Apparatus and method for imaging with wavefields using inverse scattering techniques

A method of reconstructing an image of an object using a central processing unit (CPU) programmed to process data derived from wavefield energy that has been transmitted at one or more frequencies and scattered by said object, said method comprising the steps of:

• (a) propagating wavefield energy waves, each said wavefield energy wave having one or more frequencies, toward said object from one or more transmitter positions;
• (b) electronically storing one or more digitized electronic signals derived by said CPU from said propagated wavefield energy and said one or more transmitter positions, said digitized electronic signals representing an incident field obtained at each said frequency;
• (c) detecting at one or more receivers wavefield energy waves, each said wavefield energy wave having one or more frequencies, scattered by said object;
• (d) electronically storing one or more digitized electronic signals representing all orders scattering obtained at each said frequency and derived by said CPU from the scattered wavefield energy waves detected at said one or more receivers;
• (e) said CPU setting an initialized estimate of the scattering potential for said object at each said frequency, and storing each said scattering potential estimate;
• (f) said CPU performing a convergence step at each said frequency comprising the following steps:
• (1) said CPU preparing, using a Green's function, an estimate of an internal field at each said frequency and at each scattering point within said object derived from:
• ((a)) said incident field, and
• ((b)) said scattering potential estimate, where said estimate of said internal field at each said frequency comprises all orders of scattering;
• (2) deriving, using a Green's function, a calculated scattered field from:
• (a) said scattering potential estimate, and
• (b) said estimate of said internal field;
• (3) comparing said scatter field detected at said one or more receiver positions to said calculated scattered field determined by said CPU to derive a comparator;
• (4) when said comparator is greater than a preselected tolerance, said CPU determining, using a Green's function, and storingan updated scattering potential from:
• ((a)) said estimate of said internal field,
• ((b)) said calculated scattered field determined by said CPU,
• ((c)) said scattering potential estimate,
• ((d)) said scattered field detected at said receiver positions;
• ((e)) said CPU utilizing the Jacobian of the calculated scattered field with respect to the scattering potential estimate, said Jacobian utilization being implemented exclusively with shift invariant kernels;
• and then setting said scattering potential estimate equal to said updated scattering potential;
• (g) repeating said CPU convergence step until said comparator is less than or equal to said preselected tolerance, said CPU thereafter reconstructing from said updated scattering potential said image of said object;
• and outputting at an output device a visually perceptible display of said image.

A method of producing an image of an object from wavefield energy that has been transmitted into and scattered by the object, said image comprising a high resolution map of the scattering potential at all points within the object, said image being stored in a memory of a central processing unit (CPU), and said method comprising the steps of:

• (a) electronically transmitting an electric signal to a laser means, said laser means transducing said electric signal into wavefield energy at one or more frequencies which are propagated toward said object from one or more of transducer transmitter positions;
• (b) electronically processing said electric signal to determine an incident field corresponding to said propagated wavefield energy, said incident field being stored in the memory of the CPU in the form of digitized electric signals;
• (c) detecting at an intensity measurement means said wavefield energy transmitted into and scattered by said object;
• (d) deriving from said wavefield energy detection at said intensity measurement means the amplitude and the phase of said detected wavefield energy;
• (e) deriving a detected wavefield energy from the amplitude and the phase;
• (f) electronically processing said detected wavefield energy so as to transform said detected wavefield energy into one or more digitized electric signals stored in said memory of said CPU and corresponding to a scattered field detected;
• (g) said CPU setting an initialized estimate of the scattering potential for said object at each said frequency and storing each said scattering potential estimate in said memory;
• and
• said CPU computing an updated scattering potential from said incident field and said scattered field detected.

A method of producing an image of an object from wavefield energy that has been transmitted into and scattered by the object, said image comprising a high resolution map of the scattering potential at all points within the object, said image being stored in a memory of a central processing unit (CPU), and said method comprising the steps of:

• (a) electronically transmitting an electric signal at one or more frequencies and transducing said electric signal at each said frequency into wavefield energy propagated toward said object from one or more of antennae transmitter positions;
• (b) electronically processing said electric signal to determine an incident field corresponding to said propagated wavefield energy, said incident field being stored in the memory of the CPU in the form of digitized electric signals;
• (c) detecting at one or more of antennae receiver positions said wavefield energy transmitted into and scattered by said object;
• (d) electronically processing said detected wavefield energy so as to transform said detected wavefield energy into one or more digitized electric signals stored in said memory of said CPU and corresponding to a scattered field detected at said one or more antennae receiver positions;
• (e) said CPU setting an initialized estimate of the scattering potential for said object at each said frequency and storing each said scattering potential estimate in said memory:
• and
• (f) said CPU computing an updated scattering potential from said incident field and said scattered field detected.

A method of producing an image of an object from wavefield energy that has been transmitted into and scattered by the object, said image comprising a high resolution map of the scattering potential at all points within the object, said image being stored in a memory of a central processing unit (CPU), and said method comprising the steps of:

• (a) electronically transmitting an electric signal at one or more frequencies and transducing said electric signal at each said frequency into wavefield energy propagated toward said object from one or more of transducer transmitter positions;
• (b) electronically processing said electric signal to determine from said one or more transmitter positions an incident field corresponding to said propagated wavefield energy, said incident field being stored in the memory of the CPU in the form of transmission stored signals;
• (c) detecting at one or more of transducer receiver positions said wavefield energy transmitted into and scattered by said object;
• (d) electronically processing said detected wavefield energy so as to transform said detected wavefield energy into one or more reception stored signals stored in said memory of said CPU and corresponding to a scattered field detected at said one or more transducer receiver positions;
• (e) said CPU setting, an initialized estimate of the scattering potential for said object at each said frequency and storing each said scattering potential estimate in said memory;
• (f) said CPU performing a convergence step at each said frequency comprising the following steps:
• (1) said CPU preparing, using a Green's function, an estimate of the internal field of said object derived from:
• ((a)) said incident field, and
• ((b)) said scattering potential estimate, where said estimate of said internal field at each said frequency comprises all orders of scattering;
• (2) deriving, using a Green's function, a calculated scattered field from:
• (a) said scattering potential estimate, and
• (b) said estimate of said internal field;
• (3) comparing said scatter field detected at said one or more receiver positions to said calculated scattered field determined by said CPU to derive a comparator;
• (4) when said comparator is greater than a preselected tolerance, said CPU determining, using a Green's function, and storing in said memory an updated scattering potential from:
• ((a)) said estimate of said internal field,
• ((b)) said calculated scattered field determined by said CPU,
• ((c)) said scattering potential estimate,
• ((d)) said scattered field detected at said receiver positions;
• and
• ((e)) said CPU utilizing the Jacobian of the calculated scattered field with respect to the scattering potential estimate, said Jacobian utilization being implemented exclusively with shift invariant kernels;
• and then setting said scattering potential estimate equal to said updated scattering potential;
• (g) repeating said CPU convergence step until said comparator is less than or equal to said preselected tolerance, said CPU thereafter using said updated scattering potential to reconstruct and store said image in said CPU memory.