Abstract

A new framework for in-plane transformations of digital holograms (DHs) is proposed, which provides improved control over basic geometrical features of holographic images reconstructed optically in full color. The method is based on a Fourier hologram equivalent of the adaptive affine transformation technique [Opt. Express 18, 8806 (2010) [CrossRef]  ]. The solution includes four elementary geometrical transformations that can be performed independently on a full-color 3D image reconstructed from an RGB hologram: (i) transverse magnification; (ii) axial translation with minimized distortion; (iii) transverse translation; and (iv) viewing angle rotation. The independent character of transformations (i) and (ii) constitutes the main result of the work and plays a double role: (1) it simplifies synchronization of color components of the RGB image in the presence of mismatch between capture and display parameters; (2) provides improved control over position and size of the projected image, particularly the axial position, which opens new possibilities for efficient animation of holographic content. The approximate character of the operations (i) and (ii) is examined both analytically and experimentally using an RGB circular holographic display system. Additionally, a complex animation built from a single wide-aperture RGB Fourier hologram is presented to demonstrate full capabilities of the developed toolset.

© 2017 Optical Society of America

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References

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2017 (1)

2016 (7)

H. Kang, E. Stoykova, and H. Yoshikawa, “Fast phase-added stereogram algorithm for generation of photorealistic 3d content,” Appl. Opt. 55, A135–A143 (2016).
[Crossref]

S. Montresor and P. Picart, “Quantitative appraisal for noise reduction in digital holographic phase imaging,” Opt. Express 24, 14322–14343 (2016).
[Crossref]

Y. Lim, K. Hong, H. Kim, H.-E. Kim, E.-Y. Chang, S. Lee, T. Kim, J. Nam, H.-G. Choo, J. Kim, and J. Hahn, “360-degree tabletop electronic holographic display,” Opt. Express 24, 24999–25009 (2016).
[Crossref]

V. Bianco, P. Memmolo, M. Paturzo, and P. Ferraro, “On-speckle suppression in IR digital holography,” Opt. Lett. 41, 5226–5229 (2016).
[Crossref]

A. Gołoś, W. Zaperty, G. Finke, P. Makowski, and T. Kozacki, “Fourier RGB synthetic aperture color holographic capture for wide angle holographic display,” Proc. SPIE 9970, 99701E (2016).
[Crossref]

W. Zaperty, T. Kozacki, and M. Kujawińska, “Multi-SLM color holographic 3D display based on RGB spatial filter,” J. Disp. Technol. 12, 1724–1731 (2016).
[Crossref]

P. Memmolo, V. Bianco, M. Paturzo, and P. Ferraro, “Numerical manipulation of digital holograms for 3-D imaging and display: an overview,” Proc. IEEE 105, 1–14 (2016).

2015 (5)

2014 (3)

2012 (4)

2011 (2)

2010 (2)

2009 (2)

2008 (2)

2004 (1)

2002 (1)

1965 (2)

R. W. Meier, “Magnification and third-order aberrations in holography,” J. Opt. Soc. Am. 55, 987–992 (1965).
[Crossref]

G. W. Stroke, “Lensless Fourier-transform method for optical holography,” Appl. Phys. Lett. 6, 201–203 (1965).
[Crossref]

Barada, D.

Bianco, V.

Blinder, D.

Brady, D. J.

Caulfield, H.

H. Caulfield, The Art and Science of Holography: A Tribute to Emmett Leith and Yuri Denisyuk, H. John Caulfield, ed. (SPIE, 2004), Vol. PM124, pp. 202–209.

Caulfield, H. J.

H. J. Caulfield, The Art and Science of Holography: A Tribute to Emmett Leith and Yuri Denisyuk (SPIE, 2004), Vol. PM124.

Chang, E.-Y.

Chen, J.-S.

Chen, N.

Cheung, K. W. K.

Choi, H.-J.

Choi, K.

Choo, H.-G.

Chu, D. P.

Distante, C.

