What produces blindness in the peripheral visual field of each eye's temporal hemiretinal half?

Hemi-field loss. Is usually due to a pathology posterior (behind) to the eye itself. A lesion or area of pathology will usually be located from the area of the pituitary gland (approx. just forward of central brain) where the optic nerves cross to anywhere along the optic radiation ending at the occipital lobe (portion of the brain at the lower back of the skull). An MRI or CT can usually identify the cause.