A patient interface for an ophthalmic system can include an attachment portion, configured to attach the patient interface to a distal end of the ophthalmic system; a contact portion, configured to dock the patient interface to an eye; and a contact element, coupled to the contact portion, configured to contact a surface of a cornea of the eye as part of the docking of the patient interface to the eye, and having a central portion with a central radius of curvature Rc and a peripheral portion with a peripheral radius of curvature Rp, wherein Rc is smaller than Rp.