We present the first part of our DARTTS-S (Disks ARound TTauri Stars with SPHERE) survey: Observations of 8 TTauri stars which were selected based on their strong (sub-)mm excesses using SPHERE / IRDIS polarimetric differential imaging (PDI) in the J and H bands. All observations successfully detect the disks, which appear vastly different in size, from $approx$80 au in scattered light to $>$400 au, and display total polarized disk fluxes between 0.06% and 0.89% of the stellar flux. For five of these disks, we are able to determine the three-dimensional structure and the flaring of the disk surface, which appears to be relatively consistent across the different disks, with flaring exponents $alpha$ between $approx$1.1 and $approx$1.6. We also confirm literature results w.r.t. the inclination and position angle of several of our disk, and are able to determine which side is the near side of the disk in most cases. While there is a clear trend of disk mass with stellar ages ($approx$1 Myr to $>$10 Myr), no correlations of disk structures with age were found. There are also no correlations with either stellar mass or sub-mm flux. We do not detect significant differences between the J and H bands. However, we note that while a high fraction (7/8) of the disks in our sample show ring-shaped sub-structures, none of them display spirals, in contrast to the disks around more massive Herbig Ae/Be stars, where spiral features are common.
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