resolution of the optical setup at the position of the SLM, one given frequency component illuminates several pixels of the SLM. To describe this effect, we convolve $\Gamma(\omega_i, \omega_s)$ with the point spread function $$\label{eq:PSF}
PSF(\omega_i,\omega_s)=\exp\left(-\frac{(\omega_i^2+\omega_s^2)\, 2\ln2}{\Delta \omega_{PSF}^2}\right)$$ to obtain $$\label{eq:gamma_PSF}
\Gamma_{PSF}(\omega_i,\omega_s)\propto(\Gamma\otimes PSF)(\omega_i,\omega_s).$$ The width $\Delta \omega_{PSF}$ depends on the imaging distances and the optical elements within the experimental setup. Equation (\[eq:gamma\_PSF\]) is in particular used to determine the Schmidt basis functions in section \[Schmidt\]. Figure \[fig:Gamma\] depicts $\Gamma(\omega_i,\omega_s)$ and $\Gamma_{PSF}(\omega_i,\omega_s)$ showing that the effect of the PSF is a considerable broadening of the joint spectral amplitude along the diagonal direction.

Entanglement quantification
---------------------------

In order to quantify the degree of entanglement between the idler and signal photon we use the von Neumann entropy $E=-\Tr(\hat{\rho}_{i,s}\log_2 \hat{\rho}_{i,s})$. The entropy is commonly referred to be a valid quantifier of entanglement between two subsystems of a pure entangled state with individual density operators $\hat{\rho}_{i,s}$ [@bennett1996]. Through a numerical approximation method [@wihler2012] we calculated the entropy of $\Lambda(\omega_i,\omega_s)$ and $\Gamma(\omega_i,\omega_s)$ for a pump spectral bandwidth of $\Delta \nu_p=5$ MHz and further experimental parameters of the preparation and the detection crystals. For $\Lambda(\omega_i,\omega_s)$ we obtain $E=(21.8 \pm 0.1)$ ebits. The entropy is calculated to be 