Inhomogeneous Optical Properties Research Articles

Resolution-enhanced multi-core fiber imaging learned on a digital twin for cancer diagnosis.

Deep learning enables label-free all-optical biopsies and automated tissue classification. Endoscopic systems provide intraoperative diagnostics to deep tissue and speed up treatment without harmful tissue removal. However, conventional multi-core fiber (MCF) endoscopes suffer from low resolution and artifacts, which hinder tumor diagnostics. We introduce a method to enable unpixelated, high-resolution tumor imaging through a given MCF with a diameter of around 0.65mm and arbitrary core arrangement and inhomogeneous transmissivity. Image reconstruction is based on deep learning and the digital twin concept of the single-reference-based simulation with inhomogeneous optical properties of MCF and transfer learning on a small experimental dataset of biological tissue. The reference provided physical information about the MCF during the training processes. For the simulated data, hallucination caused by the MCF inhomogeneity was eliminated, and the averaged peak signal-to-noise ratio and structural similarity were increased from 11.2dB and 0.20 to 23.4dB and 0.74, respectively. By transfer learning, the metrics of independent test images experimentally acquired on glioblastoma tissue ex vivo can reach up to 31.6dB and 0.97 with 14fps computing speed. With the proposed approach, a single reference image was required in the pre-training stage and laborious acquisition of training data was bypassed. Validation on glioblastoma cryosections with transfer learning on only 50 image pairs showed the capability for high-resolution deep tissue retrieval and high clinical feasibility.

Development of a hybrid autoencoder model for automated edible bird’s nest impurities inspection

There is a dire need for vision automation for edible bird’s nest (EBN) hygiene inspection. To date, an effective impurities detection method for EBNs has yet to be realized owing to the inhomogeneous optical properties, various types and sizes of impurities, and limited sample size. The impurities inspection was formulated as an anomaly detection task, and a hybrid autoencoder model that contains an autoencoder and a single layer convolutional network is proposed. The model was trained to reconstruct only nonimpurity regions of the EBN for impurities segmentation and detection as anomalies. The results showed that with only 50 EBN sample images, the hybrid model achieved a recall of 0.9282, a precision of 0.7718, and a 5.63% undetected rate for impurities. Furthermore, a misclassification rate of 21.53% was recorded due to artifacts mostly with sizes <0.20 mm that were detected as false positive. Nonetheless, the applicability of the proposed autoencoder model was confirmed, with >92 % of successful impurities detected. Therefore, the hybrid autoencoder model is further explored for improvement and practical application.

A broadband infrared radiative transfer scheme including the effect related to vertically inhomogeneous microphysical properties inside water clouds

Clouds play an important role in the Earth-atmosphere system. Due to the condensation of water vapour inside clouds, liquid water content and droplet radius vertically increase. It leads to the vertical inhomogeneity of cloud optical properties. However, current climate models divide clouds into a few or several dozen vertically homogeneous layers and ignore this important character. In order to handle the vertical inhomogeneity of cloud optical properties, a broadband infrared radiative transfer (IRT) scheme is proposed in this study. In the scheme, we use exponential expressions to describe vertically inhomogeneous optical properties and handle IRT by combining the perturbation method, the two-stream discrete ordinate method and the adding method. The accuracy of the proposed IRT scheme is evaluated in an idealized single layer case. We also apply the proposed scheme into the radiative transfer model which is used in CanAM4 to simulate IRT in two cloudy atmospheric profiles. By comparing to the benchmark scheme, we find that ignoring the effect related to vertically inhomogeneous microphysical properties of clouds has little impact on the downward flux calculation. However, it causes a bias of 2.53 W/m2 at cloud top and a bias of 1.51 W/m2 at the top of the atmosphere in the upward flux calculation. The proposed IRT scheme can reduce these biases to -0.23 W/m2 and -0.004 W/m2. Similar results are also shown in the heating rate calculation. From a perspective of computational time, the proposed IRT scheme is four times more expensive as compared to the conventional two-stream discrete ordinate scheme when considering scheme itself. When we apply both schemes to the radiative transfer model, the proposed IRT scheme takes approximately double time of the conventional scheme. All results show that the proposed IRT scheme is accurate and provide a solution to take cloud’s vertical inhomogeneity into account in the climate simulation.

