Piston Phase Research Articles

Aero-optical effects, part I. System-level considerations: tutorial

This paper serves as part I of a two-part tutorial on “aero-optical effects.” We first present background information to assist with our introduction of the topic. Next, we use the aerodynamic environment associated with a hemisphere-on-cylinder beam director to decompose the resulting aberrations (that arise due to aero-optical effects) in terms of piston, tilt, and higher-order phase errors. We also discuss the performance implications that these phase errors have on airborne-laser systems. Recognizing the complexity of these environments, we then discuss how one measures these phase errors using standard wavefront-sensing approaches and the impact these phase errors have on imaging performance. These system-level considerations provide the material needed to survey several sources of aberrations such as boundary layers and shear layers, as well as mechanical contamination, shock waves, and aero-acoustics—all of which we cover in part II of this two-part tutorial.

Using a broadband long-wavelength channel to increase the capture range of segment piston phase retrieval for segmented-aperture systems

Segmented-aperture systems, such as the James Webb Space Telescope (JWST), require fine piston alignment between primary mirror segments. Computer simulation experiments show that using a broadband long-wavelength channel, illustrated with the Mid Infrared Instrument (MIRI) onboard the JWST, can extend the capture range of segment piston phase retrieval significantly (in the case of JWST with MIRI, up to hundreds of microns), greatly reducing the requirements on coarse phasing.

Numerical study on a Franchot double-acting heat-driven thermoacoustic-Stirling cryocooler for natural gas liquefaction

Compact heat-driven cryocoolers can harness the thermal energy produced by burning a small quantity of natural gas to accomplish liquefaction. This addresses the requirements of distributed natural gas stations in remote locations. This paper introduces a Franchot double-acting heat-driven thermoacoustic-Stirling cryocooler designed for natural gas liquefaction. It conducts a comparative analysis of the mechanical and electrical systems, focusing on the acoustic field, available energy loss, and performance. Simulation results indicate that the optimized mechanical configuration system achieves peak performance with a piston area ratio of 0.84 and a piston phase angle of 90°. It yields a cooling power of 1964 W@130 K when driven by an 873 K heat source, resulting in an overall system efficiency of 28.3%. This marks a notable enhancement compared to current thermoacoustic systems. While the electrical configuration provides superior stability, the performance is constrained by significant losses in acoustic-electric conversion of linear alternators and compressors. To further enhance efficiency, it is worthwhile to establish direct power transfer between the pistons, for example, by aligning the expansion piston and compression piston coaxially. The evolved duplex configuration eliminates the loss from electrical energy conversion, leading to a remarkable 64.7% increase in overall efficiency. Simultaneously, this evolutionary approach offers a new perspective to elucidate the inherent connections among Stirling heat engines of Franchot double-acting and duplex. It provides valuable theoretical insights for the subsequent analysis and design of Stirling heat-driven refrigerators or cryocoolers.

Energy conversion efficiency improvement of a Stirling type PTR for dual temperature cooling by adopting two active work-recovery phase shifters

Deep space exploration is required to solve the problem of energy acquisition and efficient utilization. Improving energy conversion efficiency is vital to this issue. The Stirling type pulse tube refrigerators (PTR) that work in dual temperature zones play a pivotal role in the field of space detection, and the phase shifter of PTR profoundly affects the conversion efficiency of the exergy to cooling capacity. However, the typical phase shifter causes the acoustic power at the hot end of the cold finger to be dissipated into the form of heat, limiting energy efficiency. With the intention of improving the energy conversion efficiency in the PTR, a novel type of active phase shifter with work recovery on a dual temperature zone PTR is proposed and investigated in this article. Based on the pulse tube refrigerator with two separated cold fingers, inertance tubes with reservoirs, active piston phase shifters, and active work-recovery piston phase shifters have been comparatively investigated. While the refrigerator adopts active work-recovery piston phase shifters, a relative Carnot efficiency of 15.5% is obtained in the 35 K and 85 K temperature zones, which is the highest efficiency ever achieved in these temperature areas.

