Software Correlator - II

The angular resolution of radio telescopes can be improved by using the principles of interferometry. Interferometry depends upon detecting the combination of voltage signals assumed to be originating from the same source. In a simple two-element radio interferometer, the signals from a point source alternately arrive in phase and out of phase as the Earth rotates and causes a change in the difference in path from the radio source to the two elements of the interferometer. This produces interference fringes in a manner similar to that in Young's double-slit interference experiment, shown below.

The figure below shows how two waves from the same point source reach the two antennas on ground with a certain geometric path difference. If we multiple the two voltages generated at the antennas due to the waves reaching their respective locations, an interference pattern is observed (see third figure further down). Note how the appearance is exactly identical to the interference pattern generated by a two-slit interferometer using two slits as point sources, shown above.

The 'geometric' path difference due to spatial orientation of the source is similar to the path difference in 2-slit interference experiment. We probe phenomenon of 'temporal coherence' in 2-slit Young's experiment, that is we study the stability of phase difference between two sources (slits) over time. If the phase difference betwee two slits varied randomly, fringes will not have any absolute dark fringe ('zero' of intensity).

On the other hand, in 2-antenna interference, the phase difference arises due to different locations of the 2 antennas as seen by the source. If the source was not a point source on the sky, fringes will not be perfect (no absolute zero of intensity). Thus, we study 'spatial coherence' of waves, that is if our source has a finite size.

Software Correlator - I

(Hopefully, the first of many entries on this subject)

Mandar is working to create a program which will replace a bulk of old, creaking machines at GMRT and other similar synthesis-imaging instruments, which produce a stream of cross-correlations between different antennas that are separated from each other by a huge distance.

The first (baby) steps are to create a program to compute cross-correlations from a stream of numbers. Then, we develop the same algorithm for an input of quantized numbers. After correcting for source delays (fringe-stopping and fractional delay correction), we compute an FFT of the cross-correlation series, to obtain the power spectrum of correlations. Finally, we tie this bit with astronomical source co-ordinates.

Data Acquisition System

We would like to make radio maps using Earth-rotation aperture synthesis . This technique requires us to record raw voltages at two antennas and compute complex visibility (cross-correlation) for different frequency channels.

The block diagram of the receiver and acquisition is shown in the figure on the left.

Each of 4 antennas will have a heterodyne receiver system which will translate a signal at the radio frequency (RF) of 73.9-MHz to an intermediate frequency (IF) of 1.9 MHz.

Four such signals reach the data acquisition system marked in the diagram. Each signal will be converted to digital using a 12-bit ADC, and then sampled at the rate of 0.5 MHz using only the most significant 2-bits.

Aniket carried out feasibility studies and design of the DAS to acquire Nyquist-sampled voltages from a bandwidth-limited signal (0.25 MHz). These quantized voltages are stored on a computer disk. There is a provision of acquiring from 4 antennas, so total data rates are 0.5*4 = 2 M-samples/s. Each sample consists of 2 bits each. Hence it is 8 M-bits/s = 1 MB/s storage rate on a PC.

Antenna Length, RF Band and Impedance Matching

Our antenna band appeared to be shifted to 71 or 76 MHz.

Preeti and Roopa were looking up reasons for which the antenna might not be working at the desired frequency. They came across this fact on this page.

Antenna length

The length of a dipole is the main determining factor for the operating frequency of the dipole antenna. Although the antenna may be an electrical half wavelength, or multiple of half wavelengths, it is not exactly the same length as the wavelength for a signal travelling in free space. There are a number of reasons for this and it means that an antenna will be slightly shorter than the length calculated for a wave travelling in free space.

Hence, we feel that we have actually used a longer length than necessary...giving us a smaller frequency at 72 MHz. We will try reducing the length tomorrow and checking.

Also regarding the impedance matching..a Sleeve Balun is commonly used in VHF range. You can find more details on this page .

Bandwidth and antenna windings

Our dipole antenna element was fixed on wooden frame using nails. The dipole wire was wound around a nail to make it taut. When we introduced a wound around the nail, they acted as an inductors on ends of the wire (Rad's comment with a chuckle).

We need to put plastic caps on each end, and then use some material to fix the dipole wire, possibly some rope or hard plastic cover on usual copper wire. see this link.




As for the interference outside the "allowed band" of the dipole, let us wait for Onkar to fetch the co-axial cable from NCRA/TIFR, Pune.

Antenna and the bandwidth

We put up our first dipole antenna element on Friday (?) afternoon. Here is Roopa trying to keep the antenna wire taut, and Onkar's pic does not need a caption ;-)

The picture on the right shows the band. Even though Onkar tried to measure the length of the dipole as LAMBDA/4 on each side, the band is centered on 71.5 MHz. What gives? The bandwidth is barely 1 MHz, kind of a let down. At the same time, there is a lot of interference from the surroundings. Perhaps our antenna wire (not a co-axial yet) is too prone to pickup from around.

AD633 for multiplier

Vamsi suggests using Analog Devices' AD633 as the multiplier in our project. The circuit consists of a standard implementation mentioned in the datasheet. (Fig. 3).



Specifications

Transfer Function		[(X1–X2)(Y1–Y2)/10] + Z
Slew Rate (V/µs		20V/µs
Supply Voltage (V max)		±18V
Supply Current (max)		6mA
Temp Range		-40 to 85°C
Package		DIP/SOIC

From Analog Devices website. The datasheet.

AD633 seems cheap, and very popular. Good for it. Also, AD seem very forthcoming to give free samples. I will try something about that.