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Interferómetro

Pathfinder to large-format interferometer

1. Introduction

Although till the moment imaging instruments are broadly used, systematic errors and their requirement of a telescope system, make the interferometers to be considered the future solution to obtain CMB ultra-sensitive measurements. The sensitivity of the instruments is proportional to the number of receivers that is limited, for imaging instruments, by the telescope focal plane area. The interferometers do not present this limitation because they do not require such a telescope, but the correlation a lot of wideband microwave signals result very complex in a technological sense. In the frame of this EPI Consolider project it has been done a detailed study to clarify the type of correlator more intended to be used in a large-format interferometer with hundreds or even thousands of receivers.

2. Digital Correlators

It was considered the use of digital correlators due to their great flexibility and easy to control systematic and phase errors. We have used two commercial FPGA from Agilent Technologies, in particular the U1071A model, each one with two 500 MHz bandwidth channels (see Figure 1). Correlation tests were done using both sinusoidal signals at 100 and 250 MHz (Figure 2a) and filtered white noise signals with a bandwidth of 80 MHz and centered in 100 and 200 MHz (Figure 2b). Additionally, a method to correct the phase errors introduced by the instrument receivers and frequency down-conversion stage was developed and tested successfully.

In spite of the achieved good results, digital correlation presents disadvantages as high cost, power consumption, volume and weight. In addition the bandwidth is still reduced in terms of specifications for CMB measurement instrumentation. The reported FPGAs real-time operation bandwidth is of about 200 MHz, so the number of FPGAs needed to implement a 100-receiver interferometer would be 5.000. This makes totally nonviable a correlator digital implementation.

 

Figure 1: Digital correlator implemented by means of two FPGA U1071A mounted in a PC.

 

 

(a)                                                                   (b)

Figure 2: Two sinusoidal signals (a) and two band-filtered white noise signals (b) digital correlation.

3. Michelson Type Analogical Correlators

Another possibility is to use analogue correlators. In principle they were considered Michelson type interferometer structures (signal correlation by pairs). A base-band correlator was implemented following the scheme used in the VSA interferometer (Figure 3a). The single base-line implemented correlator is shown in Figure 3b. This option is based in the Ryle configuration where both input signals are phase-switched between 0 and 180 degrees. The prototype was tested by using sinusoidal excitation signals at 250 and 250,001 MHz (see Figure 4a) and the video bandwidth was measured, resulting in a value of about 10 KHz (see Figure 4b). It can be observed the achieved good results in terms of low-frequency noise due to the phase-switching application. This option was finally discarded due to the need of a complex frequency down-conversion stage and the corresponding phase-error control.

In order to avoid the use of a frequency down-conversion stage, it was also implemented a 26 to 36 GHz bandwidth correlator using a correlation and detection module designed for the QUIJOTE Thirty Gigahertz Instrument (TGI) (see Figure 5). One advantage of this kind of correlators is that they can provide directly the real and imaginary part of the visibilities only by subtraction of the outputs 1 and 2 (real part) and 3 and 4 (imaginary part). Figure 6(a) shows the measurement test-set used to achieve a video bandwidth of about 70 KHz and Figure 6(b) shows the visibility’s frequency spectrum when correlating two 10 GHz wideband signals with different power levels. This kind of correlators were finally discarded due to the complexity coming from the high number of base-lines (n(n-1)/2) and also from the complex routing of the microwave signals that increase a lot the correlator cost.

 

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(b)

Figure 3: ‘Plus-minus’ configuration correlator (a) and circuit mounted over FR4 substrate (b).

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Figure 4: Correlated signal spectrum from two sinusoidal signals at 250 and 250,001 MHz (a) and video bandwidth measurement result (b).

 

Figure 5: Scheme of the 26-36 GHz Correlation and Detection Module of QUIJOTE TGI

 

 

Figure 6: (a) Measurement Test-Set of the 30 GHz and 10 GHz bandwidth correlation module. (b) Visibilities achieved by correlation of two 10 GHz bandwidth signals with different power levels.

 

4. Fizeau Type Analogical Correlators

In Fizeau type interferometers the signals are combined all with all at the same time. It was analysed the possibility of using Rotman Lenses (RLs) implemented over Printed Circuit Boards (PCBs). Figure 7 shows a simplified scheme of an interferometer with a correlator based in RLs. A two inputs and four outputs RL was designed and simulated by means of the software HFSS. Figure 8 shows the simulated design (a) and the achieved matching parameters of their input and output ports (b). The design works well only in the center of the bandwidth producing errors in the phases between the input and output ports. The required wideband makes very difficult a correct phase control, so, taking into account that this is a critical point for an interferometer it was decided to discard also this option.

