Fourth-order-product phase difference autofocus

Claim 2

A phase difference autofocus computational method for use in processing range compressed video phase history (VPH) data of a SAR data to correct for phase errors contained therein, said method comprising the steps of: dividing an array of range compressed VPH data into first and second subarrays; forming a third subarray of range compressed VPH data comprising a portion of the array; complex-conjugate multiplying the first subarray with the third subarray to produce a first second-order-product subarray; complex-conjugate multiplying the third subarray with the second subarray to produce a second second-order-product subarray; complex-conjugate multiplying the first second-order-product subarray with the second second-order-product subarray to produce a first fourth-order-product subarray; time reversing and complex-conjugate multiplying the second second-order-product subarray with the first second-order-product subarray to produce a second fourth-order-product subarray; separately performing Fourier transforms on the first and second fourth-order-product subarrays to produce respective FFT filter banks; separately performing magnitude-detections on respective FFT filter banks to produce respective autofocus functionals; summing the respective autofocus functionals over all range bins; respectively determining the locations of the peak response values of the autofocus functionals; computing quadratic and cubic phase error values from the respective peak response locations; combining the quadratic and cubic phase error values in accordance with a predefined relationship to produce a phase error correction signal; and multiplying the range compressed VPH data with the phase error correction signal to produce phase-corrected VPH data.

Claim 3

The method of claim 1 wherein: the array of data is divided into first and second equal subarrays comprising respective halves of the array; and the third subarray comprises a center portion of the array.

Claim 4

The method of claim 2 which further comprises the step of: separately amplitude weighting the first and second fourth-order-product subarrays prior to performing the Fourier transforms on them.

Claim 5

A phase difference autofocus computational method for use in processing range compressed video phase history (VPH) data of a SAR data to correct for phase errors contained therein, said method comprising the steps of: dividing an array of range compressed VPH data into first and second equal subarrays that comprise respective halves of the data comprising the array; forming a third subarray of range compressed VPH data comprising a center portion of the array, and which comprises the same amount of data as the first and second subarrays; complex-conjugate multiplying the first subarray with the third array to produce a first second-order-product subarray; complex-conjugate multiplying the third subarray with the second array to produce a second second-order-product subarray; complex-conjugate multiplying the first second-order-product subarray with the second second-order-product subarray to produce a first fourth-order-product subarray; time reversing and complex-conjugate multiplying the second second-order-product subarray with the first second-order-product subarray to produce a second fourth-order-product subarray; separately performing Fourier transforms on the first and second fourth-order-product subarrays to produce respective FFT filter banks; separately performing magnitude-detections on respective FFT filter banks to produce respective autofocus functionals; summing the respective autofocus functionals over all range bins; respectively determining the locations of the peak response values of the autofocus functionals; computing quadratic and cubic phase error values from the respective peak response locations; combining the quadratic and cubic phase error values in accordance with a predefined relationship to produce a phase error correction signal; and multiplying the range compressed VPH data with the phase error correction signal to produce phase-corrected VPH data.

Claim 6

A phase difference autofocus computational method for use in processing range compressed video phase history (VPH) data of a SAR data to correct for phase errors contained therein, said method comprising the steps of: dividing an array of range compressed VPH data into first and second equal subarrays that comprise respective halves of the data comprising the array; forming a third subarray of range compressed VPH data comprising a center portion of the array, and which comprises the same amount of data as the first and second subarrays; complex-conjugate multiplying the first subarray with the third array to produce a first second-order-product subarray; complex-conjugate multiplying the third subarray with the second array to produce a second second-order-product subarray; complex-conjugate multiplying the first second-order-product subarray with the second second-order-product subarray to produce a first fourth-order-product subarray; time reversing and complex-conjugate multiplying the second second-order-product subarray with the first second-order-product subarray to produce a second fourth-order-product subarray; separately performing Fourier transforms on the first and second fourth-order-product subarrays to produce respective FFT filter banks; separately performing magnitude-detections on respective FFT filter banks to produce respective autofocus functionals; summing the respective autofocus functionals over all range bins; respectively determining the locations of the peak response values of the autofocus functionals; computing quadratic and cubic phase error values from the respective peak response locations; combining the quadratic and cubic phase error values in accordance with a predefined relationship to produce a phase error correction signal; and multiplying the range compressed VPH data with the phase error correction signal to produce phase-corrected VPH data.

Claim 7

The method of claim 4 which further comprises the step of: separately amplitude weighting the first and second fourth-order-product subarrays prior to performing the Fourier transforms on them.

