Abstract

We analyze and synthesize one type of planachromatic microscope objective lens (planachromats). Formulas are described for the calculation of basic parameters of such optical systems for various configurations of the optical system. The application of the described technique is shown on an example of the optical design of planachromat.

© 2010 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. H. Boegehold, Das Optische System des Mikroskops (Verlag Technik, 1958).
  2. C. G. Wynne, “Flat-field microscope objective,” J. Sci. Instrum. 38, 92–94 (1961).
    [CrossRef]
  3. H. C. Clasen, “Microscope objectives with plano-correction,” Appl. Opt. 3, 993–1003 (1964).
    [CrossRef]
  4. H. Beyer, Handbuch der Mikroskopie (VEB-Verlag Technik, 1973).
  5. H. Gross, F. Blechinger, and B. Achtner, Handbook of Optical Systems: Survey of Optical Instruments (Wiley, 2008), Vol.  4.
  6. C. Liang, K.-B. Sung, R. R. Richards-Kortum, and M. R. Descour, “Design of a high-numerical-aperture miniature microscope objective for an endoscopic fiber confocal reflectance microscope,” Appl. Opt. 41, 4603–4610 (2002).
    [CrossRef] [PubMed]
  7. http://www.olympusamerica.com/seg_section/uis2/seg_uis2_uplsapo.asp.
  8. www.zemax.com.
  9. www.lambdares.com.
  10. www.opticalres.com.
  11. www.optenso.com.
  12. G. Schulz, “Higher order aplanatism,” Opt. Commun. 41, 315–319 (1982).
    [CrossRef]
  13. A. Mikš, Applied Optics (Czech Technical U., 2009).
    [PubMed]
  14. M. Born and E. Wolf, Principles of Optics (Cambridge U. Press, 1999).
  15. A. Mikš, “Modification of the formulas for third-order aberration coefficients,” J. Opt. Soc. Am. A. 19, 1867–1871 (2002).
    [CrossRef]
  16. W. T. Welford, Aberrations of Optical Systems (Taylor & Francis, 1986).
  17. H. H. Hopkins, Wave Theory of Aberrations (Oxford U. Press, 1950).
  18. B. Havelka, Geometrical Optics I, II (Czech Academy of Science Press, 1955).
  19. D. Argentieri, Ottica Industriale (Hoepli, 1942).
  20. H. Chretien, Calcul des Combinaisons Optiques (Masson, 1980).
  21. M. Berek, Grundlagen der Praktischen Optik (Walter de Gruyter, 1970).
    [CrossRef]
  22. A. Mikš, J. Novák, and P. Novák, “Method of zoom lens design,” Appl. Opt. 47, 6088–6098 (2008).
    [CrossRef] [PubMed]
  23. H. H. Hopkins and V. V. Rao, “The systematic design of two component objectives,” Opt. Acta 17, 497–514 (1970).
    [CrossRef]
  24. M. I. Khan, “Cemented triplets: a method for rapid design,” Opt. Acta 31, 873–883 (1984).
    [CrossRef]
  25. M. Herzberger, “Replacing a thin lens by a thick lens,” J. Opt. Soc. Am. 34, 114–115 (1944).
    [CrossRef]
  26. A. Mikš and J. Vondřich, “Methods for design of superachromatic systems,” Fine Mechanics and Optics 10, 79–84(1966).
  27. H. Pulvermacher, “Theorie der Restspektren von Simpletts,” Optik (Jena) 30, 297–313 (1969).
  28. M. Herzberger and H. Pulvermacher, “Die Farbfehlerkorrektion von Multipletts,” Opt. Acta 17, 349–361 (1970).
    [CrossRef]

2008

2002

1984

M. I. Khan, “Cemented triplets: a method for rapid design,” Opt. Acta 31, 873–883 (1984).
[CrossRef]

1982

G. Schulz, “Higher order aplanatism,” Opt. Commun. 41, 315–319 (1982).
[CrossRef]

1970

H. H. Hopkins and V. V. Rao, “The systematic design of two component objectives,” Opt. Acta 17, 497–514 (1970).
[CrossRef]

M. Herzberger and H. Pulvermacher, “Die Farbfehlerkorrektion von Multipletts,” Opt. Acta 17, 349–361 (1970).
[CrossRef]

1969

H. Pulvermacher, “Theorie der Restspektren von Simpletts,” Optik (Jena) 30, 297–313 (1969).

1966

A. Mikš and J. Vondřich, “Methods for design of superachromatic systems,” Fine Mechanics and Optics 10, 79–84(1966).

1964

1961

C. G. Wynne, “Flat-field microscope objective,” J. Sci. Instrum. 38, 92–94 (1961).
[CrossRef]

1944

Achtner, B.

