Abstract

A new instrument for measuring the evolution of index profiles during diffusion in hot (500°C) glass is presented. This instrument, called the oven interferometer, has a spatial resolution of 10 μm at 0.6471 μm and a phase resolution of λ/50. The development of index profiles with both time-dependent and constant boundary conditions is shown.

© 1988 Optical Society of America

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References

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  1. L. G. Atkinson, S. N. Houde-Walter, D. T. Moore, D. P. Ryan, J. M. Stagaman, “Design of a Gradient-Index Photographic Objective,” Appl. Opt. 21, 993 (1982).
    [CrossRef] [PubMed]
  2. P. O. McLaughlin et al., “Design of a Gradient-Index Binocular Objective,” Proc. Soc. Photo-Opt. Instrum. Eng. 237, 369 (1980).
  3. J. B. Caldwell et al., “Gradient-Index Binocular Objective Design,” Appl. Opt. 25, 3345 (1986).
    [CrossRef] [PubMed]
  4. D. T. Moore, “Gradient-Index Optics: a Review,” Appl. Opt. 19, 1035 (1980).
    [CrossRef] [PubMed]
  5. J. Crank, The Mathematics of Diffusion (Oxford U. P., London, 1956).
  6. R. H. Doremus, “Mixed-Alkali Effect and Interdiffusion of Na and K Ions in Glass,” J. Am. Ceram. Soc. 57, 478 (1974).
    [CrossRef]
  7. S. N. Houde-Walter, D. T. Moore, “Delta-n Control in GRIN Glass by Additives in AgCl Diffusion Baths,” Appl. Opt. 25, 3373 (1986).
    [CrossRef] [PubMed]
  8. S. Misawa, M. Oikawa, K. Iga, “Maximum and Effective Numerical Apertures of a Planar Microlens,” Appl. Opt. 23, 1784 (1984).
    [CrossRef] [PubMed]
  9. Y. Asahara, H. Sakai, S. Shingaki, S. Ohmi, S. Nakayama, K. Nakagawa, T. Izumitani, “One-Directional Gradient-Index Slab Lens,” Appl. Opt. 24, 4312 (1985).
    [CrossRef] [PubMed]
  10. E. Okuda, I. Tanaka, T. Yamasaki, “Planar Gradient-Index Glass Waveguide and Its Applications to a 4-Port Branched Circuit and Star Coupler,” Appl. Opt. 23, 1745 (1984).
    [CrossRef] [PubMed]
  11. D. T. Moore, D. P. Ryan, “Measurement of the Optical Properties of Gradient Index Materials,” J. Opt. Soc. Am. 68, 1157 (1978).
    [CrossRef]
  12. J. J. Miceli, “Infrared Gradient Index Optics: Materials, Fabrication and Testing,” Doctoral Thesis, U. Rochester (1982).
  13. J. M. Stagaman, “Anamorphic Gradient Index Lens Systems,” Doctoral Thesis, U. Rochester (1985).
  14. H. L. Rutan, “Ultrasonic Machining Impact Grinding,” in Technical Digest, Topical Meeting on Optical Fabrication and Testing (Optical Society of America, Washington, DC, 1984), paper THD-A5.
  15. Code V by Optical Research Associates, Irvine, CA.
  16. D. T. Moore, “Gradient Index Optics: Aspects of Design, Testing, Tolerancing, and Fabrication,” Doctoral Thesis, U. Rochester (1974).
  17. P. O. McLaughlin, “Thermal Expansion and Temperature Dependence of the Refractive Index in Gradient Refractive Index Glasses,” Doctoral Thesis, U. Rochester (1982).
  18. S. N. Houde-Walter, “Gradient-Index Profile Control by Ion Exchange in Glass,” Doctoral Thesis, U. Rochester (1987).
  19. D. S. Kindred, D. T. Moore, “Fabrication and Testing of a Gradient Index Binocular Objective,” in Technical Digest, Topical Meeting on Gradient-Index Optical Imaging Systems (Optical Society of America, Washington, DC, 1987), paper FB1.
  20. R. H. Doremus, “Diffusion in Non-Crystalline Silicates,” in Modern Aspects of the Vitreous State (Butterworths, London, 1962), Chap. 1.

