# Airborne SAR Imaging Algorithm for Ocean Waves Based on Optimum Focus Setting

^{1}

^{2}

^{3}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Theoretical Analysis of the Optimum Focus Setting for Different Targets

#### 2.1. Analysis of the Optimum Focus Setting for Rigid Targets

#### 2.2. Analysis of the Optimum Focus Setting for Surface Waves

## 3. Airborne SAR Imaging Algorithm for Ocean Waves Based on Optimum Focus Setting

#### 3.1. Selection of Sub-Block Data

#### 3.2. Calculation of Focus Setting Variation Section

#### 3.3. Sub-block Data Refocusing

#### 3.4. Calculation of the Optimum Focus Setting

#### 3.5. Image Block Refocusing

## 4. Validation of the Proposed Algorithm with Simulations and Field Data

#### 4.1. Validation of the Algorithm with Simulations

#### 4.1.1. Simulation Model

#### 4.1.2. Simulation Results

#### 4.2. Validation of the Proposed Algorithm with Field Data

#### 4.2.1. Results of Field Data Processing

#### 4.2.2. Quantitative Analysis of the Focus of Surface Waves

## 5. Discussion and Analysis

#### 5.1. Analysis of the Selection of Focus Setting Variation Section

#### 5.1.1. Analysis of the Selection of $\Delta v$

#### 5.1.2. Analysis of the Selection of $k$

#### 5.2. Analysis of the Applicability of the Proposed Algorithm

## 6. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

- Tomiyasu, K. Tutorial review of synthetic-aperture radar (SAR) with applications to imaging of the ocean surface. Proc. IEEE
**1978**, 66, 563–583. [Google Scholar] [CrossRef] - Cumming, I.G.; Wong, F.H. Digital Processing of Synthetic Aperture Radar Data: Algorithms and Implementation; Artech House: Norwood, MA, USA, 2005. [Google Scholar]
- Raney, R.K. Synthetic Aperture Imaging Radar and Moving Targets. IEEE Trans. Aerosp. Electron. Syst.
**1971**, AES-7, 499–505. [Google Scholar] [CrossRef] - Hayt, D.W.; Alpers, W.; Burning, C.; Dewitt, R.; Henyey, F.; Kasilingam, D.P.; Keller, W.C.; Lyzenga, D.R.; Plant, W.J.; Schult, R.L. Focusing simulations of synthetic aperture radar ocean images. J. Geophys. Res. Oceans
**1990**, 95, 16245–16261. [Google Scholar] [CrossRef] - Kasilingam, D.P.; Hayt, D.W.; Shemdin, O.H. Focusing of synthetic aperture radar ocean images with long integration times. J. Geophys. Res.
**1991**, 96, 16935–16942. [Google Scholar] [CrossRef] - Alpers, W.; Rufenach, C. The effect of orbital motions on synthetic aperture radar imagery of ocean waves. IEEE Trans. Antennas Propag.
**1979**, 27, 685–690. [Google Scholar] [CrossRef] - Raney, R. Wave orbital velocity, fade, and SAR response to azimuth waves. IEEE J. Ocean. Eng.
**1981**, 6, 140–146. [Google Scholar] [CrossRef] - Stopa, J.E.; Ardhuin, F.; Chapron, B.; Collard, F. Estimating wave orbital velocity through the azimuth cutoff from space-borne satellites. J. Geophys. Res. Oceans
**2015**, 120, 7616–7634. [Google Scholar] [CrossRef] - Grieco, G.; Lin, W.; Migliaccio, M.; Nirchio, F.; Portabella, M. Dependency of the Sentinel-1 azimuth wavelength cut-off on significant wave height and wind speed. Int. J. Remote Sens.
**2016**, 37, 5086–5104. [Google Scholar] [CrossRef] - Stopa, J.E.; Mouche, A. Significant wave heights from Sentinel-1 SAR: Validation and applications. J. Geophys. Res. Oceans
**2017**, 122, 1827–1848. [Google Scholar] [CrossRef] - Ouchi, K. Recent Trend and Advance of Synthetic Aperture Radar with Selected Topics. Remote Sens.
**2013**, 5, 716–807. [Google Scholar] [CrossRef] [Green Version] - Du, Y.; Vachon, P.W.; Wolfe, J. Wind direction estimation from SAR images of the ocean using wavelet analysis. Can. J. Remote Sens.
**2002**, 28, 498–509. [Google Scholar] [CrossRef] - Horstmann, J.; Koch, W. Measurement of Ocean Surface Winds Using Synthetic Aperture Radars. IEEE J. Ocean. Eng.
**2006**, 30, 508–515. [Google Scholar] [CrossRef] - Schulz-Stellenfleth, J. Ocean Wave Measurements Using Complex Synthetic Aperture Radar Data; American Society of Civil Engineers: Reston, VA, USA, 2004. [Google Scholar]
- Kanevsky, M.B. Radar Imaging of the Ocean Waves; Elsevier: Amsterdam, The Netherlands, 2009. [Google Scholar]