Coherent beam combining array arrangement with a large number of elements

Improving the beam quality is the constant pursuit of the coherent beam combining (CBC), and CBC is developing toward a large number of elements. In this work, we employed the Fermat spiral array (FSA) in CBC and investigated the CBC effects, compared with traditional periodic arrays. With the element number increasing, the filling factor was increased for FSA, while it was decreased for the hexagonal and ring arrays. In particular, the achieved power in the bucket (PIB) of the CBC with FSA was higher than that of the CBC with hexagonal and ring arrays. Furthermore, the CBC with FSA shows the same tolerance to piston phase error as the CBC with the periodic array, according to numerical calculations. These results provide an effective approach to obtaining better CBC effects, as the CBC develops toward a large number of elements.

Identification and analysis of the factors to realizing variable intake/exhaust phases in opposed-piston two-stroke diesel engines

The opposed-piston, two-stroke (OP2S) diesel engine is a potential power system to promote thermal efficiency, but the engine has an inferior scavenging performance. Through variable intake/exhaust times, the combustion process can be effectively facilitated. For example, the VVT technology is used in traditional engines. However, this technology has not been applied to OP2S diesel engines. This present work analyzed parameters influencing the intake/exhaust times to find a way to realize variable intake/exhaust times in OP2S diesel engines. These parameters affecting intake/exhaust times were mainly focused on, for example, crank to link ratio (CLR), piston phase difference (PPD), and port height (PH). Through investigating their influence on IMEP, scavenging efficiency, and trapping efficiency, we evaluated the different schemes from performance, intake/exhaust phases, and realization cost. The results show that the PH scheme significantly precedes the PPD and CLR schemes for realizing the variable intake/exhaust times. The PH scheme owns a more extensive phase adjustment range of 31°CA, the IMEP of 0.75 MPa, and the scavenging efficiency of 0.74. To achieve better power and scavenging performance, the EPH should be 37.5% higher than IPH, and the PPD should be kept below 15°CA.

Redundant apodization for direct imaging of exoplanets

Context. Direct imaging and spectroscopy of Earth-like planets and young Jupiters require contrast values up to 106−1010 at angular separations of a few dozen milliarcseconds. To achieve this goal, one of the most promising approaches consists of using large segmented primary mirror telescopes with coronagraphic instruments. While they are able to reach high contrast at small angular separations, coronagraphs are highly sensitive to wavefront errors, however. The segmentation itself is responsible for phasing errors and segment-level vibrations that have to be controlled at a subnanometric accuracy. Aims. We propose an innovative method for a coronagraph design that allows a consequent relaxation of the segment phasing and stability constraints for low segment-count mirrors and generates an instrument that is more robust to segment-level wavefront errors. Methods. This method is based on an optimization of the coronagraph design that includes a segment-level apodization. This is repeated over the pupil to match the segmentation redundancy and improves the contrast stability beyond the minimum separation set by the single-segment diffraction limit. Results. We validate this method on a Giant Magellan Telescope (GMT)-like pupil (seven circular segments) for two coronagraph types: apodized pupil Lyot coronagraphs, and apodizing phase plate coronagraphs. For the apodized pupil Lyot coronagraphs, redundant apodization enables releasing the piston phasing constraints by a factor of 5-20 compared to classical designs. For the apodizing phase plate coronagraphs, the contrast remains almost constant up to 1 radian RMS of the phasing errors. We also show that redundant apodizations increase the robustness of the coronagraph to segment tip-tilt errors, as well as to missing segment errors. Conclusions. Redundant apodization enables reducing or even removing any constraints on the primary mirror segment phasing at the price of larger angular separations and lower throughputs. This method cannot be applied to higher-segment count mirrors such as the ELT or the TMT, but it is particularly suitable for low segment-count mirrors (fewer than ~20 segments) such as the GMT aperture. These mirrors aim for high-contrast imaging of debris disks or exoplanets down to 100 mas.

Experimental research on a multi-aperture phase modulation technique based on a corner-cube reflector array.

In this paper, a novel phase modulation technique based on a corner-cube reflector (CCR) array is proposed and demonstrated experimentally. The piezoceramics are linked behind each CCR. When the beams irradiate on the CCR array, the phase modulation can be realized by applying a voltage to piezoceramics to control the spatial location of each CCR. The piston phase errors of the device itself are compensated by employing the stochastic parallel gradient descent (SPGD) algorithm. Then, the piezoceramics are loaded with preset voltages to obtain the expected phase, and the anticipative optical field is generated. In the experiment, the piston phase errors of the 7-way and 19-way CCR array are corrected well. In order to further verify the phase control capability of the device, a vortex beam carrying orbital angular momentum (OAM) of 1 is generated by utilizing the 6-way CCR array. The experimental results confirm the feasibility of the concept.

