Abstract

We propose a method for an estimation of wavelength difference using scale adjustment in two- wavelength digital holographic interferometry. To estimate wavelength difference, two holograms recorded with different wavelengths are reconstructed on the basis of the Fresnel diffraction integral, and pixel sizes in the reconstruction plane, which depend on the wavelength in recording hologram, are analyzed. In the analysis, a zero-padding method and an intensity correlation function are used to adjust pixel sizes in the reconstruction plane and then obtain a wavelength difference given by a difference between the pixel sizes. Theoretical predictions and experimental results are shown to indicate the usefulness of the proposed method in this paper.

© 2011 Optical Society of America

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2011 (1)

T. Kakue, M. Kuwamura, Y. Shimozato, T. Tahara, Y. Awatsuji, K. Nishio, S. Ura, T. Kubota, and O. Matoba, “Optical-path-length-shifting color digital holography,” Opt. Rev. 18, 180–183 (2011).
[CrossRef]

2010 (3)

2009 (5)

2008 (6)

2007 (5)

2006 (5)

2005 (2)

2004 (2)

2003 (2)

2002 (2)

2000 (2)

C. Wagner, W. Osten, and S. Seebacher, “Direct shape measurement by digital wavefront reconstruction and multiwavelength contouring,” Opt. Eng. 39, 79–85 (2000).
[CrossRef]

G. Pedrini, H. J. Tiziani, and M. E. Gusev, “Pulsed digital holographic interferometry with 694- and 347 nm wavelengths,” Appl. Opt. 39, 246–249 (2000).
[CrossRef]

1999 (3)

1997 (1)

T. M. Kreis and W. P. O. Jüptner, “Suppression of the dc term in digital holography,” Opt. Eng. 36, 2357–2360 (1997).
[CrossRef]

Alfieri, D.

P. Ferraro, S. Grilli, L. Miccio, D. Alfieri, S. De Nicola, A. Finizio, and B. Javidi, “Full color 3-D imaging by digital holography and removal of chromatic aberrations,” J. Disp. Technol. 4, 97–100 (2008).
[CrossRef]

S. Yeom, B. Javidi, P. Ferraro, D. Alfieri, S. De Nicola, and A. Finizio, “Three-dimensional color object visualization and recognition using multi-wavelength computational holography,” Opt. Express 15, 9394–9402 (2007).
[CrossRef] [PubMed]

D. Alfieri, G. Coppola, S. De Nicola, P. Ferraro, A. Finizio, G. Pierattini, and B. Javidi, “Method for superposing reconstructed images from digital holograms of the same object recorded at different distance and wavelength,” Opt. Commun. 260, 113–116 (2006).
[CrossRef]

B. Javidi, P. Ferraro, S. H. Hong, S. De Nicola, A. Finizio, D. Alfieri, and G. Pierattini, “Three-dimensional image fusion by use of multiwavelength digital holography,” Opt. Lett. 30, 144–146 (2005).
[CrossRef] [PubMed]

S. De Nicola, A. Finizio, G. Pierattini, D. Alfieri, S. Grilli, L. Sansone, and P. Ferraro, “Recovering correct phase information in multiwavelength digital holographic microscopy by compensation for chromatic aberrations,” Opt. Lett. 30, 2706–2708 (2005).
[CrossRef] [PubMed]

P. Ferraro, S. De Nicola, G. Coppola, A. Finizio, D. Alfieri, and G. Pierattini, “Controlling image size as a function of distance and wavelength in Fresnel-transform reconstruction of digital holograms,” Opt. Lett. 29, 854–856 (2004).
[CrossRef] [PubMed]

Anand, A.

Awatsuji, Y.

T. Kakue, M. Kuwamura, Y. Shimozato, T. Tahara, Y. Awatsuji, K. Nishio, S. Ura, T. Kubota, and O. Matoba, “Optical-path-length-shifting color digital holography,” Opt. Rev. 18, 180–183 (2011).
[CrossRef]

T. Kakue, T. Tahara, K. Ito, Y. Shimozato, Y. Awatsuji, K. Nishio, S. Ura, T. Kubota, and O. Matoba, “Parallel phase-shifting color digital holography using two phase shifts,” Appl. Opt. 48, H244–H250 (2009).
[CrossRef] [PubMed]

Baumbach, T.

