In this paper we demonstrate a non-destructive, non-contact detection method for small defects in thin polymer plates using an air coupled ultrasonic (ACUS) setup. There exist many applications for such methods, e.g. quality control in the manufacturing process or failure prevention by periodical inspections during the lifetime of a product. We demonstrate a setup for the inspection of plates together with signal analysis algorithms to process the measured data, meeting the challenges to handle the dispersive signals and establishing a robust failure criterion. Pressure waves from the transmitter excite different modes of Lamb waves inside the plate. These Lamb waves propagate in the plate and reradiate pressure waves into the air that are then detected by the receiver. Lamb mode conversion is used for defect detection. A numerical model allows the visualization of the propagating waves in the air as well as the Lamb waves inside the plate. Four key parameters of the setup are identified, two angles and two distances. The transmitter and the receiver angles are used to select which Lamb mode (anti-symmetric A or symmetric S) is mainly excited and detected, respectively. For the acquisition of the Lamb wave signal the distance from the transmitter to the receiver should be as large as possible but is limited by the attenuation of the signal. Measurements for different values of this distance are essential for signal analysis. The distance between transducer and plate surface should be as small as possible even if it may introduce secondary Lamb waves due to reflections of the pressure wave between transmitter and plate surface. Two algorithms, a model based one and a data driven one, are presented to separate Lamb modes that overlap in time. In these separated signals, the Lamb mode conversion from A to S is shown, allowing a localization of the defect. We conclude that defect detection and localization with Lamb mode conversion is possible with an air coupled ultrasonic setup. Multiple measurements along the propagation direction of the Lamb waves are necessary to allow a thorough signal analysis and visualize the mode conversion.