| Poster Session 6 |
Image Retrieval Theory of Synthetic Aperture Radiometer for Microwave Remote Sensing
III Base Line Oriented and Spatial Frequences
In the preceding section we have derived and defined the spatial frequencies as in (9), which is a function of both measurement geometry and base line geometry including the length and oriented of it. It is recognized that u is linearly related with the platform movement x' according to this first order approximations.
For a good quality image retrieval in the along track direction and particularly for remote sensing applications, we would like to have the full spatial frequency response up to the limit that provided by the base line D. therefore, there is an optimum design for the base line orientation. According to u, cosb is the slope of the line function which will determine the measured spatial range. For a given length base line, large slope corresponds a large coverage of spatial frequency of a fixed data collection window. For this reason, we take the derivative of the slope S of (9) and let it equals to zero,
Solve and obtain,
cos b=y 1csin a=sin qosin a (13)
Where qo is the incident angle while the platform is at the origin. Substitute this into (9) we obtain the most efficient spatial frequency,
Since appears as the intercept of the line function in (9) and (14), it has to be selected carefully. Fig. 2 shows that two different a values give completely different spatial frequency response/coverage. Noted that the spatial frequency is normalized by the base line length D/ l in the figure.
Fig. 2 Spatial frequency bandwidth,
IV Numerical Simulation and Result
To show the validation of the above analysis, we now taking a numerical simulation of a one dimensional along track aperture synthesis.
Let the platform altitude h be 800 km and the image area is 400 km aside from nadir or y c = 400 km. The image data has a dimension of 180 km which means that x a=90 km and in accordance the data collection window is 180 km long which gives x ranging from -80 to 80 km. This measurement geometry gives the incident angle changing from 26.56 to 28.5 degrees. The gap between the date collection windows of two images are 20 km which gives 2.56 seconds of time for the antenna to scan back preparing for the next image where the speed of the spacecraft is assumed to be 7.8 km per second.
According to the discussions in Section III, we would use three base lines to cover the spatial frequency response needed. The geometry of those base lines is listed in Table1.
From the sampling criteria, it is calculated that Dx= 80 m for this example and Du »4.97. For each base line given above, three examples will be taken at x=-80, 0 and 80 km of each baseline. For u = 0., we take an auto-correlation measurement of any of the four antennas. With all these samples, we will have V (u, where u = 0, ± 4.97, ±9.94, ±14.91, ±19.88, ±24.85, ±29.82. ±34.79, ±39.76, ±44.73), in total 19 sampling points for inverse. Fourier transform. Noted that measured but obtained from V(u)=V*(-u).
Fig.3 shows four different inverse Fourier transform theory has the ability to provide an approximate retrieved image. Since the more to the edges of the image, the bigger error will occur in the approximation, the result at the edges of the coverage has some degree of ambiguities. A suggested procedure for practice image retrieval is to use numerical optimization. However, the Fourier transform theory could still be used as the guidance of the system design and as the initial point of the numerical optimization.
VI. Conclusions
The image retrieval theory for along track synthetic aperture radiometer is presented. As conclusions, we now would like to address the following points:
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For along track aperture synthesis measuremnt, side looking measurement is a better configurations that nadir looking.
- Platform movement does provide some spatial frequency variations in the along track direction, however, it is important to chose the optimum base line length and oriented for a particular measurement geometry and spatial resolution required.
- The data collection window along track should be smaller than the image area in the along track direction since the antenna beam should scan during the measurement and should scan back after the measurement for the previous image and preparing for the next image. During the measurement, the beam should pointing to the center of the image area.
- Since the along track aperture synthesis can thin the aperture very much , it will use mush less element and correlate's than the conventional two dimensional aperture synthesis technique, for example the Y shape or U shape synthetic aperture radiometers.
We believe than the along track aperture synthesis technique is an attractive new technology in passive microwave remote sensing field. The present paper is basic and could not cover all aspects related to this topic. More work should be done and some of them are undergoing.
References
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Ruf, C. S., C. T. Swift, et. al., " Interferometeric synthetic aperture microwave radiometry for the remote sensing of the earth", IEEE Trans. GRS, Vol.26, pp.597-611, 1998.
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Le Vine, D.M., M. Kao, et al., "Inintail results in the development of a synthetic aperture microwave radiometer", IEEE Trans. , GRS, Vol. 28, pp.614-619, 1990.
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Komiyama, K., "High resolution imaging by super synthesis (SSR) for the passive microwave remote sensing of the earth", Electronic Letters, Vol.27, pp.389-390.
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Laursen, B., et al., " The TUD synthetic aperture radiometer demonstrate model", Proceeding of the Remote Sensing of the Environments, Rome, Feb., 1994.
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Martin-Neira, M., et al, "Integration of MIRAS breadboard and future activities", Proceedings of IGARSS'96, 1996.
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Edelsohn, C., et al., "RADSAR (RADiometric SAR) experimental results", Proceeding of IGARSS'98, 1998.
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US Patent No. 4,990, 925.
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Dong, X.L., J. Wu, J.S. Jiang, "The signal analysis and imaging of synthetic aperture radiometer", Proceedings of IGARSS,98, 1998.
- Jackson, T.J., D.M. Le Vine, C.t. swift, T.J. Schmugge and F.R. Schiebe, "Large area mapping of soil moisture using the ESTAR passive microwave radiometer in Washita'92", Remote sensing of Environment Vol. 53.
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Le Vine, D.M., et al., "Passive microwave remote sensing with the synthetic aperture radiometer ESTAR during the southern great plane experiments", Proceeding of IGRASS'98, 1998.
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Thompson, A.R., J.M. Moran and G.W. Swenson, Jr. Interferometry and synthesis in radio astronomy, Krieger Publishing Company, Malabar, Florida, 1994.
Fig.4 Results of numerical simulation,
-Original , ----retrieved
| | a | b | g | D/l | Spatial Frequency Coverage |
| No.1 | 79.9 | 63.9 | 151.7 | 56.45 | 4.97~14.91 |
| No.2 | 65.9 | 65.9 | 144.7 | 60.86 | 19.88~29.82 |
| No.3 | 54.4 | 68.7 | 136.7 | 68.31 | 34.79~44.73 |
Table 1, base lines geometry and spatial frequency coverage.
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