Landauer’s principle provides a fundamental lower bound for energy dissipation occurring with information erasure in the quantum regime. While most studies have related the entropy reduction incorporated with the erasure to the lower bound (entropic bound), recent efforts have also provided another lower bound associated with the thermal fluctuation of the dissipated energy (thermodynamic bound). The coexistence of the two bounds has stimulated comparative studies of their properties; however, these studies were performed for systems where the time-evolution of diagonal (population) and off-diagonal (coherence) elements of the density matrix are decoupled. In this paper, we aimed to broaden the comparative study to include the influence of quantum coherence induced by the tilted system–reservoir interaction direction. By examining their dependence on the initial state of the information-bearing system, we find that the following properties of the bounds are generically held regardless of whether the influence of the coherence is present or not: the entropic bound serves as the tighter bound for a sufficiently mixed initial state, while the thermodynamic bound is tighter when the purity of the initial state is sufficiently high. The exception is the case where the system dynamics involve only phase relaxation; in this case, the two bounds coincide when the initial coherence is zero; otherwise, the thermodynamic bound serves the tighter bound. We also find the quantum information erasure inevitably accompanies constant energy dissipation caused by the creation of system–reservoir correlation, which may cause an additional source of energetic cost for the erasure. Information processing accompanies inevitable energy dissipation. According to Landauer’s principle , the ultDespite the conventional Landauer’s principle being rooted in the information theory, recent studies in quantum thermodynamics provide another lower bound related to the thermal fluctuation of the dissipated energy ,23. BecaIn this paper, we provide a systematic study of the relative tightness of the bounds for the spin–boson model consisting of a single spin-1/2 and an infinitely large bosonic reservoir with a tilted system–reservoir interaction direction. By adjusting the angle of the interaction direction, we control the coupling between the population and the coherence. Our analysis is based on the full-counting statistics (FCS) formalism of the bounds  with thethe protocol involves an information-bearing system S and a thermal reservoir R, both described by certain Hamiltonians, denoted the reservoir R is initially in the thermal equilibrium with a certain inverse temperature the system S and the reservoir R are initially uncorrelated, the erasure process itself proceeds by a unitary evolution generated by the total Hamiltonian In the original work Ref. , R. LandFollowing the above framework, we consider a specific protocol of a quantum information erasure: we erase an information content of a spin S by interacting it with an infinite bosonic reservoir R until it reaches a steady-state satisfying The above-formulated information erasure accompanies unavoidable energy exchange, or “energy dissipation”, between the system and the reservoir. The actual amount of the dissipated energy can be evaluated asLandauer’s principle claims that the dissipated energy has a lower bound, meaning that the information erasure requires a specific energetic cost, and it may not be zero. In the present paper, we systematically compare two lower bounds with different physical origins: (a) the entropic bound defined by the entropy change during the erasure process and (b) the thermodynamic bound defined by the thermal fluctuation of the dissipated energy. Let us briefly review each bound in the rest of the present section.In Refs. ,31, an e process ,31. The entropic bound.We thus refer to  as the eRecently, growing interest in the thermodynamics of quantum systems has induced a closer examination of the relation between the dissipated energy and its fluctuation in the quantum information erasure process . By consthermodynamic bound.We thus refer to  as the tt is therefore given by counting field associated with The dissipated energy nergy HR ,30,32. TDespite the usual definition of the cgf employing the mean value of eiχΔQ , here weEquation  as(11)ΘThus, the thermodynamic bound is directly obtained from the cgf asThe full-counting statistics provides a systematic procedure to evaluate the cgf . By usinequation ,39,40,41The superoperator tion HSR , the supEquation .With these formalisms, the mean value of the dissipated energy see Ref.  for detak-th bosonic mode of the reservoir and x-axisk-th bosonic mode. By adjusting the parameter For simplicity, we hereafter use units with us study . For θ=πWe note that the above-presented model is equivalent to a system consisting of a single spin subjected to a tilted magnetic field and the bosonic reservoir as shown in z-components respectively represent coherence and population.By assuming a sufficiently weak system–reservoir coupling, we employ the second-order TCL master equation (Equations –16)) to) to16)) In the presence of the counting field, the density operator of the spin Using the Bloch vector representation, the master equation (Equation ) is castquations ) are proquations . PhysicaIn terms of the Bloch vector, the bounds are formally expressed asSince the cumulant generating function is expressed as Equation , is rewrFrom these formal expressions, we find that both the thermodynamic bound t was taken sufficiently long as the system reached the steady-state. To describe the system–reservoir coupling, we use the Ohmic spectral density with the exponential cutoff We examine the relative tightness of the bound quations –26). In. InBT,E Let us first examine the initial state dependence of the relative tightness in the case where the time evolutions of the population and the coherence are coupled. In In the figures, we see the following difference: the dissipated energy  in Ref. , indicatThe only exception is the pure-dephasing case, The constant energy dissipation can be understood from the uncorrelated initial state The thermodynamics bound is constantly zero. It is a direct consequence of the invariance of the trace Let us now examine the dependences of the bounds on the strength of the coherence–population coupling, controlled by the parameter From the figures, we find that the dissipated energy and the bounds are insensitive to In the present paper, we have examined the properties of two lower bounds for energy dissipation associated with Reeb and Wolf’s quantum information erasure under the influence of quantum coherence. As a working model, we considered a single spin-By setting the angle to be switching on the population–coherence coupling, we found that the bounds show the following trends: the entropic bound serves as the tighter bound if the initial state is sufficiently mixed; while, if the purity of the initial state is sufficiently high, the thermodynamic bound is tighter. These trends are in agreement with the case in which the population and the coherence are decoupled . It indiThe only exception is the case where the angle of the interaction direction is set to Apart from the quantum coherence between the ground state and the excited state of the spin, the constant energy dissipation caused by the system–reservoir interaction (see In this paper, we have studied the quantum information erasure stored in the single spin system by contacting a bosonic reservoir and bringing the spin to its steady state. Even though such a setup is universally found in energy dissipation in open systems, it is rather minor as the information erasure protocol in quantum information processing. Indeed, recent studies ,27 focusWhile we have considered in this paper the spin-ng spins ,45,46,47ng spins ,49,50 orng spins ,52, coupng spins ,54. Thus


The existing dehazing algorithms hardly consider background interference in the process of estimating the atmospheric illumination value and transmittance, resulting in an unsatisfactory dehazing effect. In order to solve the problem, this paper proposes a novel global illumination compensation-based image-dehazing algorithm (GIC). The GIC method compensates for the intensity of light scattered when light passes through atmospheric particles such as fog. Firstly, the illumination compensation was accomplished in the CIELab color space using the shading partition enhancement mechanism. Secondly, the atmospheric illumination values and transmittance parameters of these enhanced images were computed to improve the performance of atmospheric-scattering models, in order to reduce the interference of background signals. Eventually, the dehazing result maps with reduced background interference were obtained with the computed atmospheric-scattering model. The dehazing experiments were carried out on the public data set, and the dehazing results of the foggy image were compared with cutting-edge dehazing algorithms. The experimental results illustrate that the proposed GIC algorithm shows enhanced consistency with the real-imaging situation in estimating atmospheric illumination and transmittance. Compared with established image-dehazing methods, the peak signal-to-noise ratio (PSNR) and the structural similarity (SSIM) metrics of the proposed GIC method increased by 3.25 and 0.084, respectively. Haze is an atmospheric phenomenon where dust, smoke and other dry particles obscure the clarity of the atmosphere. This results in a loss of contrast, visibility and vividness in images required for vision technology ,2 due toThe single image-dehazing technology in recent years can be divided into three categories: (1) The image-dehazing method based on a physical model. Under the framework of the atmospheric-scattering model , prior kAmong the above methods, although the fusion-based method guarantees the gradient information of multi-scale input, its image restoration strength is insufficient to some degree. The deep-learning-based methods usually need considerable well-labeled samples, indicating high cost in data collection and curation. Based on the atmospheric-scattering model, we analyze the shortcomings of the DCP method and the fog-imaging principle. It is believed that the brightness and color of a pixel of the input image will be affected by the surrounding pixels in a limited range. Therefore, in order to eliminate or reduce the interference from the background and obtain the real prior information, this paper proposes the GIC algorithm. Before estimating atmospheric illumination and transmittance, the GIC algorithm eliminates or weakens the interference of the background on the color distribution of the image, thereby obtaining more accurate model parameters. Our main contributions are summarized as follows:(1) We propose an image-dehazing method based on global illumination compensation. Compared with other image-dehazing methods, the GIC method eliminates or reduces the influence of surrounding pixels on the target pixel through the shading partition enhancement mechanism before performing a priori analysis. In evaluation experiments on public datasets, the GIC method achieves better image evaluation metrics than the candidate methods, yet keeps high computational efficiency.