The interaction of the laser beam with the material is critical for determining laser processing quality, with ray tracing methods mostly used in energy transfer research. These techniques generally rely on only the volume of fluid (VOF) method or level set (LS) function to track the molten pool free surface, resulting in either accuracy loss or difficulty in ensuring mass conservation of the interface. The few coupled algorithms are built on geometric notions that are difficult to understand while being limited to structural grids. In this paper, we have proposed a revised ray tracing framework, so-called ARCLS, to derive the exact intersections of the rays with the keyhole wall which is represented by a continuous LS surface algebraically rebuilt on top of the VOF interface. It is easy to code and convenient for unstructured meshes. This framework is tested through a V-groove case and a set of Ti6Al4V titanium alloy laser welding examples. The findings reveal that the reconstructed LS surface perfectly matches the VOF interface, and the predicted molten pool profile agrees with the actual data well. The keyhole morphology and molten flow patterns are also consistent with the physical truths. Spattering, porosity, necking, and swelling are observed in the developing keyhole, which are the possible reasons for the potential welding defects. Further investigation suggested that the ARCLS-based algorithm collected more laser rays at the keyhole bottom compared to the standard technique, achieving a deeper keyhole profile and a reflection pattern that was more optically logical. The work presents a reliable approach for estimating laser energy distribution, which can be effectively applied to the heat-fluid coupling simulation for laser manufacturing processes in order to forecast the dynamic behaviors of keyhole and molten pool.