## 1 Introduction  
Laser technology has played an important role in advanced manufacturing processes, including 3D additive manufacturing (AM), welding, cutting, and micro/nano processing, etc. With low-cost, higher-power laser sources widely available to many manufacturing industries, there is a growing transition trend using high-power lasers in the multi-kilowatt (kW) range for material processing. The benefits of these high-power lasers are (1) scaling-up processing productivity by increasing the laser spot size, the hatch spacing, and layer thickness and (2) expanding more materials such as refractory and highly reflective metals and ceramics, which usually need higher-power lasers [1]. However, laser material processing using high-power lasers may also create new challenges such as thermal-induced effects [2, 3]. A high-power laser beam passing through an optical lens could locally heat up the optical elements in the laser head. The nonuniform temperature distribution will then induce thermal deformations, changes in temperature-dependent refractive properties, and thermal stress in both optical and mechanical components. The above phenomena will have an adverse impact on optical lens distortions, laser beam focal shift or defocusing errors, and even degradation of laser power irradiation quality, which detrimentally affect the manufacturing process and product quality [4, 5]. In order to mitigate these thermal effects, an optimal design of the optical laser head is desired to minimize the effect of the sources of thermal environmental changes in high-power laser material processing. The optical laser head for material processing, such as in welding and additive manufacturing, is an integrated structural-thermal-optical system. Therefore, a systematic design and modeling strategy is required. Traditionally, optical design and mechanical design simulations are conducted separately or sequentially due to a lack of a design and modeling data shared platform. Recently, a combined structural-thermal-optical-performance (STOP) analysis approach was proposed as a systematical design modeling solution for performance improvement in the telescope, camera, and precise optical instrument applications [6; 7; 8; 9]. Model data mapping approximated from one physics model to another model was adopted. Thermal effects in the protective window during different selective laser meting (SLM) scanning processes were also analyzed by using a multiphysics simulation model [10]. However, there are few references relating the use of the STOP simulation approach in designing and optimizing an optical laser head. On the other hand, product design optimization through the design of computer experiments (DoCE) is an efficient and practical engineering approach in developing manufacturing processes. Sensitivity analyses by DoCE can further evaluate the sensitive effects of design parameter settings on product performance. The purpose of a sensitivity analysis is to find optimal design settings of the input variables so that optimal performance can be achieved. Over the past years, the response surface model (RSM) has been widely employed in product design and optimization for best performance. RSM utilizes a set of statistical and mathematical methods to predict the robustness and optimal design [11; 12]. It was initially developed in design optimization based on experiments or field testing by building a polynomial mathematical model between independent design variables and dependent responses [13; 14]. Based on the fitted mathematical model, optimal responses were predicted using the optimization technique and validated with experiments. Now, RSM-based DoCE is also used in the simulation-based optimal product and process design in many industrial applications [14; 15; 16]. Additive manufacturing using lasers has been attracting more and more interest in both academia and industry applications for processing high-value-added components.