Claim 8

A phase difference autofocus computational method for use in processing range compressed video phase history (VPH) data of a SAR data to correct for phase errors contained therein, said method comprising the steps of: dividing an array of range compressed VPH data into first and second equal subarrays {X(n)}, {Y(n)}; forming a third subarray {Z(n)} of range compressed VPH data comprising a center portion of the array; complex-conjugate multiplying the first subarray {X(n)} with the third subarray {Z(n)} to produce a first second-order-product subarray {P(n)}; complex-conjugate multiplying the third subarray {Z(n)} with the second subarray {Y(n)} to produce a second second-order-product subarray {Q(n)}; complex-conjugate multiplying the first second-order-product subarray {P(n)} with the second second-order-product subarray {Q(n)} to produce a first fourth-order-product subarray {H(n)}; time reversing and complex-conjugate multiplying the second second-order-product subarray {Q(n)} with the first second-order-product subarray {P(n)} to produce a second fourth-order-product subarray {G(n)}; separately amplitude weighting the first and second fourth-order-product subarrays {G(n)}, {H(n)}; separately performing Fourier transforms on the amplitude weighted first and second fourth-order-product subarrays {G(n)}, {H(n)} to produce respective FFT filter banks; separately performing magnitude-detections on respective FFT filter banks to produce respective autofocus functionals; summing the respective autofocus functionals over all range bins; respectively determining the locations of the peak response values of the autofocus functionals; computing quadratic and cubic phase error values from the respective peak response locations; combining the quadratic and cubic phase error values in accordance with a predefined relationship to produce a phase error correction signal; and multiplying the range compressed VPH data with the phase error correction signal to produce phase-corrected VPH data.

Claim 9

A phase difference autofocus computational method for use in processing range compressed video phase history (VPH) data of a SAR data to correct for phase errors contained therein, said method comprising the steps of: dividing an array of range compressed VPH data into first and second equal subarrays {X(n)}, {Y(n)}; forming a third subarray {Z(n)} of range compressed VPH data comprising a center portion of the array; complex-conjugate multiplying the first subarray {X(n)} with the third subarray {Z(n)} to produce a first second-order-product subarray {P(n)}; complex-conjugate multiplying the third subarray {Z(n)} with the second subarray {Y(n)} to produce a second second-order-product subarray {Q(n)}; complex-conjugate multiplying the first second-order-product subarray {P(n)} with the second second-order-product subarray {Q(n)} to produce a first fourth-order-product subarray {H(n)}; time reversing and complex-conjugate multiplying the second second-order-product subarray {Q(n)} with the first second-order-product subarray {P(n)} to produce a second fourth-order-product subarray {G(n)}; separately amplitude weighting the first and second fourth-order-product subarrays {G(n)}, {H(n)}; separately performing Fourier transforms on the amplitude weighted first and second fourth-order-product subarrays {G(n)}, {H(n)} to produce respective FFT filter banks; separately performing magnitude-detections on respective FFT filter banks to produce respective autofocus functionals; summing the respective autofocus functionals over all range bins; respectively determining the locations of the peak response values of the autofocus functionals; computing quadratic and cubic phase error values from the respective peak response locations; combining the quadratic and cubic phase error values in accordance with a predefined relationship to produce a phase error correction signal; and multiplying the range compressed VPH data with the phase error correction signal to produce phase-corrected VPH data.

Claim 10

The method of claim 6 wherein: the dividing an array into first and second subarrays and forming a third subarray comprises creating first, second and third subarrays of length 2N+1 defined by X(n)=S(n-L)=σe.sup.jφ(n-L), -N<n<N, Y(n)=S(n+L)=σe.sup.jφ(n+L), -N<n<N, and Z(n)=S(n)=σe.sup.jφ(n), -N<n<N, and wherein a full array of length 2M+1 is defined by S(m)=σe.sup.jφ(m), -M,<m<M, defines the locations of the first and second subarrays, σ is a magnitude and φ(m) is a phase variation having the form φ(m)=2π (A+Bm+Cm.sup.2 +Dm.sup.3), -M≦m≦M, for constants A, B, C and D; the complex conjugate multiplying the first subarray {X(n)} with the third subarray {Z(n)} to produce a first second-order-product subarray {P(n)} is defined by P(n)=X*(n) Z(n) and the complex-conjugate multiplying the third subarray {Z(n)} with the second subarray {Y(n)} to produce a second second-order-product subarray {Q(n)} is defined by Q(n)=Z*(n) Y(n); the separately amplitude weighting the first and second fourth-order-product subarrays {G(n)} and {H(n)} are defined by G(n)=P(n)Q*(-n), -N≦n≦N, and H(n)=P*(n) Q(n), -N≦n≦N, and are predetermined as G(n)=σ.sup.4 e.sup.+j2π4CLn, and H(n)=σ.sup.4 e.sup.+j2π6DL.spsp.2 n; respectively determining the locations of the autofocus functional is determined by: the peak response is located at τ g =4CLK if a K-point FFT is performed on the first fourth-order-product subarray {G(n)}, and the peak response is located at τ h =6DL 2 K if a K-point FFT is performed on the second fourth-order-product subarray {H(n)}; and the computing the quadratic and cubic phase error values in accordance with a predefined relationship to produce a phase error correction signal is specified as center-to-end quadratic phase error Φ q is given by Φ q =2πτ g M 2 /(4LK), and the center-to-end cubic phase error Φ c is given by Φ c =2πτ g M 3 /(6LK).