Recent research in haptic feedback is motivated by the crucial role that tactile perception plays in everyday touch interactions. In this paper, we describe psychophysical experiments to investigate the perceptual threshold of individual fingers on both the right and left hand of right-handed participants using active dynamic touch for spatial period discrimination of both sinusoidal and square-wave gratings on ultra-sonic haptic touchscreens. Both one-finger and multi-finger touch were studied and compared. Our results indicate that users' finger identity (index finger, middle finger, etc.) significantly affect the perception of both gratings in the case of one-finger exploration. We show that index finger and thumb are the most sensitive in all conditions whereas little finger followed by ring are the least sensitive for haptic perception. For multi-finger exploration, the right hand was found to be more sensitive than the left hand for both gratings. Our findings also demonstrate similar perception sensitivity between multi-finger exploration and the index finger of users' right hands (i.e. dominant hand in our study), while significant difference was found between single and multi-finger perception sensitivity for the left hand.