\Delta \lambda_i$$

where $\Delta \lambda_i$ is the increment of wavelength per pixel. Finally, using the spectroscopic redshift ($z$) we calculate the rest frame [H$\alpha$]{} EW ($H\alpha_{EW_{rest}}$), which we use throughout the paper: $$\label{eq:Ha_EW_rest}
H\alpha\ EW = \frac{H\alpha\ EW_{obs}}{1+z}$$

We calculate EW errors by bootstrap re-sampling the flux of each spectra randomly within limits specified by its error spectrum. We re-calculate the EW iteratively 1000 times and use the 16$\mathrm{^{th}}$ and 84$\mathrm{^{th}}$ percentile of the distribution of the EW measurements as the lower and upper limits for the EW error, respectively. Since the main uncertainty arises from the continuum fitting, we do not consider the error of the [H$\alpha$]{} flux calculation in our bootstrap process.

The robustness of an EW measurement relies on the clear identification of the nebular emission line and the underlying continuum level. The latter becomes increasingly hard to quantify at high redshift for faint star forming sources due to the continuum not being detected. Therefore we derive continuum detection limits to identify robustly measured continua from non-detections.

In order to establish the limit to which our method can reliably measure the continuum, we select 14 2D slits with no continuum or nebular emission line detections to extract 