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The wavefront distortion caused by atmospheric turbulence seriously affects the performance of free-space optical communication (FSOC) system. Adaptive optics (AO) technology has been proven to be an effective method to suppress atmospheric turbulence. Two laser communication terminals equipped with AO system are designed and manufactured, which are used in the horizontal link near the ground. In the laboratory simulation, 100-Gbps data transmission can be realized under moderate turbulence (D / r0 10), and the BER is better than 1 × 10 − 6. The BER is high in the practical communication test under the urban horizontal link of 1 km (D / r0 = 10), the BER is 1 × 10 − 3, and the coupling efficiency is 12% to 20%. Finally, to achieve the goal of 100-Gbps FSOC for near ground and long distance, based on the experimental performance of the existing two sets of laser communication system, the solution of laser communication system is proposed, which provides a reference for relevant researchers.

We present a theoretical study and simulation of an adaptive modal liquid crystal lens (AMLCL) where the magnitude and distribution of the surface resistance in the modal layer can be manipulated via radiation. The modal layer of the presented AMLCL is composed of various semiconductor materials that, consequently, define its surface resistance. To modulate the magnitude and distribution of its surface resistance via radiation, a photoconductive layer can be added to the modal layer. We model an AMLCL with 5-mm aperture and 20-μm thickness theoretically. The results show that the lens reaches its maximum optical power at a surface resistance of 160 MΩ / □ and a driving voltage of 6 V for a frequency fixed at 1 kHz, which is in close agreement with a previously reported experiment. The effect of irradiation with a Gaussian beam on the optical power of the AMLCL is analyzed for different beam waists. Results indicate that the optical power of the lens increases by 15% and remains constant until the beam waist of the pump light reaches 70% of the aperture diameter. At the same time, AMLCL aberration is reduced by 10%. The optical power decreases rapidly when the beam waist exceeds 70% of the aperture diameter.

A method of fine pointing of laser beams using laser arrays has been developed. The telescope system combines a lens system and a vertical cavity surface emitting laser/photodetector array. It does not use moving parts. In computer simulations, it is applied to CubeSats satellites that use body pointing. Body pointing was used by the Aerospace Corporation for CubeSats in LEO at 450 km in NASA’s Optical Communications and Sensors Demonstration (OCSD) program. Computer simulations of this fine pointing capability have been applied previously to CubeSats in the OCSD program. Computer simulations of this laser pointing are applied to CubeSats in LLO at 100 km. With more accurate pointing, a laser beam with smaller divergence can be used. For the case of the AeroCube-7B vehicle that was used in the OCSD program, computer simulations show, for example, that the divergence of the output beam can be reduced from ∼0.06 deg to 0.014 deg. For the proposed electro-optical system, reaction times to pointing changes and vibrations are on a nanosecond time scale, much faster than those for fine pointing systems that use moving parts, such as fast steering mirrors or that use quad-cell photodetectors to improve the body pointing of the CubeSat.

Recent research in augmented reality (AR) eyewear has prompted interest in using volume holographic optical elements for this application. However, many sensing operations in AR systems require the use of wavelengths in the near-infrared (NIR) (750 to 900 nm). These wavelengths typically exceed the sensitivity range of available commercial holographic recording materials (450 to 650 nm), which complicates the design of optical elements with power since significant aberrations result when the reconstruction wavelength differs from the construction wavelength. Several methodologies for designing a waveguide hologram imaging system in NIR are reviewed and evaluated. The design approach presented in our work integrates the most effective practices such as fabrication point source location optimization and aberration analysis to realize effective holographic waveguide couplers formed with visible wavelength light and reconstructed in the NIR. The technique is demonstrated by designing and fabricating an input waveguide hologram in conjunction with a multiplexed output coupling hologram. The resulting input/output waveguide holograms can achieve an image resolution of (∼3 lp / mm) with a 0.6-mm-thick glass substrate that has a refractive index of 1.8.

A design of high-precision 4-in. transmission spheres that can work in wide-band interferometric measurement is proposed. A motorized precision rotation mount is used to drive one of the lenses in the design to make the transmission sphere work at any wavelength in the wavelength range of 532 to 1550 nm, where the F-number of the transmission sphere remains constant during the movement of the lens. OpticStudio software is utilized to verify the design under F-numbers of 1.0, 2.2, and 3.3, and the results show that a transmission sphere with an F-number of 1.0 to 3.3 can be designed based on our model. The tolerance analysis and the secondary adjustment results show that the peak-to-valley transmission wavefront error of the transmission sphere can be controlled within λ / 20 in actual machining and assembly, which meets the requirement of high-precision interferometric measurement.

