Abstract

When a transparent plane-parallel plate is illuminated at the edge region by a quasi-monochromatic parallel beam of light, diffraction fringes appear on a plane perpendicular to the transmitted beam direction. The sharp change in the refractive index at the plate boundary imposes an abrupt change on the phase of the illuminating beam that leads to the Fresnel diffraction. The visibility of the diffraction fringes depends on the plate thickness, refractive index, light wavelength, and angle of incidence. In this report we show that, by recording the visibility repetition versus incident angle, one can measure the plate refractive index, its thickness, and light wavelength very accurately. It is also shown that the technique is indispensable for specifying color dispersion in plate shape samples. The technique is applied to the measurement of dispersion in a fused silica plate and the refractive indices of soda lime slides.

© 2012 Optical Society of America

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References

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2012 (2)

2010 (1)

2009 (2)

2008 (1)

2007 (4)

M. Daimon and A. Masumura, “Measurement of the refractive index of distilled water from the near-infrared region to the ultraviolet region,” Appl. Opt. 46, 3811–3820 (2007).
[CrossRef]

S.-H. Lu, S.-P. Pan, T.-S. Liu, and C.-F. Kao, “Liquid refractometer based on immersion diffractometry,” Opt. Express 15, 9470–9475 (2007).
[CrossRef]

M. Amiri and M. T. Tavassoly, “Fresnel diffraction from 1D and 2D phase steps in reflection and transmission mode,” Opt. Commun. 272, 349–361 (2007).
[CrossRef]

A. Sabatyan and M. T. Tavassoly, “Application of Fresnel diffraction to nondestructive measurement of the refractive index of optical fibers,” Opt. Eng. 46, 128001 (2007).
[CrossRef]

2005 (1)

M. T. Tavassoly, M. Amiri, E. Karimi, and H. R. Khalesifard, “Spectral modification by line singularity in Fresnel diffraction from 1D phase step,” Opt. Commun. 255, 23–34 (2005).
[CrossRef]

2002 (1)

S. Singh, “Refractive index measurement and its applications,” Phys. Scr. 65, 167–180 (2002).
[CrossRef]

1999 (1)

1997 (1)

M. Ohmi, T. Shiraishi, H. Tajiri, and M. Haruna, “Simultaneous measurement of refractive index and thickness of transparent plates by low coherence interferometry,” Opt. Rev. 4, 507–515 (1997).
[CrossRef]

1996 (1)

M. de Angelis, S. De Nicola, P. Ferraro, A. Finizio, and G. Pierattini, “A reflective grating interferometer for measuring the refractive index of liquids,” J. Opt. A 5, 761–765(1996).
[CrossRef]

1992 (1)

1984 (1)

Alipour, R.

Amiri, M.

M. T. Tavassoly, M. Amiri, A. Darudi, R. Alipour, A. Saber, and A. R. Moradi, “Optical diffractometry,” J. Opt. Soc. Am. A 26, 540–547 (2009).
[CrossRef]

M. Amiri and M. T. Tavassoly, “Fresnel diffraction from 1D and 2D phase steps in reflection and transmission mode,” Opt. Commun. 272, 349–361 (2007).
[CrossRef]

M. T. Tavassoly, M. Amiri, E. Karimi, and H. R. Khalesifard, “Spectral modification by line singularity in Fresnel diffraction from 1D phase step,” Opt. Commun. 255, 23–34 (2005).
[CrossRef]

Beaumont, A.

Daimon, M.

Darudi, A.

de Angelis, M.

M. de Angelis, S. De Nicola, P. Ferraro, A. Finizio, and G. Pierattini, “A reflective grating interferometer for measuring the refractive index of liquids,” J. Opt. A 5, 761–765(1996).
[CrossRef]

de Greef, C.

De Nicola, S.

M. de Angelis, S. De Nicola, P. Ferraro, A. Finizio, and G. Pierattini, “A reflective grating interferometer for measuring the refractive index of liquids,” J. Opt. A 5, 761–765(1996).
[CrossRef]

Ferraro, P.

