Wavelength Scanning Interferometry Research Articles

Aspheric surface measurement by absolute wavelength scanning interferometry with model-based retrace error correction.

This paper presents a non-nulling absolute interferometric method for fast and full-area measurement of aspheric surfaces without the necessity of any mechanical movement. Several single frequency laser diodes with some degree of laser tunability are used to achieve an absolute interferometric measurement. The virtual interconnection of three different wavelengths makes it possible to accurately measure the geometrical path difference between the measured aspheric surface and the reference Fizeau surface independently for each pixel of the camera sensor. It is thus possible to measure even in undersampled areas of the high fringe density interferogram. After measuring the geometrical path difference, the retrace error associated with the non-nulling mode of the interferometer is compensated for using a calibrated numerical model (numerical twin) of the interferometer. A height map representing the normal deviation of the aspheric surface from its nominal shape is obtained. The principle of absolute interferometric measurement and numerical error compensation are described in this paper. The method was experimentally verified by measuring an aspheric surface with a measurement uncertainty of λ/20, and the results were in good agreement with the results of a single-point scanning interferometer.

High depth resolution wavelength scanning interferometry with narrow scanning bandwidth via sinewaves separation

Wavelength scanning interferometry (WSI) is a promising tomographic imaging technique. However, the depth resolution is fundamentally limited by a narrow wavelength scanning bandwidth, which brings challenges to the frequency extraction for depth information. In this work, we proposed a parameter estimation (PE) paradigm via sinewaves separation, which allows high depth resolution tomographic measurement with narrow-band sources. To obtain accurate depth information, a sinewaves separation model is designed to estimate the frequency of the overlapped signals and it can achieve higher depth resolution without any prior knowledge even under limited scanning bandwidth. Moreover, the estimated frequency is used for phase retrieval and the multi-layer 3D profile measurement can be further implemented. The simulation and experimental results show that the PE method can reach the same depth resolution level as discrete Fourier transform (DFT) even reducing 60% scanning bandwidth when PSNR is higher than 35 dB.

Synthetic wavelength scanning interferometry for 3D surface profilometry with extended range of height measurement using multi-colour LED light sources

We report three-dimensional surface profilometry with extended range of height measurements using synthetic wavelength scanning interferometry without tunable filters, wavelength-tuning lasers, grating elements. We have used inexpensive multiple colour light emitting diodes (LEDs) and operate them sequentially one by one or combination of two or more colours simultaneously to visualize synthetic wavelength light source. Multiple colour LED light source was synthesized and entire visible range from violet to deep red colour was covered. A wide range of synthetic wavelengths were obtained. Five step phase shifting algorithm was used to recover phase maps with Mirau type interferometer which can be further utilized for 3D height measurements. A simple phase subtraction method was used to reconstruct the phase map at synthetic wavelength. The present system provides extended range of height measurements from sub-wavelength to tens of wavelengths. Experimental results of 3D-surface profile measurements of Si-IC chip and standard step object are presented.

Absolute wavelength scanning interferometry for measuring the thickness of optical elements.

A technique for measurement of the thickness of optical elements using absolute wavelength scanning interferometry is presented in this paper. To achieve high-grade optical components and systems, the thickness of both planar and non-planar optical components must be measured with an accuracy of a few micrometers. The proposed technique is based on the Fizeau interferometer and interconnects data from three different tunable laser diodes yielding a long effective wavelength range and thus low measurement uncertainty. The uncertainty of the central thickness measurement ranges from hundreds of nanometers to a few microns. The method allows to measure the thickness of both flat optical elements as well as lenses with curved surfaces. Moreover, the areal information provided by the interferometry and its high angle sensitivity help to quickly and precisely align the measured component and reduce misalignment errors. The results of thickness measurements have been validated and cross-tested with other techniques. In addition to the thickness, the technique provides some additional information (wedge, surface form error) in the case of flat samples and can be easily and quickly modified (mounting of a Fizeau transmission sphere) to measure other essential parameters of optical elements. Thus, this one approach can replace many single-purpose measuring devices while maintaining high accuracy.

Deep learning approach for full-field displacement estimation in depth-resolved wavelength-scanning interferometry

To minimize the effect of optical crosstalk-generated noise (crosstalk), we present a deep learning approach to precisely estimate the full-field displacements for depth-resolved wavelength-scanning interferometry (DRWSI). A deep convolution neural network, where the transformer block is introduced to effectively capture higher-order features of the wrapped phase difference map in a strong noise environment, is applied for phase unwrapping. Furthermore, a binary phase noise map is used to update the loss function in an improved training model, enhancing the network generalization. Finally, the full-field displacements are estimated from phase unwrapping maps with a high signal-to-noise ratio. The simulation and the loading experiment verified that a higher accuracy reconstruction of displacement is implemented using our approach. The contribution of this work can make the DRWSI more practical in quantifying the mechanical property inside the sample.

