Abstract

A hologram is a recording of the interference between an unknown object wave and a coherent reference wave. Providing the object and reference waves are sufficiently separated in some region of space and the reference beam is known, a high-fidelity reconstruction of the object wave is possible. In traditional optical holography, high-quality reconstruction is achieved by careful reillumination of the holographic plate with the exact same reference wave that was used at the recording stage. To reconstruct high-quality digital holograms the exact parameters of the reference wave must be known mathematically. This paper discusses a technique that obtains the mathematical parameters that characterize a strongly divergent reference wave that originates from a fiber source in a new compact digital holographic camera. This is a lensless design that is similar in principle to a Fourier hologram, but because of the large numerical aperture, the usual paraxial approximations cannot be applied and the Fourier relationship is inexact. To characterize the reference wave, recordings of quasi-planar object waves are made at various angles of incidence using a Dammann grating. An optimization process is then used to find the reference wave that reconstructs a stigmatic image of the object wave regardless of the angle of incidence.

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References

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  1. M. K. Kim, “Applications of digital holography in biomedical microscopy,” J. Opt. Soc. Korea 14, 77–89 (2010).
    [Crossref]
  2. F. Zhang, J. D. R. Valera, I. Yamaguchi, M. Yokota, and G. Mills, “Vibration analysis by phase shifting digital holography,” Opt. Rev. 11, 297–299 (2004).
    [Crossref]
  3. S. Seebacher, W. Osten, and W. P. O. Jueptner, “Measuring shape and deformation of small objects using digital holography,” Proc. SPIE 3479, 104–115 (1998).
    [Crossref]
  4. X. Sang, “Applications of digital holography to measurements and optical characterization,” Opt. Eng. 50, 91311 (2011).
    [Crossref]
  5. T. H. Jeong, “Basic principles and applications of holography BT—fundamentals of photonics,” in Fundamentals of Photonics (2008), p. 381–417.
  6. J. W. Goodman and R. W. Lawrence, “Digital image formation from electronically detected holograms,” Appl. Phys. Lett. 11, 77–79 (1967).
    [Crossref]
  7. J. W. Goodman, Introduction to Fourier Optics, 2nd ed. (1996), Vol. 35.
  8. R. Jozwicki and S. Pasko, “Influence of reference beam aberrations in digital holography on the image quality,” in Optical Measurement Systems for Industrial Inspection III (SPIE, 2003), Vol. 5144, pp. 132–137.
  9. J. Hahn, D. L. Marks, K. Choi, S. Lim, and D. J. Brady, “Thin holographic camera with integrated reference distribution,” Appl. Opt. 50, 4848–4854 (2011).
    [Crossref]
  10. D. Malacara, Optical Shop Testing, Wiley Series in Pure and Applied Optics (Wiley, 2007).
  11. E. Cuche, P. Marquet, and C. Depeursinge, “Simultaneous amplitude-contrast and quantitative phase-contrast microscopy by numerical reconstruction of Fresnel off-axis holograms,” Appl. Opt. 38, 6994–7001 (1999).
    [Crossref]
  12. T. R. Hillman, T. Gutzler, S. A. Alexandrov, and D. D. Sampson, “High-resolution, wide-field object reconstruction with synthetic aperture Fourier holographic optical microscopy,” Opt. Express 17, 7873–7892 (2009).
    [Crossref]
  13. P. Qiu, Z. Mei, and T. Pang, “Extracting the parameters of digital reference wave from a single off-axis digital hologram,” J. Mod. Opt. 62, 816–821 (2016).
    [Crossref]
  14. R. Riesenberg and M. Kanka, “Self-calibrating lensless inline-holographic microscopy by a sample holder with reference structures,” Opt. Lett. 39, 5236–5239 (2014).
    [Crossref]
  15. Sony, “IMX219PQ,” http://www.sony-semicon.co.jp/products_en/new_pro/april_2014/imx219_e.html .
  16. H. Melkonyan, K. Al Qubaisi, A. Khilo, and M. Dahlem, “Optical fibre lens with parabolic effective index profile fabricated using focused ion beam,” in CLEO: Science and Innovations (SM1P—3) (2016).
  17. J. Huang, A. Alqahtani, J. Viegas, and M. S. Dahlem, “Fabrication of optical fibre gratings through focused ion beam techniques for sensing applications,” in Photonics Global Conference (PGC) (2012), Vol. 3, pp. 1–4.
  18. C. Obermüller and K. Karrai, “Far field characterization of diffracting circular apertures,” Appl. Phys. Lett. 67, 3408–3410 (1995).
    [Crossref]
  19. E. N. Leith and J. Upatnieks, “Reconstructed wavefronts and communication theory,” J. Opt. Soc. Am. 52, 1123 (1962).
    [Crossref]
  20. T. Fricke-Begemann and J. Burke, “Speckle interferometry: three-dimensional deformation field measurement with a single interferogram,” Appl. Opt. 40, 5011–5022 (2001).
    [Crossref]
  21. V. N. Mahajan and G. Dai, “Orthonormal polynomials in wavefront analysis: analytical solution,” J. Opt. Soc. Am. A 24, 2994–3016 (2007).
    [Crossref]
  22. J. Jahns, M. M. Downs, M. E. Prise, N. Streibl, and S. J. Walker, “Dammann gratings for laser beam shaping,” Opt. Eng. 28, 1267–1275 (1989).
    [Crossref]
  23. MathWorks, “fminsearch,” https://uk.mathworks.com/help/matlab/ref/fminsearch.html .

