Abstract

We describe a way of selecting pairs of glasses for both thin cemented achromatic doublets and thin aplanatic achromatic doublets with a reduced secondary spectrum. By taking one pair of glasses at a time, we can compute and display the secondary spectrum in increasing value. The number of solutions based on the magnitude of the secondary spectrum alone is huge: 40,804 pairs. Some tests are applied at different stages of the design procedure to reduce the number of acceptable solutions. Aberrations that cannot be corrected, namely, spherochromatism and fifth-order spherical aberration, are further calculated to reduce drastically the number of acceptable solutions. To do this, we establish tolerance conditions based on the relationship between the Strehl intensity ratio and the rms wave-aberration error so that the rms wave error is minimized in the presence of the secondary spectrum, spherochromatism, and the fifth-order spherical aberration.

© 2001 Optical Society of America

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References

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  1. P. N. Robb, “Selection of optical glasses. 1: Two material,” Appl. Opt. 24, 1864–1877 (1985).
    [CrossRef]
  2. P. N. Robb, “Selection of optical glasses,” in Proceedings of the 19th International Lens Design Conference, W. H. Taylor, ed., Proc. SPIE554, 60–75 (1985).
  3. P. N. Robb, R. I. Mercado, “Calculation of refractive indices using Buchdahl’s chromatic coordinate,” J. Opt. Soc. Am. 71, 1639 (1981).
  4. R. D. Siglet, “Glass selection for airspaced apochromats using the dispersion equation,” Appl. Opt. 25, 4311–4320 (1986).
    [CrossRef]
  5. Schott Optical Glass Catalog, 1992 ed. (Schott Glaswerke Optisches Glas, Hattenbergstrabe 10, W-6500 Mainz, Germany).
  6. J. L. Rayces, M. Rosete-Aguilar, “Differential equation for normal glass dispersion and evaluation of secondary spectrum,” Appl. Opt. 38, 2028–2039 (1999).
    [CrossRef]
  7. J. Hoogland, “The design of apochromatic lenses,” in Recent Developments in Optical Design, R. A. Ruloff, ed. (Perkin-Elmer, Norwalk, Conn., 1968), pp. 6-1–6-8.
  8. R. Kingslake, Lens Design Fundamentals (Academic, New York, 1978), Chap. 5.
  9. I. C. Gardner, “Application of the algebraic aberration equations to optical design,” in Scientific Papers of the Bureau of Standards, No. 550 (Part of Vol. 22) (U.S. Government Printing Office, Washington, D.C., 1927).
  10. J. L. Rayces, M. Rosete-Aguilar, “Selection of glasses for achromatic doublets with reduced secondary spectrum,” in Current Developments in Lens Design and Optical Systems Engineering, R. E. Fischer, W. Smith, W. H. Swantner, eds., Proc. SPIE4093, 36–46 (2000).
    [CrossRef]
  11. M. Rimmer, M.S. thesis (Institute of Optics, University of Rochester, Rochester, N.Y., 1963).
  12. H. A. Buchdahl, Optical Aberration Coefficients (Oxford University, London, 1954).
  13. Lord Rayleigh, “Investigations in optics, with special reference to the spectroscope,” Philos. Mag. 8, 403–411 (1879).
  14. R. Kingslake, Lens Design Fundamentals (Academic, New York, 1978), p. 174.

1999

1986

1985

1981

P. N. Robb, R. I. Mercado, “Calculation of refractive indices using Buchdahl’s chromatic coordinate,” J. Opt. Soc. Am. 71, 1639 (1981).

1879

Lord Rayleigh, “Investigations in optics, with special reference to the spectroscope,” Philos. Mag. 8, 403–411 (1879).

Buchdahl, H. A.

H. A. Buchdahl, Optical Aberration Coefficients (Oxford University, London, 1954).

Gardner, I. C.

I. C. Gardner, “Application of the algebraic aberration equations to optical design,” in Scientific Papers of the Bureau of Standards, No. 550 (Part of Vol. 22) (U.S. Government Printing Office, Washington, D.C., 1927).

