Projection mapping (PM) exhibits suboptimal performance in well-lit environments because of the interference caused by ambient light. This interference degrades the contrast of the projected images. Consequently, conventional methodologies restrict the application of PM to dimly lit settings, leading to an unnatural visual experience, as only the PM target is prominently illuminated. To overcome these limitations, we introduce an innovative approach that leverages a mixed light field, blending traditional PM with ray-controllable ambient lighting. This methodological combination, despite its simplicity, is effective because it ensures that the projector exclusively illuminates the PM target, preserving the optimal contrast. Precise control of ambient light rays is essential to prevent them from illuminating the PM target while adequately illuminating the surrounding environment. Furthermore, we propose the integration of a kaleidoscopic array with integral photography to generate dense light fields for ray-controllable ambient lighting. Additionally, we present an efficient binary-search-based calibration method tailored to this intricate optical system. Our optical simulations and the developed system collectively validate the effectiveness of our approach. Our results show that PM targets and ordinary objects coexist naturally in environments that are brightly lit as a result of our method, enhancing the overall visual experience.