Abstract

We describe the anisotropic response of a silver chloride photographic emulsion after exposure to a linearly polarized achromatic signal. As it is described in previous papers, such a plate is a uniaxial medium with its optic axis parallel to the direction of the light vibration that induced anisotropy. It exhibits dichroism and birefringence, which are respectively equal to zero for two wavelengths independently of the exposure time. We calculate the refractive and absorption indices of such a colloidal medium following a method proposed by Garnett in 1905. The medium is assumed to be formed by three kinds of particles: silver chloride isotropic particles, silver isotropic particles generated by the action of linearly polarized short wavelengths on the silver chloride, and ellipsoidal silver particles resulting from the partial destruction of the previous ones by the linearly polarized long wavelengths. Finally, the amplitude response of the plate consists of two terms: an isotropic term that characterizes the isotropic darkening of the plate, which decreases linearly when exposure increases, and a term, which is proportional to the square of the exposure, that characterizes the anisotropic bleaching of the plate. Finally, we investigate the polarity of the signal reconstructed from the anisotropic recording of a black-and-white transparency. We show that the polarity is always the same as that of the original object, whatever the wavelength of the reading beam may be, when the plate is observed between crossed polarizers.

© 1983 Optical Society of America

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References

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  1. A. E. Cameron and A. M. Taylor, “Photophysical changes in silver–silver chloride systems,” J. Opt. Soc. Am. 24, 316–330 (1934).
    [CrossRef]
  2. S. Tcherdyncev, “Sur le photodichroisme des sels d’argent,” IXème Congrès Int. Photo. S. et Appl. Paris 1935122–131 (1936).
  3. A. Narath and K. Wasserroth, “Sur la théorie de l’effet Weigert,” Sci. Ind. Photogr. 23A, 38–46 (1951).
  4. N. F. Borelli, J. B. Chodak, and G. B. Hares, “Optically induced anisotropy in photochromic glasses,” J. Appl. Phys. 50, 5978–5987 (1979).
    [CrossRef]
  5. J. M. C. Jonathan and M. May, “Application of Weigert effect to the contrast reversal of a black and white transparency,” Opt. Commun. 28, 30–34 (1979).
    [CrossRef]
  6. J. M. C. Jonathan and M. May, “Anisotropy induced in a silver chloride emulsion by two incoherent and perpendicular light vibrations,” Opt. Commun. 28, 295–299 (1979).
    [CrossRef]
  7. J. M. C. Jonathan and M. May, “Application of the Weigert effect to optical processing in partially coherent light,” Opt. Eng. 19, 828–833 (1980).
    [CrossRef]
  8. M. P. Henriot and M. May, “Image deblurring methods using the Weigert effect,” Appl. Opt. 20, 2060–2065 (1981).
    [CrossRef] [PubMed]
  9. D. H. McMahon and W. T. Maloney, “Measurements of the stability of bleached photographic phase hologram,” Appl. Opt. 9, 1363–1368 (1970).
    [CrossRef] [PubMed]
  10. J. Upatnieks and C. Leonard, “Diffraction efficiency of bleached photographically recorded interference patterns,” Appl. Opt. 8, 85–89 (1969).
    [CrossRef] [PubMed]
  11. I. Kamiya, “Photodichroism of printed out silver. I, Some experimental evidences in favor of the view that the photodichroism of printed out silver is an anisotropic Herschel effect,” Bull. Chem. Soc. Jpn. 30, 6–9 (1957).
    [CrossRef]
  12. J. R. Haynes and W. Shockley, “The mobility of electrons in silver chloride,” Phys. Rev. 82, 935–943 (1951).
    [CrossRef]
  13. N. F. Mott and R. W. Gurney, Electronic Processes in Ionic Crystals (Dover, New York, 1964),p. 243.
  14. V. P. Cherkashin, “Spectral reversal of dichroism in silver halides,” Sov. Phys. Solid State 14, 1083–1084 (1972).
  15. J. M. C. Jonathan, “Traitement optique du signal par effet Weigert,” D. Sc. Thesis (Université Paris VI, Paris, 1981).
  16. J. C. Maxwell Garnett, “Colours in metal glasses and in metallic films,” Phil. Trans. R. Soc. London Ser. A 203, 385–420 (1905).
  17. H. C. van de Hulst, Light Scattering by Small Particles (Wiley, New York, 1957), Chap. 6.

