Quantitative phase microscopy of biological samples using a

OPTICS LETTERS / Vol. 37, No. 11 / June 1, 2012
Quantitative phase microscopy of biological samples
using a portable interferometer
Natan T. Shaked
Department of Biomedical Engineering, Faculty of Engineering, Tel Aviv University, Tel Aviv 69978, Israel
Received January 19, 2012; revised March 21, 2012; accepted March 24, 2012;
posted March 27, 2012 (Doc. ID 161779); published May 30, 2012
This Letter presents the τ interferometer, a portable and inexpensive device for obtaining spatial interferograms of
microscopic biological samples without the strict stability and the highly coherent illumination that are usually
required for interferometric microscopy setups. The device is built using off-the-shelf optical elements and can
easily operate with low-coherence illumination, while being positioned in the output of a conventional inverted
microscope. The interferograms are processed into the quantitative amplitude and phase profiles of the sample.
Based on the phase profile, the optical-path-delay profile is obtained with temporal stability of 0.18 nm and spatial
stability of 0.42 nm. Further experimental demonstration of using the τ interferometer for imaging the quantitative
thickness profile of a live red blood cell is provided. © 2012 Optical Society of America
OCIS codes: 090.1995, 090.2880, 170.3880, 180.3170.
Interferometric microscopy can be used to simultaneously record the quantitative spatial profiles of both
the amplitude and the phase of mostly transparent biological samples. Using interferometric microscopy, time recording of the phase profile can yield remarkable optical
thickness or optical-path-delay stability of less than a
nanometer, with acquisition rates of several thousands
of full frames per second, and without the need for using
contrast agents such as fluorescence dyes. Since the
technique provides the optical thickness per each spatial
point on the sample, various biologically relevant morphological and mechanical parameters can be obtained
in a noncontact, label-free manner [1–3].
These unique advantages could be attractive for many
clinical applications. However, at this point, there are not
many options for commercial interferometric microscopes compared to other microscopy techniques, and
this tool is mostly used by optical and biomedical engineers for research purposes. One reason for this is the
difficulty of obtaining high-quality and stable interference
patterns with modest and portable equipment and without the need for an expert user.
The interference pattern, superimposing the light that
has interacted with the sample and a reference beam that
comes directly from the source, captures the quantitative
amplitude and phase profiles of the sample. The commonly used interferometric setups are usually constructed in open and custom-built microscopes and
operated by a user with knowledge in optics. To ensure
the stability of the interference pattern, the entire system
is positioned on an optical table to avoid mechanical
vibrations and is boxed inside an enclosure to avoid
differential air perturbations between the interferometric
This situation may be changed in the near future with
the introduction of portable and inexpensive wavefront
sensing setups that do not necessitate careful alignment
of the system before each experiment [4–13]. Furthermore, the fact that many of these new setups operate
in common-path interferometric geometry (in which both
the sample and the reference beams mostly propagate
together) significantly increases the stability of the
system and, in some cases, even eliminates the need
of positioning the system on an optical table.
One of these setups is the interferometric chamber
(InCh) microscope [4]. In this system, all the interferometric elements are encapsulated into a single, rigid,
and factory-designed reflective chamber. Although this
system uses common-path geometry (and thus can operate without an optical table), it can still create off-axis
interferograms of the sample (and thus only one frame
is required for acquiring the amplitude and the phase profiles of the sample, which is suitable for highly dynamic
samples). However, the InCh microscope cannot use
high magnifications due to the fact that the microscope
objective also needs to collect the tilted reference beam.
In addition, this microscope requires highly coherent illumination sources since the optical-path difference between the reference and the sample beams is twice the
optical thickness of the chamber.
Other setups for common-path or self-interference
quantitative phase microscopy have been presented lately by Popescu et al. [5,6], Jang et al. [7], Kemper et al. [8],
Coppola et al. [9], Mico et al. [10], and Bon et al. [11]. In
the first type of setups [5,6,10,11], a diffraction grating or
other specialized optical elements are used, whereas in
the second type of setups [7,8], a Michelson interferometer in the output of a microscope (or similar digital processing [9]) is used, so that the sample beam interferes
with itself, with the limitation that half of the sample
is empty.
