SAR(Synthetic Aperture Radar) 공식들
1. 해상도
1.1. 거리 해상도
\[{\delta}R_s=\dfrac{c}{2B}\text{,}\quad\quad\quad{\delta}R_g=\dfrac{c}{2B\sin\left({\eta}\right)}\]1.2. 방위 해상도
\[\delta R_a = \dfrac{2\pi}{|\Omega_n|} = \dfrac{2\pi}{2k\sin\theta_n\left(L/2\right)-2k\sin\theta_n\left(-L/2\right)} \approx \dfrac{x_n \lambda}{2L \cos^2\theta_n\left(0\right)} \approx \dfrac{K_a \lambda_c}{2 \Delta \theta}\] \[\delta R_a = \frac{\text{vel}}{\text{PRF}}\]2. 이득
2.1. 거리 이득
\[G_r = 10 \text{log}_{10}\left(B \times T_p\right) \text{ [dB]}\]3. Doppler Equations
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방위 해상도 Limitation $\dfrac{2\pi}{4k}=\dfrac{\lambda}{4}$
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Instantaneous Frequency($K_{un}\left(u\right)$)
\(K_{un}\left(u\right)=2k\sin\theta_n\left(u\right)\) -
Doppler Range
\(\left[2k\sin\theta_n\left(-L/2\right), 2k\sin\theta_n\left(L/2\right)\right]\) -
Doppler Center(${\Omega}_{nc}$)
\({\Omega}_{nc}\approx 2k\sin\theta_n\left(0\right)\) -
Doppler Bandwidth($ {\Omega}_n $) $$ {\Omega}_n =2k\sin\theta_n\left(L/2\right)-2k\sin\theta_n\left(-L/2\right)\approx \dfrac{2kL}{x_n}\cos^2\theta_n\left(0\right)\approx \dfrac{2{V}_{a}^{2}\cos^2(\theta_n(0))}{R_a \lambda_c}T_a$$
| Symbol | 단위 | 설명 | Symbol | 단위 | 설명 |
|---|---|---|---|---|---|
| B | hz | Bandwidth | c | m/s | Speed of light |
| $\eta$ | rad | Incidence Angle | u | m | Platform Azimuth Position |
| $\theta_n$ | rad | n번째 Pulse의 Aspect Angle, Squint Angle | L | m | Synthetic Aperture Length |
| $Y_0$ | m | Azimuth Swath | $T_a$ | sec | Aperture Time |
| $T_p$ | sec | Pulsewidth | |||