Abstract

A method is presented for the calculation of paraxial design parameters of a double-sided telecentric zoom lens with easy variation of the magnification range. The telecentric lens consists of a zoom lens with a fixed distance between focal points and a lens with a fixed focal length. The third-order aberration analysis is also performed, and spot diagrams are calculated for two f-number values.

© 2012 Optical Society of America

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References

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  1. http://www.opto-engineering.com/ .
  2. http://www.schneiderkreuznach.com/ .
  3. http://www.edmundoptics.com/ .
  4. http://www.silloptics.de/ .
  5. http://www.ibe-optics.com/ .
  6. http://navitar.com/ .
  7. http://www.goyooptical.com/ .
  8. http://www.moritexusa.com/ .
  9. http://en.lensation.de/ .
  10. http://www.toshiba.com/taec/adinfo/cmos/ .
  11. C.-L. Chang, K.-C. Huang, W.-H. Wu, and Y.-H. Lin, “The design and fabrication of telecentric lens with large field of view,” Proc. SPIE 7786, 778612 (2010).
    [CrossRef]
  12. H. Bai and S. P. Sadoulet, “Large-format telecentric lens,” Proc. SPIE 6667, 666705 (2007).
    [CrossRef]
  13. S. Bloch and E. I. Betensky, “Telecentric zoom lens used in metrology applications,” Proc. SPIE 4487, 42–52 (2001).
    [CrossRef]
  14. J. R. Zinter and M. C. Sanson, “Telecentric zoom lens,” Proc. SPIE 4487, 130–139 (2001).
    [CrossRef]
  15. M. A. Pate, “Optical design and specification of telecentric optical systems,” Proc. SPIE 3482, 877 (1998).
    [CrossRef]
  16. G. Erdei, G. Szarvas, P. Kallo, and E. Loerincz, “Telecentric/inverse-telecentric objective for optical data storage purposes,” Proc. SPIE 3573, 380–383 (1998).
    [CrossRef]
  17. L. Zhang, H. Zhao, W. Dong, N. Cao, and P. Zhang, “Design of an optical system consisting of a special telecentric lens for side-scattering measurement on individual cells,” Opt. Eng. 49, 053001 (2010).
    [CrossRef]
  18. G. Baldwin-Olguin, “Telecentric lens for precision machine vision,” Proc. SPIE 2730, 440–443 (1996).
    [CrossRef]
  19. P. B. Catrysse and B. A. Wandell, “Roadmap for CMOS image sensors: Moore meets Planck and Sommerfeld,” Proc. SPIE 5678, 1–13 (2005).
    [CrossRef]
  20. P. B. Catrysse and B. A. Wandell, “Optical efficiency of image sensor pixels,” J. Opt. Soc. Am. A 19, 1610–1620 (2002).
    [CrossRef]
  21. C. C. Fesenmaier, Y. Huo, and P. B. Catrysse, “Optical confinement methods for continued scaling of CMOS image sensor pixels,” Opt. Express 16, 20457–20470 (2008).
    [CrossRef]
  22. T. Kryszczyński, “Development of the double-sided telecentric three-component zoom systems by means of matrix optics,” Proc. SPIE 7141, 71411Y (2008).
    [CrossRef]
  23. M. Herzberger, Modern Geometrical Optics (Wiley-Interscience, 1958).
  24. M. Herzberger, “Gaussian optics and Gaussian brackets,” J. Opt. Soc. Am. 33, 651–652 (1943).
    [CrossRef]
  25. A. Miks, J. Novak, and P. Novak, “Method of zoom lens design,” Appl. Opt. 47, 6088–6098 (2008).
    [CrossRef]
  26. A. Miks, “Modification of the formulas for third-order aberration coefficients,” J. Opt. Soc. Am. A 19, 1867–1871 (2002).
    [CrossRef]
  27. M. Berek, Grundlagen der Praktischen Optik (Walter de Gruyter, 1970).
  28. W. T. Welford, Aberrations of Optical Systems (Taylor & Francis, 1986).
  29. H. Chretien, Calcul des Combinaisons Optiques (Masson, 1980).
  30. H. H. Hopkins and V. V. Rao, “The systematic design of two component objectives,” Opt. Acta 17, 497–514 (1970).
    [CrossRef]
  31. M. I. Khan, “Cemented triplets: a method for rapid design,” Opt. Acta 31, 873–883 (1984).
    [CrossRef]
  32. C. H. Chen and S. G. Shiue, “Method of solving a triplet comprising a singlet and a cemented doublet with given primary aberrations,” J. Mod. Opt. 44, 1279–1291 (1997).
    [CrossRef]
  33. D. Argentieri, Ottica industriale (U. Hoepli, 1942).
  34. A. Szulc, “Improved solution for the cemented doublet,” Appl. Opt. 35, 3548–3558 (1996).
    [CrossRef]
  35. M. H. Sussman, “Cemented aplanatic doublets,” J. Opt. Soc. Am. 52, 1185–1186 (1962).
    [CrossRef]
  36. S. Banerjee and L. Hazra, “Experiments with a genetic algorithm for structural design of cemented doublets with prespecified aberration targets,” Appl. Opt. 40, 6265–6273 (2001).
    [CrossRef]
  37. M. I. Khan and J. Macdonald, “Cemented doublets, a method for rapid design,” Opt. Acta 29, 807–822 (1982).
    [CrossRef]

