A Low-cost Fiber-based Near-Infrared Heterodyne Interferometer Laurent Pallanca, Cristobal Vio, Ernest A. Michael
University of Chile, Dept. of Electrical Engineering, Astronomical Instrumentation Group, Avenida Tupper 2007, Santiago de Chile, Chile.
ABSTRACT
We are presenting a low-cost near-infrared heterodyne interferometer based on 1.55µm fiber-components, amateur telescopes and a 3-GSPS-ROACH-based correlator. While first performance is estimated to be sufficient for the brightest stars, we expect science-relevant astronomical performance given various improvements we are working on, as stabilization of fiber coupling, detectors near the quantum limit requiring lowest possible local oscillator power, and fiber line-length correction. These will enable the investigation of extremely long baselines, adaption of existing medium-class telescopes, and testing at the pointing-telescope slots of ALMA, and/or the extension to three of more baselines.
Heterodyne detection from visible to mm-wavelengths is nowadays a well-established technique which is used in astronomical instrumentation to combine the advantage of high signal-to-noise ratio and very high resolution [1], [2] and in communication system in which the coherent optical detection provide a high sensitivity and frequency selectivity [3]. We report here our investigations to develop a heterodyne interferometer operating in the near-infrared range, i.e. 1.55µm, which is based on coupling of the collected star-light to single-mode fibers, and fiber transmission of this signal and the common laser local oscillator to the photodetectors. To our knowledge such an approach has not been implemented to date (see Table 1). Since the sensitivity of heterodyne detectors increase with the wavelength [4] their use with a CO2 laser is attractive because of atmospheric transmission windows in the range 8-14µm. Such long wavelengths would be preferred for planet detection, due to planets are much cooler than their host star. However, for our purpose to demonstrate the resolution of a star, we are using a near-infrared laser at 1.55 µm, also with the benefit of a transparent atmospheric window around this frequency. This wavelength is the fiber-telecommunication wavelength, and therefore very low absorption is given in monomode fibers, and economic commercial off-the-shelf components can be used. If desired in later upgrades, the distributed 1.55 µm LO signal can then be used to phase-lock any longer-frequency LO at the telescopes. A correlator of 1.5 GHz bandwidth (performing multiplication of the two signals, one of both is time-shifted, and subsequent integration of the product over the time shift) measures the complex degree of coherence. From radio frequencies to infrared, the relative bandwidth of a heterodyne system decreases [5]. Nevertheless, the reduction of the bandwidth provides larger time coherence, and allows an easier fringe acquisition and a better visibility measurement even in presence of important phase differences due to mechanical path length correction or atmospherics turbulences. This technique is used in radio and sub-mm interferometer (e.g. VLBI, ALMA), however, in the infrared range, heterodyne interferometry is only used at the ISI-Array (Infrared Spatial Interferometer Array), at 10.6µm, with powerful and stable laser local oscillator [13], [14].
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1.2 Astronomical motivation
Optical and NIR interferometry has made the greatest impact in the area of stellar astrophysics, in particular the study of nearby single stars, given the limited nature of single baseline interferometers and limited sensitivity of first generation instruments. In the concern of stellar astrophysics we could cite stellar diameter measurements, atmospheric structure characterization, limb darkening, measurement of pulsating AGB stars, and the study of binary stars. Interferometers can also be used to probe the environments around stars, both at visible light and infrared wavelengths. As the sensitivity of facilities increase, lower surface brightness features can be measured. Advances in interferometric imaging are particularly relevant here, since gas and dust around stars might not be distributed uniformly and may be changing in time. While there has not been true imaging accomplished by long baseline interferometers in this area yet, we have included some of the unexpected recent results from Keck aperture masking [6]. Hα envelopes around hot stars, accretion disks and young stellar object, dust shells and molecules in evolved Stars, colliding winds are examples of circumstellar environment investigations. A heterodyne interferometer is capable of highest spectral resolution and therefore it should be able to follow up Doppler shifts in narrow line emission and reveal dynamics in the above mentioned features around stars.
