Page 84 - Modern Optical Engineering The Design of Optical Systems

Optical System Considerations 67

the object effectively parallel to the plane of the image. In a projector
this means that the field of view of the projection lens must be
increased on one side of the axis by the amount that the beam is tilted
above the horizontal.
Note that a curved surface is imaged as a curved surface with the
same curvature and sign as the object surface. A sphere of radius ( R),
for example, is imaged as a sphere of radius ( R). This is because the
height y of a point on a surface is imaged as my and the sag z of a point
2
on the surface is imaged as m z.

4.6 Summary of Sign Conventions
1. Light normally travels from left to right.

2. Focal length is positive for converging lenses.
3. Heights above the axis are positive.
4. Distances to the right of a reference point are positive.
5. A radius or curvature is positive if the center of curvature is to the
right of the surface.

6. Angles are positive if the ray is rotated clockwise to reach the
normal or the axis.
7. After a reflection (when light direction is reversed), the signs of
subsequent indices and spacings are reversed; i.e., if light travels
from right to left, the index is negative; if the next surface is to the
left, the space is negative.
It may be noted that, although the discussions of this chapter have
centered about spherical surfaces, and the equations derived have
utilized the radii and curvatures of spherical surfaces, the paraxial
expressions are equally valid for all continuous surfaces of rotation
centered on the optical axis when the osculating radius (i.e., the
radius of the surface at the axis) of the surface is used. This includes
both conic sections and generalized aspheric surfaces.

Bibliography
Bass, M., Handbook of Optics, Vol. 1, New York, McGraw-Hill, 1995.
Fischer, R. E. and Tadic-Galeb, B., Optical System Design, New York, McGraw-Hill, 2000.
Greivenkamp, J., Field Guide to Geometrical Optics, Bellingham, WA, SPIE, 2004.
Kingslake, R., Optical System Design, Orlando, Academic, 1983.
Smith, W. J., Modern Lens Design, New York, McGraw-Hill, 2002.
Smith, W. J., Practical Optical System Layout, New York, McGraw-Hill, 1997.