Surface measurement of silicon wafer using harmonic phase-iterative analysis and wavelength-scanning Fizeau interferometer

Wavelength-scanning interferometry has been widely used for surface measurements of silicon wafers with a high reflection factor owing to its non-contact and high-resolution measurement. However, the measurement results are degraded by the second-order harmonics of the signal and nonlinearity of phase modulation in wavelength scanning. In this study, a harmonic phase-iterative technique using five-frame experimental interferograms was developed for the surface measurement of a silicon wafer, while simultaneously compensating for the second-order harmonics and nonlinear phase modulation. Considering the reflection factor of the silicon wafer and the harmonics of the signal, a harmonic phase-iterative technique was derived. Furthermore, by combining the proposed iterative technique with the harmonic convergence condition and the selected pixel technique, the harmonic phase-iterative technique was insensitive to divergence errors and considerably reduced the computational time of phase extraction. The surface of the silicon wafer was measured using the harmonic phase-iterative technique and five-frame interferograms obtained using a wavelength-scanning Fizeau interferometer. The repeatability error of the silicon wafer surface measurement was 2.617 nm. Finally, it was confirmed that the harmonic phase-iterative technique had superior phase-extraction ability in terms of residual ripples and repeatability errors compared to the conventional iterative technique and phase-modulation technique.

Carré Phase Shifting Algorithm for Wavelength Scanning Interferometry

Wavelength scanning interferometry is an interferometric technique for measuring surface topography without the well-known 2π phase ambiguity limitation. The measurement accuracy and resolution of this technique depends, among other factors, on the algorithm used to evaluate its sinusoidal interference pattern. The widely used fast Fourier transform analysis experiences problems such as waviness error across the measured surface due to spectral leakage. This paper introduces a new fringe analysis method based on the Carré phase shifting algorithm combined with a least squares fitting approach. Numerical simulation was carried out to assess the performance of the Carré algorithm in comparison to fast Fourier transform analysis, and the same was validated by presenting four experimental case study examples (a surface flat, a ceramic ball bearing, a flexible thin film, and a discontinuous step height sample). The analysis results show that the proposed Carré algorithm with least squares fitting can significantly eliminate the waviness error, especially when measuring steep surfaces.

High Depth Resolution Wavelength Scanning Interferometry with Narrow Scanning Bandwidth Via Sinewaves Separation

High Depth Resolution Wavelength Scanning Interferometry with Narrow Scanning Bandwidth Via Sinewaves Separation

Multi-mode interferometric measurement system based on wavelength modulation and active vibration resistance.

Optical interferometers are widely used in the measurement of micro- and nanoscale surface topography. However, their accuracy and resolution can be seriously affected by environmental noise. We present a multi-mode interferometric measurement system based on wavelength modulation and active vibration resistance. This supports two measurement modes: wavelength-scanning interferometry, which is suitable for structured surfaces, and wavelength-tuning interferometry, which is suitable for smooth continuous surfaces. In addition, the system can measure the optical path difference of the current position in real time, which is convenient for making system adjustments and improving the measurement accuracy. The proposed system was used to measure 1.806 µm and 43.2 nm step height standards. Under different degrees of vibration, the measured heights in the two modes agreed well with the calibrated values.

Estimating the number of layers for precise wavelength scanning interferometry

Wavelength scanning interferometry (WSI) is a promising imaging technique for measuring the three-dimensional structure of the inner tissues in biomedicine. One of the important problems in WSI is how to estimate the number of layers without prior knowledge of the tissues. In this paper, a subspace decomposition-based virtual multichannel (SDVM) algorithm has been proposed for this problem, in which the interference signal of each pixel is first cast into a virtual multichannel model by the sum-to-product formula of trigonometric functions, and then, by combining the subspace decomposition method of multichannel-signal processing, the layers of the sample can be estimated in an unsupervised manner. The experimental results illustrate that SDVM is a robust algorithm with a success rate greater than 85%.