2. DESCRIPTION OF THE GENERAL CONCEPT A highly coherent NIR-Laser (1555nm-125mW Koheras Benchtop Laser) is used as a Local Oscillator and its beam is distributed via monomode optical fibers in two receiving optical paths to be combined with the stellar signals. The LO phase and polarization at the mixer needs to be conserved. This implies the use of polarization controllers, a LLC (Line Length Corrector) system (with a fiber stretcher from ALMA, frequency shifter and faraday rotator mirror as part of this correcting loop) and a phase controller. Like in the ALMA photonic LO system, it is proposed, once the interferometer is operational on short baselines of a couple of meters, to implement a line-length corrector (LLC) for realizing long baselines: in one optical arm (the long one, the other can be kept short, left side in Figure 3-1) the LO signal is frequency shifted at far end before it is sent back within the same fiber to generate a beat signal with the original LO signal on a photodiode. Counting the maxima in this signal (fringes) gives the length change information of the optical path length in the fiber, and stabilizing on one fringe stabilizes the fiber length. The need for this procedure comes from that the thermal and mechanical changes in the fiber optical path length have to be compensated, in order to maintain a fixed phase relationship between the split LO signals at the two telescopes. Using this signal, a LLC as a compensation system would adjust the optical path length to the telescope (Fiber Stretcher in ALMA or pair of parallel mirrors in ISI Telescopes).
GI2T FR Calern 2x1.5m 12-65 1986 0.57-0.7 M ISI USA Mt.Wilson 3x1.65m 4-70 1988 10.6 H
COAST UK Cambridge 5x0.65m 48 1991 vis M SUSI AUS Narrabri 5x0.14m 5-640 1993 0.40-0.75 M IOTA USA Mt.Hopkins 3x0.45m 5-38 1993 1-2.4 M NPOI USA Flagstaff 6x0.5m 2-437 1994 0.45-0.85 M PTI USA Mt.Palomar 3x0.4m 110 1995 2-2.4 M
CHARA USA Mt.Wilson 6x1m 34-331 1999 0.55-2.4 M,MF KECK USA Mauna Kea 2x10m 85 2001 2.2-10 M MIRA J Mitaka 2x0.3 30 2001 0.8 M VLTI ESO Mt.Paranal 4x8.2m 4x1.8m 20-200 2001 1-12 M
OHANA USA Mauna Kea 7x10 85-800 2004 Nir MF LBT USA Mt.Graham 2x6.5 22.8 2005 1-20 Fz MRO USA N. Mexico 6x1.4 7.5-350 2008 0.6-2.4 M
Table 1. Optical interferometer from “Observation en Astrophysique- P.Lena-2007”. (*)Type: M:Michelson, H:Heterodyne, MF: Michelson with Fiber, Fz: Fizeau
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To make possible larger baselines we propose to prove the applicability of the technically highly developed ALMA fiber optical path length correction scheme for the purpose of infrared heterodyne interferometry at 1.55 µm. Against the expected atmospheric path length drifts (order of 1μm/s), a phase-precision of <λ/2 at 1.55μm is already good enough for long-baseline fiber-based heterodyne interferometry in the infrared range. At the mixers (e.g. fast photodiodes), the combination with the cosmic signal provides a signal at much lower frequency (50MHz – 3GHz), while the phase and amplitude relationships between the 2 starlight signals are preserved. This resulting intermediate frequency (IF) signal is then amplified (70dB LNA) and filtered (Bandpass), with a small signal-to-noise ratio by the means of standard microwave electronics [7]. In both arms IF-delay lines are placed (one of them is needed depending on the pointing direction) to compensate the geometrical delay. Finally a FPGA double side band correlator would be able to measure the degree of coherence of the observed source. The correlator contains circuitry which produces a signal proportional to the average of the product of the signals from the individual mixers. The result from the correlator is a fringe signal which contains the desired information about the phase relationship between the receiving interferometer arms.
Fig. 1: NIR-fiber based heterodyne interferometer setup
3. HETERODYNE DETECTION 3.1 The Near-IR heterodyne receiver
As presented in Figure 1, we tested the NEP of our detection by completing our frontend (photodiode + LNA) to a full integrating heterodyne receiver, which consists of the following elements:
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- A beam combiner, monomode optical waveguide which combine 99% of the signal power with 1% of the local oscillator power. The local oscillator power is easily controlled and can be amplified if necessary with a 37dBm Erbium Doped Fiber Amplifier.