Simulation of stray radiation from optical window with temperature-dependent spectral properties.

Stray radiation analysis coupled with a temperature field is performed for a semitransparent window, focusing on the temperature-dependent optical properties. The transient temperature response of the optical window-based encapsulation structure is first investigated under an external transient high-heat flux loading. The spectral selectivity of the window to thermal radiation is involved. Subsequently, several typical cases for stray radiation are conducted, considering the inhomogeneous optical properties caused by the temperature heterogeneity. It is found that the stray radiation distribution is more chaotic compared to the results with optical properties independent of temperature. In addition, the stray radiation power has a large deviation (150%) if one neglects the temperature dependence. Meanwhile, the difference in wave band power decreases with the wavelength rising. Additionally, the stray radiation power generated by the window is far less in the visible wave band than that in the near-infrared wave band. The results reveal that the temperature dependence in optical properties of a semitransparent window should be seriously considered when calculating the stray radiation, especially in high-precision detection devices.

Impurities Detection in Intensity Inhomogeneous Edible Bird’s Nest (EBN) Using a U-Net Deep Learning Model

As an important export, cleanliness control on edible bird’s nest (EBN) is paramount. Automatic impurities detection is in urgent need to replace manual practices. However, effective impurities detection algorithm is yet to be developed due to the unresolved inhomogeneous optical properties of EBN. The objective of this work is to develop a novel U-net based algorithm for accurate impurities detection. The algorithm leveraged the convolution mechanisms of U-net for precise and localized features extraction. Output probability tensors were then generated from the deconvolution layers for impurities detection and positioning. The U-net based algorithm outperformed previous image processing-based methods with a higher impurities detection rate of 96.69% and a lower misclassification rate of 10.08%. The applicability of the algorithm was further confirmed with a reasonably high dice coefficient of more than 0.8. In conclusion, the developed U-net based algorithm successfully mitigated intensity inhomogeneity in EBN and improved the impurities detection rate.

Noncollinear degenerate phase modulation in samples with inhomogeneous optical nonlinear properties [Invited

Digital inline pump-probe holography can be applied to estimate parameters of samples' optical nonlinear properties. Here we propose a mathematical model to describe noncollinear degenerate phase modulation in samples with inhomogeneities of nonlinear refractive index over all three dimensions, namely, two-layered samples and samples with local impurities. The impact of sample parameters in the considered configurations is analyzed. We show that analysis of inline digital holograms obtained by time-resolved inline digital holography can be successfully used for rapid detection and characterization of various types of nonlinear refractive index inhomogeneities.

Multi-layer solar radiative transfer considering the vertical variation of inherent microphysical properties of clouds.

A multi-layer solar radiative transfer (RT) scheme is proposed to deal with the vertical variation of inherent microphysical properties of clouds in this study. The exponential expressions are used to represent the vertical variation of optical properties caused by inhomogeneous microphysical properties. A perturbation method, coupled with the Eddington approximation, is used to solve the RT equation. In order to have a more accurate estimation of reflectance/transmittance for every single layer, the optical properties are adjusted following the theory of delta scaling in the proposed scheme. In addition, a modified adding method based on Chandrasekhar's invariance principle is introduced to solve the multi-layer RT. The accuracy of the proposed scheme is investigated by comparing the reflectance/absorptance to the benchmark for two double-layer cases, and each layer with vertically inhomogeneous optical properties. Results show that the bias related to vertically inhomogeneous optical properties reaches 13.8 % for reflectance and 29.2 % for absorptance while the bias of the proposed scheme is only -0.8 % for reflectance and 1.7 % for absorptance. We also apply the proposed scheme as well as the conventional Eddington approximation to the CanadianClimate Center RT model which handle RT in CanAM4. The calculations are performed in the following four solar wavenumber bands 2500-4200, 4200-8400, 8400-14500 and 14500-50000 cm-1. The result also shows that the proposed scheme also improved the accuracy in both flux and heating rate calculation by taking the vertical variation of inherent microphysical properties into account. The proposed scheme is approximately three times more computationally expensive compared to the Eddington approximation when we only consider the algorithm itself. The computational time is doubled compared to the Eddington approximation when we take the complete radiative transfer process into account. Due to its accuracy and efficiency, the proposed scheme is suitable to improve the RT calculations regarding the vertical variation of inherent microphysical properties in climate models.

