# A Simple Model to Predict Machined Depth and Surface Profile for Picosecond Laser Surface Texturing
## 1 Introduction  
In recent years, surface texturing has been one of the major research topics of interesting due to potential applications in improving surface tribological property [1; 2; 3], wetting behavior [4; 5; 6], adhesion performance [7; 8; 9], reflectivity [10; 11; 12], and others. For these applications, the dimensions of the created micro-features play a vital role in tailoring of final surface functional performances. Over the last decade or so, laser surface texturing (LST) is a commonly utilized technology to fabricate designed micro-features on surfaces owing to the tool-less nature, high precision, high flexibility and ease of use [13]. During LST, the final geometry of the created micro-features is determined by plenty of process parameters, like laser power, frequency, wavelength, pulse diameter and overlap, etc. Hence, the laser process parameters should be rationally chosen to create designed micro-features. Developing predictive models for the geometry is an efficient means to choose optimal laser process parameters. A considerable amount of literature has been published on constructing the predictive models for the machined depths or geometries during laser machining process. For example, [PERSON] [14; 15] employed boundary element method to develop two numerical models which can be used to predict groove shape during laser cutting process. [PERSON] et al. [16] built a numerical model that considers the instant material removal to predict the surface recession and to obtain the ablation depth. [PERSON] et al. [17; 18] developed multiphysics-multistep computational models combining the heat transfer, hydrodynamic boundary conditions and thermomechanical properties to simulate the temperature and surface profile. For ultrafast laser micromachining, the twotemperature model has been successfully employed to simulate the evolution of the temperatures and to predict the final geometry [19; 20; 21; 22; 23]. However, numerical modeling is computationally expensive, and has some difficulty when materials used do not have extensive property data readily available. Based on abundant experimental data, an artificial neural networks (ANN) model was developed by [PERSON] et al. [24] to predict the T-shaped deep features in laser machining and to identify optimum process settings. [PERSON] et al. [25] built a multi-layered neural network to predict the machined depth and diameter of the groove during laser cutting process. [PERSON] et al. [26] used response surface method (RSM) to develop a mathematical model to calculate the width, depth and surface roughness during the fabrication of micro-channels on polycrystalline diamond by nanosecond laser. [PERSON] et al. [27] developed a second-order regression and a least squares support vector machines (LS-SVM) model to predict the machined depth and profile of micro-channels on medical needles using a picosecond laser. A lot of experiments need to be conducted to improve the prediction accuracy of these experiment-based models, however, so this process is time consuming. An analytical model combined with several experiments is also a promising method to obtain the proper results. For example, a similar model was built by [PERSON] et al. [28] to predict the width of created micro-channels and to calculate the ablation threshold. [PERSON] et al. [29] constructed a mathematical model to obtain the ablated depth and the texture of targeted surfaces by considering the surface gradient and focal length as well as dynamic and energetic parameters. In this model, baseline experiments were initially conducted to calibrate the material response to laser energetic parameters. Micro-channels are the fundamental building elements in LST and can be arrayed to create patterns with different geometries. In contrast with the previous models characterised by complex multi-physics and/or abundant experimental data, a simple mathematical model is developed in this paper to predict the machined depth and profile of micro-channels by a picosecond laser.