The mathematical tools to calculate surface and wavefront local curvatures have been growing in importance because, when studying and evaluating some optical systems, the local curvature becomes extremely important. Many practical methods have been created to measure the wavefront shape and local curvatures as well as many mathematical tools to describe them. These methods are very useful in ophthalmology mainly for corneal evaluation, but the methods are now being used in other fields of optical metrology, especially in optical testing, interferometric wavefront description, and others. In some instruments and optical devices, mainly ophthalmic and optometric instruments, the local curvatures distribution over the pupil of an optical system is more important than the wavefront topography. A typical example is a human eye, in which corneal topographers, eye aberrometers, and several other instruments are used to measure the local curvatures. In particular, the main aspects of the curvature calculation at a given point for different slopes in any direction are introduced. The principal curvatures, mean, Gaussian, cylindrical, tangential, and sagittal curvatures are described. In the second part of this review, we describe the main methods and devices for wavefront sensing, measuring elevations, slopes, or curvatures. We conclude with a description of some methods to measure and calculate local curvatures from wavefront sensors by measuring the wavefront elevations, the transverse aberrations (slopes), or directly the curvatures.

The design and initial experimental results from an event-based, rotating-polarizer, imaging polarimeter are presented. The speed of division-of-time imaging systems is traditionally constrained by the frame rate of the focal plane sensor and the need to sample several polarization angles during rotation. The asynchronous event reporting of event-based cameras (EBCs) frees these constraints but introduces challenges. The Stokes vectors used to describe polarization are based on irradiance, but EBCs are inherently change-detection systems that struggle to estimate irradiance. Two methods of estimating the polarization state without first recovering irradiance images are presented and compared. The DAVIS 346 sensor enables simultaneous recording of events with conventional frame-based images, enabling direct comparison of event-based polarization estimates to traditional techniques.

In augmented reality (AR), focal accommodation for real objects and augmented imagery is essential for comfortable viewing, and this requires a depth of field (DoF) in AR displays. Wide DoFs have been achieved in various display systems, but these systems are often bulky, highly power-consuming, and computationally complex. Hence, we propose a simple and effective optical method to extend the DoF in AR displays. The proposed method harnesses a focus tuning block consisting of a multifocal lens (MFL) and a focus tunable lens. Through the multi-variable focusing unit, virtual imagery is displayed at spatially separated focal depths using the MFL; then, the focus tunable lens dynamically tunes the foci. This enables the individual virtual objects to be sequentially focused on the same image plane, helping to register them with the real objects in the user’s eye accommodation. The proposed approach was numerically simulated, and its performance was experimentally evaluated with an AR display equipped with the focusing unit, which extended the DoF from 0.3 m (3.3 diopters) to 2 m (0.5 diopters).

The computed tomography imaging spectrometer (CTIS) is a hyperspectral imaging (HSI) approach where spectral and spatial information of a scene is mixed during the imaging process onto a monochromatic sensor. This mixing is due to a diffractive optical element integrated into the underlying optics and creates a set of diffraction orders. To reconstruct a three-dimensional hyperspectral cube from the CTIS sensor image, iterative algorithms were applied. Unfortunately, such methods are highly sensitive to noise and require high computational time for reconstruction thus hindering their applicability in real-time and high frame-rate applications. To overcome such limitations, we propose a lightweight and efficient deep convolutional neural network for hyperspectral image reconstruction from CTIS sensor images. Compared with classical approaches our model delivers considerably better reconstruction results on synthetic as well as real CTIS images in under 0.17 s, which is over 60 times faster compared with the standard iterative approach. In addition, the reshaping method we have developed enables a lightweight network architecture with over 100 times fewer parameters than previously reported.

Transport of intensity equation (TIE) relates the longitudinal intensity derivative of propagating light wave to the transverse phase gradient. The phase is retrieved by measuring the intensity of propagating light wave at two or more longitudinally displaced planes by moving the detector and then solving the TIE. We present a single-shot transport of intensity equation-based phase retrieval using a prism-mirror based module to capture the two defocused intensity images simultaneously. The results obtained by single-shot transport of intensity equation-based phase retrieval have been compared with interferometry and profilometer-based measurements. We highlight an important aspect of the TIE-based approach that this formulation decouples the intensity and the unwrapped phase of the unknown field. Intensity and phase are individually low-bandwidth functions when compared to the complex field associated with the unknown wavefront. When compared to interferometry, the TIE-based approach therefore inherently has many reduced sampling requirements. For a given array sensor, TIE can therefore measure large phase deviations for which an interferometer would produce very high density fringes that are impossible to sample as per the Nyquist criterion. The prism-mirror module shown in this work is easy to fabricate, align, and can be easily integrated with an experimental setup. The applications of the proposed method for the wavefront measurement of spherical and aspheric lenses are demonstrated.