Discussion on Piston-Type Phase Ambiguity in a Coherent Beam Combining System

Coherent beam combining (CBC) with closely arranged centrosymmetric arrays is a promising way to obtain a high-brightness laser. An essential task in CBC is to actively control the piston phases of the input beams, maintaining the correct phasing to maximize the combination efficiency. By applying the neural network, the nonlinear mapping relationship between the far-field image and the piston phase could be established, so that the piston phase can be corrected quickly with one step, which caused widespread concern. However, there exists a piston-type phase ambiguity problem in the CBC system with centrosymmetric arrays, which means that multiple different piston phases may generate the same far-field image. This will prevent the far-field image from correctly reflecting the phase information, which will result in a performance degradation of the image-based intelligent algorithms. In this paper, we make a theoretical analysis of phase ambiguity. A method to solve phase ambiguity is proposed, which requires no additional optical devices. We designed simulations to verify our conclusions and methods. We believe that our work solves the phase ambiguity problem in theory and is conducive to improving the performance of image-based algorithms.

Experimental Phase Stabilization of a 397-Channel Laser Beam Array Via Image Processing in Dynamic Noise Environment

A phase-locking module is firstly validated for coherent beam combining (CBC) systems of near 400 laser beams in dynamic noise environment. It is based on a 2-dimensional image processing in the phase-locking module to calculate the piston phase of the laser array in the CBC systems. Through the designed phase-locking module, the piston phase distribution of the laser array can be corrected simultaneously, accurately, and rapidly as fast as <inline-formula><tex-math notation="LaTeX">${\sim }$</tex-math></inline-formula> 2000 Hz. Proof-of-concept experiment is demonstrated for coherent beam combining of up to 397 fiber laser emitters based on the designed phase-locking system to correct the phase noises measured from a real fiber amplifier below 1 kHz. The ratio of power in the Airy disk is as high as 59.51 &#x0025; when the phase compensation is carried out for the piton phase noise measured in a kW-class fiber amplifier. The phase residue error in the close-loop is better than <inline-formula><tex-math notation="LaTeX">${\lambda }$</tex-math></inline-formula>/31.

Constructal design of a circular micro-channel Stirling regenerator based on exergy destruction minimization

Regenerator is a key component in Stirling engines, and its characteristics have a significant influence on engine performance. Herein, subjected to the global constraints of the fixed total volume and porosity, constructal design of a circular micro-channel regenerator was conducted to achieve its optimal structures. The total exergy destruction rate in the irreversible regenerative process, which includes three types of individual exergy destruction contributions caused by the heat transfer with a finite temperature difference, flow resistance, and axial heat conduction of the solid matrix, was adopted as the optimization objective. The optimal channel diameter was obtained, and the effects of the regenerator inner radius, total volume of regenerators, regenerator porosity, engine speed, piston phase angle, hot part temperature, charge pressure, and thermal conductivity ratio due to the segmentation of regenerators on the optimization results were analyzed. The results show that the total exergy destruction rate offers a minimum at a relatively low channel diameter of around 0.5 mm under the given parameter values. All the parameters studied have an obvious effect on the minimum total exergy destruction rate, and the regenerator inner radius, total volume and porosity of regenerators, and engine speed also have an evident influence on the optimal structure of the regenerator. These indicate that the regenerator performance can be further improved by selecting appropriate global geometric parameter values of regenerators and operating parameter values of engines. The findings of this study can provide some guidelines for the optimal design of micro-channel regenerators and the performance improvement of Stirling engines.

