Page 119 - Modern Optical Engineering The Design of Optical Systems

102 Chapter Five

Bibliography

Bass, M., Handbook of Optics, Vol. 1, New York, McGraw-Hill, 1995.
Fischer, R. E. and B. Tadic-Galeb, 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.
Welford, W., Aberrattions of Optical Systems, London, Hilger, 1986.

Exercises
1 The longitudinal spherical aberration of two axial rays which have been
traced through a system is 1.0 and 0.5; the ray slopes (tan U) are 0.5 and
0.35 respectively. What are the transverse aberrations (a) in the paraxial
focal plane, and (b) in a plane 0.2 before the paraxial focal plane?
ANSWER: (a) In the paraxial focal plane the transverse aberration is the lon-
gitudinal aberration times (minus) the ray slope
TA LA tan U ( 1) ( 0.5) 0.5 for ray #1 and
( 0.5) ( 0.35) 0.175 for ray #2.
(b) In a plane which is 0.2 before the paraxial focus the transverse spherical is
TA [LA ( 0.2)] ( 1 0.2) ( 0.5) 0.4 for ray #1, and
( 0.5 0.2) ( 0.35) 0.105 for ray #2.

2 A lens has coma T 1.0. Plot the focal plane intercepts of the rays which
pass through: (a) the marginal zone, (b) the 0.707 zone, and (c) the 0.5 zone.
See Fig. 5.6.
ANSWER: Rays from an annular zone of the aperture intersect the focal plane
in a circle, the diameter of which varies as the square of the size of the zone of
the aperture. For primary coma the circles are tangent to two lines making an
angle of 60 . The distance from the apex of the two lines to the top of the cir-
cle is the tangential coma. From the Fig. 5.26 it can be seen that the radius R
of the circle is the short leg of a 30 –60 right triangle whose hypotenuse
equals 2R. This hypotenuse equals (coma T – R), so 2R (coma T – R), and since
the coma is equal to 1.0, R must equal 1/3. The center of the circle is 2/3 from
the apex of the two lines.
The diagram for the other zones can be similarly derived. The coma varies
as the square of the aperture, so the coma for the 0.707 zone is 0.5, and for the
0.5 zone it is 0.25.

3 A certain type of lens has the following primary aberrations at a focal length
of 100, an aperture of 10, and a field of 5°: Longitudinal spherical 1.0;
Coma 1.0, and X T 1.0. What are the aberrations of this type of lens when:
(a) f 200, aperture 10, field 2.5 ?
(b) f 50, aperture 10, field 10°?
ANSWER: (a) At a focal length of 200, all the dimensions are doubled, and all
the aberrations become 2.0. When the aperture is reduced from 20 to 10, the