Abstract

A new laser differential confocal ultra-long focal length measurement (LDCFM) method is proposed with the capability to self-calibrate the reference lens (RL) focal length and the axial space between the test lens and RL. Using the property that the focus of laser differential confocal ultra-long focal length measurement system (LDCFS) precisely corresponds to the null point of the differential confocal axial intensity curve, the proposed LDCFM measures the RL focal length f R′ by precisely identifying the positions of the focus and last surface of RL, measures the axial space d 0 between RL and test ultra-long focal length lens (UFL) by identifying the last surface of RL and the vertex of UFL last surface, and measures the variation l in focus position of LDCFS with and without test UFL, and then calculates the UFL focal length f T′ by the above measured f R′, d 0 and l. In addition, a LDCFS based on the proposed method is developed for a large aperture lens. The experimental results indicate that the relative uncertainty is less than 0.01% for the test UFL, which has an aperture of 610 mm and focal length of 31,000 mm. LDCFM provides a novel approach for the high-precision focal-length measurement of large-aperture UFL.

© 2015 Optical Society of America

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References

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  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 .
    [Crossref]
  2. C. Jin, S. Liu, Y. Zhou, X. Xu, C. Wei, and J. Shao, “Study on measurement of medium and low spatial wavefront errors of long focal length lens,” Chin. Opt. Lett. 12, S21203 (2014).
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    [Crossref] [PubMed]
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    [Crossref] [PubMed]
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    [Crossref] [PubMed]
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    [Crossref] [PubMed]
  7. H. Changlun, B. Jian, H. Xiyun, S. Chen, and Y. Guoguang, “Novel method for testing the long focal length lens of large aperture,” Opt. Lasers Eng. 43(10), 1107–1117 (2005).
    [Crossref]
  8. J. Luo, J. Bai, J. Zhang, C. Hou, K. Wang, and X. Hou, “Long focal-length measurement using divergent beam and two gratings of different periods,” Opt. Express 22(23), 27921–27931 (2014).
    [Crossref] [PubMed]
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    [Crossref] [PubMed]
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    [Crossref] [PubMed]
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    [Crossref] [PubMed]

2014 (2)

C. Jin, S. Liu, Y. Zhou, X. Xu, C. Wei, and J. Shao, “Study on measurement of medium and low spatial wavefront errors of long focal length lens,” Chin. Opt. Lett. 12, S21203 (2014).

J. Luo, J. Bai, J. Zhang, C. Hou, K. Wang, and X. Hou, “Long focal-length measurement using divergent beam and two gratings of different periods,” Opt. Express 22(23), 27921–27931 (2014).
[Crossref] [PubMed]

2012 (1)

2010 (1)

2005 (2)

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]

H. Changlun, B. Jian, H. Xiyun, S. Chen, and Y. Guoguang, “Novel method for testing the long focal length lens of large aperture,” Opt. Lasers Eng. 43(10), 1107–1117 (2005).
[Crossref]

2003 (1)

1991 (1)

1987 (1)

1985 (1)

Aggarwal, A. K.

Bai, J.

Bhattacharya, J. C.

Changlun, H.

H. Changlun, B. Jian, H. Xiyun, S. Chen, and Y. Guoguang, “Novel method for testing the long focal length lens of large aperture,” Opt. Lasers Eng. 43(10), 1107–1117 (2005).
[Crossref]

Chen, S.

H. Changlun, B. Jian, H. Xiyun, S. Chen, and Y. Guoguang, “Novel method for testing the long focal length lens of large aperture,” Opt. Lasers Eng. 43(10), 1107–1117 (2005).
[Crossref]

DeBoo, B.

Faridi, M. S.

Glatt, I.

Guoguang, Y.

H. Changlun, B. Jian, H. Xiyun, S. Chen, and Y. Guoguang, “Novel method for testing the long focal length lens of large aperture,” Opt. Lasers Eng. 43(10), 1107–1117 (2005).
[Crossref]

Hou, C.

Hou, X.

Jian, B.

H. Changlun, B. Jian, H. Xiyun, S. Chen, and Y. Guoguang, “Novel method for testing the long focal length lens of large aperture,” Opt. Lasers Eng. 43(10), 1107–1117 (2005).
[Crossref]

Jin, C.