M. de Angelis, S. De Nicola, P. Ferraro, A. Finizio, and G. Pierattini, “A reflective grating interferometer for measuring the refractive index of liquids,” J. Opt. A 5, 761–765(1996).
[CrossRef]

Finizio, A.

M. de Angelis, S. De Nicola, P. Ferraro, A. Finizio, and G. Pierattini, “A reflective grating interferometer for measuring the refractive index of liquids,” J. Opt. A 5, 761–765(1996).
[CrossRef]

Finsy, R.

Haghighi, I. M.

Hammer, D. X.

Hart, C.

Haruna, M.

M. Ohmi, T. Shiraishi, H. Tajiri, and M. Haruna, “Simultaneous measurement of refractive index and thickness of transparent plates by low coherence interferometry,” Opt. Rev. 4, 507–515 (1997).
[CrossRef]

Hassani, K.

Kao, C.-F.

Karimi, E.

M. T. Tavassoly, M. Amiri, E. Karimi, and H. R. Khalesifard, “Spectral modification by line singularity in Fresnel diffraction from 1D phase step,” Opt. Commun. 255, 23–34 (2005).
[CrossRef]

Khalesifard, H. R.

M. T. Tavassoly, M. Amiri, E. Karimi, and H. R. Khalesifard, “Spectral modification by line singularity in Fresnel diffraction from 1D phase step,” Opt. Commun. 255, 23–34 (2005).
[CrossRef]

Khorshad, A. A.

Liu, T.-S.

Lu, S.-H.

Masumura, A.

Moradi, A. R.

Moreels, E.

Nahal, A.

Nemoto, S.

Noojin, G. D.

Ohmi, M.

M. Ohmi, T. Shiraishi, H. Tajiri, and M. Haruna, “Simultaneous measurement of refractive index and thickness of transparent plates by low coherence interferometry,” Opt. Rev. 4, 507–515 (1997).
[CrossRef]

Pan, S.-P.

Pierattini, G.

M. de Angelis, S. De Nicola, P. Ferraro, A. Finizio, and G. Pierattini, “A reflective grating interferometer for measuring the refractive index of liquids,” J. Opt. A 5, 761–765(1996).
[CrossRef]

Rezvani Naraghi, R.

Rockwell, B. A.

Sabatyan, A.

A. Sabatyan and M. T. Tavassoly, “Application of Fresnel diffraction to nondestructive measurement of the refractive index of optical fibers,” Opt. Eng. 46, 128001 (2007).
[CrossRef]

Saber, A.

Shiraishi, T.

M. Ohmi, T. Shiraishi, H. Tajiri, and M. Haruna, “Simultaneous measurement of refractive index and thickness of transparent plates by low coherence interferometry,” Opt. Rev. 4, 507–515 (1997).
[CrossRef]

Singh, S.

S. Singh, “Refractive index measurement and its applications,” Phys. Scr. 65, 167–180 (2002).
[CrossRef]

Stolarski, D. J.

Tajiri, H.

M. Ohmi, T. Shiraishi, H. Tajiri, and M. Haruna, “Simultaneous measurement of refractive index and thickness of transparent plates by low coherence interferometry,” Opt. Rev. 4, 507–515 (1997).
[CrossRef]

Tavassoly, M. T.

Tedaldi, M.

Thomas, R. J.

Tomlins, P. H.

Welch, A. J.

Woolliams, P.

Appl. Opt. (5)

J. Opt. A (1)

M. de Angelis, S. De Nicola, P. Ferraro, A. Finizio, and G. Pierattini, “A reflective grating interferometer for measuring the refractive index of liquids,” J. Opt. A 5, 761–765(1996).
[CrossRef]

J. Opt. Soc. Am. A (2)

Opt. Commun. (2)

M. T. Tavassoly, M. Amiri, E. Karimi, and H. R. Khalesifard, “Spectral modification by line singularity in Fresnel diffraction from 1D phase step,” Opt. Commun. 255, 23–34 (2005).
[CrossRef]

M. Amiri and M. T. Tavassoly, “Fresnel diffraction from 1D and 2D phase steps in reflection and transmission mode,” Opt. Commun. 272, 349–361 (2007).
[CrossRef]