A visual vibration measurement method based on single-frame coded illumination and compressive sensing is proposed. The projector projects concentric rectangles with different sizes at different time points in a single camera exposure. According to the size of the rectangles, the image collected by the camera is separated into different sub frames. The centroids of the concentric rectangles are considered as the virtual feature points to record the vibration information of the object. The projector operates according to the random unequal interval trigger signal, and the projection is used as the sampling signal to encode the measured object. Discrete cosine transform is used as sparse basis, and sparsity adaptive matching pursuit and spectral projected gradient for L1 minimization (SPGL1) are used for signal reconstruction. Simulation analysis shows that the proposed method is feasible, and SPGL1 algorithm is more suitable for our signal reconstruction. The experiments indicate that the maximum absolute error of the proposed method for frequency measurement is 0.2985 Hz, and the maximum relative error is 1.6587  ×  ^{10  −  3}. It is also applicable to multi-frequency measurement.

In spite of the robustness and simplicity of the self-mixing interferometry (SMI) concept, interpreting the SMI signal is often complicated in practice, which is detrimental to its measurement value. SMI based on machine learning is presented to extract the phase directly from pure SMI signals. A simple phase decomposition neural network (PDNN) was constructed to realize direct phase extraction. A special feature of the PDNN is that it can use the simulation data directly to train the model, and the trained model can be used directly for measurement. In the training process of the PDNN model, the simulated cosine-like signal and the flag signal were used as inputs, and the simulated phase was used as the label. Thus, the training set was easy to prepare, the model structure was simple, and the training speed was very fast. Experimentally, we measured targets with cosine-like movements directly using the trained model, and the results obtained were consistent with the simulation. This contributes to simplifying the signal processing of interferometry in practical engineering applications.

A time-of-flight measurement-based three-dimensional (3D) profiler system employing a lightweight scanning system is demonstrated. To reduce the weight of the scanning system, and thereby achieve faster scanning speeds, two Fresnel prism sheets were employed as the scanning optics and installed to work as a pair of Risley prisms. Each Fresnel prism sheet has a diameter of 102 mm and mass of 15 g, which is about 12 times lighter than ordinary bulky prism. By scanning the laser beam with the developed scanning system, a 3D point cloud image of a target object located 8 m away could be successfully obtained. The image distortion was removable by correcting six geometrical parameters of the scanner using a simple optimization algorithm. It was confirmed by the experiment that once the distortion has been corrected, it is valid for other scanning speeds (and trajectories), enabling 3D profile measurements that do not require postprocessing of measured data. Measurement results for a standard target composed of square extrusions were in good agreement with the reference values, with deviations of <1  mm.

Featuring high resolution, excellent stability, great rapidity, and small size, the laser displacement sensor (LDS) has been extensively utilized in multiple domains. However, its accuracy is severely constrained by data acquisition (DAQ) errors. To solve this problem, we concentrate on the problem that DAQ errors seriously deteriorate the LDS measuring accuracy. Based on laser triangulation, we analyze the impact of laser beams and convergent spot centroid on the system measuring accuracy and establish mathematical models for quantitatively calculating LDS measured surface dip errors and charge-coupled device (CCD) dip errors. Further, these models can be used to compensate for the data collected by the LDS in real-time. Finally, experimental results show that after these two compensation models are used to correct measuring results, the accuracy of LDS-based DAQ is greatly improved, the measurement error is well controlled within 0.008 mm, and the LDS measuring accuracy on spiral curved surfaces is effectively boosted.

