Fourier Telescopy Research Articles

Improved field performance of Fourier telescopy in real atmosphere turbulence using new phase closure iteration for object spatial spectrum reconstruction

Fourier telescopy is a remote imaging method that generates several interfering fringes from a coherent laser transmitter array. In this technique, the spatial spectrum of an object is acquired by sweeping fringes of different spatial frequencies and directions on the object. Most traditional triplet phase closure iterations are accomplished by three beams and are used to alleviate the phase aberration induced by atmospheric effects. For reducing the effect of scintillation, which is an atmospheric turbulence effect, we propose a phase closure method wherein the complex amplitude of four beams are combined in iteration. We evaluated the performance of the proposed method both theoretically and experimentally. We conducted the field experiments at 200 m and 1.2 km. The results demonstrated that the proposed phase closure method performs well in enhancing the image quality in a multibeam array when there is scintillation in the atmosphere.

Field experiment and image reconstruction using a Fourier telescopy imaging system over a 600-m-long horizontal path.

To confirm the effect of uplink atmospheric turbulence on Fourier telescopy (FT), we designed a system for far-field imaging, utilizing a T-type laser transmitting configuration with commercially available hardware, except for a green imaging laser. The horizontal light transmission distance for both uplink and downlink was ∼300 m. For both the transmitting and received beams, the height upon the ground was below 1 m. The imaging laser's pointing accuracy was ∼9.3 μrad. A novel image reconstruction approach was proposed, yielding significantly improved quality and Strehl ratio of reconstructed images. From the reconstruction result, we observed that the tip/tilt aberration is tolerated by the FT system even for Changchun's atmospheric coherence length parameter (r0) below 3 cm. The resolution of the reconstructed images was ∼0.615 μrad.

Analysis of the redundancy of Fourier telescopy transmitter array and its redundancy-strehl ratio-target texture distribution characteristic

The Fourier telescopy is a kind of active illumination imaging with high resolution by using multi-interfering fringes generated by the multi-beams from the large transmitter arrays. According to the imaging principle, the beams from one laser source are split and each beam is applied with a different tiny frequency shift so that the interfering fringes may moving across the target. The configuration of the beams changes so that they would generate fringes in different spatial frequencies and different directions. Recently, most of researches focused on the factors such as the baseline scale and data sampling efficiency that may affect the imaging quality. However, there are other two factors, i.e., the configuration of the transmitter and its redundancy, which need studying. In Fourier telescopy, if the direction and spatial frequency of the fringe patterns that are generated by the change of different baseline configurations match each other, the target surface information would be a crucial factor that affects the image quality.In the first part of this article, the practicability of zero redundancy of baseline is analyzed. The results show that the baseline cannot have zero redundancy due to the iteration algorithm. Then the minimum redundancy is analyzed and the minimum redundancy line is proposed. By using the Strehl ratio as the merit of the imaging quality, the concept of redundancy-strehl ratio-target texture distribution (RST) and calculation method are proposed. This method integrates the transmitter redundancy, target detail information and image quality together. The distribution of RST value on the frequency plane is compared with the minimum redundancy line. If the RST point is located on the horizontal side compared with the line, the target detail information on this baseline is mainly in the horizontal direction. On the other hand, if the RST point is located on the longitude side, the target information is mainly in the longitude direction. Therefore this new proposed method reveals the relationship between target spatial information and the baseline configuration. In this article T-shaped transmitter array is adopted, and the Fourier components are mainly distributed on the rectangle plane. According to this relationship and calculated RST value, the working transmitter may continuously rectify its scale and shifting patterns so that the spatial frequencies and directions of fringes may match the target Fourier components in time. In this article, three simulated images and two real images are tested by the proposed method, and the results show that the RST values and the distributions well reveale the relationship between the detailed information and the baseline configurations.Now the Fourier telescopy follows the procedure from laboratory setup to the real system research. Considering the convenience and cost of project realization, this method is helpful for analyzing the real system of the transmitter configuration and enhancing working efficiency.

