Showing papers in "Applied Optics in 2016"

Refractive indices of common solvents and solutions at 1550 nm.

Abstract: Using a large-angle refractometer, the refractive indices of water, methanol, acetonitrile, acetone, ethanol, formaldehyde solution, 2-propanol, hexanes, 1-propanol, 2-butanol, tetrahydrofuran, dichloromethane, 1,4-dioxane, cyclohexane, N,N-dimethylformamide, ethylene glycol, N,N-dimethylacetamide, chloroform, glycerol, trichloroethylene, dimethylsulfoxide, p-xylene, ethylbenzene, toluene, m-xylene, benzene, and o-xylene were measured at 1550 nm and compared to literature values. In addition, the refractive indices of 48 aqueous sucrose solutions, 34 aqueous sodium chloride solutions, 40 DMSO-water, 40 ethylene glycol-water, and 40 glycerol-water mixtures were also measured at different concentrations and fit with third-order polynomial expressions. This study provides near-infrared refractive indices that were not previously available and may help with the calibration of refractive index sensors that operate at or near 1550 nm.

Metal powder absorptivity: modeling and experiment.

Abstract: We present results of numerical modeling and direct calorimetric measurements of the powder absorptivity for a number of metals. The modeling results generally correlate well with experiment. We show that the powder absorptivity is determined, to a great extent, by the absorptivity of a flat surface at normal incidence. Our results allow the prediction of the powder absorptivity from normal flat-surface absorptivity measurements.

Fusion of infrared and visible images for night-vision context enhancement

Abstract: Because of the poor lighting conditions at night time, visible images are often fused with corresponding infrared (IR) images for context enhancement of the scenes in night vision. In this paper, we present a novel night-vision context enhancement algorithm through IR and visible image fusion with the guided filter. First, to enhance the visibility of poorly illuminated details in the visible image before the fusion, an adaptive enhancement method is developed by incorporating the processes of dynamic range compression and contrast restoration based on the guided filter. Then, a hybrid multi-scale decomposition based on the guided filter is introduced to inject the IR image information into the visible image through a multi-scale fusion approach. Moreover, a perceptual-based regularization parameter selection method is used to determine the relative amount of the injected IR spectral features by comparing the perceptual saliency of the IR and visible image information. This fusion method can successfully transfer the important IR image information into the fused image, and simultaneously preserve the details and background scenery in the input visible image. Experimental results show that the proposed algorithm is able to achieve better context enhancement results in night vision.

Real-time 3D digital image correlation method and its application in human pulse monitoring.

Abstract: In industrial measurements and online monitoring, full-field and high-efficiency deformation analysis has been increasingly important and highly demanded in recent years. In this paper, a fast three-dimensional digital image correlation (3D-DIC) method was proposed to implement real-time measurement. Two improvements were suggested to accelerate the computation speed without sacrificing the accuracy. First, an efficient inverse compositional Gauss-Newton (IC-GN) algorithm was developed to avoid redundant computation. Moreover, a seed point-based parallel method was extended for 3D-DIC to achieve parallel computation and faster convergence speed. The detailed process of the real-time measurement using the proposed method was also introduced. Benefiting from the efficient IC-GN algorithm and parallel processing software we developed, full-field, real-time 3D deformation monitoring was realized at a frame rate of 10 frames/s with resolution of 5000 points per frame. For validation, the displacement field of a four-point bending beam was determined by the real-time 3D-DIC. As an application, the real-time human pulse diagnosis was also performed based on the presented technique. Experimental results verify that the proposed real-time 3D-DIC is practicable and effective for traditional Chinese medicine.

Quantitative measurement of dynamic nanostrain based on a phase-sensitive optical time domain reflectometer.

Abstract: A sensing system is proposed for quantitative measurement of large-range dynamic nanostrain based on a phase-sensitive optical time domain reflectometer, where the coherent detection and I/Q demodulation methods are employed to demodulate both the phase and the amplitude of the Rayleigh scattering light in real time. A nanopositioning translation stage is utilized to apply precise nanostrain to fiber. By measuring phase differences between two adjacent sections, the quantitative nanostrain with a large measurement range is demonstrated; this is also a method to measure the strain parameter of refractive index. For the Panda polarization-maintaining fiber under test in the experiment, the strain parameter of phase difference is measured to be 8.714 mrad/(ne·m), while the strain parameter of refractive index is measured to be −0.3751e−1. As a proof of the concept, the dynamic strain sensing with a range of 10–1000 ne is experimentally demonstrated, and the strain resolution is 1 or 2 ne, corresponding to 5 or 2.5 m spatial resolution, respectively. The experimental measurement also shows a triangular wave with a 12-Hz vibrating frequency and a 100-ne strain amplitude as well as a 188-Hz resonant signal of the tensile section.