H. Gross, F. Blechinger, and B. Achtner, Handbook of Optical Systems: Survey of Optical Instruments (Wiley, 2008), Vol.  4.

Argentieri, D.

D. Argentieri, Ottica Industriale (Hoepli, 1942).

Berek, M.

M. Berek, Grundlagen der Praktischen Optik (Walter de Gruyter, 1970).
[CrossRef]

Beyer, H.

H. Beyer, Handbuch der Mikroskopie (VEB-Verlag Technik, 1973).

Blechinger, F.

H. Gross, F. Blechinger, and B. Achtner, Handbook of Optical Systems: Survey of Optical Instruments (Wiley, 2008), Vol.  4.

Boegehold, H.

H. Boegehold, Das Optische System des Mikroskops (Verlag Technik, 1958).

Born, M.

M. Born and E. Wolf, Principles of Optics (Cambridge U. Press, 1999).

Chretien, H.

H. Chretien, Calcul des Combinaisons Optiques (Masson, 1980).

Clasen, H. C.

Descour, M. R.

Gross, H.

H. Gross, F. Blechinger, and B. Achtner, Handbook of Optical Systems: Survey of Optical Instruments (Wiley, 2008), Vol.  4.

Havelka, B.

B. Havelka, Geometrical Optics I, II (Czech Academy of Science Press, 1955).

Herzberger, M.

M. Herzberger and H. Pulvermacher, “Die Farbfehlerkorrektion von Multipletts,” Opt. Acta 17, 349–361 (1970).
[CrossRef]

M. Herzberger, “Replacing a thin lens by a thick lens,” J. Opt. Soc. Am. 34, 114–115 (1944).
[CrossRef]

Hopkins, H. H.

H. H. Hopkins and V. V. Rao, “The systematic design of two component objectives,” Opt. Acta 17, 497–514 (1970).
[CrossRef]

H. H. Hopkins, Wave Theory of Aberrations (Oxford U. Press, 1950).

Khan, M. I.

M. I. Khan, “Cemented triplets: a method for rapid design,” Opt. Acta 31, 873–883 (1984).
[CrossRef]

Liang, C.

Mikš, A.

A. Mikš, J. Novák, and P. Novák, “Method of zoom lens design,” Appl. Opt. 47, 6088–6098 (2008).
[CrossRef] [PubMed]

A. Mikš, “Modification of the formulas for third-order aberration coefficients,” J. Opt. Soc. Am. A. 19, 1867–1871 (2002).
[CrossRef]

A. Mikš and J. Vondřich, “Methods for design of superachromatic systems,” Fine Mechanics and Optics 10, 79–84(1966).

A. Mikš, Applied Optics (Czech Technical U., 2009).
[PubMed]

Novák, J.

Novák, P.

Pulvermacher, H.

M. Herzberger and H. Pulvermacher, “Die Farbfehlerkorrektion von Multipletts,” Opt. Acta 17, 349–361 (1970).
[CrossRef]

H. Pulvermacher, “Theorie der Restspektren von Simpletts,” Optik (Jena) 30, 297–313 (1969).

Rao, V. V.

H. H. Hopkins and V. V. Rao, “The systematic design of two component objectives,” Opt. Acta 17, 497–514 (1970).
[CrossRef]

Richards-Kortum, R. R.

Schulz, G.

G. Schulz, “Higher order aplanatism,” Opt. Commun. 41, 315–319 (1982).
[CrossRef]

Sung, K.-B.

Vondrich, J.

A. Mikš and J. Vondřich, “Methods for design of superachromatic systems,” Fine Mechanics and Optics 10, 79–84(1966).

Welford, W. T.

W. T. Welford, Aberrations of Optical Systems (Taylor & Francis, 1986).

Wolf, E.

M. Born and E. Wolf, Principles of Optics (Cambridge U. Press, 1999).

Wynne, C. G.

C. G. Wynne, “Flat-field microscope objective,” J. Sci. Instrum. 38, 92–94 (1961).
[CrossRef]

Appl. Opt.