- A mixer which is a fiber coupled high-speed InGaAs photodiode, with 2 GHz bandwidth and 800-1600 nm spectral range. Incident on this is the signal (coherent or thermal radiation) and the local oscillator (LO). These have frequencies νS , νLO and powers PS, PLO respectively. The photodiode response is then a beat frequency between the signal and LO waves which correspond to the intermediate frequency (IF) given by:
IF LO Sν = ν −ν (1) This photodector has been characterized with a current voltage source-meter as shown in Figure 2.
- Two low-noise IF (LNA) amplifiers (Wenteq, Inc.) in series with G = 2 x 35 dB = 70 dB, in the 0.02-3GHz frequency range each with a noise figure F=1.3.
- A square-law detector, 0.1-4GHz, which rectifies the IF to give an output proportional to the IF power. Linear dependence of the output voltage from the input power was measured to be given from -35 to -15dBm (see Fig.2).
- A low-frequency filter or integrating circuit which precedes the final recording device.
Fig. 2: Schematic diagram of one heterodyne receiver
In the interferometer, the square-law detector and filter are replaced by a 3GBPS analog-digital converter card (iADC) which feeds the FPGA-based correlator of the ROACH-board. Between iADC and the correlator a digital delay will be implemented in both channels.
In our experiment we use a PIN InGaAs photodiode (Thorlabs FGA04) with the following properties:
Wavelength Range (nm) : 800-1700 Rise time (ps) : <100 Peak wavelength (nm) : 1550 Bandwidth (GHz) : 3.2 Responsivity (linear regime) (A/W) : 0.95 Bias Voltage (-V) : 12 Quantum efficiency : 0.76 Diode Capacity (pF) : 1.0 Dark current (nA) : 0.7-2.5
-101.2-101.3-101.4-101.5100
101
102
Heterodyne Signal Output [dBm] (e.g. Square Law detector Input)
Fig. 3a: Square law detector: Output voltage from input power Fig. 3b: LNA : Output Power from input frequency
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We measured I-V curves of the photodiode at different LO powers in order to compare with the specified dark current and responsivity, and to determine its saturation regime. The results show a lower responsivity (0.72A/W which lead to a 0.58 quantum efficiency) and a higher dark current of 3.7nA at the specified -12V reverse bias than specified (see Fig.2). Saturation effects start to be visible from 20 mW.
3.2 Signal-to-noise and Noise Equivalent Power
3.2.1 Determination of NEP with a fiber-coupled LED
In our heterodyne detection scheme the strong LO and the signal are combined through a nearly polarization independent 2x1 monomode coupler before being focused on the sensitive area of the photodiode. The monomode fiber provides the necessary mode matching for the heterodyne process. The photocurrent generated is given by:
( )2 cosph LO S LO S IFeI I I P P t
hη
= + + ω +ϕν
(2)
The dc-current is dominated by the LO power since LO SP P :
dc LOeI P
hη
=ν
(3)
The rms value of the heterodyne signal current is given from Eq.(2)
2 2H LO S LO SeI P P P P
hη
= = ℜν
(4)
where /e hη νℜ= is the responsivity of the photodiode. For sufficient LO power (>2mW) and reverse-biased photodiode the noise current arising is given by the shot noise due to the LO power, 2 2n LOI eI B= where B is the bandwidth of the following amplifier. The background noise and the Johnson noise then have a negligible contribution at the LO frequency and power. The signal-to-noise power ratio and the related (ideal) noise equivalent power are then given by:
2
2SH
n
PISNRI h Bh BNEP
η= =
νν
=η
(5)
Fig. 4: Measured photodiode characteristics. Left panel: I-V curves for different illumination levels up to 38 mW. Right panel: I-P curves for different reverse bias voltages larger 10V.
bias voltage optical input power
optical input power Reverse bias voltaje (< -10V)
current
current
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This corresponds to 0.4 nW at ν = 192 THz (1.55 µm), B = 3 GHz, η = 0.5. The measured SNR in the 3 GHz bandwidth and the theoretical value are presented in Fig.3a. A fiber-coupled super-luminescent LED (SLED) was used as the broadband signal to characterize the receiver. Its spectrum is presented in Fig.3b. The NEP was first estimated with a spectrum analyzer, through the broadband signal power which produced a smallest observable increase (estimated to be 0.5dB) from the noise floor (see Fig. 4). This way, the observed NEP was 190.56 / 3 1.9 10 /nW GHz W Hz−= ⋅ at 1555 nm. It is close to the quantum limit due to the sufficiently high LO power (see in section 3.3.). This power is equivalent to 1 µW in the full bandwidth of the SLED (58 nm). This small power was realized by fiber attenuators from a reduced emission power at lowest possible but stable-operation current (ca. 1 mW, max. power 20 mW).
