Tip/Tilt Error Correction Of Synthetic Aperture Imaging System

Large optical telescopes have significant applications in many fields,such as weather forecasting,earth resources surveying,environmental inspection,astronomical observation,military reconnaissance,and space situation awareness.According to the Rayleigh criterion,high-resolution optical imaging systems require large apertures for distinguishing distant objects.However,due to the mass,volume,cost and carrier load constraints,unlimited increase of the aperture size is unrealistic.To overcome these restrictions,A.B.Meinel proposed the concept of synthetic aperture telescope in 1970.Via interferometry and the combination of multiple small aperture systems,the Airy disk of the synthetic aperture imaging system is narrower than that of the monolithic optical system.The synthetic aperture imaging technology not only avoids greatly increasing the mass,volume and cost,but also greatly simplifies the maintenance and operation of the system,which is of convenience to carry out modular design and adjustment,while improving the spatial angular resolution.Therefore,current trends in high-resolution imaging are to develop synthetic aperture imaging technology.The main factor that affects the imaging quality of the synthetic aperture system is the beam combining errors.The tip/tilt errors,as a kind of low-order aberrations,have a particularly prominent impact on the imaging.The tip/tilt aberrations arising from the system assembly,carrier jitter,actuator creep,thermal drift and air turbulence shift the sub-spots that should be converged at the same position on the focal plane.In this case,the diffraction spots cannot completely overlap,which will decrease the interference performance of the system.Therefore,keeping the tip/tilt errors within a certain tolerance is a key issue in synthetic aperture imaging technology.In this paper,the tip/tilt alignment of the synthetic aperture imaging system is the subject,and the Fizeau telescope system is chose to be the research object.To achieve the tip/tilt alignment,the tip/tilt detection and the control strategy have to be studied.According to the investigation of the present tip/tilt detection method,it is hard to achieve real-time tip/tilt detection under the full field of view.The Phase Diversity algorithm can only detect the tip/tilts within /8.When the tip/tilts are so small that the sub-spots are already partially overlapped on the image plane,the ELASTIC algorithm cannot detect the tip/tilts,and the Shift Detecting method inevitably requires complex optical hardware to decouple the tip/tilts.Compared with the Phase Diversity algorithm and the ELASTIC algorithm,the Shift Detecting method does not demand complex calculation.Therefore,an improvement based on the Shift Detecting method is made so that a simple tip/tilt alignment scheme via defocus-based sub-spot separation(TADS)is proposed.The TADS is able to decouple the tip/tilt errors by introducing defocus aberrations on the entire pupil plane,which gets rid of the limitation of optical hardware.In this paper,the feasibility of TADS has been theoretically proved by wave optics and the principle of geometric optics.At the same time,the given image processing algorithm guarantee that the tip/tilt errors of each subaperture can be calculated without limitation of the sub-aperture amount,despite that the light spots have already interfered with each other.The control strategy determines the correction accuracy and bandwidth of the system.After investigating the present control scheme of synthetic aperture imaging system,a charge-coupled device(CCD)is chosen as the sensor,because of CCD’s high integration,small size,high resolution,low noise and digital transmission.Fast steering mirror is chosen as the actuator,adjusting the beam pointing to compensate the tip/tilt errors,and the fast steering mirror is driven by piezoelectric ceramics,because the piezoelectric ceramics driver has small size,small inertia and low resonance frequency.Besides,the classic,simple and effective PID controller based on negative feedback control structure is used as the control algorithm.In order to verify the practicability of the TADS,a Fizeau telescope testbed with seven individual sub-apertures is built,and a series of experiments is conducted.Experimental results show that the TADS can decouple interfered sub-spots positions,and accurately extract the tip/tilt errors of each sub-aperture.Compared with the openloop manner,the tip/tilt errors in the closed-loop manner is reduced by at least 51%,and even up to 81%.Furthermore,the closed-loop real-time correction accuracy meets the imaging requirements(the Strehl ratio is not less than 0.98).Therefore,the proposed TADS in this paper enables the synthetic aperture imaging system to not only ensure real-time control when correcting the tip/tilt errors,but also is not limited by the error range and complex optical hardware,which promotes the tip/tilt alignment technology.However,the amplitude spectral density analysis of the experimental results demonstrates that the system can only achieve low-frequency tip/tilt correction,the mid-and high-frequency errors mainly introduced by carrier jitter cannot be compensated,the reason of which is that the bandwidth of the control algorithm used in this paper is severely limited by the system time-delay.Therefore,in order to improve the suppression bandwidth,a scheme of introducing combined control into the synthetic aperture imaging system is proposed in this paper.In this scheme,a feedforward controller can be designed to eliminate the influence of disturbance on the system,with an inertial sensor detecting the carrier jitter.According to the theoretical analysis and the simulation,how to decouply construct accurate disturbance transfer functions is the crucial to the combined control technology.Apart from the mid and low-frequency errors of the laboratory platform,the synthetic aperture imaging system based on the moving carrier needs to correct higherfrequency tip/tilt errors introduced by the carrier jitter,so the combined control technology needs to be studied in the future research.In addition,in order to mark the reference signal in advance,a manual calibration of the optical axis of the system has to be done when practicing TADS.Hence,how to realize the automatic optical axis calibration technology of the synthetic aperture imaging system is another unresolved issue of the follow-up works.