Abstract

We present a spatially incoherent dual path Fourier holographic system. Conceptually it is similar to Fourier incoherent single channel holography (FISCH). Although our incoherent off-axis Fourier holographic (IOFH) system does not have the robustness of a single channel system, it has three advantages over FISCH, with two being quite obvious from setup. First, no SLM is required, thus making the system simple and cost-effective. Second, it is capable of high light throughput because in FISCH, the use of SLM reduces light intensity in half by splitting one beam into two; furthermore, an analyzer is required to create interference which also reduces light intensity. The third advantage, which makes this IOFH system applicable even for on-axis samples (as opposed to samples in a half plane as is necessary for FISCH), is achieved by tilting one mirror. Here we demonstrate our system with a sample in half plane as in FISCH for different axial positions, and then by placing the object on an optical axis and tilting one mirror. The reconstructed images demonstrate holographic capabilities of our IOFH system for both on-axis and half plane sample locations.

© 2016 Optical Society of America

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References

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    [Crossref]
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    [Crossref] [PubMed]
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    [Crossref] [PubMed]
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    [Crossref]
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    [Crossref] [PubMed]
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    [Crossref]
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2014 (1)

2013 (3)

2012 (3)

2011 (2)

2010 (1)

2008 (1)

2007 (1)

2006 (1)

2003 (1)

2001 (1)

2000 (1)

1997 (1)

I. Yamaguchi and T. Zhang, “Phase-shifting digital holography,” Opt. Express 22(16), 1268–1270 (1997).

1979 (1)

1970 (1)

1965 (1)

G. W. Stroke and R. C. Restrick, “Holography with spatially noncoherent light,” Appl. Phys. Lett. 7(9), 229–231 (1965).
[Crossref]

1948 (1)

D. Gabor, “A new microscopic principle,” Nature 161(4098), 777–778 (1948).
[Crossref] [PubMed]

Abookasis, D.

Brooker, G.

Bryngdahl, O.

Cuche, E.

Depeursinge, C.

Gabor, D.

D. Gabor, “A new microscopic principle,” Nature 161(4098), 777–778 (1948).
[Crossref] [PubMed]

Goodman, J. W.

J. W. Goodman, Introduction to Fourier Optics (Roberts and Company Publishers, 2005).

Hong, J.

Indebetouw, G.

Itoh, M.

Katz, B.

Kelner, R.

Kim, M. K.

Korpel, A.

Li, Y.

Lohmann, A.

Man, T.

Marquet, P.

Naik, D. N.

Osten, W.

Pedrini, G.

Poon, T. C.

Restrick, R. C.

G. W. Stroke and R. C. Restrick, “Holography with spatially noncoherent light,” Appl. Phys. Lett. 7(9), 229–231 (1965).
[Crossref]

Rosen, J.

R. Kelner, J. Rosen, and G. Brooker, “Enhanced resolution in Fourier incoherent single channel holography (FISCH) with reduced optical path difference,” Opt. Express 21(17), 20131–20144 (2013).
[Crossref] [PubMed]

R. Kelner and J. Rosen, “Spatially incoherent single channel digital Fourier holography,” Opt. Lett. 37(13), 3723–3725 (2012).
[Crossref] [PubMed]

B. Katz, J. Rosen, R. Kelner, and G. Brooker, “Enhanced resolution and throughput of Fresnel incoherent correlation holography (FINCH) using dual diffractive lenses on a spatial light modulator (SLM),” Opt. Express 20(8), 9109–9121 (2012).
[Crossref] [PubMed]

G. Brooker, N. Siegel, V. Wang, and J. Rosen, “Optimal resolution in Fresnel incoherent correlation holographic fluorescence microscopy,” Opt. Express 19(6), 5047–5062 (2011).
[Crossref] [PubMed]

J. Rosen, N. Siegel, and G. Brooker, “Theoretical and experimental demonstration of resolution beyond the Rayleigh limit by FINCH fluorescence microscopic imaging,” Opt. Express 19(27), 26249–26268 (2011).
[Crossref]

B. Katz and J. Rosen, “Super-resolution in incoherent optical imaging using synthetic aperture with Fresnel elements,” Opt. Express 18(2), 962–972 (2010).
[Crossref] [PubMed]