 

Figure 7: Scheme of a RLs-based interferometer.

 

 

     

(a)                                                                                                                 (b)

Figure 8: RL design with two input and four output ports (a) and matching of the Lens ports (b).

 

In Figure 8b it can be observed that the design works well in the center of the bandwidth, but in the ends the results are not good. The same can be observed in the Figure 9, where the phase shift between the input and output ports are shown. From these results, it seems that, due to the great wideband required, the phase control result very complicate with this technology. So, taking into account that this is a critical point for an interferometer, it was decided to discard also this correlation option.

 

5. Optical Correlators

The most viable option to get a large format interferometer is considered to be the use of Mach-Zehnder optical modulators (MZM) to reduce remarkably the correlator complexity (Figure 9). The basic idea is to modulate L band (1550 nm) laser signals with the CMB microwaves to route and correlate the signals by means of an optical system based on fibres, lenses and near-infrared (NIR) cameras (Figure 10). MZMs (Figure 9a) divide one optical signal into two arms with a LiNbO3 substrate and a refraction index modified by means of the microwave electrical field (Figure 9b). This technology allows the implementation of two types of interferometer: Michelson and Fizeau (see Figure 10). Due to the highest complexity of the Michelson version we selected the Fizeau option, as the one to be developed to get a large format interferometer. Figure 11 shows a scheme of the large format interferometer that could be achieved by using the QUIJOTE experiment TGI receivers and the proposed optical correlator. The same concept of this Fizeau option is used in bolometric interferometers as QUBIC. We are collaborating with the PI of QUBIC to get advantage of their experience in simulation and calibration activities.

The main bottleneck of the optical correlator concept is the use of wideband commercial MZM due to the high cost of the LiNbO3 technology. At this moment we are leading an Explora project (AYA2015-72768-EXP) to get an integrated version of a frequency up-conversion stage based on MZMs implemented in a technology allowing integration as Si, or InP to assure the viability of the proposed interferometers. In the meanwhile, for this EPI project, due to the high cost of the required 40 GHz commercial MZM we have acquired only 4 units of the MZM shown in Fig. I9a. Following the scheme of Fig. 11 we could achieve the synthetized image of one of the 4 receiver outputs (I±Q, I±U) from only 4 receivers, so the resulting image would be very poor in terms of beam performances. In the following, a summary about the up-conversion stage and optical correlator characterization activities developed until the end of the project is reported.

 

 

 

Figure 9: a: 40 GHz bandwidth MZMs. Source: http://www.thorlabs.de; b: MZMs operating scheme.

 

Figure 10: Fizeau and Michelson MZM-based interferometer simplified schemes.

 

Figure 11: MZM-based interferometer scheme using the receivers of QUIJOTE TGI.

 

5.1 Frequency Up-Conversion Stage

The main components of the up-conversion stage (see Figure 12) have been purchased and tested in the laboratory with the help of the Photonic Engineering Group of the UC (http://gif.teisa.unican.es/) and also the IFCA’s Photonics Group (http://www.ifca.unican.es/en/photonics). Four MZM were purchased with a 40 GHz bandwidth and the ability of attenuating one of the lateral bands and the optical carrier (SSB-SC modulation). To assure that the 4 MZM operate in the same nonlinear state, four in-line polarizers are used to fix the polarization of the four optical carriers. A 1x4 optical coupler is used to drive the MZM by means of a single laser source operating at 1550 nm.

 

Figure 12: Main components of the up-conversion stage for the optical correlator.

5.1.1 NIR Laser

The laser SFL1550S from Throlabs (Figure 13(a)) was selected to drive the microwave signals to the NIR due to the reduced linewidth (50-100 Hz) that is able to provide. Its optical output power was preliminary measured under different bias current conditions and with a controlled temperature of 31º C. It was proved that the laser is able to provide until 35 mw of optical power that is enough to drive four MZM (and more) at the same time.