2010 (2)

C.-L. Chang, K.-C. Huang, W.-H. Wu, and Y.-H. Lin, “The design and fabrication of telecentric lens with large field of view,” Proc. SPIE 7786, 778612 (2010).
[CrossRef]

L. Zhang, H. Zhao, W. Dong, N. Cao, and P. Zhang, “Design of an optical system consisting of a special telecentric lens for side-scattering measurement on individual cells,” Opt. Eng. 49, 053001 (2010).
[CrossRef]

2008 (3)

2007 (1)

H. Bai and S. P. Sadoulet, “Large-format telecentric lens,” Proc. SPIE 6667, 666705 (2007).
[CrossRef]

2005 (1)

P. B. Catrysse and B. A. Wandell, “Roadmap for CMOS image sensors: Moore meets Planck and Sommerfeld,” Proc. SPIE 5678, 1–13 (2005).
[CrossRef]

2002 (2)

2001 (3)

S. Banerjee and L. Hazra, “Experiments with a genetic algorithm for structural design of cemented doublets with prespecified aberration targets,” Appl. Opt. 40, 6265–6273 (2001).
[CrossRef]

S. Bloch and E. I. Betensky, “Telecentric zoom lens used in metrology applications,” Proc. SPIE 4487, 42–52 (2001).
[CrossRef]

J. R. Zinter and M. C. Sanson, “Telecentric zoom lens,” Proc. SPIE 4487, 130–139 (2001).
[CrossRef]

1998 (2)

M. A. Pate, “Optical design and specification of telecentric optical systems,” Proc. SPIE 3482, 877 (1998).
[CrossRef]

G. Erdei, G. Szarvas, P. Kallo, and E. Loerincz, “Telecentric/inverse-telecentric objective for optical data storage purposes,” Proc. SPIE 3573, 380–383 (1998).
[CrossRef]

1997 (1)

C. H. Chen and S. G. Shiue, “Method of solving a triplet comprising a singlet and a cemented doublet with given primary aberrations,” J. Mod. Opt. 44, 1279–1291 (1997).
[CrossRef]

1996 (2)

A. Szulc, “Improved solution for the cemented doublet,” Appl. Opt. 35, 3548–3558 (1996).
[CrossRef]

G. Baldwin-Olguin, “Telecentric lens for precision machine vision,” Proc. SPIE 2730, 440–443 (1996).
[CrossRef]

1984 (1)

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

1982 (1)

M. I. Khan and J. Macdonald, “Cemented doublets, a method for rapid design,” Opt. Acta 29, 807–822 (1982).
[CrossRef]

1970 (1)

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

1962 (1)

1943 (1)

Argentieri, D.