2016 (1)

P. Qiu, Z. Mei, and T. Pang, “Extracting the parameters of digital reference wave from a single off-axis digital hologram,” J. Mod. Opt. 62, 816–821 (2016).
[Crossref]

2014 (1)

2011 (2)

J. Hahn, D. L. Marks, K. Choi, S. Lim, and D. J. Brady, “Thin holographic camera with integrated reference distribution,” Appl. Opt. 50, 4848–4854 (2011).
[Crossref]

X. Sang, “Applications of digital holography to measurements and optical characterization,” Opt. Eng. 50, 91311 (2011).
[Crossref]

2010 (1)

2009 (1)

2007 (1)

2004 (1)

F. Zhang, J. D. R. Valera, I. Yamaguchi, M. Yokota, and G. Mills, “Vibration analysis by phase shifting digital holography,” Opt. Rev. 11, 297–299 (2004).
[Crossref]

2001 (1)

1999 (1)

1998 (1)

S. Seebacher, W. Osten, and W. P. O. Jueptner, “Measuring shape and deformation of small objects using digital holography,” Proc. SPIE 3479, 104–115 (1998).
[Crossref]

1995 (1)

C. Obermüller and K. Karrai, “Far field characterization of diffracting circular apertures,” Appl. Phys. Lett. 67, 3408–3410 (1995).
[Crossref]

1989 (1)

J. Jahns, M. M. Downs, M. E. Prise, N. Streibl, and S. J. Walker, “Dammann gratings for laser beam shaping,” Opt. Eng. 28, 1267–1275 (1989).
[Crossref]

1967 (1)

J. W. Goodman and R. W. Lawrence, “Digital image formation from electronically detected holograms,” Appl. Phys. Lett. 11, 77–79 (1967).
[Crossref]

1962 (1)

Al Qubaisi, K.

H. Melkonyan, K. Al Qubaisi, A. Khilo, and M. Dahlem, “Optical fibre lens with parabolic effective index profile fabricated using focused ion beam,” in CLEO: Science and Innovations (SM1P—3) (2016).

Alexandrov, S. A.

Alqahtani, A.

J. Huang, A. Alqahtani, J. Viegas, and M. S. Dahlem, “Fabrication of optical fibre gratings through focused ion beam techniques for sensing applications,” in Photonics Global Conference (PGC) (2012), Vol. 3, pp. 1–4.

Brady, D. J.

Burke, J.

Choi, K.

Cuche, E.

Dahlem, M.

H. Melkonyan, K. Al Qubaisi, A. Khilo, and M. Dahlem, “Optical fibre lens with parabolic effective index profile fabricated using focused ion beam,” in CLEO: Science and Innovations (SM1P—3) (2016).

Dahlem, M. S.

J. Huang, A. Alqahtani, J. Viegas, and M. S. Dahlem, “Fabrication of optical fibre gratings through focused ion beam techniques for sensing applications,” in Photonics Global Conference (PGC) (2012), Vol. 3, pp. 1–4.

Dai, G.

Depeursinge, C.

Downs, M. M.

J. Jahns, M. M. Downs, M. E. Prise, N. Streibl, and S. J. Walker, “Dammann gratings for laser beam shaping,” Opt. Eng. 28, 1267–1275 (1989).
[Crossref]

Fricke-Begemann, T.

Goodman, J. W.

J. W. Goodman and R. W. Lawrence, “Digital image formation from electronically detected holograms,” Appl. Phys. Lett. 11, 77–79 (1967).
[Crossref]

J. W. Goodman, Introduction to Fourier Optics, 2nd ed. (1996), Vol. 35.

Gutzler, T.

