Bring forth thy righteousness as the light, &c.— i.e. "Perfectly clear up and vindicate thy integrity; which may for a time be obscured by calumnies and slanders, as the sun is by mists and clouds." Judgment, in the next clause, is only another word for righteousness or integrity.
Related Commentaries of Psalms 37:6
Psalms 37:6
6 And he shall bring forth thy righteousness as the light, and thy judgment as the noonday.