Fig. 5a: Measured NEP and theoretical SNR for InGaAs reverse-biased local oscillator pumped photodiode at 1.55µm.
Fig. 5b: SLED spectrum used as broadband source at maximum diode current.
3.2.2 System Noise Temperature
The system noise, or the noise figure (NF), has been measured using two different methods:
Adjusting the optical input power from the SLED so that the output noise power level is double of that without signal, which leads to NF=25dB (less precise).
With the Y-factor method (more precise): NF=26.4dB.
, ,
1in hot in cold
system noise
P Y PP
Y− ⋅
=−
, , ,/out hot out coldY P P= , , ,( )out hot system noise optical in hotP G P P= ⋅ + ,
, ,( )out cold system noise optical in coldP G P P= ⋅ +
where the noise figure NF is defined over out optical inP G NF P= ⋅ ⋅ .
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Fig. 5: Receiver output noise power for 0, 44.5 and 226nW (within the 3GHz bandwidth) of optical input power.
The NEP determined from the system noise figure is -174 dBm/Hz + 25 = -149 dBm/Hz or 3.8 nW in the 3GHz bandwidth, where -174 dBm/Hz is the Johnson noise limit at 290 K. This is considerably more ( x 7) than estimated with the naïve first method above. The noise equivalent temperature (NET) of the receiver (or system temperature, or receiver temperature) is given by ( )1 290 90000sysT F K= − ⋅ ≈ , where /1010 316NFF = ≈ .
Another way to find sysT is given in [15]: ( / ) /rec LO mixer BT h NEP kν η= + . For the quantum limit,
/het LONEP hν η= , this simplifies to: 2 / 2 /sys LO B het BT h k NEP kν η= = . In the above case of NEP = 190.56 / 3 1.9 10 /nW GHz W Hz−= ⋅ , this leads to Tsys = 32200 K, or for 183.8 / 3 1.27 10 /nW GHz W Hz−= ⋅ we
would have Tsys = 110000 K. Tsys is known to be used in the radiometer formula [7],
/sysT T BΔ = ⋅ τ
(6)
from which the integration time τ can be computed which is needed to detect a specific source weaker than the NEP with a desired signal-to-noise ratio SNR. For the following we assume that we can set s BP SNR k T= ⋅ Δ , so that the integration time would be:
2 2
,
21 1B sys het
S S
k T NEPSNR SNRB P B Pν
τ⎡ ⎤ ⎡ ⎤
= ≤⎢ ⎥ ⎢ ⎥⎢ ⎥ ⎣ ⎦⎣ ⎦
or 2
SPSNR BNEP
τ= (7)
The right side of the inequality is an approximation if one puts there the measured NEP which is larger than the quantum limit. It has the advantage that one can use for NEP and PS also the total values for the used bandwidth, NEP NEP Bν= ⋅ and ,S S vP P B= ⋅ . For illustration, the strongest star on sky, Betelgeuse, has 35000 Jy
22 2 13.5 10 W m Hz− − −= ⋅ at 1.5 µm. Through a 20 cm telescope, over 3 GHz, and one polarization, this is PS = 16 fW. (Using the Planck formula with T=3000K and 55 mas star diameter gives indeed the same result). Using the NEP of 3.8 nW or the Tsys = 100000 K, to detect it at a SNR of 10, integration for about 2000 s is necessary. Improving to Tsys=30000 K or NEP = 1 nW, it would reduce to under 200 s. For such long integration times, a high receiver stability
Noise Floor
Noise power for a 226nW optical input power
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and signal-reference chopping is necessary. Given this, we can expect from the interferometer that the additional noise of both IF-chains (LNA noise figure) is uncorrelated and is disappearing, therefore revealing an NEP more near to the quantum limit. After Hale et al [14] we have then for fringe detection with a heterodyne interferometer
2,
/S
Fringe C
V PSNR t B
hν τ
ν η⋅⎛ ⎞
= ⎜ ⎟⎝ ⎠
(8)
