A wavelet-based optical flow analysis (wOFA) method for processing background-oriented schlieren (BOS) images is presented and demonstrated on synthetic and experimental data. Optical flow is inherently well suited to BOS, because the background pattern and lighting conditions are specified and controlled by the user and can be chosen to play to the strengths of optical flow processing. Analysis of the synthetic BOS data show that a two-dimensional sinusoidal background produces the highest reconstruction accuracy for both wOFA and iterative least squares (ILS) algorithms. wOFA outperforms ILS in terms of overall accuracy for displacement fields with sufficiently high spatial frequency content. In addition, wOFA provides higher spatial resolution, about an order of magnitude in terms of the total number of pixels in the final BOS image. Finally, wOFA is demonstrated on two sets of experimental data: a heat gun plume experiment with nearly ideal imaging characteristics, and experiments in a supersonic wind tunnel flow with more realistic restrictions on the acquisition of images. BOS images computed with wOFA are shown to have higher spatial resolution and sensitivity than ILS, without introducing additional noise. Therefore, wOFA of BOS images are able to reveal flow features not detected by ILS analysis.

提出了一种基于小波的光流分析（wOFA）方法，用于处理背景定向的纹影（BOS）图像，并在合成和实验数据上进行了演示。光流本来就非常适合BOS，因为背景图案和照明条件由用户指定和控制，可以选择以发挥光流处理的优势。对合成BOS数据的分析表明，二维正弦背景对于wOFA和迭代最小二乘（ILS）算法均产生最高的重建精度。对于具有足够高空间频率含量的位移场，wOFA的整体精度优于ILS。另外，wOFA提供了更高的空间分辨率，大约是最终BOS图像中像素总数的一个数量级。最后，wOFA在两组实验数据上得到了证明：具有近乎理想的成像特性的热风羽流实验，以及在对图像采集有更多实际限制的超音速风洞流中进行的实验。使用wOFA计算的BOS图像显示出比ILS具有更高的空间分辨率和灵敏度，而不会引入额外的噪声。因此，BOS图像的wOFA能够揭示ILS分析未检测到的流动特征。