Imaging of transparent phase samples using a wire grid polarizer (WGP)-based shearing interferometer is demonstrated. The proposed setup employs a WGP as a beam splitter in a triangular cyclic interferometer setup, so that the two counterpropagating beams are rendered linearly polarized in orthogonal directions as they emerge from the interferometer. These sheared waved fronts are made to pass through the phase sample. The magnitude of shear is affected by controlled angular shifts of one mirror about the reference X and Y axes. For each of these directional shears, the polarization phase shifting is implemented so as to generate a three-dimensional phase pattern, which is digitally combined and integrated to yield the sample phase. The proposed setup is robust, sufficiently tolerant to ambient vibrations, and shows very encouraging experimental results.

The wavefront distortion caused by atmospheric turbulence leads to the decrease of the coupling efficiency of spatial light to optical fiber. Adaptive optics technology was employed to improve the coupling efficiency of free-space coherent optical communication. Accordingly, the effect of the discrete distorted wavefront on the coupling efficiency could be determined. The experimental results showed that the average coupling power was −31.97, −31.42, −30.79, −32.05, and −35.31 dBm when turbulence strength D / r0 was 0.2, 0.5, 1, 2, and 5, respectively. After eliminating the noncommon path aberration, the fiber coupling optical power increased from −35 to −27 dBm. After the optical wavefront was transmitted at indoor (0.5 m), 600 m, 1, 5, 10, and 100 km, the coupling efficiency increased from 10.1%, 1.3%, 11.4%, 2.8%, 7.2%, and 8.2% to 95.2%, 83.4%, 93.5%, 56.7%, and 42.4%, respectively, after wavefront correction. This will improve the performance of free-space coherent optical communication system.

A method based on the Zernike coefficients transformation is proposed for the wavefront sensing of a sparse aperture system. We deduce a matrix that allows the Zernike transformation between the sub-apertures’ wavefronts and the global counterparts in a sparse aperture system. With the matrix and the given global aberrations, the aberrations of the sub-apertures can be calculated through the transformation. The simulation results indicate that the increase of filling factor of the sparse aperture system could lead to the increase of orders of the Zernike polynomials, which describe the sub-aperture’s wavefront. The root mean square value of the detected Zernike coefficients of the sub-aperture is determined by its azimuth angle when the filling factor is fixed.

The atmospheric turbulence can cause wavefront distortion when vortex beam carrying orbital angular momentum (OAM) propagates in free space. This brings challenges to the recognition of OAM modes. To realize effective recognition of multichannel vortex beams in atmospheric turbulence, a hybrid interference-convolutional neural network (CNN) scheme is proposed. Here, we compare two different approaches to identify the topological charges under different turbulence levels: the first is based on CNN only and the second is the hybrid scheme of interference and CNN. The simulation shows that the recognition performance of multiple vortex beams under different turbulence levels is improved by our hybrid scheme. Compared with the traditional CNN-based method, the interference-CNN scheme can further identify the sign of topological charge. Moreover, we generalize its feasibility through different kinds of vortex beams with a radial index of p ≠ 0. This provides a versatile tool for large-capacity optical communication based on OAM modes.

A programmable ultraviolet light-emitting diode (UVLED) array with a transfer lens forms an adjustable intensity distribution upon a mask, whether for the uniform distribution or variable distribution for compensate wavefront error introduced by the lithographic lens, so as to fabricate an aberration-free pattern on a wafer. The collimating and aligning all rays in one aperture lens with a N × N two-dimensional UVLED array is designed and fabricated by integrating with lithographic lens to form aberration-free smallest linewidth in integrated circuit wafer. Our work provides a transfer lens for the UVLED array to manipulate the intensity distribution fitted for the aligner in the soft- and near-contact mode and steppers.

Gratings with low diffracted wavefront errors are crucial in many applications. Existing methods to reduce the diffracted wavefront errors of holographically produced gratings mainly address misalignment errors during exposure system adjustment, leaving the inevitable residual errors of collimation lenses uncorrected. The broad-beam scanning exposure method was recently proposed to fabricate gratings with large size and low stray light. We explore its ability to reduce the diffracted wavefront errors caused by both system misalignment and lens errors. During the exposure, the substrate translates in the direction perpendicular to the grating lines to pass through the exposure area, so the aberrations over different parts of the interference field along the scanning path are averaged. We prove the validity of this method by a theoretical analysis and numerical simulations. The averaging effect on different aberrations and with different scanning lengths is discussed. The peak-valley values of diffracted wavefront errors of gratings fabricated with an exposure field of defocus aberration and a more complicated aberration were reduced by 42.5% and 50%, respectively.

A dielectric elliptic cylinder is chosen as a nanostructure unit to design unusual deflecting metasurface and multifunctional metalens. Based on Pancharatnam–Berry (PB) phase principle, the abrupt phase change is investigated by adjusting the rotation angle of the nanostructure unit. The relationship between abrupt phase change and rotation angle is optimized. Using this relationship, we have designed different metasurface elements working in the visible-light range. The designed metasurfaces can arbitrarily control the phase of the light wave, and also convert the incident left-handed circularly polarized (LCP) and right-handed circularly polarized (RCP) light into each other. One of the designed structures is a deflecting metasurface, which can deflect incident LCP and RCP light by the same angle while the bending directions are different. By cascading multiple gradient phase metasurfaces, an innovative type of multiplex beam splitter is constructed. The other is a metalens that can converge the incident LCP light and diverge the incident RCP light. In addition, two types of bifocal metalenses are dexterously designed using alternately arranged nanostructures, which can arbitrarily control two focal lengths of each metalens. This is promising for developing nano-integrated elements and interconnection.

