Abstract

A modification of hologram interferometry applicable to the study of transparent objects of moderate optical quality has been devised which combines hologram and moiré techniques and allows the observation of high contrast, relatively unlocalized, interferometric fringes under conditions less critical than those of the conventional hologram interferometer. By spatially modulating one beam of the interferometer during exposure, moiré fringes may be obtained in the reconstruction which distort and move with optical phase changes in either beam of the interferometer. An analysis of the origin and nature of these distortions is given and experimental verification of the analysis is presented.

© 1967 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. M. H. Horman, Appl. Opt. 4, 333 (1965); H. H. Chau, M. H. Horman, Appl. Opt. 5, 1237 (1966).
    [CrossRef] [PubMed]
  2. R. J. Collier, E. T. Doherty, K. S. Pennington, Appl. Phys. Letters 7, 223 (1965).
    [CrossRef]
  3. R. E. Brooks, L. O. Heflinger, R. F. Wuerker, Appl. Phys. Letters 7, 248 (1965); L. O. Heflinger, R. F. Wuerker, R. E. Brooks, Appl. Phys. 37, 642 (1966).
    [CrossRef]
  4. B. P. Hildebrand, K. A. Haines, Appl. Opt. 5, 172 (1966).
    [CrossRef] [PubMed]
  5. K. A. Haines, B. P. Hildebrand, Appl. Opt. 5, 595 (1966).
    [CrossRef] [PubMed]
  6. L. H. Tanner, J. Sci. Instr. 43, 81 (1966).
    [CrossRef]
  7. R. Kraushaar, J. Opt. Soc. Am. 40, 480 (1950).
    [CrossRef]
  8. J. A. Simpson, Rev. Sci. Instr. 25, 1105 (1954).
    [CrossRef]
  9. H. Mendlowitz, J. A. Simpson, J. Opt. Soc. Am. 52, 520 (1962).
    [CrossRef]
  10. J. Zimmerman, Appl. Opt. 2, 759 (1963).
    [CrossRef]
  11. Y. Nishijima, G. Oster, J. Opt. Soc. Am. 54, 1 (1964).
    [CrossRef]
  12. G. Oster, M. Wasserman, C. Zwerling, J. Opt. Soc. Am 54, 169 (1964).
    [CrossRef]
  13. R. E. McCurry, J. Opt. Soc. Am. 37, 467, 479 (1966).
  14. M. Nisida, H. Saito, Sci. Papers, Inst. Phys. Chem. Res. (Tokyo) 59, 5 (1965).
  15. A. Kozma, J. Opt. Soc. Am. 56, 428 (1966)
    [CrossRef]
  16. S. B. Herskovitz, Rev. Sci. Instr. 37, 452 (1966).
    [CrossRef]
  17. M. S. Shumate, Appl. Opt. 5, 327 (1966).
    [CrossRef] [PubMed]

1966

1965

M. H. Horman, Appl. Opt. 4, 333 (1965); H. H. Chau, M. H. Horman, Appl. Opt. 5, 1237 (1966).
[CrossRef] [PubMed]

M. Nisida, H. Saito, Sci. Papers, Inst. Phys. Chem. Res. (Tokyo) 59, 5 (1965).

R. J. Collier, E. T. Doherty, K. S. Pennington, Appl. Phys. Letters 7, 223 (1965).
[CrossRef]

R. E. Brooks, L. O. Heflinger, R. F. Wuerker, Appl. Phys. Letters 7, 248 (1965); L. O. Heflinger, R. F. Wuerker, R. E. Brooks, Appl. Phys. 37, 642 (1966).
[CrossRef]

1964

G. Oster, M. Wasserman, C. Zwerling, J. Opt. Soc. Am 54, 169 (1964).
[CrossRef]

Y. Nishijima, G. Oster, J. Opt. Soc. Am. 54, 1 (1964).
[CrossRef]

1963

1962

1954

J. A. Simpson, Rev. Sci. Instr. 25, 1105 (1954).
[CrossRef]

1950

Brooks, R. E.