(2) In order to eliminate the interference from the background in the process of dehazing, the GIC algorithm employs a contrast-enhancement technique named the shading partition enhancement mechanism to distinguish the light and dark information of the image. The shading partition enhancement mechanism calculates the real atmospheric illumination observation points and eliminates or reduces the interference of surrounding pixels to target pixels by means of local enhancement.(3) The GIC algorithm uses the global illumination compensation factor and guided filtering for transmittance map refinement to ensure a dehazed image with no halo artifacts. The global illumination compensation factor is a local weighted average algorithm that can make the transmission map have sharper edges.The remainder of this paper is organized as follows: In In this section, we introduce the atmospheric-scattering model which is the basic underlying model of image dehazing. Then we introduce some existing methods used in this paper to calculate haze-related parameters. Finally, we analyze the foggy imaging process that inspired the idea of this paper.The atmospheric-scattering model  describeThis subsection mainly introduces the two methods used in this paper to calculate the haze-related parameters.The dark channel prior method is mainly designed for outdoor haze-free images. In these non-sky areas, there exists one-color channels that have pixels with intensity close to zero. The dark channel is defined as the minimum value of the RGB of pixels in the local area of the image:Guided filtering  is a novTo determine the linear coefficients Under various haze imaging conditions, the image captured by the camera is formed by the light reflected from the object penetrating the air diffusely. There are three main sources of light hitting an object. The first source indicates that the light is irradiated on the object by the light source directly. In the second situation, the light is reflected on the object after the light source irradiates the surrounding object diffusely. In the third case, the diffuse reflection light of the surrounding objects is irradiated on the atmospheric particles and then scattered to the object. Shown in Model-based methods often estimate atmospheric illumination and transmittance by analyzing the local and global color distribution of the input foggy image. However, it can be seen from Algorithm 1. Global Illumination Compensation-Based Image-Dehazing algorithm.Input: foggy image .Procedure:   #Mechanism 1 The Shading Partition Enhancement Mechanism   Get the L-channel image matrix    Obtain the local bright and dark matrices    Estimate the range of bright and dark areas    Obtain the bright and dark area information    Combine    Convert back to RGB color space to get enhanced image Perform DCP calculations on Calculate the global illumination compensation factor    #Mechanism 2 Global Illumination Compensation Factor   Perform DCP calculations on    Calculate the mean over a small range centered at pixel Optimize Combine Output: clear image The atmospheric-scattering model in He et al.  first obThe shading partition enhancement mechanism processes the light and dark areas of the L-channel of the input image, in order to enhance the contrast of the image in the light and dark areas. The basic process of shading partition enhancement is shown in In the first step, the enhancement mechanism normalizes the L-channel of the input image, and obtains the largest  pixel from the L-channel using an n × n window . Finally, we go back from the Lab color space to the RGB color space to get our enhanced image. This mechanism can eliminate or reduce the influence of surrounding pixels on the target pixel effectively.After eliminating the influence of surrounding pixels, the atmospheric illumination value is calculated by . The expThe GIC method first calculates DCP on the enhanced image to obtain the atmospheric illumination value, then performs the optimization of the transmittance.With the computed atmospheric illumination values, the DCP principle is used to calculate the dark channel of the atmospheric-scattering model:According to the DCP principle, the dark channel of the image should be close to zero under fog-free conditions, so there are:After eliminating or reducing the influence from the surrounding scene through the shading partition enhancement mechanism. The overall outline of the calculated initial transmittance map is not clear enough. Therefore, we introduce a global illumination compensation factor on the basis of the enhanced dark channel image, with the purpose of optimizing the transmittance. Assuming that the target pixel is affected by the surrounding pixels in a local area and the average information of the surrounding pixels is consistent, this paper introduces a weight coefficient to In the GIC algorithm, we obtain the enhanced image through the shading partition enhancement mechanism and combine the DCP to obtain the atmospheric illumination value from the enhanced image. To optimize the initial transmittance, we use global illumination compensation factor and guided filtering to smooth the image and highlight image edges. By Equation (13), the haze-free image can be recovered easily.MSE (mean square error) is the mean square error of the processed image X and the ground-truth image Y; To evaluate the dehazing performance quantitatively, two popular metrics are adopted in this study: PSNR and SSIM . Given aThe SSIM index measures image similarity in terms of brightness, contrast, and structure. Its calculation method is shown in Equation (15) where P is the probability map of the pixel in the spectrum.However, a completely clear haze-free image cannot be obtained in reality and the two indexes themselves are limited and difficult to keep consistent with the quality of human perception. Therefore, two no-reference IQA indexes were selected—spatial and spectral entropies quality (SSEQ)  and natuNIQE represents the quality of the distorted image by the distance between the natural scene statistic (NSS) feature model and the multivariate Gaussian (MVG) extracted from the distorted image features. The calculation method of this indicator is shown in Equation (17), where Note that a higher PSNR and SSIM value and a lower SSEQ and NIQE value indicate higher quality in the dehazing process.In order to verify the effectiveness of the shading partition enhancement mechanism in image dehazing, we analyzed its correctness for obtaining atmospheric illumination observation points and compared it with the established dehazing methods, including Dhara , Berman In the STOS dataset, the position of the observation point of the atmospheric illumination value and the brightness value of the surrounding pixels were calculated in  and the In order to verify the effectiveness of the light–dark partition enhancement mechanism proposed in this paper in image dehazing, we compared it with various image enhancement algorithms. Method B1 does not perform image enhancement, method B2 uses histogram equalization processing, method B3 denotes contrast-limited adaptive histogram equalization (CLAHE)  processiIndoor synthetic foggy images were used in the SOTS dataset to conduct simulation experiments to evaluate the feasibility of the above algorithms from both subjective and objective aspects. Image-dehazing algorithms of Dhara , Berman It can be observed from Considering that the fog concentration has a direct impact on the image-dehazing effect, ten different concentrations were set in the verification process to test the algorithm performance. For the same indoor images under ten different fog concentrations, we used the above methods to dehaze the sample image set respectively, as shown in In general, high levels of fog tend to a negative impact on the quality of image dehazing. With the increase of fog concentration, except for the SSEQ index obtained by the Cho  method wAfter processing the simulated images to achieve good results, we conducted experiments on real outdoor foggy images in the SOTS dataset, and compared the results with the dehazing algorithms of Dhara , Berman In the visual analysis, we increased the dehazing effect of the He method. The comparison results of outdoor images are shown in The GIC method preprocesses the input image through the shading partition enhancement mechanism, which compensates for the light intensity scattered by atmospheric particles such as fog. Meanwhile, the influence of surrounding pixels on the target pixel is also eliminated. Realistic observation points of atmospheric illumination can be found in the enhanced image. The global illumination compensation factor optimizes transmittance in order to obtain a sharper profile transmittance map. In this way, the GIC method completes the fog removement with the atmospheric-scattering model. Experimental results show that the GIC method had improved performance on outdoor foggy images, illustrated by reduced image distortion and darkening in the restoration result.We also test the computational efficiency of candidate dehazing methods, as shown in Under the framework of the atmospheric-scattering model, this paper designs and implements the GIC algorithm. Introducing the global illumination factor compensation and the shading partition enhancement can eliminate or reduce the interference from the background effectively and improve the image-dehazing quality and effect. The experimental results show that the proposed method can effectively reduce the background interference through the shading partition enhancement and the global illumination compensation factor, and the obtained atmospheric illumination and transmittance are more in line with the real situation during imaging. From the perspective of quantitative analysis, the GIC method can achieve higher PNSR and SSIM indexes for outdoor scene images, which are better than the selected candidate algorithms; it has a better dehazing effect on indoor low-density foggy images. From the perspective of subjective observation, the GIC algorithm can maintain the natural color of the image well and produce clear dehazing images with high operating efficiency.


