title: Angular and linear fields of view of Galilean telescopes and telemicroscopes.
abstract: OBJECTIVE
  The calculation of the angular fields of view (FOVs) of Galilean telescopes generally necessitates the calculation of the pupils and ports. This, in turn, requires knowledge of the optical design of the telescope, in particular, the focal lengths or powers of the objective and ocular lenses. Equations for finding the FOV that obviate the need to calculate pupils and ports, or even to know the lens powers of the telescope, are presented in this article. The equations can be used to find the FOVs in image space of real Galilean telescopes of known magnification, merely by measuring the distance between the objective and ocular lenses and the diameter of the objective lens. The equations include the effects of eye pupil diameter and eye relief. Linear FOVs (LFOVs) of Galilean telemicroscopes are similarly determined.
  
  
  METHODS
  Two image space angular FOV equations were derived: (1) an equation to determine the angular FOVs of a telescope with various amounts of vignetting and eye relief; and (2) an equivalent equation for the LFOVs of telescopes fitted with lens caps for near vision.
  
  
  RESULTS
  The FOV increases linearly with increasing vignetting. Increasing the eye relief results in a nonlinear decrease in the FOV, shown as a fraction of the normalized value for zero eye relief. Decrements in the FOVs with increasing eye relief as a fraction of the normalized field angle when the eye relief = 0 are shown to be constant regardless of the vignetting level. A transition of the objective lens from field stop to aperture stop occurs when the eye pupil diameter exceeds the diameter of the objective lens divided by the magnification.
  
  
  CONCLUSIONS
  Equations have been derived for Galilean telescopes and telemicroscopes that make it unnecessary to find pupils and ports, or to know the powers of the lenses. They provide a direct and simple evaluation of angular and LFOVs as functions of magnification, objective lens diameter, eye pupil diameter, eye relief, and vignetting, and enable comparisons of actual telescopes.
authors.affiliation: SUNY College of Optometry, State University of New York, 33 West 42nd Street, New York, NY 10036, USA. mkatz@sunyopt.edu
authors.forename: Milton
authors.initials: M
authors.lastname: Katz
mesh_terms: D004867:Equipment Design; D005139:Eyeglasses / Q000592:standards*; D006801:Humans; D007498:Iris / Q000033:anatomy & histology; D008433:Mathematics; D011680:Pupil / Q000502:physiology; D015203:Reproducibility of Results; D015354:Vision, Low / Q000628:therapy*