Towards 3D-photonic, multi-telescope beam combiners for mid-infrared astrointerferometry

Romina Diener; Jan Tepper; Lucas Labadie; Thomas Pertsch; Stefan Nolte; Stefano Minardi

doi:10.1364/OE.25.019262

1. Introduction

Astronomical interferometry is a technique allowing the synthesis of extremely large, diffraction-limited virtual telescopes through the coherent combination of electromagnetic radiation collected by several separate, relatively small-size telescopes. The foundations of this technique lie in the Van Cittert-Zernike theorem, which states that the spatial coherence function of light is the Fourier transform of the angular brightness distribution of the light source [1]. Today, astronomical interferometers operating at radio [2], sub-millimeter [3], infrared [4] or visible [5] wavelengths can deliver images of astronomical objects with angular resolutions at the milliarcsecond level (1 milliarsecond = 5 nrad). These resolution levels allow several unique science cases, such as the observation of relativistic jets ejected by accreting supermassive black holes in active galaxies [6], the observation of spots and temperature gradients on nearby giant stars [7–9] or the understanding of the inner structure of proto-planetary disks surrounding young stars [10,11]. In the last two decades, near-infrared (1.5–2.5 µm) interferometry has strongly benefitted from the application of advanced photonic technologies to astronomical instrumentation (astrophotonics [12]). Since the first demonstration that high precision light coherence measurements can be achieved by combining telescopes in single mode, optical fibre couplers [13], interferometric instruments moved swiftly from optical fibre to integrated optics (IO) technology [14,15]. Beside precision, IO technology can deliver additional calibration stability and miniaturisation of multi-telescope beam combination units. The current state-of-the-art in near-infrared interferometric astrohotonic instrumentation is represented by the GRAVITY instrument [16], which features an IO chip combining simultaneously up to 4 telescopes [17]. The success of the integrated optics approach to interferometry has motivated a few groups around the world to study the extension of integrated optics combiners to spectral bands beyond near-infrared [18–20], to implement IO reformatters for sparse aperture interferometry [21], to increase the number of combined telescopes [22], or to include nulling capabilities in the devices [23–25]. In this context, the three-dimensional (3D) structuring capability of ultrafast laser inscription [26,27] both enables the development of new beam combination geometries as well as components designed for optical bands ranging from visible to mid-infrared [19,20,28–31]. Interestingly, the progress in IO multi-channel interferometric beam combiners can also find valuable applications beyond astronomy, in particular in the field of miniaturised sensors for biophotonic [32] and quantum optics [33,34].

Here we report the progress towards the development of multi-telescope 3D-IO beam combiners optimised for the mid-infrared band centred at a wavelength of 3.4µm (known in astronomy as L-band). We present an experimental test of first prototypes allowing the combination of 2-and 4-telescopes based on two different architectures, namely the ABCD pairwise combiner [17] and the discrete beam combiner (DBC [35]). The experiments proved the capability of both our calibrated prototypes to retrieve precisely the amplitude of the visibility with signal to noise ratios exceeding 10 with several 100 counts per input channel and exposure. Phase could also be retrieved to a level sufficient to resolve the nonlinearity of our delay line. In the absence of an absolute photometric calibration of our cameras, we relied on numerical Monte-Carlo simulations to estimate the numerical stability of the fringe visibility retrieval algorithms for different levels of photon fluxes using the experimental and the ideal transfer matrix of the combiner. As result we could quantify the existing performance gap between the manufactured components and their ideal counterparts.

2. Mathematical description of interferometric beam combiners

Astronomical interferometric imaging requires a dense spatial sampling of the first order correlation function of electromagnetic fields, which is accomplished by combining pairs of (often movable) telescopes separated by a baseline. While the amplitude and phase of radio waves can be measured directly at the telescope and correlated at a later time, at optical frequencies only the measurement of the power of an interference modulation can be used to derive the field correlation functions. Because the fidelity of the reconstructed image increases with the number of sampled baselines, instruments allowing the simultaneous combination of more than two telescopes can reduce the acquisition time of the coherence function and provide snapshot images of the astronomical object. In general, simultaneous measurements of the coherence of all possible combinations of N optical fields ${\vec{E}}_{i} = {\hat{e}}_{i} E_{i}$ can be accomplished by measuring the irradiance of their linear superposition:

P = {〈 | \sum_{i = 1}^{N} {\vec{E}}_{i} | 〉}^{2} = \sum_{i = 1}^{N} 〈 | E_{i} |^{2} 〉 + \sum_{i \neq j}^{N} C_{i, j} 〈 E_{i} E_{j}^{*} 〉 = \sum_{i = 1}^{N} Γ_{i, i} + 2 \sum_{i = 1}^{N - 1} \sum_{j = 1}^{N} C_{i, j} ℜ Γ_{i, j}

where C_i,j = ê_i · ê_j takes into account the polarisation mismatch of the interfering fields (instrumental visibility) and

Γ_{i,j} = Γ_{j, i}^{*} \equiv 〈 E_{i} E_{j}^{*} 〉

are the mutual coherence functions (complex visibilities) [1]. In a beam combiner, the individual mutual coherence terms are in general retrieved by modulating in space or time the relative phase between the interfering fields. Irrespective of the combination technique, a multiple-field interferometric beam combiner can be described by a complex transfer matrix {U} relating the N input fields to M output fields. The power measured at the n^th output port of the device can be thus be written as:

\begin{array}{l} P_{n} = \sum_{i = 1}^{N} 〈 | U_{n,}_{i} E_{i} |^{2} 〉 + 2 \sum_{i = 1}^{N - 1} \sum_{j = i}^{N} C_{i, j} ℜ 〈 U_{n, i} E_{i} U_{n, j}^{*} E_{j}^{*} 〉 \\ = \sum_{i = 1}^{N} {| U_{n, i} |}^{2} Γ_{i, i} + 2 \sum_{i = 1}^{N - 1} \sum_{j = i}^{N} C_{i, j} [ℜ (U_{n, i} U_{n, j}^{*}) \cdot ℜ Γ_{i, j} - ℑ (U_{n, i} U_{n, j}^{*}) \cdot ℑ Γ_{i, j}] . n = 1, \dots M \end{array}

