## 1 Introduction  
Induction heating is a well-known technique, as it is very efficient, fast, clean and accurately controlled [1]. Nowadays, it is not only used in the industry, but also for domestic applications, as induction cookers, and for medical purposes, as hyperthermia therapy [1]. In the case of induction thermography, the sample to be inspected is placed inside or close to an induction coil. During and after applying a short heating pulse, which is usually between 50 ms and 1 s, heat will be induced inside the material and an infrared camera records the temperature distribution. Evaluation of the temperature images and their temporal changes represents an excellent technique for crack detection, as it is a non-destructive, contact-free technique and can be very well fully automated using image processing methods. In the last few years, several investigations have been published by different groups proving the applicability of this method. The first industrial application was reported around 30 years ago [2]. Steel bars and billets have been tested for surface cracks during motion through an induction coil and by evaluating the signal of four infrared line scanners placed around the steel bar. In the last 20 years, FPA (focal-plane-array) cameras became more powerful and dropped in price, maintaining more scientific research in the area of thermographic inspection [3]. Inductive thermography is one of the active thermography methods, which have been studied and developed by several groups in the few last years. The working group around [PERSON] investigated induction thermography to detect subsurface defects in steel and in CFRP (carbon fiber reinforced polymer) samples in a modulated way (lock-in technique) and with pulse heating (burst thermography) [4]. Aluminum fatigue surface cracks have been also detected using the lock-in technique [5]. Analytical and numerical models [6; 7; 8] have been set up for modeling cracks perpendicular to the surface in steel materials. In these simplified models, the cracks were modeled either as a long notch or as a short slot going through the whole sample thickness [7; 8]. Experimental results for surface crack detection with induction thermography have been reported by several groups in different ferro-magnetic samples, for example, in forged parts [9; 10] and in rail surfaces [11; 12]. As these head checks lay typically inclined to the surface, further numerical models have been set up for angular defects [12; 13; 14]. As induction thermography became an important NDT (non-destructive testing) method for detecting surface cracks in industrial applications [15], many efforts have been undertaken [16] to set up a standard [17]. This paper presents several investigations on the influence of different experimental and material parameters on surface crack detection. However, important emphasis was placed on how the position is obtained and on how the depth of a crack can be estimated from the detected signal. In the first part of the paper, finite element simulations are carried out to show how experimental parameters, such as excitation frequency and pulse duration, as well as material parameters and the properties of the crack, such as depth and inclination angle, affect the results. Four different cases were investigated: cases where the penetration depth was small, cases where the penetration depth was similar large as the crack depth, and these in combination with cases where the crack was perpendicular to the surface, and cases where the crack lay under a given inclination angle. For each of these combinations, experimental results are presented. Several samples with artificial and \"natural\" cracks were measured, and the results are compared with the simulated ones. The main goal of this study was to derive general, normalized functions for vertical cracks, which are independent of the material parameters and depend only on two ratios: the ratio of the crack depth to the penetration depth, and the ratio of the crack depth to the thermal diffusion length.