1. Introduction

Currently, the biggest monolithic or segmented optical telescopes such as the Very Large Telescope [1], the Keck [2] or Subaru telescopes [3], have diameters in the range of 10 m. This size limitation leads to an angular resolution in the range of 0.1 μ rad for a 1 μ m wavelength. To overcome this problem, it is possible to use the aperture synthesis technique, which was firstly demonstrated by Michelson [4]. For this purpose, the optical fields collected by two telescopes T_iT_j, spaced by a distance called baseline, are combined together. This two-telescope array works as a two-arm interferometer, and its highest angular resolution is related to the longest baseline. These diluted apertures are used to reach nano-radian angular resolution in ground based observatories such as VLTI [5] and CHARA [6] or in space missions [7]. These kinds of optical instruments are designed to analyze the spatial angular intensity distribution of an astronomical object. At the output of the interferometer, the detected signal, hereafter called the interferometric signal, is a fringe pattern modulated by the theoretical complex fringe visibility V_th = C_th exp(jφ_th). For a pair of telescopes, C_th is the fringe contrast and φ_th the phase, both related to the object spectrum. As discussed below in this letter, the Zernike Van Cittert theorem gives a relation between the visibility V_th and the object spatial angular intensity distribution O(Ω⃗), with Ω⃗ the angular separation of the object under test. Figure 1 gives an example of C_th and φ_th plotted as a function of the normalized baseline. Note that for these two non-symmetric objects, spectra have the same modulus but different phases. Therefore, the ability to measure the phase of V_th remains mandatory for non-symmetric image reconstruction. Unfortunately, atmospheric turbulence and/or instrument instabilities (particularly in space mission) induce random phase shifts on the visibility function. Consequently, a direct measurement of φ_th is impossible. To overcome this limitation, Jennison proposed the use of the phase closure technique [8]. The phase closure term is theoretically unaffected by the atmospheric turbulences or by the instrument instabilities, and allows for example: image reconstruction [9], the detection of close faint companions in astronomy [10] or the signature of planet transit events [11]. The phase closure technique can be achieved only with a three (or more) arm interferometer. In this paper, we report for the first time to our knowledge, the observation of an infrared source by a sum-frequency conversion interferometer, using the Jennison’s phase closure technique. In the following, this interferometer will be called upconversion interferometer. In our upconversion interferometer, the infrared light of the object under test, collected by each T_i telescope, is converted from infrared to visible wavelength. This way, the V_th complex visibility is acquired in the visible spectral domain. This experimental test has been achieved with a in-laboratory proof of principle experiment. This type of high angular resolution imaging instrument has to provide reliable contrasts and phase closure measurements. For this purpose, we took care to comply with the polarization [12] and spatial filtering [13, 14] requirements related to spatial coherence analysis. In a first step, we have developed our upconversion interferometer using telecommunication components to check that V_th is faithfully transfered from infrared to visible wavelength domain. In a previous work, the C_{i j} contrasts had been retrieved successfully in a two-arm upconversion interferometer [15]. The core of this paper describes the acquisition of the phase closure using our three-arm upconversion interferometer.

 

Fig. 1 Two different configurations of a non-symmetric object. The contrast and the phase of the object spectrum are plotted as a function of the normalized baseline between two telescopes. Without atmospheric turbulences, this phase is not corrupted and can be measured.

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2. Description of the Jennison’s phase closure technique

Figure 2 shows the principle of a one-dimension telescope array able to provide high angular resolution images for optical astronomy. The object under test is an unbalanced binary star with a spatial angular intensity distribution O(Ω⃗), where Ω⃗ is the angular separation. In our experimental setup, the binary star and the telescope array are along the same axis, so Ω₀ is the projection of Ω⃗ on the axis of the telescope. In the Fig. 2 configuration, the baseline T ₁ T ₂ (i.e the distance between T ₁ and T ₂) is fixed and equal to b. The distance T ₂ T ₃ can be set to nb with n an integer.

