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On the feasibility for determining the amplitude zeroes in polychromatic fields

Oleg V. Angelsky, Steen G. Hanson, Alexander P. Maksimyak, and Peter P. Maksimyak

Open Access Open Access

Abstract

The technique of an inverted chromascope is introduced for determining the points of amplitude zeroes for the spectral components of a polychromatic radiation field. Applications of this technique for processing of experimentally obtained light distributions are demonstrated, both arising from birefringence and from speckle fields.

©2005 Optical Society of America

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Figures (13)
Fig. 1.
Fig. 1. Spatial intensity distribution over an isolated fragment of a speckle-field produced by three spectral components.

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Fig. 2.
Fig. 2. Spatial phase distribution of an isolated fragment of a speckle-field produced by red (a); green (b); blue (c) and for all three spectral components (d).

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Fig. 3.
Fig. 3. Color distribution resulting from processing of the isolated fragment of a speckle-field by a chromascope. Fragment (1) depicts a zone of low intensity of the distribution shown in Fig. 1.

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Fig. 4.
Fig. 4. Color distribution resulting from processing of an isolated fragment of a speckle-field by the inverted chromascope.

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Fig. 5.
Fig. 5. Spatial phase distribution of an isolated fragment of a speckle-field produced by red (a); green (c); blue (e), and spatial distribution of amplitude zeroes of the isolated fragment of a speckle-field for red (b); green (d); blue (f) spectral component.

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Fig. 6.
Fig. 6. The experimental optical arrangement: 1 - source of light; 2,4,8 - objectives; 3 - diaphragm; 5 - polarizer; 6 - film; 7 - analyzer; 9 - CCD-camera; 10 - computer.

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Fig. 7.
Fig. 7. Conoscopic patterns obtained for matched polarizer and analyzer (a), and for crossed polarizer and analyzer (b).

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Fig. 8.
Fig. 8. Patterns shown in Fig. 7 processed by a chromascope for matched polarizer and analyzer (a), and for crossed polarizer and analyzer (b).

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Fig. 9.
Fig. 9. Pattern shown in Fig. 7(a) processed by the inverted chromascope.

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Fig. 10.
Fig. 10. Patterns illustrating the positions of amplitude zeroes of the field for red (a), green (b) and blue (c) spectral components.

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Fig. 11.
Fig. 11. Fragment of polychromatic speckle-field resulting from scattering by a rough surface.

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Fig. 12.
Fig. 12. The pattern obtained by applying a chromascope (a) and inverse chromascope (b) to the experimentally found intensity distribution shown in Fig. 11.

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Fig. 13.
Fig. 13. The patterns illustrating the positions of amplitude zeroes of the speckle-field for red (a), green (b) and blue(c) spectral components.

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Equations (4)

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U ( ξ , η ) = z i λ ∬ A ( x , y ) R 2 ( x , y , z , ξ , η ) exp { − ik [ R ( x , y , z , ξ , η ) + ( n − 1 ) h ( x , y ) ] } dxdy ,
( R G B ) CR = ( R G B ) ⁄ max ( R , G , B ) .
( R G B ) INV = 1 − ( R G B ) CR
( R G B ) Y = { 1 , for Y INV + δ Y ≥ 1 0 , for Y INV + δ Y < 1 and Y = 0 ,
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