A practical antenna has been designed and developed for INMARSAT mobile satellite communications. The design uses low cost materials such as foam and copper foil to create a stacked microstrip antenna array. Several t...A practical antenna has been designed and developed for INMARSAT mobile satellite communications. The design uses low cost materials such as foam and copper foil to create a stacked microstrip antenna array. Several techniques were adopted to enhance the impedance bandwidth and axial ratio bandwidth. The final design parameters were optimized by EM simulation. Finally, the L-strip fed six-element stacked microstrip antenna array was constructed and tested. Simulated and measured results show that in the whole INMARSAT work band, the VSWR of the antenna is less than 1.6, its antenna gain is higher than 15dB and wide-angle axial ratio （AR） 3dB is more than 21°. The antenna has been successfully used with a HNS 9201 terminal.展开更多
In this paper,a new compact ultrawideband(UWB)circularly polarized(CP)antenna array for vehicular communications is proposed.The antenna array consists of a 2×2 sequentially rotated T-shaped cross dipole,four par...In this paper,a new compact ultrawideband(UWB)circularly polarized(CP)antenna array for vehicular communications is proposed.The antenna array consists of a 2×2 sequentially rotated T-shaped cross dipole,four parasitic elements,and a feeding network.By loading the T-shaped cross dipoles with parasitic rectangular elements with cut corners,the bandwidth can be expanded.On this basis,the radiation pattern can be improved by the topology with sequential rotation of four T-shaped cross-dipole antennas,and the axial ratio(AR)bandwidth of the antenna also can be further enhanced.In addition,due to the special topology that the vertical arms of all Tshaped cross dipoles are all oriented toward the center of the antenna array,the gain of proposed antenna is improved while the size of the antenna is almost the same as the traditional cross dipole.Simulated and measured results show that the proposed antenna has good CP characteristics,an impedance bandwidth for S11<-10 d B of about 106.1%(3.26:1,1.57-5.12 GHz)and the 3-d B AR bandwidth of about 104.1%(3.17:1,1.57-4.98 GHz),a wide 3-d B gain bandwidth of 73.3%as well as the peak gain of 8.6 d Bic at 3.5 GHz.The overall size of antenna is 0.56λ×0.56λ×0.12λ(λrefers to the wavelength of the lowest operating frequency in free space).The good performance of this compact UWB CP antenna array is promising for applications in vehicular communications.展开更多
This paper proposes a communication system for nanosatellite Earth observa-tion preliminary design technique as useful tools for managing and improving various aspects of regional and national resources. Under analysi...This paper proposes a communication system for nanosatellite Earth observa-tion preliminary design technique as useful tools for managing and improving various aspects of regional and national resources. Under analysis was pro-posed a design process for the low Earth orbit nanosatellite communication system. In proposed paper have been formulated and solved next goals: re-viewed Earth observation systems and studied their design parameters, ana-lyzed the on-board antennas design background and provided analytical esti-mations, such as design a passband quadrature phase shift keying transmitter and receiver in Simulink, was obtained a bit error rate curves by using a Sim-ulink/MathWorks, generated an offset quadrature phase shift keying waveform and investigated their characteristics, observed and analyzed the diagrams, constellation, and the signal trajectories of quadrature phase shift keying ac-cording contemporary design concept. As a result, this allows to propose in-novative communication system design techniques applied for the nanosatel-lite category.展开更多
A compact,reconfigurable antenna supporting multiple wireless services with a minimum number of switches is found lacking in literature and the same became the focus and outcome of this work.It was achieved by designi...A compact,reconfigurable antenna supporting multiple wireless services with a minimum number of switches is found lacking in literature and the same became the focus and outcome of this work.It was achieved by designing a Th-Shaped frequency reconfigurable multi-band microstrip planar antenna,based on use of a single switch within the radiating structure of the antenna.Three frequency bands(i.e.,2007–2501 MHz,3660–3983MHz and 9341–1046 MHz)can be operated with the switch in the ON switch state.In the OFF state of the switch,the antenna operates within the 2577–3280MHz and 9379–1033MHz Bands.The proposed antenna shows an acceptable input impedance match with Voltage Standing Wave Ratio(VSWR)less than 1.2.The peak radiation efficiency of the antenna is 82%.A reasonable gain is obtained from 1.22 to 3.31 dB within the operating bands is achieved.The proposed antenna supports UniversalMobile Telecommunication System(UMTS)-1920 to 2170 MHz,Worldwide Interoperability and Microwave Access(WiMAX)/Wireless Broadband/(Long Term Evolution)LTE2500–2500 to 2690 MHz,Fifth Generation(5G)-2500/3500 MHz,Wireless Fidelity(Wi-Fi)/Bluetooth-2400 to 2480 MHz,and Satellite communication applications in X-Band-8000 to 12000 MHz.The overall planar dimension of the proposed antenna is 40×20mm2.The antennawas designed,along with the parametric study,using Electromagnetic(EM)simulation tool.The antenna prototype is fabricated for experimental validation with the simulated results.The proposed antenna is low profile,tunable,lightweight,cheap to fabricate and highly efficient and hence is deemed suitable for use in modern wireless communication electronic devices.展开更多
