Interferometric Testing Research Articles

Modelling Newtonian noise of vibroacoustic origin in the Virgo gravitational wave detector

With ~100 detections by the LIGO-Virgo-KAGRA network, gravitational astronomy has definitely begun. The Virgo detector is a modified Michelson interferometer with two arms of 3km each, made of optical resonator housing ~100 kW laser beams. It can measure a gravitational strain (ΔL/L) of ~10^(-21). The detector is susceptible to various sources of noise within specific frequency bands. Among these, the "Newtonian" or "gravity-gradient" noise (seismic and atmospheric/acoustic) could limit the low-frequency sensitivity (below a few tens of Hz) of LIGO and Virgo as they reach their full sensitivity, as well as that of next-generation detectors such as the European Einstein Telescope and the US Cosmic Explorer. This paper focuses on modeling Newtonian noise of acoustic origin, which refers to the small fluctuations in the gravity field resulting from the acoustic field present in the experimental halls. The fluctuating gravitational field directly causes random forces on sensitive optical elements, such as the interferometer test masses. The induced noise is quantified using a numerical acoustic model of the experimental room when it is excited by the air conditioning system.

Positioning of the test surface in a CGH null test by cat's eye interference

Interferometric null test of optical aspheres and freeforms is one of the most established methods, in spite of recognized limitations related to positioning of the test surface. Slight misalignment of the surface in the null test system can introduce remarkable wave aberrations. Current approaches for positioning the test surface are based on a series of fiducial marks or retroreflectors set at given spots around the test surface, which consequently suffer the problem of datum transformation. We propose a method for positioning the test surface in a null test by cat's eye interference without any fiducial marks or retroreflectors. A computer-generated hologram (CGH) is used as null optics fabricated with null test pattern, alignment pattern and positioning pattern. A part of test beam with relatively small f/number is diffracted through the positioning pattern and then focuses on certain spots of the test surface. The cat's eye reflection from the test surface returns to the interferometer and interferes with the reference beam. It is then possible to precisely position the test surface by measuring the wavefront error of the cat's eye interference. The design method for such a CGH positioning pattern is presented, following the physical constraint that the surface normal at the cay's eye reflection is right the angular bisector of the positioning beam. Analysis on the positioning performance is then presented to show the sensitivity to misalignment including defocus, lateral shift and tip-tilt, which at last is experimentally verified by measuring an even asphere with a CGH.

Improved performance of three mirror anastigmat telescope with freeform surface: Optical design, testing and validation aspects

"In this paper, the optical design of a Three Mirror Anastigmat (TMA) Telescope is modified by substitution of a convex freeform secondary and optimization carried out to obtain improved performance. The proposed convex freeform surface is precisely manufactured using the bonnet polishing technique and tested with a sub-aperture stitched algorithm, meeting the specified surface accuracy requirements. Further, to validate the design, the realized secondary freeform optic is tested in conjunction with primary and tertiary optics in the conceived TMA configuration. The telescope system performance is established using a double-pass interferometric test setup. The modified design enhances the telescope system's performance in the extended field of view (FoV) from ±2.5° to ±3.5° across the track and from ±0.4° to ±0.6° along the track. Measured performance results demonstrate an average modulation transfer function (MTF) of 0.56 and an average Strehl ratio of 0.64 at all field points. The effective focal length of the system is computed to be 975 mm. In summary, the proposed freeform surface significantly improves the optical system performance within the available real estate of the envisaged space telescope system."

Absolute testing of rotationally symmetric surfaces with computer-generated holograms.

