Fizeau Interferometry Research Articles

Implementing multiwavelength fringe tracking for the Large Binocular Telescope Interferometer’s phase sensor, PHASECam

PHASECam is the fringe tracker for the Large Binocular Telescope Interferometer (LBTI). It is a near-infrared camera which is used to measure both tip/tilt and fringe phase variations between the two adaptive optics (AO) corrected apertures of the Large Binocular Telescope (LBT). Tip/tilt and phase sensing are currently performed in the $H$ (1.65 $\mu$m) and $K$ (2.2 $\mu$m) bands at 1 kHz, but only the $K$-band phase telemetry is used to send corrections to the system in order to maintain fringe coherence and visibility. However, due to the cyclic nature of the fringe phase, only the phase, modulo 360 deg, can be measured. PHASECam's phase unwrapping algorithm, which attempts to mitigate this issue, occasionally fails in the case of fast, large phase variations or low signal-to-noise ratio. This can cause a fringe jump, in which case the OPD correction will be incorrect by a wavelength. This can currently be manually corrected by the operator. However, as the LBTI commissions further modes which require robust, active phase control and for which fringe jumps are harder to detect, including multi-axial (Fizeau) interferometry and dual-aperture non-redundant aperture masking interferometry, a more reliable and automated solution is desired. We present a multi-wavelength method of fringe jump capture and correction which involves direct comparison between the $K$-band and $H$-band phase telemetry. We demonstrate the method utilizing archival PHASECam telemetry, showing it provides a robust, reliable way of detecting fringe jumps which can potentially recover a significant fraction of the data lost to them.

Angular differential kernel phases

Context. To reach its optimal performance, Fizeau interferometry requires that we work to resolve instrumental biases through calibration. One common technique used in high contrast imaging is angular differential imaging, which calibrates the point spread function and flux leakage using a rotation in the focal plane. Aims. Our aim is to experimentally demonstrate and validate the efficacy of an angular differential kernel-phase approach, a new method for self-calibrating interferometric observables that operates similarly to angular differential imaging, while retaining their statistical properties. Methods. We used linear algebra to construct new observables that evolve outside of the subspace spanned by static biases. On-sky observations of a binary star with the SCExAO instrument at the Subaru telescope were used to demonstrate the practicality of this technique. We used a classical approach on the same data to compare the effectiveness of this method. Results. The proposed method shows smaller and more Gaussian residuals compared to classical calibration methods, while retaining compatibility with the statistical tools available. We also provide a measurement of the stability of the SCExAO instrument that is relevant to the application of the technique. Conclusions. Angular differential kernel phases provide a reliable method for calibrating biased observables. Although the sensitivity at small separations is reduced for small field rotations, the calibration is effectively improved and the number of subjective choices is reduced.

Determination of Nonlinear Refractive Index of Zinc Phthalocyanine by Pump Induced Fizeau Interferometry

Experimental measurement of intense light induced refractive index is demonstrated using Fizeau interferometer. Refractive index is induced in a specific region of the sample with intense light pulse of a linearly polarized, Q- switched Nd:YAG laser at 1064nm wavelength. The respective change in optical path difference (OPD) is measured using Fizeau interferometer. The OPD so obtained is mapped in terms of change in refractive index in the area of interaction of pump beam and sample. The measured induced refractive index is then used to calculate thermo-optic coefficient of the ZnPc embedded polymeric sample.

Dynamic adaptive X-ray optics. Part I. Time-resolved optical metrology investigation of the bending behaviour of piezoelectric bimorph deformable X-ray mirrors.

Piezoelectric bimorph deformable mirrors (`bimorphs') are routinely used on many synchrotron and free-electron laser beamlines to provide active variation in the size and shape of the X-ray beam. However, the time-domain potential of such optics has never been fully exploited. For the first time, the fast dynamic bending response of bimorphs is investigated here using Fizeau interferometry. Automated scripts for acquisition and analysis were developed to collect Fizeau data at a rate of 0.1 Hz to record dynamic changes in the optical surface as voltages were applied to the electrodes of the piezoelectric actuators. It is demonstrated that residual drift in the tangential radius of curvature of a bimorph can be significantly reduced using enhanced opto-mechanical holders and a fast programmable high-voltage power supply. Further improvements are achieved by applying small opposing voltages to compensate for piezoelectric creep. The present study shows that bimorphs can truly be used as high-speed adaptive optics for the X-ray domain, even without closed-loop feedback correction. This opens the possibility for relatively simple real-time tuning of the profile of X-ray bimorphs. Part II of this study [Alcock, Nistea, Signorato, Owen, Axford, Sutter, Foster & Sawhney (2019), J. Synchrotron Rad. 26, 45-51] builds upon these results and demonstrates how bimorphs can rapidly provide customisable sizes and shapes of synchrotron X-ray beams, specifically tailored to suit the experimental samples being investigated.

