Abstract

The standard aspheric surface definition has been used successfully to correct aberrations in a wide variety of systems. However, in some current applications a more general surface definition is needed. We present a more general approach that uses parametrically defined optical surfaces for the optical design of imaging and illumination systems.

© 2000 Optical Society of America

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References

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  1. code v Reference Manual (Optical Research Associates, Pasadena, Calif., 1997).
  2. zemax, Optical Design Program User Guide, Version 7.0 (Focus Software, Tucson, Ariz., 1998).
  3. oslo Version 5, Program Reference (Sinclair Optics, Fairport, N.Y., 1996).
  4. W. J. Smith, Modern Lens Design: a Resource Manual (McGraw-Hill, New York, 1992).
  5. P. M. Fitzpatrick, Advanced Calculus: a Course in Mathematical Analysis (PWS, Boston, Mass., 1996).
  6. D. L. Toth, “On ray tracing parametric surfaces,” ACM (Assoc. Comput. Mach.) Trans. Graphics 19, 171–179 (1985).
    [CrossRef]
  7. J. M. Sasian, S. A. Lerner, J. H. Burge, “Certification of a null corrector via a diamond-turned asphere: design and implementation,” in 18th Congress of the International Commission for Optics, A. J. Glass, J. W. Goodman, M. Chang, A. H. Guenther, T. Asakura, eds., Proc. SPIE3749, 284–285 (1999).
    [CrossRef]
  8. W. Elmer, “The optics of reflectors for illumination,” IEEE Trans. Ind. Appl. IA-19, 776–778 (1983).
    [CrossRef]
  9. S. A. Lerner, J. M. Sasian, “Test modeling of conformal surfaces,” presented at OSA Annual Meeting, Baltimore, Md., 4–9 October 1998.
  10. S. A. Lerner, J. M. Sasian, J. E. Greivenkamp, R. O. Gappinger, S. R. Clark, “Interferometric metrology of conformal domes,” in Window and Dome Technologies and Materials VI, S. R. Clark, ed., Proc. SPIE3705, 221–226 (1999).
    [CrossRef]

1985 (1)

D. L. Toth, “On ray tracing parametric surfaces,” ACM (Assoc. Comput. Mach.) Trans. Graphics 19, 171–179 (1985).
[CrossRef]

1983 (1)

W. Elmer, “The optics of reflectors for illumination,” IEEE Trans. Ind. Appl. IA-19, 776–778 (1983).
[CrossRef]

Burge, J. H.

J. M. Sasian, S. A. Lerner, J. H. Burge, “Certification of a null corrector via a diamond-turned asphere: design and implementation,” in 18th Congress of the International Commission for Optics, A. J. Glass, J. W. Goodman, M. Chang, A. H. Guenther, T. Asakura, eds., Proc. SPIE3749, 284–285 (1999).
[CrossRef]

Clark, S. R.

S. A. Lerner, J. M. Sasian, J. E. Greivenkamp, R. O. Gappinger, S. R. Clark, “Interferometric metrology of conformal domes,” in Window and Dome Technologies and Materials VI, S. R. Clark, ed., Proc. SPIE3705, 221–226 (1999).
[CrossRef]

Elmer, W.

W. Elmer, “The optics of reflectors for illumination,” IEEE Trans. Ind. Appl. IA-19, 776–778 (1983).
[CrossRef]

Fitzpatrick, P. M.

P. M. Fitzpatrick, Advanced Calculus: a Course in Mathematical Analysis (PWS, Boston, Mass., 1996).

Gappinger, R. O.

S. A. Lerner, J. M. Sasian, J. E. Greivenkamp, R. O. Gappinger, S. R. Clark, “Interferometric metrology of conformal domes,” in Window and Dome Technologies and Materials VI, S. R. Clark, ed., Proc. SPIE3705, 221–226 (1999).
[CrossRef]

Greivenkamp, J. E.

S. A. Lerner, J. M. Sasian, J. E. Greivenkamp, R. O. Gappinger, S. R. Clark, “Interferometric metrology of conformal domes,” in Window and Dome Technologies and Materials VI, S. R. Clark, ed., Proc. SPIE3705, 221–226 (1999).
[CrossRef]

Lerner, S. A.