Extremely high accuracy is demanded for optics working at very short wavelength. Interferometric testing of optical aspheres or freeform surfaces requires null optics, typically computer-generated holograms (CGHs), to balance the wave aberrations. The measurement uncertainty is primarily limited by the accuracy of the test wavefront, which is predominantly influenced by the CGH and the interferometer optics. Absolute testing is fundamental to achieving accuracy much higher than that of the test wavefront through error separation. This paper presents a method for absolute testing of rotationally symmetric surfaces with CGH null optics. The basic assumption is that the off-axis hologram fabricated by raster scanning beam writing has negligible error of rotationally symmetric component due to pattern error of the CGH. Consequently, the wavefront error contributed by the CGH and the transmission flat can be completely separated from the absolute surface shape by combining the N-position method and the shift-rotation method. A theoretical model for absolute testing is proposed under the assumption. Experimental cross test is then presented to validate the method with sub-nanometer uncertainty. The assumption is further confirmed by characterizing the fabrication error of the hologram structures using a white light interferometer. Finally, the effect of noise, translation error, rotation error and eccentricity of rotation on the absolute testing is analyzed.

Bayesian inference for near-field interferometric tests of collapse models

We explore the information which proposed matterwave interferometry experiments with large test masses can provide about parameterizable extensions to quantum mechanics, such as have been proposed to explain the apparent quantum to classical transition. Specifically, we consider a matterwave near-field Talbot interferometer and Continuous Spontaneous Localization (CSL). Using Bayesian inference we compute the effect of decoherence mechanisms including pressure and blackbody radiation, find estimates for the number of measurements required, and provide a procedure for optimal choice of experimental control variables. We show that in a simulated space-based experiment it is possible to reach masses of ∼109u, and we quantify the bounds which can be placed on CSL. These specific results can be used to inform experimental design, and the general approach can be applied to other parameterizable models. Published by the American Physical Society 2024

Effective removal of uranium (VI) with a SDBS doped PPy-SUS304 electrode from alkaline wastewater using electrodeposition strategy

The immobilization of uranium in nuclear wastewater is of paramount importance for environmental and human health. However, there is a paucity of research on the immobilization of uranium in alkaline wastewater, particularly with regards to the application of novel electrodes. This article presents the utilization of an electrochemically polymerized polypyrrole stainless steel (PPy-SUS304) electrode for the effective electrochemical deposition and removal of uranium from alkaline wastewater containing uranium. According to the electrodeposition results, the uranium deposition efficiency of the novel electrode reached 96.82 %, with a uranium deposition rate of 0.048 mg U/(h·cm2) and a charge efficiency of 0.055 mg U/C. These findings demonstrate the successful electrochemical reduction of UO2(CO3)34- in alkaline uranium-containing wastewater using the novel electrode, resulting in improved charge deposition efficiency. The electrode surface products were investigated using scanning electron microscopy (SEM), Energy-dispersive X-ray spectroscopy (EDS), and X-Ray Photoelectron Spectroscopy (XPS). The SEM and EDS results demonstrate the formation of a uniform PPy film on the surface of SUS304. In addition, the White light interferometer (WLI) test reveals that the PPy-SUS304 electrode exhibits increased roughness compared to the SUS304 electrode. The XPS results revealed that the electrode surface products of PPy-SUS304 were actually U compounds constituted of U(IV) oxides or hydroxides. This study provides a new perspective for the development of novel electrodes to suppress side reactions and efficiently recover uranium from alkaline uranium-containing wastewater.

Improving the accuracy of interferometer testing with absolute surface calibration and power spectral density analysis

A novel absolute surface calibration method for interferometer testing based on power spectral density analysis has been proposed. The method involves obtaining the loss of signal at different frequencies as a function of various rotation angles by signal analysis to choose the rotation angle for calibration. A model is developed to evaluate the calibration method by creating random surface shapes based on the Power Spectral Density. Using this algorithm, the precision of the absolute testing method during the testing process exceeds 0.28 %. Error propagation during the experimental process, such as testing optic clamping, angular errors, eccentricity, vibrations and airflow disturbances, were calibrated. Ultimately, the absolute detection test results were verified using high-precision flat mirrors. The experimental result indicates an RMS of 4.275 nm, 4.263 nm, and 4.265 nm in different rotation angle, and the calibrated result shows an RMS of 4.880 nm. The shape of surface errors in the absolute test results and calibration results is consistent.