Enhanced two-frequency phase-shifting method

Abstract: One of the major challenges of employing a two-frequency (or two-wavelength) phase-shifting algorithm for absolute three-dimensional shape measurement is its sensitivity to noise. Therefore, three- or more-frequency phase-shifting algorithms are often used in lieu of a two-frequency phase-shifting algorithm for applications where the noise is severe. This paper proposes a method to use geometric constraints of digital fringe projection system to substantially reduce the noise impact by allowing the use of more than one period of equivalent phase map for temporal phase unwrapping. Experiments successfully verified the enhanced performance of the proposed method without increasing the number of patterns.

Propagation of an optical vortex carried by a partially coherent Laguerre–Gaussian beam in turbulent ocean

Abstract: The analytical formulas for the orbital angular momentum (OAM) mode probability density, signal OAM mode detection probability, and spiral spectrum of partially coherent Laguerre-Gaussian (LG) beams with optical vortices propagation in weak horizontal oceanic turbulent channels were developed, based on the Rytov approximation theory. The effect of oceanic turbulence and beam source parameters on the propagation behavior of the optical vortices carried by partially coherent LG beams was investigated in detail. Our results indicated that optical turbulence in an ocean environment produced a much stronger effect on the optical vortex than that in an atmosphere environment; the effective range of the signal OAM mode of LG beams with a smaller ratio of the mode crosstalk was limited to only several tens of meters in turbulent ocean. The existence of oceanic turbulence evidently induced OAM mode crosstalk and spiral spectrum spread. The effects of oceanic turbulence on the OAM mode detection probability increased with the increase of radial and azimuthal mode orders, oceanic turbulent equivalent temperature structure parameter, and temperature-salinity balance parameter. The spatial partial coherence of the beam source would enhance the effect of turbulent aberrations on the signal OAM mode detection probability, and fully coherent vortex beams provided better performance than partially coherent ones. Increasing wavelength of the vortex beams would help improve the performance of this quantum optical communication system. These results might be of interest for the potential application of optical vortices in practical underwater quantum optical communication among divers, submarines, and sensors in the ocean environment.

Ultraviolet (250-550 nm) absorption spectrum of pure water.

Abstract: Data for the spectral light absorption of pure water from 250 to 550 nm have been obtained using an integrating cavity made from a newly developed diffuse reflector with a very high UV reflectivity. The data provide the first scattering-independent measurements of absorption coefficients in the spectral gap between well-established literature values for the absorption coefficients in the visible (>400 nm) and UV (<200 nm). A minimum in the absorption coefficient has been observed in the UV at 344 nm; the value is 0.000811±0.000227 m−1.

Polarization-maintaining low-loss porous-core spiral photonic crystal fiber for terahertz wave guidance.

Abstract: A polarization-maintaining porous-core spiral photonic crystal fiber is proposed for efficient transmission of polarization-maintaining terahertz (THz) waves. The finite element method with perfectly matched layer boundary conditions is used to characterize the guiding properties. We demonstrate that by creating artificial asymmetry in the porous core, an ultrahigh birefringence of 0.0483 can be obtained at the operating frequency of 1.0 THz. Moreover, a low effective material loss of 0.085 cm−1 and very small confinement loss of 1.91×10−3 dB/cm are achieved for the y-polarization mode with optimal design parameters. This article also focuses on some crucial design parameters such as power fraction, bending loss, and dispersion for usability in the THz regime.

Laguerre-Gauss and Bessel-Gauss beams propagation through turbulence: analysis of channel efficiency.

Abstract: As a means of increasing the channel capacity in free-space optical communication systems, two types of orbital angular momentum carrying beams, Bessel–Gauss and Laguerre–Gauss, are studied. In a series of numerical simulations, we show that Bessel–Gauss beams, pseudo-nondiffracting beams, outperform Laguerre–Gauss beams of various orders in channel efficiency and bit error rates.