This paper is dedicated to the challenging issue of the cooperative attitude tracking control of a multi-spacecraft system under communication delays. A state estimator using the attitude information of the neighbors is designed for each follower spacecraft to estimate the time-varying attitude information of the leader spacecraft in the case that the leader spacecraft cannot directly communicate with all following spacecraft. By constructing auxiliary variables based on estimated values and proposing a fixed-time control law to ensure that the auxiliary variables of the spacecraft can reach zero in fixed time, which is independent of the initial state, the effects of time-varying reference attitudes on the system can be reduced. The attitude error and the estimation error are proven to converge to the region containing the origin by input-to-state stability theory combined with the Lyapunov–Krasovskii approach. To further illustrate the effectiveness of the proposed control algorithm, numerical simulation results are presented. With this algorithm, the attitude of each spacecraft was synchronized; however, the attitude value of this synchronization was not set in advance, which means that the final spacecraft attitude was uncertain. Under the assumption that all followers obtained the leader’s acceleration, the coordinated tracking problem with a dynamic leader was investigated in Hong et al.3, and the proposed algorithm ensures that the attitude of each spacecraft can track the desired trajectory asymptotically. Du et al.4 studied the multi-spacecraft attitude tracking problem, and the proposed control algorithms could guarantee that each spacecraft tracks the desired time-varying attitude. Moreover, Zou et al.5 proposed a cooperative attitude control algorithm without velocity measurement.Multi-spacecraft distributed cooperative attitude control, an important branch of cooperative control, has received extensive attention in recent years. Compared with traditional centralized coordination methods, distributed cooperative attitude control has the advantages of high efficiency, strong robustness, and high reliability. Distributed attitude cooperative control is dedicated to synchronizing the attitude of each spacecraft to a common value. In Zhang and Demetriou6 proposed a finite-time control scheme, which achieved finite-time convergence of spacecraft attitude error under arbitrary communication topologies. To improve the robustness of the system, Zou and Kumar7 studied the multi-spacecraft distributed attitude coordination control problem in the consideration of external disturbances, and the proposed control algorithms could guarantee that the system achieves finite-time stability. The existing literature on finite-time cooperative attitude control algorithms for multiple spacecraft systems has achieved fruitful results; however, the settling time of finite-time control algorithms is dependent on the initial conditions of the system. In Polyakov8, fixed-time convergence was proposed, which guarantees that the settling time is independent of the initial states; thus, the settling time of fixed-time algorithms is dependent on only the design parameters. Shi and Zhou9 studied the fixed-time attitude tracking problem of multi-spacecraft, and the algorithms could guarantee the convergence time of the system states within a fixed time. Following the idea exposed by Ton and Petersen10, a disturbance observer was employed in the fixed-time control algorithms to reduce the interference of the multi-spacecraft system. Similarly, taking the external interference and uncertainties of the system into account, the proposed algorithm guaranteed that the system states converge to the regions containing the origin in fixed time in Gao and Cai11.The aforementioned literature on leader-follower multi-spacecraft guarantees only the asymptotic convergence of the spacecraft attitude error under the premise that all followers can obtain information from the leader spacecraft. Compared to asymptotic convergence, Liang et al.12 proposed an attitude synchronization scheme that solves the leaderless problem under directed interconnection between rigid bodies with constant communication delays. Similarly, the frequency domain approach was employed to investigate the stability of linear systems under communication delays in Wang13.The Lyapunov–Krasovskii function method is an effective approach for nonlinear systems with time-varying delays. In the case that the reference attitude is time-varying and can be obtained by each spacecraft, the back-stepping technique and the Lyapunov–Krasovskii method contribute to the control law design in Guo et al.14. Zhou et al.15 proposed state feedback attitude synchronization tracking control algorithms and analyzed the delay-dependent stability of the delay system. However, the existing literature on attitude cooperative control for multiple spacecraft with time-varying communication delays focuses on leaderless synchronization or tracking with a dynamic leader under the assumption that the information of the leader is obtained by each follower.In addition to the convergence rate of the system, the communication delay, which affects the control performance and even undermines the stability of the system, must be addressed for attitude tracking control. Researchers have made great efforts to study the communication delay problem in linear and nonlinear multiagent systems. Abdessameud and TayebiMotivated by the above facts, a distributed attitude cooperative tracking control algorithm is proposed for a multi-spacecraft system with time-varying communication delays. Modeled by the Euler–Lagrange equation, the control objective is to ensure that each follower spacecraft attitude error converges to the region containing the origin when only a part of the follower spacecraft can acquire the dynamic attitude of the leader spacecraft. For the auxiliary variables constructed in this paper, a fixed-time control algorithm is added to make the convergence time of the auxiliary variables independent of the initial state, thereby reducing the influence of the time-varying reference state on the system.15 and Liang et al.6, not all follower spacecraft have access to the time-varying attitude information of the leader spacecraft under the directed communication topology. A distributed estimator is employed to estimate the attitude trajectory of the leader for each spacecraft using its neighbors’ information under communication delays. Second, compared with Zou and Kumar7 and Zhao and Jia16, in the controller design, a fixed-time control algorithm is combined so that the settling time of the auxiliary variable is independent of the initial state. This can reduce the impact of the time-varying reference target state on the overall system. Third, in contrast to Zhai and Xia17 in which the algorithm focused on the static leader case, the attitude tracking control algorithms with communication delays in this paper focus on tracking with a dynamic leader spacecraft.Compared with existing works, the main contributions of this study are as follows. First, compared with Zhou et al.Notations:n followers, labeled as spacecraft ith spacecraft denoting the attitude orientation of the body-fixed frame with respect to the inertial frame. ith rigid body with respect to the inertial frame expressed in the body frame of the ith rigid body. Consider a multiple rigid spacecraft system consisting of The matrix ith spacecraft in the system are described byith spacecraft and ith spacecraft. The n followers are represented with Euler–Lagrange equations by combining  If graphhas a directed spanning tree, all eigenvalues of matrixHhave positive real parts.