where max min max min( ) / ( )V i i i i= − + is the fraction of seen source power which provides interference, therefore we add also the quantum efficiency of the detectors η. . tC is the mean time in which the atmospheric phase fluctuation is less than 1 rad, or ideally stable and then followed by a sudden arbitrary change. The individual times should be exponentially distributed with probability / Ct te− . tC can be as good as 3 s for shorter baselines, and we expect even better values at some extraordinary sites in Chile. Assuming this, for Betelgeuse with 24 1
, 5.3 10SP W Hzν− −= ⋅ , we
would have 4.7FringeSNR = after 200 s, for a 20 cm telescope with NEP=1nW/3GHz, V=0.5. If tC approaches τ, or if atmospheric phase fluctuations could even be corrected out [17] , integration time would keep contributing linearly to SNR at arbitrary time scales. Long time-scales for integration are possible since the fringe beating can be stopped using the frequency shifting technique known from ALMA and VLA, which can be implemented with fiber frequency shifters. 3.2.3 Characterization of the receiver stability: Allan plot
In order to characterize the receiver stability we employ the method first described by D.W. Allan [8]. The broadband source from a SLED is mixed with the LO at the photodiode. One option in this experiment is to couple enough source power to get a clear signal (e.g. Ps=50µW over its full 58nm bandwidth at the photodiode). The LO power is fixed at 2mW at the photodiode. The IF-signal is amplified by two 35 dB gain LNA in series. The output of the square law detector dc-signal is digitalized and stored over 30min by means of a DAQ card (e.g. Meilhaus 9600, 2kHz sample rate). Given N samples of period τ, each of them represent the difference of measured signal minus reference during a fixed period, the Allan variance is defined:
( ) ( )22
1
0.51
N
A nn
T d dN =
σ = ⋅ −− ∑ (5)
where a certain number N of differences of two sets of data (e.g. sx ”mean signal-on”, rx ”mean signal-off) is used. The variance is computed for multiples of the period T (the Allan period, 100ms in our experiment):
( )1
1 1, ( , ) ' 'Nt
s r nt Tn
d x x x T t s t dt , d dT N−
=
= − = ⋅ = ⋅∑∫ (6)
where s(t) is the modulated signal function. The results of the Allan standard deviation are shown in a log-log plot on Fig. 6 along with the overlapping Allan STD, modified Allan STD and overlapping Hadamard STD [9]. The Allan plot can also be executed with no signal at all, just sampling pure noise. Then no chopping is required. In this form the method is applied at the ALMA receivers and gives good results, so that we apply it also for the plot in Fig. 6.
~
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Fig. 8: 30 minutes of stored data at 2kHz sampling rate
PSD of Data
log(F/Fs) -1 -2 -3 -4 -5 -6 -7 -8 -9
Log(
PSD
)
-15
-16
-17
-18
-19
-20
-21
-22
-23
-24
-25
-26
-27
-28
The Allan variance plot provides information about the maximum stable integration time (in our case. 1s), after which a chopping technique (signal – reference, “Dicke switch” receiver type) would be required to calibrate out the drifts. If needed, this optimum integration time may be increased by stabilizing the temperature environment of the amplifiers. 3.3 LO power dependence
We suppose the internal resistance of the photodiode does not change significantly along with the optical local oscillator power. Along with increasing the light power, its responsivity will linearly change, until the detector will be in saturated
τ0.001 0.01 0.1 1 10 100
σ(τ)
0.001
0.01
Overlapping Allan STDModified Allan STDOverlapping Hadamard STD
Fig. 7: Measured Allan Variance Plot
Fig. 9: Power Spectrum Density fitting to ( ) 0.48S f f
−= shows a spectrum close to white FM (1/f2). FS
is the sampling frequency (2kHz).