 

Fig. 2 Overview of a one-dimension telescope interferometer dedicated to high resolution imaging. O(Ω₀): spatial angular intensity distribution, Ω₀: angular separation. T_i is the i_th telescope. T ₃ can be relocated in different positions equal to nb with n an integer and b the baseline between T ₁ T ₂. Output data: fringe contrasts C_{i j} and object spectrum phases φ_{i j} related to a pair of telescopes T_iT_j corrupted by the turbulences phases φ_i at T_i and φ_j at T_j.

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As seen previously, the complex visibility is equal to:

In presence of atmospheric disturbances, the experimental complex visibility V_{i j} is given by Eq. (4). The phase closure ϕ is the linear combination of the arguments of the three experimental complex visibilities V ₁₂, V ₂₃ and V ₃₁ related to the pairs of telescopes T ₁ T ₂, T ₂ T ₃ and T ₃ T ₁ respectively:

The following part is dedicated to the description of an upconversion interferometer and how the phase closure technique was implemented.

3. Test of a laboratory high angular resolution upconversion interferometer

In this proof-of-principle experiment, the frequency upconversion took place in each arm of the upconversion interferometer. All the optical devices used in our test bench are polarization maintaining components and spatially single-mode. The wavelength conversion of a 1541 nm laboratory star to 630 nm was achieved in a Periodically Poled Lithium Niobate (PPLN) waveguide pumped by a 1064 nm YAG laser.

As seen previously, the phase closure technique requires at least, a three arm interferometer, so a third interferometric arm was added to our previous test bench. In order to demonstrate that the phase closure information can be transferred from the infrared to the visible spectral domain, we designed and implemented the three telescope interferometers as shown in Fig. 3. The experimental setup can be split up into four main subsystems:

 

Fig. 3 Experimental setup of the upconversion test bench. DFB: Distributed Feed Back laser at 1541 nm, CL: Collimating Lens, nb the baseline between a pair of telescopes T_iT_j with n an integer, Mux: allows the combination of the signal at 1541 nm and 1064 nm, PPLN: Periodically Pooled Niobate Lithium, MAFL: Multi-Aperture Fibre Linked Interferometer, T(° C): temperature controller, IF: Interference Filter at λ = 630 nm ± 20 nm, L: Lens. The delay lines are used for precision optical path length control in the infrared and visible interferometers.

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For our proof of principle experiment, we used telecommunication wavelength sources and components for practical and cost reasons. Nonetheless, these experimental results can be transposed to other wavelength domains. In our experiment, the object to be imaged was an unbalanced laboratory binary star. For this purpose, a 1 to 2 fibre coupler, with an adjustable photo-metric ratio called μ, allowed to route the optical light emitted by a distributed feed back laser (DFB)(λ_IR = 1541 nm). The two fibre outputs acted as a point like sources spaced by 27.9 μ m. The first coupler output was used directly as a point-like source. To ensure the spatial incoherence of this binary star, a 500 m fibred delay line was inserted in the second path, to induce an optical path difference longer than the 100 m coherence length of the DFB laser. The two fibre ends were placed in the focal plane of a collimating lens with a 1900 mm focal length and a 190 mm diameter. The resulting characteristics of our laboratory object corresponded to a binary star with an Ω₀ = 14.7 μ rad angular separation and an adjustable photometric ratio (μ). In our experimental configuration, the fluctuation of the air path between the star and the telescopes, and the small mechanical vibrations of the test bench acted as the atmospheric turbulence in a real telescope array.

