Fizeau Interferometer Research Articles

Wide aperture piezoceramic deformable mirrors for aberration correction in high-power lasers

The deformable mirror with the size of $410~\text{mm}\times 468~\text{mm}$ controlled by the bimorph piezoceramic plates and multilayer piezoceramic stacks was developed. The results of the measurements of the response functions of all the actuators and of the surface shape of the deformable mirror are presented in this paper. The study of the mirror with a Fizeau interferometer and a Shack–Hartmann wavefront sensor has shown that it was possible to improve the flatness of the surface down to a residual roughness of $0.033~{\rm\mu}\text{m}$ (RMS). The possibility of correction of the aberrations in high-power lasers was numerically demonstrated.

基于Fizeau 干涉仪的大气多普勒频移检测技术

The wind speed measurement technology based on laser stripe image is studied. According to the Fizeau interferometer transmittance function and atmospheric scattering spectrum function of molecular scattering spectral characteristics for its optimization design, We obtain a set of Fizeau interferometer system parameters based on any incident light beam. The cavity length is 12 mm, the reflectivity is 0.65 from plate and the apex is 10 murad. At last, under the condition of 20 mj, repetition frequency of 100 Hz and receiving diameter of 200 mm, the simulating results indicate that when wind velocity error is 1 m/s, the detection ability is 17.8 km above ground.

Characterization of a piezo bendable X-ray mirror.

A full-scale piezo bendable mirror built as a prototype for an offset mirror at the European XFEL is characterized. The piezo ceramic elements are glued onto the mirror substrate, side-face on with respect to the reflecting surface. Using a nanometre optical component measuring machine and a large-aperture Fizeau interferometer, the mirror profile and influence functions were characterized, and further analysis was made to investigate the junction effect, hysteresis, twisting and reproducibility.

Measuring Method of Radius of Curvature Based on Dual-Frequency Laser Interferometer

In order to achieve high-accuracy measurement of radius of curvature of optical sphere, ultra-high accuracy radius of curvature testing device is developed by dual-frequency laser interferometer and Fizeau interferometer based on cat’s eye and confocal method. Through analyzing the error source models of radius of curvature testing, optical configuration of the testing device has been optimized. Precise environment control and real-time monitoring system is also established to reduce the errors caused by environment. Through the above processes, the radius of curvature measurement relative accuracy is better than 2 ppm. One optical sphere, R88.5 mm, test aperture 59 mm, has been tested. Testing result is 88499.465 ± 0.176 μm, meeting the design requirement. The method has high accuracy and practical advantages.

QUBIC: A Fizeau Interferometer Targeting Primordial B-Modes

Q and U Bolometric Interferometer for Cosmology (QUBIC) is a Fizeau interferometer sensitive to linear polarisation, to be deployed at the Antarctic station of Dome C. This experiment in its final configuration will be operated at 97, 150 and 220 GHz and is intended to target CMB primordial B-modes in a multipole window . A sensitivity of (95 % CL) can be reached by the first module alone, after 2 years of operation. Here we review in particular its working principles, and we show how the QUBIC interferometric configuration can be considered equivalent to a pupil-plane filtered imaging system. In this context, we show how our instrument can be self-calibrated. Finally, we conclude by showing an overview of the first dual-band module (150/220 GHz), which will serve also as a demonstrator for the subsequent units, and review the technological choices we made for each subsystem, with particular emphasis on the detection system.

Fabrication of a thin silicon detector with excellent thickness uniformity

We have fabricated and tested a thin silicon detector with the specific goal of having a very good thickness uniformity. SOI technology was used in the detector fabrication. The detector was designed to be used as a ΔE detector in a silicon telescope for measuring solar energetic particles in space. The detector thickness was specified to be 20μm with an rms thickness uniformity of±0.5%. The active area consists of three separate elements, a round centre area and two surrounding annular segments. A new method was developed for measuring the thickness uniformity based on a modified Fizeau interferometer. The thickness uniformity specification was well met with the measured rms thickness variation of 43nm. The detector was electrically characterized by measuring the I–V and C–V curves and the performance was verified using a 241Am alpha source.

Binary pseudo-random patterned structures for modulation transfer function calibration and resolution characterization of a full-field transmission soft x-ray microscope.

