Abstract

Different measurement methods have been used to achieve different parameter measurements of a spherical lens, and multi-parameter measurements of a spherical lens have low measurement accuracy and efficiency. This paper proposes a new, laser differential confocal interference multi-parameter measurement (DCIMPM) method for spherical lens. Based on this proposed DCIMPM, a multi-parameter comprehensive measurement system is developed for spherical lens, which uses the laser differential confocal parameter measurement technique to measure the radius of curvature, thickness, and refractivity of spherical lens, and uses the laser interference measurement technique to measure the surface figure of a spherical lens. Therefore, the DCIMPM system, for the first time, achieves high-accuracy multi-parameter comprehensive measurements of a spherical lens on a single instrument. Experiments indicate that the developed DCIMPM system can achieve a measurement accuracy of 5 × 10−6 for the lens radius, 2.5 × 10−4 for the lens thickness, 2.2 × 10−4 for the lens refractivity, and a peak to valley of λ/20 for the surface figure of the lens. The proposed DCIMPM principle and developed system provide a new approach to achieve multi-parameter comprehensive measurements for spherical lens.

© 2016 Optical Society of America

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References

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  1. G. H. Miller, E. I. Moses, and C. R. Wuest, “The national ignition facility,” Opt. Eng. 43(12), 2841–2853 (2004).
    [Crossref]
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    [Crossref] [PubMed]
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    [Crossref] [PubMed]
  5. L. A. Selberg, “Radius measurement by interferometry,” Opt. Eng. 31(9), 1961–1966 (1992).
    [Crossref]
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  10. W. Q. Zhao, J. M. Yang, and L. R. Qiu, “Method and device for measuring multiple parameters of differential confocal interference component,” China Invention Patent, Priority number: ZL201010621159.7, Application date: 2010–12–24.
  11. W. Zhao, R. Sun, L. Qiu, and D. Sha, “Laser differential confocal radius measurement,” Opt. Express 18(3), 2345–2360 (2010).
    [Crossref] [PubMed]

2016 (1)

2015 (1)

2010 (2)

2007 (1)

2005 (1)

M. Kunkel and J. Schulze, “Noncontact measurement of central lens thickness,” Glass Sci. Technol. 78, 245–247 (2005).

2004 (1)

G. H. Miller, E. I. Moses, and C. R. Wuest, “The national ignition facility,” Opt. Eng. 43(12), 2841–2853 (2004).
[Crossref]

1992 (1)

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

1982 (1)

Auerbach, J. M.

Bowers, M. W.

Burke, J.

Dixit, S. N.

Erbert, G. V.

Guo, D. M.

Haynam, C. A.

Heestand, G. M.

Henesian, M. A.

Hermann, M. R.

Jancaitis, K. S.

Kunkel, M.

M. Kunkel and J. Schulze, “Noncontact measurement of central lens thickness,” Glass Sci. Technol. 78, 245–247 (2005).

Li, Y.

Manes, K. R.

Marshall, C. D.

Mehta, N. C.

Menapace, J.

Miller, G. H.

G. H. Miller, E. I. Moses, and C. R. Wuest, “The national ignition facility,” Opt. Eng. 43(12), 2841–2853 (2004).
[Crossref]

Moses, E.

Moses, E. I.

G. H. Miller, E. I. Moses, and C. R. Wuest, “The national ignition facility,” Opt. Eng. 43(12), 2841–2853 (2004).
[Crossref]

Murray, J. R.

Ni, X. Q.

Nostrand, M. C.

Orth, C. D.

Patterson, R.

Qiu, L.

Sacks, R. A.

Schulze, J.

M. Kunkel and J. Schulze, “Noncontact measurement of central lens thickness,” Glass Sci. Technol. 78, 245–247 (2005).

Selberg, L. A.

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

Sha, D.

Shaw, M. J.

Smith, G.

Spaeth, M.

Sun, R.

Sutton, S. B.

Tan, Y. D.

Van Wonterghem, B. M.

Wang, M.