1981 (1)

1980 (1)

J. M. C. Jonathan and M. May, “Application of the Weigert effect to optical processing in partially coherent light,” Opt. Eng. 19, 828–833 (1980).
[CrossRef]

1979 (3)

N. F. Borelli, J. B. Chodak, and G. B. Hares, “Optically induced anisotropy in photochromic glasses,” J. Appl. Phys. 50, 5978–5987 (1979).
[CrossRef]

J. M. C. Jonathan and M. May, “Application of Weigert effect to the contrast reversal of a black and white transparency,” Opt. Commun. 28, 30–34 (1979).
[CrossRef]

J. M. C. Jonathan and M. May, “Anisotropy induced in a silver chloride emulsion by two incoherent and perpendicular light vibrations,” Opt. Commun. 28, 295–299 (1979).
[CrossRef]

1972 (1)

V. P. Cherkashin, “Spectral reversal of dichroism in silver halides,” Sov. Phys. Solid State 14, 1083–1084 (1972).

1970 (1)

1969 (1)

1957 (1)

I. Kamiya, “Photodichroism of printed out silver. I, Some experimental evidences in favor of the view that the photodichroism of printed out silver is an anisotropic Herschel effect,” Bull. Chem. Soc. Jpn. 30, 6–9 (1957).
[CrossRef]

1951 (2)

J. R. Haynes and W. Shockley, “The mobility of electrons in silver chloride,” Phys. Rev. 82, 935–943 (1951).
[CrossRef]

A. Narath and K. Wasserroth, “Sur la théorie de l’effet Weigert,” Sci. Ind. Photogr. 23A, 38–46 (1951).

1936 (1)

S. Tcherdyncev, “Sur le photodichroisme des sels d’argent,” IXème Congrès Int. Photo. S. et Appl. Paris 1935122–131 (1936).

1934 (1)

1905 (1)

J. C. Maxwell Garnett, “Colours in metal glasses and in metallic films,” Phil. Trans. R. Soc. London Ser. A 203, 385–420 (1905).

Borelli, N. F.

N. F. Borelli, J. B. Chodak, and G. B. Hares, “Optically induced anisotropy in photochromic glasses,” J. Appl. Phys. 50, 5978–5987 (1979).
[CrossRef]

Cameron, A. E.

Cherkashin, V. P.

V. P. Cherkashin, “Spectral reversal of dichroism in silver halides,” Sov. Phys. Solid State 14, 1083–1084 (1972).

Chodak, J. B.

N. F. Borelli, J. B. Chodak, and G. B. Hares, “Optically induced anisotropy in photochromic glasses,” J. Appl. Phys. 50, 5978–5987 (1979).
[CrossRef]

Gurney, R. W.

N. F. Mott and R. W. Gurney, Electronic Processes in Ionic Crystals (Dover, New York, 1964),p. 243.

Hares, G. B.

N. F. Borelli, J. B. Chodak, and G. B. Hares, “Optically induced anisotropy in photochromic glasses,” J. Appl. Phys. 50, 5978–5987 (1979).
[CrossRef]

Haynes, J. R.

J. R. Haynes and W. Shockley, “The mobility of electrons in silver chloride,” Phys. Rev. 82, 935–943 (1951).
[CrossRef]

Henriot, M. P.

Jonathan, J. M. C.

J. M. C. Jonathan and M. May, “Application of the Weigert effect to optical processing in partially coherent light,” Opt. Eng. 19, 828–833 (1980).
[CrossRef]

J. M. C. Jonathan and M. May, “Application of Weigert effect to the contrast reversal of a black and white transparency,” Opt. Commun. 28, 30–34 (1979).
[CrossRef]

J. M. C. Jonathan and M. May, “Anisotropy induced in a silver chloride emulsion by two incoherent and perpendicular light vibrations,” Opt. Commun. 28, 295–299 (1979).
[CrossRef]

J. M. C. Jonathan, “Traitement optique du signal par effet Weigert,” D. Sc. Thesis (Université Paris VI, Paris, 1981).

Kamiya, I.

