{'fraction_non_alphanumeric': 0.01634877384196185, 'fraction_numerical': 0.0, 'mean_word_length': 5.930817610062893, 'pattern_counts': {'":': 0, '<': 0, '<?xml version=': 0, '>': 0, 'https://': 0, 'lorem ipsum': 0, 'www.': 0, 'xml': 0}, 'pii_count': 0, 'substrings_counts': 0, 'word_list_counts': {'cursed_substrings.json': 0, 'profanity_word_list.json': 0, 'sexual_word_list.json': 0, 'zh_pornsignals.json': 0}}
Numerical ultrasonic holographic imaging by direct backward propagation

In this contribution the results are presented of numerical ultrasonic holographic imaging, by direct backward propagation of a recorded complex object wave. Direct backward propagation allows for the total elimination of the step of hologram formation, whether ultrasonically, electronically or numerically. This relieves the reconstructed images from the virtual and non-diffracted waves, from which classical numerical reconstructions suffer. By means of numerical simulations of holographic recording and reconstruction, the advantage of direct backward reconstruction, over classical holographic reconstruction is shown. The possibility is demonstrated of taking into account the finite dimensions of the transducer used for scanning the hologram plane. This allows to obtain relatively high resolution images, with classical ultrasonic apparatus, as is used for pulse-echo C-scanning for example. The technique is applied to the study of the sound pressure distribution inside the beam emitted by an ultrasonic transducer.