Sinusoidal wavelength-scanning interferometers for shape measurements

Two different sinusoidal wavelength-scanning (SWS) interferometers with a SWS light source using a superluminescent laser diode are proposed for step-profile measurement and real-time distance measurement, respectively. An optical path difference (OPD) longer than a wavelength is measured from detection of sinusoidal phase- modulation amplitude Zb of the interference signal that is proportional to the OPD and the scanning width 2b. In step-profile measurement, if measurement error in the OPD obtained from Zb is smaller than a half wavelength, this measured value of the OPD is combined with a fractional value of the OPD obtained from the conventional phase of the interference signal. This combination enables us to measure the OPD longer than a wavelength with a high accuracy of a few nm. In real-time distance measurement, the amplitude Zb is kept at a specified constant value for changes of OPD by controlling the scanning width 2b of the wavelength with a feedback system. The amplitude Zb is detected by processing the interference signal with electric circuits in real-time. The value of b is easily controlled in the SWS light source, and an OPD longer than a wavelength is measured from the value of b with an accuracy of about a wavelength.© (1999) COPYRIGHT SPIE--The International Society for Optical Engineering. Downloading of the abstract is permitted for personal use only.

A halogen lamp and an acousto-optic tunable filter are used to construct a sinusoidal wavelength-scanning interferometer with the scanning width of 210 nm. A linear wavelength-scanning with the scanning width of 220 nm is utilized to determine amplitudes of three different interference signals produced from multiple-reflection lights by front and rear surfaces of a thin film. Amplitudes of time-varying phases produced by a sinusoidal wavelength-scanning and constant phases in the interference signals are estimated by minimizing a difference between detected signals and theoretical ones. From the estimated values, the positions of the front and rear surface of the thin film with a thickness of about 460 nm are measured with an error less than 4 nm.

Spectrometers based on acousto-optic tunable filters (AOTFs) have several advantages, such as stable temperature adaptability, no moving parts, and wavelength selection through electrical modulation, compared with the traditional grating and Fourier transform spectrometers. Therefore, AOTF spectrometers can realize stable in situ measurement on the lunar surface under wide temperature ranges and low light environments. AOTF imaging spectrometers were first employed for in situ measurement of the lunar surface in the Chinese Chang’e project. The visible and near-infrared imaging spectrometer and the lunar mineralogical spectrometer have been successfully deployed on board the Chang’e-3/4 and Chang’e-5 missions. In this review, we investigate the performance indicators, structural design, selected AOTF performance parameters, data acquisition of the three lunar in situ spectral instruments used in the Chang’e missions. In addition, we also show the scientific achievement of lunar technology based on in situ spectral data.

Compared with conventional high-end optical systems, application of freeform optics offers many advantages. Their widespread use, however, is held back by the lack of a suitable measurement method.The NANOMEFOS project aims at realizing a universal freeform measurement machine to fill that void.The principle of operation of this machine requires a novel sensor for surface distance measurement, the development and realization of which is the objective of the work presented in this thesis. The sensor must enable non-contact, absolute distance measurement of surfaces with reflectivities from 3.5% to 99% over 5 mm range, with 1 nm resolution and a 2s measurement uncertainty of 10 nm for surfaces perpendicular to the measurement direction and 35 nm for surfaces with tilts up to 5°. To meet these requirements, a dual-stage design is proposed: a primary measurement system tracks the surface under test by translating its object lens, while the secondary measurement system measures the displacement of this object lens. After an assessment of various measurement principles through comparison of characteristics inherent to their principle of operation and the possibilities for adaptation, the differential confocal measurement has been selected as the primary measurement method. Interferometry is used as secondary measurement method. To allow for correction of tilt dependent error through calibration, a third measurement system has been added, which measures through which part of the aperture the light returns. An analytical model of the differential confocal measurement principle has been derived to enable optimization. To gain experience with differential confocal measurement, a demonstrator has been built, which has resulted in insights and design rules for prototype development. The models show satisfactory agreement with the experimental results generated using the demonstrator, thus building confidence that the models can be applied as design and optimization tools. Various properties that characterize the performance of a differential confocal measurement system have been identified. Their dependence on the design parameters has been studied through simulations based on the models. The results of this study are applied to optimize the sensor for use in NANOMEFOS. An optical system has been designed in which the interferometer and the differential confocal systems are integrated in a compact design. The optical path of the differential confocal system has been folded using prisms and mirrors so that it can be realized within the allotted volume envelope. For the same reason, many components are adapted from commercially available parts or are custom made. An optomechanical and mechatronic design has been made around the optical system. A custom focusing unit has been designed that comprises a guidance mechanism and actuator to enable tracking of the surface. To achieve a low measurement uncertainty, it aims at accurate motion, high bandwidth and low dissipation. The lateral position of the guidance reproduces within 20 nm and from the frequency response, it is expected that a control bandwidth of at least 800 Hz can be realized. Power dissipation depends on the form of the freeform surface and is a few mW for most expected trajectories. Partly custom electronics are used for signal processing, and to drive the laser and the focusing unit. Control strategies for interferometer nulling, focus locking and surface tracking have been developed, implemented and tested. Various tests have been performed on the system to evaluate the performance. Calibrations must be carried out to achieve the required measurement uncertainty. One calibration is based on a new method to measure tilt dependency of distance sensors. The sensor realized has 5 mm measurement range, -2.5 µm to 1.5 µm tracking range, sub-nanometer resolution, and a small-signal bandwidth of 150 kHz. Using the test results, the 2s measurement uncertainty after calibration is estimated to be 4.2 nm for measurement of rotationally symmetric surfaces, 21 nm for measurement of medium freeform surfaces and 34 nm for measurement of heavily freeform surfaces. To test the performance of the machine with the sensor integrated, measurements of a tilted flat have been carried out. In these measurements, a tilted flat serves as a reference freeform with known surface form. The measurements demonstrate the reduction of tilt dependent error using the new calibration method. A tilt robust, single point distance sensor with millimeter range and nanometer uncertainty has been developed, realized and tested. It is installed in the freeform measurement machine for which it has been developed and is currently used for the measurement of optical surfaces.