We notice that the power at the outputs is a linear combination of the self-coherence functions Γ_i,i (i.e. the power at the input ports) and the quadratures of the mutual coherence functions (real and imaginary parts of Γ_i,j). By arranging the coherence functions on a vector of length N²,

\vec{J} = {(Γ_{1, 1}, \dots Γ_{N, N}, ℜ Γ_{1, 2}, \dots ℜ Γ_{N - 1, N}, ℑ Γ_{1, 2}, \dots ℑ Γ_{N - 1, N})}^{T},

we can write Eq. (2) as:

\vec{P} = V 2 PM \cdot \vec{J},

where

\vec{P} = {P n}

is the vector with the power measurements at the output ports of the combiner, and V2PM is a M × N² real-valued matrix known in astrointerferometry as Visibility to Pixel Matrix [36]. The V2PM is often employed to extract complex visibilities from measurements with multi-telescope interferometric instruments [37]. From Eq. (2), it is straightforward to derive that the elements of the V2PM are related to the transfer matrix of the beam combiner by [35]:

\begin{array}{l} V 2 {PM}_{n, i} & = & i_{n, i} = {| U_{n, i} |}^{2} i = 1 \dots N \\ V 2 {PM}_{n, p(i, j)} & = & c_{n, p (i, j)} = 2 C_{i, j} ℜ (U_{n, i} U_{n, j}^{*}) & i < j j = 2 \dots N \\ V 2 {PM}_{n, q(i, j)} & = & s_{n, q (i, j)} = - 2 C_{i, j} ℑ (U_{n, i} U_{n, j}^{*}) & i < j j = 2 \dots N \end{array}

where the indices p(i, j) and q(i, j) are defined as follows:

p (i, j) = i + (j - 1) \cdot (j - 2) / 2 + N

q (i, j) = i + (j - 1) \cdot (j - 2) / 2 + N \cdot (N + 1) / 2

Given the $\vec{P}$ it is possible to find a vector $\vec{J}$ which minimise the residual $r = | V 2 PM \cdot \vec{J} - \vec{P} |$ . In practice it is necessary to compute the Moore-Penrose pseudo-inverse [38] of the·V2PM (also known as Pixel to Visibility Matrix or P2VM [36, 37]) and apply it to the known term $\vec{P}$ . Notice that a meaningful solution $\vec{J}$ exists whenever M ≥ N² (overdetermined linear system of equations). The singular value decomposition [38] of the V2PM can give a first estimate of the precision of the coherence retrieval procedure. The decomposition allows to calculate the condition number (CN) of the V2PM (defined as the ratio of the largest to the smallest singular value) which roughly gauges the noise amplification factor in the retrieval of the coherences from photometric measurements. The smaller the condition number, the more precise are the estimates of the mutual coherence functions. The V2PM elements can be used to estimate the instrumental visibility C_i,j. From the definition of the matrix elements (Eq. 5) it is possible to show [37] that:

C_{i, j}^{2} = \frac{\sum_{n = 1}^{M} (c_{n, p (i, j)}^{2} + s_{n, q (i, j)}^{2})}{\sum_{n = 1}^{M} 4 \cdot (i_{n, i} i_{n, j})} .

Regarding notations, in the following we will comply to the usual astronomical custom of expressing the retrieved mutual coherence functions in terms of their normalised amplitude V_i,j (the Michelson fringe visibility):

V_{i, j} = \sqrt{\frac{{(ℜ Γ_{i, j})}^{2} + {(ℑ Γ_{i, j})}^{2}}{Γ_{i, i} Γ_{j, j}},} i \neq j

and its phase ϕ_i,j:

ϕ_{i, j} = \tan^{- 1} \frac{ℑ Γ_{i, j}}{ℜ Γ_{i, j}} .

3. Fabrication of samples

We fabricated all devices by means of ultrafast laser inscription (ULI) in Gallium Lanthanum Sulfide (GLS) glass substrates [39], a glass featuring a wide transparency window ranging from the visible to the mid-infrared (cut-off wavelength 9–10 µm). ULI uses tightly focused, high intensity femtosecond laser beams to induce permanent, local structural modifications in dielectric media (see [26,27] for reviews). Depending on the material and laser parameters, the laser-induced modifications can enhance [19] or depress [20] the refractive index of the irradiated dielectric medium allowing the structuring of photonic devices (such as waveguides, and couplers) in three dimensions (3D). From the viewpoint of our application, the 3D capabilities are essential to avoid losses and cross-talk from waveguide crossover in pairwise ABCD combiners or to enable the beam combination capability in arrays of coupled waveguides ([40], see also below).