Analysis on reconstruction of virtual images of Fourier telescopy

Fourier telescopy can realize high resolution imaging to remote, small and dim target by using laser as the light source. The signal-to-noise ratio of imaging system is easy to improve by increasing the area of receiver. However, numerical simulation shows that the reconstruction images sometimes has a virtual phenomenon. It reduces the quality of reconstruction images, and even cannot have a resolution to the imaging target. Based on Fourier telescopy imaging principle, using T type transmitting array, the reason of forming virtual images is indicated by mathematical deduction. The spatial frequency error between the actual getting and setting would be produced when the laser beams scan the x or y axis with pitch error. The error would cause the random phase influence when calculating the single Fourier frequency of target by using phase closure on the axis and quadrant scan. Using integrated spatial frequency of transmitter array to reconstruct the image of target would cause a virtual phenomenon. By contrasting reconstruction images it is found that the image quality is reduced seriously, even the virtual phenomenon appears when the transmitting system is axially scanned with pitch error, and it decreases slightly on quadrant scan. In the present paper, we consider the reason of the phase closure of quadrant of T type transmitting array relies on axial frequency. At the same pitch error, different scan methods would cause different reconstruction images. The directions of virtual images are the same within the axial error. The computer simulation confirms the validity of the above analysis by three different modes of transmitter array through using the next field experiment parameters.

准相位闭合在傅里叶望远镜图像重构算法中的应用

准相位闭合在傅里叶望远镜图像重构算法中的应用

基于最小二乘法拟合估计傅里叶望远镜的缺失分量

基于最小二乘法拟合估计傅里叶望远镜的缺失分量

傅里叶望远镜成像质量分析与评价

Strehl ratio is often used as a method for evaluation of the Fourier telescope imaging quality. This method computes the correlation of the reconstructed image and the ideal image to evaluate the image quality,which is mainly applicable in the computer simulation analysis.However,the object to be observed may be unknow in the real world,which means there is no ideal image for use.Based on laboratory imaging data,the feasibility of the non-reference image evaluation method applied to Fourier telescopy is proposed and analyzed.The gray mean grads(GMG)method and Laplacian Sum(LS)are adopted to describe how much detail information the reconstructed image has.For the same object, Employ Strehl ratio and GMG,LS to evaluate the simulated image and the laboratory imaging result, respectively.Statistical results show that the two kinds of evaluations are identical in changing tendency. It proves the GMG and LS methods are applicable in Fourier telescopy as a non-reference image evaluation.

Analyses on limitations of coherent field imaging principle

The theoretical basis of coherent field imaging technique (also called the Fourier telescopy) is reconsidered. The limitations of the technique principle are analyzed by defining the measured object and deriving rigorously mathematical expressions. The reconstructed image of the technique ineluctably contains the gradient information about the object; as a result the technique cannot acquire the reflectivity of the object exactly. The computer simulation verifies the conclusion. Based on the conclusion, the reconstructed image of the technique can be evaluated and three-dimensional coherent field imaging technique may be developed.

Fourier Telescopy extrapolation based on the sampling theorem

Fourier Telecopy (FT) technique plays a promising role in deep space target detection. To improve the imaging quality of circular transmitting telescope array FT, a new processing method which adopts an extrapolation method based on the sampling theorem is proposed. Simulation results show that the extrapolation method can obviously improve system imaging resolution as well as reconstructed image quality. Even at a relative low SNR level the method improves system imaging resolution to a certain extent.

从傅里叶望远镜接收信号中获取目标速度的方法

The signals received by Fourier telescopy are analyzed and demonstrated to contain not only image information but also two-dimensional velocity information of the measured target. The velocities on each component can be calculated by the periodic signal frequencies that can be extracted from received signals. Then the two-dimension velocity is composited. The frequency of the signal is extracted by fast Fourier transform analysis for coarse frequency estimate, and by ratio frequency correction algorithms using Hanning window for precise frequency correction. Simulation is made to measure the flight velocity of the missile by Fourier telescopy. The result shows that the target velocity acquired by this method has almost no error without noise, while it has relatively high precision with noise when SNR is higher than 5 dB. The velocity acquisition method from receiving signal of Fourier telescopy is demonstrated to have high precision, a good anti-noise property and to be theoretically feasible.

基于非均匀周期采样的傅里叶望远镜时域信号采集方法

In order to clearly reconstruct targets in a dim and deep space under the condition of the Lower Signal to Noise(SNR),a new time domain signal acquisition method of Fourier Telescopy(FT) based on Non-uniform Periodic Sampling(NUPS) was proposed.The simulation experiments on the proposed method were performed and the reconstructed images by NUPS method and traditional uniform sample method were compared.With the NUPS method,100 points were respectively collected at the sampling frequency 1 MHz and 5 MHz.Then the signals of two sequences were respectively fast Fourier transformed and the concern frequency information was averaged.With traditional uniform sampling methods,200 points were collected at 1 MHz and 5 MHz sampling frequency and then demodulated average was developed.Compared results show that the Strehl ratio of reconstructed image with diffraction-limited image is enhanced 0.03 compared to the original method when SNR is 50,and the Strehl ratio is 0.531 1 that is improved 0.223 3 compared with uniform sampling when SNR is 20.Obviously,imaging quality is improved by the NUPS method under conditions of low SNRs,thus the laser power is reduced.The NUPS lays the technical foundation for the implementation of the FT engineering system.

