Equipment and methods for refractive surgery, including for keratoplasty. The invention describes equipment and methods for the production and implantation of a lamella of a tissue or material for the purpose of correcting a corneal geometry at maximum precision that is thus improved in relation to the prior art. The invention facilitates restoration of normal corneal geometry together with optical functionality of the cornea which is improved in relation to the prior art. A planning device, a treatment system and a planning method are designed to couple a device coordinate systems of the laser devices involved and characterization devices by application of registration and to uniquely register the supplied measurement data for generating the lamella to be implanted to the device coordinate systems by a specific, defined edge geometry of a blank from which the lamella is produced, and by the lamella, and by additional system and method aids.