R. E. Brooks, L. O. Heflinger, R. F. Wuerker, Appl. Phys. Letters 7, 248 (1965); L. O. Heflinger, R. F. Wuerker, R. E. Brooks, Appl. Phys. 37, 642 (1966).
[CrossRef]

Collier, R. J.

R. J. Collier, E. T. Doherty, K. S. Pennington, Appl. Phys. Letters 7, 223 (1965).
[CrossRef]

Doherty, E. T.

R. J. Collier, E. T. Doherty, K. S. Pennington, Appl. Phys. Letters 7, 223 (1965).
[CrossRef]

Haines, K. A.

Heflinger, L. O.

R. E. Brooks, L. O. Heflinger, R. F. Wuerker, Appl. Phys. Letters 7, 248 (1965); L. O. Heflinger, R. F. Wuerker, R. E. Brooks, Appl. Phys. 37, 642 (1966).
[CrossRef]

Herskovitz, S. B.

S. B. Herskovitz, Rev. Sci. Instr. 37, 452 (1966).
[CrossRef]

Hildebrand, B. P.

Horman, M. H.

Kozma, A.

Kraushaar, R.

McCurry, R. E.

R. E. McCurry, J. Opt. Soc. Am. 37, 467, 479 (1966).

Mendlowitz, H.

Nishijima, Y.

Nisida, M.

M. Nisida, H. Saito, Sci. Papers, Inst. Phys. Chem. Res. (Tokyo) 59, 5 (1965).

Oster, G.

Y. Nishijima, G. Oster, J. Opt. Soc. Am. 54, 1 (1964).
[CrossRef]

G. Oster, M. Wasserman, C. Zwerling, J. Opt. Soc. Am 54, 169 (1964).
[CrossRef]

Pennington, K. S.

R. J. Collier, E. T. Doherty, K. S. Pennington, Appl. Phys. Letters 7, 223 (1965).
[CrossRef]

Saito, H.

M. Nisida, H. Saito, Sci. Papers, Inst. Phys. Chem. Res. (Tokyo) 59, 5 (1965).

Shumate, M. S.

Simpson, J. A.

Tanner, L. H.

L. H. Tanner, J. Sci. Instr. 43, 81 (1966).
[CrossRef]

Wasserman, M.

G. Oster, M. Wasserman, C. Zwerling, J. Opt. Soc. Am 54, 169 (1964).
[CrossRef]

Wuerker, R. F.

R. E. Brooks, L. O. Heflinger, R. F. Wuerker, Appl. Phys. Letters 7, 248 (1965); L. O. Heflinger, R. F. Wuerker, R. E. Brooks, Appl. Phys. 37, 642 (1966).
[CrossRef]

Zimmerman, J.

Zwerling, C.

G. Oster, M. Wasserman, C. Zwerling, J. Opt. Soc. Am 54, 169 (1964).
[CrossRef]

Appl. Opt.

Appl. Phys. Letters

R. J. Collier, E. T. Doherty, K. S. Pennington, Appl. Phys. Letters 7, 223 (1965).
[CrossRef]

R. E. Brooks, L. O. Heflinger, R. F. Wuerker, Appl. Phys. Letters 7, 248 (1965); L. O. Heflinger, R. F. Wuerker, R. E. Brooks, Appl. Phys. 37, 642 (1966).
[CrossRef]

J. Opt. Soc. Am

G. Oster, M. Wasserman, C. Zwerling, J. Opt. Soc. Am 54, 169 (1964).
[CrossRef]

J. Opt. Soc. Am.

J. Sci. Instr.

L. H. Tanner, J. Sci. Instr. 43, 81 (1966).
[CrossRef]

Rev. Sci. Instr.

J. A. Simpson, Rev. Sci. Instr. 25, 1105 (1954).
[CrossRef]

S. B. Herskovitz, Rev. Sci. Instr. 37, 452 (1966).
[CrossRef]

Sci. Papers, Inst. Phys. Chem. Res. (Tokyo)

M. Nisida, H. Saito, Sci. Papers, Inst. Phys. Chem. Res. (Tokyo) 59, 5 (1965).

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 (5)

Fig. 1
Fig. 1

Modified hologram interferometer for transparent objects. Modulating gratings were Ronchi rulings varying from 2–10 lines/mm.

