Abstract

Many optical experiments and applications require the use of devices called optical wedges which are thin-sheet optical modulators having a continuous, usually linear, change in optical density with either distance or angle. The optical density of a sample area on an optical wedge depends on the size and shape of the aperture and the characteristics of the wedge. The relationship of the effective density of the whole sample to the density at the center of the sample has been derived for wedges of rectilinear and circular form and sampling apertures in the form of rectangles, circles, and circular sectors. The theory has applications in the microdensitometry of photographic edges.

© 1976 Optical Society of America

PDF Article

References

  • View by:
  • |
  • |
  • |

  1. E. Goldberg, The Preparation of Gelatine Wedges, Br. J. Photogr. 57, 642 (1910).
  2. E Goldberg, "The Preparation of Prismatic Wedges of Neutral Colour for Photometric Work," Br. J. Photogr. 57, 648 (1910).
  3. F. C. Toy and J. C. Ghosh, "The Absorption of Light by the Goldberg Wedge," Philos. Mag. 40, (6), 775 (1920).
  4. G. M. B. Dobson and D. N. Harrison, "Ultra-Violet Photometry," Nature 117, 724 (1926).
  5. G. M. B. Dobson, I. O. Griffith, and D. N. Harrison, Photographic Photometry (Clarendon, Oxford, 1926), p. 18.
  6. E. Goldberg, Der Aufbau des Photographischen Bildes (Knapp, Halle, 1922), p. 81.
  7. C. S. McCamy, "Concepts, Terminology, and Notation for Optical Modulation," Photogr. Sci. Eng. 10, 314 (1966).
  8. "American National Standard Terms, Symbols, and Notation for Optical Transmission and Reflection Measurements," PH2. 36–1974. Available from American National Standards Institute, Inc., 1430 Broadway, N. Y., 10018.
  9. C. S. McCamy, "The Theory of Optical Wedges," J. Opt. Soc. Am. 58, 724 (1968).
  10. Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables, National Bureau of Standards, Applied Mathematics Series No. 55 (U. S. GPO, Washington, D. C. 1964).
  11. W. Magnus and F. Oberhettinger, Formulas and Theorems for the Special Functions of Mathematical Physics (Chelsea, New York, 1949).
  12. I. S. Gradshteyn and I. M. Ryzhik, Tables of Integrals, Series, and Products (Academic, New York, 1965).

1968 (1)

C. S. McCamy, "The Theory of Optical Wedges," J. Opt. Soc. Am. 58, 724 (1968).

1966 (1)

C. S. McCamy, "Concepts, Terminology, and Notation for Optical Modulation," Photogr. Sci. Eng. 10, 314 (1966).

1964 (1)

Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables, National Bureau of Standards, Applied Mathematics Series No. 55 (U. S. GPO, Washington, D. C. 1964).

1926 (1)

G. M. B. Dobson and D. N. Harrison, "Ultra-Violet Photometry," Nature 117, 724 (1926).

1920 (1)

F. C. Toy and J. C. Ghosh, "The Absorption of Light by the Goldberg Wedge," Philos. Mag. 40, (6), 775 (1920).

1910 (2)

E. Goldberg, The Preparation of Gelatine Wedges, Br. J. Photogr. 57, 642 (1910).

E Goldberg, "The Preparation of Prismatic Wedges of Neutral Colour for Photometric Work," Br. J. Photogr. 57, 648 (1910).

Dobson, G. M. B.

G. M. B. Dobson and D. N. Harrison, "Ultra-Violet Photometry," Nature 117, 724 (1926).

G. M. B. Dobson, I. O. Griffith, and D. N. Harrison, Photographic Photometry (Clarendon, Oxford, 1926), p. 18.

Ghosh, J. C.