Bingham, P. R.

Carl, D.

Charrière, F.

Colomb, T.

Coppola, G.

D. Alfieri, G. Coppola, S. De Nicola, P. Ferraro, A. Finizio, G. Pierattini, and B. Javidi, “Method for superposing reconstructed images from digital holograms of the same object recorded at different distance and wavelength,” Opt. Commun. 260, 113–116 (2006).
[CrossRef]

P. Ferraro, S. De Nicola, G. Coppola, A. Finizio, D. Alfieri, and G. Pierattini, “Controlling image size as a function of distance and wavelength in Fresnel-transform reconstruction of digital holograms,” Opt. Lett. 29, 854–856 (2004).
[CrossRef] [PubMed]

Cuche, E.

Dakoff, A.

De Nicola, S.

P. Ferraro, S. Grilli, L. Miccio, D. Alfieri, S. De Nicola, A. Finizio, and B. Javidi, “Full color 3-D imaging by digital holography and removal of chromatic aberrations,” J. Disp. Technol. 4, 97–100 (2008).
[CrossRef]

S. Yeom, B. Javidi, P. Ferraro, D. Alfieri, S. De Nicola, and A. Finizio, “Three-dimensional color object visualization and recognition using multi-wavelength computational holography,” Opt. Express 15, 9394–9402 (2007).
[CrossRef] [PubMed]

P. Ferraro, L. Miccio, S. Grilli, M. Paturzo, S. De Nicola, A. Finizio, R. Osellame, and P. Laporta, “Quantitative phase microscopy of microstructures with extended measurement range and correction of chromatic aberrations by multiwavelength digital holography,” Opt. Express 15, 14591–14600(2007).
[CrossRef] [PubMed]

D. Alfieri, G. Coppola, S. De Nicola, P. Ferraro, A. Finizio, G. Pierattini, and B. Javidi, “Method for superposing reconstructed images from digital holograms of the same object recorded at different distance and wavelength,” Opt. Commun. 260, 113–116 (2006).
[CrossRef]

B. Javidi, P. Ferraro, S. H. Hong, S. De Nicola, A. Finizio, D. Alfieri, and G. Pierattini, “Three-dimensional image fusion by use of multiwavelength digital holography,” Opt. Lett. 30, 144–146 (2005).
[CrossRef] [PubMed]

S. De Nicola, A. Finizio, G. Pierattini, D. Alfieri, S. Grilli, L. Sansone, and P. Ferraro, “Recovering correct phase information in multiwavelength digital holographic microscopy by compensation for chromatic aberrations,” Opt. Lett. 30, 2706–2708 (2005).
[CrossRef] [PubMed]

P. Ferraro, S. De Nicola, G. Coppola, A. Finizio, D. Alfieri, and G. Pierattini, “Controlling image size as a function of distance and wavelength in Fresnel-transform reconstruction of digital holograms,” Opt. Lett. 29, 854–856 (2004).
[CrossRef] [PubMed]

Demoli, N.

Depeursinge, C.

Desse, J. M.

Di, J.

Dubey, S.

Emery, Y.

Ferraro, P.

P. Ferraro, S. Grilli, L. Miccio, D. Alfieri, S. De Nicola, A. Finizio, and B. Javidi, “Full color 3-D imaging by digital holography and removal of chromatic aberrations,” J. Disp. Technol. 4, 97–100 (2008).
[CrossRef]

S. Yeom, B. Javidi, P. Ferraro, D. Alfieri, S. De Nicola, and A. Finizio, “Three-dimensional color object visualization and recognition using multi-wavelength computational holography,” Opt. Express 15, 9394–9402 (2007).
[CrossRef] [PubMed]

P. Ferraro, L. Miccio, S. Grilli, M. Paturzo, S. De Nicola, A. Finizio, R. Osellame, and P. Laporta, “Quantitative phase microscopy of microstructures with extended measurement range and correction of chromatic aberrations by multiwavelength digital holography,” Opt. Express 15, 14591–14600(2007).
[CrossRef] [PubMed]

D. Alfieri, G. Coppola, S. De Nicola, P. Ferraro, A. Finizio, G. Pierattini, and B. Javidi, “Method for superposing reconstructed images from digital holograms of the same object recorded at different distance and wavelength,” Opt. Commun. 260, 113–116 (2006).
[CrossRef]