S. A. Lerner, J. M. Sasian, J. E. Greivenkamp, R. O. Gappinger, S. R. Clark, “Interferometric metrology of conformal domes,” in Window and Dome Technologies and Materials VI, S. R. Clark, ed., Proc. SPIE3705, 221–226 (1999).
[CrossRef]

J. M. Sasian, S. A. Lerner, J. H. Burge, “Certification of a null corrector via a diamond-turned asphere: design and implementation,” in 18th Congress of the International Commission for Optics, A. J. Glass, J. W. Goodman, M. Chang, A. H. Guenther, T. Asakura, eds., Proc. SPIE3749, 284–285 (1999).
[CrossRef]

S. A. Lerner, J. M. Sasian, “Test modeling of conformal surfaces,” presented at OSA Annual Meeting, Baltimore, Md., 4–9 October 1998.

Sasian, J. M.

S. A. Lerner, J. M. Sasian, “Test modeling of conformal surfaces,” presented at OSA Annual Meeting, Baltimore, Md., 4–9 October 1998.

J. M. Sasian, S. A. Lerner, J. H. Burge, “Certification of a null corrector via a diamond-turned asphere: design and implementation,” in 18th Congress of the International Commission for Optics, A. J. Glass, J. W. Goodman, M. Chang, A. H. Guenther, T. Asakura, eds., Proc. SPIE3749, 284–285 (1999).
[CrossRef]

S. A. Lerner, J. M. Sasian, J. E. Greivenkamp, R. O. Gappinger, S. R. Clark, “Interferometric metrology of conformal domes,” in Window and Dome Technologies and Materials VI, S. R. Clark, ed., Proc. SPIE3705, 221–226 (1999).
[CrossRef]

Smith, W. J.

W. J. Smith, Modern Lens Design: a Resource Manual (McGraw-Hill, New York, 1992).

Toth, D. L.

D. L. Toth, “On ray tracing parametric surfaces,” ACM (Assoc. Comput. Mach.) Trans. Graphics 19, 171–179 (1985).
[CrossRef]

ACM (Assoc. Comput. Mach.) Trans. Graphics (1)

D. L. Toth, “On ray tracing parametric surfaces,” ACM (Assoc. Comput. Mach.) Trans. Graphics 19, 171–179 (1985).
[CrossRef]

IEEE Trans. Ind. Appl. (1)

W. Elmer, “The optics of reflectors for illumination,” IEEE Trans. Ind. Appl. IA-19, 776–778 (1983).
[CrossRef]

Other (8)

S. A. Lerner, J. M. Sasian, “Test modeling of conformal surfaces,” presented at OSA Annual Meeting, Baltimore, Md., 4–9 October 1998.

S. A. Lerner, J. M. Sasian, J. E. Greivenkamp, R. O. Gappinger, S. R. Clark, “Interferometric metrology of conformal domes,” in Window and Dome Technologies and Materials VI, S. R. Clark, ed., Proc. SPIE3705, 221–226 (1999).
[CrossRef]

J. M. Sasian, S. A. Lerner, J. H. Burge, “Certification of a null corrector via a diamond-turned asphere: design and implementation,” in 18th Congress of the International Commission for Optics, A. J. Glass, J. W. Goodman, M. Chang, A. H. Guenther, T. Asakura, eds., Proc. SPIE3749, 284–285 (1999).
[CrossRef]

code v Reference Manual (Optical Research Associates, Pasadena, Calif., 1997).

zemax, Optical Design Program User Guide, Version 7.0 (Focus Software, Tucson, Ariz., 1998).

oslo Version 5, Program Reference (Sinclair Optics, Fairport, N.Y., 1996).

W. J. Smith, Modern Lens Design: a Resource Manual (McGraw-Hill, New York, 1992).

P. M. Fitzpatrick, Advanced Calculus: a Course in Mathematical Analysis (PWS, Boston, Mass., 1996).

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Figures (15)

Fig. 1
Fig. 1

Configuration to certify a null lens with an aspheric null certifying mirror.

Fig. 2
Fig. 2

Given the surface description of an astronomical primary mirror, we can analytically solve for the parametric surface that describes the null certifier. A ray that intersects the astronomical mirror at normal incidence in the test configuration will intersect the null certifier at normal incidence in the certifying configuration.

Fig. 3
Fig. 3

Ray behavior for highly aberrated wave fronts is highly nonlinear. We plot the ray angle versus the ray height near the surface of the null certifying mirror.