Structural–dimensional synthesis of laser variosystems (LVSs) for the formation of output Gaussian beam waist with smooth changes in its position and size according to a given law is considered. Synthesized variosystems can be used in setups and technological complexes with extended functionality: processing of materials, manufacturing of complex spatial configuration parts, moving micro-objects, etc. The method of automated dimensional synthesis of two-component LVSs on different operation principles with constraints on their parameters has been developed using the theory of laser optics. The method allows determining the best dimensional parameters of LVS, and in their absence, options of changing the initial data to obtain the solution of dimensional problem. Application of the method is demonstrated by examples of dimensional synthesis of LVSs of different types and extended functionality.

Hyperspectral (HS) imaging retrieves information from data obtained across broadband spectral channels. Information to retrieve is a 3D cube, where two coordinates are spatial and the third one is spectral. This cube is complex-valued with varying amplitude and phase. We consider shearography optical setup, in which two phase-shifted broadband copies of the object projections are interfering at a sensor. Registered observations are intensities summarized over spectral channels. For phase reconstruction, the variational setting of the phase retrieval problem is used to derive the iterative algorithm, which includes the original proximity spectral analysis operator and the sparsity modeling of the complex-valued object 3D cube. We resolve the HS phase retrieval problem without random phase coding of wavefronts typical for the most conventional phase retrieval techniques. We show the performance of the algorithm for object phase and thickness imaging in simulation and experimental tests. publishedVersion

We present two techniques to improve as-built miniature lenses that are defined with high-order aspheric surfaces without losing optical quality and without significantly modifying the layout of the lens. We note that miniature lenses are often defined with more aspheric coefficients than needed. This redundancy can lead to poor as-built lenses. The first technique consists of gradually reducing the number of high-order aspheric coefficients while reoptimizing the lens and maintaining the performance. The second technique consists of desensitizing the lens through a multi-configuration process where different configurations are defined and optimized at the same time. These are the nominal configuration and several perturbed configurations that include lens decenter and tilt. Both techniques are shown to work for improving as-built lenses as we show in two examples from the lens literature.

Recently, much attention has been paid to optical components with complex surfaces because they can significantly optimize the aberrations of optical systems. However, a complex surface introduces several difficulties for precise measurement. To address this challenge, we propose tilted-wave point diffraction interferometer (TPDI) for measurements of complex surfaces. TPDI combines the advantages of tilted-wave interferometry and point diffraction interferometry, thus enabling high-precision measurements of complex surfaces; moreover, this method has demonstrated good efficiency and versatility. We adopt a fiber array (FA) to generate diffractive tilted waves to compensate for the local gradient of the test specimen. Unlike the classical PDI, which focuses more on the beam quality of the on-axis diffractive wave, the proposed system requires better quality for both the on-axis and off-axis diffractive waves. Therefore, the main parameters of the FA that may introduce measurement errors are analyzed, including the end face roughness of the array, the quality of diffractive wavefronts, and the initial optical path differences. Finally, the measurement result of the high-order hyperboloid verifies that our TPDI is effective and its precision of testing a complex surface is better than λ / 37 (rms, λ = 632.8 nm).

Aspheric lenses help meet the most demanding optical requirements while the precision injection molding technique hits the target for precision and cost. We developed a method of analyzing aberration terms in the transmitted “wavefront measurement,” determined by Shack–Hartmann wavefront sensing to estimate the fabrication errors of injection-molded aspheric elements. Considering aspheric element fabrication using a small training data set and F-measure fuzzy cluster analysis, an unsupervised learning method was applied to extract typical aberration terms from the wavefront polynomial. The experimental results suggest that these aberration terms, which are related to spherical (third-, fifth-, and seventh-order) and coma (third-order) aberration terms in the transmitted wavefront polynomial expansion, can be employed to estimate the surface error and decenter, respectively, of a lens from a specific mold cavity. The sampling lenses evaluated in the proposed measuring process were collected from different mold cavities according to their total working performance in the modulated transfer function measurement for the whole camera module. The performances of the typical aberration terms were discussed by comparing to the ones obtained from an interferometer and a profilometer. The proposed method could provide high detection efficiency and can thus be applied for the quality control of aspheric elements for mobile phones, where the existing errors are mainly spherical, coma, and astigmatism aberrations.

Coherent diffractive ptychographic imaging via a modified multi-state ptychographic algorithm can be used to simultaneously detect double orbital angular momentum (OAM) modes in monochromatic bi-OAM-mode multiplexing. The wavefronts for individual vortex beams modulated by two-dimensional amplitude and temporal pulses and mixed together can be reconstructed independently. In contrast to most other OAM detection methods, this approach solves for the OAM detection in a monochromatic dynamic multi-OAM beam and can be applied as an early step in OAM mode demultiplexing.

