Dry Eye Disease (DED) is an eye condition characterized by abnormalities in tear film stability. Despite its high prevalence, screening for DED remains challenging, primarily due to the invasive nature of most diagnostic tests. The Fluorescein Break-Up Time (FBUT) test, which involves instilling fluorescein dye in the eye, is a widely used method for assessing tear film stability. In this work, we propose DEDector, a low-cost, smartphone-based automated Non-Invasive Break-Up Time (NIBUT) measurement for DED screening. Utilizing a 3D-printed Placido ring attachment on a smartphone's camera, DEDector projects concentric rings onto the cornea, capturing a video for subsequent analysis using our proposed video processing pipeline to identify tear film stability. We conducted a real-world evaluation on 46 eyes, comparing DEDector with the traditional FBUT method. DEDector achieved a sensitivity of 77.78% and specificity of 82.14%, outperforming FBUT.