Broadband satellite communications can enable a plethora of applications in customer services, global nomadic coverage and disaster prediction and recovery. Terahertz(THz) band is envisioned as a key satellite communi...Broadband satellite communications can enable a plethora of applications in customer services, global nomadic coverage and disaster prediction and recovery. Terahertz(THz) band is envisioned as a key satellite communication technology due to its very broad bandwidth, astrophysical observation advantages and device maturing in recent years. In this paper, a massive-antenna-array-enabled THz satellite communication system is proposed to be established in Tanggula, Tibet, where the average altitude is 5.068 km and the mean-clear-sky precipitable water vapor(PWV) is as low as 1.31 mm. In particular, a link budget analysis(LBA) framework is developed for THz space communications, considering unique THz channel properties and massive antenna array techniques. Moreover, practical siting conditions are taken into account, including the altitude, PWV, THz spectral windows, rain and cloud factors. On the basis of the developed link budget model, the massive antenna array model, and the practical parameters in Tanggula, the performances of signal-to-noise ratio(SNR) and capacity are evaluated. The results illustrate that 1 Tbit/s is attainable in the 0.275~0.37 THz spectral window in Tanggula, by using an antenna array of the size 64.展开更多
In order to determine an appropriate attitude of three-axis stabilized communication satellites, this paper describes a novel attitude determination method using direction of arrival （DOA） estimation of a ground sig...In order to determine an appropriate attitude of three-axis stabilized communication satellites, this paper describes a novel attitude determination method using direction of arrival （DOA） estimation of a ground signal source. It differs from optical measurement, magnetic field measurement, inertial measurement, and global positioning system （GPS） attitude determination. The proposed method is characterized by taking the ground signal source as the attitude reference and acquiring attitude information from DOA estimation. Firstly, an attitude measurement equation with DOA estimation is derived in detail. Then, the error of the measurement equation is analyzed. Finally, an attitude determination algorithm is presented using a dynamic model, the attitude measurement equation, and measurement errors. A developing low Earth orbit （LEO） satellite which tests mobile communication technology with smart antennas can be stabilized in three axes by corporately using a magnetometer, reaction wheels, and three-axis magnetorquer rods. Based on the communication satellite, simulation results demonstrate the effectiveness of the method. The method could be a backup of attitude determination to prevent a system failure on the satellite. Its precision depends on the number of snapshots and the input signal-to-noise ratio （SNR） with DOA estimation.展开更多
This paper reveals a new design of UHF CubeSat antenna based on a modified Planar Inverted F Antenna(PIFA)for CubeSat communication.The design utilizes a CubeSat face as the ground plane.There is a gap of 5 mm beneath...This paper reveals a new design of UHF CubeSat antenna based on a modified Planar Inverted F Antenna(PIFA)for CubeSat communication.The design utilizes a CubeSat face as the ground plane.There is a gap of 5 mm beneath the radiating element that facilitates the design providing with space for solar panels.The prototype is fabricated using Aluminum metal sheet and measured.The antenna achieved resonance at 419 MHz.Response of the antenna has been investigated after placing a solar panel.Lossy properties of solar panels made the resonance shift about 20 MHz.This design addresses the frequency shifting issue after placing the antenna with the CubeSat body.This phenomenon has been analyzed considering a typical 1U and 2U CubeSat body with the antenna.The antenna achieved a positive realized gain of 0.7 dB and approximately 78%of efficiency at the resonant frequency with providing 85%of open space for solar irradiance onto the solar panel.展开更多
Modeling and attitude control methods for a satellite with a large deployable antenna are studied in the present paper. Firstly, for reducing the model dimension, three dynamic models for the deploying process are dev...Modeling and attitude control methods for a satellite with a large deployable antenna are studied in the present paper. Firstly, for reducing the model dimension, three dynamic models for the deploying process are developed, which are built with the methods of multi-rigid-body dynam- ics, hybrid coordinate and substructure. Then an attitude control method suitable for the deploying process is proposed, which can keep stability under any dynamical parameter variation. Subse- quently, this attitude control is optimized to minimize attitude disturbance during the deploying process. The simulation results show that this attitude control method can keep stability and main- tain proper attitude variation during the deploying process, which indicates that this attitude con- trol method is suitable for practical applications.展开更多