Fine Mechanics and Optics

A. Mikš and J. Vondřich, “Methods for design of superachromatic systems,” Fine Mechanics and Optics 10, 79–84(1966).

J. Opt. Soc. Am.

J. Opt. Soc. Am. A.

A. Mikš, “Modification of the formulas for third-order aberration coefficients,” J. Opt. Soc. Am. A. 19, 1867–1871 (2002).
[CrossRef]

J. Sci. Instrum.

C. G. Wynne, “Flat-field microscope objective,” J. Sci. Instrum. 38, 92–94 (1961).
[CrossRef]

Opt. Acta

H. H. Hopkins and V. V. Rao, “The systematic design of two component objectives,” Opt. Acta 17, 497–514 (1970).
[CrossRef]

M. I. Khan, “Cemented triplets: a method for rapid design,” Opt. Acta 31, 873–883 (1984).
[CrossRef]

M. Herzberger and H. Pulvermacher, “Die Farbfehlerkorrektion von Multipletts,” Opt. Acta 17, 349–361 (1970).
[CrossRef]

Opt. Commun.

G. Schulz, “Higher order aplanatism,” Opt. Commun. 41, 315–319 (1982).
[CrossRef]

Optik (Jena)

H. Pulvermacher, “Theorie der Restspektren von Simpletts,” Optik (Jena) 30, 297–313 (1969).

Other

A. Mikš, Applied Optics (Czech Technical U., 2009).
[PubMed]

M. Born and E. Wolf, Principles of Optics (Cambridge U. Press, 1999).

W. T. Welford, Aberrations of Optical Systems (Taylor & Francis, 1986).

H. H. Hopkins, Wave Theory of Aberrations (Oxford U. Press, 1950).

B. Havelka, Geometrical Optics I, II (Czech Academy of Science Press, 1955).

D. Argentieri, Ottica Industriale (Hoepli, 1942).

H. Chretien, Calcul des Combinaisons Optiques (Masson, 1980).

M. Berek, Grundlagen der Praktischen Optik (Walter de Gruyter, 1970).
[CrossRef]

H. Boegehold, Das Optische System des Mikroskops (Verlag Technik, 1958).

H. Beyer, Handbuch der Mikroskopie (VEB-Verlag Technik, 1973).

H. Gross, F. Blechinger, and B. Achtner, Handbook of Optical Systems: Survey of Optical Instruments (Wiley, 2008), Vol.  4.

http://www.olympusamerica.com/seg_section/uis2/seg_uis2_uplsapo.asp.

www.zemax.com.

www.lambdares.com.

www.opticalres.com.

www.optenso.com.

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (7)

Fig. 1
Fig. 1

Optical systems of different microscope objective lenses.

Fig. 2
Fig. 2

Front part—plano–convex lens and aplanatic meniscus.

Fig. 3
Fig. 3

Front plano–convex lens.

Fig. 4
Fig. 4

Aplanatic meniscus.

Fig. 5
Fig. 5

General meniscus.

Fig. 6
Fig. 6

Front part with two meniscus lenses.

Fig. 7
Fig. 7

Optical scheme of microscope objective lens.

Tables (5)

Tables Icon

Table 1 Calculated Paraxial Heights and Angles (Planachomat 10 × )

Tables Icon

Table 2 Parameters of Rear Part of Objective Lens (Variant 1)

Tables Icon

Table 3 Parameters of Rear Part of Objective Lens (Variant 2)

Tables Icon

Table 4 Calculated Parameters ( r , d , n ) —Microscope Lens

Tables Icon

Table 5 Aberrations of Objective Lens (Planachromat 10 × )

Equations (14)

