ConstructingthebackendoftheKapteynInterferometerforShort-BaselineSolarObservations(KISS) U G

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B

ACHELOR

T

HESIS

Constructing the backend of the Kapteyn Interferometer for Short-Baseline Solar

Observations (KISS)

Author:

Casper FARRET JENTINK

Supervisors:

Dr. Ronald HESPER

Dr. John P. MCKEAN

Prof. Dr. Andrey BARYSHEV

2^ndExaminer:

Dr. Ir. Willem JELLEMA

Abstract:

In this thesis the construction of the backend of KISS, a two element interferometer is treated. The interferometer is in the end used to determine the apparent angular

size of the Sun in the radio regime. Assuming the Sun radiates as a disk in the 11.21-11.29 GHz band, the angular size of the Sun is equal to 0.54±0.02 degrees.

Keeping in mind the distance to the Sun of 150·10⁶km, this implies a physical size of(7.07±0.26) ·10⁵km. This is well within the uncertainty margins from

literature.

Kapteyn Astronomical Institute

July 13, 2018

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i

Acknowledgements

This thesis could not have been fulfilled without the aid of Dr. Ronald Hesper. His profession and expertise in radio receivers guided me through the adaptions which I needed to make to the receivers. He also helped me in testing the setup. I would also like to thank Dr. John McKean and Prof. Dr. Andrey Baryshev for supplying the thesis, their support and the many insights they brought throughout the project. This thesis was part of the construction of the Kapteyn Interferometer for Short Baseline Solar Observations (KISS). Other parts and simulations were completed by Mathijn Lensen and Jasper Steringa whom I would also like to thank for helping out. At last I would like to mention the people atSRONandNOVA, the Netherlands Institute for Space Research and Netherlands Research School for Astronomy respectively, who helped a great deal in the construction of many of the parts of KISS.

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Introduction

Radio interferometry started back in 1946 with the invention of aperture synthesis using multiple radio antennas by Martin Ryle and Tony Hewish. For their achieve- ments they jointly received the Nobel Prize in Physics in 1974, 28 years later. One of the first working interferometers to be used for astronomical observations was the Sea Cliff Interferometer, also invented back in 1946 by Joseph Lade Pawsey, but utilizing the basic principle of Lloyds mirror. This first model radio interferometer relies on reflections of meter-wave signals on bodies of water. The first working model was located at Dover Heights, Australia [Wild,1987].

(A) The Sea Cliff Interferometer model as used by Martin Ryle & Joseph Lade Pawsey on Dover Heights back in 1946.

Image made by Stigmatella Aurantiaca, distributed under a CC-BY 2.0 license.

(B) An 8 element Yagi Antenna from 1951 at Dover Heights, very similar to the model Ryle & Pawsey used. Photograph

in property by CSIRO.

FIGURE1.1: The Sea Cliff Interferometer.

Figure 1.1a shows the basic principle of Sea Cliff Interferometry. Light from a distant source is reflected on the sea and after that received by an antenna, which also receives the original signal. Ruby Payne-Scott, Joseph Lade Pawsey and Lind- say McCready, all pioneers in radio interferometry, were the first astronomers to observe interference patterns in drift scans of the Sun as it passed the horizon at sun- rise using this device. Their interest for meter wave observations of the Sun came from reports of strongly fluctuating radio signals, interfering with communication signals on Earth during the Second World War. These were believed to originate from sunspot activity. This turned out to be correct. Their Sea Cliff Interferometer was of high enough angular resolution to resolve a large group of sunspots, which they later confirmed to be the source of this strong radio emission. The observations Pawsey, Payne-Scott and McCready conducted were fundamental in the world of radio interferometry which, nowadays, is used as the most powerful tool in the world of radio astronomy.

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Chapter 1. Introduction 2

In this thesis, the technology and physics behind the backend of a two element interferometer will be discussed. The final aim is to design and build the backend of the Kapteyn Interferometer for Short-Baseline Solar Observations (KISS) to do Solar drift scans, similar to the observations conducted by Pawsey, Payne-Scott and McCready back in 1946.

The KISS is a project composed of three parts, the front-end, the backend and simulations. The aim of the project is to design, model and build a two element interferometer with which observations of the Sun and various other objects can be done. The final telescope will be used by astronomy students of the Kapteyn Astro- nomical Institute in Groningen, the Netherlands, to learn the basics of interferometry and get the chance to process the data.

We will start by looking at the theory behind interferometers and what steps need to be taken to observe interferometric fringes. This is followed by a design proposal for the setup resulting from theory. It will go through the steps needed to build an interferometer from two satellite dishes and low-noise-block converters normally used to receive TV-signals. The entire setup is used to do Solar drift scans for varying baselines. These measurements are then used to compute visibilities to, in the end, fit a visibility function to and determine the shape and angular size of the Sun.

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Chapter 2

Theory

2.1 Radio interferometry

Radio interferometry has grown to be the leading method for doing observations with an angular resolution of less than an arcsecond. The resolution of an interferometer does not rely on the dish size of a single antenna, but on the maximum baseline length. This implies that the resolution is not given by

θ = ^λ

D, (2.1)

but by

θ= ^λ

B, (2.2)

where θ is the angular resolution in radians, λ is the observed wavelength, D is the diameter of the dish and B the baseline. Note that D, B and λ have to share the same units.

An interferometer essentially measures the interference pattern between multiple signals. Ordinary observatories measure light directly and this is where an interferometer greatly differs from single dish observations. Processing these individual signals and correlating them into a single observation is called aperture synthesis. To be able to do this, the phase and amplitude of the incoming signal for every telescope needs to be known. Correlation can be done afterwards. The following chapters will go through the workings of a two element interferometer and the mathematics behind the correlation of both powers.

2.1.1 UV-plane

As a coordinate system in the world of radio interferometry the uv-plane comes in useful. An interferometer measures the interference pattern of multiple apertures (what radio astronomers like to call the visibilities) over various baselines. These baselines are usually not in the same line but spread over multiple coordinates in east-west north-south directions. We can define this grid or spiderweb of baselines on a uv-plane, on which baselines (often in λ as units) can be plotted as a transfor- mation of their projected visibilities on the sky. This can be done as the baseline length relates to a certain angular resolution on the sky via Equation 2.2. The measured visibilities are often defined as a function of u and v: V(u, v). The inverse 2D Fourier transform of this interference pattern is the sky brightness distribution [Zernike,1938].