High-resolution imaging with large ground-based telescopes is limited by atmospheric turbulence. The observed images are usually blurred with unknown point spread functions (PSFs) defined in terms of the wavefront distortions of light. To effectively remove the blur, numerical postprocessing with a good approximation of the wavefront is required. The gradient measurements of the wavefront recorded by Shack–Hartmann wavefront sensor (WFS) can be used to estimate the wavefront. A gradients measurement model for Shack–Hartmann WFS is built. This model is based on the frozen flow hypothesis and uses a least-squares-fit of tip and tilt across the subaperture in the WFS to genarate the averaged gradient measurements. Then a high-resolution wavefront reconstruction method using multiframe Shack–Hartmann WFS measurements is presented. The method uses high cadence WFS data in a Bayesian framework and takes into account the available a priori information of the wavefront phase. Numerical results show that the method can effectively improve the spatial resolution and accuracy of the reconstructed wavefront in different seeing conditions.

High speed time-resolved wavefront and imaging measurements were taken synchronously in-flight through both boundary layer and shear layer environments around the Airborne Aero-Optical Laboratory for Beam Control. Instantaneous modulation transfer functions and point spread functions (PSFs), which characterize image degradation, were generated using wavefront data. Instantaneous power-in-bucket ratios were extracted from both the image data and computed from the wavefront data, and the ratios were found to correlate well with each other. The lower power-in-bucket values and related increased blurring that occurred predominantly in the streamwise direction were associated with large-scale, large-amplitude wavefront spatial variations due to large organized vortical structures present in the shear layer. The boundary layer did not create any significant image blurring due to the low level of aero-optical distortions. Finally, spatial autocorrelation functions were extracted from the wavefront data using the stitching method and were used to compute time-averaged PSFs for different aperture diameters.

Due to the unique mechanical and optical characteristics, it is difficult to carry out experimental research and online measurement for large-aperture ICF frequency converters. To analyze and optimize the performance of the frequency converters under complex process loads, we present an integrated optomechanical method that correlates actual process loads with laser critical characteristics. Based on the established optomechanical model, the key factor that induces the loss of harmonic generation efficiency is identified. In addition, the proposed method is conductive to rapid evaluation, prediction, and optimization of comprehensive performance of frequency converters. Thereby, we propose an adaptive frequency conversion system (AFCS). The results indicate that AFCS can not only minimize the phase mismatching of second harmonic generation doubler but also significantly improve the quality of far-field focal spot.

A calibration method of shear amount based on the optical layout of point source microscope (PSM) for lateral shearing interferometric (LSI) wavefront sensor is proposed. A simulation model of quadriwave LSI is introduced to analyze the influence of the window size of the spatial filter and the shear amount on the accuracy of the shearing wavefront feature extraction (SWFE) method. Simulation results show that the accuracy of the SWFE method deteriorates at small shear amounts. The proposed calibration method makes use of the optical layout of PSM to generate spot images of the point source at the detector plane of the sensor itself. The shear amount is calibrated by the relationship between the lateral distance of the spot images and the distribution of the diffraction orders of the grating. In the experiments, an SID4 wavefront sensor and a circular-aperture modified Hartmann mask LSI wavefront sensor are calibrated by the proposed method. A phase plate etched with patterns has been manufactured as the test specimen. The etching depth is characterized by the two wavefront sensors, and the testing results are compared with that by a commercial ZYGO® interferometer. The feasibility and accuracy of the proposed calibration method are validated. This calibration method provides an easily conducted approach for calibrating the shear amount of LSI wavefront sensor with high accuracy.

The single collimating lens-based dual-beam exposure system is a holographic exposure system that is suitable for fabricating long-period gratings. The interference wavefront aberration in this system requires optimization. We analyzed the coma of a single collimating lens-based dual-beam exposure system, and the linear relationships between the coma and the positions of the pinholes and substrate are obtained. Based on these relationships, we can eliminate the coma by adjusting the pinholes or substrate along the optical axis of the collimating lens. Consequently, the defocus aberration, astigmatism, low-order spherical aberration, and coma are all simultaneously optimized by adjusting the exposure system to meet the pinhole symmetry condition and coma optimization condition. Because the optimized interference wavefront aberration includes only high-order aberrations with low peak to valley values, a high-quality exposure wavefront can be obtained. Furthermore, a 5-μm period grating exposure system is constructed with a spherical collimating lens of 0.6λ spherical aberration. Through the optimization process, a low spacing error of ∼0.04λ within an aperture of 65 × 65 mm2 is achieved (the theoretical value is 0.002λ).