Due to limited antenna space,high communication requirements,and strict regulatory constraints,the design of antennas for modern mobile phones has become an exceedingly challenging task.In recent years,numerous studie...Due to limited antenna space,high communication requirements,and strict regulatory constraints,the design of antennas for modern mobile phones has become an exceedingly challenging task.In recent years,numerous studies have been conducted in this area,leading to significant advancements.This review paper comprehensively summarizes recent progress made in antenna design for modern mobile phones.Firstly,the challenges faced in antenna design for modern mobile phones are described,including bandwidth enhancement,integration and decoupling techniques,mm-wave array antennas,satellite communication antennas,as well as interactions between mobile antennas and the human body.Secondly,the basic antenna types(such as inverted-F,slot,loop,and planar inverted-F antennas)commonly used in modern metal-bezel mobile phones along with their key characteristics are briefly summarized.Thirdly,the commonly exployed methods used in practical applications for designing wideband antennas within compact sizes and achieving decoupling among multiple antennas with wide bandwidths are collected.Fourthly,recent advances in the design of compact,wideband,and wide-angle scanning mm-wave arrays for modern mobile phones are summarized.Fifthly,recent progress made in satellite communication antenna designs for modern mobile phones,including broadside and end-fire radiation patterns,is presented.Sixthly,recent studies on the interaction between mobile antennas and the human body are briefly concluded.Finally,the future challenge of antenna design for mobile phones is briefly discussed.It is our hope that this comprehensive review will provide readers with a systematic understanding of antenna design principles applicable to modern mobile phones.展开更多
In mobile satellite communication networks employing digital beam forming technology,beam alignment imposes great influence on link quality and network efficiency.Owing to complex coupling motion by low earth orbit(LE...In mobile satellite communication networks employing digital beam forming technology,beam alignment imposes great influence on link quality and network efficiency.Owing to complex coupling motion by low earth orbit(LEO)satellite and ship,direction of arrival(DOA)of target satellite varies rapidly and nonlinearly.It then causes difficulty to accurately track the DOA.In this work,an adaptive tracking algorithm is proposed by exploiting advantages of flexible parameter configuration of digital phased-array antenna.The alignment process basically consists of observation and tracking.In the observation stage,two-dimensional(2-D)multiple signal classification(MUSIC)is applied by the ship-borne digital phased-array antenna to estimate beam direction of satellite;in the tracking stage,an extended Kalman filter(EKF)based adaptive tracking is designed to achieve fast and accurate alignment.The proposed adaptive tracking improves performance by adaptively estimating tracking parameters in EKF firstly.The estimation results are then used as feedback to adaptively adjust digital phased-array antenna parameters to improve estimation accuracy of DOA.Simulation results under sea state 5 show that the proposed tracking algorithm improves tracking accuracy and stability over conventional ones.展开更多
In satellite laser communication technology, which is built between planets and between a planet and the Earth, the optical antenna is the key point. Thus, research on optical system design is important. The off-axis ...In satellite laser communication technology, which is built between planets and between a planet and the Earth, the optical antenna is the key point. Thus, research on optical system design is important. The off-axis reflective system has no obscuration and hence possesses a high efficiency for energy transfer. This study proposes a novel method for designing a free-form off-axis reflective imaging system. This study also introduces differential equations that depend on Fermat＇s principle and sine condition. Finally, a free-form off-axis two-mirror optical system was designed by using the differential equation method. This system includes one intermediate image plane, in which the field of view （FOV） is -5° to -4° in the y-axis and -1° to 0° in the x-axis. The modulation transfer function was greater than 0.7 at 50 lp/mm, and the efficiency of energy transmission was high. The free-form off-axis two-mirror optical system involves a wide range of application prospects in the optical antenna used in the satellite laser communication systems. Moreover, the design method that used differ- ential equations was proven simple and effective.展开更多
文摘A practical antenna has been designed and developed for INMARSAT mobile satellite communications. The design uses low cost materials such as foam and copper foil to create a stacked microstrip antenna array. Several techniques were adopted to enhance the impedance bandwidth and axial ratio bandwidth. The final design parameters were optimized by EM simulation. Finally, the L-strip fed six-element stacked microstrip antenna array was constructed and tested. Simulated and measured results show that in the whole INMARSAT work band, the VSWR of the antenna is less than 1.6, its antenna gain is higher than 15dB and wide-angle axial ratio （AR） 3dB is more than 21°. The antenna has been successfully used with a HNS 9201 terminal.
