## 1 Introduction  
Strain-controlled low cycle fatigue (LCF) testing is widely used to assess the time-dependent inelastic properties of materials. ASTM E606 [1] defines a standard test method to acquire relevant stress-strain curves at constant strain rates \(\dot{\epsilon}\) and constant strain amplitude \(\epsilon_{0}\). The results are triangular strain cycles \(\epsilon(t)\) with typical cycle frequencies in the range of 0.1 to 10 Hz. For closed-loop operation, ASTM E606 recommends an accuracy of 1% of the full-scale amplitude, which implies at least 400 strain measurements per triangular cycle, or strain measurement rates in the range of 40 to 4000 Hz, depending on the cycle frequency. Mechanical extensometers achieve these measurement rates whereas CPU-based optical sensors with 2D digital image correlation (2D-DIC) are limited to less than 200 Hz or cycle frequencies of 0.5 Hz [2; 3; 4; 5; 6]. We did not find a specification of the dead time in literature although it is a critical parameter for PID controlled systems [7]. Because of the speed limitation, many authors use two different strain sensors within the same experiment: a mechanical extensometer measuring average strain for the PID controller at higher sampling rates, and an additional DIC system for other mechanical quantities like crack parameters measured in the spatially resolved strain field at lower frame rates [8; 9; 10; 11]. An accelerated DIC system capable of both, average strain measurement at a frame rate in the range of 1 kHz and simultaneous strain-field measurement, would simplify many LCF experiments significantly, since only one combined strain sensor is necessary. As DIC systems work non-tactile, they do not suffer from slip between the extensometer tips and the sample surface which is in particular advantageous at high temperatures where materials become soft [12; 13; 14]. In addition, the sensors for strain, temperature, and the heating systems share the same surface on the specimen and might interfere with each other. Therefore, reducing the number of sensors does not only reduce costs, but also increases data quality. Last but not least, the DIC method also works in the micro and nano scale where other methods are far less applicable [15]. The most computation intensive calculation in DIC systems is the correlation between \(\mathbf{n_{T}}\times\mathbf{n_{T}}\) pixel template subsets from a reference image and the corresponding \(n_{S}\times n_{S}\) pixel search subsets from a measurement image. On conventional'single instruction, single data' (SISD) processors, this step is of the complexity \(\mathbf{n}\)\(\mathbf{log_{2}}\)\(\mathbf{n}\) with \(\mathbf{n}=\mathbf{n_{T}}+\mathbf{n_{S}}\)**-1** if fast-Fourier-transformation (FFT) is applied. Typical template sizes \(\mathbf{n_{T}}\) are in the range of 21 to 61 pixel and typical displacements in the range of \(\pm\)1% of the free specimen length, i.e., between the fixed mount of the testing machine and the opposite end of the field-of-view. If this free specimen length is assumed to be three times the field-of-view, a \(\pm\) 1% strain causes a \(\pm\) 3% displacement in the image (i.e., \(\pm\)60 pixel in a 2048 \(\times\) 2048-pixel image). The minimum size \(\mathbf{n_{S}}=n_{T}+2d_{max}\) of the search subset is defined by the template size \(\mathbf{n_{T}}\) and the maximum displacement \(d_{max}\) to be measured, resulting in search subset size \(\mathbf{n_{S}}\) of 141 to 181 pixel. As FFT algorithms require \(\mathbf{n}\) to be a power of 2, \(\mathbf{n}~{}=~{}\mathbf{256}\) can be considered as a typical value. Many DIC systems based on CPU processors combine the solution for higher order shape functions implicitly with minimal size of \(\mathbf{n}\) by using so-called tracking techniques. They assume the differences between the subsequent images to be small, i.e., \(n_{S}\approx n_{T}\), and reposition the search image according to the previous measurement [16; 17].