Spatial interpolation using radial basis functions (RBFs) is compared with standard natural neighbor interpolation for the purpose of populating dead zones in optical path difference (OPD) wavefront data collected through aero-optics turbulence. Both methods, and some other commonly used basis functions, are described in detail. These candidates are applied to experimental subscale turbulent wind tunnel data collected with a conformal window hemispherical turret over a range of turret look-back angles spanning 60 deg to 135 deg. Interpolation performance is evaluated using both OPD magnitude and fractal (Hurst exponent) analysis. Interpolating aero-optical OPDs using the thin-plate RBF reduces the symmetric mean absolute percent error of the OPD magnitude and the Hurst exponent by an average of 28% and 50%, respectively, compared with the natural neighbor interpolation method. The improved interpolation accuracy should likewise increase the quality of subsequent postprocessing analysis requiring uniformly populated rectangular regions as inputs, such as optical flow algorithms. A MATLAB implementation of the pseudocubic spline RBF is provided.

Pupil densification is a technique to improve contrast in a direct imaging interferometer. By enlarging the size of each aperture in a sparse array, the fraction of energy contained in the central point spread function peak can be increased. However, the effective field of view is reduced as the contrast improves. Our work investigates the optimal strategy for pupil densification in the context of extended source imaging. Analytical expressions are derived to optimize the signal-to-noise ratio at the edge of the field of view for a variety of hypertelescope configurations. Free-space beam transport and fiber-optic beam transport are both considered. The relative advantages and disadvantages between the considered hypertelescope configurations are discussed.

Traceable, highly accurate calibration of wavefront sensors such as Shack–Hartmann sensors is a challenging task and an active field of research. We have developed a measurement system for the traceable calibration of wavefront sensors employing spherical wavefronts and a point light source in combination with a three-axis linear stage. We obtain an absolute calibration of sensor errors, including the reference spot position and wavefront gradient-dependent errors for each microlens individually. We discuss the main error influences and present an initial measurement uncertainty budget for the calibration. The calibration can be performed with an expanded measurement uncertainty (95% coverage interval) of better than 5 μrad for the wavefront gradient deviation.

A technique for providing neural network-coached alignment of optical systems is described in detail. The goal is to increase the speed of convergence to an aligned optical system. The neural network model is trained with the wavefront errors (WFEs) of thousands of randomly misaligned instances of the lens system that are modeled in Zemax OpticStudio®. The optical specialist measures the WFE of the misaligned system, then a neural network suggests specific adjustments to be made to the alignment fixturing (which adjuster, which direction, and by what amount). The technique has been developed into a MATLAB®-based tool called rapid optical system alignment with neural network assist that is shown to analytically and experimentally increase the speed of alignment. It is capable of achieving WFEs that are within a few percent of the nominally aligned condition. The ultimate goal is to deploy such a tool to enable an optical specialist to more quickly align challenging optical systems employing freeform or segmented surfaces. Analytical and experimental results for spherically symmetric systems are shown along with an outline of future work.

A method for designing a metalens with electrically tunable focal length is proposed and analyzed. Metasurfaces are defined as low-thickness devices to initiate and generate the abrupt electromagnetic wavefront variation. However, there is no way to control them actively. Our research proposes the design of a metalens that consists of cross-shaped apertures (CSAs) in a gold film and a graphene layer. The CSAs have different lengths and rotation angles. By applying bias voltage to graphene, the focal length can be varied and controlled electrically. When the Fermi energy of the graphene changes from 0.1 to 0.5 eV, the focal length changes from 10.5 to 12.67 mm. The structure is simulated by the finite-difference time-domain numerical method. By splitting graphene layers to several parts and biasing each of them with different bias voltages, the transmitted focused beam could be rotated up to 35 deg. As an application of the metalens device, a refractive index sensor with sensitivity of 80 μm per refractive index unit (μm / RIU) is proposed.

An experiment was conducted to study turbulence along a 149-km path between the Mauna Loa and Haleakala mountain tops using digital cameras and light-emitting diode (LED) beacons. Much of the path is over the ocean, and a large portion of the path is 3 km above sea level. On the Mauna Loa side, six LED beacons were placed in a roughly linear array with pair spacings from 7 to 62 m. From the Haleakala side, a pair of cameras separated by 83.8 cm observed these beacons. Turbulence along the path induces tilts on the wavefronts, which results in displacements of the LED spots in the images. The image motion is caused by unwanted noise sources such as camera platform motion. Differential motion between spots cancels much of this noise, and this differential motion is weighted by the turbulence along the path in different ways depending on the geometry between the sources and the cameras. A camera motion insensitive weighting function is developed to deal with this observational issue. A linear combination of these weighting functions is then used to generate a composite weighting function, which better rejects turbulence near the sources and receivers and is most sensitive to turbulence in the portion of the path out over the ocean. This technique is used to estimate turbulence in this region. The long range involved caused very strong scintillation in the image, which added new challenges to the data processing. A resulting estimate for Cn2 of 4 × 10 − 17 m − 2 / 3 is in good agreement with the Hufnagel–Valley HV5/7 model and the results of numerical weather modeling.

