The first filtering step is displayed in Figure \ref{fig:grcmd} where we present a \(g\) vs \(g-r\) color-magnitude diagram combining the SDSS, CFHT/Megacam, and CAHA123 photometry. We chose \(g-r\) over the more extinction-sensitive \(u-g\) because the \(u-\)band observations are significantly shallower, and extremely sensitive to excesses related to accretion and activity.

The first diagram (on the left) represents the \(g\) vs \(g-r\) color-magnitude diagram for all sources in our combined database. The three color-magnitude diagrams to the right are a subset of the first, containing only sources projected against increasing contours of dust extinction of the Orion A cloud (about 4, 5, and 6 magnitudes of visual extinction). These column density thresholds were estimated from the \(^{13}\)CO map of \citet{Bally87}, cross-calibrated with the extinction map of \cite{Lombardi2011}. While directly using the extinction map of \cite{Lombardi2011} gives similar results, we preferred to avoid dealing with any possible systematics affecting this map caused by a potential substantial population of foreground sources. Because we imposed the condition of keeping only sources that are seen against increasing levels of dust extinction, the number of stars naturally decreases, because the solid angle on the sky decreases, and a clearly defined sequence appears. This sequence is not what is expected from the general Galactic population between Earth and the Orion A cloud at 400 pc, as confirmed with the Besaçon stellar population model \citep{Robin03}. From this step we retained the subsample of sources that is seen in projection against column densities higher than \(\sim5\) visual magnitudes of extinction (third panel in Figure \ref{fig:grcmd}), or a total of 2169 sources from more than 1.25\(\times 10^5\) sources in the combined SDSS–Megacam–CAHA123 catalog. Most of the discarded sources have colors consistent with unreddened and slightly reddened unrelated field stars toward the background of the Orion A cloud. Among the sources that pass the first filter there could be some with g-band excess emission, but these should have a negligible effect in the selection process, in particular because the next filtering step is performed in the near-infrared.

The second filtering step consists of discarding extincted sources. We aimed to remove any source from the sample that might be associated with the cloud (young stellar objects still embedded in the cloud, for example), as well as background sources that are bright enough to be detected at \(\sim\)0.487\(\mu\)m (g-band) through A\(_V\sim5\) mag of cloud material. We performed this filtering with a J\(-\)H vs. H\(-\)K color-color diagram where extincted sources are easily identified along the reddening band, away from their unreddened main sequence (and giant) colors \citep[e.g.][]{1992ApJ...393..278L,1998ApJ...506..292A,2001A&A...377.1023L}. We present in Figure \ref{fig:jhkcc} the J\(-\)H vs. H\(-\)K color-color diagram for the 2169 sources that passed the first filtering step. The size of the symbols in this figure is proportional to the J-band brightness. The selection criteria used to identify the likely foreground population were:

\label{eq:1} H <

\label{eq:2} J < 15

\label{eq:3} J-H<0.74 H-K>-0.2 H-K<0.43

Sources that are consistent with having no extinction within the photometric errors are marked in blue, while rejected sources are marked in red. Condition (1), the main filter, is taken as the border between extincted and non-extincted sources, which was selected to be roughly parallel to the main-sequence early M-star branch (to about the color of a M4-M5 star). Condition (2) and (3) additionally reject sources that are faint or have dubious near-infrared colors (either bluer than physically possible, or redder than main-sequence stars, suggestive of a near-infrared excess). Condition (2) in particular makes the selection more robust against photometric errors (the typical photometric error imposed by condition (2) is J\(_{err} \sim\) 0.03\(\pm\)0.01, H\(_{err} \sim\) 0.03\(\pm\)0.01, and K\(_{err} \sim0.03\pm0.01\) mag, which translates into a maximum A\(_V\) error of \(\sim\) 1 mag), and should reach a sensitivity limit capable of including M4 main-sequence stars at the distance of the cloud (J \(\sim\) 15 mag). More than two thirds of the 2169 sources are rejected (red sources) and a total of 624 sources have colors consistent with foreground stars suffering no or negligible amounts of extinction.¹