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regime at 23mW. The shot noise current from the LO power still predominate but the heterodyne photocurrent, the shot noise and the thermal noise should be expressed has [10]:
( )22
2
2
2 / 2
2
4
IF LO S
S LO
T
I P P
I eB P
kTBIR
= ℜ
= ℜ
=
: responsivity
quantum efficiency electron chargePlanck constant
frequency
ηe=hν
η :e :h :ν :
ℜ
: load resistivity
: phys. load temperature
R
T
(6)
As the LO power increases the photodiode response leaves its linear regime and can be approximated as: 2
0 LO LOI P P=ℜ −α + γ (7)
The parameters 0ℜ , α and γ of the photodiode can be determined from the I-V curve from Fig.2 (e.g. in our experiment
0ℜ = 0.8916 , α=10.107, and γ=2e-3). The photodiode responsivity 0ℜ can be derived from Eq.7
0 2 LOdI dP Pℜ = =ℜ − α and lead to the signal-to-noise ratio:
( )
( )
220
2 2
0
2 242 2
IF LO LO Sp
S TLO LO
I P P PSNR
kTI I B e P PR
ℜ − α= =
⎡ ⎤+ ℜ − α +⎢ ⎥⎣ ⎦
(8)
The optimized local oscillator power can then be derived from Eq.(8). In Fig.8 the maximum SNR is found for a LO power of 4.5mW. In case of a broad band signal PS is to be understood as distributed over the bandwidth B,
S SP p B= ⋅ , and the SNR is independent of the bandwidth.
Fig. 10: SNR versus LO power for signal power from 100pW to 1nW.
4. INTERFEROMETRY BETWEEN TWO RECEIVERS 4.1 Correlation and Fringe Detection
It is expected that the white noise of two individual receiver chains is canceled during correlation, and so the S/N-ration of fringes is very much enhanced. However, this has still to be investigated with our setup. Unfortunately, the implementation of the ROACH board takes longer than envisioned from the plenty of open source software available online through the CASPER community, and is still work in progress. The problems was yet that the model depends on theindividual drivers installed on the computer with runs the Xilinx Simulink compilation, which needs a special combination of Matlab and Linux (RedHat) versions. However, a proof of principle was demonstrated meanwhile digitizing the 20kHz-bandpass outputs from an old vector voltmeter, and correlating them off-line in Matlab.
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5. BEHAVIOR OF THE FIBERS 5.1 Free-space to fiber coupling efficiency
Coupling starlight into a single mode fiber is limited by atmospheric turbulence, mechanical misalignments, pointing errors and the optical merit function of the telescope optics which could cause a mismatching between the wavefront phase and amplitude and the nearly Gaussian fundamental mode of the SM fiber.
The single mode fiber is placed in the focal plane of the instrument: ideally the amplitude of the incoming wavefront is described by a Bessel function (Airy pattern). Because this is not well matched to a Gaussian function the maximum coupling efficiency is only about 80% [11]. When turbulence is present the coupling efficiency further decreases. The quality of the seeing is determined by the Fried’s parameter r0 which scales by r0 ∞ λ6/5. The seeing is also highly dependent of the observation site. We are planning a fiber coupling lock-loop to stabilize the star to first order to the fiber aperture.
5.2 Seeing and stabilization of the fiber input coupling
The seeing can be as good as 2” but can also be as bad as 20” [13]. It is formed in first order (for small telescopes) by a diffraction-limited star image moving around in this disk at a speed of about 20 Hz, and therefore can be corrected by a tip-tilt adaptive optics. The size of this seeing disk corresponds to up to 100 µm in the focal plane of a Newton telescope with f = 1 m. Our approach will be to use a dichroic beam splitter to reflect the visible light focal image of a star onto a quadruple silicon photodiode, while the near infrared (1550 nm) focal image is transmitted to the fiber. The fiber is mounted on a xy-piezoelectric translation stage with 100 µm range, which is controlled over a PID-lock-loop fed by the signal from the quad fotodiodes. The piezo allows correction speeds up to several hundreds of hertz. Instead of the quad photodiode, a more flexible option might be to use CCD astro cameras together with a lock-loop based on fast real-time software, which includes then also additional computer monitoring of the star positions in the two telescopes.