湍流大气中激光传输对傅里叶望远镜成像质量的影响

湍流大气中激光传输对傅里叶望远镜成像质量的影响

Resolution of coherent field imaging technique

According to the relevant theory of optical transfer function (OTF), the OTF and point spread function of coherent field imaging technology (also known as Fourier telescopy) are derived. The formulas for calculating the resolution power of coherent field imaging system with T type and O type transmitter arrangement are given, which provides a theoretic basis of analyzing the limited angle resolution of coherent field imaging system. Based on this study, the relationship between resolutions of the coherent field imaging system with T type and O type transmitter arrangement is investigated.

非均匀采样的傅里叶望远镜数值模拟研究

非均匀采样的傅里叶望远镜数值模拟研究

Time-average Fourier telescopy: a scheme for high-resolution imaging through horizontal-path turbulence

The problem of high-resolution imaging through long horizontal-path ground-level turbulence has gone unsolved since it was first addressed many decades ago. In this paper I describe a method that shows promise for diffraction-limited imaging through ground-level turbulence with large (meters) apertures and at large (kilometers) distances. The key lies in collecting image data in the spatial frequency domain via the method of Fourier telescopy and taking suitable time averages of the magnitude and phase of the Fourier telescopy signal. The method requires active illumination of the target with laser light, and the time averages required will likely be over many tens of seconds if not tens of minutes or more. The scheme will thus not be suitable for time-varying scenes. The basic scheme is described, and principle challenges briefly discussed.

基于全相位谱分析的傅里叶望远镜外场实验数据处理

To improve the imaging quality of a Fourier Telescopy(FT) and to implement the high-resolution imaging for moving targets,the data processing methods to inhibit the spectral leakage generated by the frequency shift error from an acousto-optic frequency shifter,the bias of an optical device and truncating signals were researched and how to calculate the signal frequency in real time was given.Firstly,an all phase spectrum analysis technology was used to process sampling signals of a static target and a search algorithm was taken to capture the maximum frequency value of each interferometric beam.Then,the actual frequencies of any two beams were calculated by an all phase time shift phase difference correcting spectrum method.Finally,the frequency deviation and demodulated target's Fourier information were obtained and the demodulation frequency of the non-whole point was estimated by the least square fitting.The results show that the Strehl ratio of reconstructed image by proposed method is increased by 3% as compared with that of traditional methods.Furthermore,the new method has a higher inhibiting ability for spectral leakage,better reconstructed image,and it can provide the reference for data processing of moving targets.

Design and simulation of a high resolution active imaging technique utilizing Fresnel telescopy

A new technique for high resolution active laser imaging of space objects is demonstrated. The technique, referred as Fresnel telescopy, is a variant of Fourier telescopy, which additionally uses Fresnel zone plates to scan objects. The design scheme of a compact schematic of transmitting and receiving system for Fresnel telescopy is proposed. We provide simulations results for imaging of a photograph of satellite to illustrate and clarify the proposed idea. The technique is found to have substantial practical value and offers significant practical benefit for high resolution imaging of objects in the field of military applications.

傅里叶望远术中天线阵列配置对成像质量的影响

傅里叶望远术中天线阵列配置对成像质量的影响

傅里叶望远镜外场实验与结果分析

In order to study effects of outdoor factors to Fourier telescopy imaging and validate properties of imaging immune to down-link atmospheric turbulence,outdoor experiments were developed.Under the ground of lab experiments,outdoor experiments added primary mirror,secondary mirror and condense lens to simulate the real system imaging.The distance between object and primary mirror and the distance between primary mirror and secondary mirror was put away 100m,separately,to validate the property of Fourier telescopy imaging immune to atmospheric turbulence.Using 2 different satellite films as objects,the outdoor reconstructed images were gotten with the Strehl value 0.44 and 0.39 without turbulence,separately,and Strehl value 0.43 and 0.38 with turbulence,separately.Compared the reconstructed images of outdoor with lab,the conclusion was gained that libration had obvious effect on imaging.The result that the Strehl value of outdoor imaging was similar to lab imaging confirmed the fact that Fourier telescopy imaging was immune to down-link atmospheric turbulence.

实验室中傅里叶望远术频谱抽取方式

实验室中傅里叶望远术频谱抽取方式