Dynamic adaptive X-ray optics. Part II. High-speed piezoelectric bimorph deformable Kirkpatrick-Baez mirrors for rapid variation of the 2D size and shape of X-ray beams.

The tangential curvature of actively bent X-ray mirrors at synchrotron radiation and X-ray free-electron laser (XFEL) facilities is typically only changed every few hours or even days. This operation can take tens of minutes for active optics with multiple bending actuators and often requires expert guidance using in situ monitoring devices. Hence, the dynamic performance of active X-ray optics for synchrotron beamlines has historically not been exploited. This is in stark contrast to many other scientific fields. However, many areas of synchrotron radiation and XFEL science, including macromolecular crystallography, could greatly benefit from the ability to change the size and shape of the X-ray beam rapidly and continuously. The advantages of this innovative approach are twofold: a large reduction in the dead time required to change the size of the X-ray beam for different-sized samples and the possibility of making multiple changes to the beam during the measurement of a single sample. In the preceding paper [Part I; Alcock, Nistea, Signorato & Sawhney (2019), J.Synchrotron Rad. 26, 36-44], which accompanies this article, high-speed visible-light Fizeau interferometry was used to identify the factors which influence the dynamic bending behaviour of piezoelectric bimorph deformable X-ray mirrors. Building upon this ex situ metrology study, provided here is the first synchrotron radiation beamline implementation of high-speed adaptive X-ray optics using two bimorphs operating as a Kirkpatrick-Baez pair. With optimized substrates, novel opto-mechanical holders and a next-generation high-voltage power supply, the size of an X-ray beam was rapidly and repeatedly switched in <10 s. Of equal importance, it is also shown that compensation of piezoelectric creep ensures that the X-ray beam size remains stable for more than 1 h after making a major change. The era of high-speed adaptive X-ray optics for synchrotron radiation and XFEL beamlines has begun.

Testing and characterization of challenging optics and optical systems with Shack Hartmann wavefront sensors

The Shack-Hartman wavefront sensor is a common metrology tool in the field of laser, adaptive optics and astronomy. However, this technique is still scarcely used in optics and optical system metrology. With the development of manufacturing techniques and the increasing need for optical characterization in the industry, the Shack-Hartmann wavefront sensor emerges as an efficient complementary tool to the well-established Fizeau interferometry for optical system metrology. Moreover, the raise of smart vehicles equipped with optical sensors and augmented reality, the optical characterization of glass and transparent flat materials becomes an issue that can be addressed with Shack-Hartmann sensors. Aberration measurements of challenging optics will be presented such as optical filters, thin flat optics, aspheric lenses and large optical assemblies.

High-speed Fizeau interferometry for film topography measurement during spray film interaction.

This work presents a novel high-speed interferometric thickness measurement system for thin films (1 μm-23 μm). The system is based on a Fizeau-interferometer and combines a high-speed camera for 2-D topographic fringe images with a spectrally resolved white light interferometer. The aim of this combination is to overcome the ambiguities of the phase demodulation process during fringe pattern analysis. The system is able to measure spatially and temporally resolved film thickness distributions during fast processes. The measurement error of the system is around 5% compared to a commercial 0-D interferometer. First, the results during a diesel spray impingement onto a predefined diesel film are shown, and at the impingement point, an increase in a fluid volume of 24.3% can be seen.

Fizeau interferometer with binary phase Fresnel-zone plate reference for precision measurement of large convex lens

A method of obtaining precision transmission wavefront of large convex lens interferometrically using binary Fresnel zone plate (FZP) was presented. We present the results from a set of experiments that demonstrate the accuracy, flexibility, and the simplicity of performing the FZP test. A direct comparison of the FZP measurement with results from a Fizeau interferometry method shows excellent agreement. Finally, measurement uncertainty of lens due to alignment error and FZP fabrication processes is analyzed. This resulting analysis shows less than λ/10 accuracy for measuring the transmission wavefront of a sphere lens with 31.25 m focal length and Φ410 mm clear aperture.

Measurement of surface profile and thickness of multilayer wafer using wavelength-tuning fringe analysis

Wavelength-tuning interferometry has been widely used to measure and estimate the surface profile of optical components. However, in multilayer interferometry, the coupling error between the higher harmonics and the phase-shift error causes a considerable systematic error in the calculated phase. In this research, the new 7N − 6 phase-shifting algorithm was developed using the characteristic polynomial theory. The coupling errors calculated by various types of phase-shifting algorithms were analyzed. The surface profile and optical thickness deviation of the lithium niobate crystal wafer were measured simultaneously using wavelength-tuning Fizeau interferometry and the 7N − 6 algorithm. The experimental results were compared in terms of observed ripples and measurement repeatability.

