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Compact and portable low-coherence interferometer with off-axis geometry for quantitative phase microscopy and nanoscopy

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Abstract

We present a simple-to-align, highly-portable interferometer, which is able to capture wide-field, off-axis interference patterns from transparent samples under low-coherence illumination. This small-dimensions and low-cost device can be connected to the output of a transmission microscope illuminated by a low-coherence source and measure sub-nanometric optical thickness changes in a label-free manner. In contrast to our previously published design, the τ interferometer, the new design is able to fully operate in an off-axis holographic geometry, where the interference fringes have high spatial frequency, and the interference area is limited only by the coherence length of the source, and thus it enables to easily obtain high-quality quantitative images of static and dynamic samples. We present several applications for the new design including nondestructive optical testing of transparent microscopic elements with nanometric thickness and live-cell imaging.

©2013 Optical Society of America

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Supplementary Material (1)

Media 1: MPEG (148 KB)     

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Figures (11)

Fig. 1
Fig. 1 Schematic system diagrams of: (a) the conventional τ interferometer [20]; (b) the off-axis τ interferometer. L1,L2 – lenses in a 4f configuration, BS – beam splitter, M1,M2 – mirrors, P – pinhole, RR – retro-reflector made of a two-mirror construction.
Fig. 2
Fig. 2 Explanation for the retro-reflector (RR) operation using ray tracing of the sample and the reference beams in the off-axis τ interferometer, as it would be seen if they were on the same optical axis.
Fig. 3
Fig. 3 The off-axis τ interferometer, connected in the output of an inverted microscope, which is illuminated by a tunable low-coherence source. MO – microscope objective, L0,L1,L2 – lenses, where L1 and L2 are in a 4f configuration, BS – beam splitter, M,M2 – mirrors, P – pinhole, RR – two-mirror retro-reflector. Inset: Wide-field off-axis interferogram of red blood cells obtained with the system, and its cross-section at the location indicated by the white line.
Fig. 4
Fig. 4 OPD sensitivities in a dry sample: (a) Spatial sensitivity: OPD standard deviation across a single OPD map for each of the 150 OPD maps. (b) Temporal sensitivity: OPD standard deviation for each diffraction-limited spot across the 150 OPD maps.
Fig. 5
Fig. 5 OPD maps of a volume phase holographic grating obtained under low-coherence illumination by: (a) the off-axis τ interferometer; and (b) the off-axis Mach-Zehnder interferometer.
Fig. 6
Fig. 6 SEM image of an element similar to our first lithographed phase target.
Fig. 7
Fig. 7 OPD maps of the first phase target created by FIB lithography, containing variable depths elements (see Fig. 6), as obtained using: (a) the off-axis τ interferometer with a low-coherence source; (b) the off-axis Mach-Zehnder interferometer with a low-coherence source; and (c) the off-axis Mach-Zehnder interferometer with a high-coherence source (HeNe laser).
Fig. 8
Fig. 8 OPD maps of the second phase target created by FIB lithography, containing variable depth elements, as obtained using: (a) the off-axis τ interferometer with a low-coherence source; (b) the off-axis Mach-Zehnder interferometer with a low-coherence source; and (c) the off-axis Mach-Zehnder interferometer with a high-coherence source (HeNe laser).
Fig. 9
Fig. 9 OPD and physical thickness maps of RBCs, obtained using a low-coherence source in: (a) the off-axis τ interferometer; and (b) the off-axis Mach-Zehnder interferometer. The standard deviation of the OPD and of the physical thickness maps for: (c) the off-axis τ interferometer; and (d) the off-axis Mach-Zehnder interferometer.
Fig. 10
Fig. 10 Measurements of Blepharisma organism swimming in water using the off-axis τ interferometer, demonstrating the system capabilities for quantitative imaging of fast dynamics on relatively large field of view due to its true off-axis configuration, and as opposed to the conventional τ interferometer [20]. See video in Media 1.
Fig. 11
Fig. 11 Schematics of the sample and immersion medium thicknesses and refractive indices.

Equations (11)

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θ=arctan(Δy/f),
I= | V s + V r | 2 = I s + I r + G +1 + G 1 .
G +1 = I s I r ×exp[ |OP D total | l c (x,y) ]×exp[ j 2π λ OP D total ]×exp[ j 2π λ ysin(θ) ],
OP D s (x,y)=[ n ¯ s (x,y) n m ]× h s (x,y),
n ¯ s (x,y)= 1 h s (x,y) 0 h s (x,y) n s (x,y,z)dz .
G +1 = V s * (t)× V r (t+τ)= I s I r ×exp[ | τ | τ c ]×exp[ j2π c λ τ ],
t 1 = d c ; t 2 = 1 c { [d h m (x,y)]+[ h m (x,y) h s (x,y)]× n m (x,y)+ h s (x,y)× n ¯ s (x,y) }; τ= t 2 t 1 = 1 c { h s (x,y)×[ n ¯ s (x,y) n m (x,y)]+ h m (x,y)×[ n m (x,y)1] },
OP D total (x,y)=cτ = h s (x,y)×[ n ¯ s (x,y) n m (x,y)]+ h m (x,y)×[ n m (x,y)1] =OP D s +OP D m ,
G +1 = I s I r ×exp[ | OP D total c | c l c ]×exp[ j2π c λ OP D total c ] = I s I r ×exp[ | OP D total l c | ]×exp[ j 2π λ OP D total ].
l c
G +1 = I r I s exp[ |OP D total | l c (x,y) ]×exp[ j 2π λ OP D total ]×exp[ j 2π λ ysin(θ) ],
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