Assessment of tissues’ inhomogeneous optical properties based on a portable microscope under partially coherent illumination

Abstract Assessing tissues’ inhomogeneous optical properties is helpful for diagnosis, but high-cost measurement and experimental setups limit its development, data collecting and applications. In this paper, a portable microscope is proposed to assess the inhomogeneous optical properties of the sample. In the single LED illumination mode, accurate quantitative phase (QP) map can be recovered from 5 intensity images captured at different axial positions. Then based on the scattering-phase theorem and statistical dispersion relation (SDR), the inhomogeneous optical properties of the sample can be quantitatively assessed from these QP maps. In the incoherent dark field illumination mode, strong scattering structures can be observed easily without post processing. An improved resolution comparing with bright field imaging and qualitative optical properties would be obtained. In contrast to DHM and SLIM, our setup is cost-effective, use-flexible, and with a small amount of data acquisition, thus having the potential to promote the development of assessing tissues’ inhomogeneous optical properties, especially in resource-limited areas.

A New Radiative Transfer Method for Solar Radiation in a Vertically Internally Inhomogeneous Medium

The problem of solar spectral radiation is considered in a layer-based model, with scattering and absorption parallel to the plane for each medium (cloud, ocean, or aerosol layer) and optical properties assumed to be vertically inhomogeneous. A new radiative transfer (RT) method is proposed to deal with the variation of vertically inhomogeneous optical properties in the layers of a model for solar spectral radiation. This method uses the standard perturbation method to include the vertically inhomogeneous RT effects of cloud and snow. The accuracy of the new inhomogeneous RT solution is investigated systematically for both an idealized medium and realistic media of cloud and snow. For the idealized medium, the relative errors in reflection and absorption calculated by applying the homogeneous solution increase with optical depth and can exceed 20%. However, the relative errors when applying the inhomogeneous RT solution are limited to 4% in most cases. Observations show that stratocumulus clouds are vertically inhomogeneous. In the spectral band of 0.25–0.69 μm, the relative error in absorption with the inhomogeneous solution is 1.4% at most, but that with the homogeneous solution can be up to 7.4%. The effective radius of snow varies vertically. In the spectral band of 0.25–0.69 μm, the relative error in absorption with the homogeneous solution can be as much as 72% but is reduced to less than 40% by using the inhomogeneous solution. At the spectral wavelength of 0.94 μm, the results for reflection and absorption with the inhomogeneous solution are also more accurate than those with the homogeneous solution.

Implementation and evaluation of a generalized radiative transfer scheme within canopy in the soil‐vegetation‐atmosphere transfer (SVAT) model

AbstractThe process of radiative transfer over vegetated areas has a profound impact on energy, water, and carbon balances over the terrestrial surface. In this paper, a generalized radiative transfer scheme (GRTS) within canopy is implemented in the Simplified Simple Biosphere land surface model (SSiB). The main concept and structure of GRTS and its coupling methodology to a land model are presented. Different from the two‐stream method, the GRTS takes into account the effects of complex canopy morphology and inhomogeneous optical properties of leaves on radiative transfer process within the canopy. In the offline SSiB/GRTS simulation for the period of 2001–2012, the nonuniform leaf angle distribution within canopy layers is considered in SSiB/GRTS in the areas of evergreen broadleaf trees. Compared with the SSiB/two stream method, SSiB/GRTS produces lower canopy reflectance and higher transmittance, which leads to more realistic albedo simulation. The canopy‐absorbed radiation flux in SSiB/GRTS simulation is lower than that in SSiB/two stream method simulation throughout the year in the areas of evergreen broadleaf trees. The largest difference of −18.4 W/m2 occurs in the Amazon region in the autumn. The ground‐absorbed radiation flux increases in the SSiB/GRTS simulation, especially in the spring and autumn. The largest difference in the ground‐absorbed radiation flux between SSiB/GRTS simulation and SSiB/two stream method simulation is 25.45 W/m2. In the boreal winter season, compared with the two‐stream method in the SSiB, the GRTS gives higher surface albedo in the areas with high snow cover fraction over leaf.

Diffuse optical tomography using multichannel robotic platform for interstitial PDT.