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

r 1 = , r 2 = n 2 n 2 + 1 ( n 2 n 1 s 1 + d 1 ) , s 2 = r 2 ( n 2 + 1 ) , m = n 2 2 ,
r 1 = s 1 , r 2 = n 2 n 2 + 1 ( r 1 d ) , s 2 = n 2 ( r 1 d ) , m = u 1 / u 2 = n 2 ,
S IV = i = 1 k 1 r i ( 1 n i + 1 1 n i ) = i = 1 k 1 h i ( u i + 1 n i u i n i + 1 ) = i = 1 k N i h i .
S IV = i = 1 k φ i n i = p i = 1 k φ i .
r 1 = s 1 ( n 2 n 1 ) m M n 1 ( n 2 2 m M ) , r 2 = 1 n 2 n 2 ( S IV n 2 n 1 r 1 n 1 n 2 ) , d = s 1 m M n 1 n 2 r 2 1 + n 2 n 2 , h 1 = s 1 u 1 , u 2 = u 1 n 1 n 2 / m M , h 2 = h 1 d u 2 , u 3 = u 2 / n 2 , s 2 = h 2 / u 3 ,
r 1 = s 1 ( n 2 n 1 ) m f n 1 n 4 ( n 2 2 m f / n 4 ) , r 2 = 1 n 2 n 2 ( S I V n 2 n 1 r 1 n 1 n 2 ) , d 1 = s 1 m f n 1 n 2 n 4 r 2 1 + n 2 n 2 , h 1 = s 1 u 1 , u 2 = u 1 n 1 n 2 n 4 / m f , h 2 = h 1 d 1 u 2 , u 3 = u 2 / n 2 , h 3 = h 2 d 2 u 3 , u 4 = u 3 , h 4 = h 3 d 3 u 4 , u 5 = u 4 / n 4 , s 4 = h 4 / u 5 , r i = n i + 1 n i n i + 1 u i + 1 n i u i , ( i = 3 , 4 ) ,
φ 5 = ( u 6 u 5 ) / h 5 , φ 6 = ( u 7 u 6 ) / h 6 , φ b = φ 5 + φ 6 d 5 φ 5 φ 6 , m b = m / m f , s 5 = ( 1 / m b 1 + d 5 φ 6 ) / φ b , s 6 = ( 1 m b d 5 φ 5 ) / φ b ,
a 5 h 2 5 + a 4 h 2 4 + a 3 h 2 3 + a 2 h 2 2 + a 1 h 2 + a 0 = 0.
a 5 = p G d 5 , a 4 = a p G d 5 + p + d 5 ( S IV ) sum , a 3 = b p G d 5 p ( A + B + C ) + d 5 N 4 + d 5 N 3 + d 5 N 2 a d 5 ( S IV ) sum , a 2 = c p G d 5 + p ( A B + A E + B E ) d 5 N 4 ( A + C ) d 5 N 3 ( B + C ) a d 5 N 2 + b d 5 ( S IV ) sum , a 1 = p A B E + d 5 N 4 A C + d 5 N 3 B C + b d 5 N 2 d 5 c ( S IV ) sum , a 0 = d 5 N 2 c ,
h 1 = s 1 u 1 , u 2 = u 1 n 1 n 2 n 4 / m f , u 3 = u 2 / n 2 , u 4 = u 3 , u 5 = u 4 / n 4 , u 7 = u 5 m f / m , h 6 = ( L d 5 ) u 7 , p = 0.65 , N i = u i + 1 / n i u i / n i + 1 , ( i = 1 , 2 , 3 , 4 ) A = d 2 u 3 , B = A + d 3 u 4 , C = B + d 4 u 5 , D = ( h 6 + C ) / d 5 , E = ( D + u 5 ) d 5 , F = ( u 7 + D ) / h 6 , G = 1 / ( h 6 d 5 ) , a = A + B + C , b = A B + A C + B C , c = A B C .
d 1 = ( h 1 h 2 ) / u 2 , h 3 = h 2 A , h 4 = h 2 B , h 5 = h 2 C , u 6 = h 2 / d 5 D , φ 5 = ( u 6 u 5 ) / h 5 , φ 6 = ( u 7 u 6 ) / h 6 , r i = n i + 1 n i n i + 1 u i + 1 n i u i , ( i = 1 , 2 , 3 , 4 ) .
( S I ) 56 = i = 5 6 h i 4 φ i 3 M ¯ i + 2 i = 5 6 h i 4 φ i 3 Y i N ¯ i + 1.06 i = 5 6 h i 4 φ i 3 Y i 2 , ( S II ) 56 = i = 5 6 h i 3 h ¯ i φ i 3 M ¯ i + i = 5 6 h i 2 φ i 2 ( 2 h i h ¯ i φ i Y i + 1 ) N ¯ i + i = 5 6 h i 2 φ i 2 Y i ( 1.06 h i h ¯ i φ i Y i + 1.31 ) , ( S III ) 56 = i = 5 6 h i 2 h ¯ i 2 φ i 3 M ¯ i + 2 i = 5 6 h i h ¯ i φ i 2 ( h i h ¯ i φ i Y i + 1 ) N ¯ i + i = 5 6 h i h ¯ i φ i 2 Y i ( 1.06 h i h ¯ i φ i Y i + 2.62 ) + i = 5 6 φ i .
Y i = s i + s i s i s i = m i + 1 m i 1 = 1 2 s i φ i = 1 2 s i φ i , Y i + 1 = h i φ i h i + 1 φ i + 1 ( Y i 1 ) 1.
u 1 = 0.3 , s 1 = 12 mm , m = 10 , m I = 3.5 , d 2 = 0.5 mm , d 3 = 3 mm , d 4 = 4 mm , d 5 = 15 mm , L = 162 mm , n 1 = 1 , n 2 = 1.755 ( LaK33A ) , n 3 = 1 , n 4 = 1.754 , n 5 = 1 , n 6 = 1 , n 7 = 1 , p = 0.65 , S I = 0 , S II = 0 , S III = 0 , S IV = 0 , M ¯ 5 = 1.

Metrics