Hahn, J.

Hillman, T. R.

Huang, J.

J. Huang, A. Alqahtani, J. Viegas, and M. S. Dahlem, “Fabrication of optical fibre gratings through focused ion beam techniques for sensing applications,” in Photonics Global Conference (PGC) (2012), Vol. 3, pp. 1–4.

Jahns, J.

J. Jahns, M. M. Downs, M. E. Prise, N. Streibl, and S. J. Walker, “Dammann gratings for laser beam shaping,” Opt. Eng. 28, 1267–1275 (1989).
[Crossref]

Jeong, T. H.

T. H. Jeong, “Basic principles and applications of holography BT—fundamentals of photonics,” in Fundamentals of Photonics (2008), p. 381–417.

Jozwicki, R.

R. Jozwicki and S. Pasko, “Influence of reference beam aberrations in digital holography on the image quality,” in Optical Measurement Systems for Industrial Inspection III (SPIE, 2003), Vol. 5144, pp. 132–137.

Jueptner, W. P. O.

S. Seebacher, W. Osten, and W. P. O. Jueptner, “Measuring shape and deformation of small objects using digital holography,” Proc. SPIE 3479, 104–115 (1998).
[Crossref]

Kanka, M.

Karrai, K.

C. Obermüller and K. Karrai, “Far field characterization of diffracting circular apertures,” Appl. Phys. Lett. 67, 3408–3410 (1995).
[Crossref]

Khilo, A.

H. Melkonyan, K. Al Qubaisi, A. Khilo, and M. Dahlem, “Optical fibre lens with parabolic effective index profile fabricated using focused ion beam,” in CLEO: Science and Innovations (SM1P—3) (2016).

Kim, M. K.

Lawrence, R. W.

J. W. Goodman and R. W. Lawrence, “Digital image formation from electronically detected holograms,” Appl. Phys. Lett. 11, 77–79 (1967).
[Crossref]

Leith, E. N.

Lim, S.

Mahajan, V. N.

Malacara, D.

D. Malacara, Optical Shop Testing, Wiley Series in Pure and Applied Optics (Wiley, 2007).

Marks, D. L.

Marquet, P.

Mei, Z.

P. Qiu, Z. Mei, and T. Pang, “Extracting the parameters of digital reference wave from a single off-axis digital hologram,” J. Mod. Opt. 62, 816–821 (2016).
[Crossref]

Melkonyan, H.

H. Melkonyan, K. Al Qubaisi, A. Khilo, and M. Dahlem, “Optical fibre lens with parabolic effective index profile fabricated using focused ion beam,” in CLEO: Science and Innovations (SM1P—3) (2016).

Mills, G.

F. Zhang, J. D. R. Valera, I. Yamaguchi, M. Yokota, and G. Mills, “Vibration analysis by phase shifting digital holography,” Opt. Rev. 11, 297–299 (2004).
[Crossref]

Obermüller, C.

C. Obermüller and K. Karrai, “Far field characterization of diffracting circular apertures,” Appl. Phys. Lett. 67, 3408–3410 (1995).
[Crossref]

Osten, W.

S. Seebacher, W. Osten, and W. P. O. Jueptner, “Measuring shape and deformation of small objects using digital holography,” Proc. SPIE 3479, 104–115 (1998).
[Crossref]

Pang, T.

P. Qiu, Z. Mei, and T. Pang, “Extracting the parameters of digital reference wave from a single off-axis digital hologram,” J. Mod. Opt. 62, 816–821 (2016).
[Crossref]

Pasko, S.

R. Jozwicki and S. Pasko, “Influence of reference beam aberrations in digital holography on the image quality,” in Optical Measurement Systems for Industrial Inspection III (SPIE, 2003), Vol. 5144, pp. 132–137.

Prise, M. E.

J. Jahns, M. M. Downs, M. E. Prise, N. Streibl, and S. J. Walker, “Dammann gratings for laser beam shaping,” Opt. Eng. 28, 1267–1275 (1989).
[Crossref]

Qiu, P.

P. Qiu, Z. Mei, and T. Pang, “Extracting the parameters of digital reference wave from a single off-axis digital hologram,” J. Mod. Opt. 62, 816–821 (2016).
[Crossref]

Riesenberg, R.

Sampson, D. D.

Sang, X.

X. Sang, “Applications of digital holography to measurements and optical characterization,” Opt. Eng. 50, 91311 (2011).
[Crossref]

Seebacher, S.

