Abstract

We present a Twyman–Green interferometer (TGI)-based polarization phase-shifting shearing interferometric technique for testing the conical surface of an axicon (AX) lens. In this technique, the annular beam generated due to the passing of an expanded collimated laser beam traveling along the axis of revolution of the transparent glass AX element is split up into its reflected and transmitted components, having the plane of polarization in the orthogonal planes, by the polarization beam splitter (PBS) cube of the TGI-based optical setup. The split-up components are made to travel unequal paths along the two arms of the TGI and are recombined by the PBS. Because of the difference in path lengths traveled by the annular conical beams, a linear shear is introduced along the radial direction between the interfering components. Thus, the resulting interference pattern gives a map of the optical path difference (OPD) between two successive close points along a radial direction on the conical surface of the AX lens. The OPD map along radial directions, and hence the slopes/profiles of the conical surface, are obtained by applying polarization phase-shifting interferometry. Results obtained for an AX lens are presented.

© 2011 Optical Society of America

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References

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    [CrossRef]
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    [CrossRef]
  3. Z. Jaroszewicz, A. Burvall, and A. T. Friberg, “Axicon—the most important optical element,” Opt. Photon. News 16(4), 34–39 (2005).
    [CrossRef]
  4. T. Kololuoma, K. Kataja, S. Juuso, and J. Aikio, “Fabrication and characterization of hybrid-glass-based axicons,” Opt. Eng. 41, 3136–3140 (2002).
    [CrossRef]
  5. Z. Ding, H. Ren, Y. Zhao, J. S. Nelson, and Z. Chen, “High resolution optical coherence tomography over a large depth range with an axicon lens,” Opt. Lett. 27, 243–245 (2002).
    [CrossRef]
  6. P. Dufour, M. Piche, Y. De Koninck, and N. McCarthy, “Two-photon excitation fluorescence microscopy with a high depth of field using an axicon,” Appl. Opt. 45, 9246–9252 (2006).
    [CrossRef] [PubMed]
  7. F. P. Schafer, “On some properties of axicons,” Appl. Phys. B 39, 1–8 (1986).
    [CrossRef]
  8. W. D. Kimura, G. H. Kim, R. D. Romea, L. C. Steinhauer, I. V. Pogorelsky, K. P. Kusche, R. C. Fernow, X. Wang, and Y. Lin, “Laser acceleration of relativistic electrons using the inverse Chernokov effect,” Phys. Rev. Lett. 74, 546–549(1995).
    [CrossRef] [PubMed]
  9. M. D. Wei, W. L. Shiao, and Y. T. Lin, “Adjustable generation of bottle and hollow beams using an axicon,” Opt. Commun. 248, 7–14 (2005).
    [CrossRef]
  10. I. Manek, Y. B. Ovchinnikov, and R. Grimm, “Generation of a hollow laser beam for atom trapping using an axicon,” Opt. Commun. 147, 67–70 (1998).
    [CrossRef]
  11. G. Scott and N. McArdle, “Efficient generation of nearly diffraction free beams using axicon,” Opt. Eng. 31, 2640–2643(1992).
    [CrossRef]
  12. J. Arlt and K. Dholakia, “Generation of higher order Bessel beams by use of an axicon,” Opt. Commun. 177, 297–301(2000).
    [CrossRef]
  13. D. Zeng, W. P. Latham, and A. Kar, “Shaping of annular laser intensity profiles and their thermal effects for spatial trepanning,” Opt. Eng. 45, 014301 (2006).
    [CrossRef]
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    [CrossRef] [PubMed]
  17. M. de Angelis, S. D. Nicola, P. Ferraro, A. Finizio, and G. Pierattini, “Test of a conical lens using a two beam shearing interferometer,” Opt. Lasers Eng. 39, 155–163(2003).
    [CrossRef]
  18. S. Chatterjee, Y. P. Kumar, and B. Bhaduri, “Measurement of surface figure of plane optical surfaces with polarization phase-shifting Fizeau interferometer,” Opt. Laser Tech. 39, 268–274 (2007).
    [CrossRef]
  19. M. Strojnik, G. Paez, and M. Mantravadi, “Lateral shear interferometers,” in Optical Shop Testing, D.Malacara, ed. (Wiley, 2007), pp. 122–184.
    [CrossRef]
  20. P. Hariharan, “Phase shifting interferometry: minimization of systematic errors,” Opt. Eng. 39, 967–969 (2000).
    [CrossRef]
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    [CrossRef]
  23. D. Malacara, S. Malacara, and Z. Malacara, in Interferogram Analysis for Optical Testing (Marcel Dekker, 1998), pp. 248–255.