Holo-shear lens-based interferometer is demonstrated to study the influence of gradient magnetic fields (i.e., upward decreasing and upward increasing) and uniform magnetic field on the temperature and temperature profile of a wick stabilized micro diffusion flame created from the candle. Sheared interferograms in the absence and presence of microflame are captured using CCD camera. Fourier fringe analysis method is used to extract the phase-gradient information of ambient air without flame and heated air of microflame separately. The phase difference map of microflame and ambient air is used for the extraction of refractive index difference and temperature distribution inside the microflame. The experimental investigations reveal that temperature and temperature stability of the microflame increase in the upward decreasing and uniform magnetic field, while the temperature and temperature stability inside the microflame decrease in upward increasing magnetic field in comparison to temperature inside the microflame in the absence of magnetic field. Increment in the temperature of the microflame in uniform magnetic field is contrary to macro diffusion flame, where there is a negligible influence on the temperature in uniform magnetic field. Holo-shear lens-based interferometer is simple, lightweight, easy to implement, less vibration-sensitive, and can cover microflame to macroflame under investigation.

Optical metrology is a critical and complex technique for the fabrication of precision optics in which the surface figure is better than peak-to-valley 1 / 10λ or RMS 1 / 30λ. Careful calibration of the intrinsic system errors of the experimental setup, including the alignment error of the metrology tool and the manufacturing error of the reference optics, should be performed. However, any surface deformation caused by the mounting supporter or a gravity effect can result in an incorrect surface figure correction, especially in mid-to-large optics. The system error of the experimental setup and deformation by external conditions of the optics, such as temperature drift, air turbulence, and vibration, affect the measured result. In the proposed method, the magnitude and phase of all nonrotationally symmetrical Zernike coefficients were obtained through multiple measurements by rotating the optics. These coefficients were used to analyze absolute low-spatial frequency figures. To verify the reproducibility of the proposed method, three metrology tools with distinct measurement methods were used to obtain surface figures and the results were then compared.

Transverse translation-diverse phase retrieval (TTDPR), a ptychographic wavefront-sensing technique, is a viable method for freeform optical surface metrology due to its relatively simple hardware requirements, flexibility, and demonstrated accuracy in other fields. In TTDPR, a subaperture illumination pattern is scanned across an optic under test, and the reflected intensity is gathered on an array detector near focus. A nonlinear optimization algorithm is used to reconstruct the wavefront aberration at the test surface from which we can solve for surface error, using intensity patterns from multiple scan positions. TTDPR is an advantageous method for aspheric and freeform metrology because measurements can be performed without null optics. We report on the development of a concave freeform mirror measurement using this technique. Simulations were performed to test algorithmic performance as a function of various parameters, including detector signal-to-noise ratio and position uncertainty of the illumination, with

Long-range optical imaging applications are typically hindered by atmospheric turbulence. The effect of turbulence on an imaging system can manifest itself as an image blur effect usually quantified by the phase distortions present in the system. The blurring effect can be understood on the basis of the measured strength of atmospheric optical turbulence along the propagation path and its impacts on phase perturbation statistics within the imaging system. One method for obtaining these measurements is by the use of a dynamically ranged Rayleigh beacon system that exploits strategically varied beacon ranges along the propagation path, effectively obtaining estimates of the aberrations affecting an optical imaging system. We developed a method for extracting tomographic turbulence strength estimations from a dynamically ranged Rayleigh beacon system that uses a Shack–Hartmann sensor as the phase measurement device. The foundation for extracting tomographic information from strategically range-varied beacon measurements obtained in rapid sequence is presented along with modeled example cases for typical turbulence scenarios. Additionally, the processing algorithm was used to simulate identification of isolated strong turbulence layers. We present the chosen processing algorithm’s foundation and provide discussion of the utility of this algorithm as an atmospheric turbulence profiling methodology.

Wavefront aberration measurements are required to test an extreme ultraviolet (EUV) imaging system. For a high-NA EUV imaging system, where conventional wavefront-sensing techniques show limitations, ptychography can be used for this purpose. However, at the wavelength region of EUV (i.e., 13.5 nm), the position accuracy of the scanning mask that is defined for ptychography is stringent. Therefore, we propose ptychography combined with mask position correction. The simulated intensity patterns, the ones we use, resemble expected EUV experimental data. Finally, we show the results in the presence of Poisson noise and the tolerance of the position correction method for error in mask positions.

Spot location algorithms greatly influence the wavefront measurement error of the Shack–Hartmann wavefront sensor. Based on numerical simulations and experiments, we compare the wavefront reconstruction error of several spot location algorithms under different signal-to-noise ratio (SNR) conditions. We solve the problem of how to select the most suitable spot location algorithm and optimal parameters under different SNR conditions, which mimic the realistic working environment of the adaptive optics system changes. We find the optimal threshold and optimal window setting rules of the center of gravity (COG), intensity weighted centroiding, and weighted center of gravity (WCOG) algorithms. The correctness of our recommendation of spot location algorithms under different SNR conditions is supported by numerical simulations and experiments. We find that when the SNR is extremely low, that is the SNR is lower than 2, the cross-correlation algorithm and the thresholding WCOG algorithm are the best choices. When the SNR is moderately low, that is the SNR ranges from 2 to 10, the best choice is the thresholding WCOG algorithm. When the SNR is high, that is, the SNR is higher than 10, the simple algorithm of thresholding COG is the best choice.