The ULI setup is based on an amplified Yb:KGW laser (PHAROS, Light Conversion) emitting 200 fs pulses at a wavelength of 1026 nm with a settable repetition rates up to 1 MHz. The setup includes a rotatable λ/2-plate and a linear polariser for precise tuning the laser power. The formation of nano-gratings [41] is avoided by converting the beam polarisation to circular with a λ/4-plate just before being focused in the substrate with a NA = 0.35 microscope objective. The substrate is placed on a movable 3-axis nano-positioning stage. We wrote the components using laser parameters and translation speed wich could induce positive variation of the refractive index of GLS, so that laser irradiation affected the core of the waveguides only. Writing parameters were optimised in order to obtain single mode waveguides featuring nearly circular propagating modes at a wavelength of 3.4 µm (18.6 µm ×21.7 µm mode field diameter) with a propagation loss of 0.9 ± 0.3 dB/cm (measured directly with cut back method). The waveguides exhibit a rectangular cross section (9.4 µm ×24.8 µm) and were manufactured by multipass writing [42] with 21 lines separated by 300 nm and the following laser settings: pulse length 500 fs, repetition rate 500 kHz, laser power 40 mW and speed 1 mm/s.

3.1. 2-telescope ABCD combiner

In astrointerferometry the term ‘ABCD beam combination’ stands for a 4-levels phase shifting interferometry method to determine unambiguously the phase of an interference pattern [43]. In practice, the spatial or temporal fringe is sampled at 4 equidistant phases separated by π/2. An implementation with integrated optics of the ABCD combination scheme is at the basis of the GRAVITY beam combiner [16] and consist on a 2-level construction of waveguide splitters and combiners [17]. At the first level, each of the two input waveguides are split in two. At the second level, pairs of waveguides (each originating from a different input waveguide) are combined in 2×2 directional couplers providing pairs of outputs which sample the fringe in phase opposition. To achieve the ABCD sampling, a section of waveguide with modified propagation constant is inserted in one of the waveguides feeding one of the output 2×2 couplers in order to introduce a π/2 phase shift between the combined fields. The realisation of this component with planar IO technology necessarily requires a waveguide X-crossing, which contributes to the cross-talk between the M = 4 output channels.

Our intention was to manufacture a component exploiting the capability of ULI to write waveguides in 3D and avoid the X-crossing. A sketch of the device is illustrated in Fig. 1(a). The design of the splitters at the first level (indicated by 1 and 2 in Fig. 1(a)) is based on the template of the 2×2 directional coupler we recently developed in GLS glass [31], which has an interaction length of 4 mm, a gap of 20.5 µm and features 75µm-high raised-sine s-bend waveguides of 7 mm length for the input and output waveguides. For test convenience we retained the two inputs waveguide of each of the couplers at the first level. The outputs of the first level of couplers were bended in the x-dimension to address the inputs of couplers 3 and 4 at the second level (maximal elongation 150 µm, total length 14 mm). The X-crossing of the waveguides was avoided by an additional 50 µm-high double raised-sine s-bend in the z-dimension. To preserve the optical path difference at the input of the couplers at the second level both output waveguides of coupler 1 have a negative z-displacement, while the output waveguides of coupler 2 have a positive z-displacement. The π/2 phase delay was introduced on one output waveguide of coupler 1 by a local increase of the writing speed (red segment in Fig. 1(a)). According to our measurements on single waveguides, an increase of the writing speed corresponds to a decrease of the propagation constant of the waveguide, so that a phase shift can be engineered between waveguides of equal geometrical path but different writing speeds. In our samples the writing speed was raised gradually from 1 mm/s to 1.4 mm/s over a 2.5-mm-long section, kept constant for another 1.2 mm and then decreased back to 1 mm/s within the final 2.5 mm. The gradual transition was necessary to avoid transition losses at the ends of the waveguide patch written at higher speed. While the design is not yet optimised, we mention that all s-bends had radii of curvature larger than 26 mm, in order to ensure losses below 1 dB per s- bend [31]. From independent measurements on straight and bended waveguides we estimated the losses of the manufactured ABCD combiner in about 6 dB (3.6 dB propagation losses and 2.4 dB from s-bends).

Fig. 1 Scheme of the 3D beam combiners tested in the experiments. (a) 2-telescope ABCD combiner with cross-over avoidance by 3D displacement of the waveguide path. Red path: region of the taper for insertion of a π/2 phase delay. Numbers on yellow background indicate the 4 couplers of the ABCD combiner. (b) 4-telescope discrete beam combiner featuring 23 straight coupled waveguides arranged in a zig-zag lattice geometry. The two interlaced layers are highlighted by the blue (lower array) and the red colors (upper array). (c) Transverse view of the zig-zag array indicating the numbering convention, the geometric parameters, and the input waveguides (in black).

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3.2. 4-telescope discrete beam combiner

Discrete beam combiners (DBC, [35]) are arrays of evanescently coupled waveguides (photonic lattices) designed to measure interferometric observables. A sufficient condition for the array to operate as an interferometric beam combiner is the presence of coupling between waveguides beyond the nearest neighbour [40]. This long-range coupling can be engineered by arranging the waveguides on a two-dimensional lattice. Three-telescope DBC featuring square lattice arrangements were manufactured and tested with monochromatic light [28] at visible wavelength. By a suitable dispersion of the output channels, the operation with polychromatic light was also proofed for applications in low-resolution spectro-interferometry [29]. We recently devised the zig-zag lattice geometry (Fig. 1(b) and (c)) as a way to satisfy at the same time the requirements of long-range coupling and the possible use of the device for high-resolution spectro- interferometry [44]. Two interlaced linear arrays featuring a total of M = 23, 25-mm-long straight waveguides are used for the purpose of beam combination. With reference to Fig. 1(c), the horizontal core-to-core separation of the waveguide is h = 21µm. The linear arrays are separated vertically by v = 10.8µm and shifted horizontally by s = h/2 = 10.5µm. Four 25-mm-long input waveguides were added to the waveguide array at the positions 5, 10, 14, 19 (black cores in Fig. 1(c)) to ensure the excitation of individual waveguides of the array. Because the ULI induces stress fields in the area surrounding each waveguide and leads to refractive index variations of at least 2 · 10⁻⁵ [44], we improved the uniformity of coupling across the array by increasing the inscription velocity linearly with the waveguide number at a rate of +0.075 mm/s per waveguide. We found experimentally that this correction improves the symmetry of the discrete diffraction patterns excited by symmetrically positioned input waveguides and additionally reduces the polarisation dependence of the output field. A possible explanation of the effect of this writing protocol is that it compensates for the additional refractive index change induced by the long range stress field induced by ULI.