- Lyzenga, D.R. Numerical Simulation of Synthetic Aperture Radar Image Spectra for Ocean Waves. IEEE Trans. Geosci. Remote Sens.
**1986**, GE-24, 863–872. [Google Scholar] [CrossRef] - Lyzenga, D.R. An analytic representation of the synthetic aperture radar image spectrum for ocean waves. J. Geophys. Res. Oceans
**1988**, 93, 13859–13865. [Google Scholar] [CrossRef] - Kasilingam, D.P.; Shemdin, O.H. Theory for synthetic aperture radar imaging of the ocean surface: With application to the Tower Ocean Wave and Radar Dependence Experiment on focus, resolution, and wave height spectra. J. Geophys. Res.
**1988**, 93, 13837. [Google Scholar] [CrossRef] - Raney, R.K.; Vachon, P.W. Synthetic aperture radar imaging of ocean waves from an airborne platform: Focus and tracking issues. J. Geophys. Res. Oceans
**1988**, 93, 12475–12486. [Google Scholar] [CrossRef] - Vachon, P.W.; Raney, R.K.; Emergy, W.J. A simulation for spaceborne SAR imagery of a distributed, moving scene. IEEE Trans. Geosci. Remote Sens.
**1989**, 27, 67–78. [Google Scholar] [CrossRef] - Shuchman, R.; Shemdin, O. Synthetic aperture radar imaging of ocean waves during the marineland experiment. IEEE J. Ocean. Eng.
**1983**, 8, 83–90. [Google Scholar] [CrossRef] - Shemer, L. On the focusing of the ocean swell images produced by a regular and by an interferometric SAR. Int. J. Remote Sens.
**1995**, 16, 925–947. [Google Scholar] [CrossRef] - Ouchi, K.; Burridge, D.A. Resolution of a controversy surrounding the focusing mechanisms of synthetic aperture radar images of ocean waves. IEEE Trans. Geosci. Remote Sens.
**1994**, 32, 1004–1016. [Google Scholar] [CrossRef] - Wei, X.; Wang, X.; Chong, J. Local region power spectrum-based unfocused ship detection method in synthetic aperture radar images. J. Appl. Remote Sens.
**2018**, 12, 016026. [Google Scholar] [CrossRef] - Burridge, D.A.; Smith, R.W. Highly space-variant imaging system: Optical simulation of the synthetic-aperture radar. J. Opt. Soc. Am. A
**1991**, 8, 1195–1206. [Google Scholar] [CrossRef] - Tajirian, E.K. Multifocus processing of L band synthetic aperture radar images of ocean waves obtained during the Tower Ocean Wave and Radar Dependence Experiment. J. Geophys. Res. Oceans
**1988**, 93, 13849–13857. [Google Scholar] [CrossRef] - Vachon, P.; Krogstad, H.; Scottpaterson, J. Airborne and spaceborne synthetic aperture radar observations of ocean waves. Atmosphere
**1994**, 32, 83–112. [Google Scholar] [CrossRef] [Green Version] - Hwang, P.A.; Toporkov, J.V.; Sletten, M.A.; Menk, S.P. Mapping Surface Currents and Waves with Interferometric Synthetic Aperture Radar in Coastal Waters: Observations of Wave Breaking in Swell-Dominant Conditions. J. Phys. Oceanogr.
**2012**, 43, 563–582. [Google Scholar] [CrossRef] - Shemer, L. Interferometric SAR imagery of a monochromatic ocean wave in the presence of the real aperture radar modulation. Int. J. Remote Sens.
**1993**, 14, 3005–3019. [Google Scholar] [CrossRef] - Shemer, L.; Kit, E. Simulation of an interferometric synthetic aperture radar imagery of an ocean system consisting of a current and a monochromatic wave. J. Geophys. Res. Oceans
**1991**, 96, 22063–22073. [Google Scholar] [CrossRef] - Raney, R.K. SAR processing of partially coherent phenomena. Int. J. Remote Sens.
**1980**, 1, 29–51. [Google Scholar] [CrossRef] - Hasselmann, K.; Hasselmann, S. On the nonlinear mapping of an ocean wave spectrum into a synthetic aperture radar image spectrum and its inversion. J. Geophys. Res. Oceans
**1991**, 96, 10713–10729. [Google Scholar] [CrossRef] - Alpers, W.R.; Bruening, C. On the relative importance of motion-related contributions to the SAR imaging mechanism of ocean surface waves. IEEE Trans. Geosci. Remote Sens.
**1986**, GE-24, 873–885. [Google Scholar] [CrossRef] - Shemer, L. An analytical presentation of the monochromatic ocean wave image by a regular or an interferometric synthetic aperture radar. IEEE Trans. Geosci. Remote Sens.
**1995**, 33, 1008–1013. [Google Scholar] [CrossRef] - Jain, A.; Shemdin, O. L band SAR ocean wave observations during MARSEN. J. Geophys. Res. Oceans
**1983**, 88, 9792–9808. [Google Scholar] [CrossRef]