We demonstrate simultaneous topography and tomography of latent fingerprints using full-field swept-source optical coherence tomography (OCT). The swept-source OCT system comprises a superluminescent diode (SLD) as broad-band light source, an acousto-optic tunable filter (AOTF) as frequency tuning device, and a compact, nearly common-path interferometer. Both the amplitude and the phase map of the interference fringe signal are reconstructed. Optical sectioning of the latent fingerprint sample is obtained by selective Fourier filtering and the topography is retrieved from the phase map. Interferometry, selective filtering, low coherence and hence better resolution are some of the advantages of the proposed system over the conventional fingerprint detection techniques. The present technique is non-invasive in nature and does not require any physical or chemical processing. Therefore, the quality of the sample does not alter and hence the same fingerprint can be used for other types of forensic test. Exploitation of low-coherence interferometry for fingerprint detection itself provides an edge over other existing techniques as fingerprints can even be lifted from low-reflecting surfaces. The proposed system is very economical and compact.

We describe an optical displacement sensor based on optical feedback interferometry in a blue-light emitting GaN laser diode. Also presented are preliminary results from measuring variations in the optical path length (OPL) of an external cavity (EC) in the 0- to 240-nm range. These results show that, within the specified range, the sensor follows linearly the OPL variation of the EC. Moreover, the slope between a reference and the measured OPL is 1.0003, and the average deviation from the linear slope is 5 nm in this range. Finally, we also consider the stability of the interference signal in long-term measurements.

Nanometer-scale displacement sensing using self-mixing interferometry with a correlation-based signal processing technique

This paper describes the use of white light scanning interferometry with a Super luminescent diode (SLD) for thin film surface measurement. The technique provides 3D top surface and thickness profiles of transparent films, as well as detailed properties of multilayer film stacks, including material optical properties. The setup involves splitting a laser beam with a beam splitter, generating interference signals detected by a photodetector, and then converting analog signals to digital using an A/D converter for further analysis with LabView and MATLAB software. In this paper, the theoretical analysis and simulation study of white light scanning interferometry for transparent film measurement is discussed. This approach offers a flexible tool for both engineering and structured surface measurements.

Deflectometry with structured light for high-precision measurement of optical specular surfaces has attracted considerable attention. However, conventional deflectometry schemes often encounter challenges when they deal with lens-like transparent objects due to parasitic reflections arising from the rear side of objects. To address this issue, we propose a novel stereo deflectometry method that replaces traditional phase-shift patterns with Fourier-based patterns inspired by single-pixel imaging. This method enables the acquisition of Fourier spectra of light response coefficients for each camera pixel. Specifically, through inverse discrete Fourier transform and the Fourier slice theorem, we obtain the light response coefficients of the light source to the camera pixel. Subsequently, a geometry optical analysis method is proposed to separate the light response coefficients components associated with the front surface given the lack of epipolar constraint between the camera and LCD screen. An iterative algorithm integrated with Particle swarm optimization is proposed to accelerate the reconstruction process and obtain the surface normal field of the upper surface of the lens-like transparent object. The wavefront reconstruction algorithm for gradient integration is used on the normal vector field to enables high-precision reconstruction of the object's surface shape. Experiments on actual optical components demonstrate that the proposed method can accurately reconstruct the front surface of transparent lens by eliminating the interference from parasitic reflection, and an error of less than 200 nm is obtained.