C. Jin, S. Liu, Y. Zhou, X. Xu, C. Wei, and J. Shao, “Study on measurement of medium and low spatial wavefront errors of long focal length lens,” Chin. Opt. Lett. 12, S21203 (2014).

Kafri, O.

Liu, S.

C. Jin, S. Liu, Y. Zhou, X. Xu, C. Wei, and J. Shao, “Study on measurement of medium and low spatial wavefront errors of long focal length lens,” Chin. Opt. Lett. 12, S21203 (2014).

Luo, J.

Murata, K.

Nakano, Y.

Qiu, L.

Sasian, J.

Sha, D.

Shakher, C.

Shao, J.

C. Jin, S. Liu, Y. Zhou, X. Xu, C. Wei, and J. Shao, “Study on measurement of medium and low spatial wavefront errors of long focal length lens,” Chin. Opt. Lett. 12, S21203 (2014).

Shi, L.

Singh, P.

Sirohi, R. S.

Sun, R.

Wang, K.

Wei, C.

C. Jin, S. Liu, Y. Zhou, X. Xu, C. Wei, and J. Shao, “Study on measurement of medium and low spatial wavefront errors of long focal length lens,” Chin. Opt. Lett. 12, S21203 (2014).

Wu, H.

Xiyun, H.

H. Changlun, B. Jian, H. Xiyun, S. Chen, and Y. Guoguang, “Novel method for testing the long focal length lens of large aperture,” Opt. Lasers Eng. 43(10), 1107–1117 (2005).
[Crossref]

Xu, X.

C. Jin, S. Liu, Y. Zhou, X. Xu, C. Wei, and J. Shao, “Study on measurement of medium and low spatial wavefront errors of long focal length lens,” Chin. Opt. Lett. 12, S21203 (2014).

Yang, J.

Zhang, J.

Zhao, W.

Zhou, Y.

C. Jin, S. Liu, Y. Zhou, X. Xu, C. Wei, and J. Shao, “Study on measurement of medium and low spatial wavefront errors of long focal length lens,” Chin. Opt. Lett. 12, S21203 (2014).

Appl. Opt. (5)

Chin. Opt. Lett. (1)

C. Jin, S. Liu, Y. Zhou, X. Xu, C. Wei, and J. Shao, “Study on measurement of medium and low spatial wavefront errors of long focal length lens,” Chin. Opt. Lett. 12, S21203 (2014).

Opt. Express (3)

Opt. Lasers Eng. (1)

H. Changlun, B. Jian, H. Xiyun, S. Chen, and Y. Guoguang, “Novel method for testing the long focal length lens of large aperture,” Opt. Lasers Eng. 43(10), 1107–1117 (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 .
[Crossref]

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Figures (14)

Fig. 1
Fig. 1 Principle of combination lens measurement.
Fig. 2
Fig. 2 LDCFM principle. MO is the microscope objective, PH is the pinhole, LB is the beam splitter, LC is the collimating lens, UFL is the ultra-long focal length lens, RL is the reference lens, LR is the reflector, DMI is the distance cmeasuring instrument, BS is the beam splitter, M is the offset of the Detectors from the focus of Lc.
Fig. 3
Fig. 3 Focal length measurement of RL.
Fig. 4
Fig. 4 Axial space measurement of combination lens.
Fig. 5
Fig. 5 LDCFS main structure.
Fig. 6
Fig. 6 LDCFS design effect.
Fig. 7
Fig. 7 LDCFM instrument.
Fig. 8
Fig. 8 Uncertainty transfer coefficients.
Fig. 9
Fig. 9 Schematics with different offsets.
Fig. 10
Fig. 10 Angles between LDCFS axes.
Fig. 11
Fig. 11 Flow chart of experimental steps.
Fig. 12
Fig. 12 Measurement curves of RL focal length.
Fig. 13
Fig. 13 Differential curves of RL focus and combination lens focus.
Fig. 14
Fig. 14 (a) Experiments for repeatability. (b) Experiments for reproducibility.