The estimated losses of the DBC combiner are essentially propagation losses and amount to 4.5 dB.

4. Calibration and monochromatic interferometric test of the beam combiners

The test of the components consisted in calibrating initially their monochromatic V2PM and then use the P2VM to retrieve interferometric observables (quadratures and phase of the normalised coherence functions) from video recordings of the light distribution at the output of the components excited by pairs of phase-modulated optical fields.

The calibration of the V2PM follows the method discussed in Ref. [29] and consists in recording the photometry of the output channels of the device for single beam and twin-beam excitation. As can be inferred from Eq. (5), the normalised photometry with single beam excitation of the inputs of the device consists in the first N columns of the V2PM. The determination of the remaining columns is accomplished by recording the time varying photometry of all possible N · (N − 1)/2 input field combinations, which are modulated in phase through a delay line traveling at constant speed. The phase modulation induces sinusoidal oscillations at the M outputs (M = 4 for the 2-telescope ABCD, M = 23 for the 4- telescope DBC) of the component whose normalised amplitude and phase are projected onto quadratures, corresponding to the following N · (N − 1) columns of the V2PM. To improve the precision of the calibration, the raw photometric data were electronically filtered with a moving average to remove a high frequency electronic noise which artificially raises the visibility of the fringes [31].

The acquisition of the dataset with twin-beam input excitation is performed with a Michelson interferometer. A suitably collimated 3.39 nm He-Ne laser beam is split into two beams which are focused by a lens onto separate input waveguides of the components by slightly tilting one beam respect to the other. A computer-controlled, motorised delay line was used in one arm of the interferometer to introduce a controllable phase delay between the inputs. The minimal incremental delay of the stepping-motor is 100 nm (corresponding to a phase of 0.18 radians at λ = 3.39µm) and a positioning accuracy of 0.5%. The samples were mounted on a multi-axis positioning stage and their outputs imaged with a suitable dioptric system onto an InSb mid-infrared camera (measured noise level ~7 counts rms).

To test the numerical stability of the algorithm retrieving the interferometric quantities, we derived the P2VM from the experimentally determined V2PM and applied it to the calibration dataset. These measurements allowed us to estimate the standard deviation of the retrieved visibility and phase. From the average visibility $\bar{V}$ and its standard deviation σ_V we estimated experimentally the signal to noise ratio of the visibility amplitude as $SNR = \bar{V} / σ_{V}$ .

4.1. Retrieval of visibility and phase with the 2-telescope ABCD combiner

An insight on the characteristics of the ABCD beam combiner is given by the plots in Figs. 2(a) and 2(b), which represent the calibrated and ideal V2PM respectively. For single beam excitation the distribution of the light among the 4 outputs of the manufactured component is rather uniform, as indicated by the first two columns of the V2PM. The pattern of the last two columns of the experimental V2PM resembles the ideal. The amplitudes of the experimental pattern are smaller than the ideal due to a low instrumental visibility, which was measured to be C_1,2 = 0.30. Such a low instrumental visibility is most probably originating from long range stress birefringence induced by ULI. From the last two columns of the experimental V2PM the phase delay induced by the phase-shifter of the ABCD combiner can be measured, as the matrix elements are proportional to the quadratures of the cross-products of the field transfer function of the combiner (see Eq.(5)). The measured phase shift is 2.2 rad, which is about 0.6 radian more than the optimal delay value.

Fig. 2 False color representation of the experimental (a) and ideal (b) V2PM matrix of the 2-telescope ABCD beam combiner unit.

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Direct application of the calibrated P2VM on the dataset allows to retrieve a visibility V_1,2 = 0.92 ± 0.06, which is compatible with the the expected visibility of our laser source (V_1,2 = 1). However, because the first two columns of the experimental V2PM have nearly equal elements, the condition number of the matrix is very high (~ 65, the ideal V2PM is in fact singular for a 2T-ABCD combiner) and an improved retrieval of the visibility can be obtained by measuring independently the transmitted power of the individual beam and splitting the retrieval algorithm in two steps involving the use of two sub-matrices of the V2PM (see Ref. [37] for details). Figure 2 shows the results of the latter retrieval algorithm for the 2-telescope ABCD combination unit. The retrieved quadratures of the normalised visibility function (Fig. 3(a)) are distributed over a circle of average radius V_1,2 = 0.96 ± 0.034 (visibility signal to noise ratio of 28). The linear phase ramp between the two input fields (Fig. 3(b)) is measured correctly with a standard deviation of the residuals of σ = 0.20 rad, a value which can mostly be accounted for by the nonlinearity of the delay line (expected maximal deviation over the shown range < 0.4 rad). The average transmitted power of the two input beams were measured in ~2500 and ~ 1300 counts per frame, respectively.

Fig. 3 Experimental estimate of the retrieval precision of interferometric quantities for a 2-telescope ABCD combination unit. (a) plot of the the retrieved normalised quadratures of the coherence function (blue) as compared to the expected values (red circle). (b, Top) Retrieved unwrapped phase difference between the input fields and their deviation from linearity (b, Bottom) as a function of time-consecutive frames.