Fig. 4
Fig. 4

Wave-front residual for a standard aspheric null certifier by use of ten coefficients. The peak-to-valley wave-front residual is approximately 2000 waves for a test wavelength of 633 nm.

Fig. 5
Fig. 5

Wave-front residual for the TPT null certifier by use of eight coefficients. The peak-to-valley wave-front residual is approximately 0.003 waves for a test wavelength of 633 nm.

Fig. 6
Fig. 6

Spherical primary Cassegrain-type telescope. Note that the aspheric secondary mirror is placed near the ray caustic.

Fig. 7
Fig. 7

Wave-front residual for telescope by use of a standard aspheric description with ten coefficients. The peak-to-valley wave-front residual is approximately two waves for a wavelength of 633 nm.

Fig. 8
Fig. 8

Wave-front residual for telescope by use of a TPT description with eight coefficients. The peak-to-valley wave-front residual is approximately 0.02 waves for a wavelength of 633 nm.

Fig. 9
Fig. 9

Diagram of the four-to-one reflector.

Fig. 10
Fig. 10

Ray trace of a four-to-one reflector with an implicitly defined surface. Note that the reflected ray angle is one third of the incident ray angle.

Fig. 11
Fig. 11

Periodic deformation added to an explicitly defined optical surface. As the surface normal becomes perpendicular to the optical axis, the deformation remains oriented parallel to the optical axis.

Fig. 12
Fig. 12

Periodic deformation added to a parametrically defined PAL optical surface such that the deformation is everywhere oriented normal to the optical surface. The period of the deformation remains constant along the surface.

Fig. 13
Fig. 13

Theoretical null configuration that uses a highly aspheric surface to compensate the high degree of wave-front asphericity produced by the conformal element.

Fig. 14
Fig. 14

Wave-front residual for the theoretical null configuration by use of the standard aspheric surface with ten terms is 0.3 waves peak to valley. The scale of plot is 0.25 waves at a wavelength of 3.9 µm.

Fig. 15
Fig. 15

Wave-front residual for the theoretical null configuration by use of a surface with a TPT description with ten coefficients is 0.1 waves peak to valley. The scale of plot is 0.25 waves at a wavelength of 3.9 µm.

Tables (1)

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Table 1 First-Order Design Parameters for a Cassegrain-Type Telescope with a Spherical Primary Mirror

Equations (38)

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

-z+Fx, y=-z+cx2+y21+1-1+kc2x2+y21/2+i=1l a2ix2+y2i=0,
δaW040=a4+kc38ρ4Δn,
δaW131=4y¯yδaW040,
δaW222=4y¯y2δaW040,
δaW220P=0,
δaW311=4y¯y3δaW040,
r=fθ=b1 sin θ,
z=gθ=-a0+a0 cos θ,
r=fθ=b1 sin θ+j=1m b2j+1 sin2j+1 θ,
z=gθ=-a0+a0 cos θ+i=1l a2ib1 sin θ2i.
r=ft=t+j=1m b2j+1t2j+1,
z=gt=-a0+a01-t2b121/2+i=1l a2it2i.
ti+1=ti-ft-rft.
dzdx=dzdtdtdrdrdx=gtftxx2+y2,
dzdy=dzdtdtdrdrdy=gtftyx2+y2.
z=z+P cosθ-P,
r=r-P sinθ,
z=t22R,
r=t.
tanθ=dzdr=t/R1,
t=R tanθ.
z=R tan2θ2,
r=R tanθ.
z=R tan2θ2+P cosθ-P,
r=R tanθ-P sinθ.
za2θ2+a4θ4+a6θ6++a2lθ2l,
rb1θ+b3θ3+b5θ5++b2m+1θ2m+1.
θr=-2 33b1+32 9 b2  r+3 4b13+27b2r2 2/362/3b2 9b2  r+3 4b13+27b2r2 1/3.
lnrf= tanα-β2dα,
lnrf= tanα-α32dα=-3 lncosα3,
r=fcosα33.
z=fcosα33cos α,
y=fcosα33sin α.
r=b sin θ+NrFd,
z=a cos θ+NzFd,
Nr=a sin θb2 cos2 θ+a2 sin2 θ1/2,
Nz=b cos θb2 cos2 θ+a2 sin2 θ1/2,
d=a 0ta2 cos2 t+b2 sin2 t1/2dt=aEt, 1-b2a2l1t+l2t2+l3t3+.

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