基金supported in part by the National Natural Science Foundation of China(NSFC)under Grant No.62071306in part by Shenzhen Science and Technology Program under Grants JCYJ202001091-13601723,JSGG20210802154203011 and JSGG-20210420091805014。
文摘In this paper,a new compact ultrawideband(UWB)circularly polarized(CP)antenna array for vehicular communications is proposed.The antenna array consists of a 2×2 sequentially rotated T-shaped cross dipole,four parasitic elements,and a feeding network.By loading the T-shaped cross dipoles with parasitic rectangular elements with cut corners,the bandwidth can be expanded.On this basis,the radiation pattern can be improved by the topology with sequential rotation of four T-shaped cross-dipole antennas,and the axial ratio(AR)bandwidth of the antenna also can be further enhanced.In addition,due to the special topology that the vertical arms of all Tshaped cross dipoles are all oriented toward the center of the antenna array,the gain of proposed antenna is improved while the size of the antenna is almost the same as the traditional cross dipole.Simulated and measured results show that the proposed antenna has good CP characteristics,an impedance bandwidth for S11<-10 d B of about 106.1%(3.26:1,1.57-5.12 GHz)and the 3-d B AR bandwidth of about 104.1%(3.17:1,1.57-4.98 GHz),a wide 3-d B gain bandwidth of 73.3%as well as the peak gain of 8.6 d Bic at 3.5 GHz.The overall size of antenna is 0.56λ×0.56λ×0.12λ(λrefers to the wavelength of the lowest operating frequency in free space).The good performance of this compact UWB CP antenna array is promising for applications in vehicular communications.
文摘This paper proposes a communication system for nanosatellite Earth observa-tion preliminary design technique as useful tools for managing and improving various aspects of regional and national resources. Under analysis was pro-posed a design process for the low Earth orbit nanosatellite communication system. In proposed paper have been formulated and solved next goals: re-viewed Earth observation systems and studied their design parameters, ana-lyzed the on-board antennas design background and provided analytical esti-mations, such as design a passband quadrature phase shift keying transmitter and receiver in Simulink, was obtained a bit error rate curves by using a Sim-ulink/MathWorks, generated an offset quadrature phase shift keying waveform and investigated their characteristics, observed and analyzed the diagrams, constellation, and the signal trajectories of quadrature phase shift keying ac-cording contemporary design concept. As a result, this allows to propose in-novative communication system design techniques applied for the nanosatel-lite category.
基金the Deanship of Scientific Research,Najran University.Kingdom of Saudi Arabia,for funding this work under the Research Collaborations funding program Grant Code Number(NU/RC/SERC//11/5).
文摘A compact,reconfigurable antenna supporting multiple wireless services with a minimum number of switches is found lacking in literature and the same became the focus and outcome of this work.It was achieved by designing a Th-Shaped frequency reconfigurable multi-band microstrip planar antenna,based on use of a single switch within the radiating structure of the antenna.Three frequency bands(i.e.,2007–2501 MHz,3660–3983MHz and 9341–1046 MHz)can be operated with the switch in the ON switch state.In the OFF state of the switch,the antenna operates within the 2577–3280MHz and 9379–1033MHz Bands.The proposed antenna shows an acceptable input impedance match with Voltage Standing Wave Ratio(VSWR)less than 1.2.The peak radiation efficiency of the antenna is 82%.A reasonable gain is obtained from 1.22 to 3.31 dB within the operating bands is achieved.The proposed antenna supports UniversalMobile Telecommunication System(UMTS)-1920 to 2170 MHz,Worldwide Interoperability and Microwave Access(WiMAX)/Wireless Broadband/(Long Term Evolution)LTE2500–2500 to 2690 MHz,Fifth Generation(5G)-2500/3500 MHz,Wireless Fidelity(Wi-Fi)/Bluetooth-2400 to 2480 MHz,and Satellite communication applications in X-Band-8000 to 12000 MHz.The overall planar dimension of the proposed antenna is 40×20mm2.The antennawas designed,along with the parametric study,using Electromagnetic(EM)simulation tool.The antenna prototype is fabricated for experimental validation with the simulated results.The proposed antenna is low profile,tunable,lightweight,cheap to fabricate and highly efficient and hence is deemed suitable for use in modern wireless communication electronic devices.
