Performing range resampling formulated by��n(1+��0i)=��0(1+��0i)(4)where ��0=4��f0ccos��0cos��0 is our site a constant, we can have the phase history asfr(n,��)=expj��0(1+��0��)(sxtan��n?sy+��(n)).(5)For selleck chem Erlotinib the purpose of Inhibitors,Modulators,Libraries clearness and simplicity, we still use i instead of �� in the following discussion. Then, Equation (5) is expressed asfr(n,i)=expj��0(1+��0i)(sxtan��n?sy+��(n))(6)If the space sampling position n satisfied tan ��n = d��n, where d�� is constant, the range resampled signal can be modeled asfr(n,i)=expj��0(1+��0i)(sxd��n?sy+��(n)).(7)3.?Two Dimensional Inhibitors,Modulators,Libraries Overlapped Subaperture Polar format Algorithm (PFOSA) [9]Equation (7) is the phase history after range resampling.
In full aperture PFA image formation, we get the image by performing an azimuth resampling Inhibitors,Modulators,Libraries followed by a 2-D DFT, or an azimuth chirp-z transform (CZT) followed by a range DFT.
However, due to the space-variant phase error term ��(n), the focused scene size Inhibitors,Modulators,Libraries Inhibitors,Modulators,Libraries of interest is constrained to be very small in ultra-high resolution SAR. Subaperture algorithm, which can provide coarse resolution images before Inhibitors,Modulators,Libraries the final fine resolution image formation, has been proposed to overcome this constraint [9]. Due to the coarse information of the individual scatter’s location extracted from the coarse resolution images, the compensation of space-variant phase error becomes applicable. In the following, we briefly review of the PFOSA proposed in [9].
First, we Entinostat divide the azimuth and range aperture into subapertures, respectively, by makingn=m1+��2m2i=k1+��2k2(8)where m1 is the azimuth intra-subaperture index limited within ?M1 /2�� m1 �� M1 /2 ? 1, m2 is the azimuth inter-subaperture index limited within ?M2/2��m2��M2/2 ? 1, ��2 is the azimuth Inhibitors,Modulators,Libraries data decimation factor, k1 is the range intra-subaperture index limited within ?K1 /2 �� k1 Inhibitors,Modulators,Libraries �� K1 / 2 ? 1, k2 is the range inter-subaperture index limited within ?K2/2��k2 ��K2/2?1, and m2 is the range data decimation factor. Using Equation (8), we rewrite the Equation (7) asfr(m1,m2;k1,k2)=expj��0(1+��0(k1+��2k2))(sxd��(m1+��2m2)?sy+��(m1+��2m2)).
(9)Next, applying the quadratic order approximation of ��(n) and rearrange Equation (9) following the index m1, k1, m2, k2 sequentially, we getfr(m1,m2;k1,k2)=expj��0(?sy+?0)?expj��0(1+��0(k1+��2k2))((sxd��+?1+2?2��2m2)m1+?2m12)?expj��0��0(sxd����2m2?sy+?0+?1��2m2+?2(��2m2)2)k1?expj��0(1+��0��2k2)((sxd����2+?1��2)m2+?2(��2m2)2)?expj��0��0��2(?sy+?0)k2(10)where, new post the first term is a constant, which is neglected in the following discussion.
The second and third terms are the azimuth and range intra-subaperture terms, which correspond to coarse resolution image. The fourth and fifth terms are the inter-subaperture terms, which correspond to fine resolution image. Also note that each Batimastat exponential term selleck inhibitor contains some undesired error phase.