Opt. Eng. (1)

A. Sabatyan and M. T. Tavassoly, “Application of Fresnel diffraction to nondestructive measurement of the refractive index of optical fibers,” Opt. Eng. 46, 128001 (2007).
[CrossRef]

Opt. Express (1)

Opt. Lett. (3)

Opt. Rev. (1)

M. Ohmi, T. Shiraishi, H. Tajiri, and M. Haruna, “Simultaneous measurement of refractive index and thickness of transparent plates by low coherence interferometry,” Opt. Rev. 4, 507–515 (1997).
[CrossRef]

Phys. Scr. (1)

S. Singh, “Refractive index measurement and its applications,” Phys. Scr. 65, 167–180 (2002).
[CrossRef]

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Figures (7)

Fig. 1.
Fig. 1.

As a parallel quasi-monochromatic beam of light strikes a transparent plane-parallel plate at the edge, the diffraction pattern appears on a plane perpendicular to the beam direction because of sharp change in the phase at the plate boundary.

Fig. 2.
Fig. 2.

Geometry that is used to calculate the phase change at the plate boundary.

Fig. 3.
Fig. 3.

Typical diffraction patterns and their intensity profiles, for He–Ne laser light diffracted from the edge of a transparent plane-parallel plate of thickness 1.0 mm for phase change (a)  φ = m π , (b)  φ = ( m + 4 / 9 ) π , and (c)  φ = ( m + 14 / 9 ) π , where m is an odd integer.

Fig. 4.
Fig. 4.

Theoretical visibility of the three central diffraction fringes versus phase of the light diffracted from the edge of a plate of thickness h = 1.0 mm and refractive index N = 1.5 at incident angles (a), (b) 6 ° θ 10 ° ; (c), (d) θ 56 ° ; and (e), (f) θ 75 ° for s and p polarizations.

Fig. 5.
Fig. 5.

Plate with a step, for producing edge diffraction fringes of visibility range between 0 and 1 in transmission.

Fig. 6.
Fig. 6.

Scheme of the experimental setup. The laser beam that is expanded by BE strikes a transparent plate mounted on stage G , and the diffraction pattern formed on CCD is observed in PC.

Fig. 7.
Fig. 7.

Dispersion curve of a fused silica plate of thickness 3.2366 mm.

Tables (4)

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Table 1. Refractive Indices of a Fused Silica Plate for Different Wavelengths

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Table 2. Refractive Indices of Soda Lime Glass Slide for Two Different Wavelengths

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Table 3. Thickness of a Fused Silica Plate Obtained by the Fresnel Diffraction of Light from the Plate Edge for Different Wavelengths

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Table 4. Thicknesses of a Soda Lime Glass Slide Obtained by Applying the Fresnel Diffraction of Light to the Slide Edge

Equations (6)

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

u P = A K [ t p x 0 e i k r r d x + t m e i φ x 0 + e i k r r d x ] ,
I P = I 0 t p t m [ cos 2 ( φ 2 ) + 2 ( C 0 2 + S 0 2 ) sin 2 ( φ 2 ) + ( C 0 S 0 ) sin φ ] + I 0 2 [ ( 0.5 + C 0 2 + S 0 2 ) ( t p t m ) 2 + ( C 0 + S 0 ) ( t m 2 t p 2 ) ] ,
C 0 = 0 v 0 cos π v 2 2 d v , S 0 = 0 v 0 sin π v 2 2 d v and v 0 = x 0 2 λ L ,
φ = 2 π λ h N [ n 2 sin 2 θ cos θ ] ,
V = 1 2 ( I max , L + I max , R ) I min , C 1 2 ( I max , L + I max , R ) + I min , C ,
P 1 + P 2 P 1 = [ n 2 sin 2 θ 3 cos θ 3 ] [ n 2 sin 2 θ 1 cos θ 1 ] [ n 2 sin 2 θ 2 cos θ 2 ] [ n 2 sin 2 θ 1 cos θ 1 ] .

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