Subaperture stitching wavelength scanning interferometry for 3D surface measurement of complex-shaped optics

Subaperture stitching wavelength scanning interferometry with a high-accuracy multi-axis position stage is proposed for measuring complex surface shapes such as aspherical and freeform optics. Typical optical approaches suffer due to poor fringe visibility when it comes to complex-shaped optics. Our proposed technique allows a proper solution to this challenging issue by keeping the optical probe perpendicular to the surface slope, which provides good fringe visibility during the wavelength scan regardless of how steep the surface is. Also, the full-aperture surface map of a test sample can be obtained by stitching multiple subaperture measurement results with high precision. We tested and verified our method by measuring several representative samples and comparing the measurement results with a well-established stylus method.

Phase noise reduction in wavelength scanning interferometry using a phase synthesis approach

We proposed a method to reduce the phase noise in wavelength scanning interferometry (WSI). The method utilizes the two different mechanisms of Fourier transform and the least squares algorithm to produce a synthetic phase map. For validation, the deformation of a fiberglass reinforced resin matrix composite specimen under mechanical loading was measured using a self-built WSI system. The results demonstrate the decrease of phase noise points by more than 20% without sacrificing spatial resolution. The reduction of phase noise can provide high quality phase unwrapping and increase the accuracy of deformation measurements.

Super-resolution reconstruction of speckle phase in depth-resolved wavelength scanning interference using the total least-squares analysis.

Depth-resolved wavelength scanning interferometry (DRWSI) is a tomographic imaging tool that employs phase measurement to visualize micro-displacement inside a sample. It is well known that the depth resolution of DRWSI is restricted by a wavelength scanning range. Recently, a nonlinear least-squares analysis (NLS) algorithm was proposed to overcome the limitation of the wavelength scanning range to achieve super-resolution; however, the NLS failed to measure speckle surfaces owing to the sensibility of initial values. To the best of our knowledge, the improvement of depth resolution on measuring a speckle surface remains an open issue for DRWSI. For this study, we redesigned the signal processing algorithm for DRWSI to refine the depth resolution when considering the case of speckle phase measurement. It is mathematically shown that the DRWSI's signal is derived as a model of total least-squares analysis (TLSA). Subsequently, a super-resolution of the speckle phase map was obtained using a singular value decomposition. Further, a numerical simulation to measure the micro-displacements for speckle surfaces was performed to validate the TLSA, and the results show that it can precisely reconstruct the displacements of layers whose depth distance is 5μm. This study thus provides an opportunity to improve the DRWSI's depth resolution.

A Review of Thickness Measurements of Thick Transparent Layers Using Optical Interferometry

Thickness is a typical parameter related to length, of which measurements are conducted in various industrial fields, such as the automotive, aviation, ship-building, semiconductor, and display industries. Among various measurement techniques, optical interferometry is very attractive in terms of reliability owing to the direct realization of the metre. Moreover, the nature of this non-contact method is such that it does not damage samples. In this review, optical interferometric methods for measuring thicknesses of thick transparent layers are introduced through a discussion of basic principles and applications. With consideration of optical layouts and analysis methods of interference signals, monochromatic laser interferometry, low-coherence interferometry, and spectral interferometry are introduced and discussed in chapters 2, 3 and 4, respectively. With regard to spectral interferometry, the two different key technologies of spectrally resolved interferometry and wavelength-scanning interferometry are covered in different subsections of chapter 4.

Modified wavelength scanning interferometry for simultaneous tomography and topography of the cornea with Fourier domain optical coherence tomography.

Visual acuity is dependent on corneal shape and size. A minor variation in surface geometry can cause a deformation of corneal geometry, which affects its optical performance. In this work we demonstrate an algorithm for the simultaneous measurement of corneal tomography and topography with a traditional point-scanning Fourier domain optical coherence tomography (FD-OCT) system. A modified wavelength scanning interferometry (mWSI) algorithm enabled topographical evaluation of the surface with nanometer-scale resolution, which is superior to the micrometer-scale resolution of traditional OCT structural imaging. We validated the technique with an optically flat mirror, standard roughness gauges, and atomic force microscopy (AFM). The mirror results show nanometer-scale sensitivity (~3.5 nm), and the mWSI measurements were in good agreement (error ~5%) with the specifications of the roughness comparator and AFM, demonstrating the accuracy of the technique. Following validation, the measurements were made on pig corneas in situ at various artificially controlled intraocular pressures (IOP) and before and after cross-linking (CXL). The results show that the mean surface roughness increased by ~65% after removal of the epithelium in preparation for CXL but did not change as a function of IOP. The demonstrated method could be used for simultaneous measurement of tissue tomography with micrometer-precision and topography with nanometer-precision.