(Ren and CaoConsider the following system:Polyakov8) The equilibrium of system ((f system  is fixed8) If there exists a continuous radially unbounded functionsuch thatfor any solutionx(t) of  of  satisfie(Polyakov20) Consider the systemwheref is continuously differentiable and globally Lipschitz in , uniformly in t. If the unforced systemhas a globally exponentially stable equilibrium point at the originthen the system  LetThen(Zuo and Lin22) For any scalarsymmetric positive definite matrixand vector functionsuch that the following integration holds:where The block matrixif and only if in , howeverT satisfies W and reasonably matrices Z such thatThe time-varying communication delay Z reasonably. The positive definite H could make matrix Z reasonably. Compared with Wang et al.26, although the LMI forms are similar, the design of this paper can guarantee each block matrix on main diagonal negative definite, thus guaranteeing the correctness of the proof. We first give the boundedness proof for the relevant states (According to Lemma t states . Consideentclass1pt{minimaDefine auxiliary variables asith follower spacecraft is proposed asCombining  and 18)18), the Considering the multi-spacecraft attitude system \documenttituting , 18) an an\documtituting  into 5)\documentConsider the Lyapunov function candidate asTaking the time derivative of the Lyapunov function ith spacecraft will converge to zero in fixed time with a settling timeSince The proof of Theorem Define  Rewrite  and 16)\documentConsider the following systemH have positive real parts. In the case of the establishment of Assumption F is positive definite by reasonably selecting positive constant U can be a positive definite matrix.According to Lemma Consider the linear system with communication delays described by  holds:then system statexconverges to zero asymptotically. Under Assumptionsandthe distributed estimator Consider 27). Similar to the analysis in Remark 3, the corresponding solutions 28). In LMI  has been proven to be bounded and converge to zero in fixed time in Theorem s(t) from Lemma s(t) and the state By substituting  into 3232, linear system  is asympgiven by  and 25)\documentmentclass2pt{minimmentclass2pt{minim systems  and (25)T is set as In this section, to demonstrate the validity of the proposed control algorithms, numerical simulations for a multi-spacecraft system are conducted, and the communication topology is described by Fig. entclass1pt{minimantroller  are set entclass1pt{minimaThis paper studies the problem of distributed coordinated control of spacecraft attitude tracking under time-varying communication delays, where the communication topology is described as a directed graph and the reference attitude is dynamic. Since the reference attitude information is available to only some of the following spacecraft, a distributed estimator that uses neighbor information under communication delay is proposed to estimate the reference attitude information. An auxiliary variable is designed based on the estimated information. By means of the fixed-time control method, a fixed-time control algorithm is proposed that achieves convergence of the auxiliary variable with fixed time, and the convergence time is independent of the initial state. This means that the influence of the constantly changing initial conditions on the system is reduced. By using the Lyapunov–Krasovskii functional approach and input-to-state stability theory, the proposed control algorithms guarantee that the attitude of each following spacecraft can be asymptotically synchronized with the dynamic attitude of the leader spacecraft.


Acute lymphoblastic leukemia (ALL) is a deadly cancer characterized by aberrant accumulation of immature lymphocytes in the blood or bone marrow. Effective treatment of ALL is strongly associated with the early diagnosis of the disease. Current practice for initial ALL diagnosis is performed through manual evaluation of stained blood smear microscopy images, which is a time-consuming and error-prone process. Deep learning-based human-centric biomedical diagnosis has recently emerged as a powerful tool for assisting physicians in making medical decisions. Therefore, numerous computer-aided diagnostic systems have been developed to autonomously identify ALL in blood images. In this study, a new Bayesian-based optimized convolutional neural network (CNN) is introduced for the detection of ALL in microscopic smear images. To promote classification performance, the architecture of the proposed CNN and its hyperparameters are customized to input data through the Bayesian optimization approach. The Bayesian optimization technique adopts an informed iterative procedure to search the hyperparameter space for the optimal set of network hyperparameters that minimizes an objective error function. The proposed CNN is trained and validated using a hybrid dataset which is formed by integrating two public ALL datasets. Data augmentation has been adopted to further supplement the hybrid image set to boost classification performance. The Bayesian search-derived optimal CNN model recorded an improved performance of image-based ALL classification on test set. The findings of this study reveal the superiority of the proposed Bayesian-optimized CNN over other optimized deep learning ALL classification models. Leukemia is a fatal malignancy that attacks blood cells. It is prevalent in children as well as adults aged 65 and beyond . LeukemiAcute Lymphocytic Leukemia, or ALL, is the most prevalent form of leukemia, in which lymphoid cells proliferate abnormally in the bone marrow. ALL primarily affects children and adolescents. Leukemia, unlike other types of cancer, does not produce a tumor that could be detectable by medical imaging. Therefore, leukemia is identified using further medical procedures, such as complete blood count, lumbar punctures, myelograms, and bone marrow biopsies . InitialImage classification algorithms have been used to detect blood cancer in medical images in recent years. There are two types of classification approaches for leukemia diagnosis : standarIn recent years, a huge interest in deep learning has grown . It has Model hyperparameters are points of configuration of the learning process that allow a machine learning model to be customized for a specific task and dataset . HyperpaDevelopment of a new optimized deep learning CNN for the detection of ALL in microscopic blood smear images.Formation of a hybrid dataset by integrating two public ALL datasets to supplement the input data.Augmentation of the hybrid dataset using several image transformations to promote classification performance.Determination of the optimal architecture and hyperparameters of the proposed CNN using the Bayesian optimization approach.Comparison between the optimized model and a non-optimized model to investigate the effectiveness of Bayesian optimization in improving classification performance.Classification performance comparison of the optimal ALL CNN model with that of the state of the art.In this study, we propose a customized CNN that has been trained from scratch to detect the presence of Acute Lymphoblastic Leukemia in a hybrid set of microscopic blood smear images. The Bayesian optimization approach is utilized to determine the optimal CNN architecture and optimize the hyperparameters of the proposed deep network. Optimizing the architecture and hyperparameters of the proposed deep learning network would improve the capability of distinguishing between normal and diseased blood images, increase the classification performance, and thus provide a robust automatic ALL-CAD system. The main contributions of this study are listed as follows:The paper is organized as follows: K-nearest neighbor, support vector machine, decision tree, and ensemble random under-sampling boost were applied on a leukemia dataset. The authors applied Jaya algorithm to optimize the rules generated from the classification algorithms. Their findings showed that the classification accuracy of the used classifiers was improved after optimizing with the Jaya algorithm. Agaian et al.  pixels. Afterwards the ranges of the optimization hyperparameters were set. The ranges of the initial learning rate, CBD, regularization coefficient, and SGDM momentum as well as the search functions were used to set variables over the optimization iterations are depicted in −4 or less. Each objective function evaluation was executed in 150 epochs. At the first optimization iteration, the optimization variables, hyperparameters, were set randomly within the specified ranges. The number of convolutional blocks of the proposed CNN was set accordingly, and the network was trained, evaluated, and the objective function was computed and recorded. The Bayesian optimizer then selected the next set of hyperparameters for the second iteration based on the acquisition function maximization. During the second iteration, the selected hyperparameters were used to set the structure of the CNN, train and evaluate the model, and compute the objective function. The Bayesian optimizer used the results of the previous iteration and decided the next set of hyperparameters. The process continued until reaching the predefined maximum number of iterations, 30 iterations, or meeting the stopping criterion. The model that achieved the least objective was considered the optimal model and tested on the test set. The SGDM algorithm was used to train the proposed network using the training subset with a mini-batch size of 128 images, piecewise drop rate for the learning rate of 0.1 per 40 epochs and mean and variance batch normalization decay rates of 0.1. Dropout approach with a probability of 0.5 was adopted to avoid the occurrence of overfitting. The number of objective function evaluations was set to 30. However, a stopping condition was set if the objective function recorded a value of 10−10, and The architecture of the optimal CNN is composed of two basic blocks per convolutional