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Chapter 2. Theory 4

2.1.2 Aperture synthesis

To form a fully filled aperture it is convenient for an interferometer to have many baselines [Ryle and Hewish,1960]. Per baseline, a fringe function can be extracted from the data (essentially a single visibility). Over time, due to Earth’s rotation, these (apparent) baselines shift or turn over the uv-plane and change in length, filling the aperture over time. As the baselines change in length the visibility also changes.

This is a process which can very well be illustrated with an east-west array like the Westerbork Synthesis Radio Telescope (WSRT) shown in Figure 2.1. For a snapshot the aperture of this telescope will simply form dots on a line. In 12 hours of time, an aperture in the shape of an ellipse will be formed (or a line when pointed at the equator). If the uv-plane is well covered, an inverse Fourier transform will result in an image of the sky.

FIGURE2.1: The uv-plane coverage over time for different pointings of the Westerbork Synthesis Radio Telescope (WSRT) [Interferometry

and Aperture Synthesis].

2.1.3 Basic principles

In this thesis a two element adding interferometer will be built and used. Mathe- matical derivations can be found in further detail in [Koda et al.,2016]. An adding interferometer is a device which consists of multiple receivers and adds the signals together afterwards. Figure 2.2 shows a schematic illustration on how this process works. As the two receivers are spatially separated by a baseline B, a delay τ is added to one of the signals. Figure 2.3 displays the relation between telescope pointing and geometric delay.

Trivial geometry tells us that the relationship between the time delay of the two signals is related to both angles and the baseline B in the following manner (Equa- tion 2.3):

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FIGURE2.2: Two receivers separated by an apparent baseline B. The direction in which the telescope is pointing is θ and the direction to

the source is θ0.

FIGURE2.3: The geometric delay due to the offset between baseline, source direction and telescope pointing.

τ= ^{B sin}(θ−θ₀)

c ≈ ^B(θ−θ₀)

c (2.3)

c is equal to the speed of light in this relation. Generally θ−θ₀ is very small, therefore we utilise the small angle approximation.

Figure 2.3 also shows the output of both receivers. The received signals are elec- tromagnetic waves at frequency ν. The following mathematical derivations will go into the output of correlation in an adding type interferometer which will be used in this thesis.

The total received power in an adding type interferometer is equal to the sum over both powers from Figure 2.3:

Etot(t) =E₁(t) +E2(t, τ), (2.4) where Etotis the total received power. What is finally measured is the total power, which is generally the square of the time-averaged total electric field strength:

P(θ) = hE²_tot(θ)i (2.5)

= hE²(θ₀){_cos²[_2πνt] +_2cos[_2πνt] ×_cos[_2πν(t−τ)] +_cos²[_2πν(t−τ)]}i_, _(2.6)

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Chapter 2. Theory 6

which can be rewritten to

P(θ) =E²(θ₀)[1+cos(2πντ)]. (2.7) We can substitute from Equation 2.3 and write the baseline B in units of wavelength B_λ, B_λ = B/λ. It can then be generalized for an extended source to the integral in Equation 2.8:

P(θ) =

Z

ε(θ₀)dθ₀{1+cos[2πB_λ(θ−θ₀)]}. (2.8) In Equation 2.8, ε(θ₀)is the energy distribution of the object. We can see that the power output relies on periodic behaviour. We expect fringes (periodic variations in power output) as we move over the object and vary θ.

2.1.4 Visibilities

The Van Cittert-Zernike theorem states that under certain conditions the Fourier transform of the mutual coherence function of a distant, incoherent source is equal to its complex visibility [Zernike, 1938]. An interferometer typically measures the Fourier Transform of the energy distribution ε(θ₀) [Koda et al.,2016]. First, let us rewrite Equation 2.8 to

P(θ) =

Z

ε(θ₀)dθ₀+

Z

ε(θ₀)cos[2πB_λ(θ−θ₀)]dθ₀ (2.9)

≡S₀[₁+V(_{θ, B}_λ)]_, _(2.10) where

S₀ ≡

Z

ε(θ₀)dθ₀. (2.11)

Also,

V(θ, B_λ) ≡ ¹ S0

Z

ε(θ₀)cos[2πB_λ(θ−θ₀)]dθ₀ (2.12)

= ¹ S₀

cos(2πB_λθ)

Z

ε(θ₀)cos(2πB_λθ₀)dθ₀+sin(2πB_λθ)

Z

ε(θ₀)sin(2πB_λθ₀)dθ₀ (2.13)

≡V₀(B_λ)cos[2πB_λ(θ−_∆θ)]. (2.14) In which∆θ is the phase shift and V0(B_λ)the visibility. They are represented by,

V₀(B_λ)cos(2πB_λ∆θ) = ¹ S₀

Z

ε(θ₀)cos(2πB_λθ₀)dθ₀ (2.15) and,

V₀(B_λ)_sin(_2πB_λ_∆θ) = ¹ S0

Z

ε(θ₀)_sin(_2πB_λθ₀)dθ₀. (2.16) Combining Equations 2.15 and 2.16 leads to:

V₀(B_λ) =e^i2πB^λ^∆θ 1 S₀

Z

ε(θ₀)e^i2πB^λ^θ⁰dθ₀. (2.17)

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e^i2πB^λ^∆θis a phase shift of the complex visibility. The amplitude is therefore given by:

|V₀(B_λ)| = | ¹ S₀

Z

ε(θ₀)e^i2πB^λ^θ⁰dθ₀|. (2.18) Equation 2.18 is the Fourier element of the object with energy distribution ε(θ₀) at a baseline B_λ. 1/B_λ is the angular size of the Fourier part which is expressed in radians. This implies that at large baselines, structures of small size are detected. At a short baseline, larger structures can be measured.

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8

Chapter 3

LNB receiver modification

Consumer mass-market Low Noise Block (LNB) receivers were used in the construction of the Kapteyn Interferometer. These LNB’s are superheterodyne receivers downconverting the 10.7∼11.7 GHz signal to a 950∼1950 MHz signal. Normally these receivers are used to receive satellite TV signals in the X band, which ranges from 8 to 12 GHz.

3.1 Heterodyne receivers

3.1.1 Basic principles

Heterodyne receivers rely on the underlying physical process called heterodyning.

This effect was discovered by Reginald Fessenden in 1901. By mixing two frequencies, two new frequencies are generated, called heterodynes. These frequencies lie at the original frequencies added and subtracted [Fessenden,1901]. By filtering out the original frequencies and the higher heterodyne, a single frequency band is left, at lower frequency than the original signal. The advantage of this entire system is that one can observe at high frequencies without needing the sampling rate in their measuring devices.