This Letter proposes the τ interferometer, a new portable and high-accuracy interferometric setup that combines the advantages of both types of methods described
above and eliminates part of their disadvantages.
Figure 1 presents an inverted microscope composed of
a microscope objective (MO) and a tube lens (L0 ) that
are positioned in 4f configuration [2]. In the output of
the interferometer, instead of porting a digital camera,
the τ interferometer is positioned. This interferometer receives the magnified image of the sample from the inverted microscope and Fourier transforms it by lens
L1 , while splitting it into two beams by the cube beam
splitter (BS). A pinhole, placed in the Fourier plane of
© 2012 Optical Society of America
June 1, 2012 / Vol. 37, No. 11 / OPTICS LETTERS
Fig. 1. (Color online) The τ interferometer ported into the output of an inverted microscope. The interference is created by
splitting the magnified image from the inverted microscope and
effectively erasing the information from one of the beams before combining the beams again. S, sample; MO, microscope
objective; L0 , L1 , L2 , spherical lenses; BS, beam splitter; M0 ,
M1 , M2 , mirrors; P, pinhole (confocally positioned). Inset: expanded figure for the reference-beam mirror M2 .
one of the interferometric arms, effectively erases the
sample information by only passing the zero spatial frequencies of the image Fourier transform, which creates a
reference beam. The two beams are then reflected by
mirrors and combined by the beam splitter. Another lens
(L2 ), positioned in 4f configuration with the first lens
(L1 ), back Fourier transforms the two beams and projects them onto the camera, where an interferogram of
the sample is created, while capturing both the amplitude
and the phase profiles of the sample. The setup provides
an on-axis interferometric microscope, and an electric
control connected to one of the mirrors can create
several phase-shifted interferograms that are needed to
retrieve the quantitative phase profile of the sample.
However, to enable single-exposure operation, off-axis
interferograms can be acquired by shifting the mirrors
or the camera to high-spatial-frequency region, within
the source coherence length as defined later.
Note that only simple optical elements and no gratings
or other diffractive elements are used inside the interferometric system, in contrast to the setups proposed
in [5,6,10,11]. In addition, there is no limitation on the
confluence of the sample (thus, we do not need to use
a half-empty sample), in contrast to the setups proposed
in [7–9].
Since the sample beam only splits in the end of the system, the proposed setup can be considered as a commonpath interferometer, and its stability will be significantly
higher compared to regular interferometers. In addition,
in contrast to [5,6], in which the reference and the sample
beams pass through different locations in free space as
soon as they are split by a grating, the sample and the
reference beams in our case mostly pass through the
glass of the cube beam splitter, and thus there are fewer
differential air perturbations between the interferometric
arms, even if the interferometer is not boxed. Moreover,
since splitting the beam is done inside the 4f system, the
τ interferometer is closer to the common path than the
configurations proposed in [5,6], in which the splitting
is done in the beginning of the 4f system.
In the τ interferometer, the mirrors are placed right in
the outputs of the beam splitter, and since the beams are
tightly focused on each of the mirrors (in contrast to
[7,8]), it is significantly easier to match the beam paths,
and thus it is possible to obtain interference with lowcoherence sources.
To demonstrate using the τ interferometer, the system
shown in Fig. 1 was constructed. A temporally lowcoherence plane wave was created by passing a supercontinuum fiber-laser light (from SC400-4, Fianium)
through a computer-controlled acousto-optical tunable
filter (SC-AOTF, Fianium), selecting a central wavelength
of 633 nm with a full-width-at-half-maximum bandwidth
of 6.6 nm, as measured by a compact spectrometer
(USB4000, Ocean Optics), coinciding with coherence
length of lc 26.8 μm. The light was collimated using
relay optics and input into the inverted microscope.
Alternatively, a highly coherent source [633 nm,
helium–neon (He–Ne) laser] was used in the input of
the inverted microscope.