The laser source driver allows changing both its bias current and temperature, thus providing different NIR signal wavelengths. Figure 13(b) shows the measured dependence of the laser wavelength with the temperature for a bias-current value of 333 mA. As the slope of the curve is 42 pm/ºC and the temperature can be controlled in intervals of at least 0.1 ºC, we can tune the laser wavelength with intervals of at least 4 pm. The resulting fine-tuning capability can be used to correct the fabrication errors of the optical filter that is going to be used to remove the modulated signals’ carrier and one of the lateral bands. Figure 13(c) shows in red the operation regions where the laser behaviour is monochromatic (only one wavelength). This is a critical point since the correlator would not work at all if the laser falls in a multi-mode operation point.

 

Figure 13: (a): Laser SFL1550S from Thorlabs operating at 1550nm. (b): Laser wavelength as a function of the temperature for a Bias current of 333 mA. (c): Monochromatic operation zones of the laser presented in red. Blue points represent multi-mode operation of the laser.

 

5.1.2 1x4 Coupler

The coupler FCQ1315 from Thorlabs was also tested and a coupling ratio of 25±1% was measured in each of the four outputs. This is a very important result to assure that the four MZMs operate in the same nonlinear state to up-convert the microwave incoming signals.

5.1.3 Fiber Polarizers

The fiber polarizers ILP1550PM-FC from Thorlabs were tested by measuring the polarization state of their output signals when inserting input signals from the SFL1550S connected to the 1x4 coupler. The measured Stokes parameters were the same for all the polarizers, demonstrating that they provide the same polarization state and assuring so, that the four MZMs will operate in the same nonlinear state when up-converting the microwave signals.

5.1.4 MZM

Figure 14(a) shows a configuration scheme of the LN86P MZM from Thorlabs. The modulators were preliminary tested by injecting a 30 GHz modulating signal coming from a Gunn-diode which is able to provide 10 dBm of power. Figure 14 shows the test-set (b) and one of the achieved measurement result (c). With these measurements it was proven that a high degree of amplification is required in the microwave receivers, due to the detected requirement of about 0 dBm for the MZM input microwave signals. This value is 20 dB higher than the achieved with the receivers of the QUIJOTE TGI. On the other hand, as can be observed in Figure 14(c), although one of the side bands can be completely removed the optical carrier remains too high compared with the desired side band signal, so one optical filter will be required to remove the optical carrier to a low enough level. In order to see the results in a more realistic case, Figure 14(d) shows the measurement result when modulating with a 10 GHz bandwidth noise-like signal centred at 30 GHz and a power level of 0 dBm. It can be also observed the requirement of filtering the optical carrier.

A stability problem was identified concerning to the operation of the MZM. The modulators’ optimal DC operating points were characterized in terms of carrier and one lateral band power level reduction. The stability problem has two aspects. The first is that after setting the optimal bias point, the power levels of the carrier and lateral bands change in several minutes. On the other hand, the second aspect is that when using the same operation point during another day, the power levels are also different to the achieved previously. These differences and the evolution with time show clearly a stability problem in the MZM DC operation point that has been solved by the application of a closed-loop feedback, when setting the MZM bias points. As can be seen in Fig. 14(a), the MZM have two photodiodes that provide DC signals proportional to the two internal parallel MZM’s NIR output power. These detected signals can be amplified using lock-in amplifiers an added to the ones of DC sources to set the two bias points of these internal MZM. By this method it is possible to get a much more stable DC operating point. Figure 15 shows the measurement set-up used to test the stabilization method (a) and the achieved results in terms of modulated signal power evolution with time (b). It can be observed that the SSB-SC modulation is well achieved only by using the optimal DC bias point but in any case it is important to apply a volume bragg optical filter (VBG) to prevent eventual increases of the carrier level due to temperature variations.

Figure 14: (a): MZM pin-out and scheme. (b): Measurement test-set. (c): Modulated output signal achieved in one of the cases. (d): Measurement result when modulating with a 30 GHz and 10 GHz bandwidth signal.

 

Figure 15: Measurement set-up used to test the stabilization method (a) and the achieved results in terms of modulated signal power evolution with time (b).

 

 

5.2 Optical Correlator

As can be seen in Fig. 11 the main components of the optical correlator are a fiber bundle mimicking the antenna array structure of the instrument’s Front-End, a system of correlation lenses and the filter to remove the optical carrier to a very low level and finally a NIR camera to get the synthetized image of the CMB polarization parameters.

