State of the art astrophysics demands extremely stable wavelength measurements, e.g. few cm/s scale Doppler radial velocimetry for Earth-like planet detection or multi-year cosmic redshift drift measurements. We present new techniques for 500 − 1000× improvement in stability using an interferometer in series with a spectrograph to form an Externally Dispersed Interferometer (EDI). When the received spectrum suffers a wavelength jitter, the phase of the moir´e pattern from the interferometer delay shifts in opposite directions for two signal paths, nonfringing and fringing; with appropriate weightings (“crossfading”) the net phase reaction cancels, stabilizing the spectrum. We present an improvement to our previous technique of multiple delays, using a single delay to crossfade, and demonstrate stabilization of ≳ 500× on existing Hale Telescope data. Single-delay EDIs are easier to construct and operate than those with multiple delays, and the EDI ensures that exactly the same pixels are used for the science and calibration signals, and in constant proportion under intensity fluctuations, greatly easing positional requirements.
We built an externally dispersed interferometer (EDI) testbed for exploring methods of improving high resolution spectrograph performance. We tested the EDI on the Keck Planet Finder (KPF) spectrograph May 11, 2022 measuring a Fabry-Perot (FP) etalon back lit by white light. This is also the first time an EDI has been used to measure a periodic source. The data shows that the EDI is useful for diagnosing the point spread function (PSF) width and shape, in particular the asymmetry of the PSF. This EDI ability comes because EDI can simultaneously measure both the conventional nonfringing spectrum, and the fringing derived spectrum. A conventional spectrograph resolution is limited by slit blur– the EDI resolution is not. A heterodyning effect shifts the fringing sensitivity peak to arbitrarily higher frequency, set by the interferometer delay value, and thus its resolution can exceed the spectrograph used alone. By comparing the Fourier transforms of the two measured signals, we can compare the phase shift changes, which gives information about the small asymmetry of the spectrograph blur, independent of the much larger asymmetry of the FP source spectrum. We show that comparing the phases of the nonfringing and fringing components versus harmonic number in the Fourier Transform is a useful method for measuring the asymmetry in the PSF. We report the first measurements of an EDI measuring a periodic source, which is a Fabry-Perot (FP) interferometer back illuminated by white light. The periodic character of the FP source created spikes in the Fourier transform, which was very convenient for analysis.
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