Also, if the stop is located at an aspheric surface, the ypr there will be zero, and the only aberration to be affected by the asphericity is the spherical aberration.

11.7.4 A Thin Lens in the Plane of an Image

This case is exemplified by a field lens or a field flattener. We cannot now use the thin-lens contribution formulas already given because both the stop and the image cannot lie in the same plane. Consequently, we have to return to the surface contribution formulas and add them up for the case in which y ¼ 0. When this is done, we find that for a thin lens situated in an image plane

SC ¼ CC ¼ AC ¼ 0; LchC ¼ TchC ¼ 0

The Petzval sag PC has its usual value of –12 h002=f 0N, where N is the index of the glass. The distortion must be carefully evaluated. It turns out to be

where f 0 is the focal length of the thin lens. The distortion contribution depends on the shape of the thin lens in addition to its focal length and refractive index.

ENDNOTES

1H. Coddington, A Treatise on the Reflexion and Refraction of Light, p. 66. Simpkin and Marshall, London (1829).

2Coddington’s book was digitized by the Google Books Project and is freely available to read at http://books.google.com/books/download/A_Treatise_on_the_Reflection_and_Refract. pdf?id¼WI45AAAAcAAJ&output¼pdf&sig¼ACfU3U0eX3OvIkczIHZL5iJSyLEFEJza- A. This 1829 treatise likely was read by Gauss and Petzval, the contributions by both occurring over a decade later. Those interested in understanding the fundamentals of optics should read Coddington’s book. Coddington credits the works of Professor Airy and Mr. Herschel’s invaluable (sic) article on light in the Encyclopedia Metropolitana.

3A. E. Conrady, p. 588.

4T. Smith, “The contributions of Thomas Young to geometrical optics,” Proc. Phys. Soc., 62B:619 (1949).

5Not to be confused with the entrance pupil coordinate.

6A. E. Conrady, p. 739.

7A. E. Conrady, pp. 290-294.

8B. K. Johnson, Optical Design and Lens Computation, p. 118, Hatton Press, London (1948).

9H. H. Emsley, Aberrations of Thin Lenses, p. 194, Constable, London, (1956).

10B. K. Johnson, pp. 93-118.

11R. Barry Johnson, “Balancing the astigmatic fields when all other aberrations are absent,” Appl. Opt., 32(19):3494-3496 (1993).

13Seymour Rosin, “Concentric Lenses,” JOSA, 49(9):862-864 (1959).

14R. Barry Johnson, Texas Instruments, Dallas, Texas.

15Allen Mann, Infrared Optics and Zoom Lenses, Second Edition, pp. 60-61, SPIE Press, Bellingham, WA (2009).

16In addition to spherical aberration discussed in Section 6.4, coma and astigmatism are also present.

17See also Section 7.4.3.

18Donald C. O’Shea, Elements of Modern Optical Design, pp. 214-215, Wiley, New York (1985).

19U.S. Patent 404,506 (1888).

20A stop is located 11.75 before the first surface of the doublet lens, which is the location of the front or anterior focal point. The stop is also the entrance pupil. The principal ray passes through the front focal point and emerges from the lens parallel to the optical axis at the corresponding image height. This is known as the telecentric condition.

21D. P. Feder, “Conrady’s chromatic condition,” J. Res. Nat. Bur. Std., 52:47 (1954); Res. Paper 2471.

22For at least the monochromatic case, the entrance and exit pupil will be located at the nodal points if the aperture stop is placed at the optical center of the lens. The limitations of the entrance pupil shape and position related to large field angles still apply. See Section 3.3.7.

23A. E. Conrady, pp. 314, 751.

24D. P. Feder, “Optical calculations with automatic computing machinery,” J. Opt. Soc. Am., 41:633 (1951).

25It should be realized that the j4 term and the conic constant both affect the primary aberrations; however, they do not create the same surface contour and should not in general ever be used at the same time on a specific surface. It is most common to use the conic constant. Any aspheric coefficient affects its own order level and those higher but not lower.