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4.2. Retrieval of visibility and phase with the 4-telescope DBC

We used the calibrated V2PM of the 4-telescope DBC (not shown) to estimate the instrumental visibility of for each baseline and found values ranging from 0.868 to 0.943 depending on the combined fields. These values are much higher than the values reported for the ABCD combiner possibly indicating a more balanced distribution of the stress birefringence in the DBC.

The relatively low condition number of the V2PM (~14) allowed us to retrieve the coherence functions applying directly the P2VM to a set of unfiltered photometric data for the pairwise excitation of the 4-telescope DBC. The quadratures of the normalised complex visibility and its phase are reported in Figs. 4 and 5. The experimental data are all scattered around circles of radius V_i,j = 0.96 − 1.04 depending on the chosen pair of inputs with a standard deviation compatible with the hypothesis of unitary coherence of the input laser beams. The SNR of the visibility measurement varies from 12 to 25. The linear phase ramp is also retrieved correctly with a standard deviation from linearity ranging from σ = 0.13 to σ = 0.17 (corresponding to λ/48 and λ/36, respectively), showing that the phase retrieval algorithm can reach a precision sufficient to measure the nonlinearities of the delay line (expected maximal deviation over the shown range < 0.2rad). The measured transmitted power for each input beam is about 1200 counts per frame.

Fig. 4 Experimentally retrieved quadratures of the complex visibility function for the 4-telescope DBC for all possible combinations of the input beams. The individual input sites are indicated with T followed by a number. As in Fig. 3, the red circle indicated the expected distribution of the quadratures for fully coherent interfering fields.

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Table 1. Instrumental visibilities for the baselines of the 4-telescope DBC as estimated from its calibrated V2PM.

View Table

5. Discussion of the results and outlook

The presented data show that the manufactured IO beam combiners can already be calibrated to retrieve precisely visibility and phase on pairs of monochromatic, mid-infrared excitation beams. However, because the absolute photon flux could not be calibrated in the experiments, we evaluated by means of a Monte Carlo simulation the relative performance of the calibrated combiners respect to the ideal V2PM of the ABCD and DBC architectures. The simulation tests the numerical stability of the retrieval algorithm by emulating the experimental determination of the signal-to-noise ratio of the amplitude of the fringe visibility for fully coherent input fields (V = 1). We created a statistical ensemble of 10000 synthetic photometric measurements by application of the V2PM (experimental or ideal) to an input consisting of fields of constant amplitude (equal for all combined telescopes and corresponding to the the detected photon number per telescope and exposure) and random phase. A random number with variance equal to the number of measured photons was added to the synthetic photometric data to simulate the photon shot noise in the photon-rich measurement regime. The visibility amplitude (Eq. 9) for each noise realisation was then calculated from the application of the P2VM to the synthetic photometric data and the SNR estimated from the average value and standard deviation of the ensemble.

Figure 6 illustrates the results of the simulations for the 2-telescope ABCD combiner (Fig. 6(a)) and the 4-telescope DBC (Fig. 6(b)). The blue lines represent the expected SNR for the ideal combiner, while the red lines represent the results obtained by using the experimentally measured V2PM. The multiple lines appearing in the DBC simulation correspond to different input combinations (baselines), which represents a peculiar feature of the DBC architecture. This feature can be exploited to equalise the SNR of the coherence measurements in arrays featuring telescopes of different diameter (such as the Very Large Telescope Interfreometer) by connecting the larger telescopes to the baselines featuring lower SNR. The comparison between the red and blue lines show that the manufactured components are not yet optimal. The ideal combiners have a SNR higher by a factor 3.6 and 1.7 than the experimental 2-telescope ABCD combiner and the 4-telescope DBC, respectively. Because the SNR scales as the square root of the detected photon number, the amelioration of the matching (at constant throughput) between the ideal and real component by improved manufacturing process could deliver devices with a better sensitivity evaluated at the level of +2.8 and +1.1 astronomical magnitudes for the ABCD and the DBC, respectively. Since the calibration data had a large signal-to-noise ratio, our understanding is that the gap in sensitivity between the experimental and the ideal combiner mainly reside in the departure of the transfer function of the manufactured combiners respect to the ideal one.

Regarding the relative sensitivity of the chosen architectures, the fact that for fixed number of photons the ABCD combiners show higher SNR than DBC is mostly due to the fact that the number of combined fields is different. In fact, because multi-telescope beam combiners have to split the N input light fluxes on more output channels, the signal-to-noise ratio of the visibility scales as $\propto \sqrt{I_{0} / N}$ , I₀ being the input detected flux per telescope [45]. Taking this scaling into account and assuming the same throughput for the two chips our conclusion is that both manufactured chips have comparable sensitivity (SNR~60 for 10⁵ detected photons/telescope/exposure). However, in the current implementation, the ABCD combiner is penalised by the bend losses which reduce the throughput respect to the DBC combiner by an estimated 1.5 dB.

Fig. 5 Experimentally retrieved linear phase ramps for the 4-telescope DBC for all 6 possible combinations of the input fields (baselines). The residual of a linear fit are also plot as a function of time, here given in number of consecutive frames. The standard deviation of the phase residual are indicated for each baseline.

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Fig. 6 Results of a Monte-Carlo simulation of the performance of the manufactured (red) and ideal (blue) beam combiners in the presence of photon shot noise (see details in the text). The signal-to-noise ratio of the retrieved visibility amplitude is plotted against the detected number of photons per input channel and exposure for the 2-telescope ABCD combiner (a) and the 4-telescope DBC (b). A feature of the DBC is that different baselines feature different sensitivities, as can be seen by the many lines of the same color in the plot.