N. T. Shaked and J. Rosen, “Multiple-viewpoint projection holograms synthesized by spatially incoherent correlation with broadband functions,” J. Opt. Soc. Am. A 25(8), 2129–2138 (2008).
[Crossref]

J. Rosen and G. Brooker, “Digital spatially incoherent Fresnel holography,” Opt. Lett. 32(8), 912–914 (2007).
[Crossref] [PubMed]

J. Rosen, G. Indebetouw, and G. Brooker, “Homodyne scanning holography,” Opt. Express 14(10), 4280–4285 (2006).
[Crossref]

Y. Li, D. Abookasis, and J. Rosen, “Computer-generated holograms of three-dimensional realistic objects recorded without wave interference,” Appl. Opt. 40(7), 2864–2870 (2001).
[Crossref]

Sando, Y.

Shaked, N. T.

Siegel, N.

Stroke, G. W.

G. W. Stroke and R. C. Restrick, “Holography with spatially noncoherent light,” Appl. Phys. Lett. 7(9), 229–231 (1965).
[Crossref]

Wan, Y.

Wang, D.

Wang, V.

Yamaguchi, I.

I. Yamaguchi and T. Zhang, “Phase-shifting digital holography,” Opt. Express 22(16), 1268–1270 (1997).

Yatagai, T.

Zhang, T.

I. Yamaguchi and T. Zhang, “Phase-shifting digital holography,” Opt. Express 22(16), 1268–1270 (1997).

Appl. Opt. (3)

Appl. Phys. Lett. (1)

G. W. Stroke and R. C. Restrick, “Holography with spatially noncoherent light,” Appl. Phys. Lett. 7(9), 229–231 (1965).
[Crossref]

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

Nature (1)

D. Gabor, “A new microscopic principle,” Nature 161(4098), 777–778 (1948).
[Crossref] [PubMed]

Opt. Express (9)

R. Kelner, J. Rosen, and G. Brooker, “Enhanced resolution in Fourier incoherent single channel holography (FISCH) with reduced optical path difference,” Opt. Express 21(17), 20131–20144 (2013).
[Crossref] [PubMed]

D. N. Naik, G. Pedrini, and W. Osten, “Recording of incoherent-object hologram as complex spatial coherence function using Sagnac radial shearing interferometer and a Pockels cell,” Opt. Express 21(4), 3990–3995 (2013).
[Crossref] [PubMed]

J. Rosen, G. Indebetouw, and G. Brooker, “Homodyne scanning holography,” Opt. Express 14(10), 4280–4285 (2006).
[Crossref]

G. Brooker, N. Siegel, V. Wang, and J. Rosen, “Optimal resolution in Fresnel incoherent correlation holographic fluorescence microscopy,” Opt. Express 19(6), 5047–5062 (2011).
[Crossref] [PubMed]

J. Rosen, N. Siegel, and G. Brooker, “Theoretical and experimental demonstration of resolution beyond the Rayleigh limit by FINCH fluorescence microscopic imaging,” Opt. Express 19(27), 26249–26268 (2011).
[Crossref]

B. Katz, J. Rosen, R. Kelner, and G. Brooker, “Enhanced resolution and throughput of Fresnel incoherent correlation holography (FINCH) using dual diffractive lenses on a spatial light modulator (SLM),” Opt. Express 20(8), 9109–9121 (2012).
[Crossref] [PubMed]

I. Yamaguchi and T. Zhang, “Phase-shifting digital holography,” Opt. Express 22(16), 1268–1270 (1997).

B. Katz and J. Rosen, “Super-resolution in incoherent optical imaging using synthetic aperture with Fresnel elements,” Opt. Express 18(2), 962–972 (2010).
[Crossref] [PubMed]

Y. Wan, T. Man, and D. Wang, “Incoherent off-axis Fourier triangular color holograph,” Opt. Express 22(7), 8565–8573 (2014).
[Crossref] [PubMed]

Opt. Lett. (6)

Other (1)

J. W. Goodman, Introduction to Fourier Optics (Roberts and Company Publishers, 2005).

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Figures (5)

Fig. 1
Fig. 1 Schematic of the dual path incoherent off-axis Fourier holographic (IOFH) system, RC resolution chart, BPF band pass filter, Lo, L1 lenses with focal length fo, f, BS beam spliter, M1, M2 mirrors, CCD charge-coupled device.

