The Risley-prism system is applied in imaging LADAR to achieve precision directing of laser beams. The image quality of LADAR is affected deeply by the laser beam steering quality of Risley prisms. The ray-tracing method was used to predict the pointing error. The beam steering uncertainty of Risley prisms was investigated through Monte Carlo simulation under the effects of rotation axis jitter and prism rotation error. Case examples were given to elucidate the probability distribution of pointing error. Furthermore, the effect of scan pattern on the beam steering uncertainty was also studied. It is found that the demand for the bearing rotational accuracy of the second prism is much more stringent than that of the first prism. Under the effect of rotation axis jitter, the pointing uncertainty in the field of regard is related to the altitude angle of the emerging beam, but it has no relationship with the azimuth angle. The beam steering uncertainty will be affected by the original phase if the scan pattern is a circle. The proposed method can be used to estimate the beam steering uncertainty of Risley prisms, and the conclusions will be helpful in the design and manufacture of this system.
The Risley-prism-based light beam steering apparatus delivers superior pointing accuracy and it is used in imaging LIDAR and imaging microscopes. A general model for pointing error analysis of the Risley prisms is proposed in this paper, based on ray direction deviation in light refraction. This model captures incident beam deviation, assembly deflections, and prism rotational error. We derive the transmission matrixes of the model firstly. Then, the independent and cumulative effects of different errors are analyzed through this model. Accuracy study of the model shows that the prediction deviation of pointing error for different error is less than 4.1×10-5° when the error amplitude is 0.1°. Detailed analyses of errors indicate that different error sources affect the pointing accuracy to varying degree, and the major error source is the incident beam deviation. The prism tilting has a relative big effect on the pointing accuracy when prism tilts in the principal section. The cumulative effect analyses of multiple errors represent that the pointing error can be reduced by tuning the bearing tilting in the same direction. The cumulative effect of rotational error is relative big when the difference of these two prism rotational angles equals 0 or π, while it is relative small when the difference equals π/2. The novelty of these results suggests that our analysis can help to uncover the error distribution and aid in measurement calibration of Risley-prism systems.
Applied to remote sensing, a temporally and spatially modulated Fourier-transform imaging spectrometer (TSMFTIS) relies on the push broom of the flying platform to obtain an interferogram of the detected target. If the moving state of the flying platform changes during the imaging process, the target interferogram picked up from the remotely sensed image sequence will deviate from the ideal interferogram, and the recovered target spectrum will not reflect the real characteristics of the ground target object. On the basis of research on TSMFTISs, the coordinate relationship between the detector pixel and the corresponding target ground object in the photogrammetric coordinate system can be precisely described on the basis of the central projection imaging collinear equation, and the motion imaging error model of the TSMFTIS is derived using a linear spectral mixture model. The TSMFTIS motion imaging process is simulated by an actual spectrum data cube and the altitude of the airborne platform, and a sequence error image with interference fringes is acquired. Finally, an experiment is performed to validate the motion imaging error model using the TSMFTIS and a motorized stage, and the evaluation results demonstrate its feasibility.
Temporally and Spatially Modulated Fourier Transform Imaging Spectrometer (TSMFTIS) is a new imaging spectrometer without moving mirrors and slits. The interferogram of the target point can be consisted by sequentially arranging the interference information extracted from the same target point of the sequential images, and the spectrum can be recovered by using fast Fourier transform. In the practical application, there is nonuniform sampling in the interference data, and many researchers have carried out researches on nonuniform sampling with the fast Fourier transform algorithm. As to the issue of interference data in the nonuniform sampling, the nonuniform sampling degree’s impact on the recovered spectrum precision is currently and mainly analyzed. This paper has adapted several typical nonuniform fast Fourier transform (NUFFT) methods, carried out spectrum recovery precision comparison on the interferogram of the nonuniform sampling point with the above methods, and further analyzed the impact of kernel function type, oversampling ratio and kernel function width’s on spectrum recovery precision in the above mentioned methods. The experiment result indicates that, when the oversampling ratio is 4 and the kernel function width is 4, the spectrum recovery precision with NUFFT based on Blackman type kernel function is optimal, however, the Gaussian kernel function is stable.
Temporally and Spatially Modulated Fourier Transform Imaging Spectrometer (TSMFTIS) is a new imaging spectrometer without moving mirrors and slits. As applied in remote sensing, TSMFTIS needs to rely on push-broom of the flying platform to obtain the interferogram of the target detected, and if the moving state of the flying platform changed during the imaging process, the target interferogram picked up from the remote sensing image sequence will deviate from the ideal interferogram, then the target spectrum recovered shall not reflect the real characteristic of the ground target object. Therefore, in order to achieve a high precision spectrum recovery of the target detected, the geometry position of the target point on the TSMFTIS image surface can be calculated in accordance with the sub-pixel image registration method, and the real point interferogram of the target can be obtained with image interpolation method. The core idea of the interpolation methods (nearest, bilinear and cubic etc) are to obtain the grey value of the point to be interpolated by weighting the grey value of the pixel around and with the kernel function constructed by the distance between the pixel around and the point to be interpolated. This paper adopts the gauss-based kernel regression mode, present a kernel function that consists of the grey information making use of the relative deviation and the distance information, then the kernel function is controlled by the deviation degree between the grey value of the pixel around and the means value so as to adjust weights self adaptively. The simulation adopts the partial spectrum data obtained by the pushbroom hyperspectral imager (PHI) as the spectrum of the target, obtains the successively push broomed motion error image in combination with the related parameter of the actual aviation platform; then obtains the interferogram of the target point with the above interpolation method; finally, recovers spectrogram with the nonuniform fast Fourier transform algorithm. Compared with the accurate spectrogram, the spectrogram recovered with the relative deviation-based kernel regression interpolation method has remarkable improvement over the previous methods.
Interferogram obtained by Temporally-Spatially Modulated Fourier Transform Spectrometers should be recovered to spectrum by fast Fourier transform method (FFT). However, the interferogram sometimes is nonuniformly sampled, which cannot use FFT directly. In this paper, we propose a wavelet basis fitting method to interpolate the interferogram onto an equal-spaced grid. Hence, we can utilize FFT to recover spectrum. The simulated result of the recovered spectrum indicates that the proposed interferogram wavelet basis fitting method can interpolate the nonuniformly sampled interferogram effectively. The preliminary results show that this method introduces less errors than the Polynomial fitting method does.
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