**Figure 1.**Probing geometry of SAR imaging of different targets. The moving rigid target moves with speed $C$ in azimuth direction. The angle between surfaces waves travel direction and azimuth is $\varphi $.

**Figure 2.**Flow chart of the proposed algorithm. As can be seen, the proposed algorithm mainly contains 5 parts.

**Figure 3.**Simulation result of SAR surface waves imaging when waves travel along azimuth direction. The red-dashed box in the figure is chosen to calculate the optimum focus setting.

**Figure 4.**Simulation result when $\varphi ={0}^{\circ}$. (

**a**) Focusing curve for the simulated wave. (

**b**) Imaging results of the wave when $\Delta V=0$ (the blue line) and $\Delta V=5.6\mathrm{m}/\mathrm{s}$ (the red line).

**Figure 5.**Simulation result when $\varphi ={30}^{\circ}$. (

**a**) Focusing curve for the simulated wave. (

**b**) Imaging results of the wave when $\Delta V=0$ (the blue line), $\Delta V=6.4\mathrm{m}/\mathrm{s}$ (the red line) and $\Delta V=8.4\mathrm{m}/\mathrm{s}$ (the yellow line).

**Figure 6.**Simulation results when $\varphi ={60}^{\circ}$. (

**a**) Focusing curve for the simulated wave. (

**b**) Imaging results of the wave when $\Delta V=0$ (the blue line), $\Delta V=11.2\mathrm{m}/\mathrm{s}$ (the red line) and $\Delta V=16.2\mathrm{m}/\mathrm{s}$ (the yellow line).

**Figure 7.**SAR image of data 1. The black box in the upper-right corner shows the selected sub-block data, which contains only surface waves.

**Figure 8.**Processing result of data1. (

**a**) Focusing curve for the dominant wave. (

**b**) Imaging result obtained by the proposed algorithm.

**Figure 9.**SAR image of data 2. The black box in the middle-right is the selected sub-block data, which contains only the surface waves.

**Figure 10.**Processing result of data 2. (

**a**) Focusing curve for the dominant wave. (

**b**) Imaging result obtained by the proposed algorithm.

**Figure 11.**SAR image of data 3. The upper-left black box is the selected sub-block data, which contains only the surface waves.