Performance of the Gemini Planet Imager's adaptive optics system

Abstract: The Gemini Planet Imager's adaptive optics (AO) subsystem was designed specifically to facilitate high-contrast imaging. A definitive description of the system's algorithms and technologies as built is given. 564 AO telemetry measurements from the Gemini Planet Imager Exoplanet Survey campaign are analyzed. The modal gain optimizer tracks changes in atmospheric conditions. Science observations show that image quality can be improved with the use of both the spatially filtered wavefront sensor and linear-quadratic-Gaussian control of vibration. The error budget indicates that for all targets and atmospheric conditions AO bandwidth error is the largest term.

Revealing the radial modes in vortex beams.

Abstract: Light beams that carry orbital angular momentum are often approximated by modulating an initial beam, usually Gaussian, with an azimuthal phase variation to create a vortex beam. Such vortex beams are well defined azimuthally, but the radial profile is neglected in this generation approach. Here, we show that a consequence of this is that vortex beams carry very little energy in the desired zeroth radial order, as little as only a few percent of the incident power. We demonstrate this experimentally and illustrate how to overcome the problem by complex amplitude modulation of the incident field.

Dual-wavelength common-path digital holographic microscopy for quantitative phase imaging based on lateral shearing interferometry.

Abstract: A dual-wavelength common-path digital holographic microscopy based on a single parallel glass plate is presented to achieve quantitative phase imaging, which combines the dual-wavelength technique with lateral shearing interferometry. Two illumination laser beams with different wavelengths (λ1=532 nm and λ2=632.8 nm) are reflected by the front and back surfaces of the parallel glass plate to create the lateral shear and form the digital hologram, and then the hologram is reconstructed to obtain the phase distribution with a synthetic wavelength Λ=3339.8 nm. The experimental configuration is very compact, with the advantages of vibration resistance and measurement range extension. The experimental results of the laser-ablated pit, groove, and staircase specimens show the feasibility of the proposed configuration.

Method for out-of-focus camera calibration.

Abstract: State-of-the-art camera calibration methods assume that the camera is at least nearly in focus and thus fail if the camera is substantially defocused. This paper presents a method which enables the accurate calibration of an out-of-focus camera. Specifically, the proposed method uses a digital display (e.g., liquid crystal display monitor) to generate fringe patterns that encode feature points into the carrier phase; these feature points can be accurately recovered, even if the fringe patterns are substantially blurred (i.e., the camera is substantially defocused). Experiments demonstrated that the proposed method can accurately calibrate a camera regardless of the amount of defocusing: the focal length difference is approximately 0.2% when the camera is focused compared to when the camera is substantially defocused.

Phase error analysis and compensation for phase shifting profilometry with projector defocusing.

Abstract: Phase shifting profilometry (PSP) using binary fringe patterns with projector defocusing is promising for high-speed 3D shape measurement. To obtain a high-quality phase, the projector usually requires a high defocusing level, which leads to a drastic fall in fringe contrast. Due to its convenience and high speed, PSP using squared binary patterns with small phase shifting algorithms and slight defocusing is highly desirable. In this paper, the phase accuracies of the classical phase shifting algorithms are analyzed theoretically, and then compared using both simulation and experiment. We also adapt two algorithms for PSP using squared binary patterns, which include a Hilbert three-step PSP and a double three-step PSP. Both algorithms can increase phase accuracy, with the latter featuring additional invalid point detection. The adapted algorithms are also compared with the classical algorithms. Based on our analysis and comparison results, proper algorithm selection can be easily made according to the practical requirement.

Recent progress in see-through three-dimensional displays using holographic optical elements [Invited].

Abstract: The principles and characteristics of see-through 3D displays are presented. We especially focus on the integral-imaging display system using a holographic optical element (IDHOE), which is able to display 3D images and satisfy the see-through property at the same time. The technique has the advantage of the high transparency and capability of displaying autostereoscopic 3D images. We have analyzed optical properties of IDHOE for both recording and displaying stages. Furthermore, various studies of new applications and system improvements for IDHOE are introduced. Thanks to the characteristics of holographic volume grating, it is possible to implement a full-color lens-array holographic optical element and conjugated reconstruction as well as 2D/3D convertible IDHOE. Studies on the improvements of viewing characteristics including a viewing angle, fill factor, and resolution are also presented. Lastly, essential issues and their possible solutions are discussed as future work.

