Abstract

Fresnel Incoherent Correlation Holography (FINCH) can faithfully reproduce objects above and below the optical plane of focus. However, as in optical imaging, the transverse magnification and optimal reconstruction depth changes based on the longitudinal distance of objects from the focal plane of the input lens with the exception that objects above and below the focal plane are in focus with FINCH and out of focus by standard optical imaging. We have analyzed these effects both theoretically and experimentally for two configurations of a FINCH fluorescence microscopy system. This information has been used to reconstruct a test planar object placed above or below the optical plane of focus with high dimensional and image fidelity. Because FINCH is inherently a super-resolving system, this advance makes it possible to create super-resolved 3D images from FINCH holograms.

© 2012 OSA

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References

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2012

2011

2008

J. Rosen and G. Brooker, “Non-scanning motionless fluorescence three-dimensional holographic microscopy,” Nat. Photonics2(3), 190–195 (2008).
[CrossRef]

2007

1997

Bouchal, P.

Bouchal, Z.

Brooker, G.

Chmelík, R.

Kapitán, J.

Katz, B.

Kelner, R.

Kim, M. K.

Lai, X.

Lv, X.

Rosen, J.

Siegel, N.

Wang, V.

Yamaguchi, I.

Zeng, S.

Zhang, T.

Zhao, Y.

Zhou, Z.

Nat. Photonics

J. Rosen and G. Brooker, “Non-scanning motionless fluorescence three-dimensional holographic microscopy,” Nat. Photonics2(3), 190–195 (2008).
[CrossRef]

Opt. Express

Opt. Lett.

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Figures (9)

Fig. 1
Fig. 1

Configuration 1 FINCH with the object (a) at the focus of the collimating lens, (b) above the focus of the collimating lens and (c) below the focus of the collimating lens. The diagram describes a static FINCH system operating on an object with significant depth above and below the focus of the collimating lens, thus f0, d, fd1 and zh remain constant over the three sub-diagrams.

Fig. 2
Fig. 2

A generalized diagram of FINCH showing the ability to use two spherical waves (fd1 and fd2) to form the FINCH hologram (Configuration 2). If fd1 goes to zh/2 and fd2 goes to infinity (the plane wave in Fig. 1), the system is operating with one plane wave and one spherical wave (Configuration 1).

Fig. 3
Fig. 3

Schematic representation of polarizations of interfering beams in two FINCH configurations. (a) Configuration 1, with one spherical wave and one plane wave. Only one lens pattern is displayed on the SLM; two polarizers are necessary to split the incoming beam and recombine it to achieve interference while maintaining complete coincidence of both waves. (b) Configuration 2, with two spherical waves. Two lens patterns are displayed on randomly selected pixels on the SLM, focusing the waves to different focal lengths. Only one polarizer is required to align the incoming waves polarization with the SLM.

Fig. 4
Fig. 4

The best focused reconstructed Configuration 1 FINCH (linear reconstruction) images from selected values of zs-f0. The yellow outline shows Group 8, Element 1, which were the features measured to determine the magnification in the series of holograms taken with the Nikon objective. The dashed squares on the reconstructed images show that in reference to images calculated from the hologram captured at the focus of the objective (center image), the image above (top left) and below (bottom right) the optical plane of focus from the holographic reconstructions were either smaller or larger.

Fig. 5
Fig. 5

Performance of the FINCH microscope with Configuration 1, using the Nikon 20x objective. (a) The reconstruction depth zrec of the best focused reconstructed image from the experimental holograms plotted as a function of zs-f0, the distance above or below the focus of the objective, plotted against a theoretical curve of zr based on Eq. (3) and using our experimental parameters as discussed in the text. (b) The transverse magnification MT of Element 1 of Group 8 of the USAF pattern, measured vertically and horizontally in the best reconstructed FINCH images and averaged, as a function of zs-f0. For comparison, a theoretical curve of MT is plotted, based on Eq. (4) and using our experimental parameters as discussed in the text. (c) The visibilities of the horizontal Group 9 Element 3 features of the USAF pattern. The dashed line is the level of the visibility of those features in standard optical fluorescence microscopy.