D. Argentieri, Ottica industriale (U. Hoepli, 1942).

Bai, H.

H. Bai and S. P. Sadoulet, “Large-format telecentric lens,” Proc. SPIE 6667, 666705 (2007).
[CrossRef]

Baldwin-Olguin, G.

G. Baldwin-Olguin, “Telecentric lens for precision machine vision,” Proc. SPIE 2730, 440–443 (1996).
[CrossRef]

Banerjee, S.

Berek, M.

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

Betensky, E. I.

S. Bloch and E. I. Betensky, “Telecentric zoom lens used in metrology applications,” Proc. SPIE 4487, 42–52 (2001).
[CrossRef]

Bloch, S.

S. Bloch and E. I. Betensky, “Telecentric zoom lens used in metrology applications,” Proc. SPIE 4487, 42–52 (2001).
[CrossRef]

Cao, N.

L. Zhang, H. Zhao, W. Dong, N. Cao, and P. Zhang, “Design of an optical system consisting of a special telecentric lens for side-scattering measurement on individual cells,” Opt. Eng. 49, 053001 (2010).
[CrossRef]

Catrysse, P. B.

Chang, C.-L.

C.-L. Chang, K.-C. Huang, W.-H. Wu, and Y.-H. Lin, “The design and fabrication of telecentric lens with large field of view,” Proc. SPIE 7786, 778612 (2010).
[CrossRef]

Chen, C. H.

C. H. Chen and S. G. Shiue, “Method of solving a triplet comprising a singlet and a cemented doublet with given primary aberrations,” J. Mod. Opt. 44, 1279–1291 (1997).
[CrossRef]

Chretien, H.

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

Dong, W.

L. Zhang, H. Zhao, W. Dong, N. Cao, and P. Zhang, “Design of an optical system consisting of a special telecentric lens for side-scattering measurement on individual cells,” Opt. Eng. 49, 053001 (2010).
[CrossRef]

Erdei, G.

G. Erdei, G. Szarvas, P. Kallo, and E. Loerincz, “Telecentric/inverse-telecentric objective for optical data storage purposes,” Proc. SPIE 3573, 380–383 (1998).
[CrossRef]

Fesenmaier, C. C.

Hazra, L.

Herzberger, M.

Hopkins, H. H.

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

Huang, K.-C.

C.-L. Chang, K.-C. Huang, W.-H. Wu, and Y.-H. Lin, “The design and fabrication of telecentric lens with large field of view,” Proc. SPIE 7786, 778612 (2010).
[CrossRef]

Huo, Y.

Kallo, P.

G. Erdei, G. Szarvas, P. Kallo, and E. Loerincz, “Telecentric/inverse-telecentric objective for optical data storage purposes,” Proc. SPIE 3573, 380–383 (1998).
[CrossRef]

Khan, M. I.

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

M. I. Khan and J. Macdonald, “Cemented doublets, a method for rapid design,” Opt. Acta 29, 807–822 (1982).
[CrossRef]

Kryszczynski, T.

T. Kryszczyński, “Development of the double-sided telecentric three-component zoom systems by means of matrix optics,” Proc. SPIE 7141, 71411Y (2008).
[CrossRef]

Lin, Y.-H.

C.-L. Chang, K.-C. Huang, W.-H. Wu, and Y.-H. Lin, “The design and fabrication of telecentric lens with large field of view,” Proc. SPIE 7786, 778612 (2010).
[CrossRef]

Loerincz, E.

G. Erdei, G. Szarvas, P. Kallo, and E. Loerincz, “Telecentric/inverse-telecentric objective for optical data storage purposes,” Proc. SPIE 3573, 380–383 (1998).
[CrossRef]

Macdonald, J.

M. I. Khan and J. Macdonald, “Cemented doublets, a method for rapid design,” Opt. Acta 29, 807–822 (1982).
[CrossRef]

Miks, A.

