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由于红外图像[18]采集过程中会引入非均匀性噪声,所以,在光谱反演前需要对干涉条纹图像进行预处理,通常采用两点校正算法完成。校正后的图像为:
$ I^{\prime}(\varphi)=K I(\varphi)+Q $
(1) 式中,I(φ)表示原图像,K和Q分别为校正系数,有:
$ \left\{\begin{array}{l}{K=\frac{I_{2}-I_{1}}{I_{m n}\left(\varphi_{2}\right)-I_{m n}\left(\varphi_{1}\right)}} \\ {Q=\frac{I_{m n}\left(\varphi_{2}\right) I_{1}-I_{m n}\left(\varphi_{1}\right) I_{2}}{I_{m n}\left(\varphi_{2}\right)-I_{m n}\left(\varphi_{1}\right)}}\end{array}\right. $
(2) 式中,Imn(φ1)和Imn(φ2)为定标的两帧图像,I1和I2为分束光1与分束光2的干涉图,I1和I2可表示为:
$ \left\{ {\begin{array}{*{20}{l}} {{I_1} = \frac{1}{{MN}}\sum\limits_{m = 1}^M {\sum\limits_{n = 1}^N {{I_{mn}}} } \left( {{\varphi _1}} \right)}\\ {{I_2} = \frac{1}{{MN}}\sum\limits_{m = 1}^M {\sum\limits_{n = 1}^N {{I_{mn}}} } \left( {{\varphi _2}} \right)} \end{array}} \right. $
(3) 由此可见,经过非均匀性校正的干涉条纹会将非均匀性误差进行修正,从而提高光谱反演的准确度。
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因为信号中往往包含各种各样的噪声和杂波,所以为了实现对噪声的过滤,就采用加窗的方式实现,窗实际上就是滤波器,加窗就是对信号的滤波处理。通常的处理方式是将信号与窗函数的频域相乘,而在时域中就是做卷积。由光谱频域变换关系可知,CCD上采集得到的2维空间干涉条纹与光谱分布函数是空域与频域的傅氏变换关系,干涉条纹图像I(x)和其位置上的光谱数据B(k)互为傅里叶变换函数关系,有:
$ \left\{\begin{array}{l}{I(\Delta x)=\mathscr{F}[B(k)]} \\ {B(k)=\mathscr{F}^{-1}[I(\Delta x)]}\end{array}\right. $
(4) 式中,Δx表示光程差,k表示对应入射光波的波数。由此可知,对干涉条纹图像进行傅里叶变换就能获得目标的光谱信息。在时间扫描干涉系统中,由于可以控制扫描路径的长度,所以可获得非常高的光谱分辨率,但也需要牺牲系统的稳定性和实时性作为代价,故在户外实用红外目标识别应用中往往采用静态干涉系统。静态干涉系统通过干涉具实现将空域干涉条纹信息转换为频域光谱信息,无扫描件使其稳定性好、实时性高,但因为受到干涉具尺寸的限制,最大光程差往往不会太大,光谱分辨率相对较低。在户外或存在干扰的工作环境中,应用需求往往对光谱分辨率的测试精度要求不高,但对系统稳定性要求较高,同时,实际应用中常常会要求系统具有一定的实时性,由此可见,针对该类需求时静态干涉系统具有一定的优势,其具备更高的实时性与稳定性。为了保证干涉条纹的质量,干涉图样需要节选在最大光程差范围以内。缩小的截取范围会导致频谱泄露和干扰的产生,所以,为了保证光谱反演的效果,通常采用加窗的处理方式,利用窗函数与干涉图相乘完成对干涉条纹数据的切趾。
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红外成像光谱仪标定时通常采用标准光谱仪与待标定系统对同一组光源光谱进行对比测试,再通过标准光谱仪的测试数据标定待测系统。设标准光谱仪获得的光谱为R0, 而本系统的测试结果为Rt,则标定系数e为:
$ e=R_{0} / R_{\mathrm{t}} $
(5) 设实时采集获得光谱为Pt,则标定后的光谱Pout为:
$ P_{\text {out }}=e \times P_{\mathrm{t}} $
(6)
基于FPGA红外成像光谱数据处理系统研究
Research of data processing systems for infrared imaging spectrometer based on FPGA
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摘要: 目标实时探测是红外成像光谱系统的重要研究方向之一。为了同时保障系统数据处理速度与光谱复现精度, 研究了一种高速光谱反演系统。该系统由现场可编程门阵列(FPGA)芯片实现, 对干涉条纹图像进行非均匀性校正、加窗切趾, 从而抑制干涉条纹数据中的直流噪声及杂散噪声; 再经快速傅里叶变换、相位校正、光谱标定最终获得光谱分布。结果表明, 本算法对杂散噪声具有很好的抑制效果, 非均匀性系数由11.23%降低至1.05%;对光谱的反演实验中本系统获得的光谱分布形态与MATLAB结果基本一致, 且在光谱细节部分的准确度更好一些; 系统采用流水线工作方式缩短了数据处理周期, 并且基于FPGA芯片的开发模块具有更强的兼容性。该系统具有处理速度快、体积小、稳定性高、兼容性强等优点, 在红外目标实时探测领域具有很好的应用前景。Abstract: Real-time target detection is one of the important research directions of infrared imaging spectral systems. In order to guarantee the data processing speed and spectral reproducing accuracy of the system at the same time, a high-speed spectral inversion system was studied. The system was implemented by a field-programmable gate array (FPGA) chip. Non-uniformity correction and windowed toe-cutting were applied to the interference fringe image to suppress the direct current noise and spurious noise in interference fringe data. Then spectral distribution was obtained after fast Fourier transform, phase correction and spectrum calibration. The results show that the algorithm has a good suppression effect on spurious noise. Coefficient of inhomogeneity decreases from 11.23% to 1.05%. In the experiment of spectral inversion, the spectral distribution obtained by this system is basically consistent with that obtained by MATLAB. The accuracy of spectral details is better. The system uses pipeline mode to shorten the data processing cycle. And the development module based on FPGA chip has better compatibility. The system has the advantages of fast processing speed, small volume, high stability and good compatibility. It has good application prospect in the field of infrared target real-time detection.
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