2008 (1)

2007 (1)

S. Chatterjee, Y. P. Kumar, and B. Bhaduri, “Measurement of surface figure of plane optical surfaces with polarization phase-shifting Fizeau interferometer,” Opt. Laser Tech. 39, 268–274 (2007).
[CrossRef]

2006 (2)

D. Zeng, W. P. Latham, and A. Kar, “Shaping of annular laser intensity profiles and their thermal effects for spatial trepanning,” Opt. Eng. 45, 014301 (2006).
[CrossRef]

P. Dufour, M. Piche, Y. De Koninck, and N. McCarthy, “Two-photon excitation fluorescence microscopy with a high depth of field using an axicon,” Appl. Opt. 45, 9246–9252 (2006).
[CrossRef] [PubMed]

2005 (2)

Z. Jaroszewicz, A. Burvall, and A. T. Friberg, “Axicon—the most important optical element,” Opt. Photon. News 16(4), 34–39 (2005).
[CrossRef]

M. D. Wei, W. L. Shiao, and Y. T. Lin, “Adjustable generation of bottle and hollow beams using an axicon,” Opt. Commun. 248, 7–14 (2005).
[CrossRef]

2003 (1)

M. de Angelis, S. D. Nicola, P. Ferraro, A. Finizio, and G. Pierattini, “Test of a conical lens using a two beam shearing interferometer,” Opt. Lasers Eng. 39, 155–163(2003).
[CrossRef]

2002 (2)

T. Kololuoma, K. Kataja, S. Juuso, and J. Aikio, “Fabrication and characterization of hybrid-glass-based axicons,” Opt. Eng. 41, 3136–3140 (2002).
[CrossRef]

Z. Ding, H. Ren, Y. Zhao, J. S. Nelson, and Z. Chen, “High resolution optical coherence tomography over a large depth range with an axicon lens,” Opt. Lett. 27, 243–245 (2002).
[CrossRef]

2000 (2)

P. Hariharan, “Phase shifting interferometry: minimization of systematic errors,” Opt. Eng. 39, 967–969 (2000).
[CrossRef]

J. Arlt and K. Dholakia, “Generation of higher order Bessel beams by use of an axicon,” Opt. Commun. 177, 297–301(2000).
[CrossRef]

1998 (1)

I. Manek, Y. B. Ovchinnikov, and R. Grimm, “Generation of a hollow laser beam for atom trapping using an axicon,” Opt. Commun. 147, 67–70 (1998).
[CrossRef]

1995 (1)

W. D. Kimura, G. H. Kim, R. D. Romea, L. C. Steinhauer, I. V. Pogorelsky, K. P. Kusche, R. C. Fernow, X. Wang, and Y. Lin, “Laser acceleration of relativistic electrons using the inverse Chernokov effect,” Phys. Rev. Lett. 74, 546–549(1995).
[CrossRef] [PubMed]

1992 (1)

G. Scott and N. McArdle, “Efficient generation of nearly diffraction free beams using axicon,” Opt. Eng. 31, 2640–2643(1992).
[CrossRef]

1987 (1)

1986 (1)

F. P. Schafer, “On some properties of axicons,” Appl. Phys. B 39, 1–8 (1986).
[CrossRef]

1981 (2)

1960 (1)

1954 (1)

Aikio, J.

T. Kololuoma, K. Kataja, S. Juuso, and J. Aikio, “Fabrication and characterization of hybrid-glass-based axicons,” Opt. Eng. 41, 3136–3140 (2002).
[CrossRef]

Arlt, J.

J. Arlt and K. Dholakia, “Generation of higher order Bessel beams by use of an axicon,” Opt. Commun. 177, 297–301(2000).
[CrossRef]

Bartels, R. A.

Bhaduri, B.

S. Chatterjee, Y. P. Kumar, and B. Bhaduri, “Measurement of surface figure of plane optical surfaces with polarization phase-shifting Fizeau interferometer,” Opt. Laser Tech. 39, 268–274 (2007).
[CrossRef]

Burvall, A.