基金the National Natural Science Foundation of China(No.61701300)the Shanghai Sailing(YANG FAN)Program(No.17YF1409900)HAN Chong’s"Chenguang Program"Supported by Shanghai Education Development Foundation and Shanghai Municipal Education Commission
文摘Broadband satellite communications can enable a plethora of applications in customer services, global nomadic coverage and disaster prediction and recovery. Terahertz(THz) band is envisioned as a key satellite communication technology due to its very broad bandwidth, astrophysical observation advantages and device maturing in recent years. In this paper, a massive-antenna-array-enabled THz satellite communication system is proposed to be established in Tanggula, Tibet, where the average altitude is 5.068 km and the mean-clear-sky precipitable water vapor(PWV) is as low as 1.31 mm. In particular, a link budget analysis(LBA) framework is developed for THz space communications, considering unique THz channel properties and massive antenna array techniques. Moreover, practical siting conditions are taken into account, including the altitude, PWV, THz spectral windows, rain and cloud factors. On the basis of the developed link budget model, the massive antenna array model, and the practical parameters in Tanggula, the performances of signal-to-noise ratio(SNR) and capacity are evaluated. The results illustrate that 1 Tbit/s is attainable in the 0.275~0.37 THz spectral window in Tanggula, by using an antenna array of the size 64.
基金co-supported by the National Natural Science Foundation of China (No. 61073012)the Aeronautical Science Foundation of China (No. 20111951015)
文摘In order to determine an appropriate attitude of three-axis stabilized communication satellites, this paper describes a novel attitude determination method using direction of arrival （DOA） estimation of a ground signal source. It differs from optical measurement, magnetic field measurement, inertial measurement, and global positioning system （GPS） attitude determination. The proposed method is characterized by taking the ground signal source as the attitude reference and acquiring attitude information from DOA estimation. Firstly, an attitude measurement equation with DOA estimation is derived in detail. Then, the error of the measurement equation is analyzed. Finally, an attitude determination algorithm is presented using a dynamic model, the attitude measurement equation, and measurement errors. A developing low Earth orbit （LEO） satellite which tests mobile communication technology with smart antennas can be stabilized in three axes by corporately using a magnetometer, reaction wheels, and three-axis magnetorquer rods. Based on the communication satellite, simulation results demonstrate the effectiveness of the method. The method could be a backup of attitude determination to prevent a system failure on the satellite. Its precision depends on the number of snapshots and the input signal-to-noise ratio （SNR） with DOA estimation.
文摘This paper reveals a new design of UHF CubeSat antenna based on a modified Planar Inverted F Antenna(PIFA)for CubeSat communication.The design utilizes a CubeSat face as the ground plane.There is a gap of 5 mm beneath the radiating element that facilitates the design providing with space for solar panels.The prototype is fabricated using Aluminum metal sheet and measured.The antenna achieved resonance at 419 MHz.Response of the antenna has been investigated after placing a solar panel.Lossy properties of solar panels made the resonance shift about 20 MHz.This design addresses the frequency shifting issue after placing the antenna with the CubeSat body.This phenomenon has been analyzed considering a typical 1U and 2U CubeSat body with the antenna.The antenna achieved a positive realized gain of 0.7 dB and approximately 78%of efficiency at the resonant frequency with providing 85%of open space for solar irradiance onto the solar panel.
