PIN: A PARTITIONING & INDEXING OPTIMIZATION METHOD FOR OLAP

A novel method and apparatus are provided by the invention for the precision-control of the thickness of thin work pieces under lapping in a lapping machine having an upper and lower lapping surface plates rotatable relative to each other sandwiching the work pieces with continuous supply of a lapping fluid therebetween. In the invention, the upper lapping surface place is provided with an opening in the lapping surface, in which an ultrasonic transducer means is mounted capable of projecting an ultrasonic wave to the work piece and receiving the dual echo waves reflected at the upper and the lower surface of the work piece so as that the delay time of the echo waves is transmitted as electrical signals to a control means of the lapping machine where the signals are computed in terms of the thickness of the work pieces and utilized for controlling the operation of the machine. The space between the ultrasonic transducer means and the work piece is filled with the lapping fluid so that any errors in the propagation of the ultrasonic waves can be minimized.