## 2 Experimental Setup
Towards larger and smaller wavelengths additional absorption lines are visible, however, with decreasing absorption strength according to the Gaussian envelope behavior due to the additional bandpass filter in the object arm as discussed above. The central \(g^{(2)}(\tau=0,\lambda)\) values exhibit a maximum of 1.43 at \(\lambda_{\text{A}}=1532.46\,\text{nm}\) and a local maximum of 1.36 at \(\lambda_{\text{B}}=1533.08\,\text{nm}\). In between these two maximum values, i.e., at the position of the central absorption line the normalized intensity correlations decrease to a minimum value of \(g^{(2)}(\tau=0,\lambda)=1.21\). The overall reduced second order correlation values from the maximum achievable value of two here in the spectroscopy experiment in comparison with the pure wavelength-wavelength correlation measurements (c.f. Figure 3), which there have been nearly fully observed are due to the fact that the object arm contains a wide range of uncorrelated wavelengths resulting in an overall spectral contrast reduction. This is in analogy to the spatial contrast reduction in ghost imaging when uncorrelated spatial multi-speckle contributions are superimposed in the bucket detection thus reducing the correlation signal contrast [20; 52; 53]. In order to evaluate the quality of the ghost spectrum and its coincidence with the real-world absorption spectroscopy results more quantitatively, the obtained GS values of \(g^{(2)}\left(\tau=0,\lambda_{i}\right)\) are underlined with data from the HITRAN database [49] shown in green in Figure 4 (left). The HITRAN transmission spectrum of pure acetylene has been modeled at a pressure of \(200\,\text{kPa}\), a temperature of \(296\,\text{K}\) and for an absorption length of \(10\,\text{cm}\). A corrected HITRAN spectrum \(T(\lambda)\) is then obtained by multiplying the normalized emission spectrum of the EDFA with the spectral bandpass. In order to quantify the quality of the linear correlation between the values \(g^{(2)}\left(\tau=0,\lambda_{i}\right)\) and the corrected  
Figure 4: **Left**: Ghost spectrum of an absorption feature of acetylene (C\({}_{2}\)H\({}_{2}\)) at a pressure of \(200\,\text{kPa}\) around \(1533\,\text{nm}\) measured with the setup of Figure 1. Conventionally measured standard absorption spectrum of acetylene (blue, left scale), corrected HITRAN transmission (green, left scale) and ghost spectrum (red, right scale) obtained via the spectral intensity correlations. The error bars correspond to the standard deviation of a set of 5 measurements. **Right**: Correlation between \(g^{(2)}\left(\tau=0,\lambda_{i}\right)\) and \(T\left(\lambda_{i}\right)\) evaluated in terms of the BP correlation coefficient according to Equation (3). HITRAN transmission strength \(T\left(\lambda_{i}\right)\), we make use of the Bravais-Pearson correlation coefficient \(R_{\text{BP}}\) as defined according to [54]  
\[R_{\text{BP}}=\frac{\sum_{i=1}^{n}\left(g^{\left(2\right)}\left(\tau=0,\lambda_{ i}\right)-g_{\text{mean}}^{\left(2\right)}\right)\cdot\left(T\left(\lambda_{i} \right)-\bar{T}\right)}{\sum_{i=1}^{n}\left(g^{\left(2\right)}\left(\tau=0, \lambda_{i}\right)-g_{\text{mean}}^{\left(2\right)}\right)^{2}\sum_{i=1}^{n} \left(T\left(\lambda_{i}\right)-\bar{T}\right)^{2}}. \tag{3}\]  
It gives a reliable measure on the confidentiality of a fit with \(-1<R_{\text{BP}}<1\) and \(R_{\text{BP}}=1\) representing full correlation. The variable \(n\) represents the total number of \(g^{\left(2\right)}\left(\tau=0,\lambda_{i}\right)\) values, while \(g_{\text{mean}}^{\left(2\right)}\) and \(\bar{T}\) represent the arithmetic means of all \(g^{\left(2\right)}\left(\tau=0,\lambda_{i}\right)\) and \(T\left(\lambda_{i}\right)\) respectively. The values \(T\left(\lambda_{i}\right)\) are the HITRAN transmission strengths for each wavelength of the corresponding \(g^{\left(2\right)}\left(0,\lambda_{i}\right)\) value.