La labor de la maestra 59

To perform an absolute calibration of the spectrograph, a relation between the frequency of the light and the CCD pixel it is illuminating must be established, the calibration curve. To first order, the number of the pixel on which a comb’s mode is imaged, will be proportional to the mode’s frequency. Projections, aberrations and other effects, however, will lead to a nonlinear frequency-to-pixel map. With a comb mode spacing of 3 GHz the calibration curve of the VTT spectrograph was derived in a single acquisition using 57 lines (see figure 4.4). A quadratic model is appropriate, as higher order polynomials do not reduce the scatter of the residuals further. The standard deviation of the quadratic residuals is 9 m/s, which is already better than any calibration one could hope to achieve with spectral lamps (see section 5.6). Comparing the residuals of the calibration curve with the photon noise limit of 0.8 m/s for this acquisition, it is obvious that a quadratic model is too simple

(a) (b)

Figure 4.4: (a) Fitted line center positions of 57 comb modes (black) and residuals from a linear fit (red) versus the mode number of the unfiltered comb. The filter ratio ism= 12, leading to a 3 GHz mode spacing. Some modes could not be considered as they coincided with large detector artifacts and/or the cw laser. The average slope is 172 MHz per pixel and the linear residuals still show a strong quadratic dependency. (b) Residuals from a quadratic fit to the line center versus position distribution. The standard deviation (SD) of the residuals is 9 cm/s and the quadratic fit largely reduces the residuals with respect to the linear fit. A higher order fit, however, will not improve the SD of the residuals, which is shown in the inset.

for the frequency-to-pixel map. There is probably an unmodelled, fine structure on the calibration curve that derives from pixel-to-pixel or even intrapixel sensitivity variations. With a frequency comb, this could be mapped by tuning the comb modes and thereby scanning over each pixel, but this was not done in this first test.

In cosmic astronomy, it is usually unnecessary to determine the absolute redshift of an object on the m/s scale or better. This is different when observing the Sun. For example, in helioseismology, it is interesting to measure the absolute velocity of the solar surface, i.e. whether it is moving up- or downwards. A calibration of the spectrograph with a frequency comb will be able to provide this information on the sub-m/s scale.

Calibration of a high precision,

astronomical spectrograph

5.1

The HARPS spectrograph

For many years, being able to detect changes in radial velocity below one m/s seemed an impossible task. For typical high resolution spectrographs, this varia- tion in redshift corresponds to a change of the stellar line’s position on the CCD approximately 1/1000 of a pixel or about 10 nm! A temperature variation by 1 K or the change of atmospheric pressure by 1 mbar would already produce effects on the order of 100 m/s [87]. Nevertheless, in 1998, ESO decided to develop a spectrograph dedicated to the search for extrasolar planets with a resolution of 1 m/s or better. This resulted in the “High Accuracy Radial velocity Planet Searcher” (HARPS) being constructed by a consortium led by the Geneva Observatory and installed in 2003 at ESO’s 3.6 m telescope at La Silla Observatory in Chile. It is a fiber-fed, cross-dispersed echelle spectrograph with a resolution of R= 115000. It covers the wavelength range from 380 to 690 nm in 73 echelle orders from order 89 to 161. The fiber output facet is imaged on the detector, a mosaic of two 2k × 4k CCDs. Each extracted pixel (i.e. after summing up ∼ 9 pixels in the cross-dispersed direction) can linearly accumulate more than 250000 counts, allowing for a S/N of 500. The CCDs are arranged with a gap between them, such that one echelle order (number 115, containing 530 to 534 nm) cannot be observed.

To be able to realize the ambitious sensitivity for radial velocity variations, sev- eral measures were taken to reduce both systematic and statistic uncertainties. An optimal resolution was chosen according to a carefully determined trade-off between the size of the instrument and telescope, the slit coupling efficiency (i.e. photon noise) and spectral resolution [87]. Together with the wavelength range this deter- mines the photon noise limited repeatability (see sections 2.3 and 2.5). According to equation (2.20), and considering a larger prefactor of≈ 0.55 (accounting for the spectral range, see [21]), the optimum photon noise limited repeatabiltiy of HARPS

amounts to σtotal_v ≈0.55 500 500 1.5×105 1.15×105 1.5 cm/s = 0.8 cm/s, (5.1) when calibrating the instrument with a frequency comb that has a mode spacing of 15 GHz. Although being designed for sub-m/s repeatability only, HARPS has the potential of detecting shifts on the cm/s scale, provided that instrumental drifts can be tracked reliably.

Obtaining photon noise limited uncertainty of the stellar spectra requires the elimination of all systematic effects of the detection on that level. The spectrograph is put in a vacuum vessel, evacuated to below 0.01 mbar and temperature stabilized with a long term stability on the order of 0.01 K and day-to-day variations of about 0.001 K [166]. The detector is operated at liquid nitrogen temperature with a re- sulting stability of ±0.02 K. However, not only must the instrument be as stable as possible, but the beam entering the spectrograph also must not vary. Therefore the light is fiber coupled and the position of the star’s image at the telescope’s focal plane is servo-controlled to always be centered with the fiber’s input facet. Addi- tionally, a passive fiber scrambler is installed which exchanges the fiber’s near and far field to reduce the residual preservation of an asymmetric illumination of the input facet.

With these measures and a generally very stable and robust mechanical design, HARPS has a passive stability of better than 1 m/s over a month [16]. To be able to measure the residual drifts of the spectrograph and to further improve its performance, it is fed by two fibers whose images are separated on the CCD by≈15 pixels in the cross-dispersed direction. In normal operation, one fiber delivers the starlight while the second fiber is continuously fed with calibration light. Any global drift of the instrument is monitored and can be subtracted from the data. With this simultaneous calibration scheme it could be shown that the spectrograph’s average drift is on the order of 10 cm/s during approximately an hour and a repeatability of 20 cm/s is feasible, using a Th-Ar lamp for calibration [16].

With HARPS being the most stable spectrograph to date, it is naturally the optimum choice for testing a frequency comb as a calibration source. Twice during the period of this work, in January 2009 and March 2010, we had the chance to be granted highly sought-after observation time at this instrument. The time that we had already spent at the VTT, helped us tremendously in being well prepared for a successful campaign in La Silla. In this chapter, the detailed analysis of the performance of a frequency comb as calibrator for an astronomical spectrograph is presented.

Figure 5.1: Sketch of the experimental setup of the calibration tests at HARPS. A Yb- fiber based laser frequency comb is filtered with two Fabry-P´erot cavities (FPC 1+2), which results in a mode spacing of f_r0 = 14-18 GHz. In the following second harmonic genera- tion stage (SHG) the comb spectrum is frequency doubled to ≈ 520nm. In a photonic crystal fiber (PCF) the spectrum is broadened to more than 100 nm bandwidth and then the light is coupled to a multimode fiber via a fiber collimator. Traversing a fiber shaker, the comb light is fed together with light from a conventional ThAr calibration lamp via the telescope’s calibration unit (TCU) through the telescope’s focal plane (TFP) to the HARPS spectrograph. F1, F2 and F3 refer to the fibers between the different units, which have a core diameter of 1 mm, 300µm and 70µm, respectively. At the TFP, apertures can be set, such that light coming from any of the F2 fibers or the telescope can be coupled to any of the F3 fibers. Fiber amplifiers situated before, between and directly after the FPCs are not illustrated. They compensate for the power losses due to the rejected modes of the filter stages.