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Because simulations indicate that there is room for improvement, we are currently working on the optimisation of the manufacturing process to obtain better components. In particular, we are targeting the reduction of the bend losses and improvement of the instrumental visibility of the ABCD combiner which are required before starting the development of more complex combiners allowing the combination of 4 or more telescopes with ABCD architecture. The measurement of throughput and characterisation of the samples with polychromatic light with simultaneous multi-field excitation is also foreseen in the near future. These additional data will allow us to understand the advantages of one architecture respect to the other and establish (e.g.) the trade-off between combination efficiency and effective throughput of the components.

In conclusion, we believe that the presented results provide a significant step forward towards the extension to the mid-infrared bands of integrated optics multi-channel beam combiners for astronomical interferometry, besides representing a first attempt to compare the performance of real IO beam combiners manufactured with different architectures but utilising the same technology platform and substrate material.

Funding

RD, JT, LL and SM acknowledge the support of the German Federal Ministry of Education and Research (BMBF) through the project ALSI (05A14SJA). (03Z1H534).

Acknowledgments

German Federal Ministry of Education and Research (BMBF) (05A14SJA, 03Z1H534).

References and links

1. M. Born and E. Wolf, Principles of Optics )Cambridge1999), Chap. 10. [CrossRef]

2. http://www.evlbi.org

3. https://almascience.eso.org/about-alma/alma-basics

4. http://www.eso.org/sci/facilities/paranal/telescopes/vlti.html

5. M. J. Ireland, A. Mérand, T. A. ten Brummelaar, P. G. Tuthill, G. H. Schaefer, N. H. Turner, J. Sturmann, L. Sturmann, and H. A. McAlister, “Sensitive visible interferometry with PAVO,” Proc. SPIE 7013, 701324 (2008). [CrossRef]

6. G. Giovannini, W. D. Cotton, L. Ferretti, L. Lara, and T. Venturi, “VLBI observations of a complete sample of radio galaxies: 10 years later,” Astroph. J. 552, 508–526, (2001). [CrossRef]

7. D. F. Buscher, J. E. Baldwin, P. J. Warner, and C. A. Haniff, “Detection of a bright feature on the surface of Betelgeuse,” Month. Not. R. Astron. Soc. 245, 7P–11P (1990).

8. J. D. Monnier, M. Zhao, E. Pedretti, N. Thureau, M. Ireland, P. Muirhead, J. P. Berger, R. Millan-Gabet, G. Van Belle, T. ten Brummelaar, H. McAlister, S. Ridgway, N. Turner, L. Sturmann, J. Sturmann, and D. Berger, “Imaging the Surface of Altair,” Science 317, 342–345 (2007). [CrossRef] [PubMed]

9. X. Haubois, G. Perrin, S. Lacour, T. Verhoelst, S. Meimon, L. Mugnier, E. Thiébaut, J. P. Berger, S. T. Ridgway, J. D. Monnier, R. Millan-Gabet, and W. Traub, “Imaging the spotty surface of Betelgeuse in the H band,” Astron. Astroph. 508, 923–932 (2009). [CrossRef]

10. R. van Boekel, M. Min, C. Leinert, L. B. F. M. Waters, A. Richichi, O. Chesneau, C. Dominik, W. Jaffe, A. Dutrey, U. Graser, T. Henning, J. de Jong, R. Köhler, A. de Koter, B. Lopez, F. Malbet, S. Morel, F. Paresce, G. Perrin, T. Preibisch, F. Przygodda, M. Schöller, and M. Wittkowski, “The building blocks of planets within the ‘terrestrial’ region of protoplanetary disks,” Nature 432, 479–482 (2004). [CrossRef] [PubMed]

11. ALMA Partnership, C. L. Brogan, L. M. Pérez, R. T. Hunter, W. R. F. Dent, A. S. Hales, R. E. Hills, S. Corder, E. B. Fomalont, C. Vlahakis, Y. Asaki, D. Barkats, A. Hirota, J. A. Hodge, C. M. V. Impellizzeri, R. Kneissl, E. Liuzzo, R. Lucas, N. Marcelino, S. Matsushita, K. Nakanishi, N. Phillips, A. M. S. Richards, I. Toledo, R. Aladro, D. Broguiere, J. R. Cortes, P. C. Cortes, D. Espada, F. Galarza, D. Garcia-Appadoo, L. Guzman-Ramirez, E. M. Humphreys, T. Jung, S. Kameno, R. A. Laing, S. Leon, G. Marconi, A. Mignano, B. Nikolic, L.-A. Nyman, M. Radiszcz, A. Remijan, J. A. Rodón, T. Sawada, S. Takahashi, R. P. J. Tilanus, B. Vila Vilaro, L. C. Watson, T. Wiklind, E. Akiyama, E. Chapillon, I. de Gregorio-Monsalvo, J. Di Francesco, F. Gueth, A. Kawamura, C.-F. Lee, Q. Nguyen Luong, J. Mangum, V. Pietu, P. Sanhueza, K. Saigo, S. Takakuwa, C. Ubach, T. van Kempen, A. Wootten, A. Castro-Carrizo, H. Francke, J. Gallardo, J. Garcia, S. Gonzalez, T. Hill, T. Kaminski, Y. Kurono, H.-Y. Liu, C. Lopez, F. Morales, K. Plarre, G. Schieven, L. Testi, L. Videla, E. Villard, P. Andreani, J. E. Hibbard, and K. Tatematsu, “The 2014 ALMA Long Baseline Campaign: First Results from High Angular Resolution Observations toward the HL Tau Region,” Astrophys. J. 808, L3 (2015). [CrossRef]

12. J. Bland-Hawthorn and P. Kern, “Astrophotonics: a new era for astronomical instrumentation,” Opt. Express 17, 1880–1884 (2009). [CrossRef] [PubMed]

