Picometer-scale optical vortex interferometer using azimuthal complex spectrum analysis.

An interferogram demodulation method based on azimuthal complex spectrum analysis is proposed for achieving picometer-scale accuracy with an optical vortex interferometer (OVI). The OVI uses conjugated p-radial-order Laguerre-Gaussian beams to produce a high-order petal-like interferogram. A camera with a multi-ring pattern written on its sensor is used to convert the interferogram into multiple azimuthal intensity profiles. A phase shift subjected to either uniform surface displacement or axisymmetric non-uniform surface deformation can be retrieved from the complex spectra of the azimuthal intensity profiles at the main frequency components. The experiment verified that the measurement error is 84 pm for a displacement of 10 nm and 0.359 nm for a deformation magnitude of 100 nm. The effect of surface misalignment on the measurement result is also discussed. The proposed method provides an effective and highly accurate method of interferogram demodulation for the OVI and extends the applicability of OVI from uniform surface displacement measurement to axisymmetric non-uniform surface deformation measurement.

Dynamic non-uniform phase shift measurement via Doppler frequency shift in vortex interferometer.

A vortex beam interferometer based on Doppler frequency shift is proposed to retrieve the dynamic non-uniform phase shift from the petal-like fringes produced by the coaxial superposition of high-order conjugated Laguerre-Gaussian modes. Unlike the uniform phase shift measurement in which the petal-like fringes rotate as a whole, the fringes due to the dynamic non-uniform phase shift rotate at different angles at different radii, resulting in highly twisted and stretched petals; this hinders rotation angle identification and phase retrieval via image morphological operation. To address the problem, a rotating chopper combined with a collecting lens and a point photodetector are placed at the exit of the vortex interferometer to introduce a carrier frequency in the absence of the phase shift. Once the phase starts to shift non-uniformly, the petals at different radii generate different Doppler frequency shifts, owing to their different rotation velocities. Thus, identification of spectral peaks near the carrier frequency immediately indicates the rotation velocities of the petals and the phase shifts at those radii. The results verified a relative error of phase shift measurement to be within 2.2% at the surface deformation velocities of 1, 0.5, and 0.2 µm/s. The method manifests itself to have potential in exploiting mechanical and thermophysical dynamics from the nanometer to micrometer scale.

Sensitivity enhancement in photothermal interferometry by balanced detection of the complex response to moving excitation.

The sensitivity of photothermal detection relies on both the magnitude of the response of a sample to excitation and the way the response is sensed. We propose a highly sensitive photothermal interferometry by addressing the above two issues. One is the use of moving excitation to enable a different manner in sample heating and cooling, which results in a strong thermoelastic response of the sample. The other is the use of a balanced Mach-Zehnder interferometer with a defocused probe beam to sense the complex response induced by the phase delays taking place at the sample surface and in the surrounding air. The method was verified experimentally with a Nd-doped glass to have 68-fold sensitivity enhancement over the classical photothermal common-path interferometry.

Time-resolved laser scanning photothermal microscopy for characterization of thermal properties of semi-insulating GaAs.

The strong coupling effect of thermal and plasma waves disturbs the accurate characterization of thermal properties of semiconductors under super bandgap energy photon excitation. We propose a time-resolved laser scanning photothermal microscopy to decouple the thermo-electronic effect for accurate determination of the thermal diffusivity of a semi-insulating GaAs sample. The distinct advantage of the decoupling principle relies on that the scanning excitation of a laser beam on the sample surface introduces different transient and steady-state characteristics into the thermal and electronic parts of the photothermal response, where the transients between the thermal and electronic parts have a large time-scale separation, and the steady states show an enhanced thermal effect over the electronic effect. Therefore, the plasma wave is simply responsible for a negligible constant background in the thermo-electronic coupling. The theoretical and experimental results confirmed that the time-resolved photothermal signal is insensitive to the electronic transport parameters varying even by several orders of magnitude and can be used to determine the thermal diffusivity from its best fit. Moreover, the scanning excitation nature of this method allows for high-efficiency photothermal imaging of the sample to identify the thermal defects.

Dual-wavelength Mach-Zehnder interferometry-assisted photothermal spectroscopy for characterization of surface contaminants.