I. Kamiya, “Photodichroism of printed out silver. I, Some experimental evidences in favor of the view that the photodichroism of printed out silver is an anisotropic Herschel effect,” Bull. Chem. Soc. Jpn. 30, 6–9 (1957).
[CrossRef]

Leonard, C.

Maloney, W. T.

Maxwell Garnett, J. C.

J. C. Maxwell Garnett, “Colours in metal glasses and in metallic films,” Phil. Trans. R. Soc. London Ser. A 203, 385–420 (1905).

May, M.

M. P. Henriot and M. May, “Image deblurring methods using the Weigert effect,” Appl. Opt. 20, 2060–2065 (1981).
[CrossRef] [PubMed]

J. M. C. Jonathan and M. May, “Application of the Weigert effect to optical processing in partially coherent light,” Opt. Eng. 19, 828–833 (1980).
[CrossRef]

J. M. C. Jonathan and M. May, “Anisotropy induced in a silver chloride emulsion by two incoherent and perpendicular light vibrations,” Opt. Commun. 28, 295–299 (1979).
[CrossRef]

J. M. C. Jonathan and M. May, “Application of Weigert effect to the contrast reversal of a black and white transparency,” Opt. Commun. 28, 30–34 (1979).
[CrossRef]

McMahon, D. H.

Mott, N. F.

N. F. Mott and R. W. Gurney, Electronic Processes in Ionic Crystals (Dover, New York, 1964),p. 243.

Narath, A.

A. Narath and K. Wasserroth, “Sur la théorie de l’effet Weigert,” Sci. Ind. Photogr. 23A, 38–46 (1951).

Shockley, W.

J. R. Haynes and W. Shockley, “The mobility of electrons in silver chloride,” Phys. Rev. 82, 935–943 (1951).
[CrossRef]

Taylor, A. M.

Tcherdyncev, S.

S. Tcherdyncev, “Sur le photodichroisme des sels d’argent,” IXème Congrès Int. Photo. S. et Appl. Paris 1935122–131 (1936).

Upatnieks, J.

van de Hulst, H. C.

H. C. van de Hulst, Light Scattering by Small Particles (Wiley, New York, 1957), Chap. 6.

Wasserroth, K.

A. Narath and K. Wasserroth, “Sur la théorie de l’effet Weigert,” Sci. Ind. Photogr. 23A, 38–46 (1951).

Appl. Opt. (3)

Bull. Chem. Soc. Jpn. (1)

I. Kamiya, “Photodichroism of printed out silver. I, Some experimental evidences in favor of the view that the photodichroism of printed out silver is an anisotropic Herschel effect,” Bull. Chem. Soc. Jpn. 30, 6–9 (1957).
[CrossRef]

IXème Congrès Int. Photo. S. et Appl. Paris 1935 (1)

S. Tcherdyncev, “Sur le photodichroisme des sels d’argent,” IXème Congrès Int. Photo. S. et Appl. Paris 1935122–131 (1936).

J. Appl. Phys. (1)

N. F. Borelli, J. B. Chodak, and G. B. Hares, “Optically induced anisotropy in photochromic glasses,” J. Appl. Phys. 50, 5978–5987 (1979).
[CrossRef]

J. Opt. Soc. Am. (1)

Opt. Commun. (2)

J. M. C. Jonathan and M. May, “Application of Weigert effect to the contrast reversal of a black and white transparency,” Opt. Commun. 28, 30–34 (1979).
[CrossRef]

J. M. C. Jonathan and M. May, “Anisotropy induced in a silver chloride emulsion by two incoherent and perpendicular light vibrations,” Opt. Commun. 28, 295–299 (1979).
[CrossRef]

Opt. Eng. (1)

J. M. C. Jonathan and M. May, “Application of the Weigert effect to optical processing in partially coherent light,” Opt. Eng. 19, 828–833 (1980).
[CrossRef]

Phil. Trans. R. Soc. London Ser. A (1)

J. C. Maxwell Garnett, “Colours in metal glasses and in metallic films,” Phil. Trans. R. Soc. London Ser. A 203, 385–420 (1905).

