Abstract

We developed the pupil astigmatism criteria for correcting the quadratic field-dependent aberrations. These criteria provide an elegant way to determine and correct aberrations that have quadratic field dependence and arbitrary pupil dependence in the same way that the Abbe sine condition is used for aberrations with linear field dependence. Like the sine condition, the pupil astigmatism criteria involve only the properties of the rays originating from the on-axis object point, so it is convenient to implement them in optical design. We introduce an algorithm to apply the criteria in designing new well-corrected optical systems. Some example designs are presented.

© 2002 Optical Society of America

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References

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  1. M. Born, E. Wolf, Principles of Optics (MacMillan, New York, 1964).
  2. R. Kingslake, Lens Design Fundamentals (Academic, New York, 1978).
  3. L. Mertz, Excursions in Astronomical Optics (Springer, New York, 1996).
  4. R. K. Luneburg, Mathematical Theory of Optics (University of California Press, Berkeley, Calif., 1966).
  5. H. A. Buchdall, An Introduction to Hamiltonian Optics (Cambridge U. Press, Cambridge, UK, 1970).
  6. W. T. Welford, Aberrations of Optical Systems (Hilgler, Bristol, UK, 1986).
  7. zemax is an optical design code of Focus Software, Inc., Tucson, Arizona.
  8. W. H. Press, B. P. Flannery, S. A. Teukolsky, W. T. Vetterling, Numerical Recipes (Cambridge U. Press, Cambridge, UK, 1987), Chap. 2.
  9. L. W. Johnson, R. D. Riess, Numerical Analysis (Addison–Wesley, Reading, Mass., 1977), Chap. 5.

Born, M.

M. Born, E. Wolf, Principles of Optics (MacMillan, New York, 1964).

Buchdall, H. A.

H. A. Buchdall, An Introduction to Hamiltonian Optics (Cambridge U. Press, Cambridge, UK, 1970).

Flannery, B. P.

W. H. Press, B. P. Flannery, S. A. Teukolsky, W. T. Vetterling, Numerical Recipes (Cambridge U. Press, Cambridge, UK, 1987), Chap. 2.

Johnson, L. W.

L. W. Johnson, R. D. Riess, Numerical Analysis (Addison–Wesley, Reading, Mass., 1977), Chap. 5.

Kingslake, R.

R. Kingslake, Lens Design Fundamentals (Academic, New York, 1978).

Luneburg, R. K.

R. K. Luneburg, Mathematical Theory of Optics (University of California Press, Berkeley, Calif., 1966).

Mertz, L.

L. Mertz, Excursions in Astronomical Optics (Springer, New York, 1996).

Press, W. H.

W. H. Press, B. P. Flannery, S. A. Teukolsky, W. T. Vetterling, Numerical Recipes (Cambridge U. Press, Cambridge, UK, 1987), Chap. 2.

Riess, R. D.

L. W. Johnson, R. D. Riess, Numerical Analysis (Addison–Wesley, Reading, Mass., 1977), Chap. 5.

Teukolsky, S. A.

W. H. Press, B. P. Flannery, S. A. Teukolsky, W. T. Vetterling, Numerical Recipes (Cambridge U. Press, Cambridge, UK, 1987), Chap. 2.

Vetterling, W. T.

W. H. Press, B. P. Flannery, S. A. Teukolsky, W. T. Vetterling, Numerical Recipes (Cambridge U. Press, Cambridge, UK, 1987), Chap. 2.

Welford, W. T.

W. T. Welford, Aberrations of Optical Systems (Hilgler, Bristol, UK, 1986).

Wolf, E.

M. Born, E. Wolf, Principles of Optics (MacMillan, New York, 1964).

Other (9)

M. Born, E. Wolf, Principles of Optics (MacMillan, New York, 1964).

R. Kingslake, Lens Design Fundamentals (Academic, New York, 1978).

L. Mertz, Excursions in Astronomical Optics (Springer, New York, 1996).

R. K. Luneburg, Mathematical Theory of Optics (University of California Press, Berkeley, Calif., 1966).

H. A. Buchdall, An Introduction to Hamiltonian Optics (Cambridge U. Press, Cambridge, UK, 1970).

W. T. Welford, Aberrations of Optical Systems (Hilgler, Bristol, UK, 1986).

zemax is an optical design code of Focus Software, Inc., Tucson, Arizona.

W. H. Press, B. P. Flannery, S. A. Teukolsky, W. T. Vetterling, Numerical Recipes (Cambridge U. Press, Cambridge, UK, 1987), Chap. 2.

L. W. Johnson, R. D. Riess, Numerical Analysis (Addison–Wesley, Reading, Mass., 1977), Chap. 5.

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Figures (10)

Fig. 1
Fig. 1

Three-dimensional illustration of an optical system with the object at a finite distance.

Fig. 2
Fig. 2

Three-dimensional illustration of an optical system with the object at infinity.

Fig. 3
Fig. 3

Illustration of the tangential rays of an oblique bundle of rays refracted by a surface.

Fig. 4
Fig. 4

Illustration of how to obtain the tangential and sagittal radii of curvature of a general aspheric surface with rotational symmetry. C1 is the sagittal center of curvature of the segment of the surface at P, and C2 is the tangential center of curvature of the same segment.

Fig. 5
Fig. 5

Illustration of Snell’s law.

Fig. 6
Fig. 6

Illustration of the design procedure of the three-surface system that is corrected for all spherical aberrations, coma, and some specific quadratic field-dependent aberrations.

Fig. 7
Fig. 7

Illustration of the design procedure of the four-surface system that is corrected for all spherical aberrations, coma, and quadratic field-dependent aberrations.

Fig. 8
Fig. 8

(a) Three-surface system with zero sagittal quadratic field-dependent aberrations. All three surfaces are general aspheres. (b) The spot diagrams of the system. (c) The ray aberrations of the system at 0.95 of the normalized pupil.

Fig. 9
Fig. 9

(a) Four-surface system with no quadratic field-dependent aberrations. All four surfaces are general aspheres. (b) The plot of the rms spot radius versus the field height.

Fig. 10
Fig. 10

(a) Four-mirror system with no quadratic field-dependent aberrations. The object is at the infinity. All four surfaces are general aspheres. (b) The spot diagrams of the system. (c) The plot of the rms spot radius versus the field angle.

Tables (2)

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Table 1 Prescription Data of the Three-Surface Systema

Tables Icon

Table 2 Prescription Data of the Four-Surfacea and Four Mirrorb Systems

Equations (14)

Equations on this page are rendered with MathJax. Learn more.

tθcos2θ=const.
sθ=const.
sθ=tθcos2θ.
sθ=tθcos2θ=const.
n cos2 It-n cos2 It=n cos I-n cos IRt.
ns-ns=n cos I-n cos IRs,
Rs=|PC1|=r 1+dzdr21/2dzdr,
Rt=|PC2|=1+dzdr23/2d2zdr2.
niÂ×nˆ=nrBˆ×nˆ,
niÂ-nrBˆ×nˆ=0.
PQ=the optical path length along a ray from point P to point Q,
L=OA0+A0B0+B0C0+C0I.
n3 sin βi+1=n0 sin αi+1|m|,
Ai+1Ci+1=L-OAi+1-Ci+1I.

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