Substitute for Squats

I breathe properly, have good form, but I just CANNOT handle squats. I feel like passing out with the barbells anywhere near my shoulders. Are there other workouts that can strengthen my quads as efficiently? I can squat with the weights down just fine, but I don't know if I'm gaining strength.

I am up to 80lbs for deadlifts, and about 40lbs for lunges. (Total not per hand).