Reflection of short pulses is a widely used method to detect objects in the space (RADAR, SONAR & LiDAR). However, when the pulse passes through dispersive media, the pulse arrival to the detector is delayed, and the signal could be degraded. As a result, pulse mapping of dispersive media (especially in solids) is very challenging. Prof. Eran Ofek & prof. Avishay Gal-Yam developed a dedispersion algorithm that efficiently corrects the dispersed pulse. This highly fast algorithm can be implemented in existing mapping devices to increase accuracy & speed.
Underground mapping (or other pulse signal mapping in dispersive media) is relatively complex since the signal is being degraded and delayed due to the dispersion effect, resulting in an inaccurate map. The currently available dedispersion algorithms are relatively slow and insensitive, enforcing high-energy pulses and limited scanning speed.
Profs. Eran Ofek & Avishay Gal-Yam developed the “fast dispersion measure transform” (FDMT) algorithm, which is dedispersing the signal without prior knowledge of the media properties. It is a fast algorithm that can run on regular PCs or GPUs (for even faster performance). The algorithm is implemented both in Python or Matlab.
The method includes obtaining an input array of cells, each indicating an intensity of a frequency component of the signal at a representative time. An FDMT is applied to concurrently sum the cells of the input array that lie along different dispersion curves, each curve defined by a known non-linear functional form and is uniquely characterized by a time coordinate and by a value of the dispersion measure. Application of FDMT includes initially generating a plurality of sub-arrays, each representing a frequency sub-band and iteratively combining pairs of adjacent sub-arrays in accordance with
an addition rule until all of the initially generated plurality of sub-arrays are combined into an output array of the sums, in which a cell of the output array that is indicative of a transmitted pulse is identified[i].
[i] Barak Zackay and Eran O. Ofek 2017 ApJ 835 11 https://doi.org/10.3847/1538-4357/835/1/11
- Underground mapping: gas exploration, tunnels detection, etc.
- Other mapping applications in dispersive media
- Efficient requires limited computational resources
- High-speed algorithm
- High sensitivity
- Can be easily implemented on existing devices
- Generic, can be applied to various setups (run on both regular PCs and GPUs)