Tables (1)

Tables Icon

Table 1 Uncertainty of f T′ for various focal length

Equations (27)

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I A ( u , u M ) = I 2 ( u , u M ) I 1 ( u , + u M ) = [ sin ( 2 u + u M 4 ) / ( 2 u + u M 4 ) ] 2 [ sin ( 2 u u M 4 ) / ( 2 u u M 4 ) ] 2
{ u = π 2 λ ( D f ) 2 z u M = π 2 λ ( D f C ) 2 M
I B ( u , u M ) = I 2 ( u , u M ) I 1 ( u , + u M ) = [ sin ( 2 u + u M 4 ) / ( 2 u + u M 4 ) ] 2 [ sin ( 2 u u M 4 ) / ( 2 u u M 4 ) ] 2
f T B F D = d 0 f R ' + ( f R ' ) 2 l .
f T ' = f T B F D + r b 12 1 n 1 ( r 12 r 11 ) + ( n 1 1 ) b 1 ,
I A ( u , u M ) = [ sin ( 2 u + u M 4 ) / ( 2 u + u M 4 ) ] 2 [ ( sin 2 u u M 4 ) / ( 2 u u M 4 ) ] 2
I E ( u , u M ) = [ sin ( u + u M 4 ) / ( u + u M 4 ) ] 2 [ ( sin ( u u M 4 ) / ( u u M 4 ) ] 2
f R = f R B F D + b 0 n 0 = 2 Δ L 1 + b 0 n 0
d 0 = r 01 + sin U 0 sin α ( 2 tan U 0 tan U 1 Δ L 2 b 0 r 01 ) ,
{ U 1 = arc sin ( 1 n 0 sin U 0 ) α = U 1 + arc sin ( 2 tan U 0 tan U 1 Δ L 2 b 0 r 01 r 01 sin U 1 ) arc sin ( 2 tan U 0 tan U 1 Δ L 2 b 0 r 01 r 01 n 0 sin U 1 ) ,
{ f T ' d 0 = 1 f T ' f R ' = 2 f R ' l 1 f T ' l = ( f R ' l ) 2
u ( d 0 ) = 1 3 × 0.02 % × 420 mm = 4.8 μ m
u ( f R ' ) = ( σ o f f e s e t 3 ) 2 + ( σ a x i a l 3 ) 2 + 4 ( ( σ L 3 ) 2 + ( σ Δ L 1 20 ) 2 ) ,
u ( f R ' ) = ( 12.5 3 ) 2 + ( 0.03 3 ) 2 + 4 ( ( 0.3 3 ) 2 + ( 7.31 20 ) 2 ) = 7.91 μ m
I A ( u A , u M ) = [ sin 2 u A + ( u M + u σ ) 4 2 u A + ( u M + u σ ) 4 ] 2 [ sin 2 u A u M 4 2 u A u M 4 ] 2 ,
I B ( u B , u M ) = [ sin 2 u B + ( u M + u σ ) 4 2 u B + ( u M + u σ ) 4 ] 2 [ sin 2 u B u M 4 2 u B u M 4 ] 2 ,
u A = u B = u σ 4 .
u A = π 2 λ ( D f R ) 2 z and u B = π 2 λ ( D ( f R + f T d ) d f R f T ) 2 z .
Δ l A = f R 2 f C 2 σ 4   and Δ l B =- [ f R f T / ( f R + f T d ) ] 2 f C 2 σ 4 .
σ M = Δ l A Δ l B = f R 2 f C 2 ( 1 f T 2 ( f T + f R d ) 2 ) σ 4 = ( 1 ( 1 + f R / f T d / f T ) 2 1 ) σ 4 .
σ L = 1 × 10 6 × l .
σ a , β = Δ l = cos α cos β f R ' 2 f T ' + f R ' cos α d cos α f R ' 2 f T ' + f R ' d .
u ( l ) = ( σ M 3 ) 2 +( σ a , β 3 ) 2 + ( σ L 3 ) 2 + σ l 2 .
u c ( f T ' ) = ( f T d 0 u ( d 0 ) ) 2 + ( f T f R u ( f R ' ) ) 2 + ( f T l u ( l ) ) 2 ,
u r e l ( f T ' ) = u ( f T ' ) f T ' × 100 % .
u c ( f T ' ) = ( f T d 0 u ( d 0 ) ) 2 + ( f T f R u ( f R ) ) 2 + ( f T l u ( l ) ) 2 = ( 1 × 0.0048 ) 2 + ( 22.99 × 0.0079 ) 2 + ( 143.98 × 0.0110 ) 2 , = 1.59 mm
u r e l ( f T ' ) = u ( f T ' ) f T ' × 100 % = 1.59 mm 31218.34 mm × 100 % = 0.0051 % .

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