Fig. 2
Fig. 2

Computer plot of the moiré pattern between a Ronchi ruling and a set of interferometer fringes tilted at an angle of 0.3 rad. Ten cycles of the Ronchi ruling correspond to five divisions along the x axis.

Fig. 3
Fig. 3

Application of the hologram moiré interferometer to the optical testing of laser rods. The glass rods, (a) and (b), show high optical quality. Note in (b) the rotation of the fringes due to nonparallelism of the faces. Although the crystalline material in (c) is of much poorer quality than the glass, some fringes can be observed near the edges of the sample.

Fig. 4
Fig. 4

Application of the hologram–moiré interferometer to the testing of rough glass blanks. In (a), the sample was a doughnut shaped blank ground slightly convex. The cross hatched pattern in the center represents the zero path moiré pattern. In (b), the refractive index gradient across the striation is clearly visible.

Fig. 5
Fig. 5

Cell used in the study of the feasibility of this technique as a manometer. The Brewster windows reduce stray reflections. Total cell length is 16.5 cm.

Equations (23)

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

T = T 0 - B A 1 + A 2 2 = T 0 - B ( A 1 2 + A 2 2 + A 1 A 2 * + A 2 A 1 * ) ,
A out = T ( A 3 + A 4 ) .
A out = O I + O I I + O I I I + O I V , O I = A 3 [ T 0 - B ( A 1 2 + A 2 2 ) ] - B A 4 ( A 1 A 2 * ) h , O I I = A 4 [ T 0 - B ( A 1 2 + A 2 2 ) ] - B A 3 ( A 2 A 1 * ) h , O I I I = - B A 3 ( A 1 A 2 * ) h , O I V = - B A 4 ( A 2 A 1 * ) h ,
A 1 = a 1 ( 1 + sin p x ) exp i k 1 · r , A 2 = a 2 exp i k 2 · r ,
A 4 = A 2 .
ϕ x = ( 2 π x sin α 1 ) / λ = p 1 x
ϕ y = ( 2 π x sin α 2 ) / λ = q 1 y
ϕ = ( 2 π / λ ) [ n ( x , y ) - 1 ] L ( x , y ) ,
A 3 = A 1 exp i ( p 1 x + q 1 y + ϕ ) .
O I = A 1 { [ T 0 - B a 2 2 - B a 1 2 ( 1 + sin p x ) 2 ] exp i ( p 1 x + q 1 y + ϕ ) - B a 2 2 } .
O I 2 = 1 2 a 1 2 ( 1 + sin p x ) 2 [ 1 - cos ( p 1 x + q 1 y + ϕ ) ] .
O I 2 ( rotated ) = 1 2 a 1 2 [ 1 + sin ( p x - q y ) 2 ] × [ 1 + sin ( p x + q y + ϕ ) ] ,
O I 2 a r = x x + 2 π / p O I 2 d x .
O I 2 a v = ( π a 1 2 / 2 p ) [ 3 + 2 cos ( 2 q y + ϕ ) ] ,
2 q y + ϕ ( x y ) - π / 2 = 2 m π , 2 q y + ( 2 π / λ ) [ n ( x , y ) - 1 ] L ( x , y ) - π / 2 = 2 m π ,
ϕ ( x , y ) = ϕ p ( x cos θ + y sin θ ) ,
( ϕ p cos θ ) x + ( Δ q + ϕ p sin θ ) y = 2 m π + π / 2
Δ p x + Δ q y = 2 m π + π / 2.
σ = tan - 1 Δ p / Δ q .
2 q d y / d t + d ϕ / d t = 0.
d ϕ / d t = ( 2 π L / λ ) ( d n / d t ) .
d y / d t = ( - π L / λ q ) ( d n / d t ) .
d ϕ / d p = ( 2 π L / λ ) ( d n / d p ) ,

Metrics