Continuous Tracking and Pointing of Coherent Beam Combining System via Target-in-the-Loop Concept

We demonstrate a technique to realize fine target tracking and pointing using target-in-the-loop (TIL) concept via a coherent beam combining (CBC) system. A tracking and pointing system is composed of a densely packed array of 7 phase-control elements with simultaneous piston and tilt controls of the outgoing beams wavefront phases. A photo-detector (PD) with a pinhole is used as target detection and installed on a translation stage. Energy detected by the mobile PD is used for evaluating the beam combining and scanning performance, and to provide the feedback signal for controls of piston and tilt phases of the transmitted beams by using the stochastic parallel gradient descent (SPGD) algorithm for merit function maximization.

Iteration-free, simultaneous correction of piston and tilt distortions in large-scale coherent beam combination systems.

Coherent beam combination (CBC) holds promise for scaling the output power of the laser system while maintaining good beam quality. Owing to the thermal effect and mechanics instability, piston and tilt distortions always exist and affect the performance of the combined beam. To ensure the constructive interference in the far-field, dynamic correction of the distortions is highly required. Here, we propose an approach for the simultaneous correction of piston and tilt distortions in CBC systems. Based on the position and interval information of the near-field interference fringes, the theoretical expressions for the relative piston phase and tilt errors of each array element are derived, indicating that dynamic distortions in CBC systems can be directly calculated and then corrected by employing phase control servos. To demonstrate the feasibility of the proposed approach, Monte-Carlo Simulations have been carried out for different perturbative environments. Our results indicate that both piston phase and tilt errors can be calculated and compensated accurately (λ/25 and 0.11μrad) by the proposed approach even in 169 beamlets, which also has high tolerance for defocus errors. This work could provide valuable reference on the practical implementation of high-power, phase-locked fiber laser array systems.

Wavelength-tuning multiple-surface interferometric analysis with compression of Zernike piston phase error

In this study, we propose a 6N – 3 algorithm for suppressing the Zernike piston phase error by expanding 6N – 5 algorithm using algorithmic polynomial theory. We demonstrate that the proposed algorithm can be used for simultaneous measurement of the surface profile and thickness homogeneity by rotating the characteristic diagram on the complex plane. We applied Fourier analysis to confirm the properties of 6N – 3 algorithm in the frequency domain. We then estimate the error-compensating capability of 6N – 3 algorithm, after which we compare this capability to that of classical algorithms using numerical error analysis. To verify the effectiveness, we conducted an experiment using 6N – 3 algorithm and Fizeau interferometer to measure the thickness homogeneity and surface profile of a glass plate. The standard deviation of the measured thickness homogeneity was 1.965 nm, which was significantly smaller than that of the other classical algorithms.

Generation of optical vortex lattices by a coherent beam combining system.

Owing to the unique features in intensity and phase structures, optical vortex lattices (OVLs) have attracted intensive attention and promoted various applications. However, the power scaling of OVLs always presents a critical challenge. Here we take advantage of the brightness enhancement of coherent beam combining (CBC) technology and propose an architecture for creating OVLs based on the CBC system. In the experiment, by utilizing the stochastic parallel gradient descent algorithm, the dynamic phase noises were compensated. The desired piston phase shifting of each element for tailoring the structured wavefront was implemented by the liquid crystal. When the system in a closed loop, hexagonal close-packed OVL consists of spatially distributed orbital angular momentum, beams can be generated in the far-field. This work is an important step toward future implementation of high-power structured light beams.

Parametric investigation of the phase characteristics of a beta-type free piston Stirling engine based on a thermodynamic-dynamic coupled model

In this study, to reveal the phase characteristics of a beta-type free piston Stirling engine (β-FPSE), a thermodynamic-dynamic coupled model is proposed and verified experimentally. With the phasor notation method, the influences of the heating temperature, cooling temperature, spring stiffness and damping coefficients on the phases of displacer and power piston, and the output performance are investigated. The results indicate that the phase angles of the displacer and power piston increase with the heating temperature, and decrease with the cooling temperature. In the variation of power piston phase with its spring stiffness, a point of temperature independence (PTI) is identified. In the variation in the power piston phase with the displacer damping coefficient, a point of damping balance (PDB) is identified. A hysteresis of the PDB will occur if the heating temperature increases. In addition, the output power and power angle are obtained at the same damping coefficient of the displacer, which is equal to the displacer damping coefficient at the PDB if the spring stiffness ratio is less than 3.31. Moreover, based on the PV diagrams of different spring stiffness and damping coefficients, the compression ratio and pressure ratio for the optimum output power and efficiency are determined, respectively.