Phys. Rev. (1)

J. R. Haynes and W. Shockley, “The mobility of electrons in silver chloride,” Phys. Rev. 82, 935–943 (1951).
[CrossRef]

Sci. Ind. Photogr. (1)

A. Narath and K. Wasserroth, “Sur la théorie de l’effet Weigert,” Sci. Ind. Photogr. 23A, 38–46 (1951).

Sov. Phys. Solid State (1)

V. P. Cherkashin, “Spectral reversal of dichroism in silver halides,” Sov. Phys. Solid State 14, 1083–1084 (1972).

Other (3)

J. M. C. Jonathan, “Traitement optique du signal par effet Weigert,” D. Sc. Thesis (Université Paris VI, Paris, 1981).

H. C. van de Hulst, Light Scattering by Small Particles (Wiley, New York, 1957), Chap. 6.

N. F. Mott and R. W. Gurney, Electronic Processes in Ionic Crystals (Dover, New York, 1964),p. 243.

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Figures (13)

Fig. 1
Fig. 1

Absorption spectrum of unexposed silver chloride emulsion in terms of optical density.

Fig. 2
Fig. 2

Exposure-induced absorption (optical density, Δd) in silver chloride emulsions exposed to unpolarized mercury light. Curves 1, 2, and 3 correspond to increasing exposure times.

Fig. 3
Fig. 3

Exposure-induced absorption in silver chloride emulsions exposed to linearly polarized mercury light. Curves 1, 2, and 3 correspond to increasing exposure times. (a) Optical density Δd induced in the direction parallel to optical axis. (b) Optical density Δd induced in the perpendicular direction.

Fig. 4
Fig. 4

Induced dichroism, defined as D = Δd − Δd

Fig. 5
Fig. 5

Ketteler–Helmoltz equation for absorption (k) and refractive (n) indices. The two refractive-index curves (b), corresponding to the two absorption curves (a), give a birefringence curve (c) by difference.

Fig. 6
Fig. 6

The ellipsoidal particles created by short wavelengths of linearly polarized mercury light are partly destroyed by the long wavelengths.

Fig. 7
Fig. 7

OX (induced optic axis) and OY are the privileged directions of SC after exposure. O P and O A represent the respective axes of the polarizer and the analyzer.

Fig. 8
Fig. 8

The achromatic signal imaged by the lens L is recorded onto the silver chloride emulsion SC. The incident white light is derived from a high-pressure mercury lamp.

Fig. 9
Fig. 9

SC after exposure is observed from λB illumination. The rectilinear vibration r leaving an elementary area makes an angle with the axis of P.

Fig. 10
Fig. 10

r is generated by the vectorial composition of a directly transmitted vibration t and a doubly refracted one b inclined at an antle θ on OX.

Fig. 11
Fig. 11

(a) Original transparency. (b) Signal reconstructed from the anisotropic recording of (a) illuminated in λB light and observed between crossed polarizers. (c) Reconstructed signal with π/2 + angle between the axes of P and A. (d) Reconstructed signal with π/2 + EMAX angle between the axes of Pand A.

Fig. 12
Fig. 12

SC after exposure is observed under λd light through the polarizer whose axis is inclined at −45° to OX. The light vibration leaving an elementary area is elliptically polarized with its major axis along the axis of P.

Fig. 13
Fig. 13

Signal reconstructed from the anisotropic recording of Fig. 11(a) illuminated in white light and observed between crossed polarizers.

Equations (52)