The actuator is a primary component of the fast-steering mirror (FSM), and its quality directly determines the performance of FSM. To achieve high compactness, high efficiency, large output torque, and effective linearity, a hybrid reluctance actuator (NHRA) for FSM was designed. To obtain a high-force density and small flux leakage, four permanent magnets (PMs) were designed on the side of the armature, which improves the linearity of the actuator by generating a bias flux. Meanwhile, to obtain the maximum output torque for a limited size, the structural model of the actuator was established in ANSYS Maxwell, and all structural parameters were optimized. In addition, an analytical model of the actuator was established via the equivalent magnetic circuit method. To improve the modeling accuracy, both PM and coil flux leakages were considered. The theoretical and simulation results were insignificant in agreement, and both showed the output torque of this actuator to be approximately twice that of a state-of-the-art actuator under the same volume, simultaneously improving the linearity.

In a charge-coupled device-based visual tracking system (VTS), the control bandwidth is restricted by the image sensor’s time delay, which hinders a high tracking performance. Compared with the feedback control, a delay-compensation control method called the Smith predictor (SP) could improve the tracking performance by moving the delay outside the closed loop to relax the constraint on the controller. However, the performance improvement is limited because delay still exists in the system, resulting in a deviation between input and output. In addition, in the previous VTS with SP, the controller was commonly adjusted based on experience, which would easily lead to an overly conservative design. To solve these problems, an enhanced Smith predictor (ESP) by Kalman filter prediction is introduced, and the controller design criteria based on control stability is quantitatively analyzed. Based on the typical SP, an additional Kalman filter is added to the forward path to predict the current position based on the past position information, which further eliminates the effect of the delay. Then, according to the small gain theorem, the design principle of the controller when there is a model mismatch is given to release the control performance as much as possible. Experimental results confirm that the proposed ESP method has a stronger error suppression characteristic in a low frequency when compared with the SP method.

We present a method for increasing the dynamic range of a Shack–Hartmann wavefront sensor with a hexagonal lenslet array. Increasing the dynamic range is equivalent to calculating the spot displacement correctly, when it is bigger than the subaperture radius. Our method does this by sorting and indexing the spots according to centered hexagonal number. This allows tracking of the wandering of each spot separately. Further, we also show that the system can work in a reference-free mode if we are not interested in the tip and tilt terms. The results of the work are presented along with the details of the algorithm and theory.

The high temperature around hypersonic vehicles due to aero-heating will result in air reactions. Considering how much is unknown about how these reactions’ three-dimensional effects may affect aero-optics, a direct simulation Monte Carlo (DSMC) method with a quantum–kinetic chemical reaction model is used to explore the relationship between aero-optical effects and different flying conditions of a three-dimensional sphere. Cases of inert or reactive flowfield, different incident angles of a beam, Mach numbers 7 to 20, and angles of attack −10  deg to 10 deg are simulated. By defining the boresight error and phase deviation, it is found that an error of about 14% will be introduced if real gas effects and three-dimensional effects are both neglected. The variation of aero-optical effects with Mach number in a broader range is slightly different from the existing conclusions.

We study the nonparaxial diffraction of the well-known Cartesian oval in finite and infinite conjugate configurations. We started by expressing the refraction of the Cartesian oval by analytical closed-form equations. These equations are convenient to obtain the pupil apodization function of the Cartesian oval, which is needed to compute the diffraction pattern using Richard–Wolf theory. A comparison of the diffraction patterns of the Cartesian oval with finite/infinite objects, the aplanatic lens, and the parabolic mirror for radially polarized illumination is presented. From this comparison, we conclude that a Cartesian oval for a far object is not a good candidate for tight focusing and super-resolution applications and the performance of a Cartesian oval in a finite conjugate configuration is similar to the performance of an aplanatic lens and in some scenarios, it can perform better than the aplanatic lens.

A high sensitive optical MEMS accelerometer is proposed, which works by changing the effective refractive index of a microring relied on intensity modulation of light wave. The proposed optical sensing system consists of a microring, waveguide, and a proof mass. Acceleration causes lateral displacement of the proof mass. The proof mass is in the optical coupling length of the microring, and the displacement of the proof mass changes effective refractive index of the microring. Changes of the effective refractive index of the microring result in wavelength shift. The mechanical and optical parts of the proposed accelerometer are designed, and the obtained functional characteristics are compared with other accelerometers. Simulation shows functional characteristics of the proposed design are as follows: mechanical resonant frequency of 3.7 kHz, operating bandwidth of 2.6 kHz, mechanical sensitivity of 2 nm/g, optical sensitivity of 0.7%/nm, overall sensitivity of 1.4%/g, foot print of less than 150  μm  *  170  μm, measurement range of   ∓  50  g, and mechanical noise density of 3.1  (  mg  /  Hz  )  . These functional characteristics make the design very interesting for a wide range of applications, ranging from consumer electronics and automobile to inertial navigation.