Photothermal spectroscopy (PTS) working in the mid-infrared region is an effective technique for in-situ characterization of the chemical composition of surface contaminants. The sensitivity relies on the way that the laser-induced response of the sample is detected. We present a highly-sensitive PTS assisted with a dual-wavelength Mach-Zehnder interferometer (MZI), MZI-PST in short. The MZI aims to sense all the phase delays taking place at the sample and air when the heat produced by resonance absorption of the contaminant is transferred into its surroundings and further to amplify the total phase delay to a large intensity difference of a probe beam. To guarantee a stable quadrature phase bias of the MZI working in the balanced detection mode, we employ two separate wavelengths, one for sensing and the other for phase bias feedback, to lock the working point to the quadrature point in real time. The MZI is expected to have a 7.8-fold sensitivity enhancement compared with the conventional phase-sensitive PTS in theory. The results of the proof-of-concept experiment on the olive oil contaminated on a wafer surface verify the spectral fidelity and the sensitivity enhancement as well as the capability of photothermal spectral imaging of the MZI-PST.

Dual-loop Sagnac interferometer with a geometric phase shifter for quadrature phase bias locking.

A stable quadrature phase bias is highly demanded in the balanced Sagnac interferometer to achieve sufficient detection sensitivity and unambiguity. We demonstrate a straightforward and effective quadrature phase locking technique in a free-space balanced Sagnac interferometer by using a dual-loop, one for sensing and the other for bias feedback. The sensing loop and the feedback loop operate on linearly polarized beams at two separate wavelengths and overlap for most of the area. A geometric phase shifter showing wavelength independence placed on the common path of the two loops introduces two almost identical nonreciprocal phase shifts between the counterpropagating beams for the two separate wavelengths, so that real-time compensation of the phase bias for the sensing loop can be implemented by the error signal of the feedback loop. Proof-of-concept experimental results demonstrated successful locking of the quadrature phase bias in the presence of signal fading due to the birefringence disturbance. The correction of the residual chromatism of the interferometer is discussed before the conclusion is made.

Heat coupling effect on photothermal detection with a moving Gaussian excitation beam.

A strong photothermal response is beneficial to the measurement of optical and thermal properties of optical materials using the laser-induced thermal mirror method. A highly sensitive asymmetrical thermal mirror method was recently proposed by employing a moving Gaussian excitation beam [Appl. Phys. Lett.114, 131902 (2019)APPLAB0003-695110.1063/1.5080163]. However, the heat transfer across the interface between the thermodynamic system and the surroundings is ignored, which will lead to an error in the absolute measurement of the material properties. To address the problem, we present a theoretical and experimental study of heat transfer within the heated sample and out to the air coupling fluid in the photothermal detection with a Gaussian excitation beam moving at a constant velocity. We analyze the dynamic temperature fields inside the sample and in the surrounding air, and the phase shifts induced by the thermoelastic displacement of the sample (thermal mirror) and the refractive index gradient of air (thermal lens), as well as the diffracted intensity profiles of the probe beam in the detection plane. The experiments are implemented under normal pressure and vacuum, respectively, for a fused silica glass-air heat coupling system to verify the theoretical model. The experimental results show that the thermal lens, due to the heat coupling effect, introduces a signal deviation approximately 4.2% of the total photothermal signal, which is close to the theoretical result of 5%.

Characterization of weakly absorbing thin films by multiple linear regression analysis of absolute unwrapped phase in angle-resolved spectral reflectometry.

The simultaneous determination of t, n(λ), and κ(λ) of thin films can be a tough task for the high correlation of fit parameters. The strong assumptions about the type of dispersion relation are commonly used as a consequence to alleviate correlation concerns by reducing the free parameters before the nonlinear regression analysis. Here we present an angle-resolved spectral reflectometry for the simultaneous determination of weakly absorbing thin film parameters, where a reflectance interferogram is recorded in both angular and spectral domains in a single-shot measurement for the point of the sample being illuminated. The variations of the phase recovered from the interferogram as functions of t, n, and κ reveals that the unwrapped phase is monotonically related to t, n, and κ, thereby allowing the problem of correlation to be alleviated by multiple linear regression. After removing the 2π ambiguity of the unwrapped phase, the merit function based on the absolute unwrapped phase performs a 3D data cube with variables of t, n and κ at each wavelength. The unique solution of t, n, and κ can then be directly determined from the extremum of the 3D data cube at each wavelength with no need of dispersion relation. A sample of GaN thin film grown on a polished sapphire substrate is tested. The experimental data of t and [n(λ), κ(λ)] are confirmed by the scanning electron microscopy and the comparison with the results of other related works, respectively. The consistency of the results shows the proposed method provides a useful tool for the determination of the thickness and optical constants of weakly absorbing thin films.

Line-scanning laser scattering system for fast defect inspection of a large aperture surface.