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[ α i ] = ( α i 0 0 α i )
( α c i ) = ( α c i 0 0 α c i )
P = ( g ) E 0 , P = ( g ) E 0 .
ν = n i k = ν e m + n g 2 [ E p i N o i B i ( α i α i c l ) E p 2 i N o i B i B c i ( α i α c i ) ] , ν = n i k = ν e m + n g 2 [ E p i N o i B i ( α i α i c l ) E p 2 i N o i B i B c i ( α i α c i ) ] ,
ρ i = B i E p , ρ c i = B c i E p ,
τ ( λ ) = exp ( i 2 π λ d ν ) = exp ( i 2 π λ d n ) exp ( 2 π λ d k ) , τ ( λ ) = exp ( i 2 π λ d ν ) = exp ( i 2 π λ d n ) × exp ( 2 π λ d k ) .
τ ( λ ) = | τ e m | { 1 2 π λ d n g 2 [ E p i N o i B i ( b i b i c l ) E p 2 i N o i B i B c i ( b i b c i ) ] } , τ ( λ ) = | τ e m | { 1 2 π λ d n g 2 [ E p i N o i B i ( b i b i c l ) E p 2 i N o i B i B c i ( b i b c i ) ] } exp [ i Φ ( λ , E p ) ] .
Φ ( λ , E p ) = 2 π λ d ( n n ) = 2 π λ d n g 2 [ E p i N o i B i ( a i a i ) E p 2 i N o i B i B c i ( a c i a c i ) ] ,
E p i N o i B i b i ( λ ) E p 2 i N o i B i B c i [ b i ( λ ) b c i ( λ ) ] = E p i N o i B i b i ( λ ) E p 2 i N o i B i B c i × [ b i ( λ ) b c i ( λ ) ] .
i N o i B i b i ( λ d ) = i N o i B i b i ( λ d ) ,
i N o i B i B c i [ b i ( λ d ) b c i ( λ d ) ] = i N o i B i B c i [ b i ( λ d ) b c i ( λ d ) ] .
b i ( λ ) = b i ( λ ) = b i ( λ ) ,
i N o i B i B c i b c i ( λ d ) = i N o i B i B c i b c i ( λ d ) .
a i ( λ ) = a i ( λ ) = a i ( λ ) ,
i N o i B i B c i a c i ( λ B ) = i N o i B i B c i a c i ( λ B ) .
τ ( λ ) = | τ e m ( λ ) | [ 1 K ( λ ) E p + K ( λ ) E p 2 ] , τ ( λ ) = | τ e m ( λ ) | [ 1 K ( λ ) E p + K ( λ ) E p 2 ] exp [ i Φ ( λ , E p ) ] ,
K ( λ ) = 2 π λ d n g 2 i N o i B i [ b i ( λ ) b i c l ( λ ) ] ,
K ( λ ) = 2 π λ d n g 2 i N o i B i B c i [ b i ( λ ) b c i ( λ ) ] ,
K ( λ ) = 2 π λ d n g 2 i N o i B i B c i [ b i ( λ ) b i c ( λ ) ] ,
Φ ( λ , E p ) = 2 π λ d n g 2 E p 2 i N o i B i B c i [ a c i ( λ ) a c i ( λ ) ] .
E p ( x , y ) = t p I ( x , y ) ,
I β ( x , y ) = | τ e m | 2 ( cos β { 1 K ( λ ) E p + [ K ( λ ) + K ( λ ) 2 ] E p 2 } sin β [ K ( λ ) + K ( λ ) 2 ] × E p 2 ) 2 | τ e m | 2 [ 1 K ( λ ) E p + K ( λ ) E p 2 ] × [ 1 K ( λ ) E p + K ( λ ) E p 2 ] cos 2 β sin 2 Φ 2 .
I β ( x , y ) = | τ e m | 2 × ( cos β { 1 K ( λ B ) E p + [ K ( λ B ) + K ( λ B ) 2 ] E p 2 } sin β [ K ( λ B ) + K ( λ B ) 2 ] E p 2 ) 2 ;
tan ( x , y ) = [ K ( λ B ) K ( λ B ) 2 ] E p 2 ( x , y ) 1 K ( λ B ) E p ( x , y ) + [ K ( λ B ) K ( λ B ) 2 ] E p 2 ( x , y ) .
I ( x , y ) = | τ e m | 2 [ K ( λ B ) K ( λ B ) 2 ] 2 E p 4 ( x , y ) .
β = β 0 = tan 1 1 K ( λ B ) E 0 + [ K ( λ B ) + K ( λ B ) 2 ] E 0 2 [ K ( λ B ) K ( λ B ) 2 ] E 0 2