It is a great challenge for traditional passive camouflage materials to respond to spectral changes with environmental transitions. Hence, a spectrally tunable light source (STLS) sample composed of multitype light-emitting diodes for matching different background spectra was proposed. The common background spectra were measured. These spectra can provide the guidance and verification of the STLS sample in terms of spectral matching. The STLS sample was designed by a spectral fitting method with an equal interval of the peak wavelength, and an optimization method was proposed to match the different background spectra quickly and accurately. The theoretical results show that at least 30 light sources with different peak wavelengths are required to match all the collected spectra from the typical backgrounds. The correlation index between the measured STLS spectrum and the background spectrum of the gravel clay can increase from 0.5045 to 0.9518 after the optimization, indicating an accurate match. Except for the extremely low energy spectra, the correlation indexes can be maintained above 0.9275 for the collected spectra versus the different environments and time, exhibiting the verification of matching the different background spectra. Thus, we confirm the feasibility of the proposed STLS sample, which can provide a preliminary exploration for the application and development of dynamic spectral matching.

Visible light-based positioning (VLP) is envisioned to be a promising solution to indoor positioning, orientation, and navigation because of the widespread use of light-emitting diodes for illumination. At present, several VLP schemes have been proposed, with most researchers using the line-of-sight channel and ignore the multipath reflection. However, some research works have shown that multipath reflections degrade the performance of VLP systems greatly. We propose an optimization positioning method based on reflected light depolarization characteristics to subtract the multipath reflection signals from the received signals, which can eliminate or mitigate the impact of multipath reflection to improve positioning accuracy. Further, a model is established theoretically, and simulations are carried out in a 0.82  m  ×  0.82  m  ×  0.62  m area. The simulation results show that the average positioning error and maximal error are reduced by 94.9% and 85.1%, respectively, when using the method. In the experiments, the performances are assessed and match well with our simulation results, achieving an average positioning error of 4.2 cm and a maximal positioning error of 8.4 cm, corresponding to a decrease of 62.5% and 66.0%.

Free-space optics (FSO) systems use the atmosphere as a medium to propagate data in the form of an optical signal. Using mode division multiplexing (MDM) over FSO systems increases the capacity of the FSO link. However, atmospheric turbulence is one of the main problems that seriously limit the data transmission rate in FSO systems. This causes signal distortion during transmission that leads to data loss at the receiver side totally or partially. To address this problem, a decision feedback equalization (DFE) scheme with minimum mean square error (MMSE) in MDM for FSO systems was developed in OptSim 5.2 software to mitigate the adverse effects of atmospheric turbulence. The MMSE algorithm was used to optimize both the feed-forward and feedback filter coefficients of the DFE. The proposed DFE scheme in MDM for the FSO system comprises seven parallel 2.5 Gbps MDM channels using Hermite–Gaussian modes at the transmitter to transmit 17.5 Gbps and seven DFE schemes at the receiver to mitigate the effects of atmospheric turbulence. The simulation results demonstrate that the DFE scheme can transmit 17.5 Gbps over 40 m, 800 m, 1400 m, and 2 km under medium fog, medium rain, medium haze, and clear weather, respectively. We show that the DFE scheme improves the MDM over FSO system immunity to distortion in medium fog, medium rain, medium haze, and clear weather while maintaining high throughput and desired low bit error rate.

A tunable all-optical microwave generator based on period-one (P1) dynamics of an external optically injected distributed-feedback laser diode (DFB-LD) is proposed and demonstrated. A DFB-LD implements the functions of light source, microwave frequency selection, and optical–optical modulation. To overcome the frequency drift in P1 oscillation process, a set of reference frequencies from a fiber ring laser (FRL) is introduced. Once the P1 oscillation signal and the modes of FRL are coupled, the whole system is closed and a stable frequency determined by P1 oscillation can be established. In the experimental verification, tunable photonic microwave signals with frequencies from 6.42 to 21.36 GHz are obtained. The measured single-sideband phase noise is −83  dBc  /  Hz at 10-kHz offset, which is operation frequency independent.