Structuring orbital angular momentum beams by coherent laser array systems with tip-tilt optimization

The generation and manipulation of high-power and mode switchable orbital angular momentum (OAM) beams have widespread applications such as free-space optical communication, nonlinear frequency conversion, and laser processing. To realize the power scaling and flexible mode switching, spatially structuring OAM beams with coherent laser arrays based on coherent beam combining technology provides a promising way. Up to now, the arrangement and piston phase control of the laser array system for tailoring OAM beams have been well explored. However, modulating only discrete piston phases of the array elements would limit the compensation of the dynamic aberrations and the precise generation of the desired structured light fields. In this paper, the coherent laser array system for tailoring OAM beams is improved by the introduction of the tip-tilt optimization. Based on the paraxial diffraction theory and coordinate transforming method, the theoretical model of the tip-tilt wavefront optimized coherent laser array that generates OAM beams is constructed. The results demonstrate that utilizing the tip-tilt optimization has the advantage in main ring power enhancement, and the introduction of tip-tilt control is required for compensating dynamic aberrations. Furthermore, the extended functions of the proposed laser array system in longitudinal and radial modulation of the combined OAM beams are discussed. This work could be useful for future implementation of customizing high-power and mode switchable structured light fields.

Coherent beam combining of multipass thin-disk lasers with active phase control

Coherent beam combining and the development of thin-disk lasers have provided the ability to increase the output power of solid-state laser systems. Here, coherent beam combining by active phase control of one multipass thin-disk laser amplifier and one similar multipass setup is demonstrated with powers below 100 mW. Piston phase disturbances are measured via optical heterodyne detection and compensated for by piezo mirrors. For one double pass over the disk, a root mean square phase error of λ/69 was achieved. Mechanical vibrations &lt; 5 kHz inside the multipass setup caused by the water cooling of the disk are the main source of phase noise. Thermal effects by the pumping diodes with 1 kW of optical power are negligible.

Seismic and geodetic progression of the 2018 summit caldera collapse of Kīlauea volcano

The 2018 eruption of Kīlauea volcano, Hawai'i, resulted in a major collapse of the summit caldera along with an effusive eruption in the lower East Rift Zone. The caldera collapse comprised 62 highly similar collapse cycles of strong ground deformation and earthquake swarms that ended with a magnitude 5 collapse event and one partial cycle that did not end with a collapse event. We analyzed geodetic and seismic data to better understand how the caldera collapse progressed over 3 months of activity, focusing on the cyclical activity. We identified 3 main phases of collapse: initial ring-fault activation and small explosions (Phase 1), an eastward shift in activity and freeing of the central piston (Phase 2), and a recoupling of the piston to the reservoir followed by relatively steady behavior until the eruption's end (Phase 3). Additionally, we observed geodetic evidence of tangential motion from the localization of the main ring fault (Phase 2) and the formation of a major peripheral ring fault on the eastern side of the collapse caldera during Phase 3. Both geodetic and seismic parameters suggest that the collapse may have had an eastward-component of motion after the ring fault system had formed. The cyclical seismic and geodetic parameters show no obvious signs that the collapse was coming to an end, with the only notable change being a significant increase in the ratio of cyclical displacement to co-collapse displacement observed during the last complete cycle on GNSS stations outside the caldera region.

Computational phase correction algorithms for multi-aperture systems.

Aperture cophasing can increase the resolution of a multi-aperture array while reducing optical system size and accounting for phase errors from hardware misalignments and atmospheric turbulence. Remapping apertures using an anamorphic pupil relay can separate the spatial frequency spectrum of a previously continuous modulation transfer function to facilitate a posteriori piston corrections between apertures [J. Opt. Soc. Am. A34, A47 (2017)JOAOD60740-323210.1364/JOSAA.34.000A47]. This study expands this method from two apertures to six using maximum likelihood estimation to calculate piston phase errors and least squares for tip and tilt. Perturbed test targets were generated for specific turbulence and noise values, providing random realizations of pistons, tips, tilts, and atmospheric phase screens. Results show improved Strehl ratios for corrected images in the presence of noise and atmospheric turbulence.