Absolute, high-accuracy characterization of a variable line spacing grating for the European XFEL soft X-ray monochromator.

The European XFEL is a free-electron laser (FEL) with a superconducting linear accelerator and three beamlines (SASE1, SASE2, and SASE3) covering the energy range from 250 eV to 24 keV. The SASE3 beamline is dedicated to the soft x-ray range (0.25-3 keV) and is designed to operate in both monochromatic and non-monochromatic mode. A variable line spacing - plane grating (VLS-PG) monochromator is placed along the beam transport system for the monochromatic mode. The VLS parameters of the grating profile are challenging from a manufacturing and measuring perspective, especially at the desired length of 530 mm. A shorter grating of 150 mm has been procured to allow early operation of the facility. We describe the characterization method that was used to assess the VLS parameters of the grating using Fizeau interferometry. The method is intrinsically absolute and limited only by the quality of the test grating and the noise level. Further measurements using a white-light-interferometry profilometer are also reported. We discuss the possibility of extending the method to the future 530 mm long grating.

Statistical and interferometric determination of the optical thickness of a multilayer transparent plate

Wavelength-tuning Fizeau interferometry has been widely used to measure and estimate the optical thickness of optical components. However, in multilayer interferometry, the coupling errors between the higher harmonics and phase-shift error cause systematic errors in the calculated phase distribution. This paper presents the derivation of a 15-sample phase-shifting algorithm that can compensate for the phase-shift miscalibration and up-to-first-order nonlinearity of the coupling errors between the second-order harmonic and phase-shift error. The characteristics of the 15-sample algorithm are estimated with respect to the Fourier representation in the frequency domain. The optical thickness of a highly reflective lithium niobate crystal wafer is measured using a wavelength-tuning Fizeau interferometer and 15-sample algorithm. Finally, the optical thickness is determined from the measured data using the statistical Student’s t test.

Phase extraction for dual-wavelength phase-shift Fizeau interferometry in the presence of multi-beam interference

Dual-wavelength interferometry could extend the measured range of single-wavelength interferometry by combining the two single wavelength phases, particularly for the measurement of step height. When testing the high-reflectivity surfaces with the single wavelength Fizeau interferometer, we have presented the π∕4 phase-shift carrier squeezing interferometry (QCSI) method for phase extraction with multi-beam interference (Appl. Opt. 55, 1920–1928, 2016). In this paper, we propose an integer and decimal portions synthetization (IDS) method for the multi-beam interference in the dual-wavelength Fizeau interferometer. One of the single wavelength wrapped phases is demodulated by the multi-beam interference QCSI algorithm, while the second of the single wavelength wrapped phases is extracted by the conventional two-beam interference phase-shift algorithm, so the equivalent wavelength unwrapped phase is derived from the two single wavelength wrapped phase. The decimal portion of synthesized phase is then obtained directly from the first single wavelength wrapped phase, and the integer portion of synthesized phase is obtained from the fringe order of the first single wavelength wrapped phase determined by the equivalent wavelength unwrapped phase. The proposed non-iterative IDS method avoids the common error magnification effect in the two-wavelength techniques, and only requires no more than 8 frame phase-shift interferograms for each single wavelength. Its robust performance is validated by both simulations and experiments in the presence of multi-beam interference as well as phase-shift error for measuring objects with height discontinuities.

One-dimensional stitching interferometry assisted by a triple-beam interferometer.

In this work, we proposed for stitching interferometry to use a triple-beam interferometer to measure both the distance and the tilt for all sub-apertures before the stitching process. The relative piston between two neighboring sub-apertures is then calculated by using the data in the overlapping area. Comparisons are made between our method, and the classical least-squares principle stitching method. Our method can improve the accuracy and repeatability of the classical stitching method when a large number of sub-aperture topographies are taken into account. Our simulations and experiments on flat and spherical mirrors indicate that our proposed method can decrease the influence of the interferometer error from the stitched result. The comparison of stitching system with Fizeau interferometry data is about 2 nm root mean squares and the repeatability is within ± 2.5 nm peak to valley.