We present a modulation transfer function (MTF) calibration method based on binary pseudo-random (BPR) one-dimensional sequences and two-dimensional arrays as an effective method for spectral characterization in the spatial frequency domain of a broad variety of metrology instrumentation, including interferometric microscopes, scatterometers, phase shifting Fizeau interferometers, scanning and transmission electron microscopes, and at this time, x-ray microscopes. The inherent power spectral density of BPR gratings and arrays, which has a deterministic white-noise-like character, allows a direct determination of the MTF with a uniform sensitivity over the entire spatial frequency range and field of view of an instrument. We demonstrate the MTF calibration and resolution characterization over the full field of a transmission soft x-ray microscope using a BPR multilayer (ML) test sample with 2.8 nm fundamental layer thickness. We show that beyond providing a direct measurement of the microscope's MTF, tests with the BPRML sample can be used to fine tune the instrument's focal distance. Our results confirm the universality of the method that makes it applicable to a large variety of metrology instrumentation with spatial wavelength bandwidths from a few nanometers to hundreds of millimeters.

Frequency stability of a wavelength meter and applications to laser frequency stabilization.

Interferometric wavelength meters have attained frequency resolutions down to the megahertz range. In particular, Fizeau interferometers, which have no moving parts, are becoming a popular tool for laser characterization and stabilization. In this paper, we characterize such a wavelength meter using an ultrastable laser in terms of relative frequency instability σ(y)(τ) and demonstrate that it can achieve a short-term instability σ(y)(1s)≈2×10(-10) and a frequency drift of order 10 MHz/day. We use this apparatus to demonstrate frequency control of a near-infrared laser, where a frequency instability below 3×10(-10) from 1 to 2000 s is achieved. Such performance is, for example, adequate for ion trapping and atom cooling experiments.

Retrace error reconstruction based on point characteristic function.

Figure measuring interferometers generally work in the null condition, i.e., the reference rays share the same optical path with the test rays through the imaging system. In this case, except field distortion error, effect of other aberrations cancels out and doesn't result in measureable systematic error. However, for spatial carrier interferometry and non-null aspheric test cases, null condition cannot be achieved typically, and there is excessive measurement error that is referenced as retrace error. Previous studies about retrace error can be generally distinguished into two categories: one based on 4th-order aberration formalism, the other based on ray tracing through interferometer model. In this paper, point characteristic function (PCF) is used to analyze retrace error in a Fizeau interferometer working in high spatial carrier condition. We present the process of reconstructing retrace error with and without element error in detail. Our results are in contrast with those obtained by ray tracing through interferometer model. The small difference between them (less than 3%) shows that our method is effective.

Axial alignment for high-precision interferometric measurements of steeply-curved spheres

Incorrect positioning of a steeply-curved sphere along the optical axis of a laser Fizeau interferometer introduces a measurement error that is proportional to the cosine of the inclination angle of the ray trace within the cavity, and directly proportional to the misalignment. The standard metrology solution is to subtract a fitted parabola from the 3D image, which corrects for most of the error, but neglects higher terms. As a consequence, measurements of steeply curved parts may have residual errors resembling spherical aberration. Here we calculate the magnitude of the error and present it in a graphical format that allows for straightforward quantification of the residual error as a function of the measured quadratic or power term in the measured 3D surface form. While our recommendation is to employ automated alignment for best results, we also consider options for higher-order software corrections for geometric misalignments.

Coronagraphic Demonstration Experiment Using Aluminum Mirrors for Space Infrared Astronomical Observations

For future space infrared astronomical coronagraphy, we perform experimental studies on the application of aluminum mirrors to a coronagraph. Cooled reflective optics is required for broadband mid-infrared observations in space, while high-precision optics are required for coronagraphy. For the coronagraph instrument originally proposed for the next-generation infrared astronomical satellite project SPICA (SCI: SPICA Coronagraph Instrument), we fabricated and evaluated the optics consisting of high-precision aluminum off-axis mirrors with diamond-turned surfaces, and conducted a coronagraphic demonstration experiment using the optics with a coronagraph mask. We first measured the wave front errors (WFEs) of the aluminum mirrors with a He–Ne Fizeau interferometer to confirm that the power spectral densities of the WFEs satisfy the SCI requirements. Then we integrated the mirrors into an optical system and evaluated the overall performance of the system. As a result, we estimate the total WFE of the optics to be 33 nm (rms), each mirror contributing 10–20 nm (rms) for the central 14 mm area of the optics, and obtain a contrast of 10-5.4 as a coronagraph in the visible light. At a wavelength of 5 μm, the coronagraphic system is expected to achieve a contrast of ∼10-7 based on our model calculation with the measured optical performance. Thus our experiment demonstrates that aluminum mirror optics is applicable to a highly WFE-sensitive instrument such as a coronagraph in space.