A method for inspecting near-right-angle V-groove surfaces based on dual-probe wavelength scanning interferometry

High-angled structured surfaces such as micropyramidal arrays, V-grooves and lenslet arrays are widely used in industries. However, there is currently no effective way to inspect these microstructures, resulting in very high scrap rates. This paper presents a proof-of-principle demonstration of an optical system capable of measuring V-groove structures in a single measurement acquisition. The dual-probe wavelength scanning interferometry (DPWSI) system comprises dual probes, with orthogonal measurement planes. The calibration of the DPSWI system is the key to registering the relative locations of the dual measurement planes and allowing the surface topography to be correctly reconstructed. In order to achieve this, a custom calibration artefact was manufactured comprising focused ion beam etched features on two faces of a precision cube. The procedures for the characterisation of the artefact to generate reference topography, and the subsequent calibration of the DPWSI are described in full. A measurement example from a metallised saw tooth sample featuring near-right-angles grooves having a peak-to-valley height of 32 μm and nominal pitch of 25 μm is presented and compared with a result obtained using stylus profilometry. DPWSI is shown to obtain an areal dataset in a single acquisition and is able to better resolve peak/valley points compared with the stylus, which is limited by a 2-μm tip radius. Some lateral scale error is apparent in the final DPWSI results and a discussion of this in terms of the limitations surrounding the current calibration artefact is presented.

Improvement of the fringe analysis algorithm for wavelength scanning interferometry based on filter parameter optimization.

The phase slope method which estimates height through fringe pattern frequency and the algorithm which estimates height through the fringe phase are the fringe analysis algorithms widely used in interferometry. Generally they both extract the phase information by filtering the signal in frequency domain after Fourier transform. Among the numerous papers in the literature about these algorithms, it is found that the design of the filter, which plays an important role, has never been discussed in detail. This paper focuses on the filter design in these algorithms for wavelength scanning interferometry (WSI), trying to optimize the parameters to acquire the optimal results. The spectral characteristics of the interference signal are analyzed first. The effective signal is found to be narrow-band (near single frequency), and the central frequency is calculated theoretically. Therefore, the position of the filter pass-band is determined. The width of the filter window is optimized with the simulation to balance the elimination of the noise and the ringing of the filter. Experimental validation of the approach is provided, and the results agree very well with the simulation. The experiment shows that accuracy can be improved by optimizing the filter design, especially when the signal quality, i.e., the signal noise ratio (SNR), is low. The proposed method also shows the potential of improving the immunity to the environmental noise by adapting the signal to acquire the optimal results through designing an adaptive filter once the signal SNR can be estimated accurately.

Surface topography measurement by frequency sweeping digital holography.

High-precision measurements of mechanical parts' surface topography represent an essential task in many industry sectors. Examples of such tasks are, e.g., precise alignments of opto-mechanical systems, large object deformation measurements, evaluation of object shape, and many others. Today, the standard method used for such measurements is based on use of coordinate measuring machines (CMMs). Unfortunately, CMMs have severe shortcomings: low measurement point density, long measurement time, risk of surface damage, etc. Indeed, the measurement time rapidly increases with the object complexity and with the density of measurement points. In this paper, we have developed a method for surface topography measurements called "frequency sweeping digital holography" (FSDH). Our developed FSDH method is based on the principles of wavelength scanning interferometry. It allows surface topography measurements of objects with a diameter of several hundred of mms and a high axial accuracy reaching 10μm. The greatest advantage of the presented FSDH is the fact that the surface topology data are captured in a motionless manner by means of a relatively simple setup. This makes the FSDH method a suitable technique for topography measurements of objects with complex geometries made of common materials (such as metals, plastics, etc.), as well as for the characterization of complex composite structures such as acoustic metamaterials, active acoustic metasurfaces, etc. Measurement method principles, setup details, lateral resolution, and axial accuracy are discussed.

Surface topography acquisition method for double-sided near-right-angle structured surfaces based on dual-probe wavelength scanning interferometry.

This paper proposes an approach to measure double-sided near-right-angle structured surfaces based on dual-probe wavelength scanning interferometry (DPWSI). The principle and mathematical model is discussed and the measurement system is calibrated with a combination of standard step-height samples for both probes vertical calibrations and a specially designed calibration artefact for building up the space coordinate relationship of the dual-probe measurement system. The topography of the specially designed artefact is acquired by combining the measurement results with white light scanning interferometer (WLSI) and scanning electron microscope (SEM) for reference. The relative location of the two probes is then determined with 3D registration algorithm. Experimental validation of the approach is provided and the results show that the method is able to measure double-sided near-right-angle structured surfaces with nanometer vertical resolution and micrometer lateral resolution.

Quadrature wavelength scanning interferometry.

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.