Abstract

Fourier incoherent single channel holography (FISCH) is a method for recording spatially incoherent digital Fourier holograms. We present a general design of enhanced FISCH with a smaller optical path difference between interfering beams, when compared to our initial design [Opt. Lett. 37, 3723 (2012)]. This reduction enables a proper system operation with a wider bandwidth. Potential resolution enhancement of the images reconstructed from the FISCH holograms consequentially follows.

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References

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  1. R. Kelner and J. Rosen, “Spatially incoherent single channel digital Fourier holography,” Opt. Lett.37(17), 3723–3725 (2012).
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  13. M. Born and E. Wolf, Principles of optics (Cambridge, 1999), Chap. 4.4.5, p. 176.
  14. E. Wolf, Introduction to the Theory of Coherence and Polarization of Light (Cambridge, 2007).
  15. P. Hariharan, Optical holography principles, techniques, and applications (Cambridge, 1996), Chap. 15, p. 247 and Chap. 17, p. 296.
  16. J. A. Neff, R. A. Athale, and S. H. Lee, “Two-dimensional spatial light modulators: a tutorial,” Proc. IEEE78(5), 826–855 (1990).
    [CrossRef]
  17. G. Pedrini, H. Li, A. Faridian, and W. Osten, “Digital holography of self-luminous objects by using a Mach-Zehnder setup,” Opt. Lett.37(4), 713–715 (2012).
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  18. O. Bouchal and Z. Bouchal, “Wide-field common-path incoherent correlation microscopy with a perfect overlapping of interfering beams,” J. Europ. Opt. Soc. – Rap. Pub.8, 13011 (2013).

2013

2012

2011

2010

B. Katz and J. Rosen, “Super-resolution in incoherent optical imaging using synthetic aperture with Fresnel elements,” Opt. Express18(2), 962–972 (2010).
[CrossRef] [PubMed]

1997

1990

J. A. Neff, R. A. Athale, and S. H. Lee, “Two-dimensional spatial light modulators: a tutorial,” Proc. IEEE78(5), 826–855 (1990).
[CrossRef]

1970

Athale, R. A.

J. A. Neff, R. A. Athale, and S. H. Lee, “Two-dimensional spatial light modulators: a tutorial,” Proc. IEEE78(5), 826–855 (1990).
[CrossRef]

Bouchal, O.

O. Bouchal and Z. Bouchal, “Wide-field common-path incoherent correlation microscopy with a perfect overlapping of interfering beams,” J. Europ. Opt. Soc. – Rap. Pub.8, 13011 (2013).

Bouchal, Z.

O. Bouchal and Z. Bouchal, “Wide-field common-path incoherent correlation microscopy with a perfect overlapping of interfering beams,” J. Europ. Opt. Soc. – Rap. Pub.8, 13011 (2013).

Brooker, G.

Bryngdahl, O.

Faridian, A.

Fu, L.

Katz, B.

Kelner, R.

Kim, M. K.

Lai, X.

Lee, S. H.

J. A. Neff, R. A. Athale, and S. H. Lee, “Two-dimensional spatial light modulators: a tutorial,” Proc. IEEE78(5), 826–855 (1990).
[CrossRef]

Li, H.

Lohmann, A.

Lv, X.

Naik, D. N.

Neff, J. A.

J. A. Neff, R. A. Athale, and S. H. Lee, “Two-dimensional spatial light modulators: a tutorial,” Proc. IEEE78(5), 826–855 (1990).
[CrossRef]

Osten, W.

Pedrini, G.

Rosen, J.

Siegel, N.

Wang, V.

Yamaguchi, I.

Yuan, J.

Zeng, S.

Zhang, T.

Adv. Opt. Technol.

J. Rosen and G. Brooker, “Fresnel incoherent correlation holography (FINCH) – A review of research,” Adv. Opt. Technol.1, 151–169 (2012).

Appl. Opt.

J. Europ. Opt. Soc. – Rap. Pub.

O. Bouchal and Z. Bouchal, “Wide-field common-path incoherent correlation microscopy with a perfect overlapping of interfering beams,” J. Europ. Opt. Soc. – Rap. Pub.8, 13011 (2013).

Opt. Express

B. Katz and J. Rosen, “Super-resolution in incoherent optical imaging using synthetic aperture with Fresnel elements,” Opt. Express18(2), 962–972 (2010).
[CrossRef] [PubMed]

Opt. Express

Opt. Lett.

Proc. IEEE

J. A. Neff, R. A. Athale, and S. H. Lee, “Two-dimensional spatial light modulators: a tutorial,” Proc. IEEE78(5), 826–855 (1990).
[CrossRef]

Other

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

M. Born and E. Wolf, Principles of optics (Cambridge, 1999), Chap. 4.4.5, p. 176.

E. Wolf, Introduction to the Theory of Coherence and Polarization of Light (Cambridge, 2007).

P. Hariharan, Optical holography principles, techniques, and applications (Cambridge, 1996), Chap. 15, p. 247 and Chap. 17, p. 296.