The superheterodyne receiver, invented in 1918 by Edwin Howard Armstrong is a successor of the original device invented by Fessenden [Armstrong,1924]. A superheterodyne receiver mixes the incoming signal with a local oscillator frequency (LO) and also amplifies and mixes the signal. A typical diagram of a superheterodyne receiver can be seen in Figure 3.1.

FIGURE3.1: A diagram of a typical superheterodyne receiver. Var- ious amplifiers and filters together with a mixer turn the Radio Fre- quency (RF), which is the same as your observing frequency, into an

Intermediate Frequency (IF).

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The Radio Frequency (RF) is the frequency at which observations are made. This signal is first filtered such that the right frequency band is observed. The signal is then amplified and afterwards sent into a mixer. A Local Oscillator (LO) signal is also added to the mixer. Typically this LO frequency is at a frequency just below the RF. The Intermediate Frequency (IF) resulting from this is a combination of the LO, RF, RF+LO and RF-LO. The IF filter filters out all signals except the RF-LO frequency.

Then this signal is often amplified once more.

Resulting from this entire process is a downconverted signal which is easier to handle and can be sampled at lower sampling rate. The process of heterodyning is essential to many radio and sub-millimeter receivers worldwide, especially at higher frequencies.

3.1.2 The Principle of Phase locking

Essential to heterodyning the RF is phase locking the LO. Phase locking the LO implies that the LO oscillates at a more or less stable frequency and phase during operation. This ensures a stable down conversion of the RF.

Phase locking usually involves a phase-locked loop (PLL), a diagram of it is displayed in Figure 3.2.

FIGURE3.2: A diagram of a typical PLL.

In essence, a phase-locked loop compares an incoming signal to a reference signal. Using a feedback system, the local oscillator signal is frequency locked to the incoming signal. In a typical heterodyne receiver a very stable local oscillator at low frequency supplies a signal for the system to phase-lock to. This ensures a stable downconversion of the RF signal.

3.1.3 Low-Noise-Block receivers

Low-Noise-Block (LNB) receivers are heterodyne receivers. They are designed to receive satellite TV-signals and downconvert them to a lower frequency signal. Typ- ically they observe in the 10.7 to 12.7 GHz band (in various bands) for 2 polarisations.

They then downconvert this RF signal to an IF signal which is typically in the order of 1 to 2 GHz.

3.1.4 Types of LNB receivers

There are two types of local oscillators in LNB receivers. One oscillator relies on a dielectric resonator, which is typically unstable over various temperature ranges. Its frequency can vary over±250 kHz. For applications linked to TV signal reception this is often not an issue. The important characteristic of this type of LNB receiver is that it cannot be phase locked. The second type of receiver is called the PLL LNB.

This type of LNB relies on a PLL circuit and a very stable quartz crystal (typically

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Chapter 3. LNB receiver modification 10

25 MHz) to supply its local oscillator. PLL LNB’s can very quickly be recognised by having a small block soldered onto the circuit board, which houses the crystal. Also, typically these housings have the frequency at which the crystal oscillates printed on them. As we would like to phase-lock the LNB receivers, PLL LNB’s are essential. These type of LNB’s are hard to recognise as manufacturers often do not label them as such. The reason for this is that for standard TV-signal reception they are not specifically better. Slogans like ’high frequency stability’ often give away the contents of the LNB.

3.2 A design proposal

As stated before, an interferometer measures the interference pattern between multiple signals from multiple receivers. In our case a two element interferometer implying a single interference pattern. Two important aspects of waves come into play here: phases and amplitudes. The amplitudes tell us something about the visibility and the phases tell us something about the locations of the receivers and their pointings. To do interferometry, i.e. correlate signals, one needs to record both of these properties.

The aim of this thesis is to determine visibilities for various baselines. This is where our first requirement comes into play: the baseline should be changeable. The interference patterns between signals are a result of delays in the incoming wave- fronts. If correlation is done afterwards, one can compensate for delays coming from cable length differences etc. However, for the observations we would like to make we do not need aperture synthesis. We simply would like to determine a single visibility per baseline measurement. The proposal is thus to correlate the signals in an analog fashion. To do this, we can utilise an antenna splitter, normally used to split an antenna signal in two, but now to add two signals. Afterwards we can register the power output. As the integration time is much longer than the sampling time needed to record amplitude variations of the incoming signal one will measure the correlated output together with the individual powers of both antennas squared:

(a+b)²= a²+b²+_2a·b. If all used cables are of equal length, the only phase offset will come from the geometrical delay in the observation, the exact delay that creates the fringes that we want to observe.

From the amplitude of these fringes one can determine a visibility. From the width of a fringe one can determine the baseline length. These datapoints together for various baselines will in the end result in a dataset which should be equal to the Fourier transform of the Sun’s emission in the observed frequency domain.

3.3 EVO single LNB

3.3.1 Specifications

In the construction of the backend of the interferometer, two single LNB’s of the manufacturer EVO were used.

The EVO single LNB’s are designed to be able to observe in 4 different bands.

It can change from horizontal to vertical polarisation by switching the operating voltage from 13V to 18V. The EVO Single LNB also has two observing bands, one from 10.7 to 11.7 GHz and one from 11.7 to 12.7 GHz. During normal operating conditions the LNB operates at low-band frequency. However, if a continuous(₂₂±

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TABLE3.1: EVO single LNB specifications.

Property Value

Low-Band Frequency 10.7∼11.7 GHz High-Band Frequency 11.7∼12.75 GHz

DC Power 13V/18V (110 mA)

Feed Diameter 40 mm

4)kHz tone is supplied, the LNB switches to high-band frequency. All the EVO LNB specifications are listed in Table 3.1 [Single LNB manual].

3.4 LNB modification to external RI

3.4.1 Testing for LO frequency

The superheterodyne LNB receiver is controlled by a 25 MHz crystal oscillator as reference input (RI), creating a local oscillator (LO) frequency of either 9.75 GHz or 10.6 GHz using a PLL. The 10.6 GHz LO frequency can be activated by supplying an external 22 kHz tone, which also switches the observing frequency band from 10.7∼ 11.7 GHz to 11.7 ∼ 12.75 GHz. The standard LO frequency is at 9.75 GHz as can be seen in the output of the Spectrum Analyzer attached to the output of the LNB in Figure 3.3. The peak at 1.505 GHz is caused by a Signal Generator at 11.255 GHz emitting through a small antenna in front of the LNB. The peak can very clearly be seen at 1.505 GHz in the downconverted signal, implying a downconversion as expected as 1.505 GHz + 9.75 GHz = 11.255 GHz.