**Figure 12.**Processing result of data 3. (

**a**) Focusing curve for the dominant wave. (

**b**) Imaging result obtained by the proposed algorithm.

**Figure 13.**Variation of the focus sensitivity of the waves under different parameters. (

**a**) Focusing curve as a function of integration time. (

**b**) Focusing curve as a function of wavelength. (

**c**) Focusing curve as a function of wave steepness.

**Figure 14.**The variation of the difference between $\Delta {V}_{opt,w}$ and ${C}_{x}/2$ with integration time when waves travels in different directions.

**Table 1.**Parameters of the SAR system and the waves in the simulation. The parameters refer to those of the real SAR system and surface waves in Section 4.2.

Parametric Name | Parametric Symbol | Parametric Value |
---|---|---|

Radar Wavelength (m) | $\lambda $ | 0.25 |

Platform Speed (m/s) | $V$ | 130 |

Slant Range (m) | ${R}_{0}$ | 10,000 |

Integration Times (s) | $T$ | 4 |

Coherence Time (s) | ${\tau}_{s}$ | 0.14 |

Incidence Angle (deg) | $\theta $ | 45 |

Wavelength of the wave (m) | ${\lambda}_{w}$ | 80 |

Amplitude of the wave (m) | $H$ | 1.6 |

Propagation direction of the wave (deg) | $\varphi $ | 0, 30, 60 |

Parametric Name | Parametric Symbol | Parametric Value |
---|---|---|

Radar wavelength(m) | $\lambda $ | 0.25 |

Pulse length(um) | ${T}_{r}$ | 5.4 |

Radar bandwidth (MHz) | ${B}_{r}$ | 125 |

Platform speed (m/s) | $V$ | 130 |

Platform height (m) | $H$ | 8100 |

Squint angle (deg) | ${\theta}_{sq}$ | 0 |

PRF(Hz) | ${F}_{a}$ | 900 |

Antenna length (m) | $D$ | 4 |

Polarization mode | / | VV |

Data 1 | Data 2 | Data 3 | |
---|---|---|---|

Date | September 13 | September 14 | September 18 |

Wind speed (m/s) | 10 | 11 | 8 |

Wind direction (deg) | 5 | 25 | 65 |

Significant wave height (m) | 1.5 | 1.3 | 1.2 |

Mean wave period (s) | 7.2 | 7.9 | 7.3 |

Peak wave period (s) | 8 | 8.6 | 8.1 |

Mean wave direction (deg) | 5 | 25 | 65 |

Focus Setting | $\Delta \mathit{V}=0$ | $\Delta \mathit{V}={\mathit{C}}_{\mathit{x}}/2$ | $\Delta \mathit{V}=\Delta {\mathit{V}}_{\mathit{o}\mathit{p}\mathit{t},\mathit{w}}$ | |
---|---|---|---|---|

SD | sub-block data 1 | 40.09 | 42.45 | 42.49 |

sub-block data 2 | 33.89 | 36.67 | 37.73 | |

sub-block data 3 | 41.76 | 43.53 | 45.79 | |

PBR | sub-block data 1 | 6.03 | 11.06 | 11.61 |

sub-block data 2 | 17.22 | 25.37 | 30.23 | |

sub-block data 3 | 24.74 | 33.78 | 43.56 |

© 2019 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Wei, X.; Chong, J.; Zhao, Y.; Li, Y.; Yao, X.
Airborne SAR Imaging Algorithm for Ocean Waves Based on Optimum Focus Setting. *Remote Sens.* **2019**, *11*, 564.
https://doi.org/10.3390/rs11050564

**AMA Style**

Wei X, Chong J, Zhao Y, Li Y, Yao X.
Airborne SAR Imaging Algorithm for Ocean Waves Based on Optimum Focus Setting. *Remote Sensing*. 2019; 11(5):564.
https://doi.org/10.3390/rs11050564

**Chicago/Turabian Style**

Wei, Xiangfei, Jinsong Chong, Yawei Zhao, Yan Li, and Xiaonan Yao.
2019. "Airborne SAR Imaging Algorithm for Ocean Waves Based on Optimum Focus Setting" *Remote Sensing* 11, no. 5: 564.
https://doi.org/10.3390/rs11050564