Monitoring of protective glasses (8) in laser machining heads, which are exposed to dust, sputtering and/or soiling, with the aim of predicting the contamination of the protective glass. For this purpose, image sections (19) are captured by means of at least two image capture systems (16) at capture-times, computer-readable image files are stored by means of a frequency-based compression algorithm, and a file size value (kB) is determined for each image file on the basis of its file size. A signal is generated if for a majority of the image capture systems (16) the file size values (kB) decrease and/or are below one of a predefined number of threshold values (20) for a predetermined minimum number of consecutive capture-times.