Z. Jaroszewicz, A. Burvall, and A. T. Friberg, “Axicon—the most important optical element,” Opt. Photon. News 16(4), 34–39 (2005).
[CrossRef]

Chatterjee, S.

S. Chatterjee, Y. P. Kumar, and B. Bhaduri, “Measurement of surface figure of plane optical surfaces with polarization phase-shifting Fizeau interferometer,” Opt. Laser Tech. 39, 268–274 (2007).
[CrossRef]

Chen, Z.

Creath, K.

K. Creath, “Phase measurement interferometry techniques,” in Progress in Optics, Vol.  xxviii, E.Wolf, ed. (North-Holland, 1988), pp. 349–393.
[CrossRef]

de Angelis, M.

M. de Angelis, S. D. Nicola, P. Ferraro, A. Finizio, and G. Pierattini, “Test of a conical lens using a two beam shearing interferometer,” Opt. Lasers Eng. 39, 155–163(2003).
[CrossRef]

De Koninck, Y.

Dholakia, K.

J. Arlt and K. Dholakia, “Generation of higher order Bessel beams by use of an axicon,” Opt. Commun. 177, 297–301(2000).
[CrossRef]

Ding, Z.

Dufour, P.

Eiju, T.

Fantone, S. D.

Fernow, R. C.

W. D. Kimura, G. H. Kim, R. D. Romea, L. C. Steinhauer, I. V. Pogorelsky, K. P. Kusche, R. C. Fernow, X. Wang, and Y. Lin, “Laser acceleration of relativistic electrons using the inverse Chernokov effect,” Phys. Rev. Lett. 74, 546–549(1995).
[CrossRef] [PubMed]

Ferraro, P.

M. de Angelis, S. D. Nicola, P. Ferraro, A. Finizio, and G. Pierattini, “Test of a conical lens using a two beam shearing interferometer,” Opt. Lasers Eng. 39, 155–163(2003).
[CrossRef]

Finizio, A.

M. de Angelis, S. D. Nicola, P. Ferraro, A. Finizio, and G. Pierattini, “Test of a conical lens using a two beam shearing interferometer,” Opt. Lasers Eng. 39, 155–163(2003).
[CrossRef]

Friberg, A. T.

Z. Jaroszewicz, A. Burvall, and A. T. Friberg, “Axicon—the most important optical element,” Opt. Photon. News 16(4), 34–39 (2005).
[CrossRef]

Grimm, R.

I. Manek, Y. B. Ovchinnikov, and R. Grimm, “Generation of a hollow laser beam for atom trapping using an axicon,” Opt. Commun. 147, 67–70 (1998).
[CrossRef]

Hariharan, P.

Hayes, J.

Jaroszewicz, Z.

Z. Jaroszewicz, A. Burvall, and A. T. Friberg, “Axicon—the most important optical element,” Opt. Photon. News 16(4), 34–39 (2005).
[CrossRef]

Juuso, S.

T. Kololuoma, K. Kataja, S. Juuso, and J. Aikio, “Fabrication and characterization of hybrid-glass-based axicons,” Opt. Eng. 41, 3136–3140 (2002).
[CrossRef]

Kar, A.

D. Zeng, W. P. Latham, and A. Kar, “Shaping of annular laser intensity profiles and their thermal effects for spatial trepanning,” Opt. Eng. 45, 014301 (2006).
[CrossRef]

Kataja, K.

T. Kololuoma, K. Kataja, S. Juuso, and J. Aikio, “Fabrication and characterization of hybrid-glass-based axicons,” Opt. Eng. 41, 3136–3140 (2002).
[CrossRef]

Kim, G. H.

W. D. Kimura, G. H. Kim, R. D. Romea, L. C. Steinhauer, I. V. Pogorelsky, K. P. Kusche, R. C. Fernow, X. Wang, and Y. Lin, “Laser acceleration of relativistic electrons using the inverse Chernokov effect,” Phys. Rev. Lett. 74, 546–549(1995).
[CrossRef] [PubMed]

Kimura, W. D.

W. D. Kimura, G. H. Kim, R. D. Romea, L. C. Steinhauer, I. V. Pogorelsky, K. P. Kusche, R. C. Fernow, X. Wang, and Y. Lin, “Laser acceleration of relativistic electrons using the inverse Chernokov effect,” Phys. Rev. Lett. 74, 546–549(1995).
[CrossRef] [PubMed]

Kololuoma, T.

