Abstract

Abstract: In order to achieve the precise measurement of the lenses axial space, a new lenses axial space ray tracing measurement (ASRTM) is proposed based on the geometrical theory of optical image. For an assembled lenses with the given radius of curvature rn and refractive index nn of every lens, ASRTM uses the annular laser differential confocal chromatography focusing technique (ADCFT) to achieve the precise focusing at the vertex position Pn of its inner-and-outer spherical surface Sn and obtain the coordinate zn corresponding to the axial movement position of ASRTM objective, and then, uses the ray tracing facet iterative algorithm to precisely determine the vertex position Pn of every spherical surface by these coordinates zn, refractive index nn and spherical radius rn, and thereby obtaining the lenses inner axial space dn. The preliminary experimental results indicate that ASRTM has a relative measurement error of less than 0.02%.

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References

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  1. D. M. Williamson, “Compensator selection in the tolerancing of a microlithographic lens,” Proc. SPIE 1049, 178–186 (1989).
  2. K. K. Westort, “Design and fabrication of high performance relay lenses,” Proc. SPIE 548, 40–47 (1984).
  3. T. Sure and J. Heil, “Microscope objective production: On the way from the micrometer scale to the nanometer scale,” Proc. SPIE 5180, 283–292 (2003).
    [CrossRef]
  4. L. A. Selberg, “Radius measurement by interferometry,” Opt. Eng. 31(9), 1961–1966 (1992).
    [CrossRef]
  5. W. Zhao, R. Sun, L. Qiu, and D. Sha, “Laser differential confocal ultra-long focal length measurement,” Opt. Express 17(22), 20051–20062 (2009).
    [CrossRef] [PubMed]
  6. W. Zhao, J. Tan, and L. Qiu, “Bipolar absolute differential confocal approach to higher spatial resolution,” Opt. Express 12(21), 5013–5021 (2004).
    [CrossRef] [PubMed]
  7. W. Zhao, L. Qiu, and Z. Feng, “Effect of fabrication errors on superresolution property of a pupil filter,” Opt. Express 14(16), 7024–7036 (2006).
    [CrossRef] [PubMed]
  8. L. Liu, X. Deng, and G. Wang, “Phase-only optical pupil filter for improving axial resolution in confocal microscopy,” Acta Phys. Sin. 50, 48–51 (2001).
  9. M. Born and E. Wolf, Principles of Optics (Cambridge University Press, 1999), Chap. 4, Chap. 9.

2009 (1)

2006 (1)

2004 (1)

2003 (1)

T. Sure and J. Heil, “Microscope objective production: On the way from the micrometer scale to the nanometer scale,” Proc. SPIE 5180, 283–292 (2003).
[CrossRef]

2001 (1)

L. Liu, X. Deng, and G. Wang, “Phase-only optical pupil filter for improving axial resolution in confocal microscopy,” Acta Phys. Sin. 50, 48–51 (2001).

1992 (1)

L. A. Selberg, “Radius measurement by interferometry,” Opt. Eng. 31(9), 1961–1966 (1992).
[CrossRef]

1989 (1)

D. M. Williamson, “Compensator selection in the tolerancing of a microlithographic lens,” Proc. SPIE 1049, 178–186 (1989).

1984 (1)

K. K. Westort, “Design and fabrication of high performance relay lenses,” Proc. SPIE 548, 40–47 (1984).

Deng, X.

L. Liu, X. Deng, and G. Wang, “Phase-only optical pupil filter for improving axial resolution in confocal microscopy,” Acta Phys. Sin. 50, 48–51 (2001).

Feng, Z.

Heil, J.

T. Sure and J. Heil, “Microscope objective production: On the way from the micrometer scale to the nanometer scale,” Proc. SPIE 5180, 283–292 (2003).
[CrossRef]

Liu, L.

L. Liu, X. Deng, and G. Wang, “Phase-only optical pupil filter for improving axial resolution in confocal microscopy,” Acta Phys. Sin. 50, 48–51 (2001).

Qiu, L.

Selberg, L. A.

L. A. Selberg, “Radius measurement by interferometry,” Opt. Eng. 31(9), 1961–1966 (1992).
[CrossRef]

Sha, D.

Sun, R.

Sure, T.

T. Sure and J. Heil, “Microscope objective production: On the way from the micrometer scale to the nanometer scale,” Proc. SPIE 5180, 283–292 (2003).
[CrossRef]

Tan, J.

Wang, G.

L. Liu, X. Deng, and G. Wang, “Phase-only optical pupil filter for improving axial resolution in confocal microscopy,” Acta Phys. Sin. 50, 48–51 (2001).

Westort, K. K.

K. K. Westort, “Design and fabrication of high performance relay lenses,” Proc. SPIE 548, 40–47 (1984).

Williamson, D. M.

D. M. Williamson, “Compensator selection in the tolerancing of a microlithographic lens,” Proc. SPIE 1049, 178–186 (1989).

Zhao, W.

Acta Phys. Sin. (1)

L. Liu, X. Deng, and G. Wang, “Phase-only optical pupil filter for improving axial resolution in confocal microscopy,” Acta Phys. Sin. 50, 48–51 (2001).

Opt. Eng. (1)

L. A. Selberg, “Radius measurement by interferometry,” Opt. Eng. 31(9), 1961–1966 (1992).
[CrossRef]

Opt. Express (3)

Proc. SPIE (3)

D. M. Williamson, “Compensator selection in the tolerancing of a microlithographic lens,” Proc. SPIE 1049, 178–186 (1989).