Double-pulse 2-μm integrated path differential absorption lidar airborne validation for atmospheric carbon dioxide measurement.

Abstract: Field experiments were conducted to test and evaluate the initial atmospheric carbon dioxide (CO2) measurement capability of airborne, high-energy, double-pulsed, 2-μm integrated path differential absorption (IPDA) lidar. This IPDA was designed, integrated, and operated at the NASA Langley Research Center on-board the NASA B-200 aircraft. The IPDA was tuned to the CO2 strong absorption line at 2050.9670 nm, which is the optimum for lower tropospheric weighted column measurements. Flights were conducted over land and ocean under different conditions. The first validation experiments of the IPDA for atmospheric CO2 remote sensing, focusing on low surface reflectivity oceanic surface returns during full day background conditions, are presented. In these experiments, the IPDA measurements were validated by comparison to airborne flask air-sampling measurements conducted by the NOAA Earth System Research Laboratory. IPDA performance modeling was conducted to evaluate measurement sensitivity and bias errors. The IPDA signals and their variation with altitude compare well with predicted model results. In addition, off-off-line testing was conducted, with fixed instrument settings, to evaluate the IPDA systematic and random errors. Analysis shows an altitude-independent differential optical depth offset of 0.0769. Optical depth measurement uncertainty of 0.0918 compares well with the predicted value of 0.0761. IPDA CO2 column measurement compares well with model-driven, near-simultaneous air-sampling measurements from the NOAA aircraft at different altitudes. With a 10-s shot average, CO2 differential optical depth measurement of 1.0054±0.0103 was retrieved from a 6-km altitude and a 4-GHz on-line operation. As compared to CO2 weighted-average column dry-air volume mixing ratio of 404.08 ppm, derived from air sampling, IPDA measurement resulted in a value of 405.22±4.15 ppm with 1.02% uncertainty and 0.28% additional bias. Sensitivity analysis of environmental systematic errors correlates the additional bias to water vapor. IPDA ranging resulted in a measurement uncertainty of <3 m.

Freeform illumination optics construction following an optimal transport map.

Abstract: We present a modified optimal transport (OT) ray-mapping approach for designing freeform illumination optics. After mapping the source intensity into a virtual irradiance distribution under stereographic projection, we employ an advanced OT map computation method with the ability to tackle nonstandard boundary conditions. Following the computed map, we construct the freeform optical surface directly from normal vectors by requiring that the chord between two adjacent points is perpendicular to the average of the two normal vectors at these two points and enforcing this relationship with a least squares method. Examples of designing freeform lenses for LED sources show that we can produce various uniform illumination patterns with high optical efficiencies.

Passively Q-switched erbium-doped fiber laser at C-band region based on WS₂ saturable absorber

Abstract: We demonstrate a Q-switched erbium-doped fiber laser using tungsten disulfide (WS₂) as a saturable absorber. The WS₂ is deposited onto fiber ferrules using a drop-casting method. Passive Q-switched pulses operating in the C-band region with a central wavelength of 1560.7 nm are successfully generated by a tunable pulse repetition rate ranging from 27.2 to 84.8 kHz when pump power is increased from 40 to 220 mW. At the same time, the pulse width decreases from a maximum value of 3.84 μs to a minimum value of 1.44 μs. The signal-to-noise ratio gives a stable value of 43.7 dB. The modulation depth and saturation intensity are measured to be 0.99% and 36.2 MW/cm², respectively.

High-speed (20 kHz) digital in-line holography for transient particle tracking and sizing in multiphase flows.

Abstract: High-speed (20 kHz) digital in-line holography (DIH) is applied for 3D quantification of the size and velocity of fragments formed from the impact of a single water drop onto a thin film of water and burning aluminum particles from the combustion of a solid rocket propellant. To address the depth-of-focus problem in DIH, a regression-based multiframe tracking algorithm is employed, and out-of-plane experimental displacement accuracy is shown to be improved by an order-of-magnitude. Comparison of the results with previous DIH measurements using low-speed recording shows improved positional accuracy with the added advantage of detailed resolution of transient dynamics from single experimental realizations. The method is shown to be particularly advantageous for quantification of particle mass flow rates. For the investigated particle fields, the mass flows rates, which have been automatically measured from single experimental realizations, are found to be within 8% of the expected values.