T. Kololuoma, K. Kataja, S. Juuso, and J. Aikio, “Fabrication and characterization of hybrid-glass-based axicons,” Opt. Eng. 41, 3136–3140 (2002).
[CrossRef]

Kumar, Y. P.

S. Chatterjee, Y. P. Kumar, and B. Bhaduri, “Measurement of surface figure of plane optical surfaces with polarization phase-shifting Fizeau interferometer,” Opt. Laser Tech. 39, 268–274 (2007).
[CrossRef]

Kupka, D.

Kusche, K. P.

W. D. Kimura, G. H. Kim, R. D. Romea, L. C. Steinhauer, I. V. Pogorelsky, K. P. Kusche, R. C. Fernow, X. Wang, and Y. Lin, “Laser acceleration of relativistic electrons using the inverse Chernokov effect,” Phys. Rev. Lett. 74, 546–549(1995).
[CrossRef] [PubMed]

Latham, W. P.

D. Zeng, W. P. Latham, and A. Kar, “Shaping of annular laser intensity profiles and their thermal effects for spatial trepanning,” Opt. Eng. 45, 014301 (2006).
[CrossRef]

Lin, Y.

W. D. Kimura, G. H. Kim, R. D. Romea, L. C. Steinhauer, I. V. Pogorelsky, K. P. Kusche, R. C. Fernow, X. Wang, and Y. Lin, “Laser acceleration of relativistic electrons using the inverse Chernokov effect,” Phys. Rev. Lett. 74, 546–549(1995).
[CrossRef] [PubMed]

Lin, Y. T.

M. D. Wei, W. L. Shiao, and Y. T. Lin, “Adjustable generation of bottle and hollow beams using an axicon,” Opt. Commun. 248, 7–14 (2005).
[CrossRef]

Loomis, J. S.

Malacara, D.

D. Malacara, S. Malacara, and Z. Malacara, in Interferogram Analysis for Optical Testing (Marcel Dekker, 1998), pp. 248–255.

Malacara, S.

D. Malacara, S. Malacara, and Z. Malacara, in Interferogram Analysis for Optical Testing (Marcel Dekker, 1998), pp. 248–255.

Malacara, Z.

D. Malacara, S. Malacara, and Z. Malacara, in Interferogram Analysis for Optical Testing (Marcel Dekker, 1998), pp. 248–255.

Manek, I.

I. Manek, Y. B. Ovchinnikov, and R. Grimm, “Generation of a hollow laser beam for atom trapping using an axicon,” Opt. Commun. 147, 67–70 (1998).
[CrossRef]

Mantravadi, M.

M. Strojnik, G. Paez, and M. Mantravadi, “Lateral shear interferometers,” in Optical Shop Testing, D.Malacara, ed. (Wiley, 2007), pp. 122–184.
[CrossRef]

McArdle, N.

G. Scott and N. McArdle, “Efficient generation of nearly diffraction free beams using axicon,” Opt. Eng. 31, 2640–2643(1992).
[CrossRef]

McCarthy, N.

McLeod, J. H.

Nelson, J. S.

Nicola, S. D.

M. de Angelis, S. D. Nicola, P. Ferraro, A. Finizio, and G. Pierattini, “Test of a conical lens using a two beam shearing interferometer,” Opt. Lasers Eng. 39, 155–163(2003).
[CrossRef]

Oreb, B. F.

Ovchinnikov, Y. B.

I. Manek, Y. B. Ovchinnikov, and R. Grimm, “Generation of a hollow laser beam for atom trapping using an axicon,” Opt. Commun. 147, 67–70 (1998).
[CrossRef]

Paez, G.

M. Strojnik, G. Paez, and M. Mantravadi, “Lateral shear interferometers,” in Optical Shop Testing, D.Malacara, ed. (Wiley, 2007), pp. 122–184.
[CrossRef]

Parks, R. E.

Piche, M.

Pierattini, G.

M. de Angelis, S. D. Nicola, P. Ferraro, A. Finizio, and G. Pierattini, “Test of a conical lens using a two beam shearing interferometer,” Opt. Lasers Eng. 39, 155–163(2003).
[CrossRef]

Pogorelsky, I. V.