P. Memmolo, M. Leo, C. Distante, M. Paturzo, and P. Ferraro, “Coding color three-dimensional scenes and joining different objects by adaptive transformations in digital holography,” J. Disp. Technol. 11, 854–860 (2015).
[Crossref]

Ducin, I.

Falaggis, K.

Ferraro, P.

P. Memmolo, V. Bianco, M. Paturzo, and P. Ferraro, “Numerical manipulation of digital holograms for 3-D imaging and display: an overview,” Proc. IEEE 105, 1–14 (2016).

V. Bianco, P. Memmolo, M. Paturzo, and P. Ferraro, “On-speckle suppression in IR digital holography,” Opt. Lett. 41, 5226–5229 (2016).
[Crossref]

P. Memmolo, M. Leo, C. Distante, M. Paturzo, and P. Ferraro, “Coding color three-dimensional scenes and joining different objects by adaptive transformations in digital holography,” J. Disp. Technol. 11, 854–860 (2015).
[Crossref]

P. Memmolo, V. Bianco, M. Paturzo, B. Javidi, P. A. Netti, and P. Ferraro, “Encoding multiple holograms for speckle-noise reduction in optical display,” Opt. Express 22, 25768–25775 (2014).
[Crossref]

M. Paturzo, P. Memmolo, A. Finizio, R. Näsänen, T. J. Naughton, and P. Ferraro, “Synthesis and display of dynamic holographic 3D scenes with real-world objects,” Opt. Express 18, 8806–8815 (2010).
[Crossref]

Fienup, J. R.

Finizio, A.

Finke, G.

A. Gołoś, W. Zaperty, G. Finke, P. Makowski, and T. Kozacki, “Fourier RGB synthetic aperture color holographic capture for wide angle holographic display,” Proc. SPIE 9970, 99701E (2016).
[Crossref]

T. Kozacki, M. Kujawinska, G. Finke, W. Zaperty, and B. Hennelly, “Holographic capture and display systems in circular configurations,” J. Disp. Technol. 8, 225–232 (2012).
[Crossref]

T. Kozacki, G. Finke, P. Garbat, W. Zaperty, and M. Kujawińska, “Wide angle holographic display system with spatiotemporal multiplexing,” Opt. Express 20, 27473–27481 (2012).
[Crossref]

Garbat, P.

Golos, A.

A. Gołoś, W. Zaperty, G. Finke, P. Makowski, and T. Kozacki, “Fourier RGB synthetic aperture color holographic capture for wide angle holographic display,” Proc. SPIE 9970, 99701E (2016).
[Crossref]

W. Zaperty, P. Makowski, A. Golos, T. Kozacki, and M. Kujawinska, Color Holographic Imaging Based on Digital Holographic Data with Geometrical Image Transformations (OSA, 2016), paper DM3E.4.

Guizar-Sicairos, M.

Hack, E.

C. J. R. Sheppard, S. S. Kou, P. K. Rastogi, and E. Hack, “3Dimaging with holographic tomography,” AIP Conf. Proc. 1236, 65–69 (2010).
[Crossref]

Hahn, J.

Hennelly, B.

T. Kozacki, M. Kujawinska, G. Finke, W. Zaperty, and B. Hennelly, “Holographic capture and display systems in circular configurations,” J. Disp. Technol. 8, 225–232 (2012).
[Crossref]

Hong, J.

Hong, K.

Horisaki, R.

Ichihashi, Y.

H. Sasaki, K. Yamamoto, K. Wakunami, Y. Ichihashi, R. Oi, and T. Senoh, “Large size three-dimensional video by electronic holography using multiple spatial light modulators,” Sci. Rep. 4, 6177 (2014).
[Crossref]

Ito, T.

Javidi, B.

Kakarenko, K.

Kang, H.

Kim, H.

Kim, H.-E.

Kim, J.

Kim, T.

Kim, Y.

Kolodziejczyk, A.

Kou, S. S.