Atmospheric turbulence creates a light spot on the focal plane of the receiving end scintillation and angle of arrival fluctuation in optical wireless communication. The combination of a spot centroid detection algorithm and Kalman filter (KF) is proposed for spot tracking. The theoretical calculated value of the spot circle fit is filtered to obtain an optimal estimate of the spot center. The root mean square error of the detected spot centroids is used as an evaluation metric to verify the conventional algorithm and KF algorithm for the real-time tracking of the laser spot at transmission distances of 1.3, 4.1, and 10.3 km. The results show that the root mean square error of the spot in the pitch direction decreases from 0.740, 2.537, and 7.256 pixels to 0.683, 1.792, and 4.756 pixels, respectively, whereas the root mean square error of the spot in the horizontal direction decreases from 0.481, 2.131, and 5.932 pixels to 0.463, 1.471, and 4.362 pixels, respectively, compared with the conventional algorithm at three transmission distances. The envelope fluctuation of the baseband signal at the receiving end is significantly improved using KF algorithm compared with the conventional algorithm, which improves the stability of the optical wireless communication link.

Temperature variation is a key factor affecting the stability of fiber optic frequency transfer systems. In a long-distance optical fiber frequency transfer system, a dispersion compensation fiber (DCF) placed in the machine room and a non-buried single-mode fiber (SMF) are collectively referred to as a bare optical fiber. Due to the impact of the external environment, the temperature of the bare optical fiber varies drastically, which seriously deteriorates the long-term stability (10,000 s stability) of the frequency transfer system. To investigate the relationship between the temperature variation of the bare optical fiber and the frequency transfer stability, we use VPItransmissionMaker optical simulation software to simulate and study the fiber frequency transfer system of the bare optical fiber under the impact of different temperatures. The simulation found that the system stability is 1.4  ×  10^−  16  /  10⁴  s in a 3000 km link when the temperature variation of DCF is 5°C, whereas the impact on the system stability is on the order of 10^−  16  /  10⁴  s when the length of the non-buried SMF is more than 300 km and the temperature variation is more than 10°C. To verify the correctness of the simulation, the stability of the actual 80 km fiber optic frequency transfer system was compared with that of the simulation, and the stability of the simulation was found to be 4.2  ×  ^{10  −  17}  /  ¹⁰⁴s, whereas the stability of the experimentally measured system was 7.9  ×  10^−  17  /  10⁴  s, and the simulation results were basically consistent with the experimental results.

Recently, a light-emitting diode (LED) was used as an optical source in the transmitter for underwater wireless optical communication (UWOC) because it has a large divergence angle that makes establishing the communication link easier. In practice, there are several discrete LEDs in the transmitter to enlarge its output power. However, with the increase in the number of LEDs, the parasitic resistance and inductance in the light source is larger too, which affects the quality of the modulated signal. Also, using more discrete LEDs enlarges the luminous surface, which is disadvantageous to improving the tolerance to water pressure for UWOC equipment. To reduce such influences, a transmitter is proposed with a chip-on-board LED array because it has a smaller luminous surface, parasitic resistance, and inductance. Using such a transmitter, a UWOC system is established and tested in a large experimental tank. The results show that it could realize a 19 m communication distance with a 30 Mbps rate in water with an attenuation coefficient that is about 0.26  m^−  1. The output power is 1.69 W, and the radiation intensity is approximately a Lambert distribution with a 120 deg divergence angle. Further analysis shows that the communication distance could increase to 90.5 m in clear water with a 0.02  m^−  1 attenuation coefficient, and the emission light could cover 86.5% of the solid angle of the hemisphere space. The speed is higher than the same class light source in the previous sea trails, and the combination performance of angle coverage area, distance, and speed is suitable for ocean engineering. The proposed method is useful, simple, low-cost, and pragmatic, which makes it easy to popularize and apply.

Integrated modulators are essential components for optical sensing and communication applications. However, most efforts have been focused on infrared telecommunications wavelengths, with very little consideration for visible light applications. Here, we design an electro-optic (EO) modulator at 532 nm with the waveguides formed by SU8 polymer structures on the thin-film lithium niobate (LN). The simulation results show a low loss, high modulation efficiency, and large bandwidth simultaneously for the modulator. The predicted low loss is attributed to the LN etchless waveguide and high coupling efficiency, i.e., 93%, with the single-mode fiber theoretically using a SU8 edge coupler. The simulated low voltage-length product of 1.15  V  ·  cm and a 3-dB-bandwidth of >120  GHz at a length of 5 mm are superior to any other modulator in the optical communication band. The modeling of the modulator proposed here shows great potential for visible light communications applications such as energy-efficient and large-capacity underwater wireless optical interconnects.