block . Subsequently, the optimal CNN is composed of six convolutional layers, six batch normalization layers, six ReLu layers, two average-pooling layers, one max-pooling layer, and a single softmax layer. The best model of the optimized CNN was assessed on the holdout test set. The optimal model achieved an accuracy, sensitivity, and specificity to detect ALL of 100% on the test set. Sample test images along with their predicted classes and class probability are depicted in −3, and The classification performance of the optimal CNN model is compared to a non-optimized version of the same CNN to figure out the effectiveness of using the Bayesian optimization approach to fine-tune the model hyperparameters. The performance of the optimal model of the proposed ALL detection CNN is further assessed against a number of state-of-the-art deep learning ALL detectors. In this comparison, we compared the proposed CNN with optimized and non-optimized deep learning networks developed for the classification of leukemia. The studies selected for the comparison utilized either the entire ALL-IDB dataset or only one subset of it to train and test their models. In this work, a new customized CNN is proposed for the detection of ALL in microscopic blood images. The architecture of the proposed CNN is set as an optimizable variable. The Bayesian optimization approach is utilized to determine the optimal architecture of the proposed CNN and optimize its hyperparameters. The Bayesian optimization method adopts an iterative procedure to minimize an objective function and select optimum network hyperparameters. Initial learning rate, SGDM algorithm momentum, regularization coefficient, and convolution block depth are the optimizable hyperparameters to be tuned by the Bayesian optimization method. The introduced CNN was trained and validated using a hybrid dataset which was formed by integrating the two publicly available ALL-IDB 1 and 2 datasets. To boost the classification performance of the proposed CNN, data augmentation through image transformations has been adopted to supplement the hybrid image set. The optimal CNN model selected by the Bayesian optimization method for ALL detection recorded accuracy, specificity, and sensitivity of 100% on a holdout test set. This high classification performance was obtained without the need to apply complicated image enhancement or segmentation methods on the input images. The optimized CNN model recorded higher classification accuracy than a non-optimized version of the proposed model which reveals the effectiveness of the Bayesian optimizer in fine-tuning the model hyperparameters. The optimized CNN introduced in this study outperforms the other optimized deep learning ALL classification models and strongly competes with state of the art alternatives.


We analyze the steady laminar incompressible boundary-layer magnetohydrodynamic impacts on the nanofluidic flux over a static and mobile wedge in the existence of an applied magnetic field. The Falkner–Skan wedge flow model is taken into consideration. Reynolds’ model is considered to introduce temperature-dependent viscosity. As in real life, most fluids have variable viscosity. The executive partial differential equations are converted into a set-up of ordinary differential equations by means of a similarity conversion. Numerical solutions are computed for the converted set-up of equations subjected to physical boundary conditions. The specific flow dynamics like velocity profile, streamlines, temperature behavior, and coefficient of local skin friction are graphically analyzed through numerical solutions. It is concluded that the laminar boundary-layer separation from the static and moving wedge surface is altered by the applied external electric field, and the wedge (static or moving) angle improves the surface heat flux in addition to the coefficient of skin friction. Furthermore, it is found that the methanol-based nanofluid is a less-efficient cooling agent than the water-based nanofluid; therefore, the magnitude of the Nusselt number is smaller for the water-based nanofluid. It is also observed that the addition of only 1% of these nanoparticles in a base fluid results in an enhancement of almost 200% in the thermal conductivity. The fluid mechanical aspects of the boundary layer on the static and mobile wedges  have received a lot of attention from researchers and scientists of fluid mechanics mainly because of their applications in diverse situations such as natural flow, mechanical flow, biological flow, and transport of fluids in industries. The laminar boundary-layer flow impacts for a fixed wedge engaged in the viscous incompressible fluid were first reported by earchers . Hartreeearchers  conveyedearchers  numericaearchers  investigearchers  providedearchers  interrogearchers  reportedearchers  providedThe motivation behind the huge intriguing research on the topic of nanofluids in recent years is due to an open range of practical applications in both the engineering and pharmaceutical industries. The dispersion of nano-scale particles in a base fluid provides the combination of the nanofluid and in most cases nanotubes, nanofibers, nanosheets, nanowires, or droplets being used for this purpose. It is experimentally  proved t.In all the aforementioned studies, the study of the nanofluid flow through a static and movable wedge is not reported. However, considering the immense count of practical applications in flow over the wedge, few investigators  have rep, and Motivated by the aforementioned studies and findings, we extend the work of ∞ xm, while the mobile wedge has a velocity u(x) = Uwxm. The range of The numerical computations are performed for the boundary-layer impacts on a fixed or a mobile wedge flow problem considering the nanofluids’ case of copper nanoparticles and two different base fluids, that is, methanol and water. The geometrical diagram of this wedge flow problem is presented in ollision . The curThe pertinent equations that govern this physical flow problem are given as (See Refs )∂u∂x+∂vThe relevant boundary conditions are imposed in the forms:Static wedgeMoving wedgeThe characteristics of the nanofluid model are taken  as folloThe following similarity variables are introduced to convert the problem into a set-up of ordinary differential equations as determined in The following viscosity model known as Reynold’s model is considered :μf(θ)=eOn substituting  into (2) to (4) with boundary conditions (4 and 5), the converted set-up of ordinary differential equations is given as follows:Static WedgeMoving Wedgex-direction and The coefficient of skin friction The shooting technique is utilized to numerically compute the solutions of , Khan and Pop  on streamlines is presented through m = 1, M = 2) on streamline patterns are elucidated through Streamlines are the key characteristics of the fluid flow which are mathematically found when the stream function is constant. For different values of stream function, the variation of stream lines is illustrated in • The extent of the boundary layer reduces with an upsurging magnitude of • The extent of the thermal boundary layer expands by enhancing the value of ••• Nusselt number is more for methanol nanofluids than for water nanofluids.• The Nusselt number is proportional to the viscosity parameter and wedge parameter; however, it is related in an inverse proportion to the Eckert number and Hartman number.• The parabolic nature of streamlines reduces for the –ve value to +ve value of the moving wedge parameter, and it also decreases with the increasing value of the viscosity parameter.The impacts of relevant variable parameters on the characteristics of the Falkner–Skan wedge flow of a temperature-dependent viscous effect with CNT nanofluids have been discussed. The concluding results are summarized as follows:


