Modal noise mitigation for high-precision spectroscopy using a photonic reformatter

ABSTRACT Recently, we demonstrated how an astrophotonic light reformatting device, based on a multicore fibre photonic lantern and a 3D waveguide component, can be used to efficiently reformat the point spread function of a telescope to a diffraction-limited pseudo-slit. Here, we demonstrate how such a device can also efficiently mitigate modal noise – a potential source of instability in high-resolution multimode fibre-fed spectrographs. To investigate the modal noise performance of the photonic reformatter, we have used it to feed light into a bench-top near-infrared spectrograph (R ≈ 7000, λ ≈ 1550 nm). One approach to quantifying the modal noise involved the use of broad-band excitation light and a statistical analysis of how the overall measured spectrum was affected by variations in the input coupling conditions. This approach indicated that the photonic reformatter could reduce modal noise by a factor of 6 when compared to a multimode fibre with a similar number of guided modes. Another approach to quantifying the modal noise involved the use of multiple spectrally narrow lines, and an analysis of how the measured barycentres of these lines were affected by variations in the input coupling. Using this approach, the photonic reformatter was observed to suppress modal noise to the level necessary to obtain spectra with stability close to that observed when using a single mode fibre feed. These results demonstrate the potential of using photonic reformatters to enable efficient multimode spectrographs that operate at the diffraction-limit and are free of modal noise, with potential applications including radial velocity measurements of M-dwarfs.

Prediction of Fundamental Modal Field for Graded Index Fiber in the Presence of Kerr Nonlinearity

The power series formulation for modal field of single-mode graded index fibers by Chebyshev technique has worked excellently in predicting accurately different propagation characteristics in simple fashion. Here we develop a simple iterative method involving Chebyshev formalism to predict the modal field of single-mode graded index fiber in the presence of Kerr-type nonlinearity. Taking step and parabolic index fibers as typical examples, we show that our results match excellently with the available exact results obtained vigorously. Thus, the reported technique can be considered as an accurate alternative to the existing cumbersome techniques. Accordingly, this formalism will be beneficial to the technologies for evaluation of modal noise in single-mode Kerr-type nonlinear graded index fibers.

Experimental characterization of modal noise in multimode fibers for astronomical spectrometers

Context. High resolution spectroscopy at high signal-to-noise ratios (S/Ns) is one the key techniques of the quantitative study of the atmospheres of extrasolar planets. Observations at near-infrared wavelengths with fiber-fed spectrographs coupled to extremely large telescopes are particularly important to tackle the ultimate goal of detecting biosignatures in rocky planets. Aims. To achieve high S/Ns in fiber-fed spectrogrpahs, the systematic noise effects introduced by the fibers must be properly understood and mitigated. In this paper we concentrate on the effects of modal noise in multimode fibers. Methods. Starting from our puzzling on-sky experience with the GIANO-TNG spectrometer we set up an infrared high resolution spectrometer in our laboratory and used this instrument to characterize the modal noise generated in fibers of different types (circular and octagonal) and sizes. Our experiment includes two conventional scrambling systems for fibers: a mechanical agitator and an optical double scrambler. Results. We find that the strength of the modal noise primarily depends on how the fiber is illuminated. It dramatically increases when the fiber is under-illuminated, either in the near field or in the far field. The modal noise is similar in circular and octagonal fibers. The Fourier spectrum of the noise decreases exponentially with frequency; i.e., the modal noise is not white but favors broad spectral features. Using the optical double scrambler has no effect on modal noise. The mechanical agitator has effects that vary between different types of fibers and input illuminations. In some cases this agitator has virtually no effect. In other cases, it mitigates the modal noise, but flattens the noise spectrum in Fourier space; i.e., the mechanical agitator preferentially filters the broad spectral features. Conclusions. Our results show that modal noise is frustratingly insensitive to the use of octagonal fibers and optical double scramblers; i.e., the conventional systems used to improve the performances of spectrographs fed via unevenly illuminated fibers. Fiber agitation may help in some cases, but its effect has to be verified on a case-by-case basis. More generally, our results indicate that the design of the fiber link feeding a spectrograph should be coupled with laboratory measurements that reproduce, as closely as possible, the conditions expected at the telescope.

Monitoring Index of Transverse Collaborative Working Performance of Assembled Beam Bridges Based on Transverse Modal Shape

Transverse collaborative working performance (TCWP) is of great importantce to assembled beam bridges’ safety and serviceability, which can be charaterzied by the ability of transvese connections (hinge joints) to transfer force. This paper proposes a multi-beam model connected by distributed springs for assembled beam bridges’ modal characteristic analysis. Both the strain and displacement modal shape (surface) of this multi-beam model can be expressed as a product of longitudinal base function and transverse proportional coefficient vector, which can be obtained explicitly by solving a matrix eigenvalue problem. The transverse proportional coefficient vectors in the solutions can be seen as transverse modal shapes in a cross-section. Then, two types of monitoring indexes (baseline-free and baseline-required) based on transverse modal shapes for hinge joint damage detection and TCWP monitoring are constructed. The applicability of indexes proposed is proved by numerical simulations in different damage cases and index analysis in consideration of modal noise or not.