B. Javidi, P. Ferraro, S. H. Hong, S. De Nicola, A. Finizio, D. Alfieri, and G. Pierattini, “Three-dimensional image fusion by use of multiwavelength digital holography,” Opt. Lett. 30, 144–146 (2005).
[CrossRef] [PubMed]

S. De Nicola, A. Finizio, G. Pierattini, D. Alfieri, S. Grilli, L. Sansone, and P. Ferraro, “Recovering correct phase information in multiwavelength digital holographic microscopy by compensation for chromatic aberrations,” Opt. Lett. 30, 2706–2708 (2005).
[CrossRef] [PubMed]

P. Ferraro, S. De Nicola, G. Coppola, A. Finizio, D. Alfieri, and G. Pierattini, “Controlling image size as a function of distance and wavelength in Fresnel-transform reconstruction of digital holograms,” Opt. Lett. 29, 854–856 (2004).
[CrossRef] [PubMed]

Finizio, A.

P. Ferraro, S. Grilli, L. Miccio, D. Alfieri, S. De Nicola, A. Finizio, and B. Javidi, “Full color 3-D imaging by digital holography and removal of chromatic aberrations,” J. Disp. Technol. 4, 97–100 (2008).
[CrossRef]

S. Yeom, B. Javidi, P. Ferraro, D. Alfieri, S. De Nicola, and A. Finizio, “Three-dimensional color object visualization and recognition using multi-wavelength computational holography,” Opt. Express 15, 9394–9402 (2007).
[CrossRef] [PubMed]

P. Ferraro, L. Miccio, S. Grilli, M. Paturzo, S. De Nicola, A. Finizio, R. Osellame, and P. Laporta, “Quantitative phase microscopy of microstructures with extended measurement range and correction of chromatic aberrations by multiwavelength digital holography,” Opt. Express 15, 14591–14600(2007).
[CrossRef] [PubMed]

D. Alfieri, G. Coppola, S. De Nicola, P. Ferraro, A. Finizio, G. Pierattini, and B. Javidi, “Method for superposing reconstructed images from digital holograms of the same object recorded at different distance and wavelength,” Opt. Commun. 260, 113–116 (2006).
[CrossRef]

B. Javidi, P. Ferraro, S. H. Hong, S. De Nicola, A. Finizio, D. Alfieri, and G. Pierattini, “Three-dimensional image fusion by use of multiwavelength digital holography,” Opt. Lett. 30, 144–146 (2005).
[CrossRef] [PubMed]

S. De Nicola, A. Finizio, G. Pierattini, D. Alfieri, S. Grilli, L. Sansone, and P. Ferraro, “Recovering correct phase information in multiwavelength digital holographic microscopy by compensation for chromatic aberrations,” Opt. Lett. 30, 2706–2708 (2005).
[CrossRef] [PubMed]

P. Ferraro, S. De Nicola, G. Coppola, A. Finizio, D. Alfieri, and G. Pierattini, “Controlling image size as a function of distance and wavelength in Fresnel-transform reconstruction of digital holograms,” Opt. Lett. 29, 854–856 (2004).
[CrossRef] [PubMed]

Fratz, M.

Gass, J.

Giel, D. M.

Grilli, S.

Gusev, M. E.

Hayasaki, Y.

S. Tamano, M. Otaka, and Y. Hayasaki, “Two-wavelength phase-shifting low-coherence digital holography,” Jpn. J. Appl. Phys. Part 1 47, 8844–8847 (2008).
[CrossRef]

Höfler, H.

Hong, S. H.

Ida, T.

Ishii, Y.

Ishitobi, N.

M. Yokota and N. Ishitobi, “Estimation of inner surface profile of a tube by two-wavelength phase-shifting digital holography,” Opt. Rev. 17, 166–170 (2010).
[CrossRef]

Ito, K.

Javidi, B.