Hoogland, J.

J. Hoogland, “The design of apochromatic lenses,” in Recent Developments in Optical Design, R. A. Ruloff, ed. (Perkin-Elmer, Norwalk, Conn., 1968), pp. 6-1–6-8.

Kingslake, R.

R. Kingslake, Lens Design Fundamentals (Academic, New York, 1978), Chap. 5.

R. Kingslake, Lens Design Fundamentals (Academic, New York, 1978), p. 174.

Mercado, R. I.

P. N. Robb, R. I. Mercado, “Calculation of refractive indices using Buchdahl’s chromatic coordinate,” J. Opt. Soc. Am. 71, 1639 (1981).

Rayces, J. L.

J. L. Rayces, M. Rosete-Aguilar, “Differential equation for normal glass dispersion and evaluation of secondary spectrum,” Appl. Opt. 38, 2028–2039 (1999).
[CrossRef]

J. L. Rayces, M. Rosete-Aguilar, “Selection of glasses for achromatic doublets with reduced secondary spectrum,” in Current Developments in Lens Design and Optical Systems Engineering, R. E. Fischer, W. Smith, W. H. Swantner, eds., Proc. SPIE4093, 36–46 (2000).
[CrossRef]

Rayleigh, Lord

Lord Rayleigh, “Investigations in optics, with special reference to the spectroscope,” Philos. Mag. 8, 403–411 (1879).

Rimmer, M.

M. Rimmer, M.S. thesis (Institute of Optics, University of Rochester, Rochester, N.Y., 1963).

Robb, P. N.

P. N. Robb, “Selection of optical glasses. 1: Two material,” Appl. Opt. 24, 1864–1877 (1985).
[CrossRef]

P. N. Robb, R. I. Mercado, “Calculation of refractive indices using Buchdahl’s chromatic coordinate,” J. Opt. Soc. Am. 71, 1639 (1981).

P. N. Robb, “Selection of optical glasses,” in Proceedings of the 19th International Lens Design Conference, W. H. Taylor, ed., Proc. SPIE554, 60–75 (1985).

Rosete-Aguilar, M.

J. L. Rayces, M. Rosete-Aguilar, “Differential equation for normal glass dispersion and evaluation of secondary spectrum,” Appl. Opt. 38, 2028–2039 (1999).
[CrossRef]

J. L. Rayces, M. Rosete-Aguilar, “Selection of glasses for achromatic doublets with reduced secondary spectrum,” in Current Developments in Lens Design and Optical Systems Engineering, R. E. Fischer, W. Smith, W. H. Swantner, eds., Proc. SPIE4093, 36–46 (2000).
[CrossRef]

Siglet, R. D.

Appl. Opt.

J. Opt. Soc. Am.

P. N. Robb, R. I. Mercado, “Calculation of refractive indices using Buchdahl’s chromatic coordinate,” J. Opt. Soc. Am. 71, 1639 (1981).

Philos. Mag.

Lord Rayleigh, “Investigations in optics, with special reference to the spectroscope,” Philos. Mag. 8, 403–411 (1879).

Other

R. Kingslake, Lens Design Fundamentals (Academic, New York, 1978), p. 174.

J. Hoogland, “The design of apochromatic lenses,” in Recent Developments in Optical Design, R. A. Ruloff, ed. (Perkin-Elmer, Norwalk, Conn., 1968), pp. 6-1–6-8.

R. Kingslake, Lens Design Fundamentals (Academic, New York, 1978), Chap. 5.

I. C. Gardner, “Application of the algebraic aberration equations to optical design,” in Scientific Papers of the Bureau of Standards, No. 550 (Part of Vol. 22) (U.S. Government Printing Office, Washington, D.C., 1927).