Fig. 6
Fig. 6

3D views (by direct volume rendering) of stacks of reconstructed Configuration 1 FINCH images of the USAF pattern taken at zs ranging from 30 µm above f0 to f0.The left image is the 3D view of images as calculated by Eq. (6), without any size adjustments. The right image is the 3D view of reconstructed images that were resampled based on the ratio of MT:MT0 as discussed in the text, and registered to lie directly over each other creating a clear well resolved 3D image. Notice that without correction, the smallest features in group 9 patterns are severely distorted, limiting resolution of 3D images.

Fig. 7
Fig. 7

Cropped sections from linear Configuration 2 FINCH reconstructions showing the smallest USAF groups. Images are from dual-lens pattern FINCH holograms taken at various locations with respect to the objective focus and with various spacings sfac between the lens patterns.

Fig. 8
Fig. 8

FINCH microscopy with two spherical waves. (a) The reconstruction depth zrec of the best focused reconstructed images from the experimental holograms (circles, squares, triangles) is plotted as a function of zs-f0 and shown against theoretical curves (solid lines) of zr for that sfac based on Eq. (7) and using our experimental parameters as discussed in the text. (b) The transverse magnification MT of Element 2 of Group 6 of the USAF pattern, showing the average of the horizontal and vertical measurements, as a function of zs-f0. For comparison, a theoretical curve of MT is plotted, based on Eq. (4) and using our experimental parameters as discussed in the text. (c) The visibilities of the horizontal Group 9 Element 3 features of the USAF pattern. The dashed line is the level of the visibility of those features in standard optical fluorescence microscopy.

Fig. 9
Fig. 9

NAH × MT as a function of zs-f0 for FINCH with a plane and spherical wave (Configuration 1) and two spherical waves (Configuration 2) with various spacing factors sfac for two lens patterns displayed on the SLM.

Equations (10)

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u 0 ( x 0 , y 0 )=( C 1 ( r ¯ s )L( r ¯ s z s )Q( 1 z s )Q( 1 f 0 )Q( 1 d ) ) ×[ Bexp( iθ )Q( 1 f d1 )+ B Q( 1 f d2 ) ]Q( 1 z h ),
I p (x,y)= C 2 + C 3 ( r ¯ s )L( r ¯ r z r )Q( 1 z r )exp(iθ)                     + C 3 * ( r ¯ s )L( r ¯ r z r )Q( 1 z r )exp(iθ),
z r ={ ±( f d1 z h ),for   z s = f 0     f d2 ±( ( f 1 + z h )( f e +d+ z h ) f 1 f e d ),for   z s f 0     f d2
M T =| x r x s |={ z h f 0 , for   z s = f 0    f d2 f e z h z s ( f e +d) , for   z s f 0    f d2
H F (x,y)=    H 1 (x,y)[ exp( ±i θ 3 )exp( ±i θ 2 ) ] + H 2 (x,y)[ exp( ±i θ 1 )exp( ±i θ 3 ) ] + H 3 (x,y)[ exp( ±i θ 2 )exp( ±i θ 1 ) ].
s(x,y, z rec )= H F (x,y)exp[ iπ λ z rec ( x 2 + y 2 ) ],
z r ={ ± ( z h f d1 )( z h f d2 ) f d1 f d2 , for  z s = f 0    f d2 ±( z f1 z f2 z d 2 ( f d1 f d2 ) ), for  z s f 0    f d2
exp[ iπ λa ( x 2 + y 2 )+iθ ],
s fac =( z h / f d1 )1=1( z h / f d2 ).
R n =| f dn (eff) z h f dn (eff) | R 0 ,       with         f dn (eff) = f dn ( d+ f e ) d f dn + f e ,

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