P. Ferraro, S. Grilli, L. Miccio, D. Alfieri, S. De Nicola, A. Finizio, and B. Javidi, “Full color 3-D imaging by digital holography and removal of chromatic aberrations,” J. Disp. Technol. 4, 97–100 (2008).
[CrossRef]

S. Yeom, B. Javidi, P. Ferraro, D. Alfieri, S. De Nicola, and A. Finizio, “Three-dimensional color object visualization and recognition using multi-wavelength computational holography,” Opt. Express 15, 9394–9402 (2007).
[CrossRef] [PubMed]

D. Alfieri, G. Coppola, S. De Nicola, P. Ferraro, A. Finizio, G. Pierattini, and B. Javidi, “Method for superposing reconstructed images from digital holograms of the same object recorded at different distance and wavelength,” Opt. Commun. 260, 113–116 (2006).
[CrossRef]

B. Javidi, P. Ferraro, S. H. Hong, S. De Nicola, A. Finizio, D. Alfieri, and G. Pierattini, “Three-dimensional image fusion by use of multiwavelength digital holography,” Opt. Lett. 30, 144–146 (2005).
[CrossRef] [PubMed]

Jiang, H.

Jüptner, W.

Jüptner, W. P. O.

T. M. Kreis and W. P. O. Jüptner, “Suppression of the dc term in digital holography,” Opt. Eng. 36, 2357–2360 (1997).
[CrossRef]

Kakue, T.

T. Kakue, M. Kuwamura, Y. Shimozato, T. Tahara, Y. Awatsuji, K. Nishio, S. Ura, T. Kubota, and O. Matoba, “Optical-path-length-shifting color digital holography,” Opt. Rev. 18, 180–183 (2011).
[CrossRef]

T. Kakue, T. Tahara, K. Ito, Y. Shimozato, Y. Awatsuji, K. Nishio, S. Ura, T. Kubota, and O. Matoba, “Parallel phase-shifting color digital holography using two phase shifts,” Appl. Opt. 48, H244–H250 (2009).
[CrossRef] [PubMed]

Karray, M.

Kato, J.

Kato, M.

Kebbel, V.

Kim, M. K.

Kolenovic, E.

Kreis, T.

Kreis, T. M.

T. M. Kreis and W. P. O. Jüptner, “Suppression of the dc term in digital holography,” Opt. Eng. 36, 2357–2360 (1997).
[CrossRef]

Kubota, T.

T. Kakue, M. Kuwamura, Y. Shimozato, T. Tahara, Y. Awatsuji, K. Nishio, S. Ura, T. Kubota, and O. Matoba, “Optical-path-length-shifting color digital holography,” Opt. Rev. 18, 180–183 (2011).
[CrossRef]

T. Kakue, T. Tahara, K. Ito, Y. Shimozato, Y. Awatsuji, K. Nishio, S. Ura, T. Kubota, and O. Matoba, “Parallel phase-shifting color digital holography using two phase shifts,” Appl. Opt. 48, H244–H250 (2009).
[CrossRef] [PubMed]

Kühn, J.

Kuwamura, M.

T. Kakue, M. Kuwamura, Y. Shimozato, T. Tahara, Y. Awatsuji, K. Nishio, S. Ura, T. Kubota, and O. Matoba, “Optical-path-length-shifting color digital holography,” Opt. Rev. 18, 180–183 (2011).
[CrossRef]

Laporta, P.

Li, D.

Li, J.

Mann, C. J.

Marquet, P.

Matoba, O.

T. Kakue, M. Kuwamura, Y. Shimozato, T. Tahara, Y. Awatsuji, K. Nishio, S. Ura, T. Kubota, and O. Matoba, “Optical-path-length-shifting color digital holography,” Opt. Rev. 18, 180–183 (2011).
[CrossRef]

T. Kakue, T. Tahara, K. Ito, Y. Shimozato, Y. Awatsuji, K. Nishio, S. Ura, T. Kubota, and O. Matoba, “Parallel phase-shifting color digital holography using two phase shifts,” Appl. Opt. 48, H244–H250 (2009).
[CrossRef] [PubMed]

Matsumura, T.

Mehta, D. S.

Miccio, L.

Montfort, F.

Muffoletto, R. P.

Nishio, K.

T. Kakue, M. Kuwamura, Y. Shimozato, T. Tahara, Y. Awatsuji, K. Nishio, S. Ura, T. Kubota, and O. Matoba, “Optical-path-length-shifting color digital holography,” Opt. Rev. 18, 180–183 (2011).
[CrossRef]

T. Kakue, T. Tahara, K. Ito, Y. Shimozato, Y. Awatsuji, K. Nishio, S. Ura, T. Kubota, and O. Matoba, “Parallel phase-shifting color digital holography using two phase shifts,” Appl. Opt. 48, H244–H250 (2009).
[CrossRef] [PubMed]

Osellame, R.