C. J. R. Sheppard, S. S. Kou, P. K. Rastogi, and E. Hack, “3Dimaging with holographic tomography,” AIP Conf. Proc. 1236, 65–69 (2010).
[Crossref]

Kozacki, T.

P. L. Makowski, T. Kozacki, and W. Zaperty, “Orthoscopic real-image display of digital holograms,” Opt. Lett. 42, 3932–3935 (2017).
[Crossref]

A. Gołoś, W. Zaperty, G. Finke, P. Makowski, and T. Kozacki, “Fourier RGB synthetic aperture color holographic capture for wide angle holographic display,” Proc. SPIE 9970, 99701E (2016).
[Crossref]

W. Zaperty, T. Kozacki, and M. Kujawińska, “Multi-SLM color holographic 3D display based on RGB spatial filter,” J. Disp. Technol. 12, 1724–1731 (2016).
[Crossref]

P. L. Makowski, T. Kozacki, P. Zdankowski, and W. Zaperty, “Synthetic aperture Fourier holography for wide-angle holographic display of real scenes,” Appl. Opt. 54, 3658–3665 (2015).
[Crossref]

T. Kozacki and K. Falaggis, “Angular spectrum-based wave-propagation method with compact space bandwidth for large propagation distances,” Opt. Lett. 40, 3420–3423 (2015).
[Crossref]

T. Kozacki, M. Kujawinska, G. Finke, W. Zaperty, and B. Hennelly, “Holographic capture and display systems in circular configurations,” J. Disp. Technol. 8, 225–232 (2012).
[Crossref]

T. Kozacki, G. Finke, P. Garbat, W. Zaperty, and M. Kujawińska, “Wide angle holographic display system with spatiotemporal multiplexing,” Opt. Express 20, 27473–27481 (2012).
[Crossref]

W. Zaperty, P. Makowski, A. Golos, T. Kozacki, and M. Kujawinska, Color Holographic Imaging Based on Digital Holographic Data with Geometrical Image Transformations (OSA, 2016), paper DM3E.4.

Kujawinska, M.

W. Zaperty, T. Kozacki, and M. Kujawińska, “Multi-SLM color holographic 3D display based on RGB spatial filter,” J. Disp. Technol. 12, 1724–1731 (2016).
[Crossref]

T. Kozacki, G. Finke, P. Garbat, W. Zaperty, and M. Kujawińska, “Wide angle holographic display system with spatiotemporal multiplexing,” Opt. Express 20, 27473–27481 (2012).
[Crossref]

T. Kozacki, M. Kujawinska, G. Finke, W. Zaperty, and B. Hennelly, “Holographic capture and display systems in circular configurations,” J. Disp. Technol. 8, 225–232 (2012).
[Crossref]

W. Zaperty, P. Makowski, A. Golos, T. Kozacki, and M. Kujawinska, Color Holographic Imaging Based on Digital Holographic Data with Geometrical Image Transformations (OSA, 2016), paper DM3E.4.

Lee, B.

Lee, S.

Leo, M.

P. Memmolo, M. Leo, C. Distante, M. Paturzo, and P. Ferraro, “Coding color three-dimensional scenes and joining different objects by adaptive transformations in digital holography,” J. Disp. Technol. 11, 854–860 (2015).
[Crossref]

Lim, S.

Lim, Y.

Makowski, M.

Makowski, P.

A. Gołoś, W. Zaperty, G. Finke, P. Makowski, and T. Kozacki, “Fourier RGB synthetic aperture color holographic capture for wide angle holographic display,” Proc. SPIE 9970, 99701E (2016).
[Crossref]

W. Zaperty, P. Makowski, A. Golos, T. Kozacki, and M. Kujawinska, Color Holographic Imaging Based on Digital Holographic Data with Geometrical Image Transformations (OSA, 2016), paper DM3E.4.

Makowski, P. L.

Marks, D. L.

Massig, J. H.

Meier, R. W.

Memmolo, P.