Wavefront measurement made by an off-the-shelf laser-scanning pico projector.

Focal plane testing methods such as the Shack-Hartmann wavefront sensor and phase-shifting deflectometry are valuable tools for optical testing. In this study, we propose a novel wavefront slope testing method that uses a scanning galvo laser, in which a single-mode Gaussian beam scans the pupils of the tested optics in the system. In addition, the ray aberration is reconstructed by the four-step phase-shifting measurement by modulating the angular domain. The measured wavefront is verified by a Fizeau interferometer in terms of Zernike polynomials.

Measurement of optical thickness variation of BK7 plate by wavelength tuning interferometry.

This paper presents the derivation of a 17-sample phase-shifting algorithm that can compensate the miscalibration and first-order nonlinearity of phase shift error, coupling error, and bias modulation of the intensity and satisfy the fringe contrast maximum condition. The phase error of measurements performed using the 17-sample algorithm is discussed and compared with those of measurements obtained using other algorithms. Finally, the optical thickness variation of a BK7 optically transparent plate obtained using a wavelength tuning Fizeau interferometer and the 17-sample algorithm are presented. The experimental results indicate that the optical thickness variation measurement accuracy for the BK7 plate was 3 nm.

Hygroscopic polymer microcavity fiber Fizeau interferometer incorporating a fiber Bragg grating for simultaneously sensing humidity and temperature

This work proposes a hygroscopic polymer microcavity fiber Fizeau interferometer (PMFFI) incorporating a fiber Bragg grating (FBG) for the simultaneous measurement of relative humidity (RH) and temperature (T). The PMFFI was fabricated by attaching the hygroscopic polymer to a single-mode fiber endface to form a low-finesse Fabry–Perot resonant microcavity. This work is the first to investigate polymer of the Norland Optical Adhesive (NOA) series with particular porous structures that responds well to the moisture and can thus be used in the fiber-optic sensing of relative humidity. Additionally, the NOA materials have a high thermal expansion coefficient and so can be used in the highly sensitive measurement of temperature. The adsorption/desorption of water molecules and variations in temperature both change the optical path of the microcavity, shifting the fringes in the interference spectra. Incorporating a general FBG that is nonreactive to RH but sensitive to T judges the variation in T. The combined sensor supports the simultaneous measurement of both parameters RH and T by gauging of the individual spectral responses of PMFFI and FBG, respectively. Experimental results demonstrate that the RH and T can be simultaneously measured with high sensitivity and accuracy using the proposed sensing configuration.

Sub-nanometer misalignment aberrations calibration of the Fizeau interferometer for high-numerical-aperture spherical surface ultra-precision measurement

Misalignment aberrations in Fizeau interferometric testing system can significantly influence the measurement results in the case of high-numerical-aperture test spherical surfaces, and it is hard to separate the high-order misalignment aberrations from the measured data. The traditional calibration method, which is based on linear-approximation, is applicable in calibrating only the linear misalignment aberration in measurement of high-numerical-aperture spherical surfaces. Based on modified power term for interferometry and 4-overlapping averaging 9-frame algorithm, sub-nanometer accuracy high-order calibration method is proposed to calibrate the linear misalignment aberrations as well as high-order misalignment aberrations. Both the computer simulation and experimental results confirm the feasibility and accuracy of the proposed calibration technique, and sub-nanometer misalignment aberrations can be calibrated. The proposed method can also used in spherical surface ultra-precision measurement by other interferometric setups without foreknowledge of numerical aperture of the test surface.

Surface profile measurement of a highly reflective silicon wafer by phase-shifting interferometry

In phase-shifting Fizeau interferometers, the phase-shift error and multiple-beam interference are the most common sources of systematic error affecting high-precision phase measurements. The nonsinusoidal waveforms can be minimized by applying synchronous detection with more than 4-sample. However, when the phase-shift calibration is inaccurate, these algorithms cannot eliminate the effects of nonsinusoidal characteristics. Moreover, when measuring the surface profile of highly reflective samples, the calculated phase is critically determined not only by the decrease in the fringe contrast but also by the coupling error between the harmonics and phase-shift error. In this paper, the phase errors calculated by conventional phase-shifting algorithms were estimated by considering the coupling error. We show that the 4N−3 algorithm, comprising the polynomial window function and the DFT term, has the smallest phase error among the conventional phase-shifting algorithms. The surface profile of the highly reflective silicon wafer was measured using a wavelength-tuning Fizeau interferometer and the 4N−3 algorithm.