I β 0 ( x , y ) = C | τ e m | 2 [ K ( λ B ) K ( λ B ) 2 ] 2 × { E 0 2 [ 1 K ( λ B ) E p ( x , y ) ] E p 2 ( x , y ) [ 1 K ( λ B ) E 0 ] } 2 ,
C = { ( 1 + t g 2 β 0 ) [ K ( λ B ) K ( λ B ) 2 ] E 0 4 } 1 .
β min = π 2 + MAX ,
t = | τ e m | 2 [ 1 K ( λ B ) E p ( x , y ) ] , t = | τ e m | 2 [ 1 K ( λ B ) E p ( x , y ) ] ,
b = | τ e m | 2 K ( λ B ) E p 2 ( x , y ) , b = | τ e m | 2 K ( λ B ) E p 2 ( x , y ) .
tan θ = K ( λ B ) K ( λ B ) ,
I ( π / 4 ) + θ ( x , y ) = | τ e m | 2 [ 1 K ( λ B ) E p ( x , y ) ] 2 ,
K ( λ d ) = K ( λ d ) = K 0 ( λ d ) .
I ( λ d ; x , y ) = | τ e m | 2 [ 1 K ( λ d ) E p ( x , y ) + K 0 ( λ d ) E p 2 ( x , y ) ] Φ 2 ( λ d , E p ) 4 ,
J ( x , y ) = I ( λ ; x , y ) d λ .
P = ( g ) E 0 , P = ( g ) E 0 .
P = g i [ N o i ( 1 ρ i ) α i c l + N o i ρ i ( 1 ρ c i ) α i + N o i ρ i ρ c i α c i ] , P = g i [ N o i ( 1 ρ i ) α i c l + N o i ρ i ( 1 ρ c i ) α i + N o i ρ i ρ c i α c i ] .
= g { 1 + i [ N o i α i c l + N o i ρ i ( α i α i c l ) N o i ρ i ρ c i ( α i α c i ) ] } , = g { 1 + i [ N o i α i c l + N o i ρ i ( α i α i c l ) N o i ρ i ρ c i ( α i α c i ) ] } .
= 0 ν 2 , = 0 ν 2 .
ν 2 = n g 2 { 1 + i [ N o i α i c l + N o i ρ i ( α i α i c l ) N o i ρ i ρ c i ( α i α c i ) ] } , ν 2 = n g 2 { 1 + i [ N o i α i c l + N o i ρ i ( α i α i c l ) N o i ρ i ρ c i ( α i α c i ) ] } ,
ν = n g { 1 + 1 2 i [ N i o α i c l + N o i ρ i ( α i α i c l ) N o i ρ i ρ c i ( α i α i c ) ] } , ν = n g { 1 + 1 2 i [ N o i α i c l + N o i ρ i ( α i α i c l ) N o i ρ i ρ c i ( α i α c i ) ] } ,
ν = ν e m + n g 2 i [ N o i ρ i ( α i α i c l ) N o i ρ i ρ c i ( α i α i c ) ] , ν = ν e m + n g 2 i [ N o i ρ i ( α i α i c l ) N o i ρ i ρ c i ( α i α i c ) ] ,
ν e m = n g ( 1 + 1 2 i N o i α i c l )
τ = | τ | = | τ e m | [ 1 K ( λ ) E p ( x , y ) + K ( λ ) E p 2 ( x , y ) ] , τ = | τ | exp [ i Φ ( λ , E p ) = | τ e m | [ 1 K ( λ ) E p ( x , y ) + K ( λ ) E p 2 ( x , y ) ] exp [ i Φ ( λ , E p ) ] .
X i = cos α , Y i = sin α .
X e = τ ( λ , E p ) cos α , Y e = τ ( λ , E p ) sin α ,
μ β ( x , y ) = [ τ ( λ , E p ) cos α cos ( β α ) τ ( λ , E p ) sin α sin ( β α ) ] .
μ β ( x , y ) = [ | τ ( λ , E p ) | cos α cos ( β α ) | τ ( λ , E p ) | sin α sin ( β α ) e i Φ ] .
I β ( λ , E p ) = [ | τ ( λ ) , E p ) | cos α cos ( β α ) | τ ( λ , E p ) | sin α sin ( β α ) ] 2 + | τ ( λ , E p ) | | τ ( λ , E p ) | × sin 2 α sin 2 ( β α ) sin 2 Φ 2 .
I β ( λ , E p ) = 1 4 [ cos β ( | τ | + | τ | ) sin β ( | τ | | τ | ) ] 2 | τ | | τ | cos 2 β sin 2 Φ 2 .
I β ( λ , E p ) = | τ e m | 2 { cos β [ 1 K E p + ( K + K 2 ) E p 2 ] sin β ( K + K 2 ) E p 2 } 2 | τ e m | 2 ( 1 K E p + K E p 2 ) × ( 1 K E p + K E p 2 ) cos 2 β sin 2 Φ 2 .