Abstract

A new laser differential confocal focal-length measurement method is proposed for the measurement of an ultra-long focal-length. The approach proposed uses the property of an axial intensity curve that the absolute zero precisely corresponds to the focus of the objective in a differential confocal focusing system (DCFS) to measure the variation in position of DCFS focus with and without a measured ultra-long focal-length lens (UFL), uses the distance between the two focuses to obtain the UFL focal-length, and thereby achieving the precise measurement of ultra-long focal-length. The method has a high focusing precision, a strong anti-interference capability and a short measurement light-path. The theoretical analyses and preliminary experimental results indicate that the relative measurement error is about 0.01% when the method is used for the measurement of back-focus-distance (BFD).

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References

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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef]

2005 (3)

W. Zhao, J. Tan, L. Qiu, and L. Zou, “A new laser heterodyne confocal probe for ultraprecision measurement of discontinuous contours,” Meas. Sci. Technol. 16(2), 497–504 (2005).
[CrossRef]

W. Zhao, J. Tan, L. Qiu, and P. Jin, “SABCMS, A New Approach to Higher Lateral Resolution of Laser Probe Measurement,” Sens. Actuators A Phys. 120(1), 17–25 (2005).
[CrossRef]

P. Singh, M. S. Faridi, C. Shakher, and R. S. Sirohi, “Measurement of focal length with phase-shifting Talbot interferometry,” Appl. Opt. 44(9), 1572–1576 (2005).
[CrossRef] [PubMed]

2004 (1)

2003 (1)

1999 (1)

1992 (1)

1991 (1)

1987 (1)

1985 (1)

Aggarwal, A. K.

Bhattacharya, J. C.

DeBoo, B.

Faridi, M. S.

Filippov, O. K.

Glatt, L.

Jin, P.

W. Zhao, J. Tan, L. Qiu, and P. Jin, “SABCMS, A New Approach to Higher Lateral Resolution of Laser Probe Measurement,” Sens. Actuators A Phys. 120(1), 17–25 (2005).
[CrossRef]

Kafri, O.

Kothiyal, M. P.

Meshcheryakov, V. I.

Murata, K.

Nakano, Y.

Qiu, L.

W. Zhao, J. Tan, L. Qiu, and L. Zou, “A new laser heterodyne confocal probe for ultraprecision measurement of discontinuous contours,” Meas. Sci. Technol. 16(2), 497–504 (2005).
[CrossRef]

W. Zhao, J. Tan, L. Qiu, and P. Jin, “SABCMS, A New Approach to Higher Lateral Resolution of Laser Probe Measurement,” Sens. Actuators A Phys. 120(1), 17–25 (2005).
[CrossRef]

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]

Sasian, J.

Shakher, C.

Sinel’nikov, M. I.

Singh, P.

Sirohi, R. S.

Sriram, K. V.

Tan, J.

W. Zhao, J. Tan, L. Qiu, and P. Jin, “SABCMS, A New Approach to Higher Lateral Resolution of Laser Probe Measurement,” Sens. Actuators A Phys. 120(1), 17–25 (2005).
[CrossRef]

W. Zhao, J. Tan, L. Qiu, and L. Zou, “A new laser heterodyne confocal probe for ultraprecision measurement of discontinuous contours,” Meas. Sci. Technol. 16(2), 497–504 (2005).
[CrossRef]

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]

Zhao, W.

W. Zhao, J. Tan, L. Qiu, and P. Jin, “SABCMS, A New Approach to Higher Lateral Resolution of Laser Probe Measurement,” Sens. Actuators A Phys. 120(1), 17–25 (2005).
[CrossRef]

W. Zhao, J. Tan, L. Qiu, and L. Zou, “A new laser heterodyne confocal probe for ultraprecision measurement of discontinuous contours,” Meas. Sci. Technol. 16(2), 497–504 (2005).
[CrossRef]

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]

Zou, L.

W. Zhao, J. Tan, L. Qiu, and L. Zou, “A new laser heterodyne confocal probe for ultraprecision measurement of discontinuous contours,” Meas. Sci. Technol. 16(2), 497–504 (2005).
[CrossRef]

Appl. Opt. (6)

J. Opt. Technol. (1)

Meas. Sci. Technol. (1)

W. Zhao, J. Tan, L. Qiu, and L. Zou, “A new laser heterodyne confocal probe for ultraprecision measurement of discontinuous contours,” Meas. Sci. Technol. 16(2), 497–504 (2005).
[CrossRef]

Opt. Express (1)

Sens. Actuators A Phys. (1)

W. Zhao, J. Tan, L. Qiu, and P. Jin, “SABCMS, A New Approach to Higher Lateral Resolution of Laser Probe Measurement,” Sens. Actuators A Phys. 120(1), 17–25 (2005).
[CrossRef]

Other (1)

T. G. Parham, T. J. McCarville, and M. A. Johnson, Focal length measurements for the National Ignition Facility large lenses,” Optical Fabrication and Testing (OFT 2002) paper: OWD8 http://www.opticsinfobase.org/abstract.cfm?URI=OFT-2002-OWD8 .

