Ulrike Lemke

Modal noise prediction in fibre spectroscopy – I. Visibility and the coherent model

Fibre modal noise occurs in high spectral resolution, high signal-to-noise ratio applications. It imposes fundamental limits on the photometric accuracy of state-of-the-art fibre-spectrograph systems. In order to maximize the performance of current and future instruments it is therefore essential to predict fibre modal noise. To attain a predictive model we are using a dual approach, bringing theoretical assumptions in line with the experimental data obtained using a test-bench spectrograph. We show that the task of noise prediction can be reduced to determining the visibility of the modal pattern which can be measured at the detector plane. Subsequently, the visibility dependence of essential parameters is presented. This work will soon provide a basis for prediction of modal noise limitations in fibre-coupled spectrograph designs.

End effects in optical fibres

The performance of highly multiplexed spectrographs is limited by focal ratio degradation (FRD) in the optical fibres. It has already been shown that this is caused mainly by processes concentrated around the mounting points at the ends of the fibres. We use the thickness of rings produced in the far-field when a fibre is illuminated by a collimated beam, to estimate the size of the region where the FRD is generated. This requires the development of a new model, using features of existing ray-tracing and wave-based models, which fits existing data very well. The results suggest that the amount of FRD is primarily determined by the length of fibre bonded into the supporting ferrule. We point out the implications for the production of future fibre systems.

Simulation of complex phenomena in optical fibres

Optical fibres are essential for many types of highly multiplexed and precision spectroscopy. The success of the new generation of multifibre instruments under construction to investigate fundamental problems in cosmology, such as the nature of dark energy, requires accurate modellization of the fibre system to achieve their signal-to-noise ratio (SNR) goals. Despite their simple construction, fibres exhibit unexpected behaviour including non-conservation of etendue (focal ratio degradation, FRD) and modal noise. Furthermore, new fibre geometries (non-circular or tapered) have become available to improve the scrambling properties that, together with modal noise, limit the achievable SNR in precision spectroscopy. These issues have often been addressed by extensive tests on candidate fibres and their terminations, but these are difficult and time-consuming. Modelling by ray tracing and wave analysis is possible with commercial software packages, but these do not address the more complex features, in particular FRD. We use a phase-tracking ray-tracing method to provide a practical description of FRD derived from our previous experimental work on circular fibres and apply it to non-standard fibres. This allows the relationship between scrambling and FRD to be quantified for the first time. We find that scrambling primarily affects the shape of the near-field pattern but has negligible effect on the barycentre. FRD helps to homogenize the near-field pattern but does not make it completely uniform. Fibres with polygonal cross-section improve scrambling without amplifying the FRD. Elliptical fibres, in conjunction with tapering, may offer an efficient means of image slicing to improve the product of resolving power and throughput, but the result is sensitive to the details of illumination. We also investigated the performance of fibres close to the limiting numerical aperture since this may affect the uniformity of the SNR for some prime focus fibre instrumentation.

Characterising modal noise in fibre-coupled spectrographs for astronomy

Fibre modal noise occurs in high spectral resolution, high signal-to-noise applications. It imposes fundamental limits upon the photometric accuracy of state-of-the-art fibre-spectrograph systems. In order to maximize the performance of current and future instruments it is therefore essential to predict fibre modal noise. Explicitly theoretical approaches are often restricted to specific cases, therefore this paper focuses on the conditions relevant to astronomy. The goal of this work is to derive a reliable model which can be used for the optimization of future spectrograph designs. We give a description of experimental investigations undertaken in Durham, displaying preliminary results. The first laboratory tests of a square fibre have shown modal noise characteristics that are interestingly similar to standard circular fibre.

The Göttingen Solar Radial Velocity Project: Sub-m s−1 Doppler Precision from FTS Observations of the Sun as a Star

Radial velocity observations of stars are entering the sub-m s−1 domain revealing fundamental barriers for Doppler precision experiments. Observations of the Sun as a star can easily overcome the m s−1 photon limit but face other obstacles. We introduce the Gottingen Solar Radial Velocity Project with the goal of obtaining high-precision (cm s−1) radial velocity measurements of the Sun as a star with a Fourier Transform Spectrograph. In this first paper, we present the project and first results. The photon limit of our 2 minute observations is at the 2 cm s−1 level but is currently limited by strong instrumental systematics. A drift of a few m s−1 hr−1 is visible in all observing days, probably caused by vignetting of the solar disk in our fiber-coupled setup, and imperfections of our guiding system add further offsets in our data. Binning the data into 30 minute groups shows m s−1 stability after correcting for a daily and linear instrumental trend. Our results show the potential of Sun-as-a-star radial velocity measurements that can possibly be achieved after a substantial upgrade of our spectrograph coupling strategy. Sun-as-a-star observations can provide crucial empirical information about the radial velocity signal of convective motion and stellar activity and on the wavelength dependence of radial velocity signals caused by stellar line profile variations.