Overview of Advanced LIGO adaptive optics.

Abstract: This is an overview of the adaptive optics used in Advanced LIGO (aLIGO), known as the thermal compensation system (TCS). The TCS was designed to minimize thermally induced spatial distortions in the interferometer optical modes and to provide some correction for static curvature errors in the core optics of aLIGO. The TCS is comprised of ring heater actuators, spatially tunable CO2 laser projectors, and Hartmann wavefront sensors. The system meets the requirements of correcting for nominal distortion in aLIGO to a maximum residual error of 5.4 nm rms, weighted across the laser beam, for up to 125 W of laser input power into the interferometer.

Two-dimensional phase unwrapping using the transport of intensity equation.

Abstract: We report a method for two-dimensional phase unwrapping based on the transport of intensity equation (TIE). Given a wrapped phase profile, we generate an auxiliary complex field and propagate it to small distances to simulate two intensity images on closely spaced planes. Using the longitudinal intensity derivative of the auxiliary field as an input, the TIE is solved by employing the regularized Fourier-transform-based approach. The resultant phase profile is automatically in the unwrapped form, as it has been obtained as a solution of a partial differential equation rather than as an argument of a complex-valued function. Our simulations and experimental results suggest that this approach is fast and accurate and provides a simple and practical solution for routine phase unwrapping tasks in interferometry and digital holography.

Comparative analysis of autofocus functions in digital in-line phase-shifting holography.

Abstract: Numerical reconstruction of digital holograms relies on a precise knowledge of the original object position. However, there are a number of relevant applications where this parameter is not known in advance and an efficient autofocusing method is required. This paper addresses the problem of finding optimal focusing methods for use in reconstruction of digital holograms of macroscopic amplitude and phase objects, using digital in-line phase-shifting holography in transmission mode. Fifteen autofocus measures, including spatial-, spectral-, and sparsity-based methods, were evaluated for both synthetic and experimental holograms. The Fresnel transform and the angular spectrum reconstruction methods were compared. Evaluation criteria included unimodality, accuracy, resolution, and computational cost. Autofocusing under angular spectrum propagation tends to perform better with respect to accuracy and unimodality criteria. Phase objects are, generally, more difficult to focus than amplitude objects. The normalized variance, the standard correlation, and the Tenenbaum gradient are the most reliable spatial-based metrics, combining computational efficiency with good accuracy and resolution. A good trade-off between focus performance and computational cost was found for the Fresnelet sparsity method.

Frequency-tunable metamaterial absorber using a varactor-loaded fishnet-like resonator.

Abstract: A frequency-tunable metamaterial absorber is designed with the unit cell consisting of a varactor-loaded fishnet-like resonator This geometry allows all cathode and anode pads of the unit cells to be connected to their counterparts Hence, only the ends of the periodic structure need to be biased, reducing the complexity of the bias network The absorber was modeled using a full-wave simulation tool and verified experimentally with a 20×20 unit-cell prototype Using free-space measurements, the absorber shows >90% absorption ratio from 396 to 529 GHz with a frequency tuning ratio of 287%, when the reverse voltage varied from 0 to 19 V

Low-loss and bend-insensitive terahertz fiber using a rhombic-shaped core.

Abstract: A novel porous-core photonic crystal fiber is presented, and its guiding properties are numerically investigated by using the finite element method. It is demonstrated that by introducing a rhombic-shaped core made of circular air holes inside the conventional hexagonal cladding, it is possible to obtain very low bending loss of 3.04×10−11 cm−1 at the operating frequency of 1.0 THz. In addition to this, low effective material loss of 0.089 cm−1 and very small confinement loss of 1.17×10−3 dB/cm are achieved for optimal design parameters. Other guiding properties, including effective area, dispersion, and higher order mode characteristics are also discussed thoroughly. The design of this porous fiber is relatively simple, since it contains fewer air holes and consists of circular air holes only. Due to promising wave-guiding properties, the proposed fiber would have a great potential for terahertz imaging and flexible communication applications.