J. L. Rayces, M. Rosete-Aguilar, “Selection of glasses for achromatic doublets with reduced secondary spectrum,” in Current Developments in Lens Design and Optical Systems Engineering, R. E. Fischer, W. Smith, W. H. Swantner, eds., Proc. SPIE4093, 36–46 (2000).
[CrossRef]

M. Rimmer, M.S. thesis (Institute of Optics, University of Rochester, Rochester, N.Y., 1963).

H. A. Buchdahl, Optical Aberration Coefficients (Oxford University, London, 1954).

Schott Optical Glass Catalog, 1992 ed. (Schott Glaswerke Optisches Glas, Hattenbergstrabe 10, W-6500 Mainz, Germany).

P. N. Robb, “Selection of optical glasses,” in Proceedings of the 19th International Lens Design Conference, W. H. Taylor, ed., Proc. SPIE554, 60–75 (1985).

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Figures (4)

Fig. 1
Fig. 1

Three methods of measuring a secondary spectrum: A S , axial method; W S , wave method; R S , transverse method.

Fig. 2
Fig. 2

Abbe’s diagram, the standard glass-search diagram.

Fig. 3
Fig. 3

Hoogland’s glass-search diagram.

Fig. 4
Fig. 4

Ray’s deviation through a lens at the clear aperture, as illustrated for thick lenses and finite radii. It is an approximate measure of the steepness of the lens curvatures. Thin lenses and paraxial ray are mathematical abstractions and cannot be represented in an optical schematic.

Tables (4)

Tables Icon

Table 1 Residual Aberrations Normalized to Tolerance, Air-Spaced Solutions, f = 26.66 mm, 0.480 µm < λ < 0.6439 µm

Tables Icon

Table 2 Residual Aberrations Normalized to Tolerance, Air-Spaced Solutions, f = 26.66 mm, 0.480 µm < λ < 0.6439 µm and Calcium Fluoride Included

Tables Icon

Table 3 Residual Aberrations Normalized to Tolerance, Air-Spaced Solutions, f = 26.66 mm, 0.365 µm < λ < 0.436 µm and Calcium Fluoride Included

Tables Icon

Table 4 Residual Aberrations Normalized to Tolerance, Air-Spaced Solutions, f = 225.0 mm, 0.8521 µm < λ < 2.3254 µm

Equations (32)

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1f=Kα+Kβ,  K=1r-1rNG-1,
KαVα-KβVβ=0,  where V=NG-1NB-NR
Kα=1f·VαVα-Vβ,
Kβ=-1f·VβVα-Vβ.
ς=Pα-PβVα-Vβ,  where P=NB-NGNB-NR.
Δf=ςf,  WS=ς fλNA2, RS=ςfNA.
AS=ς l2f, WS=ς l2λfNA2, RS=ς l2fNA,
Δδ=δα-δβ=-yKα-Kβ
Δδ=Vα+VβVα-Vβδ.
WΔB=18λGΔB,  RΔB=12NAΔB, AΔB=12NA2ΔB,
WB5=112λGB5,  RB5=12NAB5, AB5=12NA2B5,
SIR=1-4π2λ2Wrms2,
W2¯=0102πWρ, 2ρdρd0102π ρdρd.
Pρ=A00+A20ρ2+A40ρ4+A60ρ6.
W2¯=2 01Pρ2ρdρ.
Pρ=A20ρ2+A00.
W2¯=13A202+A20A00+A002.
A20+2A00=0, hence A00=-12A20.
mWrms=123A20,
A20<23 mWrms.
Pρ=A40ρ4+A20ρ2+A00.
W2¯=15A402+12A40A20+23A40A00+13A202+A20A00+A002.
2A40+3A20+6A00=0, 3A40+4A20+6A00=0.
A20=-A40,  A00=16A40.
mWrms=165A40,
A40<65 mWrms.
Pρ=A60ρ6+A40ρ4+A20ρ2+A00.
W2¯=214A602+412A60A40+410A60A20+48A60A00+210A402+48A40A20+46A40A00+26A202+44A20A00+12A002,
13A60+25A40+12A20+23A00=0, 25A60+12A40+23A20+A00=0, 12A60+23A40+A20+2A00=0.
A40=-32A60, A20=+35A60, A00=-120A60.
mWrms=1207A60.
A60<207 mWrms.

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