Table 7: Accuracy of the $K_{\rm S}=12$ mag criterion to separate companions and background stars. This table contains 69 out of the 72 secondaries with multi-color observations in the ADONIS or NACO dataset. Three secondaries (1 candidate companion; 2 background stars) for which no $K_{\rm S}$ magnitudes are available, are not included. The first column shows the status of the secondary (c = confirmed companion, ? = candidate companion, b = background star). Columns 2 to 5 list the distribution over status for secondaries with $K_{\rm S}<12$ mag and $K_{\rm S}>12$ mag. Depending on the true nature of the candidate companion stars, the $K_{\rm S}=12$ mag criterion correctly classifies the secondaries in $\sim$ 80% of the cases.
Status $K_{\rm S}<12$ mag $K_{\rm S}>12$ mag Total

c 23 (70%) 2 (6%) 25

? 4 (12%) 7 (19%) 11

b 6 (18%) 27 (75%) 33

Total 33 (100%) 36 (100%) 69

**Table 7:** Accuracy of the $K_{\rm S}=12$ mag criterion to separate companions and background stars. This table contains 69 out of the 72 secondaries with multi-color observations in the ADONIS or NACO dataset. Three secondaries (1 candidate companion; 2 background stars) for which no $K_{\rm S}$ magnitudes are available, are not included. The first column shows the status of the secondary (c = confirmed companion, ? = candidate companion, b = background star). Columns 2 to 5 list the distribution over status for secondaries with $K_{\rm S}<12$ mag and $K_{\rm S}>12$ mag. Depending on the true nature of the candidate companion stars, the $K_{\rm S}=12$ mag criterion correctly classifies the secondaries in $\sim$ 80% of the cases.
Status	$K_{\rm S}<12$ mag	$K_{\rm S}>12$ mag	Total
c	23	(70%)	2	(6%)	25
?	4	(12%)	7	(19%)	11
b	6	(18%)	27	(75%)	33
Total	33	(100%)	36	(100%)	69

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