Method for ultrasonic characterization of a medium in order to determine a temporal and local characterization of an ultrasonic focusing with axial correction, the method comprising: - a step of generating a series of incident ultrasonic waves (US in) 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 - a step of generating an experimental reflection matrix R ui ( t) defined between the emission basis ( i) as input and a reception basis ( u) as output; - a step of determining a focused reflection matrix RFoc ( r in, r out, δt) which comprises responses of the medium between an input virtual transducer (TV in) of spatial position r in and an output virtual transducer (TV out) of spatial position r out, the responses of the output virtual transducer (TV out) being obtained at a time instant that is shifted by an additional delay δt relative to a time instant of the responses of the input virtual transducer (TV in), - a step of determining a wavefront image for the input virtual transducer (TV in) and for an additional delay interval, said wavefront image being determined as a function of the speed of sound c 0 in the medium, and said wavefront image being determined based on: - the focused reflection matrix RFoc ( r in, r out, δt) and - a ballistic propagation relation of the type δt (Δ r out) = -sign ( Δz out) · |Δ r out |/ c 0, which makes it possible to extract values from the focused reflection matrix in order to construct the wavefront image, and where: δt is the additional delay, | Δr out | is the modulus of the vector between the input virtual transducer (TV in) and the output virtual transducer (TV out), with Δ r out = r out - r in, Δz out is the component along a depth axis Z of the spatial position vector Δ r out. said said wavefront image comprising a focal spot, - a step of determining a center of the focal spot in the wavefront image, and determining the depthwise position in the direction of axis Z of said focal spot, said depthwise position being noted Δz ( r in), and - a step of determining a corrected focused reflection matrix RFoc ( r in, r out, δt) by translation of the responses of the focused reflection matrix RFoc (r in, r out, δt) of a spatial translation in the direction of the depth axis Z, said spatial translation being a function of the depthwise position Δz ( r in). - a step of generating a series of incident ultrasonic waves (US in) 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 - a step of generating an experimental reflection matrix R ui ( t) defined between the emission basis ( i) as input and a reception basis ( u) as output; - a step of determining a focused reflection matrix RFoc ( r in, r out, δt) which comprises responses of the medium between an input virtual transducer (TV in) of spatial position r in and an output virtual transducer (TV out) of spatial position r out, the responses of the output virtual transducer (TV out) being obtained at a time instant that is shifted by an additional delay δt relative to a time instant of the responses of the input virtual transducer (TV in), - a step of determining a wavefront image for the input virtual transducer (TV in) and for an additional delay interval, said wavefront image being determined as a function of the speed of sound c 0 in the medium, and said wavefront image being determined based on: - the focused reflection matrix RFoc ( r in, r out, δt) and - a ballistic propagation relation of the type δt (Δ r out) = -sign ( Δz out) · |Δ r out |/ c 0, which makes it possible to extract values from the focused reflection matrix in order to construct the wavefront image, and where: δt is the additional delay, | Δr out | is the modulus of the vector between the input virtual transducer (TV in) and the output virtual transducer (TV out), with Δ r out = r out - r in, Δz out is the component along a depth axis Z of the spatial position vector Δ r out. said said wavefront image comprising a focal spot, - the focused reflection matrix RFoc ( r in, r out, δt) and - a ballistic propagation relation of the type δt is the additional delay, | Δr out | is the modulus of the vector between the input virtual transducer (TV in) and the output virtual transducer (TV out), with Δ r out = r out - r in, Δz out is the component along a depth axis Z of the spatial position vector Δ r out. said said wavefront image comprising a focal spot, - a step of determining a center of the focal spot in the wavefront image, and determining the depthwise position in the direction of axis Z of said focal spot, said depthwise position being noted Δz ( r in), and - a step of determining a corrected focused reflection matrix RFoc ( r in, r out, δt) by translation of the responses of the focused reflection matrix RFoc (r in, r out, δt) of a spatial translation in the direction of the depth axis Z, said spatial translation being a function of the depthwise position Δz ( r in).