In this regard, the use of supported lipid bilayers (SLB) in combination with atomic force microscopy, quartz crystal microbalance and fluorescence microscopy has proven to be a powerful tool . On the other hand, the use of tailored small, large or giant unilamellar lipid vesicles , also often referred to as liposomes, constituted a good starting point to carry out studies on the activation energies needed to trigger membrane fusion events, including membrane reshaping and promotion of membrane pore opening.Biological membranes are selectively permeable membranes that separate the interior of a cell from the external environment or adjacent cells. They are micrometre-sized structures based on two-dimensional assemblies of phospholipids carrying integral and peripheral proteins that play a crucial role for cellular function and are the core of cellular communication through direct contact or transport of chemical compounds or ions. All these phenomena are strongly correlated with the interactions of the membrane with lipids, proteins, cofactors, or ions present inside the cell or the extra-cellular environment . To bettic fluid . Membranic fluid . This ReFrançois-Martin et al.). Biometric models based on the construction of supported bilayers, or the formation of GUVs have been shown to constitute one of the most powerful models to achieve a large set of mechanical parameters of a system. Their size (1–100 μm) almost allows to reach the scale of a natural membrane system and permits direct visualization and manipulation. Hence, it is possible to obtain in a straightforward and reliable way mechanical parameters such as bending modulus or membrane viscosity. Nonetheless, the interpretation of the physico-chemical data also depends on the quality of the extracted bio-membrane. The extraction and purification of natural membranes is addressed by the separation and isolation of the inner and outer mitochondrial membranes  . The paper demonstrates that a basic, but rigorous characterization of the native bio-membrane through conventional preparative procedures, that focus on lipid, protein or sugar content, is key to ensure a correct interpretation of the biophysical parameters obtained from the bio-membrane. Using this protocol as a general guideline for the extraction of other native bio-membranes, allows the extraction and initial biophysical study of the material of interest without the need to reconstruct them bottom-up by mixing their individual components. The normalization of this type of approaches will contribute to the expansion of research on natural membranes in combination with mimetic systems.The use of molecular simulations that introduce possible hydrophobic defects of the lipid membrane bilayer allows, in combination with a reconstituted membrane model, to measure nucleation kinetics that boost lipid reorganization through a synergistic process (In summary, the study of the biological membranes using mimetic models requires broad perspective, which is currently structured as a multidisciplinary, including both theoretical and experimental approaches to provide a suitable solution to very complex problems. The study on natural membranes goes hand-in-hand with the development of successful mimetic artificial membranes. Here recent research focuses on some aspects such as membrane plasticity to protect a liposome cargo, the control and targeting at will of the liposomes, or their biocompatibility, which can be improved by mimicking intrinsic characteristics of the surface exposed proteins and lipids. This Research Topic focuses on providing a comprehensive perspective of the current understanding on the study of mimetic membranes, contributing to bridge the gap between the most fundamental aspects of these model systems, and their potential implications in understanding the biophysical aspects involving bio-membranes.


Postoperative diaphragmatic hernia (DH) following endoscopic thoracic sympathectomy for primary palmar hyperhidrosis is extremely rare. We present a 21-year-old female patient who developed a left DH with herniation of the stomach and gastric perforation on the first postoperative day after undergoing bilateral video-assisted thoracoscopic sympathectomy R4 ablation. She complained of severe dyspnea and chest pain, and an emergency chest x-ray and computed tomography revealed left pleural effusion, collapsed lung, and left DH, which allowed the stomach to herniate into the chest. Emergency thoracoscopic surgery was performed. We repaired the diaphragmatic defect intraoperatively and replaced the stomach with the peritoneal cavity from the thoracic field. The patient was discharged without complications. She did not present with recurrent symptoms at the 3-month follow-up. Postoperative DH should be considered when patients complain of gastrointestinal or respiratory symptoms after sympathectomy, although it is very rare. Primary palmar hyperhidrosis (PPH) is defined as a pathologic condition of excessive sweating over 6 months in duration that impairs daily activities without occurring secondary to other specific diseases or medications . CurrentHere we report an extremely rare case of left DH with herniation of the gastric fundus and body following bilateral video-assisted thoracoscopic sympathectomy (VATS) R4 ablation for PPH, and the patient's primary clinical manifestation was respiratory distress. We successfully repaired the DH and the stomach defect by thoracoscopy with mesh placement.2 insufflation was used for exposure. The chest was visualized, and the sympathetic chain was identified. Sympathotomy was performed with an electrocautery section of the sympathetic chain over the head of the rib, extending the burn along the rib for a length of 2–3 cm to cauterize potential bypassing branches of the chain (nerve of Kuntz). The level of sympathotomy (R4) was performed according to Chinese expert consensus  , and theonsensus . After lOn the day of surgery, she began to complain of epigastric discomfort and vomiting, and fasting therapy was given. Chest radiography revealed a pneumothorax in the left lung with an elevated left hemidiaphragm . The folEmergency surgery was performed, and the patient was administered general anesthesia with double-lumen endotracheal intubation and placed in the right hemilateral position for surgery. The operation was performed thoracoscopically and conducted through the eighth intercostal space to expose the pleural cavity. Intraoperatively, a contaminated thoracic cavity with stomach contents was observed, without pleural adhesions . There wThoracoscopic bilateral dorsal sympathectomy is the standard therapeutic method for PPH. To our knowledge, DH is a rare complication of sympathectomy and leads to life-threatening cases of strangulation or perforation as well as cardiovascular and respiratory insufficiencies . In thisThe majority of the patients with diaphragmatic defects have defects that remain small, and they only complain of gastrointestinal symptoms  and respiratory symptoms . Patients can be asymptomatic for a long time and be diagnosed with delayed iatrogenic DH after surgery . PatientConsidering the pathogenesis of DH in our case, it could be related to congenital weakness of the diaphragm. Moreover, prolonged anesthesia induction led to gastric pouch dilatation and continuous high airway pressure, which might amplify the transabdominal-pleural cavity pressure. The dilated gastric wall compressed the left diaphragm, and prolonged intense compression caused severe ischemia, which decreased the elasticity and strength of the diaphragm and eventually led to rupture of the left diaphragm and the formation of an incarcerated diaphragmatic hiatal hernia. During the surgery, the patient is intubated with positive pressure ventilation in the chest, and small perforations in the diaphragm remain collapsed and prevent the migration of abdominal structures. However, in the postoperative period, the respiration and the pressure gradient between the pleural cavity and abdomen consistently pull the small, defective diaphragm radially, gradually extending the small orifice over time until it allows abdominal organ herniation, especially on the left side, because of the cushioning effect of the liver protecting the right hemi diaphragm.Several reports have shown that initially, the chest x-ray is normal or can mimic pleural effusion, pneumonia, or pneumothorax, which can lead to a misdiagnosis. CT is the imaging modality of choice; whenever we see a chest x-ray or CT suggesting obscured diaphragmatic shadow, irregularity of the diaphragmatic contour, pleural effusion, and mediastinal shift, we should suspect the possibility of DH .There are several limitations in our approach to this case. First, on the day of the first surgery, the patient began to complain of nausea and vomiting, and we were not aware of the risk and clinical presentation of diaphragmatic hernia. Second, we should use emergent gastric decompression with a nasogastric tube that may control the situation and let us buy some time to save the patients with fluids and acid–base balance adjustment. Third, the deficiency of thoracentesis is the lack of ultrasound guidance, which is dangerous in such situations. Fourth, a total follow-up period of 3 months by a surgeon may be too short to evaluate the prognosis of the patient.In conclusion, it is important that thoracic surgeons inspect the integrity of the diaphragm at the end of surgery and consider the possibility of this rare complication in patients presenting with gastrointestinal or respiratory symptoms, especially after a left-sided thoracic procedure. After confirmation of DH, a feasible and reliable thoracoabdominal approach could be immediately used for treatment, including reduction of herniated organs and progression to more serious complications .


