## 1 Introduction
Compared to these conventional SAS systems, the main idea here is to improve resolution and coverage of related structures/details within the dimensions of an imaging device. This bears some similarities to tomographic SAS [15; 16] or semi-coherent imaging [17] where multiple versatile spatial views with different 3D angular positions are used to obtain lateral views of the scene, respectively of an object of interest. Our approach is applied to sonar sensing within the near field. One motivation is that conventional sonar devices are still usually not well suited for robotic applications, for example, for object recognition/detection or the representation of details needed for intervention missions, where hence optical sensors prevail [18]. The concentration on a restricted range for the SAS approach proposed here has two methodological advantages. Compared to, for example, seafloor mapping applications in conventional SAS systems, sound speed variations in the water for restricted ranges can be neglected. A second methodological advantage is the independence from the center frequency of the imaging system. Coherent processing of sub-apertures with fixed receiver sensors is independent from the center frequency of the system. Note that some millimeters can cause a defocus for high-resolution SAS in, for example, seabed mapping. A robust and precise pixel/voxel-based registration of subsequent sonar scans and the following exact mapping of the coherent signals is used here for synthetic aperture processing. Concretely, the relative localization is done with voxel-wise spectral registration of the scan data. This is inspired by our previous work on sonar registration for mapping. In [19; 20], for example, it is shown that a registration and alignment of sonar scan-data is possible even with severe interference and partial overlap between individual scans. While this pairwise registration--which is the basis for the work presented in this article--is already very accurate, positional information over the entire aperture can even be further improved by Simultaneous Localization and Mapping (SLAM) [21]. To facilitate the registration, a Delay and Sum (D&S) BF is employed for the reconstruction, which directly operates on pixel/voxel form on a Cartesian grid. In [22], a voxel-based format is also used to avoid the scan-conversion operation, which is otherwise necessary to convert from polar coordinates to Cartesian coordinates. The main difference to conventional SAS systems is in our approach the processing of coherent, already reconstructed images from an array system. In summary, the following contributions are presented in this article: (a) the use of registration of single raw scans is proposed as a novel basis for Synthetic Aperture Sonar (SAS), (b) a suited algorithm for the registration is presented in the form of a spectral method based on our previous work, and (c) the concrete implementation of our new approach to SAS is completed with a Delay and Sum (D&S) BF for the reconstruction operating on pixel/voxel form on a Cartesian grid. The rest of this article is organized as follows. Section 2 introduces the image reconstruction for our SAS approach. Section 3 explains necessary signal-processing parameter requirements. Section 4 derives necessary positional requirements of the sensor-platform. Registration and the corresponding transformations for the necessary scan alignment are discussed in Section 5. Section 6 demonstrates with experiments in 2D prospects and limits of the proposed imaging method. Section 7 concludes the article.