V. Bianco, P. Memmolo, M. Paturzo, and P. Ferraro, “On-speckle suppression in IR digital holography,” Opt. Lett. 41, 5226–5229 (2016).
[Crossref]

P. Memmolo, V. Bianco, M. Paturzo, and P. Ferraro, “Numerical manipulation of digital holograms for 3-D imaging and display: an overview,” Proc. IEEE 105, 1–14 (2016).

P. Memmolo, M. Leo, C. Distante, M. Paturzo, and P. Ferraro, “Coding color three-dimensional scenes and joining different objects by adaptive transformations in digital holography,” J. Disp. Technol. 11, 854–860 (2015).
[Crossref]

P. Memmolo, V. Bianco, M. Paturzo, B. Javidi, P. A. Netti, and P. Ferraro, “Encoding multiple holograms for speckle-noise reduction in optical display,” Opt. Express 22, 25768–25775 (2014).
[Crossref]

M. Paturzo, P. Memmolo, A. Finizio, R. Näsänen, T. J. Naughton, and P. Ferraro, “Synthesis and display of dynamic holographic 3D scenes with real-world objects,” Opt. Express 18, 8806–8815 (2010).
[Crossref]

Min, S.-W.

Montresor, S.

Munteanu, A.

Nam, J.

Näsänen, R.

Naughton, T. J.

Netti, P. A.

Oi, R.

H. Sasaki, K. Yamamoto, K. Wakunami, Y. Ichihashi, R. Oi, and T. Senoh, “Large size three-dimensional video by electronic holography using multiple spatial light modulators,” Sci. Rep. 4, 6177 (2014).
[Crossref]

Okano, K.

Onural, L.

Park, G.

Park, J.-H.

Paturzo, M.

V. Bianco, P. Memmolo, M. Paturzo, and P. Ferraro, “On-speckle suppression in IR digital holography,” Opt. Lett. 41, 5226–5229 (2016).
[Crossref]

P. Memmolo, V. Bianco, M. Paturzo, and P. Ferraro, “Numerical manipulation of digital holograms for 3-D imaging and display: an overview,” Proc. IEEE 105, 1–14 (2016).

P. Memmolo, M. Leo, C. Distante, M. Paturzo, and P. Ferraro, “Coding color three-dimensional scenes and joining different objects by adaptive transformations in digital holography,” J. Disp. Technol. 11, 854–860 (2015).
[Crossref]

P. Memmolo, V. Bianco, M. Paturzo, B. Javidi, P. A. Netti, and P. Ferraro, “Encoding multiple holograms for speckle-noise reduction in optical display,” Opt. Express 22, 25768–25775 (2014).
[Crossref]

M. Paturzo, P. Memmolo, A. Finizio, R. Näsänen, T. J. Naughton, and P. Ferraro, “Synthesis and display of dynamic holographic 3D scenes with real-world objects,” Opt. Express 18, 8806–8815 (2010).
[Crossref]

Picart, P.

Poon, T.-C.

Rastogi, P. K.

C. J. R. Sheppard, S. S. Kou, P. K. Rastogi, and E. Hack, “3Dimaging with holographic tomography,” AIP Conf. Proc. 1236, 65–69 (2010).
[Crossref]

Sando, Y.

Sasaki, H.

H. Sasaki, K. Yamamoto, K. Wakunami, Y. Ichihashi, R. Oi, and T. Senoh, “Large size three-dimensional video by electronic holography using multiple spatial light modulators,” Sci. Rep. 4, 6177 (2014).
[Crossref]

Schelkens, P.

Senoh, T.

H. Sasaki, K. Yamamoto, K. Wakunami, Y. Ichihashi, R. Oi, and T. Senoh, “Large size three-dimensional video by electronic holography using multiple spatial light modulators,” Sci. Rep. 4, 6177 (2014).
[Crossref]

Sheppard, C. J. R.

C. J. R. Sheppard, S. S. Kou, P. K. Rastogi, and E. Hack, “3Dimaging with holographic tomography,” AIP Conf. Proc. 1236, 65–69 (2010).
[Crossref]

Stoykova, E.

Stroke, G. W.

