在许多人的认知里，数字图像相关方法似乎不太可能解决好远低于1/1000像素的运动测量。这可能源于已出版的文献中一个经常重复的说法，即DIC的分辨率约为1/100像素，并且已经重复了近三十年。不幸的是，这是对分辨率、精度和噪声之间没有明确区分造成的。 DIC的分辨率，即在位移信号中产生可测量变化的最小运动，在理论上仅受输入数据信息内容的限制，这意味着并没有固有的分辨率限制。 DIC的精度受到许多因素的限制，例如噪声偏差和插值偏差。而通过使用先进的优化插值滤波器，Correlated Solutions的软件几乎消除了这两种类型的偏差。当然，DIC数据中的噪声还高度依赖于输入信号中的噪声，即图像本身的噪声。传统假定DIC是1/100像素的“精度/分辨率/噪声”的原因是，在典型的图像采集器硬件和典型的像素散斑质量模式下，实验人员通常会在其1/100像素附近的数据中看到本底噪声，然后该本底噪声被错误地标记为“分辨率”或“精度”。

 

用DIC进行振动测量意味着什么？对于振动测量，通常会获取具有几千幅图像的图像序列，通过DIC分析后，我们获得了一个位移信号，该信号包含（高斯）噪声和在许多频率上可能很小的振动。由于高斯噪声在整个频率范围内均匀分布，因此我们在FFT中获得了恒定的本底噪声。由于此噪声能量在整个频谱上“被涂抹”，因此每个频率仓仅包含一小部分，从而在整个频谱上具有较低的本底噪声。拍摄的图像越多，本底噪声将越小。信号本身（即振动）通常包含在FFT中很少的相邻箱中，可能有多个这样的局部“峰”。由于在频域中的这种定位，我们试图测量的信号在幅度上的降低与噪声水平没有相同。因此，可以将具有比背景噪声电平的标准偏差小的幅度的信号与噪声分离，并且在频域中很容易被检测到。

 

为了使具有数字图像相关性的振动分析切实可行，所使用的分析代码必须具有某些属性。首先，大量数据需要有效处理，以便在合理的时间范围内提供数据。由于数字图像关联是一种全场技术，因此对每个图像分析数以万计个数据点的要求并不罕见。为了在合理的时间范围内处理几千帧的图像序列，很明显，需要极其有效的处理代码。 Vic-3D的相关引擎经过高度优化，可以在最短的时间内分析密集的数据集，并且通常每小时可以处理数千张图像。

 

其次，许多振动测量应用具有以下特性：所有运动都是像素的很小一部分，即图像中的运动甚至都无法用肉眼看到。不幸的是，在运动接近于零的情况下，数字图像相关方法具有最高的噪声诱导偏差。虽然对不同的摄像机的选择会极大地影响图像中的噪声值，从而影响振动数据中的偏差值，但如果数字图像相关算法没有专门解决这个问题，则可以预期到使用所有的摄像机都会有噪声导致的残余偏差。Vic-3D相关引擎使用非线性滤波器优化技术开发的插值滤波器，比使用B样条等传统插值技术更大程度上抑制这种偏差。这使得对微小运动的精确分析没有图像噪声污染造成的偏差。

 

总之，将DIC的分辨率认定为1/100像素这一概念是完全错误的，不幸的是，这还是相当普遍的认知。通过使用高速相机获取大量图像，我们实际上可以获得更高的DIC分辨率，通过它们在频域中的定位有效地将它们与背景噪声分开，可以实现振幅很小的振动测量。

At first glance, it seems improbable to many people that the digital image correlation method is able to resolve motions well below 1/1000 pixel. This probably stems from an oft-repeated myth that the resolution of DIC is around 1/100 pixel. This value has been given in the literature and has been repeated for almost three decades. Unfortunately, no clear distinction between resolution, accuracy and noise has been made. The resolution of DIC, i.e., the smallest motion that will produce a measurable change in the displacement signal, is theoretically only limited by the information content of the input data. This means that there is no inherent resolution limit. The accuracy of DIC is limited by a number of factors, e.g., noise-induced bias and interpolation bias. Both types of bias have been virtually eliminated in CSI's software through the use of advanced optimized interpolation filters. The noise in DIC data, of course, is highly dependent on the noise in the input signal, i.e., the images themselves. The reason why 1/100 pixel "accuracy/resolution/noise" for DIC is often assumed is that with typical camera hardware and a typical speckle pattern of decent quality, experimenters typically see a noise floor in their data around 1/100 pixel. This noise floor is then incorrectly labeled as "resolution" or "accuracy".

 

What does this mean for vibration measurements with DIC? For a vibration measurement, it is typical to acquire an image sequence with a few thousand images. After analysis with DIC, we obtain a displacement signal that contains (Gaussian) noise and potentially very small vibrations at a number of frequencies. Since Gaussian noise is uniformly spread over the entire frequency range, we obtain a constant noise floor in the FFT. As this noise energy is "smeared" over the entire spectrum, each frequency bin only contains a small fraction of it, resulting in a low noise floor over the entire spectrum. The more images are taken, the smaller this noise floor will be. The signal itself (i.e., the vibration) is typically contained in very few neighboring bins in the FFT, with possibly multiple such localized "peaks". Because of this localization in the frequency domain, the signal we are seeking to measure does not experience the same reduction in amplitude as the noise level. Thus, a signal with smaller amplitude than the standard deviation of the background noise level can be separated from the noise and easily detected in the frequency domain.

 

In order to make vibration analysis with digital image correlation practical, the analysis code used has to have certain properties. First, the large data volume requires efficient processing in order to provide data within a reasonable time frame. Since digital image correlation is a full-field technique, it is not uncommon to require the analysis of tens of thousands of data points per image. To process an image sequence of several thousand frames within a reasonable time frame, it is clear that an extremely efficient processing code is required. Vic-3D's correlation engine is highly optimized to analyze dense data sets within a minimal amount of time and can typically process several thousand images per hour.

 

Second, many vibration measurement applications have the property that all motions are very small fractions of a pixel, i.e., the motion in the images cannot even be seen by eye. Unfortunately, the digital image correlation method has the highest amount of noise induced bias in cases where the motion is close to zero. While the choice of camera can greatly influence the amount of noise in the images, and thus the amount of bias in the vibration data, all cameras have some amount of noise and residual bias can be expected if the implementation of the digital image correlation algorithm does not specifically address this problem. Through the use of interpolation filters developed using non-linear filter optimization techniques, the Vic-3D correlation engine has been optimized to suppress this type of bias to a far greater extent than is possible using traditional interpolation techniques such as B-splines. This allows the accurate analysis of minuscule motions without the contaminating bias that results from image noise.

 

In summary, the notion that the resolution of DIC is limited to 1/100 pixel is completely wrong, even though it is unfortunately pretty common. In reality, much higher resolution is available. By acquiring a large number of images with high speed cameras, it is possible to measure vibrations with minuscule amplitudes, as their localization in the frequency domain effectively separates them from the background noise.

 

Hubert W. Schreier, Ph.D.
Correlated Solutions, Inc.
C.E.O., President