Off-axis three-mirror freeform telescope with a large linear field of view based on an integration mirror

Abstract: We report on the design of an off-axis three-mirror freeform telescope with a large field of view (FOV) based on an integration mirror (IM). This design is the continuation of the authors’ previous work. Based on aberration theory, we established a suitable nonrelayed three-mirror-anastigmat initial configuration for integration mirror design. For an optical freeform surface, we analyzed the qualitative aberration correction ability of a x-y polynomial surface that can provide a simple, convenient, and user-friendly relationship between freeform surface term coefficients and aberrations and then applied the x-y polynomial surface on the tertiary mirror to improve the system optimization degrees of freedom. In an example with a focal length of 1200 mm, an F-number of 12, and a FOV of 1°×30°, the tolerance performance was analyzed, and the system presented a good imaging performance. In addition, the IM structure and opto-mechanics support structure were designed and analyzed. The confirmatory design results showed that the integration of the primary mirror and tertiary mirror can improve opto-mechanical properties judged by multiple criteria. In conclusion, the integration of the primary mirror and tertiary mirror not only offers alignment convenience as described previously but also improves system opto-mechanical properties in multiple perspectives. We believe this large linear FOV system based on IM has broad future applications in the optical remote sensing field.

Increasing signal amplitude in fiber Bragg grating detection of Lamb waves using remote bonding.

Abstract: Networks of fiber Bragg grating (FBG) sensors can serve as structural health monitoring systems for large-scale structures based on the collection of ultrasonic waves. The demodulation of structural Lamb waves using FBG sensors requires a high signal-to-noise ratio because the Lamb waves are of low amplitudes. This paper compares the signal transfer amplitudes between two adhesive mounting configurations for an FBG to detect Lamb waves propagating in an aluminum plate: a directly bonded FBG and a remotely bonded FBG. In the directly bonded FBG case, the Lamb waves create in-plane and out-of-plane displacements, which are transferred through the adhesive bond and detected by the FBG sensor. In the remotely bonded FBG case, the Lamb waves are converted into longitudinal and flexural traveling waves in the optical fiber at the adhesive bond, which propagate through the optical fiber and are detected by the FBG sensor. A theoretical prediction of overall signal attenuation also is performed, which is the combination of material attenuation in the plate and optical fiber and attenuation due to wave spreading in the plate. The experimental results demonstrate that remote bonding of the FBG significantly increases the signal amplitude measured by the FBG.

Single-shot absolute 3D shape measurement with Fourier transform profilometry

Abstract: Fourier transform profilometry (FTP) is one of the frequently adopted three-dimensional (3D) shape measurement methods due to its ability to recover single-shot 3D shapes, yet it is challenging to retrieve the absolute phase map solely from one single grayscale fringe image. This paper presents a computational framework that overcomes this limitation of FTP with digital fringe projection (DFP). By using geometric constraints, an absolute phase map can be retrieved point-by-point from one single grayscale fringe image. Experiments demonstrate the success of our proposed framework with single-shot absolute 3D shape measurement capability.

Infrared spectrum blind deconvolution algorithm via learned dictionaries and sparse representation

Abstract: Band overlap and random noise are a serious problem in infrared spectra, especially for aging spectrometers. In this paper, we have presented a simple method for spectrum restoration. The proposed method is based on local operations, and involves sparse decompositions of each spectrum piece under an evolving overcomplete dictionary, and a simple averaging calculation. The content of the dictionary is of prime importance for the deconvolution process. Quantitative assessments of this technique on simulated and real spectra show significant improvements over the state-of-the-art methods. The proposed method can almost eliminate the effects of instrument aging. The features of these deconvoluted infrared spectra are more easily extracted, aiding the interpretation of unknown chemical mixtures.

Aero-optical effects of an optical seeker with a supersonic jet for hypersonic vehicles in near space.

Abstract: The aero-optical effects of an optical seeker with a supersonic jet for hypersonic vehicles in near space were investigated by three suites of cases, in which the altitude, angle of attack, and Mach number were varied in a large range. The direct simulation Monte Carlo based on the Boltzmann equation was used for flow computations and the ray-tracing method was used to simulate beam transmission through the nonuniform flow field over the optical window. Both imaging displacement and phase deviation were proposed as evaluation parameters, and along with Strehl ratio they were used to quantitatively evaluate aero-optical effects. The results show that aero-optical effects are quite weak when the altitude is greater than 30 km, the imaging displacement is related to the incident angle of a beam, and it is minimal when the incident angle is approximately 15°. For reducing the aero-optical effects, the optimal location of an aperture should be in the middle of the optical window.