1986 (2)

1985 (1)

1984 (2)

1982 (1)

1980 (2)

P. O. McLaughlin et al., “Design of a Gradient-Index Binocular Objective,” Proc. Soc. Photo-Opt. Instrum. Eng. 237, 369 (1980).

D. T. Moore, “Gradient-Index Optics: a Review,” Appl. Opt. 19, 1035 (1980).
[CrossRef] [PubMed]

1978 (1)

1974 (1)

R. H. Doremus, “Mixed-Alkali Effect and Interdiffusion of Na and K Ions in Glass,” J. Am. Ceram. Soc. 57, 478 (1974).
[CrossRef]

Asahara, Y.

Atkinson, L. G.

Caldwell, J. B.

Crank, J.

J. Crank, The Mathematics of Diffusion (Oxford U. P., London, 1956).

Doremus, R. H.

R. H. Doremus, “Mixed-Alkali Effect and Interdiffusion of Na and K Ions in Glass,” J. Am. Ceram. Soc. 57, 478 (1974).
[CrossRef]

R. H. Doremus, “Diffusion in Non-Crystalline Silicates,” in Modern Aspects of the Vitreous State (Butterworths, London, 1962), Chap. 1.

Houde-Walter, S. N.

Iga, K.

Izumitani, T.

Kindred, D. S.

D. S. Kindred, D. T. Moore, “Fabrication and Testing of a Gradient Index Binocular Objective,” in Technical Digest, Topical Meeting on Gradient-Index Optical Imaging Systems (Optical Society of America, Washington, DC, 1987), paper FB1.

McLaughlin, P. O.

P. O. McLaughlin et al., “Design of a Gradient-Index Binocular Objective,” Proc. Soc. Photo-Opt. Instrum. Eng. 237, 369 (1980).

P. O. McLaughlin, “Thermal Expansion and Temperature Dependence of the Refractive Index in Gradient Refractive Index Glasses,” Doctoral Thesis, U. Rochester (1982).

Miceli, J. J.

J. J. Miceli, “Infrared Gradient Index Optics: Materials, Fabrication and Testing,” Doctoral Thesis, U. Rochester (1982).

Misawa, S.

Moore, D. T.

S. N. Houde-Walter, D. T. Moore, “Delta-n Control in GRIN Glass by Additives in AgCl Diffusion Baths,” Appl. Opt. 25, 3373 (1986).
[CrossRef] [PubMed]

L. G. Atkinson, S. N. Houde-Walter, D. T. Moore, D. P. Ryan, J. M. Stagaman, “Design of a Gradient-Index Photographic Objective,” Appl. Opt. 21, 993 (1982).
[CrossRef] [PubMed]

D. T. Moore, “Gradient-Index Optics: a Review,” Appl. Opt. 19, 1035 (1980).
[CrossRef] [PubMed]

D. T. Moore, D. P. Ryan, “Measurement of the Optical Properties of Gradient Index Materials,” J. Opt. Soc. Am. 68, 1157 (1978).
[CrossRef]

D. T. Moore, “Gradient Index Optics: Aspects of Design, Testing, Tolerancing, and Fabrication,” Doctoral Thesis, U. Rochester (1974).

D. S. Kindred, D. T. Moore, “Fabrication and Testing of a Gradient Index Binocular Objective,” in Technical Digest, Topical Meeting on Gradient-Index Optical Imaging Systems (Optical Society of America, Washington, DC, 1987), paper FB1.

Nakagawa, K.

Nakayama, S.

Ohmi, S.

Oikawa, M.

Okuda, E.

Rutan, H. L.

H. L. Rutan, “Ultrasonic Machining Impact Grinding,” in Technical Digest, Topical Meeting on Optical Fabrication and Testing (Optical Society of America, Washington, DC, 1984), paper THD-A5.

Ryan, D. P.

Sakai, H.

Shingaki, S.

Stagaman, J. M.

Tanaka, I.

Yamasaki, T.

Appl. Opt. (7)

J. Am. Ceram. Soc. (1)

R. H. Doremus, “Mixed-Alkali Effect and Interdiffusion of Na and K Ions in Glass,” J. Am. Ceram. Soc. 57, 478 (1974).
[CrossRef]

J. Opt. Soc. Am. (1)

Proc. Soc. Photo-Opt. Instrum. Eng. (1)

P. O. McLaughlin et al., “Design of a Gradient-Index Binocular Objective,” Proc. Soc. Photo-Opt. Instrum. Eng. 237, 369 (1980).

