Stereoscopic image quality typically depends on two factors: i) the quality of the luminance image perception, and ii) the quality of depth perception. The effect of distortion on luminance perception and depth perception is usually different, even though depth is estimated from luminance images. Therefore, we present a full reference stereoscopic image quality assessment (FRSIQA) algorithm that rates stereoscopic images in proportion to the quality of individual luminance image perception and the quality of depth perception. The luminance and depth quality is obtained by applying the robust Multiscale-SSIM (MS-SSIM) index on both luminance and disparity maps respectively. We propose a novel multi-scale approach for combining the luminance and depth scores from the left and right images into a single quality score per stereo image. We also explained that a small amount of distortion does not significantly affect depth perception. Further, heavy distortion in stereo pairs will result in significant loss of depth perception. Our algorithm performs competitively over standard databases and is called the 3D-MS-SSIM index. © 2016 IEEE.