 

5.2.1 Volume Bragg Optical Filter (VBG)

A company (Optigrate) was identified to provide Volume Bragg optical filters (VBG), with the required pass-band and rejection-band characteristics. A great advantage of this kind of filters is that they can be used to filter all the optical signals to correlate, at the same time. Figure 16(a) shows an example of the simulated diffraction efficiency of one of these ultra-narrow band-pass filters. In the reported case a bandwidth of 4 GHz (32 pm) could be selected while rejecting the NIR carrier that would be placed at 31 GHz (0.248 nm) from the central frequency of the modulation bandwidth. As the central wavelength of the filter can differ from the desired one due to tolerances in the fabrication process, the NIR carrier wavelength will be tuned by controlling the bias operation point of the laser source (see Fig. 13(b)). At the moment, the same concept of optical interferometer is being used to develop a demonstrator but for lower frequencies (10-20 GHz). In the frame of that research project (ESP2015-70646-C2-1-R) we have acquired a reflective VBG that can be used following the set-up of Figure 16(b). As this VBG is designed for a lower frequency range, it can be also used for the 26-36 GHz bandwidth with even better rejection characteristics. Figure 16(c) shows the measurement results of the reflective VBG. A bandwidth of 5 GHz (40 pm) has been measured at the IAC laboratory.

 

Figure 16: (a) 4 GHz bandwidth VBG spectral characteristic for 31 GHz modulation signals. (b) Filter measurement Set-Up. (c) Measured filter characteristic.

 

5.2.2 Optical Correlation Stage Preliminary Test

Preliminary measurements of the correlation stage were made at IAC using directly the SFL1550S laser as a source signal (see Figure 17(a)). This signal was divided through optical couplers in order to be distributed and introduced in a bundle. The signals from the output of the bundle were correlated by a couple of 100mm focus lenses and finally detected by a Xenics Xeva NIR camera provided by the IAC. Figure 17(b) shows a picture of the optical measurement set-up. A 46 fibers bundle has been fabricated in order to have flexibility to optimize the distribution of different antenna array scenarios. The bundle should map directly the position of the receiver antennas in a scaled fashion (homothetic mapping). A compact geometry with 20 fibers was illuminated and two optical configurations were used: 4-f and 6-f. The 4-f configuration was used to reimage the fiber distribution illuminated in the bundle (Figure 17(c)). The 6-f configuration permits to synthesize the PSF of the fiber array distribution (Figure 17(d)). The PSF of an equivalent array distribution of antennas has been simulated, achieving results that do not match the measurements (see the following section). This could be due to problems with the homothetic mapping of the arrays and also to differences in the power of the different fibers that can be observed in Fig. 17(c). The fiber bundle will be optimised in order to overcome the reported problems.

Figure 17: (a) Sketch of the correlation stage setup. (b) Picture of the optical measurement set-up at IAC. (c) Image achieved with a 4-f configuration: Illuminated fibers distribution. (d) Image achieved with a 6-f configuration: PSF of the fiber array distribution.

 

 

5.3 Antenna Array Topology

The optimal antenna array topology has been analysed, trying to achieve an optimal configuration in terms of the synthetized beam or Point Spread Function (PSF). For a small array of elements it is not possible to achieve a clean beam with low levels of lateral lobes. Figure 18(b) shows the synthetized beam of an optimized pseudo-random array with only 4 pixels that is the maximum number that can be used with only 4 MZMs. As can be seen from that figure, an inadequate PSF shape is obtained with a poorly defined FoV of 6 degrees (the minima are at -15.4 dB). On the other hand, Figure 18(d) shows the synthetized beam when using the compact array structure of 20 elements of the fiber bundle used in the optical correlator’s previously reported tests. It can be seen, that for 20 pixels it is possible to get a 14 degrees FoV with lateral lobes lower than -20 dB. These results tell us that a demonstrator with a low number of pixels will not be able to provide a good synthetized image of the polarization parameters, so a different strategy will be considered to demonstrate the proposed correlation concept. In previous Fizzeau type interferometer prototypes, as MBI-4, the authors have demonstrated the interferometry concept by comparison of measurements an simulations of the interference patterns given by each one of the base-lines and the combination of all of them. In the next months we will follow the same strategy to test the correct behaviour of our proposed optical correlator.

 

Figure 18: Antenna array topology simulation. An optimized pseudo-random array with only 4 pixels (a) presents a FoV of about 6 degrees with -15.4 dB of lateral lobes (b). A compact array with 20 pixels (c) presents a FoV of about 14 degrees with of lateral lobes lower than -20 dB (d).