title: Design of computer-generated hologram with ring focus for nonmechanical corneal trephination with Er:YAG laser in penetrating keratoplasty.
abstract: OBJECTIVE
  To calculate a beam-shaping optical element for homogeneous intensity distribution within a focal ring to be used in nonmechanical trephination with the Er:YAG laser in penetrating keratoplasty instead of a spot guiding device.
  
  
  METHODS
  The phase distribution behind a holographic optical element (HOE) k psi(u) can be described by the addition of the hologram phase phiH(u) to the beam phase phiE(u): k psi(u) = phiH(u) + phiE(u), k = 2pi/lambda, where u denotes the coordinates inside the hologram aperture, k an integer, and lambda the laser wavelength. To avoid discontinuous wavefronts leading to speckle noise, a smooth phase function is necessary. After transforming the hologram aperture coordinates into the focal plane x in a focal distance f, psi can be retrieved from the slope equation: inverted delta psi(u) = x(u) - u/f.
  
  
  RESULTS
  Creating a ring focus can be reduced to an essentially one-dimensional problem by separation of variables due to the symmetry condition. We calculated a computer-generated eight-level phase-only HOE with 4096 x 4096 pixels from a Gaussian-distributed 2.94 Er:YAG laser spot with a beam diameter of 10 mm and a focal distance of 100 mm. Thereby, a ring focus with an inner/outer radius of 7/8 mm can be created. To avoid Poisson's spo, the symmetry of the problem was broken by circular modulation of the phase leading to a spiral-like structure. The calculated efficiency of the HOE relating the energy within the ring to the total energy was 91%.
  
  
  CONCLUSIONS
  With an HOE it is possible to redistribute the energy along the desired focal ring. The HOE design can be adapted to the intensity distribution of the impinging laser beam with its characteristic aperture shape. A circular homogeneous corneal trephination depth is possible, because the energy fluctuation from pulse to pulse does not locally affect the ablation process. A ring focus for the Er:YAG laser has the potential to render superfluous a manual beam control via micromanipulator and to allow a more rapid and more regular corneal trephination along aperture masks.
authors.affiliation: Department of Ophthalmology, University of Erlangen-Nürnberg, Erlangen, Germany.
authors.forename: A
authors.initials: A
authors.lastname: Langenbucher
authors.forename: B
authors.initials: B
authors.lastname: Seitz
authors.forename: M M
authors.initials: MM
authors.lastname: Kus
authors.forename: G
authors.initials: G
authors.lastname: van der Heyd
authors.forename: M
authors.initials: M
authors.lastname: Köchle
authors.forename: G O
authors.initials: GO
authors.lastname: Naumann
mesh_terms: D003315:Cornea / Q000601:surgery*; D004867:Equipment Design; D006696:Holography / Q000295:instrumentation*; D006801:Humans; D007091:Image Processing, Computer-Assisted; D015948:Keratoplasty, Penetrating / Q000295:instrumentation*; D053685:Laser Therapy / Q000295:instrumentation*; D055095:Optics and Photonics