FIGURE3.3: The Spectrum Analyzer output in 1.4 - 1.6 GHz bandwidth. A clear signal can be seen at 1.505 GHz, implying an original signal send out at 11.255 GHz as the LO frequency is locked at 9.75

GHz.

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FIGURE3.4: The LNB with the antenna placed in front. The antenna is attached to a Rohde & Schwarz microwave generator supplying a

11.255 GHz signal.

3.4.2 Phase Locking

To do interferometry with two or more separate LNB receivers and correlate the signals after downconversion, they need to be phase locked together. This is essential as it guarantees frequency locking, meaning that both receivers run at exactly the same frequency. Both signals can also be correlated as the phases run equal. If the LO signals are in phase, interferometric fringes will only result from phase offsets of the incoming signal which is exactly the detection we would like to make. Figure 3.5 displays this setup.

FIGURE 3.5: The modified LNB setup. The signal generator is attached to the ground and a contact point between the resistor and

capacitor within the LNB’s.

To achieve this process, it was essential to let both receivers phase-lock to the external Reference Input (RI) generated by the signal generator and not by the quartz crystal on the circuit board as there is no guarantee that the separate crystals are in phase. First, the root-mean-square (rms) voltage applied to the quartz crystal

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was measured with a voltmeter. The peak-to-peak (pp) voltage at the crystal was measured to be 500 mV. To calculate the power at the crystal for a single LNB receiver we first rewrite the pp voltage to the rms voltage,

V_rms = ¹ 2√

2V_pp, (3.1)

where V_rms is the rms voltage and V_pp the pp voltage. Keeping in mind a 50 Ohm impedance, which is standard for scientific purposes, the supplied power by the signal generator must be equal to about−2dBm if we define,

P_dBm =10 log₁₀ V_rms²

R·1 mW. (3.2)

The next step was soldering out the quartz crystal and modifying the receiver circuit board such that the new external RI could be supplied. The crystal was first soldered out. Two leads together with a capacitor and resistor were soldered in. This can be seen in Figure 3.6.

FIGURE3.6: The LNB soldering modifications. A 1 nF capacitor and a 50 Ω capacitor were soldered in with a signal generator attached to leads around the capacitor. Points 1 and 2 are the original quartz

crystal contact points.

It was unclear which original contact point of the quartz crystal was the input and which was the output. As a first try, the guess was made that contact point 1 was the input (see Figure 3.6). A 1 nF capacitor and 51 Ω resistor were soldered onto the circuit board. The capacitor was placed to block out the DC-signal and the resistor to impedance match the modifications to the cables. Figure 3.7b also shows the leads which were attached to supply the signal generator signal. These were later soldered to a BNC connector in the LNB housing which can be seen in Figure 3.8.

3.4.3 Phase-lock testing

The receiver was tested after modifications to check for phase-locking. We expected the system to work similarly to how it worked when it was phase-locked to the quartz crystal. To test the LNB response we used the same spectrum analyzer and function generator as utilised before. The full setup can be seen in Figure 3.9. The signal generator used for supplying the RI to the LNB and the spectrum analyzer were phase-locked to the microwave generator as it has a very stable temperature controlled crystal supplying the reference. The test was very similar to the test done in Chapter 3.4.1. The output of the signal generator can be seen in Figure 3.10.

Choosing contact point 1 as input for the RI turned out to work.

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(A) The LNB circuitry from the EVO Sin- gle LNB. At the bottom of the circuit the 25 MHz crystal can be seen in its housing.

(B) The modified LNB circuit with the crystal soldered out at the bottom. The circuit has been modified to match Fig- ure 3.6. The red arrow indicates the capacitor and the blue arrow the resistor.

FIGURE3.7: The LNB circuitry.

FIGURE 3.8: The LNB’s after modifications. At the top, facing the camera, two labeled connectors can be seen. One is the original output and the second is a female BNC connector for the 25 MHz input

signal from the signal generator.

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FIGURE3.9: The setup used for testing the LNB response. The LNB has an input from the function generator at 25 MHz to phase-lock.

The LNB receives a signal from an antenna at 11.225 GHz produced by a microwave generator. The output of the LNB goes to a Spec- trum Analyzer. All three devices are relying on the same reference signal produced by the microwave generator as it has a very stable

temperature controlled crystal oscillator.

FIGURE 3.10: The spectrum analyzer output after modifications made to the LNB. We can see that the plot looks very similar to Fig- ure 3.3. We can conclude that the LNB successfully phase-locked to

9.75 GHz.

3.5 LNB modification to separate power input

3.5.1 The LNB circuit

In Figure 3.7a the entire circuit of the LNB receiver can be seen. Normally the LNB receives its DC power from the coax cable over which it also transmits its output.

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Standard satellite receiver boxes, which convert the IF output to a signal which a TV can display, also supply DC power back through the coax cable to the LNB. For the setup we would like to use, this is not really an option, as the plan is to eventually attach the LNB to a power sensor and meter. The DC power comes in through the bottom-right of the LNB. Figure 3.11a shows a close-up of this part of the circuitry.

Figure 3.11b shows a simplified drawing of this part of the LNB circuit. Two dots are indicated where leads could be attached for the external power supply. Also two capacitors are indicated, both are placed to filter out possible reflections which could be created by the LNB output circling within the circuit itself.

3.5.2 Soldering in a new DC input

The modifications presented in this Chapter were not essential for the LNB to work correctly. However, to prevent very high costs for the entire project and because the modifications are pretty simplistic they are presented here. To keep the DC input via the coax cable as explained in Chapter 3.5.1 a bias tee would be needed. A bias tee is a diplexer, which means that it connects three ports via frequency-division multi- plexing (FDM) two ports onto a third one. Simply said, this allows multiple signals in different frequency bands to be transported over a single fiber or cable, like a DC input and IF output of a LNB over a single coax cable. Advanced high-quality bias tees run into hundreds of Euros so modifying the DC input is an advisable action to take. To attach a new power input, the original circuit needed a few modifications. Firstly, the original positive lead attachment was cut near the red dot from Figure 3.11b. A new lead was soldered onto this part of the LNB circuit to supply the external positive power lead. The negative lead was attached to the capacitor near the blue dot from Figure 3.11b.