Error-compensating phase-shifting algorithm for surface shape measurement of transparent plate using wavelength-tuning Fizeau interferometer

When measuring the surface shape of a transparent sample using wavelength-tuning Fizeau interferometry, the calculated phase is critically determined by not only phase-shift errors, but also by coupling errors between higher harmonics and phase-shift errors. This paper presents the derivation of a 13-sample phase-shifting algorithm that can compensate for miscalibration and first-order nonlinearity of phase shift, coupling errors, and bias modulation of the intensity, and has strong suppression of the second reflective harmonic effect. The characteristics of the 13-sample algorithm are estimated with respect to Fourier representation in the frequency domain. The phase error of measurement performed using the 13-sample algorithm is discussed and compared with those of measurements obtained using other conventional phase-shifting algorithms. Finally, the surface shape of a fused silica wedge plate obtained using a wavelength tuning Fizeau interferometer and the 13-sample algorithm are presented. The experimental results indicate that the surface shape measurement accuracy for a transparent fused silica plate is 3nm. The accuracy of the measurement is discussed by comparing the amplitudes of the crosstalk noise calculated using other conventional algorithms.

Analysis of the Effect of Interferometer Cavity Distortion on Homogeneity Tests of Large-Diameter Optical Materials

Optical homogeneity of the optical materials directly affects the wavefront quality of the refractive optical system. There are some difficulties of testing large caliber optical materials, four-step method of Fizeau interferometry is a convenient and accurate method for measuring optical homogeneity. The article used the four-step method test the same quartz glass sample in a cavity with different precision and found that the optical homogeneity test results have a larger gap. While this article compared the effect of the fixed cavity surface shape and the changing cavity surface shape on 300 mm diameter quartz glass optical homogeneity test and analyzed the effect of different positions of fixed cavity distortion on optical homogeneity testing.

Surface measurement of indium tin oxide thin film by wavelength-tuning Fizeau interferometry.

Indium-tin oxide (ITO) thin films have been widely used in displays such as liquid crystal displays and touch panels because of their favorable electrical conductivity and optical transparency. The surface shape and thickness of ITO thin films must be precisely measured to improve their reliability and performance. Conventional measurement techniques take single point measurements and require expensive systems. In this paper, we measure the surface shape of an ITO thin film on top of a transparent plate using wavelength-tuning Fizeau interferometry. The surface shape was determined by compensating for the phase error introduced by optical interference from the thin film, which was calculated using the phase and amplitude distributions measured by wavelength-tuning. The proposed measurement method achieved noncontact, large-aperture, and precise measurements of transparent thin films. The surface shape of the sample was experimentally measured to an accuracy of 5.13nm.

Measurement of absolute optical thickness of mask glass by wavelength-tuning Fourier analysis

Optical thickness is a fundamental characteristic of an optical component. A measurement method combining discrete Fourier-transform (DFT) analysis and a phase-shifting technique gives an appropriate value for the absolute optical thickness of a transparent plate. However, there is a systematic error caused by the nonlinearity of the phase-shifting technique. In this research the absolute optical-thickness distribution of mask blank glass was measured using DFT and wavelength-tuning Fizeau interferometry without using sensitive phase-shifting techniques. The error occurring during the DFT analysis was compensated for by using the unwrapping correlation. The experimental results indicated that the absolute optical thickness of mask glass was measured with an accuracy of 5nm.

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).

Correlated errors in phase-shifting laser Fizeau interferometry.

High-performance data processing algorithms for phase-shifting interferometry accommodate adjustment errors in the phase shift increment as well as harmonic distortions in the interference signal. However, a widely overlooked error source is the combination of these two imperfections. Phase shift tuning errors increase the sensitivity of phase estimation algorithms to second-order and higher harmonics present in Fizeau interference signals. I derive an analytical formula for evaluating these errors more realistically, in part to identify the characteristics of the optimal PSI algorithm. Even for advanced algorithms, it is found that multiple reflections increase the error contribution of detuning by orders of magnitude compared with the two-beam calculation and impose a practical limit of 30% in tuning error for sub-nm metrology in a 4%-4% Fizeau cavity. Consequently, a preferred approach for high precision spherical cavities is to use either wavelength tuning in place of mechanical phase shifting or an iterative solver that accommodates unknown phase shifts as a function of field position.

Measuring coalignment of retroreflectors with large lateral incoming-outgoing beam offset

A method based on phase-shifting Fizeau interferometry is presented with which retroreflectors with large incoming-outgoing beam separations can be tested. The method relies on a flat Reference Bar that is used to align two auxiliary mirrors parallel to each other to extend the aperture of the interferometer. The method is applied to measure the beam coalignment of a prototype Triple Mirror Assembly of the GRACE Follow-On Laser Ranging Interferometer, a future satellite-to-satellite tracking device for Earth gravimetry. The Triple Mirror Assembly features a lateral beam offset of incoming and outgoing beam of 600 mm, whereas the acceptance angle for the incoming beam is only about ±2 mrad. With the developed method, the beam coalignment of the prototype Triple Mirror Assembly was measured to be 9 μrad with a repeatability of below 1 μrad.