Novak, J.

Novak, P.

Pate, M. A.

M. A. Pate, “Optical design and specification of telecentric optical systems,” Proc. SPIE 3482, 877 (1998).
[CrossRef]

Rao, V. V.

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

Sadoulet, S. P.

H. Bai and S. P. Sadoulet, “Large-format telecentric lens,” Proc. SPIE 6667, 666705 (2007).
[CrossRef]

Sanson, M. C.

J. R. Zinter and M. C. Sanson, “Telecentric zoom lens,” Proc. SPIE 4487, 130–139 (2001).
[CrossRef]

Shiue, S. G.

C. H. Chen and S. G. Shiue, “Method of solving a triplet comprising a singlet and a cemented doublet with given primary aberrations,” J. Mod. Opt. 44, 1279–1291 (1997).
[CrossRef]

Sussman, M. H.

Szarvas, G.

G. Erdei, G. Szarvas, P. Kallo, and E. Loerincz, “Telecentric/inverse-telecentric objective for optical data storage purposes,” Proc. SPIE 3573, 380–383 (1998).
[CrossRef]

Szulc, A.

Wandell, B. A.

P. B. Catrysse and B. A. Wandell, “Roadmap for CMOS image sensors: Moore meets Planck and Sommerfeld,” Proc. SPIE 5678, 1–13 (2005).
[CrossRef]

P. B. Catrysse and B. A. Wandell, “Optical efficiency of image sensor pixels,” J. Opt. Soc. Am. A 19, 1610–1620 (2002).
[CrossRef]

Welford, W. T.

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

Wu, W.-H.

C.-L. Chang, K.-C. Huang, W.-H. Wu, and Y.-H. Lin, “The design and fabrication of telecentric lens with large field of view,” Proc. SPIE 7786, 778612 (2010).
[CrossRef]

Zhang, L.

L. Zhang, H. Zhao, W. Dong, N. Cao, and P. Zhang, “Design of an optical system consisting of a special telecentric lens for side-scattering measurement on individual cells,” Opt. Eng. 49, 053001 (2010).
[CrossRef]

Zhang, P.

L. Zhang, H. Zhao, W. Dong, N. Cao, and P. Zhang, “Design of an optical system consisting of a special telecentric lens for side-scattering measurement on individual cells,” Opt. Eng. 49, 053001 (2010).
[CrossRef]

Zhao, H.

L. Zhang, H. Zhao, W. Dong, N. Cao, and P. Zhang, “Design of an optical system consisting of a special telecentric lens for side-scattering measurement on individual cells,” Opt. Eng. 49, 053001 (2010).
[CrossRef]

Zinter, J. R.

J. R. Zinter and M. C. Sanson, “Telecentric zoom lens,” Proc. SPIE 4487, 130–139 (2001).
[CrossRef]

Appl. Opt. (3)

J. Mod. Opt. (1)

C. H. Chen and S. G. Shiue, “Method of solving a triplet comprising a singlet and a cemented doublet with given primary aberrations,” J. Mod. Opt. 44, 1279–1291 (1997).
[CrossRef]

J. Opt. Soc. Am. (2)

J. Opt. Soc. Am. A (2)

Opt. Acta (3)

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. I. Khan and J. Macdonald, “Cemented doublets, a method for rapid design,” Opt. Acta 29, 807–822 (1982).
[CrossRef]

Opt. Eng. (1)

L. Zhang, H. Zhao, W. Dong, N. Cao, and P. Zhang, “Design of an optical system consisting of a special telecentric lens for side-scattering measurement on individual cells,” Opt. Eng. 49, 053001 (2010).
[CrossRef]

Opt. Express (1)

Proc. SPIE (9)

T. Kryszczyński, “Development of the double-sided telecentric three-component zoom systems by means of matrix optics,” Proc. SPIE 7141, 71411Y (2008).
[CrossRef]

C.-L. Chang, K.-C. Huang, W.-H. Wu, and Y.-H. Lin, “The design and fabrication of telecentric lens with large field of view,” Proc. SPIE 7786, 778612 (2010).
[CrossRef]