Due to the extreme environmental temperature variations, solutions that enable ultra-low thermal sensitivity in a mirror assembly are crucial for high-performance aerial optical imaging sensors (AOIS). Strategies such as the elimination of the coefficient of thermal expansion (CTE) mismatch and the employment of a flexure connection at the interface cannot be simply duplicated for the application involved, demanding specific design constraints. The contributions of support point number to the surface thermal sensitivity reduction and support stiffness improvement have been studied. A synthetic six-point support system that integrates equally spaced multiple ultra-low radial stiffness mirror flexure units and assembly external interface flexure units has been demonstrated on a 260 mm apertured annular mirror that involves significant CTE mismatch and demanding support stiffness constraint. The surface deformation RMS, due to the 35 °C temperature variation, is 16.7 nm. With variations of seasons, operating locations, flight altitudes, and weather conditions, aerial optical imaging sensors (AOIS) endure extreme temperature variations that introduce a large gradient, fast rate, and significant variation. Under some extreme conditions of typical flight operation, environmental temperature change can reach nearly 100 ℃ in dozens of minutes from the ground level to the flight altitude ,3. CompaDue to the coexistence of large temperature variations and significant CTE mismatch between the mirror assembly and the external support structure, the large magnitude of thermal coupled mechanical load (TCML) significantly stresses the mirror assembly . The keyFor the purpose of high precision optical alignment, support stiffness is also one of the key concerns during the mirror assembly design process. As for high performance AOIS, the surface decenter and the surface tilt due to gravity are usually needed to be micron level and arc second level, respectively. Because the reduction in surface thermal deformation sensitivity partially correlates with the improvement in support stiffness, the implementation of an ultra-low surface thermal sensitivity mirror assembly that retains high support stiffness is crucial and extremely challenging for the high performance AOIS. Influences of the mirror support scheme on surface thermal sensitivity and mechanical stiffness have been previously reported by David Chin . In the The reduction or elimination of CTE mismatch, which is simple and much more straightforward, has been widely used. Typically, all-SiC optical modules have also been reported ,19,20. TTo find a low-cost solution to the implementation of an ultra-low thermal sensitivity mirror assembly that retains high support stiffness and can also accommodate significant CTE mismatch for high performance AOIS, we concentrated on the contributions of support point number to surface thermal deformation sensitivity reduction and support stiffness improvement. In this paper, in Illustrated as The linear thermal expansion The TCML induced surface elastic deformation Methods to reduce surface thermal deformation sensitivity include: (1) the selection of ultra-low CTE mirror material, (2) the improvement of mirror rigidity, and (3) the reduction of TCML sensitivity at the mirror support point. The selection of ultra-low CTE materials is the key to controlling surface linear thermal expansion sensitivity, particularly for applications involving large temperature variations. Mirror rigidity, which is the intrinsic property that determines the surface elastic deformation quantity due to unit external mechanical stress, determines the mirror assembly temperature variation suitability. Under any circumstances, a high rigidity mirror blank is crucial for the achievement of large temperature variation suitability. The coexistence of a large temperature variation and significant CTE mismatch between the mirror assembly and external structure generates extreme challenges for the reduction of TCML sensitivity at the mirror support point.A simplified analysis model is illustrated as Under uniform temperature variation, the CTE mismatches that occur across the mirror assembly internal interface and the external interface, respectively, cause TCMLs at different hierarchies of the connecting points. The TCML that is due to the CTE mismatch between the mirror blank and the mirror mount is the mirror assembly internal interaction, and it is called the internal thermal coupled mechanical load (ITCML). The TCML that is due to the CTE mismatch between the mirror mount and the external mirror house is the mirror assembly external interaction, and it is called the external thermal coupled mechanical load (ETCML). The ITCML acts at the mirror support point directly; however, the ETCML is attenuated by the mirror mount and acts at the mirror support point indirectly. The total TCML magnitude at each mirror support point can be expressed as,Either the ITCML sensitivity at the mirror support point or the ETCML sensitivity at mirror assembly external interface are governed by: (1) the CTE mismatch of the adjacent two parts, (2) the connecting stiffness at interface, and (3) the radius of the area encircled by the interfaces. The magnitudes of the two can be expressed as,Control strategies of the ITCML sensitivity at the mirror support point and the ETCML sensitivity at the mirror assembly external interface can be summarized as: (1) the elimination of CTE mismatch across the interface, (2) the minimization of the area encircled by the interfaces, and (3) the reduction of connecting stiffness at the interface. Each of the aspects makes a similar contribution to the TCML sensitivity reduction. If the AOIS is ideally made of one type of material, or materials which have the same CTEs, the equipment will be immune to TCML. Due to some other constraints, such as mass, cost, material availability, process maturity, etc., the straightforward elimination of CTE mismatch that contributes significantly to the TCML sensitivity control is theoretically viable, but practically less feasible for implementation to the entire AOIS. The minimization of the area encircled by interfaces which are constrained by some other requirements, such as support stiffness, fastening security, mirror size, etc., also contributes to the reduction in TCML sensitivity.The reduction of connecting stiffness at the interface is a widely used method for controlling TCML sensitivity. For the applications involving significant CTE mismatch and demanding support stiffness requirements, the excessive reduction in connecting stiffness that is derived from extreme temperature variation suitability will cause the reduction in support stiffness and generate some drawbacks to the engineering implementation, particularly for the support schemes that only use a few support points. Theoretically, the increase in connecting points contributes to the improvement of support stiffness for the entire mirror support system and therefore, has some effects on the reduction in connection stiffness at each of the mirror support points.Moreover, improving the attenuation effect of the mirror mount, which usually involves the optimizations of the mount structure stiffness and the load path configuration, can also effectively attenuate the disturbance of the ETCML exerted at the mirror assembly external interface.Under the constraint of the mirror displacement due to gravity, contributions of the support point number to the radial support stiffness and TCML induced surface deformation sensitivity have been studied. For simplification purposes, the mirror is assumed to be suspended in the plane by multiple equally spaced equal-stiffness springs that are arranged symmetrically according to the gravity direction, and only the radial stiffness of the spring connection is considered.Support modes whose support point numbers vary from 3 to 8 have been studied. The typical configurations and the force systems are illustrated as Based on the three-point support mode see g, the spSpring stiffness that fulfils the equilibrium condition for the three-point support mode is expressed as,Support radial stiffness that fulfils the equilibrium condition of gravity equals the combination of all spring forces along the typical direction for different support point number configurations, which can be described as the product of Based on the radial support stiffness requirement, which equals 1 micron side displacement due to gravity, the effects of the support point number on TCML-induced surface deformation sensitivity have been studied on an annular mirror. Surface thermal deformation due to TCML caused by a 10 °C temperature variation has been evaluated. The FEA model and curves of surface deformation RMS value vs. support point number under typical tangential stiffness are illustrated, respectively, in (a)Ideally, the radial support stiffness that balances with the mirror displacement due to gravity is inversely proportional to the support point number. Even though only the radial support stiffness is considered, the TCML-induced surface deformation sensitivity reduces dramatically with the increase in the support point number.