After these modifications, the positive and negative leads were attached to ba- nana connectors in the housing of the LNB for convenience. The LNB was tested by attaching it to a 13 Volt 110 mA input and functioned as expected.

(A) A close-up of the LNB circuitry to near the attachment to the signal output and power input. The red arrow represents the downconverted IF output whereas the yel-

low arrow represents the DC input.

(B) A simplified diagram of the circuit displayed in Figure 3.11a. The blue dot indicates the negative (ground) and the red dot indicates where a positive lead could be at-

tached.

FIGURE3.11: The LNB bias tee.

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Chapter 4

Construction

4.1 Producing interference patterns between two LNB’s

4.1.1 Requirements

To do live analog correlation with KISS, we needed to make sure all signal cables are of equal length. This is essential as it ensures there is no extra delay which is added in one of the cables such that the only phase offset in the signal results from wavefront delays of the source. The signal from the LNB has a frequency range of 0.95 GHz to 1.95 GHz in the low-band frequency channel. Average wavelength in this frequency range is 0.216 meter. To minimize aberrations it is advised to keep delays in optical systems below ₁₆^λ, implying a maximum cable length difference of about 1.3 cm. For the reference signal at 25 MHz, small cable length differences will not have as much effect.

4.1.2 Tests

To test for interference patterns the setup from Figure 4.1 was used. The emitting source at 11.225 GHz was passed in front of two LNB’s. For every λ in path-length difference from the center between both receivers a fringe was expected. By moving the antenna a clear drop in signal could be seen on the spectrum analyzer as seen in Figures 4.2a and 4.2b.

This experiment showed us that the setup was working as expected. It was time to start observations of the Sun.

4.2 Early setup

4.2.1 Cables

Two LNB receivers were modified following the modifications explained in Chap- ter 3. For convenience, correlation of the two signals from the receivers is done in an analog fashion via an antenna splitter. The advantage of this process is that no phase information of both signals has to be collected. Also, no computational work is required after measurements to correlate both signals. This saves a lot in costs and work. However, both signals need to arrive at similar times to correlate in a correct manner. Also, to phase-lock both LNB’s together, equal length cables to the function generator supplying the 25 MHz reference are needed.

In early tests, coax cables were sourced from the Netherlands Institute for Space Research (SRON) and the Netherlands Research School for Astronomy (NOVA), in particular the group working on the Atacama Large Millimeter Array (ALMA). The setup is shown in Figure 4.3.

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Chapter 4. Construction 18

FIGURE 4.1: A diagram of the setup to test for first fringes in the correlated output.

(A) Constructive interference between the two receiver outputs. The antenna can be seen in front. The central peak shows the

signal received.

(B) Destructive interference between the two receiver outputs. The antenna has moved to the right creating a pathlength dif-

ference of 0.5 λ compared to Figure 4.2a FIGURE4.2: First fringes.

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FIGURE4.3: The first setup of the KISS. Both dishes are present with in the middle a cart with a power meter below. The function generator supplying the RI, the power supply and power sensor are located

on top of the cart.

Halfway through the project, the choice was made to make custom cables for the project. As each LNB is attached to 4 cables, these were combined into a single branch of cables running 12.5 meters in length. The branch contained a coax cable for RI signal, a coax cable for the IF output of the LNB and two power cables for the positive and negative leads of the DC supply. Maximum baseline lengths for KISS were approximately 22 m with this setup.

4.2.2 Mounts and dishes

Mounts and dishes were designed and put together by [Lensen,2018]. The dishes are 0.35 meters in diameter and thus cover about 4.4 degrees in angular resolution on the sky on average for the observed frequency band of 10.7 to 11.7 GHz. This is calculated using Equation 2.1. From satellite measurements (drift scans) the half power beam width (HPBW) was determined to be 4.9 degrees.

The mounts are of equatorial type. They have the advantage that tracking the Sun is convenient and that, if pointed correctly, the Sun will pass through the dishes from bottom to top in more or less the same manner for every measurement.

4.2.3 Full setup

The full setup can be seen in Appendix C. Explanations of how all parts are con- nected are included.

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20

Chapter 5

Solar drift scans

The purpose of building KISS, was to ultimately observe the Sun and determine its shape and size based on visibility measurements and fitting the Fourier transform of a disk to the data. Fourier transforms of Solar models were done by J. Steringa.

These particular models were used in fitting through the acquired data [Steringa, 2018].

5.1 The Sun as a black body

Whereas Payne-Scott, Pawsey and McCready were able to observe sunspots with their interferometer, in the frequency band used on KISS we might be able to observe emission from them as can be seen in Figure 5.1. Sunspot emission is abundant in lower frequency ranges, it comes up just below 12 GHz. Solar emission in the 10.7- 11.7 GHz regime comes profoundly from the black-body radiation at 5778 Kelvin, the average surface temperature of the Sun. Observing this emission should not be a problem as the received radiation is well within signal-to-noise limits for our dishes [Lensen,2018].

FIGURE 5.1: Solar spectrum versus various black-body emission curves at different temperatures [Kraus,1966]. The red line indicates

the central observed wavelength of the interferometer.

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5.2 Setup

The entire setup consists of the two dishes, their mounts, a power meter and sensor, a filter, a signal generator for the RI for the LNB receivers and additional wiring and power supplies. In the next sub-chapters we will go through all electronic compo- nents individually.

5.2.1 Power meter and sensor

The power meter and sensor that were utilized were taken from the Kapteyn Radio Telescope (KRT). These were programmed and controlled using a GPIB-controller and Raspberry Pi by F. Sweijen. The integration time was set to 40 milliseconds and readouts taken every half a second. The software which was written returns the power measurement in dBm and time it has taken from the start of the measurement in seconds [Sweijen,2015].

5.2.2 Variable band-pass filter

A variable band-pass filter is essential to the success of this project. If we were to correlate signals in the full bandwidth from 10.7 GHz to 11.7 GHz, the fringes would range in width quite a lot. The width of a single fringe is given by its resolution which is given by Equation 2.2, where λ is the observed wavelength, B the baseline length and θ the resolution in radians. For a baseline of 5 m the resolution would for example vary from 0.2936^◦to 0.32106^◦, a variation of about 8.5%. However, we included a tunable band-pass filter with a bandwidth of 40 MHz as can be seen in Figure 5.2. The choice was made to set its center to 1500 MHz. Keeping in mind the heterodyne downconversion with a local oscillator at 9.75 GHz, this translates to an observing frequency range of 11.21 GHz to 11.29 GHz. This only varies the resolution by 0.7% working with Equation 2.2.