A blind deconvolution method for ground based telescopes and Fizeau interferometers

In the case of ground-based telescopes equipped with adaptive optics systems, the point spread function (PSF) is only poorly known or completely unknown. Moreover, an accurate modeling of the PSF is in general not available. Therefore in several imaging situations the so-called blind deconvolution methods, aiming at estimating both the scientific target and the PSF from the detected image, can be useful. A blind deconvolution problem is severely ill-posed and, in order to reduce the extremely large number of possible solutions, it is necessary to introduce sensible constraints on both the scientific target and the PSF.In a previous paper we proposed a sound mathematical approach based on a suitable inexact alternating minimization strategy for minimizing the generalized Kullback–Leibler divergence, assuring global convergence. In the framework of this method we showed that an important constraint on the PSF is the upper bound which can be derived from the knowledge of its Strehl ratio. The efficacy of the approach was demonstrated by means of numerical simulations.In this paper, besides improving the previous approach by the use of a further constraint on the unknown scientific target, we extend it to the case of multiple images of the same target obtained with different PSFs. The main application we have in mind is to Fizeau interferometry. As it is known this is a special feature of the Large Binocular Telescope (LBT). Of the two expected interferometers for LBT, one, LINC-NIRVANA, is forthcoming while the other, LBTI, is already operating and has provided the first Fizeau images, demonstrating the possibility of reaching the resolution of a 22.8m telescope. Therefore the extension of our blind method to this imaging modality seems to be timely.The method is applied to realistic simulations of imaging both by single mirrors and Fizeau interferometers. Successes and failures of the method in the imaging of stellar fields are demonstrated in simple cases. These preliminary results look promising at least in specific situations. The IDL code of the proposed method is available on request and will be included in the forthcoming version of the Software Package AIRY (v.6.1).

Lanthanum-gallium tantalate: Heterogeneity and point defects

In this study the important factors having influence on the occurrence of color centers (crystal growth conditions and postgrowth effect on the crystal) in LGT (La3Ga5,5Ta0.5O14, langatate) crystals were investigated. In order to check the model of defect formation in crystals of langatate the effect of ionizing radiation on the spectral dependence of the attenuation coefficients of langatate crystals was studied. The ionizing radiation doses were 1011 – 1015 cm−2. The optical homogeneity was evaluated by interferometric method on a Fizeau interferometer. The refractive indices of the crystals obtained in different atmospheres and after the isothermal annealing were measured by the prism method.

Absolute optical thickness measurement of transparent plate using excess fraction method and wavelength-tuning Fizeau interferometer.

The absolute optical thickness of a transparent plate 6-mm thick and 10 mm in diameter was measured by the excess fraction method and a wavelength-tuning Fizeau interferometer. The optical thickness, defined by the group refractive index at the central wavelength, was measured by wavelength scanning. The optical thickness deviation, defined by the ordinary refractive index, was measured using the phase-shifting technique. Two kinds of optical thicknesses, measured by discrete Fourier analysis and the phase-shifting technique, were synthesized to obtain the optical thickness with respect to the ordinary refractive index using Sellmeier equation and least-square fitting.

Thermo-optical characterization of CdZnS nanoparticle colloids

Thermo-optical properties of cadmium zinc sulfide (CdZnS) nanoparticle colloids are investigated by interferometry technique. The nanoparticle colloids are synthesized by an improved co-precipitation method. Transmission electron microscopy, UV–vis spectrometry and X-ray diffraction analysis are used to characterize the CdZnS nanocrystals. The thermo-optic coefficient of the colloids has been determined using a Fizeau interferometer. For this purpose, the interference patterns are deformed by a photothermal phase shift which is locally induced in the sample by the focused pump laser beam. The change in the refractive index at this region imposes a shift on the phase of the fringe patterns. Fourier analysis performed on the interference patterns allows us to estimate the values of the thermo-optic coefficient and nonlinear refractive index of the sample. It is shown that the CdZnS nanoparticle colloids enhance the absorption of the laser light and induce high rise in the temperature of the sample, which leads to the nonlinear phase shift.