In the operating room, time is extremely precious, and the speed of one's data acquisition system often determines whether the data will be taken or not. Our multichannel robotic platform addresses this issue by optimizing source and detector scanning procedures. Up to 16 fibers can be moved independently with resolution of 0.05 mm and speed of 50 mm/s using motors with position feedback. The initial fiber alignment employs a light beam/optical detector system for identical positioning of all motors. Peak and edge detection algorithms, for point and linear sources, are used with multiple fibers simultaneously for fast realignment of sources and detectors. The robotic platform is used to perform Diffuse Optical Tomography (DOT) measurements in solid prostate phantoms with both homogenous and inhomogeneous Optical Properties (OP). Correct positioning is critical for the accurate recovery of the OP. The light fluence rate distribution is determined by scanning multiple detector fibers simultaneously along lit linear sources placed throughout the phantom volume inside catheter needles. The scanning time for the entire DOT is about 10 seconds after the initial alignment. The OP distribution reconstruction is based on the steady-state light diffusion equation. The inverse interstitial DOT problem is solved using NIRFAST. The optical properties are recovered by iterative minimization of the difference between measured and calculated light fluence rates. Recovered OP agree with the actual values within 10%. The OP corrections are used to significantly improve light fluence accuracy for the entire volume of bulk tumor.

Investigation into inhomogeneous electrical and optical properties of indium tin oxide film using spectroscopic ellipsometry with multi-layer optical models

Indium tin oxide (ITO) films with various thicknesses are deposited on glass substrates using a DC magnetron sputtering technique. The microstructure and chemical composition of the sputtered samples are examined by scanning electron microscopy (SEM), X-Ray Diffraction (XRD) and Energy Dispersive X-Ray Spectroscopy (EDS). Two-layer and three-layer optical models of the sputtered ITO films are constructed for fitting the experimental results of the spectroscopic ellipsometry. The results obtained from the two models for the resistivity, carrier density and carrier mobility are compared with those obtained via Hall effect measurements. Finally, the three-layer optical model is used to evaluate the refractive index and extinction coefficient spectra of the various samples. In general, the present results show that the three-layer model, in which the transition layer between the ITO film and the glass substrate is included, provides a better approximation of the SE results than the two-layer model. However, both models yield a reasonable estimate of the Hall resistivity. The results obtained using the three-layer model show that the carrier density and carrier mobility in the bulk layer are lower and higher, respectively, than those in the transition layer. In addition, it is shown that the refractive index of the bulk layer is lower than that of the transition layer in the UV and visible spectrum. Moreover, the extinction coefficient of the transition layer is significantly higher than that of the bulk layer in the near IR-region.

Sensitivity of the light field under sea ice to spatially inhomogeneous optical properties and incident light assessed with three-dimensional Monte Carlo radiative transfer simulations

article i nfo Light transmittance through sea ice is affected by surface cover and ice optical properties in the vicinity of the measurement. We present three-dimensional Monte Carlo simulations of light propagation in sea ice to de- rive upper bounds on the lateral spread of light. Our results give guidance on equipment design and on the possibility of using one-dimensional light transfer models to describe transmittance. Rules were derived for simple cases of optically homogeneous slabs. In the absence of absorption, 10% and 90% of the flux detected under optically thick, homogeneous ice are incident on the surface within a radius of less than 0.3 and 2.0 times the ice thickness, respectively. Any increase in optical thickness or absorption in the ice will re- duce these radii. For example, the wavelength-dependent absorption of ice results in a 20% reduction at 700 nm. Optical anisotropy of the slab was also found to produce potentially significant spatial narrowing of the transmitted light field. In the case of direct sunlight, the photon path is displaced toward the sun rel- ative to the location of the detector. This distortion can reach 1 m or more in optically thick, ponded ice but will be negligible under a surface scattering layer or snow cover. Case studies showed that transmittance of diffuse light in the vicinity of a semi-infinite surface obstruction could be approximated with exponential and error functions. An absorbing cylindrical perturbation of 0.05 m diameter in 1 m thick ice placed 1 m from the point of measurement will absorb less than 1% of the light otherwise registered by the detector. Many results for transmitted light were independent of the mean cosine of the scattering phase function.