13. V. Coudé du Foresto, S. Ridgway, and J.-M. Mariotti, “Deriving object visibilities from interferograms obtained with a fiber stellar interferometer,” Astron. Astrophys. Supp. Ser. 121, 379–392 (1997). [CrossRef]

14. F. Malbet, P. Kern, I. Schanen-Duport, J.-P. Berger, K. Rousselet-Perraut, and P. Benech, “Integrated optics for astronomical interferometry,” Astron. Astrophys. Suppl. Ser. 138, 135–145 (1999). [CrossRef]

15. J.-P. Berger, P. Hagenauer, P. Kern, K. Perraut, F. Malbet, I. Schanen, M. Severi, R. Millan- Gabet, and W. Traub, “Integrated optics for astronomical interferometry - IV. First measurements on stars,” Astron. Astrophys. 376, L31–L34 (2001). [CrossRef]

16. L. Jocou, K. Perraut, T. Moulin, Y. Magnard, P. Labeye, V. Lapras, A. Nolot, G. Perrin, F. Eisenhauer, C. Holmes, A. Amorim, W. Brandner, and C. Straubmeier, “The beam combiners of Gravity VLTI instrument: concept, development and performance in laboratory,” Proc. SPIE 9146, 91461J (2014). [CrossRef]

17. M. Benisty, J.-P. Berger, L. Jocou, P. Labelye, F. Malbet, K. Perraut, and P. Kern, “An integrated optics beam combiner for the second generation VLTI instruments,” Astron. Astrophys. 498, 601–613 (2009). [CrossRef]

18. L. Labadie, G. Martín, N. C. Anheier, B. Arezki, H. A. Qiao, B. Bernacki, and P. Kern, “First fringes with an integrated-optics beam combiner at 10 µ m A new step towards instrument miniaturization for mid-infrared interferometry,” Astron. Astroph. 531, A48 (2011). [CrossRef]

19. A. Rodenas, G. Martin, B. Arzeki, N. D. Psaila, G. Jose, A. Jha, L. Labadie, P. Kern, A. K. Kar, and R. R. Thomson, “Three-dimensional mid-infrared photonic circuits in chalcogenide glass,” Opt. Lett. 37, 392–394 (2012). [CrossRef] [PubMed]

20. S. Gross, N. Jovanovic, A. Sharp, M. Ireland, J. Lawrence, and M. J. Withford, “Low loss mid-infrared ZBLAN waveguides for future astronomical applications,” Opt. Express 23, 7946–7956 (2015). [CrossRef] [PubMed]

21. N. Jovanovic, P. G. Tuthill, B. Norris, S. Gross, P. Stewart, N. Charles, S. Lacour, M. Ams, J. S. Lawrence, A. Lehmann, C. Niel, J. G. Robertson, G. D. Marshall, M. Ireland, A. Fuerbach, and M. J. Withford, “Starlight demonstration of the Dragonfly instrument: an integrated photonic pupil-remapping interferometer for high-contrast imaging,” Mon. Not. R. Astron. Soc. 427, 806–815 (2012). [CrossRef]

22. G. Martín, T. Pugnat, F. Gardillou, C. Cassagnettes, D. Barbier, C. Guyot, J. Hauden, E. Huby, and S. Lacour, “Novel multi-telescopes beam combiners for next generation instruments (FIRST/SUBARU),” Proc. SPIE 9907, 990738 (2016). [CrossRef]

23. R. Errmann, S. Minardi, L. Labadie, B. Muthusubamanian, F. Dreisow, S. Nolte, and T. Pertsch, “Interferometric nulling of four channels with integrated optics,” Appl. Opt. 54, 7449–7454 (2015). [CrossRef] [PubMed]

24. H.-D. Kenchington Goldsmith, N. Cvetojevic, M. Ireland, P. Ma, P. Tuthill, B. Eggleton, J. S. Lawrence, S. Debbarma, B. Luther-Davies, and S. J. Madden, “Chalcogenide glass planar MIR couplers for future chip based Bracewell interferometers,” Proc. SPIE 9907, 990730 (2016). [CrossRef]

25. A. Arriola, B. Norris, N. Cvetojevic, S. Gross, J. Lawrence, M. Withford, and P. Tuthill, “First on-sky demonstration of a compact fully-integrated Photonic Waveguide Nulling Interferometer,” in Conference on Lasers and Electro-Optics, OSA Technical Digest, paper JF2N.4.

26. K. Itoh, W. Watanabe, S. Nolte, and C. Schaffer, “Ultrafast processes for bulk modification of transparent materials,” MRS Bulletin 31, 620–625 (2006). [CrossRef]

27. R. Gattass and E. Mazur, “Femtosecond laser micromachining in transparent materials,” Nat. Phot. 2, 219–225 (2008). [CrossRef]

28. S. Minardi, F. Dreisow, M. Gräfe, S. Nolte, and T. Pertsch, “Three-dimensional photonic component for multichannel coherence measurements,” Opt. Lett. 37, 3030–3032 (2012).