FIGURE5.2: Tunable band-pass filter of∆ν 40 MHz.

5.2.3 Signal generator

The signal generator is a Rohde & Schwarz SMB 100A as can be seen in Figure 5.3. It has a frequency range of 9 kHz to 2.2 GHz. The signal generator was used to supply the 25 MHz RI signal at -2 dBm for a single LNB (also see Chapter 3). Thus for both LNB’s it supplies 1 dBm as a difference of 3 dBm is equal to a scaling factor of 2.

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Chapter 5. Solar drift scans 22

FIGURE5.3: The Rohde & Schwarz type SMB 100A signal generator and DC power supply for the LNB’s on top.

5.3 Observations

5.3.1 Pointing the dishes

Usually, pointing a telescope at the Sun is seen as a bad idea. However, for a radio telescope, the flux density is usually not high enough to severely damage your equipment. However, if a radio telescope dish also reflects a lot of light in the optical/UV spectrum this might still be a risky operation. Pointing a radio dish is hard, especially with off-axis focus as there is usually no optical component to use for pointing. However, the grey dishes which were used turned out to reflect enough visible light to be seen on the LNB receiver as can be seen in Figure 5.4. This made it very convenient to point the dishes as now the power meter was not needed to verify the focal point of the dish. Using an equatorial mount and its hour angle coordinates, one can easily set the dish in front of where the Sun will pass in a certain amount of time.

FIGURE5.4: The dishes pointing at the Sun. The LNB receiver end is illuminated by optical light from the Sun.

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5.3.2 First light

First light of KISS was achieved on the 9th of May at a measured baseline of (151± 5) cm. A drift scan was attempted starting from the center of the Sun outwards. The goal was to let the Sun move out of the beam of the telescope due to Earth’s rotation.

Results from this very first measurement can be seen in Figure 5.5.

FIGURE5.5: First light from KISS, the power has been converted to Watts and the time has been converted to the amount of degrees the

Sun has moved keeping in mind its speed of 15^◦per hour.

As can be seen the measurement displays the last part of the Sun leaving the field of view. The central maximum cannot be seen as it already passed before the start of the measurement. Three full fringes lie within the length of the observation.

5.3.3 Expectations

To explain the behaviour seen in Figure 5.5 we use the diagram displayed in Fig- ure 5.6. As the Sun passes through the beam of both dishes (they are pointed in the same direction), the projected baseline changes. For every λ of pathlength difference a fringe is expected as the phases overlap once during this process. One can see that the speed of these fringes changes with a varying baseline, a longer initial baseline will imply faster fringes throughout the measurement as the absolute change will be faster (the pathlength difference is directly proportional to the baseline). This behaviour also allows us to determine the baseline length very accurately after every measurement (also see Appendix A and B).

Besides the change in width of the fringes, we also expect the fringe contrast to change, i.e. the relative amplitude of a fringe. This fringe contrast is what we call the visibility. The behaviour of the visibility over varying baselines (or angular resolution) is what we call the visibility function. This is equal to the Fourier transform of the brightness distribution of the observed object as explained in Chapter 2.1.4 [Zernike,1938]. At a certain baseline, the angular resolution of the interferometer

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FIGURE5.6: A schematic displaying the expected behaviour of KISS.

As the apparent position of the Sun changes due to Earth’s rotation the projected baseline changes. For every λ in pathlength change we

expect a fringe.

will be equal to the projected angular size of the Sun on the sky. At this baseline we expect the visibility to drop to zero as there is no interference between both signals.

Finding this drop in the data will tell us what the angular size of the Sun is. Note that this behaviour of the fringe amplitude depends on what the Fourier Transform of the brightness distribution of the Sun is, which will be treated later.

From previous calculations and modelling it is expected that the Sun is resolved at a baseline of 2.88 meters, keeping in mind an angular size of the Sun’s disk of 0.53 degrees [Steringa,2018], the Sun’s shape and Equation 2.2.

5.3.4 Further observations

For further measurements the choice was made to do drift scans of preferably the entire passage of the Sun through the beam at different baselines. The manner in which these observations were conducted was by pointing both dishes at the Sun.

Now, as we know the Sun moves 15 degrees per hour (360 degrees in a day), the assumption was made that by pointing the dishes 20 minutes in front of the Sun, i.e. 5 degrees, the entire passage can be seen in an observation of about 40 minutes keeping in mind the HPBW of a single dish and the expected angular size of the Sun of approximately 0.5 degrees. The aim is to do enough measurements around the resolving baseline such that a Bessel function can be fitted through the computed visibilities for all measurements to determine the angular size of the Sun.

5.3.5 Data

All the acquired data is displayed together in Appendix B. Note interesting features in measurements 3 and 5. In both cases a sharp spike in power can be seen arising from the observations. In both cases someone accidentally stepped in front of the beam of one the dishes. The black-body radiation from their body heat together with their proximity to the dishes causes a high increase in flux. The observations sorted

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TABLE5.1: Observations.

Measurement Date and time Notes

1 9th of May afternoon Day of first light.

2 9th of May afternoon Day of first light.

3 24th of May 12:03 12:47 person in front of dish.

4 24th of May 14:20 One minor cloud in front of the Sun.

5 24th of May 15:25 Someone in front of one of the dishes.

6 28th of May 12:44 Very sunny day.

7 28th of May 13:11 Shortest Baseline.

8 28th of May 15:00 none.

9 28th of May 16:31 none.

10 6th of June 14:02 none.

12 6th of June 12:14 Very sunny day.

to their observing dates can be seen in Table 5.1. Table 5.1 also includes the times of observations and interesting remarks of occurrences during the observations.

5.4 Data processing

All data processing was done with help of Python. The aim was to determine a visibility and baseline including error margin per measurement. This Chapter will treat the various corrections which needed to be done to the data as well as the computation of these parameters.

5.4.1 Correcting for baseline shift

During an observation, the baseline length changes as the Earth rotates. This effect produces the fringes in the data. However, this same effect also causes the fringes to either speed up or delay throughout the measurement. One can imagine, looking at Figure 5.6, that at the end of that particular measurement, the projected baseline is shorter than in the beginning. In other words, the fringes at the end of that measurement are wider than at the start of the measurement looking at Equation 5.1.

The projected baseline changes as a cosine of the geometric baseline (the distance between the two dishes). If the Sun were to be straight in front of the dishes and the angle with respect to the baseline would thus be 90 degrees, the projected baseline would be the same as the geometric baseline.