Wang, W. P.

Wegner, P. J.

White, R. K.

Widmayer, C. C.

Williams, W. H.

Wu, D. S.

Wuest, C. R.

G. H. Miller, E. I. Moses, and C. R. Wuest, “The national ignition facility,” Opt. Eng. 43(12), 2841–2853 (2004).
[Crossref]

Yang, S. T.

Zhang, S. L.

Zhao, W.

Appl. Opt. (3)

Chin. Opt. Lett. (2)

Glass Sci. Technol. (1)

M. Kunkel and J. Schulze, “Noncontact measurement of central lens thickness,” Glass Sci. Technol. 78, 245–247 (2005).

Opt. Eng. (2)

G. H. Miller, E. I. Moses, and C. R. Wuest, “The national ignition facility,” Opt. Eng. 43(12), 2841–2853 (2004).
[Crossref]

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

Opt. Express (1)

Other (2)

W. Q. Zhao, J. M. Yang, and L. R. Qiu, “Method and device for measuring multiple parameters of differential confocal interference component,” China Invention Patent, Priority number: ZL201010621159.7, Application date: 2010–12–24.

D. Malacara, Optical Shop Testing (Wiley Intersicen Publication, 1992).

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Figures (17)

Fig. 1
Fig. 1 DCIMPM principle. The PBS is the polarized beam splitter,P is a point source, Lc is the collimating lens, LS is the standard lens, RM is the reflector, LW is the test spherical lens, BS1 and BS2 are the beam splitters, P1 and P2 are pinholes,D1 and D2 are detectors,CCD is the detector,M is the offset of the pinhole from the focal plane of LC, and Li is the imaging lens.
Fig. 2
Fig. 2 Sensitivity of Differential confocal response curves for different uM. (a). Sensitivity S(uM) (b). Differential confocal curve ID(u,uM)
Fig. 3
Fig. 3 Measurement of the ROC, thickness, and refractivity of a spherical lens. (a) ROC measurement, (b) thickness and refractivity measurement.
Fig. 4
Fig. 4 Ray tracing used for refractivity and central thickness measurement.
Fig. 5
Fig. 5 Diagram of the DCIMPM system
Fig. 6
Fig. 6 Designed DCIMPM system
Fig. 7
Fig. 7 Developed DCIMPM system
Fig. 8
Fig. 8 Measurement and control diagram of the DCIMPM system
Fig. 9
Fig. 9 Data processing interface of differential confocal parameter measurement system
Fig. 10
Fig. 10 Diagram of phase shifting interferometry measurement software
Fig. 11
Fig. 11 Data processing interface of phase-shifting interferometry measurement software
Fig. 12
Fig. 12 DCIMPM with different pinhole offset.
Fig. 13
Fig. 13 Test samples: (a) triple prism, (b) plano-concave lens
Fig. 14
Fig. 14 Measurement curves of the ROC for the test plano-concave lens
Fig. 15
Fig. 15 Ten measurement results of ROC for the test plano-concave lens using the DCIMPM system
Fig. 16
Fig. 16 Measurement curves of central thickness and refractivity for the test plano-concave lens
Fig. 17
Fig. 17 Figures measured by (a) the developed DCIMPM system and (b) the Zygo interferometer

Equations (26)