Other (10)

J. Crank, The Mathematics of Diffusion (Oxford U. P., London, 1956).

J. J. Miceli, “Infrared Gradient Index Optics: Materials, Fabrication and Testing,” Doctoral Thesis, U. Rochester (1982).

J. M. Stagaman, “Anamorphic Gradient Index Lens Systems,” Doctoral Thesis, U. Rochester (1985).

H. L. Rutan, “Ultrasonic Machining Impact Grinding,” in Technical Digest, Topical Meeting on Optical Fabrication and Testing (Optical Society of America, Washington, DC, 1984), paper THD-A5.

Code V by Optical Research Associates, Irvine, CA.

D. T. Moore, “Gradient Index Optics: Aspects of Design, Testing, Tolerancing, and Fabrication,” Doctoral Thesis, U. Rochester (1974).

P. O. McLaughlin, “Thermal Expansion and Temperature Dependence of the Refractive Index in Gradient Refractive Index Glasses,” Doctoral Thesis, U. Rochester (1982).

S. N. Houde-Walter, “Gradient-Index Profile Control by Ion Exchange in Glass,” Doctoral Thesis, U. Rochester (1987).

D. S. Kindred, D. T. Moore, “Fabrication and Testing of a Gradient Index Binocular Objective,” in Technical Digest, Topical Meeting on Gradient-Index Optical Imaging Systems (Optical Society of America, Washington, DC, 1987), paper FB1.

R. H. Doremus, “Diffusion in Non-Crystalline Silicates,” in Modern Aspects of the Vitreous State (Butterworths, London, 1962), Chap. 1.

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Figures (11)

Fig. 1
Fig. 1

Solid line, the values of B vs A necessary for electrical to optical phase linearity. The SNR is plotted in dashed line (from Ref. 13).

Fig. 2
Fig. 2

Diagram of the oven interferometer optical system.

Fig. 3
Fig. 3

Data collection scheme for the oven interferometer.

Fig. 4
Fig. 4

Schematic diagram of sample geometry.

Fig. 5
Fig. 5

Differential thermal expansion in GRIN glass.

Fig. 6
Fig. 6

Thin section of GRIN glass used for each thermal expansion measurement.

Fig. 7
Fig. 7

Michelson interferometer for measuring surface shape change in diffusing glass.

Fig. 8
Fig. 8

Maximum surface deformation in waves (0.6471 μm) after 5 h of diffusion at 505°C.

Fig. 9
Fig. 9

Comparison of optical path length at 490°C to that at 24°C (λ = 0.6471 μm).

Fig. 10
Fig. 10

Diffusion with constant boundary conditions at 500°C. Profiles are shown at 1-h intervals beginning at 4 h.

Fig. 11
Fig. 11

Anneal of index profile at 505°C. Glass was doped with silver for 1 h. The resultant index profile at 1 h and subsequent anneals are shown at one half hour intervals.

Tables (4)

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Table I Composition of BL2406 Aluminosilicate Research Glass

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Table II Error in Approximating Glass Pockets by Solid Slabs

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Table III Qualitative Trend of Transition Temperature and Softening Point as a Function of Δn

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Table IV Verification of √t Law from Virtual Source in Annealed Index Profiles

Equations (8)

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

I ( x , y , t ) = I 1 + I 2 + 2 I 1 I 2 cos [ Ψ ( x , y , t ) ] ,
Ψ ( x , y , t ) = Ө ( x , y ) Φ ( t ) .
Φ ( t ) = A sin { n ω t } + B sin { m ω t + a } ,
I ( x , y , t ) = I 1 + I 2 + 2 I 1 I 2 [ C ( t ) cos Ө + S ( t ) sin Ө ] ,
I l ω ( x , y , t ) = K cos ( Ө ± l ω t + β )
Δ t tot = l 0 ( δ α Δ T ) ,
Δ n = m λ t 0 ,
M = 2 C 0 ( D t π ) 1 / 2 ,

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