基金sponsored by the National Natural Science Foundation of China (No. 11272172)
文摘Modeling and attitude control methods for a satellite with a large deployable antenna are studied in the present paper. Firstly, for reducing the model dimension, three dynamic models for the deploying process are developed, which are built with the methods of multi-rigid-body dynam- ics, hybrid coordinate and substructure. Then an attitude control method suitable for the deploying process is proposed, which can keep stability under any dynamical parameter variation. Subse- quently, this attitude control is optimized to minimize attitude disturbance during the deploying process. The simulation results show that this attitude control method can keep stability and main- tain proper attitude variation during the deploying process, which indicates that this attitude con- trol method is suitable for practical applications.
基金This work was supported by the National Natural Science Foundation of China(Grant Nos.62101133,62271279,62271282)the Natural Science Foundation of Shanghai(Grant No.21ZR1406800)the Shanghai Rising Star Program(Grant No.22QC1400100).
文摘Due to limited antenna space,high communication requirements,and strict regulatory constraints,the design of antennas for modern mobile phones has become an exceedingly challenging task.In recent years,numerous studies have been conducted in this area,leading to significant advancements.This review paper comprehensively summarizes recent progress made in antenna design for modern mobile phones.Firstly,the challenges faced in antenna design for modern mobile phones are described,including bandwidth enhancement,integration and decoupling techniques,mm-wave array antennas,satellite communication antennas,as well as interactions between mobile antennas and the human body.Secondly,the basic antenna types(such as inverted-F,slot,loop,and planar inverted-F antennas)commonly used in modern metal-bezel mobile phones along with their key characteristics are briefly summarized.Thirdly,the commonly exployed methods used in practical applications for designing wideband antennas within compact sizes and achieving decoupling among multiple antennas with wide bandwidths are collected.Fourthly,recent advances in the design of compact,wideband,and wide-angle scanning mm-wave arrays for modern mobile phones are summarized.Fifthly,recent progress made in satellite communication antenna designs for modern mobile phones,including broadside and end-fire radiation patterns,is presented.Sixthly,recent studies on the interaction between mobile antennas and the human body are briefly concluded.Finally,the future challenge of antenna design for mobile phones is briefly discussed.It is our hope that this comprehensive review will provide readers with a systematic understanding of antenna design principles applicable to modern mobile phones.
基金This work was supported by NSFC project(No.61971379)by Zhejiang Provincial NSFC project(No.LY16F010005).
文摘In mobile satellite communication networks employing digital beam forming technology,beam alignment imposes great influence on link quality and network efficiency.Owing to complex coupling motion by low earth orbit(LEO)satellite and ship,direction of arrival(DOA)of target satellite varies rapidly and nonlinearly.It then causes difficulty to accurately track the DOA.In this work,an adaptive tracking algorithm is proposed by exploiting advantages of flexible parameter configuration of digital phased-array antenna.The alignment process basically consists of observation and tracking.In the observation stage,two-dimensional(2-D)multiple signal classification(MUSIC)is applied by the ship-borne digital phased-array antenna to estimate beam direction of satellite;in the tracking stage,an extended Kalman filter(EKF)based adaptive tracking is designed to achieve fast and accurate alignment.The proposed adaptive tracking improves performance by adaptively estimating tracking parameters in EKF firstly.The estimation results are then used as feedback to adaptively adjust digital phased-array antenna parameters to improve estimation accuracy of DOA.Simulation results under sea state 5 show that the proposed tracking algorithm improves tracking accuracy and stability over conventional ones.
基金This study was supported by the Youth Innovation Promotion Association, Chinese Academy of Sciences and the National Science Foundation for Young Scholars of China （Grant No. 61505203）.
文摘In satellite laser communication technology, which is built between planets and between a planet and the Earth, the optical antenna is the key point. Thus, research on optical system design is important. The off-axis reflective system has no obscuration and hence possesses a high efficiency for energy transfer. This study proposes a novel method for designing a free-form off-axis reflective imaging system. This study also introduces differential equations that depend on Fermat＇s principle and sine condition. Finally, a free-form off-axis two-mirror optical system was designed by using the differential equation method. This system includes one intermediate image plane, in which the field of view （FOV） is -5° to -4° in the y-axis and -1° to 0° in the x-axis. The modulation transfer function was greater than 0.7 at 50 lp/mm, and the efficiency of energy transmission was high. The free-form off-axis two-mirror optical system involves a wide range of application prospects in the optical antenna used in the satellite laser communication systems. Moreover, the design method that used differ- ential equations was proven simple and effective.