The shear ratio is an essential parameter of the lateral shearing interferometry system that affects dynamic range, signal-to-noise ratio, and accuracy. Some qualitative conclusions about the shear ratio’s influence can be found in existing reports, but no systematical analysis or quantified universal conclusion has been given. Using the sheared phase to reconstruct wavefront is the unique feature of the shearing interferometry, but it also affects the measurement accuracy significantly. The wavefront reconstruction methods can be divided into zonal and modal methods. We use the FFT reconstruction method and the least-square reconstruction method as the typical methods of modal and zonal methods to analyze the source of the reconstruction error and its relationship with the shear ratio. We conclude that the FFT reconstruction method and the least-square reconstruction method are equivalent to each other. The lost information during the shearing corresponds to some incalculable spectral values in the frequency domain and the pistons of different subgrids in the spatial domain. More spectral information will be lost if the shear ratio increased, which leads to more significant reconstruction errors. When the shear ratios are 1.6% and 6.3%, the corresponding relative reconstruction errors are about 1% and 1%, respectively. The error will be lower if the test wavefront can be represented by a limited amount of basis functions.

We present validation of a tilt angle illumination technique for height maps’ reconstruction using digital holography and propose a few solutions for improvement of the inclined probe wave front approach. The general algorithm of tilt angle digital holography approach is described and validated in experimental monitoring of a coin relief. Several approaches of height map quality improvement concerning tilt angle estimation, relation between measurement accuracy and dynamic range, and selective averaging algorithm are proposed and discussed.

Adaptive optics, beam-shaping, wavefront correction, or modification with spatial light modulators (SLMs) has been done for many years. Most of the systems used in these techniques control the change in the wavefront by using a wavefront sensor placed in a plane optically conjugated with the SLM. We present a method, specially developed for these kinds of systems, for easily aligning the phase projected on the SLM. The method is based on the minimization of the undesired Zernike coefficients generated when the phase element projected in the SLM is displaced or rotated with respect to the reference frame of the optical system. Owing to the proposed method, we were able to detect and correct a rotation of the SLM of 1.42 deg and center the projected phase with a precision equal to the size of the pixel of the SLM (8 μm in our experiment).

We discuss over three decades of progress in nonmechanical beam steering, provide a comparison of approaches being developed, and comment on promising approaches not yet fully developed. Most of the work in nonmechanical beam steering has been for narrowband optical systems, but a brief discussion is provided of broadband. The majority of the nonmechanical approaches to beam steering create a tilted optical path delay (OPD) to change the wavefront, but some directly create a phase delay. OPD-based approaches may be true time delay, with no resets or modulo 2π n optical phased arrays that have resets. Most of the nonmechanical optical beam steering approaches tilt an existing wavefront and are called space fed approaches, because the beam is already formed when the wavefront is tilted. For the majority of radar nonmechanical beam steering, the tilted wavefront is formed by individual transmit/receive modules. Periodic structures (gratings) spread different wavelengths of light in angle, thus steering light, and are also used for nonmechanical steering. Our paper is derived from a conference paper presented at Photonics West in February 2019.

We introduce a technique for recording volume holographic optical elements (vHOEs) designed for operation at a wavelength different from the recording wavelength. This technique relies on our holographic wave front printer, which employs two spatial light modulators for recording wave front generation. We present the procedure for computing the required recording wave fronts accurately and noniteratively from the desired vHOE optical transformation function. We exploit this technique for the fabrication of a converging lens vHOE with an operation wavelength of 915 nm at a recording wavelength of 515 nm. Finally, we demonstrate the holographic lens functionality directly in the infrared spectral region.

To improve the performance of wireless laser communication (WLC) systems, wavefront sensorless adaptive optics based on deformable mirror (DM) eigenmodes was used to correct the distorted far-field spot. A set of DM eigenmodes conforming to the derivative–orthogonal relationship is derived, and the system simulation model under different atmospheric turbulence intensities is established by combining Fresnel diffraction and multiphase screen transmission principle. The influence of mode bias on the correction effect is analyzed. The ability of the proposed method to correct the distorted far-field spot was studied by using Strehl ratio (SR) as the evaluation index. The influence of the proposed method on the coupling efficiency of single-mode fiber and bit error rate performance of the WLC system is discussed. Indoor and outdoor experimental systems were built. The indoor experiment results show that the proposed method can increase the SR of the system from 0.11, 0.32, and 0.56 to 0.57, 0.71, and 0.88, respectively. The outdoor experiment results show that the proposed method can effectively correct the wavefront distortion caused by dynamic atmospheric turbulence.