F. C. Toy and J. C. Ghosh, "The Absorption of Light by the Goldberg Wedge," Philos. Mag. 40, (6), 775 (1920).

Goldberg, E

E Goldberg, "The Preparation of Prismatic Wedges of Neutral Colour for Photometric Work," Br. J. Photogr. 57, 648 (1910).

Goldberg, E.

E. Goldberg, The Preparation of Gelatine Wedges, Br. J. Photogr. 57, 642 (1910).

E. Goldberg, Der Aufbau des Photographischen Bildes (Knapp, Halle, 1922), p. 81.

Gradshteyn, I. S.

I. S. Gradshteyn and I. M. Ryzhik, Tables of Integrals, Series, and Products (Academic, New York, 1965).

Griffith, I. O.

G. M. B. Dobson, I. O. Griffith, and D. N. Harrison, Photographic Photometry (Clarendon, Oxford, 1926), p. 18.

Harrison, D. N.

G. M. B. Dobson and D. N. Harrison, "Ultra-Violet Photometry," Nature 117, 724 (1926).

G. M. B. Dobson, I. O. Griffith, and D. N. Harrison, Photographic Photometry (Clarendon, Oxford, 1926), p. 18.

Magnus, W.

W. Magnus and F. Oberhettinger, Formulas and Theorems for the Special Functions of Mathematical Physics (Chelsea, New York, 1949).

McCamy, C. S.

C. S. McCamy, "The Theory of Optical Wedges," J. Opt. Soc. Am. 58, 724 (1968).

C. S. McCamy, "Concepts, Terminology, and Notation for Optical Modulation," Photogr. Sci. Eng. 10, 314 (1966).

Oberhettinger, F.

W. Magnus and F. Oberhettinger, Formulas and Theorems for the Special Functions of Mathematical Physics (Chelsea, New York, 1949).

Ryzhik, I. M.

I. S. Gradshteyn and I. M. Ryzhik, Tables of Integrals, Series, and Products (Academic, New York, 1965).

Toy, F. C.

F. C. Toy and J. C. Ghosh, "The Absorption of Light by the Goldberg Wedge," Philos. Mag. 40, (6), 775 (1920).

Br. J. Photogr. (1)

E Goldberg, "The Preparation of Prismatic Wedges of Neutral Colour for Photometric Work," Br. J. Photogr. 57, 648 (1910).

J. Opt. Soc. Am. (1)

C. S. McCamy, "The Theory of Optical Wedges," J. Opt. Soc. Am. 58, 724 (1968).

Nature (1)

G. M. B. Dobson and D. N. Harrison, "Ultra-Violet Photometry," Nature 117, 724 (1926).

Philos. Mag. (1)

F. C. Toy and J. C. Ghosh, "The Absorption of Light by the Goldberg Wedge," Philos. Mag. 40, (6), 775 (1920).

Photogr. Sci. Eng. (1)

C. S. McCamy, "Concepts, Terminology, and Notation for Optical Modulation," Photogr. Sci. Eng. 10, 314 (1966).

Other (7)

"American National Standard Terms, Symbols, and Notation for Optical Transmission and Reflection Measurements," PH2. 36–1974. Available from American National Standards Institute, Inc., 1430 Broadway, N. Y., 10018.

E. Goldberg, The Preparation of Gelatine Wedges, Br. J. Photogr. 57, 642 (1910).

G. M. B. Dobson, I. O. Griffith, and D. N. Harrison, Photographic Photometry (Clarendon, Oxford, 1926), p. 18.

E. Goldberg, Der Aufbau des Photographischen Bildes (Knapp, Halle, 1922), p. 81.

Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables, National Bureau of Standards, Applied Mathematics Series No. 55 (U. S. GPO, Washington, D. C. 1964).

W. Magnus and F. Oberhettinger, Formulas and Theorems for the Special Functions of Mathematical Physics (Chelsea, New York, 1949).

I. S. Gradshteyn and I. M. Ryzhik, Tables of Integrals, Series, and Products (Academic, New York, 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.