29. A. Saviauk, S. Minardi, F. Dreisow, S. Nolte, and T. Pertsch, “3D-integrated optics component for astronomical spectro-interferometry,” Appl. Opt. 52, 4556–4565 (2013). [CrossRef] [PubMed]

30. A. Arriola, S. Mukherjee, D. Choudhury, L. Labadie, and R. R. Thomson, “Ultrafast laser inscription of mid-IR directional couplers for stellar interferometry,” Opt. Lett. 39, 4820–4822 (2014). [CrossRef] [PubMed]

31. J. Tepper, L. Labadie, R. Diener, S. Minardi, J.-U. Pott, R. R. Thomson, and S. Nolte, “Integrated optics prototype beam combiner for long baseline interferometry in the L and M bands,” Astron. Astroph. 602, A66 (2017). [CrossRef]

32. A. Ymeti, J.S. Kanger, J. Greve, P.V. Lambeck, R. Wijn, and R.G. Heideman, “Realization of a multichannel integrated Young interferometer chemical sensor,” Appl. Opt. 42, 5649–5660 (2003). [CrossRef] [PubMed]

33. J. G. Titchener, A. S. Solntsev, and A. A. Sukhorukov, “Two-photon tomography using on-chip quantum walks,” Opt. Lett. 41, 4079–4082 (2016). [CrossRef] [PubMed]

34. R. J. Chapman, M. Santandrea, Z. Huang, G. Corrielli, A. Crespi, M.-H. Yung, R. Osellame, and A. Peruzzo, “Experimental perfect state transfer of an entangled photonic qubit,” Nat. Comm. 7, 11339 (2016). [CrossRef]

35. S. Minardi and T. Pertsch, “Interferometric beam combination with discrete optics,” Opt. Lett. 35, 3009–3011 (2010). [CrossRef] [PubMed]

36. E. Tatulli and J.-B. LeBouquin, “Comparison of Fourier and model-based estimators in single- mode multi-axial interferometry,” Month. Not. R. Astron. Soc. 368, 1159–1168 (2006). [CrossRef]

37. E. Tatulli, F. Millour, A. Chelli, G. Duvert, B. Acke, O. Hernandez Utrera, K.-H. Hofmann, S. Kraus, F. Malbet, P. Mège, R.G. Petrov, M. Vannier, G. Zins, P. Antonelli, U. Beckmann, Y. Bresson, M. Dugué, S. Gennari, L. Glück, P. Kern, S. Lagarde, E. Le Coarer, F. Lisi, K. Perraut, P. Puget, F. Rantakyrö, S. Robbe-Dubois, A. Roussel, G. Weigelt, M. Accardo, K. Agabi, E. Altariba, B. Arezki, E. Aristidi, C. Baffa, J. Behrend, T. Blöcker, S. Bonhomme, S. Busoni, F. Cassaing, J.-M. Clausse, J. Colin, C. Connot, A. Delboulbé, A. Domiciano de Souza, T. Driebe, P. Feautrier, D. Ferruzzi, T. Forveille, E. Fossat, R. Foy, D. Fraix-Burnet, A. Gallardo, E. Giani, C. Gil, A. Glentzlin, M. Heiden, M. Heininger, D. Kamm, M. Kiekebusch, D. Le Contel, J.-M. Le Contel, T. Lesourd, B. Lopez, M. Lopez, Y. Magnard, A. Marconi, G. Mars, G. Martinot-Lagarde, P. Mathias, J.-L. Monin, D. Mouillet, D. Mourard, E. Nussbaum, K. Ohnaka, J. Pacheco, C. Perrier, Y. Rabbia, S. Rebattu, F. Reynaud, A. Richichi, A. Robini, M. Sacchettini, D. Schertl, M. Schöller, W. Solscheid, A. Spang, P. Stee, P. Stefanini, M. Tallon, I. Tallon-Bosc, D. Tasso, L. Testi, F. Vakili, O. von der Lḧe, J.-C. Valtier, and N. Ventura, “Interferometric data reduction with AMBER/VLTI. Principle, estimators and illustration,” Astron. Astroph. 464, 29–42 (2007). [CrossRef]

38. W. H. Press, S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery,Numerical Recipes in C++: the Art of Scientific ComputingCambridge University Press, Cambridge, 2003.

39. H. Yayama, S. Fujino, K. Morinaga, H. Takebe, D. W. Hewak, and D. N. Payne, “Refractive index dispersion of gallium lanthanum sulfide and oxysulfide glasses,” J. Non-Cryst. Sol. 239, 187–191 (1998). [CrossRef]

40. S. Minardi, “Nonlocality of coupling and the retrieval of field correlations with arrays of waveguides,” Phys. Rev. A 92, 013804 (2015). [CrossRef]

41. Y. Shimotsuma, P.G. Kazansky, J. Qiu, and K. Hirao, “Self-Organized Nanogratings in Glass Irradiated by Ultrashort Light Pulses,” Phys. Rev. Lett. 91, 247405 (2003). [CrossRef] [PubMed]

42. Y. Nasu, M. Kohtoku, and Y. Hibino, “Low-loss waveguides written with a femtosecond laser for flexible interconnection in a planar light-wave circuit,” Opt. Lett. 30, 723–725 (2005). [CrossRef] [PubMed]

43. M. M. Colavita, “Fringe Visibility Estimators for the Palomar Testbed Interferometer,” Publ. Astron. Soc. Pac. 91,111–117 (1999). [CrossRef]

44. R. Diener, S. Minardi, J. Tepper, S. Nolte, and L. Labadie, “All-in-one 4-telescope beam combination with a zig-zag array of waveguides,” Proc. SPIE 9907, 990731 (2016). [CrossRef]

45. A. Glindemann,Principles of Stellar InterferometrySpringer, Berlin Heidelberg, 2011. [CrossRef]

Towards 3D-photonic, multi-telescope beam combiners for mid-infrared astrointerferometry

Abstract

1. Introduction

2. Mathematical description of interferometric beam combiners

3. Fabrication of samples

3.1. 2-telescope ABCD combiner

3.2. 4-telescope discrete beam combiner

4. Calibration and monochromatic interferometric test of the beam combiners

4.1. Retrieval of visibility and phase with the 2-telescope ABCD combiner

4.2. Retrieval of visibility and phase with the 4-telescope DBC

5. Discussion of the results and outlook

Funding

Acknowledgments

References and links

Cited By

Figures (6)

Tables (1)

Equations (10)

Optics Express