Luckily, this effect of baseline shifting throughout the measurement can be com- pensated numerically afterwards. If we know the original angle between the Sun and the geometric baseline at the start of the measurement, we can calculate the angle at the end of the measurement given the total time of the measurement. The cosine of the difference in angles from the start to the end of the measurement is an array of corrections and we can multiply the time axis by it. This will compress or extend (or both) the entire dataset. An example of this correction can be seen in Figure 5.7.

Determining the original angle with respect to the Sun was done using an online service named SunCalc. This program allows you to determine the angle of the Sun

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w.r.t. any location on Earth at any given point in time. In Figure 5.8 a screenshot of the program can be seen [SunCalc].

FIGURE5.7: The 82 λ baseline measurement corrected for its baseline shift.

FIGURE5.8: A screenshot of SunCalc. The satellite imagery shows the Kapteyn Astronomical Institute and its balcony, from where the

observations were taken.

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Measurement Baseline (λ)

1 104.2± 3.4

2 173.1± 4.0

3 37.2 ± 0.4

4 66.9 ± _2.5

5 90.9 ± 1.5

6 24.0 ± 2.1

7 12.9 ± _0.1

8 73.4 ± 2.5

9 71.7 ± 3.7

10 131.3± _1.6

11 120.9± 16.7

12 104.0± 3.7

13 185.2± 9.4

TABLE 5.2: Base- lines and uncer- tainties for the 13 measurements.

Measurement Visibility

1 0.026± 0.005

2 0.122± 0.002

3 0.671± 0.037

4 0.297± _0.001

5 0.169± 0.001

6 0.945± 0.008

7 0.795± _0.039

8 0.386± 0.006

9 0.219± 0.014

10 0.127± _0.009

11 0.035± 0.008

12 0.012± 0.001

13 0.052± 0.003

TABLE 5.3: Visi- bilities and uncer- tainties for the 13 measurements.

5.4.2 Baseline determination The width of a fringe is given by,

W_fringe= ^D· FW HM_beam

B , (5.1)

where B is the baseline length, D is the diameter of the dish, FW HM_beamis the full-width-half-maximum of the beam of a single dish, estimated by Equation 2.1 and W_fringeis the width of a fringe in degrees.

The derivation of Equation 5.1 can be seen in Appendix A. Using this equation we can thus also determine the baseline with help of the width of the fringes. The width of a fringe could be determined easily with a script in Python. After the corrections for the shifted baseline we can also determine the width of multiple fringes and determine the standard deviation for an error approximation. These calculations were done for all 13 measurements from Appendix B and the results can be seen in Table 5.2.

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FIGURE5.9: A close-up of measurement 2 (173.1 λ baseline) around its two central fringes. Two lines indicate the computed Imaxand Imin.

5.4.3 Visibilities

Visibilities can be determined by calculating the fringe contrast specified in Equa- tion 5.4, where I_maxis the maximum of the fringe oscillation and I_minis its minimum.

The derivation of this relation is relatively simple. Keeping in mind Chapter 2.1.4, the maximum and minimum intensity are given by Equations 5.2 and 5.3:

Imax=S0[1+V0(B_λ)] (5.2)

I_max=S₀[1−V₀(B_λ)]. (5.3) Combining these results in,

|V₀(B_λ)| = ^I^max−I_min

I_max+I_min. (5.4)

We see that for this computation gain calibration is not needed as we do not have to normalize the data by a certain factor to be able to compute visibilities as it cancels out. The only important thing to take care of is that we have to normalize the background signal to zero.

For every observation the visibility was determined around the central part of the drift scan. Figure 5.9 shows an example of how I_maxand I_minrelate to the data of the observations.

Visibilities including standard deviations were calculated for every measurement individually and are shown in Table 5.3

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5.5 Fitting models

Combining the data from Table 5.2 and Table 5.3 the plot in Figure 5.10 is produced.

FIGURE 5.10: Computed visibilities (unit-less) versus computed baselines in λ sorted by date of observation.

One can clearly see behaviour as expected. We expect the visibility to drop down from one to zero in the range of zero baseline to resolving baseline. Also, the visibilities seem to be coming back up again at larger baselines. We will be fitting the absolute value of two different Fourier transformed models to our data. Firstly a sinc function, which is the Fourier transform of a top-hat Solar model displayed in Equation 5.5. Close to this is a first order Bessel function, which is the Fourier transform of a disk displayed in Equation 5.6. In both equations V0(λ)is the visibility and B_λ the baseline length in λ. a and b are the to be fitted parameters and J₁is the first order Bessel function. In one dimension, the Sun can be approximated by a top-hat function but in two dimensions the Sun obviously takes on a different shape. We will compare both models [Steringa,2018].

The sinc model is given by,

V₀(B_λ) =a·^sin(π·B_λ·b)

π·B_λ . (5.5)

And the Bessel model for a circular shape by,

V₀(B_λ) =2·a·b·π· ^J¹(a·B_λ)

B_λ . (5.6)

5.6 Sinc function fitting

If we approximate the Sun with a top-hat function (which is a reasonable approximation in a single dimension), the to be fitted function is a sinc as it represents the Fourier transform of a top-hat. Trying to fit a visibility function through the data required a minimum amount of measurements. The first five measurements

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from Table 5.2 and Table 5.3 were insufficient to fit a function through, as shown in Figure 5.11. The likelihood estimation based on the χ²of the absolute value of Equa- tion 5.5 is shown in Figure 5.12, where both fitting parameters a and b are plotted on the axes.

FIGURE 5.11: First 5 computed visibilities (unit-less) versus com- puted baselines in λ with two minimum χ²fits.

FIGURE5.12: The χ² likelihood distribution for both parameters of Equation 5.5 for the data from Figure 5.11.

We see in Figure 5.12 that there are many vertical lines where the sinc model diverges very far from the data. There are two areas where χ² converges, these models are plotted in Figure 5.11. We see that for a low number of data points no

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certainty can be given on the best fit as multiple models are possible. More data is thus required.

Fitting through all data points in Figure 5.10 produced the fits as displayed in Figure 5.13. We know that the visibility should go to one as the baseline goes to zero. Therefore, two models were fitted, one which was forced through a visibility of one at zero baseline. A second model, which was simply a fit via least squares, was also fitted through the data. The first root of both sinc models is the baseline at which the Sun is resolved. This value lies at (0.57±0.01)^◦for the fit forced through 1 and at (0.54±0.01)^◦for the least squares fit.

