Abstract

Fresnel Incoherent Correlation Holography (FINCH) allows digital reconstruction of incoherently illuminated objects from intensity records acquired by a Spatial Light Modulator (SLM). The article presents wave optics model of FINCH, which allows analytical calculation of the Point Spread Function (PSF) for both the optical and digital part of imaging and takes into account Gaussian aperture for a spatial bounding of light waves. The 3D PSF is used to determine diffraction limits of the lateral and longitudinal size of a point image created in the FINCH set-up. Lateral and longitudinal resolution is investigated both theoretically and experimentally using quantitative measures introduced for two-point imaging. Dependence of the resolving power on the system parameters is studied and optimal geometry of the set-up is designed with regard to the best lateral and longitudinal resolution. Theoretical results are confirmed by experiments in which the light emitting diode (LED) is used as a spatially incoherent source to create object holograms using the SLM.

© 2011 OSA

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References

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2011

2010

2008

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

2007

2006

2005

2003

2001

Abookasis, D.

Allan, V. J.

D. J. Stephens and V. J. Allan, “Light microscopy techniques for live cell imaging,” Science 300(5616), 82–86 (2003).
[CrossRef] [PubMed]

Brooker, G.

El Maghnouji, A.

Foster, R.

Indebetouw, G.

Itoh, M.

Katz, B.

Li, Y.

Rosen, J.

Saleh, B. E. A.

B. E. A. Saleh and M. C. Teich, Fundamentals of Photonics (J. Wiley, 1991).
[CrossRef]

Sando, Y.

Siegel, N.

Stephens, D. J.

D. J. Stephens and V. J. Allan, “Light microscopy techniques for live cell imaging,” Science 300(5616), 82–86 (2003).
[CrossRef] [PubMed]

Teich, M. C.

B. E. A. Saleh and M. C. Teich, Fundamentals of Photonics (J. Wiley, 1991).
[CrossRef]

Van Aert, S.

Van Dyck, D.

Wang, V.

Wulich, D.

Yatagai, T.

Appl. Opt.

J. Opt. Soc. Am. A

Nat. Photonics

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

Opt. Express

Opt. Lett.

Science

D. J. Stephens and V. J. Allan, “Light microscopy techniques for live cell imaging,” Science 300(5616), 82–86 (2003).
[CrossRef] [PubMed]

Other

B. E. A. Saleh and M. C. Teich, Fundamentals of Photonics (J. Wiley, 1991).
[CrossRef]

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Figures (9)

Fig. 1
Fig. 1

Illustration of the basic principle of FINCH.

Fig. 2
Fig. 2

Comparison of 3D Point Spread Function of FINCH imaging obtained by (a) experiment and (b) simulation model for parameters f 0 = 200 mm, fd = 750 mm, Δ1 = 250 mm, and Δ2 = 600 mm.

Fig. 3
Fig. 3

Dependence of transverse resolution Δr and longitudinal resolution Δz on the ratio Δ2/fd for FINCH set-up using the collimating lens (fd = 750 mm, Δ1 = 250 mm, and f 0 = 100 mm, - - - , f 0 = 150 mm, —, f 0 = 200 mm, -.-.-).

Fig. 4
Fig. 4

Dependence of the transverse resolution Δr and the longitudinal resolution Δz on the ratio Δ2 /fd for lensless FINCH (fd = 750 mm, z 0 = -50 mm, - - - , z 0 = −75 mm, —, and z 0 = −100 mm, -.-.-).

Fig. 5
Fig. 5

Experimental set-up for measurement of transversal and longitudinal resolution of FINCH imaging.

Fig. 6
Fig. 6

Experimental determination of the lateral visibility: (a) Dependence of visibility Vx on lateral separation distance Δx of two-point object for different parameters Δ2/fd . (b) Separation distance Δx corresponding to the visibility Vx = 0.8 in dependence on the ratio Δ2/fd .

Fig. 7
Fig. 7

Transverse image spot reconstructed from holograms recorded for different lateral separation distances of a two-point source, and different positions of the CCD.

Fig. 8
Fig. 8

Experimental determination of the longitudinal visibility: (a) Dependence of visibility Vz on longitudinal separation distance Δz of two-point object for different parameters Δ2/fd . (b) Separation distance Δz related to the longitudinal visibility Vz = 0.8 in dependence on the ratio Δ2/fd .

Fig. 9
Fig. 9

Intensity distribution in the (x′, z′) plane reconstructed with different longitudinal separation distances Δz of a two-point source. Recording of holograms was carried out for the position of the CCD camera Δ2 = 0.8 fd .

Equations (58)