Osten, W.

C. Wagner, W. Osten, and S. Seebacher, “Direct shape measurement by digital wavefront reconstruction and multiwavelength contouring,” Opt. Eng. 39, 79–85 (2000).
[CrossRef]

C. Wagner, S. Seebacher, W. Osten, and W. Jüptner, “Digital recording and numerical reconstruction of lensless Fourier holograms in optical metrology,” Appl. Opt. 38, 4812–4820(1999).
[CrossRef]

Otaka, M.

S. Tamano, M. Otaka, and Y. Hayasaki, “Two-wavelength phase-shifting low-coherence digital holography,” Jpn. J. Appl. Phys. Part 1 47, 8844–8847 (2008).
[CrossRef]

Paquit, V. C.

Parshall, D.

Paturzo, M.

Pedrini, G.

Pfeifer, M.

Picart, P.

Pierattini, G.

Potcoava, M. C.

Ryle, J. P.

Sansone, L.

Seebacher, S.

C. Wagner, W. Osten, and S. Seebacher, “Direct shape measurement by digital wavefront reconstruction and multiwavelength contouring,” Opt. Eng. 39, 79–85 (2000).
[CrossRef]

C. Wagner, S. Seebacher, W. Osten, and W. Jüptner, “Digital recording and numerical reconstruction of lensless Fourier holograms in optical metrology,” Appl. Opt. 38, 4812–4820(1999).
[CrossRef]

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Yeom, S.

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[CrossRef] [PubMed]

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Appl. Opt. (11)

T. Kakue, T. Tahara, K. Ito, Y. Shimozato, Y. Awatsuji, K. Nishio, S. Ura, T. Kubota, and O. Matoba, “Parallel phase-shifting color digital holography using two phase shifts,” Appl. Opt. 48, H244–H250 (2009).
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J. Disp. Technol. (1)

P. Ferraro, S. Grilli, L. Miccio, D. Alfieri, S. De Nicola, A. Finizio, and B. Javidi, “Full color 3-D imaging by digital holography and removal of chromatic aberrations,” J. Disp. Technol. 4, 97–100 (2008).
[CrossRef]

J. Opt. Soc. Am. A (1)

Jpn. J. Appl. Phys. Part 1 (1)

S. Tamano, M. Otaka, and Y. Hayasaki, “Two-wavelength phase-shifting low-coherence digital holography,” Jpn. J. Appl. Phys. Part 1 47, 8844–8847 (2008).
[CrossRef]

Opt. Commun. (1)

D. Alfieri, G. Coppola, S. De Nicola, P. Ferraro, A. Finizio, G. Pierattini, and B. Javidi, “Method for superposing reconstructed images from digital holograms of the same object recorded at different distance and wavelength,” Opt. Commun. 260, 113–116 (2006).
[CrossRef]

Opt. Eng. (3)

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[CrossRef]

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[CrossRef]

I. Yamaguchi and M. Yokota, “Speckle noise suppression in measurement by phase-shifting digital holography,” Opt. Eng. 48, 085602 (2009).
[CrossRef]

Opt. Express (7)

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P. Ferraro, L. Miccio, S. Grilli, M. Paturzo, S. De Nicola, A. Finizio, R. Osellame, and P. Laporta, “Quantitative phase microscopy of microstructures with extended measurement range and correction of chromatic aberrations by multiwavelength digital holography,” Opt. Express 15, 14591–14600(2007).
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J. Zhao, H. Jiang, and J. Di, “Recording and reconstruction of a color holographic image by using digital lensless Fourier transform holography,” Opt. Express 16, 2514–2519 (2008).
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Opt. Lett. (12)

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S. De Nicola, A. Finizio, G. Pierattini, D. Alfieri, S. Grilli, L. Sansone, and P. Ferraro, “Recovering correct phase information in multiwavelength digital holographic microscopy by compensation for chromatic aberrations,” Opt. Lett. 30, 2706–2708 (2005).
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Opt. Rev. (2)

M. Yokota and N. Ishitobi, “Estimation of inner surface profile of a tube by two-wavelength phase-shifting digital holography,” Opt. Rev. 17, 166–170 (2010).
[CrossRef]

T. Kakue, M. Kuwamura, Y. Shimozato, T. Tahara, Y. Awatsuji, K. Nishio, S. Ura, T. Kubota, and O. Matoba, “Optical-path-length-shifting color digital holography,” Opt. Rev. 18, 180–183 (2011).
[CrossRef]

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Figures (9)

Fig. 1
Fig. 1

Optical geometry for recording a lensless Fourier transform hologram.