FIGURE5.13: Sinc fits through the data from Tables 5.2 and 5.3 with the data sorted by date of observation.

5.7 Bessel function fitting

Looking at the Sun, we expect the radio emission to be of a disk shape instead of a top-hat function if we extend our analysis into 2D space. We know that the Fourier transform of a disk is a first order Bessel function [Steringa,2018] as earlier shown in Equation 5.6. If we try fitting this particular model to the data we get the plot in Figure 5.14.

For a baseline going to zero, the visibility should go to a value of 1 as mentioned before. Therefore, just as with the sinc fitting, a fit was made which was forced through this point. However, it is unsure whether there is simply a normalization factor involved. So, besides the forced fit, another least squares Bessel fit was made.

The resolving baseline is the baseline at which the visibility goes to zero as there is no interference of both signals at this point. The resolution corresponding to this baseline can be computed using Equation 2.2. This angular resolution of the interferometer should be equal to the angular size of the Sun as it appears on the sky in the 11.21-11.29 GHz frequency band. This baseline is at the first root of the Bessel function. These points can very easily be extracted from the fits.

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FIGURE 5.14: Computed visibilities (unit-less) versus computed baselines in λ with Bessel-functions fitted and data sorted by date

of observation.

The apparent angular size of the Sun for the Bessel function which was forced through 1 lies at (0.56±0.01)^◦. For the other least squares fitted Bessel function this value lies at (0.53±0.01)^◦.

5.8 Discussion

5.8.1 Discrepancies between models and data

As can be seen in all fits, many of the datapoint error margins do not lie within the realm of the fitted models. There are two reasons why this offset occurs; either systematic errors in the measurements or wrong models. Now, both of these possi- bilities could definitely cause the observed behaviour. We will discuss both.

The measured power is the individual powers from both receivers added up and squared:

(V₁+V₂)² =V₁²+V₂²+_2V₁·V₂. (5.7) This implies that the correlated signal 2V1·V₂, needed to determine visibilities from the measurements lies on top of two Gaussians: V₁² and V₂². If the pointing of the dishes is not exactly correct these Gaussian profiles will have different mean values and be shifted from one another. If their gains are also somewhat different, a complex structure will be added to the fringes. The central peak will also be shifted from the center to wherever these two Gaussians have their central maximum together. The value calculated as a specific visibility for such a measurement is thus very likely to be off. Such an error is not unlikely to cause the discrepancy between an individual data point and the models and is also hard to quantify with a single observation for that particular baseline.

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The measurements used in the previous Chapter were taken on different dates.

Temperature fluctuations at the surface of the Sun will cause variations in flux. The measurements taken throughout this thesis lie very far apart (about a month) and the Sun will most likely have looked differently on these days as the Sun revolves around its axis and the Earth orbits the Sun. We know that long baselines are sensitive to small scale structure whereas short baselines are sensitive to large scale structure. If the temperature varies over the surface and is thus not uniformly distributed, the model will definitely not be an exact Bessel function. If the temperature in the center is for example somewhat higher than the temperature at the outer edges, the visibilities at larger baselines (needed to resolve small scale structure) will be influ- enced. Interesting to note is that no noticeable correlation can be seen between the observing dates and visibility values from Figure 5.10.

Throughout the observations the Sun changed in declination due to the rotation of the Earth. The opacity of the atmosphere will thus have changed throughout an observation. As mentioned earlier, one of the corrections which has been done to the data is subtracting the background signal. However, if this signal is not constant throughout the measurement (which it likely is not) it might create offsets in the determined visibilities.

The Sun’s emission in the 10.7 to 11.7 GHz band does not only come from black- body radiation. If we look at Figure 5.1, we see that at the observed frequency there is more emission. This emission is mostly synchrotron emission from Solar activity.

This process is highly irregular and changes over the surface of the Sun and could thus create fluctuations in the computed visibilities, especially at larger baselines.

However, it is important to say that the synchrotron emission is profoundly more abundant in lower frequency regimes.

5.8.2 Physical size of the Sun

The angular size of the Sun resulting from the fits made in the previous Chapter can tell us something about its physical size. Assuming the Sun radiates in the shape of a disk in the 11.21-11.29 GHz band, the angular size of the Sun in this frequency range is equal to (0.54 ±0.02) degrees. Given its distance of 150·10⁶ km to us, the Sun has a radius of (7.07±0.26) ·10⁵ km [Union,2012]. This value follows from trivial geometry. The assumption which is made here is that the apparent size in this radio regime is equal to its optical counterpart. For the observed frequency ranges this is a decent approximation as the corona is emitting much less than the Solar surface in the 11.21-11.29 GHz band [Bradaschia,2015].

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34

Chapter 6

Conclusion and future improvements

6.1 Future improvements and possible observations

6.1.1 Recording individual powers

The entire setup currently records the total correlated power. The result from this is that besides measuring the interference pattern, we also measure the individual powers of both receivers. This causes the fringes in the data to lie on top of some Gaussian shape. What we detect is essentially the square of the two voltages specified in Equation 5.7.

If both individual powers, V₁ and V₂, are measured their squares can be subtracted from the total power output. Resulting from this is solely the interference pattern. It is more convenient to determine visibilities with only this data. Also, error margins will likely be smaller.

However, detecting these powers will require two additional splitters and two more power meters including sensors and filters. Also splitting the signal will drop the output with an additional 3 dBm. The measured total power will be 6 dBm lower than before as both dishes will half their power output. Additional amplifiers for both dishes would be convenient as power levels are dropping to levels around -50 dBm for average observations.

6.1.2 Measuring the proper velocity of geostationary satellites

Interferometers offer many opportunities for measurements which are impossible to do with single dish telescopes. One of these observations is the measurement of geostationary satellites and determining their proper velocity.

Geostationary satellites are satellites in an orbit of 35,786 km above Earth’s equator, where their orbital period is exactly equal to Earth’s rotational period. Due to this behaviour they seem to stand still in the sky as they orbit. However, these satellites are never fully fixed within their orbit. As a result from this, the satellites will seem to drift across the sky. Radio interferometers are devices which are actually capable of detecting very minor proper velocities. Not because their angular resolution is so good but because very tiny offsets in phases of two telescopes can be detected. If the two dishes were to be pointed at a moving satellite at a large baseline, very small proper velocity will cause the phase offsets in the measurement to shift. With help of the amount of phase shift and the distance to the satellite, over a certain amount of time, the proper velocity of such a satellite could be mapped. It is however essential to measure phases of the incoming signals.