High precision wavefront correction method in interferometer testing.

A wavefront correction method is proposed for high-precision optic surfacing, addressing the discrepancy between wavefront and real surface errors in Fizeau interferometer testing. We believe this to be a proposed novel method that encompasses optical surface function parameters fitting, lateral distortion correction, misalignment error removal, and sag surface error calculation. The method's error has been thoroughly analyzed, including aspects of function parameters fitting, ray tracing, and interpolation. The effectiveness of the method was demonstrated by correcting the wavefront of an off-axis parabolic mirror in null testing configurations, significantly reducing artificially created annular errors and improving off-axis direction errors from 0.23λ to 0.05λ (λ=632.8 nm), with the PV of aspheric departures exceeding 8.5 mm.

Qualitative evaluation of a parabolic mirror with substructured Ronchi gratings

In this work we propose to qualitatively test the quality of a concave parabolic mirror by means of the Ronchi interferometric test using substructured gratings to increase the sharpness of the fringes. The substructured gratings are designed considering that the grating period is divided into several stripes of equal width that can be transparent or opaque; the transmission coefficients of the stripes along the grating period are not periodic, but a previously chosen binary sequence. Equations were derived to obtain the corresponding intensity profiles and an analysis of these profiles was performed for different sequences and positions of the substructured gratings with respect to the test mirror. It was experimentally verified that the fringes are sharper at the Rayleigh distance inside and outside the mirror focus.

Effect of Process Parameters on the Microstructure and Wear Resistance of Fe3Al/Cr3C2 Composites

In this paper, a brake cylinder coating comprising a composite material of an Fe3Al and Cr3C2 mixed powder was prepared by adding laser cladding onto carbon structural steel. We studied the influence of process parameters on the microstructure and tribological properties of the cladding materials using scanning electron microscopy (SEM), energy-dispersive spectroscopy (EDS), and 3D white light interferometer and wear tests. The influence of different processes on the morphology of the carbide strengthening phase was found to be relatively small with a Cr3C2 content of 15 wt.%. The carbides mainly exhibited a network structure in each group of cladding layers. The area of the network strengthening phase varied under different processes. Of the cladding layers formed with different processes, the scanning speed of the 0.003 m/s cladding layer had the lowest wear rate. When the laser power was too low or the powder feed rate was too high, unmelted Cr3C2 particles could be found in the cladding layer. During the wear process, the particles peeled off, causing severe abrasive wear. When the powder feeding rate was too low, more materials in the base material entered the cladding layer. This made the composition of the cladding layer similar to that of the grinding material, resulting in severe adhesive wear.

Analysis of phase preservation and interferometric offset test in sparse SAR imaging

Analysis of phase preservation and interferometric offset test in sparse SAR imaging

Primordial black holes as dark matter: interferometric tests of phase transition origin

We show that primordial black holes — in the observationally allowed mass window with fPBH = 1 — formed from late nucleating patches in a first order phase transition imply upcoming gravitational wave interferometers will see a large stochastic background arising from the bubble collisions. As an example, we use a classically scale invariant B – L model, in which the right handed neutrinos explain the neutrino masses and leptogenesis, and the dark matter consists of primordial black holes. The conclusion regarding the gravitational waves is, however, expected to hold model independently for black holes coming from such late nucleating patches.

Measurement of a Freeform Surface by Dragging Three Point Method Along with a Circular Path

Freeform surfaces can realize optical systems with a wide field of view, high throughput, and high contrast. For constructing optical systems with freeform surfaces, measuring technology is essential. However, it is difficult to measure freeform surfaces by existing measurement methods. We have developed a new measurement method of the dragging three-point method (DTPM). To realize further improvement in the accuracy of the DTPM, we propose the DTPM with a circular path. Since the circular path is closed, the measurement error can be reduced by the boundary condition that the height and slope agree with at the start and end points of the measurement. To evaluate this method, we conducted the circular path measurement of an off-axis asphere. The measurement repeatability was RMS = 1.5 nm, and the result agreed well with that of an interferometric test; the difference was RMS = 17.2 nm.