An Efficient Method for Radiative Heat Transfer Applied to a Turbulent Channel Flow

The purpose of this paper is to consider a possibility of the independent column approximation for solving the radiative heat fluxes in a 3D turbulent channel flow. This simulation method is the simplest extension of the plane-parallel radiative heat transfer. The test case of the temperature profile was obtained from the direct numerical simulation. We demonstrate the comparison between the 3D radiative transfer simulation and the independent column approximation with an inhomogeneous temperature field and optical properties. The above mentioned results show the trivial discrepancies between the 3D simulation and the independent column approximation. The required processing time for the independent column approximation is much faster than the 3D radiative transfer simulation due to the simple algorithm. Although the independent column simulation is restricted to simple configurations such as channel flow in this paper, wide application areas are expected due to the computational efficiency.

사출성형시 굴절율 변화를 고려하기 위한 플라스틱 비구면 렌즈의 광선추적기법

The present study covers an integrated simulation method to evaluate optical performance of an aspheric plastic lens by connecting an injection molding analysis with a ray tracing simulation. Traditional ray tracing methods have based on the assumption that the optical properties of a lens are homogeneous throughout the entire volume. This assumption is to a certain extent unrealistic for injection-molded plastic lenses because material properties vary at every point due to the injection molding effects. To take into account the effects of the inhomogeneous optical properties of the molded lens, a numerical scheme is developed to calculate the distribution of refractive index induced from the injection molding process. This index distribution is then reflected onto CODE simulation and used to calculate ray paths in inhomogeneous media. The proposed tracing scheme is implemented on the tracing of an aspheric lens for a mobile phone camera module.

In vivo fluorescence lifetime tomography

Local molecular and physiological processes can be imaged in vivo through perturbations in the fluorescence lifetime (FLT) of optical imaging agents. In addition to providing functional information, FLT methods can quantify specific molecular events and multiplex diagnostic and prognostic information. We have developed a fluorescence lifetime diffuse optical tomography (DOT) system for in vivo preclinical imaging. Data is captured using a time-resolved intensified charge coupled device (ICCD) system to measure fluorescence excitation and emission in the time domain. Data is then converted to the frequency domain, and we simultaneously reconstruct images of yield and lifetime using an extension to the normalized Born approach. By using differential phase measurements, we demonstrate DOT imaging of short lifetimes (from 350 ps) with high precision (+/-5 ps). Furthermore, this system retains the efficiency, speed, and flexibility of transmission geometry DOT. We demonstrate feasibility of FLT-DOT through a progressive series of experiments. Lifetime range and repeatability are first measured in phantoms. Imaging of subcutaneous implants then verifies the FLT-DOT approach in vivo in the presence of inhomogeneous optical properties. Use in a common research scenario is ultimately demonstrated by imaging accumulation of a targeted near-infrared (NIR) fluorescent-labeled peptide probe (cypate-RGD) in a mouse with a subcutaneous tumor.

Numerical Evaluation of a Plastic Lens by Coupling Injection Molding Analysis with Optical Simulation

The present study covers an integrated simulation scheme for injection-molded plastic lenses by coupling a ray tracing simulation with a finite element (FE) analysis of injection molding. Traditional ray tracing was based on the assumption that the optical properties of a lens were homogeneous throughout the entire volume. This assumption is to a certain extent unrealistic for injection-molded plastic lenses because material properties vary at every point due to the injection molding effects. To take into account the effects of the inhomogeneous optical properties of the molded lens, a modified ray tracing scheme is proposed in conjunction with an FE analysis of the injection molding. Through the injection molding analysis, the distribution of the refractive indices of the lens can be obtained on every mesh point. This information is then used to calculate the ray paths based on the FE mesh of which nodal points have unique index values. The proposed tracing scheme is implemented on the tracing of an aspheric lens for a photo pick-up device, and its validity is ascertained through experimental verifications.

Transient coupled heat transfer in an anisotropic scattering composite slab with semitransparent surfaces

Transient heat transfer of coupled radiation and conduction inside a semitransparent composite slab of absorbing–emitting-anisotropic scattering medium is examined. The composite slab includes two layers with different physical properties. Surfaces and interface between two layers are supposed to be semitransparent and total reflection will occur there at the critical angle. Specular reflection is considered and reflectivities are determined by Fresnel’s law and Snell’s law. A fully implicit control-volume method is used to solve the transient energy equation and a ray-tracing/nodal-analyzing method is used to compute the radiative information. A criterion for total reflection is proposed for solving the problem of integral singularity at the critical angle. Effects of conduction–radiation parameter, scattering albedo and refractive index on coupled heat transfer are investigated. Results show that in a semitransparent medium with natural surfaces, there are two sorts of temperature peaks appearing at transient heat transfer: one is caused by external radiation heating and environmental convection cooling, still existing in steady state; the other is due to maximum of absorption of heat caused by inhomogeneous optical properties, only existing in transients of heat transfer.