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Fig. 2
Fig. 2 (a) A portion of the hologram captured with resolution chart (RC) at zs = 200mm in half plane, (b) and its inverse Fourier transform, where both image and twin image are in focus.

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Fig. 3
Fig. 3 (a) A portion of the hologram with RC at zs = 175mm (off focus) in half plane, in (b) and (c) its reconstruction depending on propagation direction if either image or twin image is in focus.

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Fig. 4
Fig. 4 (a) A partial hologram with RC on-axis at zs = 200mm (at focus) and (b) its inverse Fourier Transform, image and twin image coincide with zero order term. (c) A portion of the hologram at the same location as in (a) but with one tilted beam. (d) Inverse Fourier transform of (c), both image and twin image are in focus in the same plane at different locations depending on tilt.

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Fig. 5
Fig. 5 (a) A portion of the hologram with on-axis RC at zs = 175mm (off focus), in (b) and (c) its reconstruction depending on propagation direction either image or twin image is in focus

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Equations (16)

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B ( x , y ; r s → , z s ) = A s c ( r s → , z s ) Q ( 1 z s ) L ( − r s → z s ) ⋅ Q ( − 1 f o )
B ( x , y ; r s → z s ) = A s c ( r s → , z s ) L ( − r s → z s ) Q ( f o − z s f o z s ) = A s c ( r s → , z s ) L ( − r s → z s ) Q ( 1 f s )
B 1 ( x , y ; r s → , z s ) = A s c ( r s → , z s ) L ( − r s → z s ) Q ( 1 f s ) * Q ( 1 d )
B 1 ( x , y ; r s → , z s ) = A s c ′ ( r s → , z s ) Q ( 1 f s + d ) L ( − r s → f s z s ( f s + d ) )
B 2 ( x , y ; r s → , z s ) = B * Q ( 1 d 12 ) ⋅ Q ( − 1 2 f ) * Q ( 1 f ) * Q ( 1 d 24 )
B 2 ( x , y ; r s → , z s ) = [ A s c ′ ( r s → , z s ) L ( − r s → z s ) Q ( 1 f s ) * Q ( 1 d 12 ) ⋅ Q ( − 1 2 f ) * Q ( 1 2 f ) ⋅ Q ( − 1 f ) * Q ( 1 d 24 ) ]
B 2 ( x , y ; r s → , z s ) = [ A s c ′ ( r s → , z s ) L ( − r s → f s z s ( f s + d 12 ) ) Q ( 1 f s + d 12 ) ] ⋅ Q ( − 1 f ) * Q ( 1 2 f ) ⋅ Q ( − 1 f ) * Q ( 1 d 24 )
B 2 ( x , y ; r s → , z s ) = [ A s c ′ ( r s → , z s ) L ( − r s → f s z s ( f s + d 12 ) ) Q ( f − f s − d 12 f ( f s + d 12 ) ) ] * ( Q ( 1 2 f ) ⋅ Q ( − 1 f ) * Q ( 1 d 24 )
B 2 ( x , y ; r s → , z s ) = [ A s c ′ ( r s → , z s ) L ( a ) Q ( 1 2 f ) ] * Q ( 1 2 f ) ⋅ Q ( − 1 f ) * Q ( 1 d 24 )
B 2 ( x , y ; r s → , z s ) = [ A s c ′ ( r s → , z s ) L ( a b a + 2 f ) Q ( 1 b + 2 f ) ] ⋅ Q ( − 1 f ) * Q ( 1 d 24 )
B 2 ( x , y ; r s → , z s ) = [ A s c ′ ( r s → , z s ) L ( a b a + 2 f ) Q ( − ( b + f ) f ( b + 2 f ) ) ] * Q ( 1 d 24 )
B 2 ( x , y ; r s → , z s ) = [ A s c ′ ( r s → , z s ) L ( E ) Q ( 1 F ) ] * Q ( 1 d 24 )
B 2 ( x , y ; r s → , z s ) = A s c ′ ( r s → , z s ) L ( E F F + d 24 ) Q ( 1 F + d 24 )
I ( x , y ; r s → , z s ) = | B 1 + B 2 | 2
I ( x , y ; r s → , z s ) = A s 2 ( c 1 2 + c 2 2 ) + B 1 B 2 * + B 2 B 1 *
H ( x , y ) = ∭ I ( x ,   y ; r s → , Z s ) d x s d y s d z s

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