A new Generation of Spectrometer Calibration Techniques based on Optical Frequency Combs
Typical astronomical spectrographs skk:appenzeller (); skk:huk2004 () have a resolution ranging between a few hundred to 200.000. Deconvolution and correlation techniques are being employed with a significance down to of a pixel. HeAr and ThAr lamps are usually used for calibration in low and high resolution spectroscopy, respectively. Unfortunately, the emitted lines typically cover only a small fraction of the spectrometer’s spectral range. Furthermore, their exact position depends strongly on environmental conditions. A problem is the strong intensity variation between different lines111see: www.eso.org/instruments/fors/inst/arc_lines_MIT/atlas_GRIS_1400V+18.jpeg – 587.6 nm He line overexposes while nearly no other line is visible between 400 and 690 nm (intensity ratios ). In addition, the brightness of the lamps is insufficient to illuminate a spectrograph via an integrating sphere, which in turn is important to calibrate a long-slit spectrograph, as this is the only way to assure a uniform illumination of the spectrograph pupil.
Laboratory precision laser spectroscopy has experienced a major advance with the development of optical frequency combs generated by pulsed femto-second lasers. These lasers emit a broad spectrum (several hundred nanometers in the visible and near infra-red) of equally-spaced ”comb” lines with almost uniform intensity (intensity ratios typically ). Self-referencing of the laser establishes a precise ruler in frequency space that can be stabilized to the 10 uncertainty level skk:stenger (); skk:zimmermann (), reaching absolute frequency inaccuracies at the 10 level per day when using the Global Positioning System’s (GPS) time signal as the reference. The exploration of the merits of this new technology holds the promise for broad-band, highly accurate and reproducible calibration required for reliable operation of current and next generation astronomic spectrometers. Similar techniques are also proposed in skk:constanza (); skk:murphy ().
1 Calibration of high resolution spectrometers
We will consider optical frequency combs based on fiber lasers that have a repetition frequency MHz, therefore producing an equally spaced spectrum with lines separated by 250 MHz. These systems have the advantage over Ti:Sapphire based frequency combs to be more reliable and require less maintenance. To resolve individual lines of the frequency comb, a resolution of more than , would be required. Therefore, astronomical spectrographs will see these devices as white light. For the calibration of high resolution spectrometers, we propose to filter the output of a frequency comb generator with external cavities as shown in Fig. 1(a). Interference inside the cavity leads to a frequency dependent transmission. The separation of transmission maxima (free spectral range: ) can be chosen via the length of the cavity, whereas the width of the maxima is determined by the reflectivity of the optical coating applied to the surfaces of the cavity mirrors.
By matching the repetition frequency of the optical comb to be an integer multiple of the cavity’s free spectral range (), the effective repetition frequency of the laser is increased to . If the transmission maxima have a spacing well exceeding the spectrometer’s resolution, and the frequency of one of the observed lines can be identified unambiguously, one can assign a precise frequency to all other observed lines simply by counting. This identification can be achieved by overlapping a cw laser (referenced to the frequency comb via one of the transmitted comb lines) with the comb spectrum before the filter cavity and observing the light of this laser on the spectrometer. At the same time, this laser serves as a reference to actively stabilize the length of the filter cavity and therefore its spectral properties. Due to limitations in the optical coatings, it is unlikely that a single filter cavity can cover the entire spectral range. A solution would be to spectrally split the output of the frequency comb laser into several wavelength regions, each filtered by an optimized cavity. The filtered output of the frequency comb will be similar to the solid line in Fig. 1(b). The recorded spectrum is a convolution between the filtered spectrum of the frequency comb and the spectrometer’s resolution (dashed line in Fig. 1(b)). The achievable quality of the optical coating (dispersion compensated bandwidth vs. reflectivity/absorption) determines the width of the transmission resonances. This may result in insufficient suppression of neighboring comb lines and thus shift the center of gravity of the line observed by the spectrometer. It will be difficult to exactly match the filter cavity’s free spectral range to the repetition frequency of the optical comb over the whole spectral range due to residual dispersion effects. This will result in an imperfect match of the comb lines to the transmission maxima of the filter cavity and thus induce a shift in the observed line center by as shown in Fig. 1(b)222Such a shift may not be an issue as long as it is reproducible and absolute frequency accuracy is not required..
In the following, we will give an estimate of the shift in line center calibration due to uncompensated dispersion in the filter cavity based on CRIRES (2 pixel Nyquist sampling resolution 1.5 GHz @ m). Emission line centers can currently be determined to within 0.05 pixels (0.001 pixels 0.75 MHz anticipated in future experiments) skk:huk2007 (). To achieve accurate fitting of the center of gravity of the maxima, a separation of 27 pixels is required. This corresponds to GHz. Fig. 2 shows the effect of a frequency shift between a comb line and a filter cavity resonance. The intensity of a single transmission maximum as seen by the spectrometer is periodic in (several comb lines contribute to each maximum with decreasing intensity as their distance from the maximum increases). The observed shift in the center of gravity exhibits plateaus as comb lines approach the transmission maximum of the cavity. From the inset in Fig. 2(b) we see that a maximum frequency shift between comb line and cavity resonance of 18 MHz can be tolerated to maintain the required line center accuracy of 0.75 MHz. Fig. 2(a) shows that at this shift, the intensity has reached 7% of its maximum value. This defines a threshold intensity below which the observed line is discarded for calibration purposes. Since the spectrum of the frequency comb can not be assumed uniform in intensity to that level, a scan of the frequency shift between cavity resonances and frequency comb teeth is required to calibrate the magnitude of the transmission maxima for each cavity resonance skk:schliesser ().
Even more stringent requirements in terms of reproducibility and resolution apply to e.g. HARPS and CODEX: At similar resolutions the required stability over a few months to several years has to be pixels skk:lovis_pepe ().
2 Calibration of mid resolution spectrometers
For medium resolution spectrometers with an effective resolution below 100.000, the stability of the frequency comb is not required. Instead, it can be replaced by a fiber laser-based high-brightness white light source that is then filtered by the cavities. In this case, the cavity transmission maxima provide the ruler required for spectrometer calibration. The dispersion properties of the cavity can be calibrated using a frequency comb as described in skk:schliesser (). We propose to use a cw laser locked to a stable reference (gas cells or a GPS-referenced frequency comb) to stabilize the length of the filter cavity to sub-MHz precision. A similar technique has been successfully implemented previously using an unstabilized cavity skk:bacon (); skk:foltz ().
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