| Abstract: |
The idea of aperture synthesis is to obtain high-resolution images with the aid of the computer by combining passive interferometric measurements, or complex visibilities, corresponding to spatial frequencies associated to pairs of receiving antennae. The concept of imaging interferometry by aperture synthesis has been developed for radio astronomy some decades ago and it has been recently used for remote sensing of the Earth surface in the microwaves range.
In conventional interferometry, the radio signals received by pairs of spatially separated antennae observing in the same direction are sampled and transported via transmission lines to a correlator unit which produces interference fringes. In such arrays, the antennae are physically connected to the correlator and the complex visibilities are obtained in real time.
For unconnected arrays, the signals received by the antennae are sampled, recorded alongside with an accurate time base, and stored on a digital media for deferred time analysis. At that later time, at the location of a correlator unit, the data are synchronized, played back together and combined just as if they were coming in real time from the antennae.
We consider here a flying formation of unconnected small satellites hosting antennae observing the Earth from a low elevation orbit. The emission from the Earth is collected by the antennae. The corresponding RF signals are amplified with LNA, filtered in a 28 MHz bandwidth centered on 1413.5 MHz and mixed with the reference signals of LO centered on 1399.5 MHz. The mixers also include I/Q demodulators to produce pairs of IF signals with 90° phase shift. These signals are digitized with ADC at 56 MHz with 8 bits. Then, they are numerically filtered in a band of interest before being self and cross-correlated.
Although the clock of the sampler onboard every satellite is the master clock driving the local oscillator, time offsets between every pairs of satellites are expected. They have to be precisely measured for synchronizing the IF signals in order to maintain coherence. Since there is no connection between the satellites, one solution is to use the reference signal of a well-known beacon. Nearby the 27 MHz protected bandwidth centered on 1413.5 MHz, active emission is allowed provided it does not affect the services in 1400-1427 MHz. This is exactly the approach presented here with a radio beacon transmitting in a narrow band centered on 1427.15 MHz from a well-known location.
Numerical simulations have been conducted within the frame of the Unconnected L-band Interferometer Demonstrator (ULID) of the French space agency. The random emission from the Earth, which is assumed to behave like a black body in thermal equilibrium, has been simulated in a wide range of frequencies, 0-4 GHz, with the aid of the simulator developed at CESBIO [IEEE JSTARS, 10(11), pp. 4666-4676, Nov. 2017]. The signal from a non-directional beacon has been superimposed and the corresponding RF signal has been transported to the satellites and passed through the instruments. Time offsets due to master clocks have been introduced as well as Gaussian jitter from ADC. In the absence of any additional metrological errors, the offsets can be retrieved with accuracy better than 1 psec with few acquisitions on a single pass over the beacon. With additional metrological errors coming from the misknowledge of the relative position of the antennae, the accuracy is governed by the corresponding uncertainty on the baseline vector. For example, the accuracy of the synchronization is better than 10 psec when the uncertainty provided by differential GPS receptors onboard each satellite is assumed to be about 3 mm. |