S. Seebacher, W. Osten, and W. P. O. Jueptner, “Measuring shape and deformation of small objects using digital holography,” Proc. SPIE 3479, 104–115 (1998).
[Crossref]

Streibl, N.

J. Jahns, M. M. Downs, M. E. Prise, N. Streibl, and S. J. Walker, “Dammann gratings for laser beam shaping,” Opt. Eng. 28, 1267–1275 (1989).
[Crossref]

Upatnieks, J.

Valera, J. D. R.

F. Zhang, J. D. R. Valera, I. Yamaguchi, M. Yokota, and G. Mills, “Vibration analysis by phase shifting digital holography,” Opt. Rev. 11, 297–299 (2004).
[Crossref]

Viegas, J.

J. Huang, A. Alqahtani, J. Viegas, and M. S. Dahlem, “Fabrication of optical fibre gratings through focused ion beam techniques for sensing applications,” in Photonics Global Conference (PGC) (2012), Vol. 3, pp. 1–4.

Walker, S. J.

J. Jahns, M. M. Downs, M. E. Prise, N. Streibl, and S. J. Walker, “Dammann gratings for laser beam shaping,” Opt. Eng. 28, 1267–1275 (1989).
[Crossref]

Yamaguchi, I.

F. Zhang, J. D. R. Valera, I. Yamaguchi, M. Yokota, and G. Mills, “Vibration analysis by phase shifting digital holography,” Opt. Rev. 11, 297–299 (2004).
[Crossref]

Yokota, M.

F. Zhang, J. D. R. Valera, I. Yamaguchi, M. Yokota, and G. Mills, “Vibration analysis by phase shifting digital holography,” Opt. Rev. 11, 297–299 (2004).
[Crossref]

Zhang, F.

F. Zhang, J. D. R. Valera, I. Yamaguchi, M. Yokota, and G. Mills, “Vibration analysis by phase shifting digital holography,” Opt. Rev. 11, 297–299 (2004).
[Crossref]

Appl. Opt. (3)

Appl. Phys. Lett. (2)

C. Obermüller and K. Karrai, “Far field characterization of diffracting circular apertures,” Appl. Phys. Lett. 67, 3408–3410 (1995).
[Crossref]

J. W. Goodman and R. W. Lawrence, “Digital image formation from electronically detected holograms,” Appl. Phys. Lett. 11, 77–79 (1967).
[Crossref]

J. Mod. Opt. (1)

P. Qiu, Z. Mei, and T. Pang, “Extracting the parameters of digital reference wave from a single off-axis digital hologram,” J. Mod. Opt. 62, 816–821 (2016).
[Crossref]

J. Opt. Soc. Am. (1)

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

J. Opt. Soc. Korea (1)

Opt. Eng. (2)

X. Sang, “Applications of digital holography to measurements and optical characterization,” Opt. Eng. 50, 91311 (2011).
[Crossref]

J. Jahns, M. M. Downs, M. E. Prise, N. Streibl, and S. J. Walker, “Dammann gratings for laser beam shaping,” Opt. Eng. 28, 1267–1275 (1989).
[Crossref]

Opt. Express (1)

Opt. Lett. (1)

Opt. Rev. (1)

F. Zhang, J. D. R. Valera, I. Yamaguchi, M. Yokota, and G. Mills, “Vibration analysis by phase shifting digital holography,” Opt. Rev. 11, 297–299 (2004).
[Crossref]

Proc. SPIE (1)

S. Seebacher, W. Osten, and W. P. O. Jueptner, “Measuring shape and deformation of small objects using digital holography,” Proc. SPIE 3479, 104–115 (1998).
[Crossref]

Other (8)

T. H. Jeong, “Basic principles and applications of holography BT—fundamentals of photonics,” in Fundamentals of Photonics (2008), p. 381–417.

J. W. Goodman, Introduction to Fourier Optics, 2nd ed. (1996), Vol. 35.

R. Jozwicki and S. Pasko, “Influence of reference beam aberrations in digital holography on the image quality,” in Optical Measurement Systems for Industrial Inspection III (SPIE, 2003), Vol. 5144, pp. 132–137.

D. Malacara, Optical Shop Testing, Wiley Series in Pure and Applied Optics (Wiley, 2007).

Sony, “IMX219PQ,” http://www.sony-semicon.co.jp/products_en/new_pro/april_2014/imx219_e.html .

H. Melkonyan, K. Al Qubaisi, A. Khilo, and M. Dahlem, “Optical fibre lens with parabolic effective index profile fabricated using focused ion beam,” in CLEO: Science and Innovations (SM1P—3) (2016).