K. K. Westort, “Design and fabrication of high performance relay lenses,” Proc. SPIE 548, 40–47 (1984).

T. Sure and J. Heil, “Microscope objective production: On the way from the micrometer scale to the nanometer scale,” Proc. SPIE 5180, 283–292 (2003).
[CrossRef]

Other (1)

M. Born and E. Wolf, Principles of Optics (Cambridge University Press, 1999), Chap. 4, Chap. 9.

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Figures (10)

Fig. 1
Fig. 1

Lenses axial space measurement.

Fig. 2
Fig. 2

ASRTM principle. L C is collimating lens, B is an annular pupil, PBS is polarized beam splitter, P is λ/4, L1 is objective, L2 is collecting lens, BS is beam splitter, CCD1 and CCD2 are detectors, MO1 and MO2 are microscope objective, M is the offset of pinhole from the focus of L2.

Fig. 3
Fig. 3

Differential confocal focusing resolution σz with different α 0 and ε.

Fig. 4
Fig. 4

Axial space calculation principle using ray tracing.

Fig. 5
Fig. 5

Effect of annular pupil on wave aberration.a) Without annular pupil B, b) With annular pupil B.

Fig. 6
Fig. 6

Intensity curves with different ε and A 040 =1.5λ .

Fig. 7
Fig. 7

Intensity curves with different ε and A 022 =0.2λ.

Fig. 8
Fig. 8

Experimental setup. 1. X80 interferometer produced by RENISHAW. 2. Interferometer measurement prisms. 3. Air bearing slider. 4. Test lens. 5. Differential confocal objective. 6. Annular pupil. 7. Collimator. 8. Laser. 9. Single-mode fiber. 10. Monitor. 11. Image capture and process software. 12. VPH 1. 13. VPH 2. 14. Material temperature sensor. 15. Air sensor.

Fig. 9
Fig. 9

Thickness Measurement of singlet.

Fig. 10
Fig. 10

Space measurement of lenses.

Equations (11)

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I ( v , u , u M , ε ) = I V P H 1 ( v , u , + u M , ε ) I V P H 2 ( v , u , u M , ε ) = | 2 ( 1 ε 2 ) ε 1 p C ( ρ ) p 1 2 ( ρ ) p 2 ( ρ ) e j ρ 2 ( 2 u + u M ) / 2 J 0 ( ρ v ) ρ d ρ | 2 | 2 ( 1 ε 2 ) ε 1 p C ( ρ ) p 1 2 ( ρ ) p 2 ( ρ ) e j ρ 2 ( 2 u u M ) / 2 J 0 ( ρ v ) ρ d ρ | 2 .
I ( 0 , u , u M , ε ) = [ sin c ( 2 u + u M 4 π ( 1 ε 2 ) ) ] 2 [ sin c ( 2 u u M 4 π ( 1 ε 2 ) ) ] 2 .
S ( 0 , 0 , u M , ε ) = I ( 0 , u , u M , ε ) u | u = 0 = 2 sin c ( u M 4 π ( 1 ε 2 ) ) cos ( u M 4 ( 1 ε 2 ) ) u M 4 ( 1 ε 2 ) sin ( u M 4 ( 1 ε 2 ) ) ( u M 4 ) 2 ( 1 ε 2 ) .
u M 5.21 × 1 1 ε 2 .
σ z = δ I ( 0 , u , u M , ε ) | 0 . 54 (1- ε 2 ) | λ 8 π sin 2 ( α 0 / 2 ) = 0.0737 λ (1- ε 2 ) S N R sin 2 ( α 0 / 2 )
{ i n = arc sin ( l n r n r n sin θ n ) i n = arc sin ( n n 1 n n sin i n ) θ n = θ n + i n i n l n = r n + sin i n sin θ n r n
{ θ n = θ n 1 + arc sin ( l n 1 d n 1 r n r n sin θ n 1 ) arc sin ( n n 1 n n l n 1 d n 1 r n r n sin θ n 1 ) l n = r n + n n 1 n n sin θ n 1 sin θ n ( l n 1 d n 1 r n ) .
{ l 0 = l 0 = z n + 1 z 1 θ 0 = θ 0
d n AXIAL = ε ρ pupil ρ pupil T ( r , n , z , arc tan ( ρ f 1 ) ) 2 π ρ d ρ π ρ pupil 2 ( 1 ε 2 )
I ( 0 , u , u M , ε ) = | 2 1 ε 2 ε 1 e 2 j A 040 ρ 4 e j ρ 2 ( 2 u + u M ) / 2 ρ d ρ | 2 | 2 1 ε 2 ε 1 e 2 j A 040 ρ 4 e j ρ 2 ( 2 u u M ) / 2 ρ d ρ | 2 .
I ( 0 , u , u M , ε ) = | 1 π ( 1 ε 2 ) 0 2 π ε 1 e j ρ 2 ( 2 u + u M ) / 2 e j 2 k A 022 ρ 2 cos θ 2 ρ d ρ d θ | 2 | 1 π ( 1 ε 2 ) 0 2 π ε 1 e j ρ 2 ( 2 u u M ) / 2 e j 2 k A 022 ρ 2 cos θ 2 ρ d ρ d θ | 2 .

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