A TFM frame costs two things: the time to acquire the full matrix capture, and the time to reconstruct the image from it. Acquisition needs one pulse per transmitting element, so it takes N_tx / PRF seconds. Reconstruction needs one delay-and-sum operation for every transmit-receive pair at every pixel, for every mode imaged: N_tx × N_rx × pixels × modes.

Both scale badly. Doubling the number of elements doubles the acquisition time and quadruples the processing load. Halving the pixel pitch quadruples the processing load alone. Adding a second wave mode set doubles it again. This is why practical TFM setups use a sub-aperture rather than all 64 or 128 elements, and why zones are kept small.

Knowing which of the two limits applies tells you what to change. If acquisition is the limit, reduce the number of transmit elements or raise the PRF. If processing is the limit, shrink the zone, coarsen the grid within the amplitude fidelity budget, or drop a mode. Changing the wrong one buys nothing.

Worked example

Transmitting elements	64
Receiving elements	64
Pixels in the zone	30351
Wave mode sets imaged	1
Processing throughput (billion operations per second)	10
Pulse repetition frequency	2000 Hz
Delay-and-sum operations per frame (millions)	124.32
Processing limited frame rate	80.44 Hz
Full matrix capture time	32 ms
Acquisition limited frame rate	31.25 Hz
Achievable frame rate	31.25 Hz

64 by 64 pairs over 30 351 pixels is 124.32 million operations per frame, which at 10 billion operations per second allows 80.44 frames per second. Capturing the matrix needs 64 pulses, i.e. 64/2000 = 32.00 ms, so acquisition caps the rate at 31.25 Hz - the lower of the two and therefore the frame rate.

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