Abstract
One of the most interesting and exciting applications of lasers lies in the fields of spatial frequency filtering and holography. In this chapter, we briefly outline the principle behind spatial frequency filtering and holography and discuss their applications.
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Notes
- 1.
For a detailed theoretical analysis of the character recognition problem, see, e.g., Ghatak and Thyagarajan (1978).
- 2.
We are assuming the fields to be monochromatic with a time dependence of the form \({e}^{{i}\omega t} \). Now, for two functions f and g with time variations of the form \({e}^{{i}\omega t} \)
$$\left\langle {{\textrm{Re}}\,f\,{\textrm{Re}}\,g} \right\rangle = \frac{1}{2}\left\langle {{\textrm{Re}}\,f^{\ast} g} \right\rangle $$where angular brackets denote time averaging and \(\textrm{Re}\,f\) stands for the real part of the function f.
- 3.
The high-pressure mercury arc lamp emits a green line at 5461 Å. The coherence length of this line is, in fact, only about 10 \(\mu \textrm{m}\). (The width of the line at 5461 Å is about \(5 \times 10^{12}\,{\textrm{Hz}}\).) On the other hand, the 6058-Å line emitted by krypton has a coherence length of ∼20 cm, but the power output per unit area of this source is very low. When one tries to increase the source area, one loses spatial coherence. The notion of coherence length has been discussed in Chapter 9.
- 4.
References
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Collier, R. J., Burckhardt, C. B., and Lin, L. H. (1971), Optical Holography, Academic Press, New York.
Gagliano, F. P., Lumley, R. M., and Watkins, L. S. (1969), Lasers in industry, Proc. IEEE 57, 114.
Ghatak, A. K., and Thyagarajan, K. (1978), Contemporary Optics, Plenum Press, New York.
Tsujiuchi, J., Matsuda, K., and Takeja, N. (1971), Correlation techniques by holography and its application to fingerprint identification, in Applications of Holography (E. S. Barrekette, W. E. Kock, T. Ose, J. Tsujiuchi, and G. W. Stroke, eds.), p. 247, Plenum Press, New York.
Stroke, G. W., Halioua, M., and Srinivasan, N. (1975), Holographic image restoration using fourier spectrum analysis of blurred photographs in computer-aided synthesis of Wiener filters, Phys. Lett. 51 A, 383.
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Thyagarajan, K., Ghatak, A. (2011). Spatial Frequency Filtering and Holography. In: Lasers. Graduate Texts in Physics. Springer, Boston, MA. https://doi.org/10.1007/978-1-4419-6442-7_15
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DOI: https://doi.org/10.1007/978-1-4419-6442-7_15
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