G. W. Stroke, “Lensless Fourier-transform method for optical holography,” Appl. Phys. Lett. 6, 201–203 (1965).
[Crossref]

Suszek, J.

Symeonidou, A.

Sypek, M.

Thurman, S. T.

Tsang, P. W. M.

Wakunami, K.

H. Sasaki, K. Yamamoto, K. Wakunami, Y. Ichihashi, R. Oi, and T. Senoh, “Large size three-dimensional video by electronic holography using multiple spatial light modulators,” Sci. Rep. 4, 6177 (2014).
[Crossref]

Yamamoto, K.

H. Sasaki, K. Yamamoto, K. Wakunami, Y. Ichihashi, R. Oi, and T. Senoh, “Large size three-dimensional video by electronic holography using multiple spatial light modulators,” Sci. Rep. 4, 6177 (2014).
[Crossref]

Yaras, F.

Yatagai, T.

Yoshikawa, H.

Zaperty, W.

P. L. Makowski, T. Kozacki, and W. Zaperty, “Orthoscopic real-image display of digital holograms,” Opt. Lett. 42, 3932–3935 (2017).
[Crossref]

A. Gołoś, W. Zaperty, G. Finke, P. Makowski, and T. Kozacki, “Fourier RGB synthetic aperture color holographic capture for wide angle holographic display,” Proc. SPIE 9970, 99701E (2016).
[Crossref]

W. Zaperty, T. Kozacki, and M. Kujawińska, “Multi-SLM color holographic 3D display based on RGB spatial filter,” J. Disp. Technol. 12, 1724–1731 (2016).
[Crossref]

P. L. Makowski, T. Kozacki, P. Zdankowski, and W. Zaperty, “Synthetic aperture Fourier holography for wide-angle holographic display of real scenes,” Appl. Opt. 54, 3658–3665 (2015).
[Crossref]

T. Kozacki, G. Finke, P. Garbat, W. Zaperty, and M. Kujawińska, “Wide angle holographic display system with spatiotemporal multiplexing,” Opt. Express 20, 27473–27481 (2012).
[Crossref]

T. Kozacki, M. Kujawinska, G. Finke, W. Zaperty, and B. Hennelly, “Holographic capture and display systems in circular configurations,” J. Disp. Technol. 8, 225–232 (2012).
[Crossref]

W. Zaperty, P. Makowski, A. Golos, T. Kozacki, and M. Kujawinska, Color Holographic Imaging Based on Digital Holographic Data with Geometrical Image Transformations (OSA, 2016), paper DM3E.4.

Zdankowski, P.

AIP Conf. Proc. (1)

C. J. R. Sheppard, S. S. Kou, P. K. Rastogi, and E. Hack, “3Dimaging with holographic tomography,” AIP Conf. Proc. 1236, 65–69 (2010).
[Crossref]

Appl. Opt. (4)

Appl. Phys. Lett. (1)

G. W. Stroke, “Lensless Fourier-transform method for optical holography,” Appl. Phys. Lett. 6, 201–203 (1965).
[Crossref]

J. Disp. Technol. (3)

P. Memmolo, M. Leo, C. Distante, M. Paturzo, and P. Ferraro, “Coding color three-dimensional scenes and joining different objects by adaptive transformations in digital holography,” J. Disp. Technol. 11, 854–860 (2015).
[Crossref]

T. Kozacki, M. Kujawinska, G. Finke, W. Zaperty, and B. Hennelly, “Holographic capture and display systems in circular configurations,” J. Disp. Technol. 8, 225–232 (2012).
[Crossref]

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H. Caulfield, The Art and Science of Holography: A Tribute to Emmett Leith and Yuri Denisyuk, H. John Caulfield, ed. (SPIE, 2004), Vol. PM124, pp. 202–209.

W. Zaperty, P. Makowski, A. Golos, T. Kozacki, and M. Kujawinska, Color Holographic Imaging Based on Digital Holographic Data with Geometrical Image Transformations (OSA, 2016), paper DM3E.4.