Inspection of defects with micrometer level on large aperture surfaces with hundreds of millimeters is one of the challenges in surface quality evaluation. Various microscopic imaging methods have been applied to inspecting the surface defects, while they are time-consuming for the small field of view and the sub-aperture stitching. To tackle this problem, a high-speed line scanning system based on the dark-field laser scattering method is proposed. The laser beam is scanned by the rotating polygon mirror to a laser line for high throughput and then the telecentric F-theta lens converges each incoming laser beam to a focused spot that creates a high intensity to enhance the signal-to-noise ratio. The scattered light from surface defect is collected by the designed integrating sphere for low background noise and the scattering signal is detected for each focused spot at a proper acquisition rate by a photomultiplier (PMT) detector with extremely short response time. In the meanwhile, the tested surface is moving perpendicular to the laser line to realize high-speed large area inspection. The defect inspection system is confirmed experimentally with laser line length of 60 mm, minimum detectable size less than 0.5 µm, and figure of merit of 9.6 cm2 s-1 µm-1. The work put forward an effective method for automatic discovery of surface defects such as scratches, digs, and contaminants on large aperture surfaces.

Individualized leukemia cell-population profiles in common B-cell acute lymphoblastic leukemia patients.

Immunophenotype is critical for diagnosing common B-cell acute lymphoblastic leukemia (common ALL) and detecting minimal residual disease. We developed a protocol to explore the immunophenotypic profiles of common ALL based on the expression levels of the antigens associated with B lymphoid development, including IL-7Rα (CD127), cytoplasmic CD79a (cCD79a), CD19, VpreB (CD179a), and sIgM, which are successive and essential for progression of B cells along their developmental pathway. Analysis of the immunophenotypes of 48 common ALL cases showed that the immunophenotypic patterns were highly heterogeneous, with the leukemic cell population differing from case to case. Through the comprehensive analysis of immunophenotypic patterns, the profiles of patient-specific composite leukemia cell populations could provide detailed information helpful for the diagnosis, therapeutic monitoring, and individualized therapies for common ALL.

Photothermal vortex interferometer with azimuthal complex spectra analysis for the measurement of laser-induced nanoscale thermal lens dynamics.

A photothermal vortex interferometer (PTVI) is proposed to fill the gap of full-field measurement of the laser-induced nanoscale thermal lens dynamics of optical elements. The PTVI produces a multi-ring petal-like interferogram by the coaxial coherent superposition of the high-order conjugated Laguerre-Gaussian beams. The non-uniform optical path change (OPC) profile resulting from the thermal lens causes the petals of the interferogram at the different radii to shift by the different azimuths. To demodulate such an interferogram, an azimuthal complex spectra analysis is presented by using a camera with a pixelated multi-ring pattern written on its sensor to extract multiple azimuthal intensity profiles synchronously from the interferogram. Therefore, the OPC profile can be determined dynamically from the complex spectra of the azimuthal intensity profiles at the main frequency components. An analytical thermophysical model of the thermal lens is given, and the basic principle of the azimuthal complex spectra analysis is revealed. A proof-of-concept experiment is demonstrated using a N-BK7 glass sample heated by a pump laser. The results verified that the PTVI achieves the measurement accuracy of 47 pm with a standard deviation of 358 pm (3σ) and can be used for full-field measurement of the nanoscale OPC profile caused by the thermal lens dynamics. Due to the picometer-scale accuracy of the PTVI, the absorption coefficient and thermal diffusivity of the glass sample were determined to be A0 = 0.126 m-1 and D = 5.63 × 10-7 m2 s-1, respectively, which agree with the nominal ones of A0 = 0.129 m-1 and D = 5.17 × 10-7 m2 s-1. Although the PTVI is only suitable for measuring the rotationally symmetric OPC, it shows less computation burden and hardware complexity, and it is proved to be a highly sensitive and effective tool in studying optical, thermo-physical, and mechanical properties of optical elements.

Carrier optical vortex interferometer using segmentation demodulation method for dynamic measurement of axisymmetric surface deformation.

The dynamic measurement of surface deformation with an axisymmetric profile at nanometer- to micrometer-scale is of great interest in understanding micromechanical and thermophysical dynamics. We propose a carrier optical vortex interferometer (COVI) to measure such surface deformation dynamically by segmentation demodulation of the petal-like interferogram that is produced by the coaxial superposition of conjugated p-radial order Laguerre-Gaussian beams. Specifically, a rotating chopper placed at the exit of the interferometer introduces a carrier frequency in the absence of surface deformation. A camera placed behind the chopper uses a multi-ring segmentation detection scheme to produce a Doppler shift relative to the carrier frequency at the radius of each ring in the presence of axisymmetric surface deformation. Locating the Doppler shifts gives the surface deformation velocities at those radii. Thus, the dynamic surface deformation profile can be obtained by integrating the velocities over time. We reveal the basic principles of the carrier frequency and the Doppler shifts in the COVI theoretically. As a proof-of-concept, an external force-induced axisymmetric mechanical surface deformation is measured dynamically to demonstrate the validity of the COVI. The results show that the measurement error of the surface deformation velocity is within (-2.1, 1.1 nm/s) for the velocity ranging from 20 to 86 nm/s. The lower limit of the measurable velocity can reach 20 nm/s. The measurement error of the surface deformation profile is less than 2.5 nm for the amplitude of the surface deformation of 500 nm.

