Method and system for ultrasonic characterization of a medium

System for ultrasonic characterization of a medium in order to determine a temporal and local characterization of an ultrasonic focusing, the system comprising:

• an array of transducers that are suitable for generating a series of incident ultrasonic waves in an area of the medium, and for recording the ultrasonic waves backscattered by said area as a function of time;
• one or more processors;
• and
• a memory storing instructions that, when executed by the one or more processors, cause the system to perform operations comprising:
• generating a series of incident ultrasonic waves (USin) in an area of said medium, by means of an array of transducers, said series of incident ultrasonic waves being an emission basis (i);
• and
• generating an experimental reflection matrix Rui(t) defined between the emission basis (i) as input and a reception basis (u) as output;
• determining a focused reflection matrix RFoc(rin, rout, δt) which comprises responses of the medium between an input virtual transducer (TVin) of spatial position rin and an output virtual transducer (TVout) of spatial position rout, the responses of the output virtual transducer (TVout) being obtained at a time instant shifted by an additional delay δt relative to a time instant of the responses of the input virtual transducer (TVin),
• determining a wavefront image for the input virtual transducer (TVin) and for an additional delay interval, said wavefront image being determined as a function of the speed of sound c0 in the medium, and said wavefront image being determined based on:
• the focused reflection matrix RFoc(rin, rout, δt) and
• a ballistic propagation relation of the type δt(Δrout)=−sign(Δzout)·|Δrout|/c0, and where:
• δt is the additional delay,
• |Δrout| is the modulus of the vector between the input virtual transducer (TVin) and the output virtual transducer (TVout), with Δrout=rout−rin,
• Δzout is the component along a depth axis Z of the spatial position vector Δrout;
• determining a depthwise position Δz(0)(rin) of the center of a focal spot in the wavefront image, and
• calculating an integrated speed of sound c(1)(rin), based on the following formula:
• c
• (
• 1
• )
• (
• r
• in
• )
• =
• c
• 0
• ⁢
• 1
• +
• Δ
• ⁢
• z
• (
• 0
• )
• (
• r
• in
• )
• z
• in
• where zin is the component along the depth axis Z of the spatial position vector rin of the input virtual transducer (TVin).