the dominant variability on interannual timescales. Observations of equatorial deep jets are available but scarce, given the EDJs’ location at depth, their small vertical scale and their long periodicity of several years. In the last few years, Argo floats have added a significant amount of measurements at intermediate depth. In this study we therefore revise estimates of the EDJ scales based on Argo float data. Mostly, we use velocity data at 1000 m depth calculated from float displacement, which yield robust estimates of the Atlantic EDJ period (4.6 years), amplitude distribution, phase distribution, zonal wavelength (146.7°), and meridional structure. We also show that the equatorial amplitude of the EDJs’ first meridional mode Rossby wave component (9.8 cm s−1) is larger than that of their Kelvin wave component (2.8 cm s−1). Additionally, we present a new estimation of the EDJs’ vertical structure throughout the Atlantic basin, based on an equatorial geostrophic velocity reconstruction from hydrographic Argo float measurements from depths between 400 and 2000 m. Our new estimates from Argo float data provide the first basin-wide assessment of the Atlantic EDJ scales, as well as having smaller uncertainties than estimates from earlier studies.

Detailed velocity measurements have been made to investigate the structure of the low-frequency vortex dislocations that appear in the indigenous wake of a circular cylinder. It is shown that one mechanism for the production of vortex dislocations is the superposition of two waves with slightly different frequencies, where the higher frequency wave is parallel to the cylinder axis and the lower frequency is an oblique wave. In contrast to the discrete vortex concept that implies discontinuous shedding frequencies, the measured amplitude and phase distribution of the interacting waves are shown to be continuous along the span of the cylinder. Both waves (parent modes) exist simultaneously and overlap in the wake. The difference mode associated with the vortex dislocations is produced by the nonlinear interaction of the parent modes, and its maximum amplitude is at the location where the parent modes have comparable magnitude. The spanwise phase and amplitude distributions of the difference mode are ‘‘predicted’’ by taking the product of the complex wave amplitudes of the parent modes.