H. Bai and S. P. Sadoulet, “Large-format telecentric lens,” Proc. SPIE 6667, 666705 (2007).
[CrossRef]

S. Bloch and E. I. Betensky, “Telecentric zoom lens used in metrology applications,” Proc. SPIE 4487, 42–52 (2001).
[CrossRef]

J. R. Zinter and M. C. Sanson, “Telecentric zoom lens,” Proc. SPIE 4487, 130–139 (2001).
[CrossRef]

M. A. Pate, “Optical design and specification of telecentric optical systems,” Proc. SPIE 3482, 877 (1998).
[CrossRef]

G. Erdei, G. Szarvas, P. Kallo, and E. Loerincz, “Telecentric/inverse-telecentric objective for optical data storage purposes,” Proc. SPIE 3573, 380–383 (1998).
[CrossRef]

G. Baldwin-Olguin, “Telecentric lens for precision machine vision,” Proc. SPIE 2730, 440–443 (1996).
[CrossRef]

P. B. Catrysse and B. A. Wandell, “Roadmap for CMOS image sensors: Moore meets Planck and Sommerfeld,” Proc. SPIE 5678, 1–13 (2005).
[CrossRef]

Other (15)

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

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

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

D. Argentieri, Ottica industriale (U. Hoepli, 1942).

M. Herzberger, Modern Geometrical Optics (Wiley-Interscience, 1958).

http://www.opto-engineering.com/ .

http://www.schneiderkreuznach.com/ .

http://www.edmundoptics.com/ .

http://www.silloptics.de/ .

http://www.ibe-optics.com/ .

http://navitar.com/ .

http://www.goyooptical.com/ .

http://www.moritexusa.com/ .

http://en.lensation.de/ .

http://www.toshiba.com/taec/adinfo/cmos/ .

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Figures (9)

Fig. 1.
Fig. 1.

Principal scheme of the first variant of a double-sided telecentric zoom lens.

Fig. 2.
Fig. 2.

Principal scheme of the second variant of a double-sided telecentric zoom lens.

Fig. 3.
Fig. 3.

Scheme of a three-element zoom lens.

Fig. 4.
Fig. 4.

Dependence of distance d1 (dashed curve) and d2 (solid curve) on focal length f of the optical system.

Fig. 5.
Fig. 5.

Dependence of the positions of object focal point sF (solid curve) and image focal point sF (dashed curve) on focal length f of optical system.

Fig. 6.
Fig. 6.

Spot diagram (y=0mm, F=5.6).

Fig. 7.
Fig. 7.

Spot diagram pro (y=4mm, F=5.6).

Fig. 8.
Fig. 8.

Spot diagram (y=0mm, F=8).

Fig. 9.
Fig. 9.

Spot diagram (y=4mm, F=8).

Tables (2)

Tables Icon

Table 1. Parameters of the Three-Element Zoom Lens

Tables Icon

Table 2. Basic Parameters of Doublets

Equations (31)

