To enhance the reproducibility and reliability of measurements of the average tilt of a laser radiation wavefront, a random amplitude transparency is brought into the optical system of a sensor based on a four-element matrix photodetector. The transparency is a "black-and-white" screen with a set of cells with randomly selected transmission coefficient values. It is shown that the presence of such a transparency makes it possible (at the cost of a decrease in sensor sensitivity) to sharply extend the measurement range and to considerably lower the requirements for spatial and energy radiation characteristics. An experimental sensor has a measurement range of ±1.5 mrad and a linearity range of ±0.6 mrad.