W. D. Kimura, G. H. Kim, R. D. Romea, L. C. Steinhauer, I. V. Pogorelsky, K. P. Kusche, R. C. Fernow, X. Wang, and Y. Lin, “Laser acceleration of relativistic electrons using the inverse Chernokov effect,” Phys. Rev. Lett. 74, 546–549(1995).
[CrossRef] [PubMed]

Ren, H.

Romea, R. D.

W. D. Kimura, G. H. Kim, R. D. Romea, L. C. Steinhauer, I. V. Pogorelsky, K. P. Kusche, R. C. Fernow, X. Wang, and Y. Lin, “Laser acceleration of relativistic electrons using the inverse Chernokov effect,” Phys. Rev. Lett. 74, 546–549(1995).
[CrossRef] [PubMed]

Schafer, F. P.

F. P. Schafer, “On some properties of axicons,” Appl. Phys. B 39, 1–8 (1986).
[CrossRef]

Schlup, P.

Scott, G.

G. Scott and N. McArdle, “Efficient generation of nearly diffraction free beams using axicon,” Opt. Eng. 31, 2640–2643(1992).
[CrossRef]

Shiao, W. L.

M. D. Wei, W. L. Shiao, and Y. T. Lin, “Adjustable generation of bottle and hollow beams using an axicon,” Opt. Commun. 248, 7–14 (2005).
[CrossRef]

Steinhauer, L. C.

W. D. Kimura, G. H. Kim, R. D. Romea, L. C. Steinhauer, I. V. Pogorelsky, K. P. Kusche, R. C. Fernow, X. Wang, and Y. Lin, “Laser acceleration of relativistic electrons using the inverse Chernokov effect,” Phys. Rev. Lett. 74, 546–549(1995).
[CrossRef] [PubMed]

Strojnik, M.

M. Strojnik, G. Paez, and M. Mantravadi, “Lateral shear interferometers,” in Optical Shop Testing, D.Malacara, ed. (Wiley, 2007), pp. 122–184.
[CrossRef]

Underwood, K. L.

Wang, X.

W. D. Kimura, G. H. Kim, R. D. Romea, L. C. Steinhauer, I. V. Pogorelsky, K. P. Kusche, R. C. Fernow, X. Wang, and Y. Lin, “Laser acceleration of relativistic electrons using the inverse Chernokov effect,” Phys. Rev. Lett. 74, 546–549(1995).
[CrossRef] [PubMed]

Wei, M. D.

M. D. Wei, W. L. Shiao, and Y. T. Lin, “Adjustable generation of bottle and hollow beams using an axicon,” Opt. Commun. 248, 7–14 (2005).
[CrossRef]

Wyant, J. C.

Zeng, D.

D. Zeng, W. P. Latham, and A. Kar, “Shaping of annular laser intensity profiles and their thermal effects for spatial trepanning,” Opt. Eng. 45, 014301 (2006).
[CrossRef]

Zhao, Y.

Appl. Opt. (5)

Appl. Phys. B (1)

F. P. Schafer, “On some properties of axicons,” Appl. Phys. B 39, 1–8 (1986).
[CrossRef]

J. Opt. Soc. Am. (2)

Opt. Commun. (3)

M. D. Wei, W. L. Shiao, and Y. T. Lin, “Adjustable generation of bottle and hollow beams using an axicon,” Opt. Commun. 248, 7–14 (2005).
[CrossRef]

I. Manek, Y. B. Ovchinnikov, and R. Grimm, “Generation of a hollow laser beam for atom trapping using an axicon,” Opt. Commun. 147, 67–70 (1998).
[CrossRef]

J. Arlt and K. Dholakia, “Generation of higher order Bessel beams by use of an axicon,” Opt. Commun. 177, 297–301(2000).
[CrossRef]

Opt. Eng. (4)

D. Zeng, W. P. Latham, and A. Kar, “Shaping of annular laser intensity profiles and their thermal effects for spatial trepanning,” Opt. Eng. 45, 014301 (2006).
[CrossRef]

T. Kololuoma, K. Kataja, S. Juuso, and J. Aikio, “Fabrication and characterization of hybrid-glass-based axicons,” Opt. Eng. 41, 3136–3140 (2002).
[CrossRef]

G. Scott and N. McArdle, “Efficient generation of nearly diffraction free beams using axicon,” Opt. Eng. 31, 2640–2643(1992).
[CrossRef]