In the inverted microscope, a 40×, 0.66 numericalaperture microscope objective and a 15 cm focal-length
tube lens (L0 in Fig. 1) are used. The τ interferometer,
ported in the output of the inverted microscope, contained two 7.5 cm focal-length lenses, positioned in 4f
configuration (L1 and L2 in Fig. 1), a cube beam splitter,
and two mirrors, with a pinhole of 20 μm positioned in
front of one of them. The mirrors were positioned very
close to the output of the beam splitter, so that there was
almost no propagation through free space after splitting
the beams and before combining them. No enclosure was
used to avoid differential air perturbations between the
interferometric arms, which makes the sample stage and
the entire setup more accessible. A monochrome digital
camera (DCC1545M, Thorlabs) with square pixels of δ 5.2 μm was positioned in the output of the τ interferometer to acquire the interferograms of the sample. Within
the coherence length of the source and an off-axis angle
of 1°, the effective number of pixels, across which interference is obtained, is 2lc ∕δ × tg1° 590 pixels, coinciding with a field of view of more than 80 μm on the
sample, which is enough for acquiring several cells together. Reference [14] shows that tilting the field of
one of the beams can yield high-frequency interference
on the entire camera plane.
OPTICS LETTERS / Vol. 37, No. 11 / June 1, 2012
Fig. 3. (Color online) Quantitative thickness profile of a red
blood cell acquired with the τ interferometer in a single camera
exposure. Color bar represents thickness in μm. Left inset: interferogram of the cell. Right inset: cross section across the diagonal of the phase profile of the cell.
Fig. 2. (Color online) Temporal stability of the optical-path delay of a diffraction-limited spot for a Michelson interferometer
using a highly coherent source (dotted curve), τ interferometer
using a highly coherent source (dashed curve), and τ interferometer using a partially coherent source (solid curve).
We acquired 100 interferograms per second and processed them into the phase profile of the sample by using
a digital spatial filtering of a cross-correlation term from
the other terms [1], followed by subtraction of the phase
profile obtained from an interferogram without the presence of the specimen, which compensates for phase
aberrations introduced by the system, and a phase unwrapping algorithm for removing 2π ambiguities [15].
The dashed curve in Fig. 2 represents the temporal optical-path delay that was obtained using the τ interferometer and the highly coherent He–Ne laser for a
representative diffraction-limited spot (approximately
4 × 4 pixels), with standard deviation of 0.41 nm. For
comparison, the dotted curve in Fig. 2 represents the
temporal optical-path delay that was obtained using
the He–Ne laser in the input of a conventional Michelson
interferometer under the same conditions (without using
an enclosure) for a representative diffraction-limited
spot, with a standard deviation of 2.4 nm. As shown
by the solid curve in Fig. 2, when using the lowcoherence source while measured in the maximum
interference area, the τ interferometer yielded temporal
optical-path delay with standard deviation of 0.18 nm.
Under low-coherence illumination, the spatial background noise of 100 × 100 diffraction-limited spots on a
single image has a standard deviation of 0.42 nm,
whereas a Michelson interferometer using the He–Ne laser yielded a spatial standard deviation of 3.8 nm, mostly
due to the presence of speckle noise.
Figure 3 shows the thickness profile of a human red
blood cell obtained by single exposure using the τ interferometer and the low-coherence source. To obtain this
thickness profile, we divided the optical-path-delay profile of the cell by the difference between the refractive
index of the cell (n 1.395), under the assumption of
homogenous refractive index for an enucleated red blood
cell [3,5], and the refractive index of the surrounding
media (n 1.34). As shown in Fig. 3, due to the use with
a low-coherence source, the background around the red
blood cell (containing only cell media) is remarkably flat,
with a standard deviation of spatially averaged opticalpath delay of 0.85 nm in liquid environment.
In conclusion, we have presented the τ interferometer,
a compact, portable, and extremely stable interfer-
ometric setup that enables recording the amplitude
and the phase profiles of biological samples using a
low coherence source, without the need for special optical elements and an expert alignment prior to every
We expect that in mass production, the cost of the τ
interferometer will be as low as a couple of hundred dollars (cost of two mirrors, two lenses, a pinhole, a beam
splitter, and a cage) and double that if a modulator is
used for acquiring phase-shifted on-axis interferograms,
with a total size that can be as low as 1 in. (2.54 cm)
across. We believe that the fact that this interferometer
can be ported in the output of an inverted microscope
and operated in a simple way, while still obtaining remarkably high accuracy, will make interferometric phase
microscopy more accessible and affordable for biologists
and clinicians, while significantly broadening its range of
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