Sensitivity analysis of thin-film thickness measurement by vertical scanning white-light interferometry.

The spectral nonlinear phase method and the Fourier amplitude method have been applied to measure the thin-film thickness profile in vertical scanning white-light interferometry (VSWLI). However, both the methods have their disadvantages, and accordingly their applications are limited. In the paper we have investigated the dependence of the sensitivities of both the methods on the thin-film thickness and refractive index, the objective numerical aperture, and the incident light spectral range of VSWLI. The relation of the Fresnel reflection coefficients on the wavelength effect is also discussed. Some important research results reveal that the combination of both Fourier amplitude and nonlinear phase methods may provide a new approach to improve the VSWLI measurement sensitivity for thin-film thickness profile.

Development of a confocal line-scan laser scattering probe for dark-field surface defects detection of transmissive optics.

Dark-field detection has long been used to identify micron/submicron-sized surface defects benefiting from the broadening effect of the actual defect size caused by light scattering. However, the back-side scattering of a transmissive optical slab is inevitably confused with the front-side scattering phenomenon, resulting in deterioration of the signal-to-noise ratio (SNR) of the scattering signal and false alarms for real defect detection. To this end, a confocal line-scan laser scattering probe equipped with optical sectioning ability is proposed to separate the back-side scattering from the front-side scattering. The optical sectioning ability is realized through a confocal light scattering collector, which overcomes the restriction imposed on the numerical aperture (NA) and the field of view (FOV), reaching an FOV length of 90 mm and NA of 0.69. The line-scan principle of the probe protects itself from crosstalk because it produces only a laser spot on the tested surface in an instant. Experimental results verified that the probe has a line-scan length of 90 mm with a uniformity better than 98%, an rms electronic noise of 3.4 mV, and an rms background noise of 6.4 mV with laser on. The probe can reject the false back-side scattering light for a 2 mm thick fused silica slab at 17.1 dB SNR and operate at a high imaging efficiency of 720 mm2/s with a minimum detectability limit of 1.4 µm at 12 dB SNR. This work put forward an effective method with great application value for submicron-sized defect detection in transmissive optics.

Achromatic phase shifter with eight times magnification of rotation angle in low coherence interference microscopy.

An achromatic phase shifter with a rotating half-wave plate (HWP) used at the input and output of the low coherence interference microscopy is presented. This novel achromatic phase-shifter configuration is first investigated, and then its performances are compared with those of traditional phase shifters theoretically by means of Jones matrices. It is evident that the achromatism and the variation of the amplitude ratio of the proposed achromatic phase-shifter configuration is much better than other traditional phase-shifter configurations, and it can provide a phase shift of eight times the rotation angle of the HWP, which is the largest magnification achieved by far. A low coherence interference microscopy system based on the proposed achromatic phase-shifter configuration is also established to confirm the eight times relation between phase-shift and rotation angle of the HWP experimentally. At last, the three-dimensional profile and the groove depth of a step height calibration standard are obtained by using the traditional four-step algorithm to illustrate the capability and the accuracy of the low coherence interference microscopy system based on the proposed achromatic phase-shifter configuration.

Automated determination of best focus and minimization of optical path difference in Linnik white light interferometry.

It is difficult to search for interference fringes in Linnik white light interferometry with an extremely short coherence length because of the optical path mismatch of two interference arms and the defocus of the reference mirror and the test surface. We present an automated method to tackle this problem in this paper. The determination of best foci of the reference mirror and the test surface is implemented by the astigmatic method based on a modified commercial DVD pickup head embedded in the interference system. The astigmatic method is improved by setting a threshold value in the sum signal to truncate the normalized focus error signal (NFES). The truncated NFES has a monotonic relationship with the displacement of the test surface, which removes the position ambiguity of the test surface during the autofocus process. The developed autofocus system is confirmed experimentally with a dynamic range of 190 µm, average sensitivity of 70 mV/µm, average standard deviation of 0.041 µm, displayed resolution of 4.4 nm, and accuracy of 55 nm. The minimization of the optical path difference of two interference arms is carried out by finding the maximum fringe contrast of the image captured by a CCD camera with the root mean square fringe contrast (RMSFC) function. The RMSFC function, combined with a 4×4 pixel binning of the CCD camera, is recommended to improve the computational efficiency. Experimental tests show that the automated method can be effectively utilized to search for interference fringes in Linnik white light interferometry.