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Figures (5)

Fig. 1
Fig. 1

Schematics of two FISCH recorder designs: RC, resolution chart; SLM, spatial light modulator; P1 and P2, polarizers; Lo and Lr, lenses. In (a) the polarization sensitive axes of the SLMs are perpendicular to each other, whereas in (b) they coincide with one another (i.e., in parallel). The symbols oe-21-17-20131-i001, oe-21-17-20131-i002 and oe-21-17-20131-i003 are polarization directions parallel, perpendicular and at 45° to the plane of the page, respectively.

Fig. 2
Fig. 2

Experimental setup of FISCH: RC, resolution chart; SLM1 and SLM2, spatial light modulators; P1 and P2, polarizers; Lo, Lr, Lc,1 and Lc,2, lenses; M1 and M2, mirrors.

Fig. 3
Fig. 3

FISCH reconstructions: (a) top left, at the Fourier plane, where the image of the upper resolution chart (RC) and its twin image are in focus; (b) top center, at the front of the Fourier plane, where only the image of the lower RC is in focus; (c) top right, at the back of the Fourier plane, where only the twin image of the lower RC is in focus. (a) is obtained by a 2D inverse Fourier transform of the final hologram, while (b) and (c) are obtained by a Fresnel propagation from the Fourier plane (a), backward in case of (b), or forward in case of (c). (d), bottom left, and (e), bottom center, are FINCH equivalents of (a) and (b), respectively. The blue curves in (f)-(i), bottom right, represent the average cross-section of the area marked by a green rectangles in (a),(b),(d), and (e), respectively. EV is the estimated visibility value, calculated as the average value of the visibility curve (in black), which was extracted from the upper (green curves) and lower (red curves) envelopes of the average cross section (blue curve).

Fig. 4
Fig. 4

Effect of bandwidth and OPD on FISCH (a)-(d) and FINCH (e)-(h) resolution: (a),(e) with fr = 100cm and a 10nm FWHM light source, where all details of the RC are clearly visible; (b),(f) with fr = 100cm and a 80nm FWHM light source, where the reconstruction quality is diminished, but most details of the RC are still visible; (c),(g) with fr→∞ and a 10nm FWHM light source, where most details of the RC are clearly visible but less clear than (a),(e); (d),(h) with fr→∞ and a 80nm FWHM light source, where most details of the RC are lost. The blue curve in each sub-figure represents the average cross-section of the area marked by a green rectangle. EV is the estimated visibility value, calculated as the average value of the visibility curve (in black), which was extracted from the upper (green curves) and lower (red curves) envelopes of the average cross section (blue curve). Reconstruction results are shown to match in size.

Fig. 5
Fig. 5

Schematic of FISCH for finding the OPD at point E in the hologram plane due to a single point source object located at the front focal plane of Lo.

Tables (1)

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Table 1 Characteristics of Various Spatially Incoherent Holography Systems

Equations (9)

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I ( x , y ; r s , z s ) = | T ( x , y ; r s , z s ) Q ( 1 f o ) Q ( 1 d 1 ) Q ( 1 f r ) Q ( 1 d 2 ) Q ( 1 f 1 ) Q ( 1 h 1 + h 2 ) + T ( x , y ; r s , z s ) Q ( 1 f o ) Q ( 1 d 1 ) Q ( 1 f r ) Q ( 1 d 2 + h 1 ) Q ( 1 f 2 ) Q ( 1 h 2 ) | 2 ,
I ( x , y ; r s , z s ) = | A s b 1 L ( r e z e f e , 1 f e , 1 + h 1 + h 2 ) Q ( 1 f e , 1 + h 1 + h 2 ) + A s b 2 L ( r e z e + h 1 f e , 2 f e , 2 + h 2 ) Q ( 1 f e , 2 + h 2 ) | 2 ,
H ( x , y ) = I ( x , y ; r s , z s ) d x s d y s d z s .
I ( x , y ; r s , f o ) = ( | b 1 | 2 + | b 2 | 2 ) I s + [ b 1 b 2 * I s L ( 2 f r r s f o 1 z 2 h 1 ) + c . c . ] ,
s ( x , y , z r e c ) = ( v [ 1 λ f r e c ] 1 { H ( x , y ) } ) Q ( 1 z r e c ) ,
M T = 2 f r e c f r f o ( z 2 h 1 )
Δ = 1.22 λ f r e c R H M T = 0.61 λ f o R S L M 1 f r d 2 f r = 0.61 λ f o R o = 0.61 λ N A ,
Δ z min = z 2 λ f o z 2 8 Δ p | r s | max f r + 0.5 ,
δ = | C E ¯ F D ¯ D E ¯ | = | D A ¯ D E ¯ E A ¯ | ,

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