Digital micromirror devices (DMDs) have become ubiquitous as spatial light modulators in the optics community, but ambiguity remains on how best to implement them in a laboratory environment. Here, we explicitly tackle the problem of generating high fidelity modes of structured light while maintaining optical efficiency. We present a theoretical characterization of the diffractive properties of the DMD, allowing us to motivate an alignment procedure that improves optical efficiency. We also present a set of best practice recommendations that cover aspects of DMD operation that are not immediately intuitive, these best practice recommendations ensure structured light is generated with the correct spatial profile and wavefront. We present experimental results that show efficiency improvements of up to 20%. Further, we demonstrate the creation of modes of structured light with fidelities in excess of 96%. The best practices presented here provide a pragmatic set of procedures for ensuring DMDs are used to their fullest potential.

A common-path spatial phase shifting digital speckle pattern shearing interferometry setup is introduced for simultaneous measurement of in-plane and out-plane strain components under dynamic loading using two laser beams with different wavelengths that symmetrically illuminate the test object and a single detector. The simplicity, stability, and efficiency of the arrangement are provided by using a glass plate as a shearing device, which is capable of tuning the sensitivity continuously. The phase is recovered from a single frame by the Fourier method. In this setup, the spatial carrier frequencies can be adjusted independent of the amount of the lateral shear. Ultimately, the desired field of view can easily be achieved by simple imaging optics. To validate the feasibility and the flexibility of our technique, the proposed setup is used to evaluate the in-plane and out-plane strain maps of an aluminum plate, which is deformed under dynamic stress in its plane. The temporal phase stability of the proposed system is also investigated.

At present, new approaches for the use of drones in high-precision optical applications are rising, especially with those known as multirotor. However, the optical turbulence effects generated by multirotor drones are not entirely understood. These optical effects can reduce the performance of the optical instruments that they transport. We present measurements of the wavefront deformation generated by the temperature fluctuations and the airflow of a drone’s propulsion system. To do so, we used a single arm of a DJI S800 EVO Hexacopter (professional drone) and measured its operating temperature with a commercial infrared camera. The resulting temperature variation, between a switched-off propulsion system at room temperature and one running at its maximum performance, was 34.2°C. Later, we performed two different interferometric tests: Takeda’s method and the phase-shifting technique, using a ZYGO interferometer. These tests show that the total deformation over an incident wavefront to the propeller airflow is lower than 0.074 λ PV and 0.007 λ RMS (HeNe laser, λ = 633 nm). We determine that the optical turbulence produced by a drone propulsion system is negligible.

Rectangular pupils are employed in many optical applications such as lasers and anamorphic optics, as well as for detection and metrology systems such as some Shack−Hartmann wavefront sensors and deflectometry systems. For optical fabrication, testing, and analysis in the rectangular domain, it is important to have a well-defined set of polynomials that are orthonormal over a rectangular pupil. Since we often measure the gradient of a wavefront or surface, it is necessary to have a polynomial set that is orthogonal over a rectangular pupil in the vector domain as well. We derive curl (called C) polynomials based on two-dimensional (2-D) versions of Chebyshev polynomials of the first kind. Previous work derived a set of polynomials (called G polynomials) that are obtained from the gradients of the 2-D Chebyshev polynomials. We show how the two sets together can be used as a complete representation of any vector data in the rectangular domain. The curl polynomials themselves or the complete set of G and C polynomials has many interesting applications. Two of those applications shown are systematic error analysis and correction in deflectometry systems and mapping imaging distortion.

The tilted wave interferometer has been developed as a fast and accurate instrument for the measurement of aspheric and freeform surfaces. We present a method for increasing its robustness and flexibility. Tilted wave interferometry crucially depends on accurate calibration and any changes to a calibrated setup require, in general, a recalibration. Therefore, we propose a method for simultaneous topography reconstruction and elimination of errors arising from such changes. An approach to identify trends in systematic errors for the complex non-null setup with a large number of blackbox model parameters is worked out. The procedure allows deriving an error removal scheme for nonrotationally symmetric components based on measurements in different rotational positions. The feasibility and benefit of the error elimination method are shown both by simulation methods and dedicated experiments. A significant reduction of systematic errors even in a miscalibrated state is achieved. Hence, recalibrations are avoided and measurement time and flexibility are improved.

A computational method is proposed to measure the aberration of a lens using an extended ptychographic iterative engine. By reconstructing the entering wavefront φin and exiting wavefront φex of the lens under detection from two sets of diffraction patterns iteratively, the lens aberration can be easily extracted by subtracting the phase of φin and theoretical lens phase from the phase of φex. Since it needs no extra reference beam and high quality optics, this suggested method has advantages of simplicity in structure, high accuracy, and low requirement on working environment, and it is free of the aberration of other optical elements in the experimental system, indicating it can find lots of applications in lens evaluation.