Method for testing freeform surfaces based on a Shack-Hartmann sensor with plane wavefront scanning and stitching.

Currently, the surface error measurement technology for freeform faces a significant contradiction between measurement accuracy and dynamic range. The study proposes a non-null testing method for measuring freeform surfaces by utilizing a Shack-Hartmann wavefront sensor to emit a small aperture parallel beam and scan along the normal direction at the center of subapertures for stitching (SHPSS). A mathematical model based on ray tracing and the reflection theorem is established to calculate the sampling points on an ideal freeform surface, the reference spot array on CCD, and the corresponding relationship between microlens array and spots. An algorithm is proposed to iteratively calculate the wavefront aberration and gradually approach the actual sampling points using the established model. Theoretical analysis and numerical simulation results indicate that SHPSS can increase the dynamic range and improve the accuracy of wavefront reconstruction. The error analysis of the SHPSS method is carried out, the measurement accuracy of full aperture freeform surface is 11.45 nm. A testing system is set up and experiments are conducted on a 100 mm aperture freeform reflective mirror. The RMS of the SHPSS test results is less than λ/30 (λ=635 nm) compared to the interferometric test results. By analyzing five groups of repeated measurement experiments, the repeatability accuracy of SHPSS method is less than 1/80 λ (RMS). This demonstrates the feasibility and measurement capabilities of the method for freeform surface testing.

Retrace error calibration for interferometric measurements using an unknown optical system.

In classical interferometric null test measurements, the measurement and reference beam path should be the same. A difference in the beam paths results in the so called retrace error. One very common approach to avoid retrace errors is to adapt the measurement wavefront to the reference wavefront with a computer generated hologram (CGH), which is costly and time consuming. A much more flexible approach is to do non nulltest measurement in combination with mathematical treatment of retrace errors. Most of such methods are based on iterative optimization or calibration of the nominal optical design of the interferometer. While this may be a convenient solution in the context of research, the more common use may be limited due to the need of the optical design of all interferometer components. In many cases, the optical designs of standard off the shelf optical assemblies are not available or disclosed by the manufacturer. This is especially true for transmission spheres of interferometers. We introduce the so called Black Box Model (BBM), used in the well known Tilted Wave Interferometry (TWI), as a mathematical model to account for retrace errors in interferometry. The Black Box Model is based on point characteristic functions which are adapted to the result and behavior of a real interferometer by calibration. With an extended calibration method, the need of a specific optical design of the interferometer is no longer necessary. Thus the method is attractive for a wide field of use in interferometry with standard off the shelf components.

Digital shearography for NDT: Determination and demonstration of the size and the depth of the smallest detectable defect

This paper presents a methodology of digital shearography for determining the size of the smallest detectable defect and the depth under different loading magnitudes for the purpose of nondestructive testing. Digital Shearography, an interferometric nondestructive testing (NDT) technique, has been proven to be a useful tool for material inspections and evaluations, especially for detecting delaminations/disbonds in composite materials and honeycomb structures. A commonly asked question in the field of NDT is about measuring sensitivity - specifically, what is the smallest detectable delamination/disbond and how deep can these be detected? Although various attempts to find the smallest detectable defect by shearography have been made, a numerical model for determining the size of the smallest detectable defect and the depth has not yet been developed. This paper did a study in this aspect, especially for NDT of delamination and disbond in polymers and honeycomb structures. First, a mechanical model based on the thin plate theory to calculate the expected bending of close-to-surface defects was proposed; the model built a relationship among the deformation caused by a defect, the size and the depth of the defect, as well as the load and the material properties. Second, the relationship between the relative deformation measured by shearography and the deformation induced by a defect was established based on the optimized shearing amount and the sensitivity of digital shearography. Based on these analyses, relationships between the size of the smallest detectable defect and the depth under different load amounts were established for different defect shapes. Finally, experimental validation based on different sizes of prefabricated defects were conducted to verify these relationships. The experimental results show that the model developed can provide useful estimation for NDT by digital shearography, especially with helping test engineers estimate the size of the smallest detectable defect and the depth with corresponding loading magnitudes.