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t j = a + b exp [ i ( θ ϑ j ) ] , j = 1 , 2 , 3 ,
U j = U r + U s j = a r exp ( i Φ r ) + a s exp [ i ( Φ s ϑ j ) ] ,
Φ j = k z j [ 1 + ( x c x j ) 2 + ( y c y j ) 2 2 z j 2 ] , j = r , s ,
I j = a r 2 + a s 2 + 2 a r a s cos ( Φ s Φ r ϑ j ) . j = 1 , 2 , 3 .
T = I 1 [ exp ( i ϑ 3 ) exp ( i ϑ 2 ) ] + I 2 [ exp ( i ϑ 1 ) exp ( i ϑ 3 ) ] + I 3 [ exp ( i ϑ 2 ) exp ( i ϑ 1 ) ] .
T = A exp [ i ( Φ s Φ r ) ] ,
T = A exp ( i Ω 0 ) exp { i k 2 f l [ ( x c X ) 2 + ( y c Y ) 2 ] } .
f l = ( 1 F ) [ ( 1 F ) f d Δ 2 ] ,
F = Δ 2 ( z 0 + f 0 ) z 0 f 0 Δ 1 ( z 0 + f 0 ) ,
X = x 0 m , Y = y 0 m ,
m = f 0 Δ 2 z 0 ( f 0 Δ 1 ) f 0 Δ 1 .
Ω 0 = k ( Δ 2 + f d F ) [ Δ 2 2 F f 0 2 F 2 ( z 0 + f 0 ) 2 ( x 0 2 + y 0 2 ) ] .
U ( r ) = Q ( x c , y c ) T ( x c , y c ) h ( x x c , y y c , z ) d x c d y c ,
U ( r ) = i A λ z exp ( i Γ ) Q ( x c , y c ) exp [ i k ( x c 2 + y c 2 2 ( 1 f l 1 z ) ] × exp { i 2 π [ x c X ¯ + y c Y ¯ ] } d x c d y c ,
Γ = Ω 0 k z + k X 2 + Y 2 2 f l k x i 2 + y i 2 2 z ,
X ¯ = 1 λ ( x z X f l ) , Y ¯ = 1 λ ( y z Y f l ) ,
U ( x , y , f l ) = i A λ f l exp ( i Γ ) δ ( X ¯ , Y ¯ ) .
d m d z 0 = ( Δ 1 f 0 ) m 2 f 0 Δ 2 .
α = f 0 2 [ 2 f d ( 1 F ) Δ 2 ] F 2 Δ 2 ( z 0 + f 0 ) 2 ,
f l F lim z 0 f 0 { f l } = f d Δ 2 ,
m F lim z 0 f 0 { m } = Δ 2 f 0 ,
α F lim z 0 f 0 { α } = Δ 2 2 f d f 0 m F .
f l L lim f 0 { f l } = ( 1 m L ) [ ( 1 m L ) f d Δ 2 ] ,
m L lim f 0 { m } = Δ 2 z 0 ,
α L lim f 0 { α } = [ 2 f d ( 1 m L ) Δ 2 ] m L 2 Δ 2 .
Q = exp ( x c 2 + y c 2 Δ ρ c 2 ) ,
Δ ρ c = min { ρ C C D , Δ ρ r , Δ ρ N } ,
U ( r ) = A exp ( i Ω 0 ) u 0 ( r ) ,
u 0 ( r ) = i π λ z q exp [ m 2 ( x 0 2 + y 0 2 ) γ i π ( x 2 + y 2 ) λ z ] × exp { π 2 q [ ( x λ z i m x 0 γ π ) 2 + ( y λ z i m y 0 γ π ) 2 ] } ,
γ = 1 Δ ρ c 2 i π λ z ,
q = 1 Δ ρ c 2 + i π λ ( 1 z 1 f l ) .
I N ( r ) = | U ( r ) | 2 | U ( x 0 m , y 0 m , f l ) | 2 .
I N ( r ) = exp ( 2 π 2 N A 2 r 2 λ 2 ) ,
Δ r = λ π N A .
D = | U ( 0 , 0 , f l + Δ z ) | 2 | U ( 0 , 0 , f l ) | 2 .
D = [ ( 1 + Δ z f l ) 2 + Δ z 2 N A 2 Δ r 2 ] 1 .
Δ z = ± λ π N A 2 1 D 1 .
Δ ρ r = ρ S L M f d ( f d Δ 2 ) ,
Δ ρ N = ( f d Δ 2 ) λ 2 Δ x C C D ,
2 Δ r = 2 λ π N A , 2 Δ z = 5 Δ r N A .
Δ r = max { Δ r 0 , f d Δ 2 Δ r 0 } ,
Δ z = f d 2 Δ 2 | Δ 2 2 f d | Δ z 0 ,
Δ r = λ | z 0 | f l L π ρ C C D Δ 2 .
Δ 2 = z 0 ( 1 + z 0 f d ) 1 / 2 .
Δ r = λ π N A ,
2 α L f l L Δ 2 f l L α L Δ 2 = 0.
T = A j = 1 2 exp ( i Ω j ) exp { i k 2 f l j [ ( x c X j ) 2 + ( y c Y j ) 2 ] } .
U T P ( r ) = A j = 1 2 exp ( i Ω j ) u j ( r ) .
I T P ( r ) = I 1 + I 2 + 2 I 1 I 2 cos ( Δ ϕ ) ,
I j ( r ) = | A | 2 u j ( r ) | 2 ,
Δ φ ( r ) = Ω 1 Ω 2 + κ 1 κ 2 ,
κ j = arctan { u j ( r ) } { u j ( r ) } , j = 1 , 2 .
V x = max { I x peak I x centre I x peak + I x centre , 0 } ,
I x peak = 1 2 { I T P [ m ( x 0 + Δ x / 2 ) , 0 , z ] + I T P [ m ( x 0 Δ x / 2 ) , 0 , z ] } ,
I x centre = I T P ( m x 0 , 0 , z ) .
V z = max { I z peak I z centre I z peak + I z centre , 0 } ,
I z peak = 1 2 { I T P [ 0 , 0 , α ( z 0 + Δ z / 2 ) ] + I T P [ 0 , 0 , α ( z 0 Δ z / 2 ) ] } ,
I z centre = I T P [ 0 , 0 , α z 0 ] .

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