An external cavity diode laser is used as source for a frequency modulated continuous wave (FMCW) interferometer intended to determine absolute optical path differences (OPD) of up to 3mm with a target accuracy of 0.3 microns. This interferometer will eventually be paired with a heterodyne interferometer to extend the accuracy of the system to 0.1nm. Rather than using injection current modulation for the FMCW subsystem, the frequency sweep is provided by moving a mirror of the external cavity with a piezo element. A noise source analysis for this particular setup is provided, and estimates of the maximum attainable accuracy are made.

In sinusoidal phase-modulating interferometry an optical path length (OPD) larger than a wavelength is measured by detection of sinusoidal phase-modulation amplitude Z(b) of the interference signal that is produced by sinusoidal scanning of the wavelength of a light source. A light source with a large scanning width of wavelength is created by use of a superluminescent laser diode for the error in the measured value obtained by Z(b) to be smaller than half of the central wavelength. In this situation the measured value can be combined with a fractional value of the OPD obtained from the conventional phase of the interference signal. A sinusoidal wavelength-scanning interferometer with the light source measures an OPD over a few tens of micrometers with a high accuracy of a few nanometers.

We present accurate signal processing techniques based on the continuous wavelet transform (CWT) for nonstationary optical coherence tomography (OCT) interference signals. OCT is attracting considerable attention in the clinical, scientific, and engineering fields. However, the temporal or spatial period of the detected interference signal is unequal because of the nonlinearity of the scanning device or the inverse proportionality of the phase to the wavelength. If these nonstationary interference signals are acquired at equal sampling intervals and processed using fast Fourier transform (FFT), measurement errors occur. We first propose techniques that compensate for the fringe intervals of the temporal interference signal based on the CWT. The accurate position measurement of a reflective surface is demonstrated. Next, we describe a novel signal processing technique that accurately determines the positions of the fringe peak and reference mirror for TD-OCT. An accurate step-height measurement is demonstrated in this study. Finally, we describe a threedimensional profile measurement method. The optical path difference can be determined through a simple relationship between the wavelength and the corresponding phase obtained by the CWT. Measurements of a step-height configured with a pair of gauge blocks and the thickness distribution of a thin glass plate are performed. In the latter case, we demonstrate that the accuracy is improved in the pulse-driven technique.

This paper extends Digital Speckle Pattern Interferometry into three dimensions. A Wavelength Scanning Interferometry (WSI) system is proposed which provides displacement fields inside the volume of semi-transparent scattering materials with high spatial resolution and three-dimensional displacement sensitivity. The main driver to develop such a system is the need to determine constitutive parameters (mainly elastic constants) of materials such as polymers and biological tissues so that their behavior can be modeled computationally. The sample is illuminated by three non-coplanar collimated beams around the observation direction. Sequences of two-dimensional interferograms are recorded while the frequency of the laser is tuned at a constant rate. Each pixel thus records and intensity signal which temporal frequency encodes the optical path difference between the illumination and reference beams for a particular point on the sample. Fourier transformation along the time axis reconstructs the magnitude and phase of the material's microstructure. Different optical paths along each illumination direction are required in order to separate or multiplex, in the frequency domain, the signals corresponding to each sensitivity vector. In this way, all the information required to reconstruct the location and the 3D displacement vector of scattering points within the volume in the material is recorded simultaneously. A controlled validation experiment is performed, which confirms the ability of the technique to provide three dimensional displacement distributions inside semitransparent scattering materials

Improving the safety of a wide range of launch and recovery operations is of great international maritime interest. Deterministic sea wave prediction (DSWP) is a relatively new branch of science that can offer such opportunities by predicting the actual shape of the sea surface and its evolution for short time in the future. Fourier transform technique is the main building block in DSWP, which requires measurements of the sea surface. Nonetheless, uniformly sampled measurements of the sea surface cannot be practically achieved for various reasons. Conventional X-band radars are the most realistic candidate to provide a low-cost convenient source of two-dimensional wave profile information for DSWP purposes. Ship movement and mechanically rotating scanning antennas are among sources of irregularity in sea surface sampling. This in turn introduces errors when traditional Fourier transform based wave prediction methods are used. In this paper we show that by modelling the radar sampling instants as random variables and using the estimator of Tarczynski and Allay to process the samples, a reliable solution for DSWP can be constituted.

A novel method to double the measurement range of wavelength scanning interferometery (WSI) is described. In WSI the measured optical path difference (OPD) is affected by a sign ambiguity, that is, from an interference signal it is not possible to distinguish whether the OPD is positive or negative. The sign ambiguity can be resolved by measuring an interference signal in quadrature. A method to obtain a quadrature interference signal for WSI is described, and a theoretical analysis of the advantages is reported. Simulations of the advantages of the technique and of signal errors due to nonideal quadrature are discussed. The analysis and simulation are supported by experimental measurements to show the improved performances.