A method for fabricating a thin film Fabry–Pérot (F–P) cavity via dual pressure-assisted acrylate AB glue was studied. The method pressurizes both the acrylate AB glue to generate bubbles and the subsequent inflated film to make it thinner and more sensitive. The F–P cavity was fabricated by attaching the ultrathin film to a glass tube end face and a single-mode fiber in the glass tube to form a two-beam interference model. On the basis of two cycles and several repeated experiments for the humidity gradient, the linear and stable characteristics, and the humidity sensitivity of the F–P cavity with a thin film was demonstrated. The humidity sensitivity was 80.68 pm/% RH and 82.17 pm/% RH under two rising humidity experiments. Acting as the humidity sensing material for the first time, the acrylate AB glue film of the F–P cavity shows good stability and repeatability. In addition, the dual pressure-assisted method introduces a way to produce fiber-optic sensors with ultrathin film.

A surface plasmon resonance (SPR) biosensor utilizing an indium phosphide (InP) semiconductor and graphene material layer and placed on an Ag metal-based biosensor is proposed to detect the sucrose concentration in water. The SPR biosensor works on the principle of attenuated total reflection. The transverse matrix method has been utilized for the reflectance calculation. The thickness of the Ag layer, InP, and graphene are taken as 45 nm, 2 nm, and 2 nm, respectively. When three layers of InP and a single layer of graphene are taken, and the maximum sensitivity of the sensor 506  deg  /  RIU is obtained. The desired values of performance parameters, such as full-width half maximum and quality factor were computed and obtained as 6.94 deg and 72.86  deg RIU^−  1 respectively, which recommend the significance of the proposed work. Graphene is used to enhance the bio-compatibility of the analyte with the sensing layer. The refractive index of the sensing medium is considered as 1.33. Indium phosphide is an air-stable optical material. SPR biosensors have wide applications in detecting and analyzing biomolecules and biochemicals.

A compressed hexagonal dual-core photonic crystal fiber (CH-DC-PCF) polarization beam splitter (PBS) with a liquid crystal filled air hole is designed. The designed CH-DC-PCF has different sizes of air holes, which are arranged in a compressed hexagonal structure in the cladding region and introduce the birefringence. In addition, the nematic liquid crystal is filled into the central air hole to enhance the beam splitting effect. To obtain a shorter PBS, the structure parameters of the CH-DC-PCF are optimized by the finite element method. The simulation results show that the length of the proposed CH-DC-PCF PBS is 109.5  μm, and the corresponding extinction ratio (ER) reaches the first peak value of 86.07 dB at wavelength 1.494  μm, then 63.14 dB at wavelength 1.55  μm, and the second peak value of 83.35 dB at wavelength 1.553  μm. Moreover, the ER is higher than 20 dB in the wavelength range of 1.402 to 1.682  μm, so the bandwidth of the PBS is up to ∼280  nm, covering the S  +  C  +  L  +  U communication band.

Rutile TiO₂ and Ti_0.9In_0.1O₂ thin films were fabricated using a pulsed laser deposition method. We employed the optical transmission spectra to reveal the good transparency of the films in the visible spectral range of 330 to 900 nm. The absorption edge of the Ti_0.9In_0.1O₂ film is blue-shifted compared with that of undoped TiO₂ film. The third-order optical nonlinearity of the films was investigated by using a z-scan method with a pulse laser operating at 532 nm with a duration of 55 ps. The results show that the Ti_0.9In_0.1O₂ and TiO₂ films exhibit nonlinear saturable absorption and negative nonlinear refraction. The doping of In ions does not change the nonlinear optical absorption of the TiO₂ film significantly. However, the nonlinear refractive index of Ti_0.9In_0.1O₂ film is about two times larger than that of undoped TiO₂ film. The local electron-pinned defect-dipoles and widening bandgap in the Ti_0.9In_0.1O₂ film can be used to explain the observed results.