3 3.5 4 4.5 5 5.5 6 6.5 7 7.5 8 8.5 9 9.5 1010
0.4
0.45
0.5
0.55
0.6
0.65
0.7
0.75
System Aperture (F#)
Cou
plin
g ef
ficie
ncy
Fig. 11: Left panel: Monomode fiber coupling efficiency with spherical surface optics: Optimized coupling is given for f# = 5.5 . Right panel: Airy pattern intensity and phase in front of the fiber.
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5.3 Stabilization of the length of the local oscillator distribution fiber for larger baselines
When going over to larger baselines, optical path length fluctuations of the fiber surely need to be corrected by a line-length corrector (LLC) like used in the ALMA photonics system. For this, we will try to integrate one of the two demonstration prototype LLCs ALMA is not using anymore. Maybe a faster phase modulator has to be added to meet the fact that first fibers will be not buried.
6. FIRST MEASUREMENTS OF PHASE AND CROSS-CORRELATION 6.1 Phase measurements using a monochromatic source
In this set-up (Fig.9) we used the same laser source for the LO and source signal. The source is then highly monochromatic and spatially coherent as coupled to a large optical collimator the mean of a monomode fiber. The source is frequency shifted with a 50MHz AOS and amplified by an EDFA. A 200mm diameter collimated beam is then received by two small telescopes (F/4 - 1/2” optics) and coupled to monomode fiber. The photodiodes detect a 50MHz beat frequency when the LO and signal polarization are matched. This IF signal is then transmitted to a 1 GHz bandwidth Vector-Voltmeter. The phase difference from both channels can then be analyzed. The vector voltmeter down-converts the 50MHz IF signals to its 20kHz output channels that can be used for phase-measurement or cross-correlation.
6.1.1 Phase measurement with free-space coupling
Using a phase-stable monochromatic source (LO frequency-shifted by 55 MHz), the phase stability of the fiber setup was characterized. Also, fringes were simulated by mounting one of the “telescopes” (2.5 cm lens free-space to fiber couplers) on a PC-controlled micrometer displacement stage and digitizing and storing the phase variations. An example is shown on Fig.13. Similar measurements for the phase stability without any path length scan were first performed just within fibers.
50/50
1i 2i
Monomode Fiber Coaxial Cable
LASER Vector Voltmeter
EDFA
PC
FFS
Celestron Telescope
Coupling to fiber
90/10
50/50
Insulator
collimated beam
over1-2 m distance
10/90
Fig. 12: Bench-top interferometer experiment with coherent source and short fibers. FFS = Fiber Frequency Shifter 55MHz, PC =Polarization Controler, PDs =Photodiodes, EDFA = Erbium Doped Fiber Amplifier , FC = Fiber Coupler, Insulator, 8” Celestron telescope as collimator, AR-coated Lenses d=1” or 2”, f=200mm.
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The phase displacement is extremely sensitive to vibration, air flow and mechanical fiber stress. A long time measurement shows the phase drift in Fig.14.
6.2 Broadband source cross-correlation
A broadband super luminescent diode is used as the source, the LO remains a highly coherent laser. The broadband source is mixed with the LO at the photodiode, and the IF signal generated is amplified by 70 dB by two LNAs in series. The vector-voltmeter receives the signals, and we used its two 20 kHz outputs to compute the cross-correlation. The results are presented in the Fig.12 and 13, to be compared with the amplifier noise correlation (e.g. without LO nor source) and the monochromatic cross-correlation (e.g. source is 50MHz shifted with respect to LO). The cross-correlation results from a dual channel acquisition at 75kHz sampling rate. It points out that the principle of broadband detection is feasible. A series of Hairpin micro strips Bandpass filter are in design in order to evaluate the cross-correlation over different bandwidths within the 3GHz range.
Fig. 13: Left panel: Measuring drift and actuations (5 µm at 1 µm/s) with a coherent source and short fibers. Note some unexplained artefacts. Right panel: Phase stability. Zones A: Phase difference oscillation at the measurement range limit of the vector voltmeter, B: mechanical vibrations, C: drift
C
A
B
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ACKNOWLEDGEMENT
REFERENCES
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[2] B.F.Lane, “High-Precision Infra-Red Stellar Interferometry,” California Institute Of Technology, Pasadena, California (2003)
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We acknowledge support from the ALMA-Conicyt fund NÜ 31090018 for Chilean Astronomy, and from the ALMA project for the loan of some decommissioned pre-production components.
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