Abstract

A non-immersive lens refractive index measurement method based on fiber point-diffraction longitudinal interferometry is presented. The lens imaging process is simplified to the single refraction of the back surface if the object point is located at the vertex of the front surface. The lens refractive index is derived through measuring its thickness, radius of curvature of the back surface, the distance between the object point and the image point. Experiments indicate its accuracy is better than 2.2 × 10−4. Since the front surface is excluded in the imaging process, even an aspherical lens could be accurately measured by this method.

© 2013 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. G. Smith, “Liquid immersion method for the measurement of the refractive index of a simple lens,” Appl. Opt.21(5), 755–757 (1982).
    [CrossRef] [PubMed]
  2. R. S. Kasana and K. J. Rosenbruch, “Determination of the refractive index of a lens using the Murty shearing interferometer,” Appl. Opt.22(22), 3526–3531 (1983).
    [CrossRef] [PubMed]
  3. K. Soni and R. S. Kasana, “The use of defocused position of a Ronchi grating for evaluating the refractive index of lens,” Opt. Laser Technol.39(7), 1334–1338 (2007).
    [CrossRef]
  4. K. Soni and R. S. Kasana, “The role of an acousto-optic grating in determining the refractive index of a lens,” Meas. Sci. Technol.18(5), 1667–1671 (2007).
    [CrossRef]
  5. R. S. Kasana, A. Goswami, and K. Soni, “Non-destructive multiple beam interferometric technique for measuring the refractive indices of lenses,” Opt. Commun.236(4-6), 289–294 (2004).
    [CrossRef]
  6. I. Glatt and A. Livnat, “Determination of the refractive index of a lens using moire deflectometry,” Appl. Opt.23(14), 2241–2243 (1984).
    [CrossRef] [PubMed]
  7. R. S. Kasana, S. Boseck, and K. J. Rosenbruch, “Use of a grating in a coherent optical-processing configuration for evaluating the refractive index of a lens,” Appl. Opt.23(5), 757–761 (1984).
    [CrossRef] [PubMed]
  8. V. K. Chhaniwal, A. Anand, and C. S. Narayanamurthy, “Determination of refractive indices of biconvex lenses by use of a Michelson interferometer,” Appl. Opt.45(17), 3985–3990 (2006).
    [CrossRef] [PubMed]
  9. A. Anand and V. K. Chhaniwal, “Measurement of parameters of simple lenses using digital holographic interferometry and a synthetic reference wave,” Appl. Opt.46(11), 2022–2026 (2007).
    [CrossRef] [PubMed]
  10. W. Zhao, Y. Wang, L. Qiu, and H. Guo, “Laser differential confocal lens refractive index measurement,” Appl. Opt.50(24), 4769–4778 (2011).
    [CrossRef] [PubMed]
  11. L. Chen, X. Guo, and J. Hao, “Refractive index measurement by fiber point diffraction longitudinal shearing interferometry,” Appl. Opt.52(16), 3655–3661 (2013).
    [CrossRef] [PubMed]
  12. W. J. Smith, Modern Optical Engineering: The Design of Optical Systems (McGraw-Hill, New York, 1990).
  13. D. Malacara, Optical Shop Testing (John Wiley & Sons, New York, 2007).

2013

2011

2007

A. Anand and V. K. Chhaniwal, “Measurement of parameters of simple lenses using digital holographic interferometry and a synthetic reference wave,” Appl. Opt.46(11), 2022–2026 (2007).
[CrossRef] [PubMed]

K. Soni and R. S. Kasana, “The use of defocused position of a Ronchi grating for evaluating the refractive index of lens,” Opt. Laser Technol.39(7), 1334–1338 (2007).
[CrossRef]

K. Soni and R. S. Kasana, “The role of an acousto-optic grating in determining the refractive index of a lens,” Meas. Sci. Technol.18(5), 1667–1671 (2007).
[CrossRef]

2006

2004

R. S. Kasana, A. Goswami, and K. Soni, “Non-destructive multiple beam interferometric technique for measuring the refractive indices of lenses,” Opt. Commun.236(4-6), 289–294 (2004).
[CrossRef]

1984

1983

1982

Anand, A.

Boseck, S.

Chen, L.

Chhaniwal, V. K.

Glatt, I.

Goswami, A.

R. S. Kasana, A. Goswami, and K. Soni, “Non-destructive multiple beam interferometric technique for measuring the refractive indices of lenses,” Opt. Commun.236(4-6), 289–294 (2004).
[CrossRef]

Guo, H.

Guo, X.

Hao, J.

Kasana, R. S.

K. Soni and R. S. Kasana, “The use of defocused position of a Ronchi grating for evaluating the refractive index of lens,” Opt. Laser Technol.39(7), 1334–1338 (2007).
[CrossRef]

K. Soni and R. S. Kasana, “The role of an acousto-optic grating in determining the refractive index of a lens,” Meas. Sci. Technol.18(5), 1667–1671 (2007).
[CrossRef]

R. S. Kasana, A. Goswami, and K. Soni, “Non-destructive multiple beam interferometric technique for measuring the refractive indices of lenses,” Opt. Commun.236(4-6), 289–294 (2004).
[CrossRef]

R. S. Kasana, S. Boseck, and K. J. Rosenbruch, “Use of a grating in a coherent optical-processing configuration for evaluating the refractive index of a lens,” Appl. Opt.23(5), 757–761 (1984).
[CrossRef] [PubMed]

R. S. Kasana and K. J. Rosenbruch, “Determination of the refractive index of a lens using the Murty shearing interferometer,” Appl. Opt.22(22), 3526–3531 (1983).
[CrossRef] [PubMed]

Livnat, A.