Can gravitational-wave memory help constrain binary black-hole parameters? A LISA case study

Besides the transient effect, the passage of a gravitational wave also causes a persistent displacement in the relative position of an interferometer's test masses through the nonlinear memory effect. This effect is generated by the gravitational backreaction of the waves themselves, and encodes additional information about the source. In this work, we explore the implications of using this information for the parameter estimation of massive binary black holes with LISA. Based on a Fisher analysis for nonprecessing black hole binaries, our results show that the memory can help to reduce the degeneracy between the luminosity distance and the inclination for binaries observed only for a short time ($\ensuremath{\sim}\mathrm{few}\text{ }\mathrm{hours}$) before merger. To assess how many such short signals will be detected, we utilized state-of-the-art predictions for the population of massive black hole binaries and models for the gaps expected in the LISA data. We forecast from tens to few hundreds of binaries with observable memory, but only $\ensuremath{\sim}\mathcal{O}(0.1)$ events in 4 years for which the memory helps to reduce the degeneracy between distance and inclination. Based on this, we conclude that the new information from the nonlinear memory, while promising for testing general relativity in the strong field regime, has probably a limited impact on further constraining the uncertainty on massive black hole binary parameters with LISA.

Convex optical freeforms using fringe Zernike overlay approach for two-mirror and three-mirror telescopes for space applications

The challenge in manufacturing and testing of convex optical parts is well known in comparison to its concave counterpart and an optimized imaging system invariably features a combination of both. Of late, freeform mirrors find lot of interest in space applications as the optical systems remain compact within the allocated envelope. As is well known, these freeform mirrors are difficult to manufacture and test due to their lack of rotational or translational symmetry and poses additional challenges if it has convex profile. In the current investigations, two new convex freeform optical surfaces are proposed which is based on fringe Zernike overlay technique. The first convex freeform envisaged is for a two-mirror off-axis telescope where the secondary mirror is an off-axis freeform and the second convex freeform for a three-mirror anastigmat telescope where the secondary mirror is an on-axis convex freeform. Substitution of these convex freeform surfaces in the two-mirror and three-mirror telescope systems aid in the correction of asymmetrical aberrations to a wider view field, thereby enhancing the performances of the de-centred and tilted systems in the respective configurations. The procedure adopted for the manufacturing of these convex freeform surfaces using bonnet polishing methods and the interferometric tests using modified-Hindle null corrector and subaperture-stitching techniques for evaluation are described in detail.

Automatic Foucault test method based on transverse cutting at two different axial positions near the foci

Foucault knife-edge method is an irreplaceable qualitative testing method in the early stage of optical processing, but it needs to accurately place the knife-edge at the focus of the mirror surface to be measured for testing. In view of the complex and difficult calibration process of the knife-edge instrument and the inability to perform quantitative testing efficiently, here the Foucault knife-edge testing method is improved by digitizing and automating it. The knife-edge instrument is first placed on the motorized precision translation stage for two programmed cutting movement perpendicular to the optical axis with controlled axial spacing. And the normal vector of each point on the mirror surface to be measured is solved through the knife-edge transverse position relationship for the bright and dark transition of the corresponding point on a series of knife-edge shadow grams obtained by two cuts. Then the automation and quantification of knife-edge method can be realized. The experimental results of this method are compared with the interferometer testing results, which have good consistency and high accuracy. This method does not require high calibration accuracy for the knife-edge instrument and can perform rapid and efficient testing. It provides a testing method with good performance for automatic and quantitative testing in the early stage of optical processing.

Interferometric test of coaxial folded mirrors for visible/near-infrared imaging systems (invited)

Interferometric test of coaxial folded mirrors for visible/near-infrared imaging systems (invited)