# Super-Frequency Sampling for Thermal Transient Analysis
## 1 Introduction  
Thermography is a well-established technique for many different applications. These include the investigation of buildings [1], bio-medical questions [2], and electronic components [3, 4]. In general, thermographic techniques can be divided into two subgroups. In passive thermography, the infrared radiation from the investigated processes is monitored, whereas in active thermography, the object is heated in a controlled manner. Various combinations of different heat sources, excitation patterns, and evaluation algorithms are in the latter category [5]. For many techniques, a high sampling frequency is preferred [6]. In particular, for methods working in frequency space, such as pulse-phase thermography, a sufficient recording frequency is mandatory. The confidence in distinguishing a defect from the sound area is directly related to the recording frequency [7]. For a sampling frequency that is too low, it becomes impossible to perform measurements on fast-reacting materials. As thermal phenomena typically develop over several orders of magnitude, there also exists a category of techniques that employ a logarithmic scaling in time. This includes techniques such as thermographic signal reconstruction (TSR) and thermographic network identification (TNI). In these techniques, the sampling rate has a significant impact on signal quality for the shortest time constant due to the logarithmic scaling. All of these techniques can benefit from an increased sampling rate. In cameras using focal plane snapshot detectors, the total time to capture each infrared image consists of an integration time and a readout time. This is typically conducted in sequence. When high frequencies are required, integration time and readout time must be as short as possible. Lowering the integration time increases the frame rate at the expense of an increased signal-to-noise ratio, particularly in the case of low temperatures. The readout time is limited by the number of A/D converters as well as their clock speed. When using a windowing mode or a lower pixel resolution, significantly higher frequencies are possible,well above 10 kHz. However, a higher spatial resolution or the use of lower-priced cameras is always desirable. Thermal transient analysis (TTA) is the process of recording temperature changes in response to a sudden event. This typically refers to switching a heating power on or off. TTA determines the time constants of a heating (or cooling) process, which allows for an accurate prediction of the peak temperatures during power spikes. One of the most common applications of TTA is the investigation of electronic components such as integrated circuits, diodes, LEDs, or power converters [8]. While such measurements are usually performed on the basis of temperature-sensitive electric parameters, an infrared camera can also be used for TTA. This combination is called thermographic network identification (TNI). The results of this method have been shown to be promising, and it is a patented method [9]. The unique advantage of transient analysis by thermography is its imaging property. In the case of complex circuits or when components are not individually electronically accessible, for example, in a micro-LED matrix such as Nichia's uPLS (micro-Pixelated Light Solution) [10], thermographic analysis is still capable of capturing the thermal response of each component. Furthermore, thermal coupling between neighboring components can be quantified. However, it remains a challenge that typical thermal time constants of electronic components are in the order of microseconds. An approach similar to thermal transient analysis was used by [PERSON] et al. [11]. In their work, the thermal properties of thin semiconductor layers were reconstructed via TTA using pump-probe thermoreflectance for heating and temperature sensing. The time constants involved were in the order of nanoseconds. They concluded that the sampling frequency should be at least ten to fifteen times faster than the fastest thermal time constant.