Abstract

Fresnel incoherent correlation holography (FINCH) records holograms under incoherent illumination. FINCH was implemented with two focal length diffractive lenses on a spatial light modulator (SLM). Improved image resolution over previous single lens systems and at wider bandwidths was observed. For a given image magnification and light source bandwidth, FINCH with two lenses of close focal lengths yields a better hologram in comparison to a single diffractive lens FINCH. Three techniques of lens multiplexing on the SLM were tested and the best method was randomly and uniformly distributing the two lenses. The improved quality of the hologram results from a reduced optical path difference of the interfering beams and increased efficiency.

©2012 Optical Society of America

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References

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2011 (3)

2010 (2)

2008 (1)

J. Rosen and G. Brooker, “Non-scanning motionless fluorescence three-dimensional holographic microscopy,” Nat. Photonics 2(3), 190–195 (2008).
[Crossref]

2007 (2)

2003 (1)

1994 (1)

J. F. Heanue, M. C. Bashaw, and L. Hesselink, “Volume holographic storage and retrieval of digital data,” Science 265(5173), 749–752 (1994).
[Crossref] [PubMed]

1992 (1)

1989 (1)

1986 (1)

Bashaw, M. C.

J. F. Heanue, M. C. Bashaw, and L. Hesselink, “Volume holographic storage and retrieval of digital data,” Science 265(5173), 749–752 (1994).
[Crossref] [PubMed]

Bouchal, P.

Bouchal, Z.

Brooker, G.

Cai, L. Z.

Chmelík, R.

Diep, J.

Guo, C.-S.

Heanue, J. F.

J. F. Heanue, M. C. Bashaw, and L. Hesselink, “Volume holographic storage and retrieval of digital data,” Science 265(5173), 749–752 (1994).
[Crossref] [PubMed]

Hesselink, L.

J. F. Heanue, M. C. Bashaw, and L. Hesselink, “Volume holographic storage and retrieval of digital data,” Science 265(5173), 749–752 (1994).
[Crossref] [PubMed]

Himes, G. S.

Kapitán, J.

Katz, B.

Liu, H.-K.

Mait, J. N.

Mok, F.

Psaltis, D.

Rong, Z.-Y.

Rosen, J.

Shamir, J.

Shiv, L.

Siegel, N.

Stein, J.

Wang, H.-T.

Wang, V.

Wang, Y.

Wulich, D.

Appl. Opt. (3)

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

Nat. Photonics (1)

J. Rosen and G. Brooker, “Non-scanning motionless fluorescence three-dimensional holographic microscopy,” Nat. Photonics 2(3), 190–195 (2008).
[Crossref]

Opt. Express (5)

Opt. Lett. (2)

Science (1)

J. F. Heanue, M. C. Bashaw, and L. Hesselink, “Volume holographic storage and retrieval of digital data,” Science 265(5173), 749–752 (1994).
[Crossref] [PubMed]

Other (3)

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

J. W. Goodman, Statistical Optics (Wiley, 1985).

E. Wolf, Introduction to the theory of coherence and polarization of light (Cambridge, 2007).

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Figures (7)

Fig. 1
Fig. 1

FINCH with two diffractive lenses created by the SLM. L1-collimating lens. SLM creates two lenses with focal length f1 and f2 with image focus at Image 1 and Image 2, respectively.

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Fig. 2
Fig. 2

Three different methods of lens multiplexing: (a) random pixel method, (b) phase sum method and (c) random ring method. Magnified views of each pattern are shown in panels d, e and f below the complete pattern for each method. Only a single phase pattern (0°) is shown, but in practice, three phase patterns of 0°, 120° or 240° phase shift are sequentially displayed on the SLM during capture of the three holograms for each method.

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Fig. 3
Fig. 3

Experimental setup. POL-Polarizer, BPF-Bandpass filter.

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Fig. 4
Fig. 4

Best in-focus reconstructed images from holograms captured with (a) random pixel method, (b) phase sum method and (c) random ring method.

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Fig. 5
Fig. 5

The reference image of the input object.

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Fig. 6
Fig. 6

MSE versus the distance between the two focuses calculated on the images of Fig. 4 in comparison with the reference image shown in Fig. 5.

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Fig. 7
Fig. 7

Images which were taken by dual lens imaging system. The input lens is always L1 with focal lens of fo = 25cm. the output lens is a diffractive lens with the focal length of (a) 40cm, (b) 64.9cm (c) 45cm and (d) 55cm. The left-hand image in each group was recorded with the random pixel method, the central was recorded with the phase sum method, and the right-hand image in each group was recorded with the random ring method.

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Equations (27)

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I H (u,v)=| I s C( r ¯ s )L( − r ¯ s f o )Q( 1 f o )Q( −1 f o )*Q( 1 d )   ×[ C 1 Q( −1 f 1 )+ C 2 exp(iθ)Q( −1 f 2 ) ]*Q( 1 z h )P( R H ) | 2 ,
H( ρ ¯ )=C' I s P( R H )L( r ¯ r z r )Q( 1 z r ),
z r =±| ( z h − f 1 )( z h − f 2 ) f 1 − f 2 |.
r ¯ r =( x r , y r )= r ¯ s z h f o .
h F ( r ¯ )=C' I s ν[ 1 λ z r ]ℱ{ L( r ¯ r z r )P( R H ) } =C'' I s Jinc( 2π R H λ z r ( x− M T x s ) 2 + ( y− M T y s ) 2 ),
C ″
ℱ
ν
ν[ a ]f( x )=f( ax )
r ¯ =( x,y )
Jinc
Jinc (r)=  J 1 (r)/r
J 1 (r)
Δ= 1.22λ z r R H M T = 1.22λ z r f o R H z h
R H = R o z h − f 1 f 1 = R o f 2 − z h f 2 ,
z h = 2 f 1 f 2 f 1 + f 2
Δ= 0.61λ f o R o = 0.61λ NA .
δ max ≤ C o Δν = λ 2 Δλ ,
δ max =| BH ¯ − AH ¯ |= ( R o + R H ) 2 + z h 2 − ( R o − R H ) 2 + z h 2 .
δ max = z h [ ( R o f 1 ) 2 +1 − ( R o f 2 ) 2 +1   ].
δ max ≅ R o 2 f 1 f 2 Δf,
Δ f max = δ max f 1 f 2   R o 2 ≅ 1 Δλ ( λ M T f o R o ) 2 .
Δ f min = π ( M T O max ) 4 128λ 3 .
tanφ=tan( tan −1 R o + R H z h + tan −1 R o − R H z h )≅ 2 R o z h ≤ λ 2 δ c ,
z h,min = 4 R o λ max{ δ c , δ s }.
MSE= 1 M⋅K ∑ i=1 M ∑ j=1 K [ P( i,j )−ξ⋅ P ˜ ( i,j ) ]  2 ,
ξ= [ ∑ i=1 M ∑ j=1 K P( i,j )⋅ P ˜ ( i,j ) ] / ∑ i=1 M ∑ j=1 K P ˜ ( i,j )⋅ P ˜ ( i,j ) .

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