## 2 Experimental Setup
For the experiment we used a gas cell also suitable for high pressure experiments as shown in Figure 2(left). Its volume amounts to 50 mL with an optical aperture of 25 mm and an absorption length of 100 mm. The optical windows consist of calcium fluoride (CaF\({}_{2}\)) suitable for spectroscopic investigations from UV to MIR with a pressure adopted thickness of 7 mm. Standard spectroscopy investigations up to a pressure of 800 kPa showed that with increasing pressure the cross broadening leads to broader lines, however, with also decreasing absorption strength. As a compromise between absorption strength and linewidth, we have finally chosen pure acetylene with an absolute pressure of 200 kPa. This selection has been also supported by HITRAN modeling [49] (see later under GS result discussion). A typical absorption spectrum measured by a Fourier Transform Interferometer (Bruker Vertex 80v) for these conditions is shown in Figure 2 (right) depicting the complex stretch and rotational vibration spectrum with more than 50 lines including the line at 1532.84 nm finally selected to be in the center of the investigations for the GS. Experimental Results and Discussions: Frequency Correlations of Light Emitted by the EDFA and Ghost Spectrum of Acetylene  
In first place, the basic requirement for a GS modality is quantified, namely the wavelength-wavelength correlations of the light source. Therefore, we exploit the broad-band ASE operation of the EDFA at an optical output power of 20 mW (corresponding to a pump power of 79 mW) resulting in a broad-band spectrum with a central wavelength of \(\lambda_{\mathrm{EDFA}}=1533\) nm, a FWHM of 3.8 nm and an obvious smaller tail up to 1570 nm (see Figure 3, magenta solid line). Figure 1: Schematic diagram of the experimental setup for the ghost spectroscopy (GS) experiment: The setup comprises the amplified spontaneous emission continuous-wave light source of an erbium-doped fiber amplifier (EDFA), collimating and focusing achromatic lenses (L), a fixed linear polarizer (LP), a non-polarizing beamsplitter (BS), a fixed reflective diffraction grating (GR) followed by a movable fiber coupling unit in the reference arm, thus enabling wavelength resolution, a high pressure gas cell filled with C\({}_{2}\)H\({}_{2}\) within the object arm, again followed by a fiber coupling unit, a single-mode fiber-based combiner (FC), a motorized linear translation stage (MS), polarization controlling elements (POL), lenses for focusing the light onto the photocathode of the PMT ( H7421-50, Hamamatsu Photonics, Hamamatsu, Japan) operated in Two-Photon-Absorption (TPA) mode and a longpass filter (LPF Schott RG1000, Schott, Mainz, Germany) preventing visible light from entering the detector. Figure 2: **Left**: High pressure absorption cell for the measurements; **right**: Conventionally measured standard absorption spectrum of acetylene around 1530 nm with an absorption length of 10 cm and an absolute pressure of 200 kPa. For the investigations of the wavelength-wavelength correlations a spectral band in one interferometer arm (here the object arm) is selected by utilizing a fiber-based fixed bandpass filter with a spectral transmission as depicted by the green line in Figure 3. Its central wavelength has been set to the maximum of the ASE spectrum of \(\lambda_{\mathrm{BFF}}=1532.3\,\mathrm{nm}\) and the spectral transmission is Gaussian-like with a FWHM of \(2.5\,\mathrm{nm}\). With an additional variable fiber-based band pass filter with a FWHM of \(1.4\,\mathrm{nm}\) in the reference arm, the reference signal has been realized and wavelength-wavelength intensity correlations have been determined. These wavelength-wavelength intensity correlations \(g^{(2)}(\tau=0,\lambda)\) are depicted as red data points in Figure 3. A dashed red line shows a Gaussian fit to the data. When the wavelengths of reference and object beam coincide, a maximum \(g^{(2)}(\tau=0)\) value of \(1.87\) is found.