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Figures (9)

Fig. 1
Fig. 1

Differential confocal focusing principle.

Fig. 2
Fig. 2

Differential confocal focusing measurement principle of ultra-long focal-length.

Fig. 3
Fig. 3

Light-path schematics of combination lens

Fig. 4
Fig. 4

Focusing sensitivity S(0,0,uM ) with different uM .

Fig. 5
Fig. 5

Differential confocal intensity curves with f 1 ' = 2f 2 ', 2.5f 2 ', 5f 2', 10f 2 ', f 1 '→∞.

Fig. 6
Fig. 6

Differential confocal focusing curves with f 1 ' = 1.5 f 2 ', 2f 2 ', 2.5f 2 ', 3f 2 ', 5f 2 ', 10f 2 ', f 1 '→∞.

Fig. 7
Fig. 7

Schematics of light path for two pinholes with different offset

Fig. 8
Fig. 8

Error propagation coefficient.

Fig. 9
Fig. 9

Differential confocal focusing curves measured.

Equations (33)

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I1(v,u,+uM)=|[201p1(ρ)e(juρ2)/2J0(ρv)ρdρ]|2×(|[201p2(ρ)ejρ2(u+uM)/2J0(ρv)ρdρ]|2)
{u=π2λ(Df)2zv=π2λ(Df)r
I2(v,u,uM)=|[201p1(ρ)e(juρ2)/2J0(ρv)ρdρ]|2×(|[201p2(ρ)ejρ2(uuM)/2J0(ρv)ρdρ]|2)
I(v,u,uM)=|[201p1(ρ)e(juρ2)/2J0(ρv)ρdρ]|2×(|[201p2(ρ)ejρ2(u+uM)/2J0(ρv)ρdρ]|2|[201p2(ρ)ejρ2(uuM)/2J0(ρv)ρdρ]|2)
I(0,u,uM)=[sin2u+uM42u+uM4]2[sin2uuM42uuM4]2
1f=1f1+1f2df1f2
fH2H22=f2l
H2H22=fdf1.
f1=df2+f22l
fBFD=f1H12V12=d0f2+f22l
f1=df2+f22l=fBFD+rb121n1(r12r11)+(n11)b1
S(0,0,uM)=I(0,u,uM)u|u=0=2sinc(uM4π)[(uM4)cos(uM4)sin(uM4)(uM4)2]
Smax=I(0,u,uM)u|u=0,uM=5.21=0.54
σzδI(0,u,uM)Smax2λπ(D/f)2
uM=π2λ(Df2)2M=5.21
k=ff2=f1f1+f2d
uM=π2λ(Df)2z=π2λ(Dkf2)2z=uM1k2=uM[f1+f2df1]2
IA(0,u1,uM)=[sin(2u1+uM+uδ4)2u1+uM+uδ4]2[sin(2u1uM4)2u1uM4]2=0
IB(0,u2,uM)=[sin(2u2+uM+uδ4)2u2+uM+uδ4]2[sin(2u2uM4)2u2uM4]2=0
u1=u2=uδ4
{Δl1=f22fLens22δ4Δl2=f2fLens22δ4
f=f1f2f1+f2d
Δl=Δl1Δl2=f22fLens22(1f12(f1+f2d)2)δ4
fBFDd0=1
fBFDf2=2f2l1
fBFDl=(f2l)2
σz=2λπSmaxSNR(D/f)2
σl=2×σz2+σL2
σf2=σz2+σRL2
σf1(fBFDd0σd0)2+(fBFDf2'σf2')2+(fBFDlσl)2
fBFD=d0f2+f22l=(26.40164.40+164.40223.9881)mm988.70mm
σfBFDfBFD((fBFDd0σd0)2+(fBFDf2σf2')2+(fBFDlσl)2)/fBFD=0.0052+12.72×0.0082+472×0.00062988.70.01%
f1=fBFD+b1n1(1r11r12)+(n11)b1r12=(988.70+101.5164×(1513.99)+(1.51641)×10)mm995.29mm

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