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THE PRINCIPAL ABERRATIONS OF LENSES        51

                                                 On-axis aberrations

                                      Blue  Green  Red





                       Chromatic                                 Spherical
                                   (a)                                       (b)


                                                 Off-axis aberrations






                                                            Astigmatism
                       Coma
                                      (c)                                    (d)


                                                      Distortion









                           Field curvature                  Barrel distortion  Pincushion distortion
                                                          (e)

                       Figure 4-8
                       Aberrations of a simple lens. (a) Chromatic aberration: Parallel incident rays of different
                       wavelength are focused at different locations. (b) Spherical aberration: Incident rays parallel
                       to the optic axis and reaching the center and the periphery of the lens are focused at
                       different locations. (c) Coma: Off-axis rays passing through the center and periphery of the
                       lens are focused at different locations. (d) Astigmatism: An off-axis aberration causes waves
                       passing through the vertical and horizontal diameters to focus an object point as a streak.
                       (e) Distortion and field curvature: The image plane is curved and not planar. So-called barrel
                       and pincushion distortions produce images that are not high in fidelity compared to the
                       object.


                          Chromatic aberration occurs because a lens refracts light differently depending on
                       the wavelength. Blue light is bent inward toward the optic axis more than red light. The
                       result is disastrous: Blue wavelengths are focused in an image plane closer to the lens
                       than the image plane for red wavelengths. Even at the best focus, point sources are sur-
                       rounded by color halos, the color changing depending on the focus of the objective, the
                       image never becoming sharp. Since each wavelength is focused at a different distance
                       from the lens, there is also a difference in magnification for different colors (chromatic
                       magnification difference). The solution is to make compound lenses made of glasses
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