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

α=[dN1,φN1,dN2,φN2,dN3,φN3,,d1,φ1,],β=[dN1,φN1,dN2,φN2,dN3,φN3,,d1],γ=[φN,dN1,φN1,dN2,φN2,dN3,,d1,φ1],δ=[φN,dN1,φN1,dN2,φN2,dN3,,d1],
[a1]=a1,[a1,a2]=a1a2+1.
[a1,a2,a3,,aN]=[a1,a2,a3,,aN2]+[a1,a2,a3,,aN1]aN.
φ=γ,sF=δ/γ,sF=α/γ,s=βαsδγs,m=sγ+α=1δsγ,
φ=γ,δ+γ(d1+d2)α=γD,
α=1d2(φ1+φ2φ1φ2d1)φ1d1,
γ=φ=(φ1+φ2+φ3)+φ1φ2d1+φ2φ3d2+φ1φ3(d1+d2)φ1φ2φ3d1d2,
δ=1d1(φ2+φ3)d2φ3+d1d2φ2φ3.
SIV=φ1/n1+φ2/n2+φ3/n3(φ1+φ2+φ3)/n=p/n,
a1d2+a0=0,
a1=(φ1+φ2)(φ1+φ2φ1φ2d1),a0=φ12d1φ;
b2d22+b1d2+b0=0,
b2=(φ1+φ2)(φ1+φ2φ1φ2d1),b1=(φ1+φ2)[D(φ1+φ2φ1φ2d1)+φ1d1(φ2d12)],b0=φ12d1(Dd1)2.
R=|b2b1b0a1a200a1a2|=c3d13+c2d12+c1d1+c0=0,
c3=φ12φ22(φ1+φ2)[φ(φ1+φ2)φ1φ2],c2=φ1φ2(φ1+φ2)[φ(φ12+φ22)+φ1φ2(4φ3(φ1+φ2))+Dφφ1φ2(φ1+φ2)],c1=φ1φ2(φ1+φ2)[2(φ1+φ2)2(Dφ2)+2φ(φ1+φ2)φ2],c0=(φ1+φ2)2[φ2+(φ1+φ2)2(2Dφ)].
a0=φ12d1φ=0,d1=f12/f.
b0=φ12d1(Dd1)2=0,d1=D/2±(f1/2)(D/f1)28.
(D/f1)280,f10.35D.
δy=yP(yP2+xP2)2(s1s¯1)3u13uKSI+y1(3yP2+xP2)2(s1s¯1)3u12uKu¯1SIIy12yP2(s1s¯1)3u1uKu¯12(3SIII+I2SIV)+y132(s1s¯1)3uKu¯13SV,δx=xP(yP2+xP2)2(s1s¯1)3u13uKSI+2y1yPxP2(s1s¯1)3u12uKu¯1SIIy12yP2(s1s¯1)3u1uKu¯12(SIII+I2SIV),
I=h1h¯1(1s11s¯1)=u1h¯1u¯1h1.
h¯1=s1s¯1s¯1s1,
h¯j=hj(h¯1+i=2jdi1hi1hi),
(SI)j=i=1Khji4φi3M¯i+2i=1Khji4φi3YjiN¯i+1.06i=1Khji4φi3Yji2,(SII)j=i=1Khji3h¯jiφi3M¯i+i=1Khji2φi2(2hjih¯jiφiYji+1)N¯i+i=1Khji2φi2Yji(1.06hjih¯jiφiYji+1.31),(SIII)j=i=1Khji2h¯ji2φi3M¯i+2i=1Khjih¯jiφi2(hjih¯jiφiYji+1)N¯i+i=1Khjih¯jiφi2Yji(1,06hjih¯jiφiYji+2.62)+i=1Kφi,(SIV)j=0.62i=1Kφi,(SV)j=i=1Khjih¯ji3φi3M¯i+i=1Kh¯ji2φi2(2hjih¯jiφiYji+3)N¯i+i=1Kh¯ji2φi2Yji(1.06hjih¯jiφiYji+3.93)+3.62i=1Kh¯jihjiφi,
Yji=sji+sjisjisji=mji+1mji1=12sjiφi,Yj(i+1)=hjiφihj(i+1)φi+1(Yji1)1,
Φ1=ν1(1+CIν2)ν1ν2,Φ2=1Φ1,K1=Φ2/2,K2=Φ1/2,
Ai=Φini+2ni,Bi=ΦiKi,Ci=Φi3[ni2(ni1)]2,Ei=Φini+1ni,
T=12(Φ1n11+Φ2n21+1),
R1=E2T+N¯E1+E2,R2=R1T,Qi=AiRi22BiRi+Ci,i=1,2,
ρ1=R1+K1+Φ12(n11),ρ2=R1+K1Φ12(n11),ρ3=R2+K2Φ22(n21),
rj=1/ρj,j=1,2,3,
|Q1+Q2M¯|δM¯,

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