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I D (u, u M )= | 0 2π 0 1 exp[ i2kw(ρ,θ) ]exp(iu ρ 2 i u M ρ 2 2 )ρdρ dθ | 2 , | 0 2π 0 1 exp[ i2kw(ρ,θ) ]exp(iu ρ 2 + i u M ρ 2 2 )ρdρ dθ | 2
I D (u, u M )= [ sin( u/2 u M /4 ) u/2 u M /4 ] 2 [ sin( u/2+ u M /4 ) u/2+ u M /4 ] 2 .
S( u M )=| I D (u, u M ) u | u=0 |=| 2sin u M 4 ( sin u M 4 u M 4 cos u M 4 ) / ( u M 4 ) 3 |.
I D (z)= [ sin( π 4λ D 2 f o 2 z1.303 ) π 4λ D 2 f o 2 z1.303 ] 2 [ sin( π 4λ D 2 f o 2 z+1.303 ) π 4λ D 2 f o 2 z+1.303 ] 2 .
φ( x,y )=arctan[ 2( I 4 I 2 ) 2 I 3 I 5 I 1 ].
w( x,y )= 1 2 × λ 2π Φ( x,y ).
r= z A z B. 
{ θ 1 =arctan(ρ N A 2 1-N A 2 ), t= r 1 + 1 n sin θ 1 sin( θ 1 +arcsin( d 1 r 1 r 1 sin θ 1 )arcsin( 1 n d 1 r 1 r 1 sin θ 1 )) ( d 1 r 1 ), θ 1 = θ 1 +arcsin( d 2 r 1 r 1 sin θ 1 )arcsin( 1 n d 2 r 1 r 1 sin θ 1 ), l 1 = r 1 + 1 n sin θ 1 sin θ 1 ( d 2 r 1 ), θ 2 = θ 1 +arcsin( l 1 t r 2 r 2 sin θ 1 )arcsin(n l 1 t r 2 r 2 sin θ 1 ), d 3 =t+ r 2 +n sin θ 1 sin θ 2 ( l 1 t r 2 ).
{ t= 0 1 t( r 1 , d 1 ,n,ρ,NA)K(ρ)2πρdρ n= 0 1 n( r 1 , r 2 , d 1 , d 2 , d 3 ,ρ,NA)K(ρ)2πρdρ ,
u( Δ d )0.25× 10 6 R.
u( Δ γ )=0.4× 10 6 R.
u( Δ a )=3.2× 10 11 f o 2 R 1 .
u( Δ w )= λ k20 × 1 3 =0.009μm.
u( Δ z )= 1 S max SNRk 2λ f o 2 π D 2 = 0.0039λ f o 2 D 2 .
I DA (u, u M )= [ sin( u/2 u M /4 ) u/2 u M /4 ] 2 [ sin( u/2+ u M /4+ u δ /4 ) u/2+ u M /4+ u δ /4 ] 2
I DB (u, u M )= [ sin( u/2 u M /4 ) u/2 u M /4 ] 2 [ sin( u/2+ u M /4+ u δ /4 ) u/2+ u M /4+ u δ /4 ] 2
u c (R)= [ u 2 ( Δ d )+ u 2 ( Δ γ )+ u 2 ( Δ a )+ u 2 ( Δ w )+2 u 2 ( Δ z )] 1 2 =(0.014μm+0.0005|R|).
u( Δ r1 )=(0.014μm+0.0005| r 1 |).
u( Δ d1 )=0.25× 10 6 d 1 .
u( Δ n )=3× 10 6 .
NA= 2[ n g 2 ( t g / d flat ) 2 ] 1 ( t g / d flat ) 2 ,
u( Δ NA )= 1 NA( d flat 2 t g 2 ) { [ ( 2 n g 2 d flat N A 2 d flat )u( Δ flat ) ] 2 + [ ( N A 2 t g 2 t g )u( Δ g ) ] 2 + [ 2 t flat 2 n g u( Δ n ) ] 2 } 1/2 ,
u t = [ ( t r 1 u( Δ r1 ) ) 2 + ( t d 1 u( Δ d1 ) ) 2 + ( t NA u( Δ NA ) ) 2 + ( t n u( Δ n ) ) 2 ] 1/2 .
u( Δ ri )=(0.014μm+0.0005| r i |).
u( Δ di )=0.25× 10 6 d i .
u n = [ ( t r 1 u( Δ r1 ) ) 2 + ( t r 2 u( Δ r2 ) ) 2 + ( t d 1 u( Δ d1 ) ) 2 + ( t d 2 u( Δ d2 ) ) 2 + ( t d 3 u( Δ d3 ) ) 2 + ( t NA u( Δ NA ) ) 2 ] 1/2 .

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