In our experiment, assuming point-like sources, we can theoretically describe the angular intensity distribution of the object by:

In each arm of the upconversion interferometer, the infrared signal of the unbalanced binary star was mixed with a narrow-band pump source at 1064 nm and then injected in a PPLN waveguide. Each Ti-indiffused waveguide of 40 mm used had a 11.3 μ m poling periodicity and was temperature stabilized at about 90°C. This way, each signal was converted to a wavelength of about 630 nm. Notice that we did not focus our study on the conversion efficiency, that has been previously addressed for instance in [18, 19]. Each upconverted signal passed through an interference filter to block the residual pump radiation and then fed a single-mode fibre at 630 nm. In each arm, the upconverted optical fields were combined together with an X-cube (2002 patent 6363186 and [20]). This device had 4 inputs and 4 outputs. In our experimental configuration, it had been used as a symmetrical 3 to 1 coupler for the visible radiation mixing. The three upconverted interferometric arms were equalized. For this purpose the delay lines were tuned and the interferometric pattern was detected with a silicon avalanche photodiode. The raw data were analyzed to extract phase closure in the infrared and visible wavelengths at the same time.

4. Data acquisition processing and results

Figure 4 plots the phase terms as a function of time. As one can appreciate, the phase term φ (T_iT_j), related to the pair of telescope T_iT_j, is not constant over the time but the phase closure remains constant over all the acquisition. The object was a point-like source and the data were recorded with the infrared interferometer.

 

Fig. 4 The Phase terms of a point-like source are plotted for the three pairs of telescopes as a function of time. The phase closure term is the sum of the three phase terms.

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For the acquisition of the phase closure, in a first step, we had to calibrate the infrared and the visible interferometer with a point-like source (one star was switched-off). The raw data coming from both interferometers were analyzed and calibrated. With a point-like star, the phase closure is theoretically equal to 0. The Fourier Transform applied to the interferometric data allowed to correct the experimental bias up to reach ϕ = 0.

In a second stage, the secondary star was switched-on and the phase closures were recorded for the infrared and the upconversion interferometers as a function of μ with a fixed baseline configuration of the telescope array. These two stages had been realized for two configurations of the telescope array (Fig. 5). In the first one, the distance between T ₁ T ₂ was equal to b and T ₂ T ₃ was equal to 2b. In the second one, the distance between T ₁ T ₂ was equal to b and T ₂ T ₃ was equal to 3b. These measurements, obtained with the visible interferometer, were compared with the theoretical data and with the infrared reference interferometer at the same time. Figure 5 shows an excellent accordance between theoretical predictions (green dashed curves) and the upconversion (blue crosses) and classical interferometric (red crosses) data. The theoretical curve is based on Eq. (8) and Eq. (5) written for a three-arm interferometer. Each experimental point results from the average over a set of 30 phase closure acquisitions. The error bars (not plotted) are on the order of 5 mrad and 10 mrad for the upconversion and the infrared interferometer respectively. These small uncertainties of the phase closure show the stability in time of our upconversion interferometer. The error bars related to the photometric ratio μ are around ±3% for each point.

 

Fig. 5 Phase closure measurements as a function of the photometric ratio μ for two configurations of the telescope array. On the left (right) hand side n=2(3). Red (blue) × plots the infrared (visible) data. Green dashed curves report the theoretical data.

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5. Conclusion

This first proof-of-principle experiment clearly demonstrated that the phase closure can be transferred without any distortion into the visible spectral domain by using our upconversion interferometer. Being a key point for high resolution imaging, the phase closure acquisition after frequency conversion clearly demonstrates the reliability of our upconversion interferometer capabilities. We have developed our upconversion interferometer using single-mode and polarization maintaining components. To fit the astronomical observational constraints, we intend to operate our instrument with lower flux level (down to the photon-counting regime). We also have to work on broadband frequency conversion. Preliminary study on this point has already been realized [21] and we will have to adapt this technique in the high resolution interferometric context. Further, this new kind of interferometer will be applied to frequency conversion of broadband medium and/or far infrared spectra. In a more general way, the frequency conversion technique allows to benefit from mature optical components mainly used in optical telecommunications (waveguides, couplers, multiplexers. . .) and efficient low-noise detection schemes down to the single-photon counting level. Consequently, it could be possible to avoid lots of technical difficulties related to infrared optics (components transmission, thermal noises, thermal cooling, spatial filtering . . .). The frequency conversion technique could be used to have access to unexplored optical windows on ground observatories.