Influence of inhomogeneous cloud fields on optical properties retrieved from satellite observations

Analyses of solar radiation exchanges between the atmosphere and clouds are vital for the understanding of climate processes and cycles. Comparisons of satellite‐to‐satellite or satellite‐to‐ground‐truth observations aiming at, elucidating the radiative behavior of atmospheric components (clouds, aerosols, gas, etc.), or validating data of a particular satellite are a common practice in global radiation investigations. In order to assess the quality of cloud optical properties derived from Geostationary Meteorological Satellite‐5/Stretched Visible Infrared Spin Scan Radiometer (GMS‐5/SVISSR), the former procedure (satellite‐to‐satellite comparison) was used. Data derived from GMS‐5/SVISSR satellite were compared with those from the polar‐orbiting Terra‐Moderate Resolution Imaging Spectroradiometer (Terra‐MODIS) satellite. This comparison showed serious discrepancies between cloud optical depth (COD) data retrieved from the two satellites' observations. GMS‐5/SVISSR‐retrieved COD appeared mostly lower than that of Terra‐MODIS. To understand the origin of such differences, an identification procedure of the major factors likely to affect these data is conducted. Some of these factors were the satellite viewing and solar conditions, the cloud thermodynamic phase differentiation and particle effective radius, and the cloud inhomogeneity. Then emphasis was put on the examination of the latter effect (i.e., the cloud inhomogeneity). The analysis procedure was as follows: First, data having close‐viewing geometries between both satellites were selected and used to understand the effects of the remaining factors. Among these, the cloud thermodynamic phase appeared to play the major role as analyses showed that most of the COD differences between both satellites were confined within ice clouds while warm clouds had the least discrepancies. This would suggest that the choice of a water cloud particle radiative transfer model to analyze a 2‐phase cloud radiation data, as used here, may produce large uncertainties in ice COD retrievals from at least one of the satellites. To avoid the cloud phase problem, a more restrictive data set comprising only water clouds (besides close‐viewing geometries between both satellites) was selected, and the impact of the degree of cloud inhomogeneity on the COD retrievals was evaluated. The study reveals that the 3‐D radiative effects deriving from the external cloud inhomogeneity, i.e., cloud asymmetry and structured sides, were the most influencing properties here. The GMS‐5/SVISSR interpretation of inhomogeneous cloud optical properties showed larger uncertainties than that of Terra‐MODIS. Furthermore, COD values of GMS‐5/SVISSR were systematically lower than those of Terra‐MODIS for the pixels at shadow sides of the cloud, while at illuminated sides they often showed higher values. For gentle or near‐plane‐parallel cloud surfaces, fewer discrepancies were noticed (the best agreement between both satellites' retrievals). At steep slopes of the shadow and illuminated cloud sides, GMS‐5/SVISSR average COD data were respectively under‐ and overestimated compared to those of Terra‐MODIS. COD differences between the two satellites could be sometimes higher than 30% for slopes steeper than 0.5 K/km.

사출성형 유한요소해석과 연계한 비구면렌즈의 광학적 특성평가

The present study covers an integrated simulation method to evaluate optical performance of an aspheric plastic lens by connecting a finite element (FE) analysis of injection molding with a ray tracing simulation. Traditional ray tracing methods have based on the assumption that the optical properties of a lens are homogeneous throughout the entire volume. This assumption is to a certain extent unrealistic for injection-molded plastic lenses because material properties vary at every point due to the injection molding effects. To take into account the effects of the inhomogeneous optical properties of the molded lens, a new.ay tracing scheme is proposed in conjunction with a FE analysis of the injection molding. A numerical scheme is developed to calculate ray paths on every element layer with more realistic information of the refractive indices which can be obtained through the FE analysis. This information is then used to calculate the ray paths based on the FE mesh of which nodal points have unique index values. The proposed tracing scheme is implemented on the tracing of an aspheric lens, and its validity is ascertained through experimental verification.