Performance estimates for spectrographs using photonic reformatters

Using a photonic reformatter to eliminate the effects of conventional modal noise could greatly improve the stability of a high resolution spectrograph. However the regimes where this advantage becomes clear are not yet defined. Here we will look at where modal noise becomes a problem in conventional high resolution spectroscopy and what impact photonic spectrographs could have. We will theoretically derive achievable radial velocity measurements to compare photonic instruments and conventional ones. We will discuss the theoretical and experimental investigations that will need to be undertaken to optimize and prove the photonic reformatting concept.

Modelling complex phenomena in optical fibres

We present a new model for predicting the performance of fibre systems in the multimode limit. This is based on ray-‐tracing but includes a semi-‐empirical description of Focal Ratio Degradation (FRD). We show how FRD is simulated by the model. With this ability, it can be used to investigate a wide variety of phenomena including scrambling and the loss of light close to the limiting numerical aperture. It can also be used to predict the performance of non-‐round and asymmetric fibres.

A new method for correcting fibre barycentre displacements in high resolution spectroscopy

Unpredictable displacements in the photocentre of an optical feed at the entrance slit of a spectrograph produce corresponding barycentre offsets that impose limits to very high resolution schemes. These limitations not only apply to direct light from a science object, but also light relayed via an optical fibre or image slicer. Several mitigation strategies are in development or are currently in use, however these all have potentially restrictive idiosyncrasies. An alternative approach is proposed to remove displacement effects from the spectra by nulling barycentre offsets. Correction is achieved by time-integrating at the detector a sequence of multiple normal and 180-degree inverted images of the input aperture, thus eliminating optical asymmetries about the axis of inversion, which is aligned orthogonal to the spectral direction. The flip is generated with a path-length compensated, non-dispersive ‘reversion prism’, driven on a high precision translation stage. The prism is periodically chopped in and out of the beam, and the resulting time-averaged image thus has an imposed central axis regardless of barycentre shifts. The method works regardless of the specifics of the spectrograph feed (fibre, multiple fibres, slit, slicer etc.) With a relatively simple and inexpensive scheme it should be possible to stabilise an image to better than one part in 104 potentially permitting detection down to cms-1 regimes. The concept is currently at a very early stage of development, so this paper outlines the basic principles and details a practical reversion component that is currently under development at Durham CfAI. There then follows a description of how the component will be implemented in a laboratory prototype scheme. The paper concludes with a proposed test plan and suggests the focus for future work.

A high-resolution Fourier transform spectrometer for astronomical observations and development of wavelength standards

At the Institute for Astrophysics Goettingen (IAG), we are purchasing a high resolution Fourier Transform Spectrograph (FTS) for astronomical observations and development of calibration standards aiming at high wavelength precision. Astronomical spectrographs that work in the regime of very high resolution (resolving powers λ/δλ≥105) now achieve unprecedented precision and stability. Precise line shifts can be investigated to conclude for an objects radial velocity relative to the observer. As a long-term scientific goal, the evolution of galaxy redshift due to dark energy can be monitored. Also, the detection of lower mass, down to Earth-like planets will become feasible. Here, M-dwarfs are promising objects where an orbiting exo-Earth can cause a wavelength shift large enough to be detected. Emitting mainly in the near infrared (NIR), these objects require novel calibration standards. Current schemes under consideration are gas cathode lamps (e.g. CN, UNe) and a highly stable Fabry-Perot interferometer (FPI) to act as a cost-efficient alternative to the laser frequency comb (LFC, [1]). In addition to experiments exploring novel wavelength calibration types, light will be fed from our telescopes at IAG. A Vacuum Tower Telescope (VTT) for solar observations and the 50 cm Cassegrain telescope allow to investigate stellar and spatially resolved light at our facilities.