Supplementary Material (1)

NameDescription
» Visualization 1       Animation sequence created from a single acquisition of a synthetic aperture RGB digital hologram. Image transformations are performed using combination of uniform stretching in the Fourier hologram plane and cropping/filling operations in the FFT pl

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Figures (8)

Fig. 1.
Fig. 1.

Conventions of the lensless Fourier hologram capture and reconstruction.

Fig. 2.
Fig. 2.

Holographic image deformations resulting from (a) scaling of the readout wave radius Z=mR reconstructing the Fourier hologram [Eq. (6)]; (b) stretching of the Fourier hologram content by factor m [Eq. (8)]; and (c) combination of the two above [Eq. (9)], leading to axial translation of the holographic image. The object size is 0.2R.

Fig. 3.
Fig. 3.

Schematic of the RGB Fourier hologram transformation routine including (i) transverse magnification, (ii) axial translation, (iii) lateral translation, and (iv) view rotation of the reconstructed object (j=R,G,B).

Fig. 4.
Fig. 4.

Schematic of the experimental holographic imaging system: (a) color synthetic aperture lensless Fourier hologram capture system; (b) multi-SLM color holographic display system.

Fig. 5.
Fig. 5.

Numerical reconstructions of an RGB SAFH, 5760×360 pixels for each primary wavelength: (a) by FFT of the captured Fourier data; (b) by Fresnel transform of the processed data ready to address a triple-SLM RGB display.

Fig. 6.
Fig. 6.

Experimental reconstructions demonstrating transverse image magnification without axial translation: (a) image reduced in transverse dimension (M=0.43) while keeping the reconstruction distance equal to the registration distance (Z=R), so that the figurine fits the limited display FoV; (b) , (c), image in the same reconstruction distance (Z=R) and in unchanged physical size (M=1) clipped by display FoV without aliasing; photographed in two planes focused on different details of the 3D surface. Vectors A and T are given in millimeters.

Fig. 7.
Fig. 7.

Experimental demonstration of pure axial translation of a holographic image. Optical display of a synthesized two-object scene with its center located at (a) Z=1060  mm, (b) Z=960  mm, and (c) Z=1260  mm. Positions (b) and (c) were obtained by transforming the synthesized hologram from case (a). The image was projected onto a pair of diffusers (distanced by 100 mm), mounted on the same stage as the camera in fixed relative position; the camera and the diffusers followed the shifted 3D scene. Vectors A and T are given in millimeters.

Fig. 8.
Fig. 8.

Animation sequence of a single static RGB hologram image utilizing all geometrical image transformations in the proposed framework: transverse magnification (M), axial translation (Tz), transverse translation (Tx,Ty), and horizontal view rotation (Ax). See Visualization 1.

Tables (1)

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Table 1. Parameters of the RGB Holographic Imaging System

Equations (14)

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I=|o+r|2=|o|2+|r|2+or*+o*r,
oR(x)=o(x)r*(x)=o(x)exp[iπx2λR],
o(x)exp[iπx2λR]+u(xo)exp[iπxo2λR]exp[i2πxxoλR]dxo.
oR(x)F{uR(xo)}(ξ)|ξ=xλR,
s(x)=exp[iπxo2λZ].
s(x)oR(x)+u(RZxo)×exp[iπxo2λZ(RZ1)]exp[iπ(xxo)2λZ]dxo,
s(x)oR(xm)+s(x)u(xom)×exp[iπxo2λm2R]exp[i2πxxoλm2R]dxo.
exp[iπx2λR]oR(xm)+u(mxo)×exp[iπxo2λ(m21)1R]exp[iπ(xxo)2λR]dxo.
exp[iπx2λmR]oR(xm)+u(xo)×exp[iπxo2λm(m1)1R]exp[iπ(xxo)2λmR]dxo.
Tz=ZR=(m1)R.
Mx=±μmR2R1,Mz=±μm2R22R12,
mMj=1μjM,
mT=ZR
mj=mMjmT,Z=R+Tz

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