J. Huang, A. Alqahtani, J. Viegas, and M. S. Dahlem, “Fabrication of optical fibre gratings through focused ion beam techniques for sensing applications,” in Photonics Global Conference (PGC) (2012), Vol. 3, pp. 1–4.

MathWorks, “fminsearch,” https://uk.mathworks.com/help/matlab/ref/fminsearch.html .

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Figures (9)

Fig. 1.
Fig. 1. Compact digital holographic camera.
Fig. 2.
Fig. 2. Array of 225 compact holographic cameras.
Fig. 3.
Fig. 3. Reference and entrance pupil.
Fig. 4.
Fig. 4. Experimental arrangement utilizing a diffraction grating as the object wave.
Fig. 5.
Fig. 5. Test hologram with |R|2 term removed.
Fig. 6.
Fig. 6. Reconstruction of the Dammann grating with initial reference beam parameters.
Fig. 7.
Fig. 7. Reconstruction of the Dammann grating after reference beam parameters have been optimized.
Fig. 8.
Fig. 8. Phase error (rad) when compared to a spherical wave.
Fig. 9.
Fig. 9. Reconstruction of multiple point sources to compare the point spread function over the entire field of view of the camera.

Equations (21)

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

H=|SA+RA|2=|SA|2+|RA|2+SA*RA+SARA*,
UA=H|RA|2RA*RARA*SA*+SA.
UB=UAG=UA(x,y)G(xx,yy)dxdy
U˜B=U˜AG˜,
G˜(kx,ky)=G(x,y)exp(j2π(kxx+kyy))dxdy,
G˜(kx,ky)=circ((λkx)2+(λky)2)×exp(j2πk0z1(λkx)2(λky)2),
circ(r)={10.50r<1r=1otherwise.
UB(RARA*SA*)G+(RA*RA*SA)G,
UB(RARA*SA*)G+SB.
RAe=A(x,y)exp(j(2πk0r+ϕ(x,y))),
ϕ(x,y)=c1ϕ1(x,y)+c2ϕ2(x,y)+cnϕn(x,y),
SB(x,y)=W(x,y)×m,nexp(j2π(mkgx+nkgy)),
UB(RΔSA)G,
I=|U˜B|2|(R˜ΔS˜A)·G˜|2,
I|(R˜ΔS˜A)|2.
I=|U˜B|2|R˜Δ(S˜BG˜*)|2.
I|R˜Δ(G˜*×(m,nW˜m,n))|2,
I|m,nW˜m,n|2.
Q=m,nmax(Im,n),
ϕ1=1,ϕ2=(3/a)x,ϕ3=3/(1a2)y,ϕ4=[5/(212a2+2a4)](3ρ21),ϕ5=[3/(a1a2)]xy,ϕ6={5/[2a2(1a2)12a2+2a4]}[3(1a2)2x23a4y2a2(13a2+2a4)],ϕ7=[21/(22754a2+62a4)](15ρ29+4a2)y,ϕ8=[21/(2a3570a2+62a4)](15ρ25+4a2)x,ϕ9={5(2754a2+62a4)/(1a2)/[2a2(2781a2+116a4+62a6)]}[27(1a2)2x235a4y2+a2(939a2+30a4)]y,ϕ10={5/[2a3(1a2)3570a2+62a4]}[35(1a2)2x227a4y2a2(2151a2+304)]x,ϕ11=[1/(8μ)][315ρ430(7+2a2)x230(92a2)y2+27+16a216a4],ϕ12=[3μ/(8a2νη)][35(1a2)2(1836a2+67a4)x4+630(12a2+2a4)x2y235a4(4998a2+67a4)y430(1a2)(710a212a4+75a667a8)x230a2(777a2+189a4193a6+67a8)y2+a2(1a2)(12a2)(70233a2+233a4),ϕ13=[21/(2a13a2+4a42a6)](5ρ23)xy,ϕ14=16τ[735(1a2)4x4540a4(1a2)2x2y2+735a8y490a2(1a2)3(79a2)x2+90a6(1a2)(29a2)y2+3a4(1a2)2(2162a2+62a4)],ϕ15={21/[2a3(1a2)13a2+4a42a6]}[5(1a2)2x25a4y2a2(39a2+6a4)]xy.
μ=(936a2+103a4134a6+67a8)1/2,ν=(49196a2+330a4268a6+134a8)1/2,τ=1/[128νa4(1a2)2],η=945a2+139a4237a6+210a867a10.

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