Fig. 2
Fig. 2

Experimental setup for recording holograms. LD: laser diode. OB: objective lens. PH: pinhole. L: lens. HM: half mirror. BS: beam splitter.

Fig. 3
Fig. 3

Test object.

Fig. 4
Fig. 4

Reconstructed image of a hologram with λ 1 = 659.626 nm .

Fig. 5
Fig. 5

Phase difference maps of reconstructed images for n = (a) 0, (b) 1, (c) 2, (d) 3, (e) 4 and (f) 5 in Δ λ = 2.002 nm , respectively. The resolution of wavelength difference is δ λ = 0.644 nm .

Fig. 6
Fig. 6

Intensity correlation function of reconstructed images in each wavelength difference. The symbols and dotted lines show the results of the zero-padding method with and without the cubic spline interpolation, respectively.

Fig. 7
Fig. 7

Comparison of wavelength differences obtained from the spectrometer and the proposed method.

Fig. 8
Fig. 8

Comparison of n value in the theoretical result and the estimated one without the interpolation. The theoretical results are given by substituting a wavelength measured by spectrometer into Eq. (25).

Fig. 9
Fig. 9

Relative errors of synthetic wavelength with and without the cubic spline interpolation.

Equations (25)

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

U ( x h ) = u ( x o ) exp [ j π λ z ( x h x o ) 2 ] d x o ,
U r ( x h ) = exp ( j π λ d x h 2 ) ,
U o ( x h ) = u o ( x o ) exp [ j π λ d ( x h x o ) 2 ] d x o ,
U o ( x h ) = exp ( j π λ d x h 2 ) u o ( x o ) exp ( j π λ d x o 2 ) exp ( j 2 π λ d x h x o ) d x o , = exp ( j π λ d x h 2 ) F λ d [ u o ( x o ) exp ( j π λ d x o 2 ) ] ,
I H ( x h ) = | U r ( x h ) + U o ( x h ) | 2 , = 1 + | U o ( x h ) | 2 + U o ( x h ) + U o * ( x h ) ,
U o ( x h ) = F λ d [ u o ( x o ) exp ( j π λ d x o 2 ) ] .
u rec ( x ) = F λ d 1 [ I H ( x h ) ] , = I H ( x h ) exp ( j 2 π λ d x h x ) d x h ,
= δ ( x ) + u o ( x ) u o * ( x ) + u o ( x ) + u o * ( x ) ,
u rec ( q Δ ξ ) = p = N / 2 N / 2 1 I H ( p Δ ξ ) exp ( j 2 π λ d q Δ ξ p Δ ξ ) ,
u rec ( q Δ ξ ) = p = N / 2 N / 2 1 I H ( p Δ ξ ) exp ( j 2 π p q N ) ,
Δ ξ = λ d N Δ ξ
V = λ d Δ ξ .
Δ ϕ ( x ) = ϕ 2 ( x ) ϕ 1 ( x ) ,
h ( x ) = Δ ϕ ( x ) 4 π Λ .
Λ = λ 1 λ 2 λ 2 λ 1 λ ¯ 2 Δ λ ,
λ ¯ = λ 1 + λ 2 2 ,
Δ λ = λ 2 λ 1 .
Δ ξ 1 = λ 1 d N Δ ξ , Δ ξ 2 = λ 2 d N Δ ξ .
Δ ξ 2 = λ 2 d ( N + n ) Δ ξ .
N + n = λ 2 λ 1 N .
Δ λ e = n δ λ ,
δ λ = λ 1 N .
λ 2 = λ 1 + Δ λ e ,
C I ( n ) = 1 σ 1 σ 2 N r / 2 1 q = N r / 2 [ I 1 ( q ) I 1 ] [ I 2 ( q ; n ) I 2 ] ,
Δ λ e = NINT ( Δ λ δ λ ) δ λ ,

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