Narayanamurthy, C. S.

Qiu, L.

Rosenbruch, K. J.

Smith, G.

Soni, K.

K. Soni and R. S. Kasana, “The role of an acousto-optic grating in determining the refractive index of a lens,” Meas. Sci. Technol.18(5), 1667–1671 (2007).
[CrossRef]

K. Soni and R. S. Kasana, “The use of defocused position of a Ronchi grating for evaluating the refractive index of lens,” Opt. Laser Technol.39(7), 1334–1338 (2007).
[CrossRef]

R. S. Kasana, A. Goswami, and K. Soni, “Non-destructive multiple beam interferometric technique for measuring the refractive indices of lenses,” Opt. Commun.236(4-6), 289–294 (2004).
[CrossRef]

Wang, Y.

Zhao, W.

Appl. Opt.

Meas. Sci. Technol.

K. Soni and R. S. Kasana, “The role of an acousto-optic grating in determining the refractive index of a lens,” Meas. Sci. Technol.18(5), 1667–1671 (2007).
[CrossRef]

Opt. Commun.

R. S. Kasana, A. Goswami, and K. Soni, “Non-destructive multiple beam interferometric technique for measuring the refractive indices of lenses,” Opt. Commun.236(4-6), 289–294 (2004).
[CrossRef]

Opt. Laser Technol.

K. Soni and R. S. Kasana, “The use of defocused position of a Ronchi grating for evaluating the refractive index of lens,” Opt. Laser Technol.39(7), 1334–1338 (2007).
[CrossRef]

Other

W. J. Smith, Modern Optical Engineering: The Design of Optical Systems (McGraw-Hill, New York, 1990).

D. Malacara, Optical Shop Testing (John Wiley & Sons, New York, 2007).

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (6)

Fig. 1
Fig. 1

Imaging by the refraction of the back surface of a lens.

Fig. 2
Fig. 2

Principle to measure the distance between the object point and its image point.

Fig. 3
Fig. 3

The distance between the object point and its image point with respect to a glass plate.

Fig. 4
Fig. 4

Experimental system for the lens refractive index measurement.

Fig. 5
Fig. 5

Processes for the lens refractive index measurement.

Fig. 6
Fig. 6

Refractive index measurement for ball lens and planar-cylindrical lens.

Tables (2)

Tables Icon

Table 1 Lens refractive index measurement results

Tables Icon

Table 2 Sensitivity coefficients at different d/ r 2

Equations (20)

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

1 l n d = 1n r 2 .
n= d r 2 d / l d+ r 2 .
n= d r 2 d / ( ΔRd ) d+ r 2 = dΔR d 2 r 2 d ( d+ r 2 )( ΔRd ) .
n= d dΔR .
Δw( x,y )=R R 2 ( x 2 + y 2 ) [ r r 2 ( x 2 + y 2 ) ] =RR 1 ( x 2 + y 2 ) / R 2 [ rr 1 ( x 2 + y 2 ) / r 2 ] RR( 1 x 2 + y 2 2 R 2 ){ rr( 1 x 2 + y 2 2 r 2 ) }= x 2 + y 2 2R x 2 + y 2 2r =k( x 2 + y 2 ).
Δ w ( x,y )=RΔR ( RΔR ) 2 ( x 2 + y 2 ) [ r r 2 ( x 2 + y 2 ) ] x 2 + y 2 2( RΔR ) x 2 + y 2 2r = k ( x 2 + y 2 ).
Δk= k k= 1 2( RΔR ) 1 2R 1 2R [ 1+ ΔR R 1 ]= ΔR 2 R 2 .
ΔR=2 R 2 Δk=2 R 2 ( k k ).
ΔR=(1 1 n )d.
ΔR=( 1 1 n )d=2 R 2 ( k k ),
R= ( n1 )d 2n( k k ) .
n=2+ d l =2+ d ΔRd .
n d = ΔR2d r 2 ( d+ r 2 )( ΔRd ) dΔR d 2 r 2 d ( d+ r 2 ) 2 ( ΔRd ) + dΔR d 2 r 2 d ( d+ r 2 ) ( ΔRd ) 2 = n d n ΔRd r 2 n d+ r 2 + n ΔRd ,
n r 2 = n ΔRd r 2 n d+ r 2 ,
n ΔR = n ΔRd r 2 n ΔRd .
ΔRd= l = d r 2 ( 1n )dn r 2 = d ( 1n )d/ r 2 n .
n d = n d n( 1n )d/ r 2 n 2 d( 1n )d+n r 2 n d+ r 2 + n( 1n )d/ r 2 n 2 d ,
n r 2 = n( 1n )d/ r 2 n 2 d( 1n )d+n r 2 n d+ r 2 ,
n ΔR = n( 1n )d/ r 2 n 2 d( 1n )d+n r 2 n( 1n )d/ r 2 n 2 d .
ΔR ΔR = 4RΔkR+2 R 2 Δk 2 R 2 Δk = 2R R + Δk Δk .

Metrics