(b)Under the given mirror displacement constraints resulting from gravity, tangential stiffness at each support point contributes to the further reduction in radial support stiffness. For the same support point number configuration, TCML induced surface deformation sensitivity can be further reduced with increases in the tangential stiffness at each support point.The results indicate that:Numerous research works have reported mirror mount system designs from aspects such as light-weight mirror optimization, support location optimization, flexure design, system performance evaluation, etc. ,26,27,28(a)Obtain an initially optimized mirror profile.Thickness of the mirror blank can be determined according to the material configuration and the allocated geometric design space. For large temperature variation suitability, a relatively thicker mirror blank is recommended. The distribution of the support points can be optimized under the constraint that the surface deformation error due to gravity along the axial direction is minimized.(b)Determine the maximum allowable compressive force at the mirror support point.Based on the initially optimized mirror profile, the maximum allowable compressive force can be evaluated by the FEA on the simplified mirror assembly model see . The mirror mount system design process is illustrated in (c)Calculate the thermally induced interface displacement mismatch.The radius of the support point distribution circle (see the (d)Obtain an initial radial stiffness that equals the required lateral support stiffness.The required lateral support stiffness (see the (e)Calculate components of the optimized stiffness vector at the mirror support point.Generally, the stiffness vector at each support point consists of an axial component, a radial component, and a tangential component see . For theAfter the data preparation at the upper stream, optimization of the stiffness vector at the mirror support point can be implemented by following the flowchart shown in During the optomechanical system engineering process of a typical high-performance AOIS, the performance of the primary mirror assembly has been allocated from the top system engineering process. The mirror surface thermal deformation RMS value due to a 35 °C temperature variation for a 260 mm apertured annular mirror used in a typical AOIS is required to be no larger than Based on the six-point side support mode, a synthetic support system that consists of six equally spaced Invar-made structure adapters (SAs) and one TC4-made BP that integrates six equally spaced MF units at the inner layer, AEIF units at outer layer, and assembly external interfaces at each AEIF center, is proposed, as shown in The MF of the support system is featured, with an ultra-low radial stiffness that enables an ultra-low response to the radial forced displacements due to the mirror assembly internal thermal expansion mismatch and the ETCML-induced BP deformation, as well as low rotational stiffness that enables an ultra-low torque sensitivity at the mirror support point. The ETCML sensitivity at each external interface has been effectively reduced by the arc-shaped AEIF. Support stiffness has been compensated for by the increased number of external interfaces. The load path from each external interface to the adjacent MF junction with BP middle layer has been deliberately designed. Thus, very limited radial displacement due to ETCML is produced at each MF junction.Fabrication of the proposed design conception involves several ordinary machining processes (at the earlier stage), wire electrical discharge machining operation (at the later stage), and a precision synthetic machining operation . The final stage precision synthetic machining is intended to achieve the coaxiality and the cylindricity of the six SA inner cylindrical faces, the fitting tolerance between the six SA inner cylindrical faces and the mirror side, and the coplanarity of the six small planes that are respectively settled on each SA and used for axial positioning of the mirror. At the assembling stage, the proposed support system can be easily positioned with the mirror along the radial direction and the axial direction respectively, and tangentially positioned with the mirror by plugging a pin into one of the six position holes that are settled on the mirror back and the SA ends, respectively. After the positioning process, a low expansion adhesive is injected into each bond area settled between the mirror side and each SA through the injection hole settled in the BP. After completing the adhesive cure process, a bond layer is formed at each support point of the mirror.During the implementation of the mirror mount system, the evaluation of the surface sensitivity to the thermal or mechanical disturbances is the core concern. The framework that can integrate information streams from three groups of analysis tools: FEA, optimization, and optical performance evaluation, plays the key role. The integrated optomechanical analysis system was proposed by Doyle, K. B., et al. . As for For large temperature variation suitability, a relatively smaller diameter to thickness ratio that enables the excellent bending stiffness of the mirror blank is selected. The weight of the mirror has been lightened by topological optimization. The area between the outer periphery and central perforation side has been defined as the design space. After topological optimization, the hollowed mirror structure that consists of six equally spaced arch ribs, each sequentially connected to one support point, a central perforation wall, and the next adjacent support point, is obtained. The mirror geometric model was rebuilt by referring to the topological optimization results a. The stAs basic unit of the mirror support system, the proposed MF as a multi-link mechanism, consists, respectively, of one movable center pad that connects each mirror support point sequentially via the bolted SA and the bond layer, two axially rotatable radial flexure arms, and tangential flexures which are symmetrically arranged The ETCML equivalent radial force that compresses (or stretches) the BP middle layer along the radial direction decreases, according to the cosine law of the groove semi-arc angle.(b)The increase in the load path length due to the groove semi-arc angle increase simultaneously causes the BP compressive stiffness reduction.(c)The rigidity of the section that is deformed by the ETCML equivalent tangential force pair (see With an increase in the groove semi-arc angle, the AEIF radial stiffness and the involved ETCML sensitivity decrease dramatically. Moreover, the effects introduced to the load path from the external interface to the MF junction are summarized as follows:When When When the The widely used optomechanical integrated analysis and optimization are crucial for the mirror assembly performance evaluation at the final stage ,33,34,35Maps of the surface deformation after the removal of rigid body displacement are shown in The aspects involved in reducing the surface thermal deformation sensitivity for the mirror assembly that involves the demanding constraints of significant CTE mismatch and high support stiffness requirements have been summarized. The contributions of the support point number to surface thermal sensitivity reduction and support stiffness improvement have also been studied.For a typical AOIS that involves significant CTE mismatch at the mirror assembly external interface, a six-point support system that employs ultra-low radial stiffness at each of the mirror support points and a dedicated AEIF at each of the mirror assembly external interfaces has been demonstrated on a 260 mm apertured annular mirror that involves the demanding constraints of a 35 °C temperature variation suitability and a 1 micron surface displacement due to gravity. The surface RMS value due to the 35 °C temperature variation reaches 16.7 nm. Compared with the three-point support scheme, the proposed solution shows great improvements, not only in the aspect of temperature variation suitability, but also in the aspect of large CTE mismatch suitability.The results indicate that increasing the support point number provides a viable strategy for the realization of an ultra-low thermal sensitivity mirror assembly which retains high support stiffness.