P. Hariharan, “Phase shifting interferometry: minimization of systematic errors,” Opt. Eng. 39, 967–969 (2000).
[CrossRef]

Opt. Laser Tech. (1)

S. Chatterjee, Y. P. Kumar, and B. Bhaduri, “Measurement of surface figure of plane optical surfaces with polarization phase-shifting Fizeau interferometer,” Opt. Laser Tech. 39, 268–274 (2007).
[CrossRef]

Opt. Lasers Eng. (1)

M. de Angelis, S. D. Nicola, P. Ferraro, A. Finizio, and G. Pierattini, “Test of a conical lens using a two beam shearing interferometer,” Opt. Lasers Eng. 39, 155–163(2003).
[CrossRef]

Opt. Lett. (1)

Opt. Photon. News (1)

Z. Jaroszewicz, A. Burvall, and A. T. Friberg, “Axicon—the most important optical element,” Opt. Photon. News 16(4), 34–39 (2005).
[CrossRef]

Phys. Rev. Lett. (1)

W. D. Kimura, G. H. Kim, R. D. Romea, L. C. Steinhauer, I. V. Pogorelsky, K. P. Kusche, R. C. Fernow, X. Wang, and Y. Lin, “Laser acceleration of relativistic electrons using the inverse Chernokov effect,” Phys. Rev. Lett. 74, 546–549(1995).
[CrossRef] [PubMed]

Other (3)

M. Strojnik, G. Paez, and M. Mantravadi, “Lateral shear interferometers,” in Optical Shop Testing, D.Malacara, ed. (Wiley, 2007), pp. 122–184.
[CrossRef]

K. Creath, “Phase measurement interferometry techniques,” in Progress in Optics, Vol.  xxviii, E.Wolf, ed. (North-Holland, 1988), pp. 349–393.
[CrossRef]

D. Malacara, S. Malacara, and Z. Malacara, in Interferogram Analysis for Optical Testing (Marcel Dekker, 1998), pp. 248–255.

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Figures (12)

Fig. 1
Fig. 1

Optical schematic of the TGI-based optical setup for the measurement of surface slopes/profile of the AX lens.

Fig. 2
Fig. 2

Generation of linear shear in the radial directions between the overlapping conical beams due to the longitudinal separation between the virtual images AX1 and AX2 of AX in M1 and M2 [Fig. 1], respectively.

Fig. 3
Fig. 3

Geometric construction for the computation of Δ s .

Fig. 4
Fig. 4

Interferogram captured with Δ s = 1.0 mm .

Fig. 5
Fig. 5

Variation of the OPD between two closely separated (Δrd) points along a radial direction [ A 1 B 2 ] (Fig. 2) denoted by x d .

Fig. 6
Fig. 6

Variation of the OPD between two closely separated (Δrd) points along a radial direction [ D 1 C 2 ] (Fig. 2) denoted by x d .

Fig. 7
Fig. 7

Variation of OPD shown in Fig. 4 after tilt subtraction.

Fig. 8
Fig. 8

Variation of OPD shown in Fig. 5 after tilt subtraction.

Fig. 9
Fig. 9

Slope variation along the section [A2B2/A1B1] of the AX in the plane of the figure (Fig. 2).

Fig. 10
Fig. 10

Slope variation along the section [C2D2/C1D1] of the AX in the plane of the figure (Fig. 2).

Fig. 11
Fig. 11

Height variation along the section [A2B2/A1B1] of the AX in the plane of the figure (Fig. 2).

Fig. 12
Fig. 12

Height variation along the section [C2D2/C1D1] of the AX in the plane of the figure (Fig. 2).

Equations (7)

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

Δ W r = W ( r ) W ( r Δ r ) ,
I ( x , y ) = I 0 ( x , y ) { 1 + V ( x , y ) cos [ ϕ ( x , y ) + α j ] } ,
ϕ = arc tan [ 2 ( I 4 I 2 ) / ( I 1 + I 5 2 I 3 ) ] .
Δ ϕ = ( ε 2 / 4 ) sin 2 ϕ ,
δ = ( λ / 2 π ) ϕ ,
Δ W S = [ Δ W r cos α / ( n 1 ) ] .
Δ W S = [ Δ W d cos θ cos α / ( n 1 ) ] .

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