Automatic defect inspection of thin film transistor-liquid crystal display panels using robust one-dimensional Fourier reconstruction with non-uniform illumination correction.

Automatic inspection of micro-defects of thin film transistor-liquid crystal display (TFT-LCD) panels is a critical task in LCD manufacturing. To meet the practical demand of online inspection of a one-dimensional (1D) line image captured by the line scan visual system, we propose a robust 1D Fourier reconstruction method with the capability of automatic determination of the period Δx of the periodic pattern of a spatial domain line image and the neighboring length r of the frequency peaks of the corresponding frequency domain line image. Moreover, to alleviate the difficulty in the discrimination between the defects and the non-uniform illumination background, we present an effective way to correct the non-uniform background using robust locally weighted smoothing combined with polynomial curve fitting. As a proof-of-concept, we built a line scan visual system and tested the captured line images. The results reveal that the proposed method is able to correct the non-uniform illumination background in a proper way that does not cause false alarms in defect inspection but also preserves complete information about the defects in terms of the brightness and darkness as well as the shape, indicating its distinct advantage in defect inspection of TFT-LCD panels.

Noise characterization and compensation for a charge-coupled-device-based pyrometer.

The pyrometer based on the charge coupled device (CCD) is a cost-effective and widely used system for temperature measurement in various industrial fields. However, due to the inter-element sensitivity deviations of the CCD-array detector and the influence of various types of noise, the digital signal output of the CCD sensor itself is not completely equal to the ideal value as expected. In this work, based on a classical calibration method, the inter-element sensitivity deviations, dark current, shot noise, and readout-quantization noise for a CCD-based pyrometer are characterized, and the influence of these noises on the temperature measurement accuracy is evaluated quantitatively. Furthermore, the non-uniformity correction coefficient for each pixel is obtained by a simple segment correction method to reduce the inter-element sensitivity deviations, and meanwhile, the Kalman filter is introduced to remove the temperature fluctuations caused by these noises. Experimental results show that mean value of the spatial standard deviation of temperature measurement results in the total measurement range (800-1200 °C) is only 2.2 °C after non-uniformity correction, and the temperature fluctuations can be reduced from 26.6 to 1.98 °C based on the Kalman filter.

Quality monitoring method based on enhanced canonical component analysis.

In continuous processes, the quality variables generally can be interpreted by the process variables due to intercorrelation. However, in particular condition, the past quality trends may be responsible for interpretation due to the auto-correlation. The existing methods only reveal one of the correlations. Considering the effects of two types of correlations for quality monitoring, this study develops enhanced canonical component analysis (ECCoA) method based on Canonical Correlation Analysis (CCA). For revealing the intercorrelation, CCA is performed to extract the quality related features from the process variables. However, the components of CCA ignore the variance formation in the data. To retain both cross-data (process variables and quality variables) correlation information and the variance information within process variables, principle projective-CCA (PP-CCA) method is proposed, generating the primary feature subspace to capture the variation of quality variables. Moreover, as for the auto-correlation, on the residual obtained in PP-CCA method, a residual-CCA (R-CCA) method is proposed for modelling and generating the complementary feature subspace, reflecting the trends of quality variables. Sequentially, statistical indexes and decision-making logic are established for online monitoring. A numerical case and the Tennessee Eastman process are tested for validation. The achieved results indicate the feasibility and efficiency of the proposed enhanced canonical component analysis method.

Calibration and measurement performance analysis for a spectral band charge-coupled-device-based pyrometer.

Commercial charge-coupled device (CCD) cameras are used widely in industrial applications. This paper uses a commercial CCD camera to develop a spectral band CCD-based pyrometer. To improve the calibration accuracy, a thermometry model based on the extended effective wavelength is introduced to describe the pyrometer. The Tikhonov regularization method is employed to acquire the stabilized solutions for the model parameters considering their sensitivities to the perturbations in the calibration data. Therefore, the relationships between the temperature measurement performances and the system parameters, namely, the electron gain and F-number, are analyzed in terms of the temperature measurement range and sensitivity. Meanwhile, the error and uniformity of the temperature measurements are also investigated using a blackbody furnace. The experimental results show that the temperature measurement range for the designed pyrometer is 800-1203 °C, in which the sensitivity is 0.4906-35.64 °C-1 and the average relative error and non-uniformity of the temperature measurements are 2.5‰ and 1.36%, respectively.