title: Potential use of cubic phase masks for extending the range of clear vision in presbyopes: initial calculation and simulation studies.
abstract: In this paper we analyse the potential use of a non-symmetrical optical element, a cubic phase mask, for extending the range of clear vision of presbyopic eyes. Additionally, we will discuss the appropriateness of the visual Strehl ratio to analyse this sort of presbyopic solution based on non-symmetrical phase masks contrasted with through-focus retinal images.
  
  
  
  In order to evaluate the performance of the cubic phase mask we employed computational Fourier Optics to compute the different visual Strehl criteria as well as simulate the retinal images. The through focus real part of the modulation transfer functions and retinal images were computed for four object distances 6.0, 1.0, 0.6 and 0.4 m which correspond to far, intermediate and near vision conditions for optotypes of visual acuity of 0.1 and 0.0 logMAR (Snellen 6/7.5 and 6/6; 0.8 and 1 in decimal Snellen). For the experimental validation we built an artificial eye consisting of a plano-convex lens with a focal length of 25.4 mm and 0.5 numerical aperture, a variable diaphragm, a 3× objective and an ORCA 285 Hamamatsu Photonics camera 8.1 μm pixel size (resulting in an effective pixel size of 2.7 μm). A set of four different VA charts adapted to monitor different visual acuities (ranging between 0.0 and 0.20 logMAR) were placed at different object distances 6, 1.0, 0.6 and 0.4 m from the artificial eye.
  
  
  
  Both numerical and experimental validation showed the suitability of the cubic phase mask for extending the range of clear vision of presbyopic eyes, providing at least a visual acuity of 0.1 logMAR (6/7.5 Snellen, 0.8 decimal Snellen) at all distances. The results show that it is possible to choose between promoting far or near vision by changing the magnitude of the defocus component. It is also possible to extend the range of clear vision, by increasing the magnitude of the cubic component. But this increment will cause a reduction in the contrast of the images as it can be observed from the Visual Strehl values and the retinal images generated numerically.
  
  
  
  A cubic phase mask in the shape 7.07 μm × (Z9-Z6)-0.9 μm × Z4is a good solution for obtaining a range of clear vision with at least 0.1 logMAR visual acuity (and close to 0.0 logMAR, 6/6, 20/20 and decimal Snellen 1.0) between 6.0 and 0.4 m for a pupil diameter of 5.0 mm. Our results seem to be a good starting point for future studies of this type of cubic phase mask solutions for presbyopia.
authors.affiliation: Departamento de Física Aplicada (área de Optometría), Facultade de Óptica e Optometría, Universidade de Santiago de Compostela, Santiago de Compostela, Spain.
authors.forename: Justo
authors.initials: J
authors.lastname: Arines
authors.affiliation: Departamento de Física Aplicada (área de Optometría), Facultade de Óptica e Optometría, Universidade de Santiago de Compostela, Santiago de Compostela, Spain.
authors.forename: Citlalli
authors.initials: C
authors.lastname: Almaguer
authors.affiliation: Departamento de Física Aplicada (área de Óptica), Facultade de Física, Universidade de Santiago de Compostela, Santiago de Compostela, Spain.
authors.forename: Eva
authors.initials: E
authors.lastname: Acosta
mesh_terms: D004867:Equipment Design; D006801:Humans; D008962:Models, Theoretical; D055095:Optics and Photonics; D010775:Photic Stimulation; D011305:Presbyopia / Q000503:physiopathology*; D011680:Pupil / Q000502:physiology*; D012160:Retina / Q000503:physiopathology*; D015348:Vision, Binocular / Q000502:physiology*; D014792:Visual Acuity / Q000502:physiology*
keywords: cubic phase; presbyopia; range of clear vision; through focus; visual Strehl