## 4 Discussion  
### Sampling Rate and Processing Speed  
This article reports a 2D-DIC system especially optimized for strain-controlled LCF testing. This closed-loop control application requires a high sampling rate above 1 kHz and a low latency in the range of a few milliseconds. Both requirements are quite hard to meet for image processing systems. Robustness is an issue because a small number of mismeasurements can already cause critical fluctuations in the feedback signal leading to specimen failure. On the other hand, the deformations of the specimen at LCF is rather small-in the range of 1%-so that rotation and shear deformations are negligible. To achieve a low latency, we chose a 'fast and simple' FFT-CC implementation neglecting shear and rotation, because it does not require iterative calculations like the more common IC-GN algorithm. As strain-control requires only a minimum of two measurement positions per image, the FFT-CC approach allows for a fast and path-independent implementation if the search field size \(n_{S}=n_{T}+2d_{max}\) is sufficient to measure the maximum displacement \(d_{max}\) in a single step. Here, the FFT-CC approach benefits in particular from the GPU architecture where the FFT calculation is of the complexity \(O(log_{2}(n))\). IC-GN, on the contrary, relies on a good initial guess, which is good if temporal or spatial neighborhood can be exploited-like in typical strain field applications with small displacement steps between subsequent images.  
To quantify these effects, Table 2 compares these parameters for some fast 2D-DIC implementations. [PERSON] et al. [(33)] published a highly speed-optimized CPU implementation based on the IC-GN algorithm processing almost 30,000 template subsets of \(21\times 21\) pixel in 0.685 s--which corresponds a processing rate of 44 kHz. As the system is CPU-based, this processing rate varies strongly with template size. For \(61\times 61\) pixel per subset, the processing rate decreases to 7.2 kHz. A year later, the same authors published a real-time extensometer measuring four templates per image at a frame rate of 117 Hz, i.e., a processing rate of 0.468 kHz [(5)]. This decrease shows how much the IC-GN implementation exploits the neighborhood of the full-field measurement. This processing rate is quite comparable to the 0.6 kHz we measured for our approach without using the GPU. [PERSON] et al. thoroughly studied different combinations of both algorithms implemented on CPU and GPU. Variation 2 was the fastest path-depending full-field implementation whereas variation 4 achieved the highest real-time processing rate in a path-independent way. Here, the path-dependent tracking increased the processing rate from 3 to 283 kHz.  
The processing rate of 9.6 kHz that we achieved in strain-controlled mode is faster than the 3 kHz published by [PERSON] [(22)] for the path-independent variation 4 and it outperforms the CPU-based real-time extensometer by [PERSON] [(5)] by more than an order of magnitude. In full-field mode, the processing rate of our system increases to 25 kHz, but it might be outperformed by an order of magnitude if tracking is allowed. In contrast to tracking based systems, where the maximum displacement is only limited by the field-of-view, our approach has a hard limit for the maximum displacement \(d_{max}\).