Three dimensional imaging device using ellipsoidal backprojection

A three dimensional active imaging device for generating a three dimensional image of reflecting points on or within objects in a three dimensional volume within which the propagation velocity of transmitted energy and the propagation velocity of echo energy are known, said device using a reduced number of transmitted pulses and utilizing a Receiver means comprising a two or three dimensional array of sparsely spaced receiver elements and a Transmitter means comprising a two or three dimensional array of sparsely spaced transmitter elements, comprising:

• (a) The Transmitter means for generating plural pulses of energy which will radiate uniformly through a wide solid angle in the three dimensional volume external to said array;
• (b) A System Timing and Control means for activating the first transmitter element means whereby the first pulse of energy is radiated;
• (c) The Receiver means for simultaneously detecting echoes, caused by said radiated pulse of energy reflecting from said reflecting points, at three or more of the sparsely spaced receiver elements;
• (d) An Echo Processor means for sampling, as a function of time, said detected echoes from each of the receiver elements of said sparsely spaced receiver elements whereby echo samples are generated;
• (e) An Image Reconstruction Processor means for combining said samples into points of the image of the three dimensional volume, whereby the image is reconstructed, said means utilizing time of flight associated with the echo samples to determine into which of said image points the echo samples should be combined, wherein said time of flight consists of the sum of:
• (1) the distance from the transmitter element to the image point divided by the velocity of the transmitted energy, and (2) the distance from the image point to the receiver element divided by the velocity of the echo energy, said time of flight computed according to the equivalent of the following equation,
• TOF(x,y,z)=(1/Ct)RTP.sub.i +(1/Ce)RPE.sub.j
• for transmitter t.sub.i
• and for receiver e.sub.j
• where
• TOF(x,y,z) is the time of flight for the image point at (x,y,z), and which is associated with transmitter i and receiver j
• Ct is the transmitted energy propagation velocity
• Ce is the echo energy propagation velocity which may be equal to Ct, or different from Ct
• and also where
• RTP.sub.i =.sqroot.[(x-xi).sup.2 +(y-yi).sup.2 +(z-zi).sup.2 ]
• is the distance from the transmitter i to the point (x,y,z)
• RPE.sub.j =.sqroot.[(x-xj).sup.2 +(y-yj).sup.2 +(z-zj).sup.2 ]
• is the distance from point (x,y,z) to the receiver j
• where also
• (xi,yi,zi) is the location of transmitter element i
• (xj,yj,zj) is the location of receiver element j
• (f) The System Timing and Control means for activating the next of the transmitter elements whereby the next pulse of energy is radiated;
• (g) The System Timing and Control means for repeating (c), (d),
• (e) whereby the echo samples generated by the receiver elements are combined into the image;
• (h) The System Timing and Control means for repeating (f) and then (g) for each of the transmitter elements in the plurality of transmitters wherein all of the transmitter elements radiate a pulse of energy and the echo samples received at each of the receiver elements resulting from each of the pulses are combined into the image.

A three dimensional active imaging method by which there is generated image points of reflecting points in a three dimensional volume residing outside of a sparse array of plural transmitting and plural sensing elements, where the transmitted energy propagation speed is known and the echo propagation speed is known, comprising the steps;

• (a) Transmitting a pulse of energy, from a transmitting element, which will propagate through all of the three dimensional volume to be imaged;
• (b) Simultaneously sensing echoes caused by the reflecting points within said volume with a two or three dimensional array of three or more sparsely spaced sensing elements;
• (c) Sampling at time interval, dt, the echoes simultaneously sensed at each sensing element whereby a set of echo time histories of sequences of echo samples for all of the sensing elements is created which is associated with the transmitter;
• (d) Repeating steps (a), (b) and (c) for each transmitter whereby sets of echo time histories, associated with each transmitter, are created;
• (e) Reconstructing one of the image points by selecting and summing together one of said echo samples from each of said echo time histories from each of said sensor elements for each of said echo time history sets associated with each of said transmitters, wherein said echo samples are selected in accordance with the equivalent of the following algorithm:
• the echo sample, echo.sub.ij, from the sensor i echo time history from the echo time history set associated with transmitter j for use in reconstructing the image point at (x,y,z) is:
• echo.sub.ij (1/dt)(1/Ct)RTP.sub.i +(1/Ce)RPE.sub.j)
• where
• (x,y,z) is the image point of the reflecting point at the location (x,y,z)
• echo.sub.ij (sn) is the (sn).sup.th sample in the echo time history set, echo.sub.ij,
• where the echoes resulted from the pulse transmitted by the transmitter i, and the echoes were sensed by sensor element j
• dt is the time interval at which the echo samples are taken
• Ct is the transmitted pulse propagation velocity
• Ce is the echo energy propagation velocity which may be equal to Ct, or different from Ct
• and where
• RTP.sub.i =.sqroot.[(x-xi).sup.2 +(y-yi).sup.2 +(z-zi).sup.2 ]
• RPE.sub.j =.sqroot.[(x-xj).sup.2 +(y-yj).sup.2 +(z-zj).sup.2 ]
• where also
• (xi,yi,zi) is the location of transmitter element i
• (xj,yj,zj) is the location of receiver element j
• (f) Repeating step (e) for each image point in the three dimensional volume.