High-dynamic-range quantitative phase imaging
with spectral domain phase microscopy
Jun Zhang,1,2Bin Rao,1Lingfeng Yu,1and Zhongping Chen1,3
1Beckman Laser Institute and the Center for Biomedical Engineering, University of California, Irvine,
Irvine, California 92612, USA
Received August 3, 2009; accepted September 17, 2009;
posted October 9, 2009 (Doc. ID 115172); published October 30, 2009
Phase microscopy for high-dynamic-range quantitative phase-contrast imaging of a transparent phase object
was demonstrated. Using a common path Fourier domain optical coherence tomography system, this tech-
nique is capable of displacement measurement with a sensitivity of 34 pm. The limitation of 2? ambiguity
restriction was overcome by the use of a phase retrieval approach performed in spectral domain. Two-
dimensional quantitative phase imaging of human neonatal dermal keratinocyte cells was demonstrated to
evaluate the performance of the system for cell imaging. © 2009 Optical Society of America
OCIS codes: 100.5088, 110.4500, 170.0180, 180.3170.
High-sensitivity and high-speed quantitative phase
measurement to retrieve nanometer or subnanom-
eter scale variation is important for applications,
such as subcellular dynamics studies and high reso-
lution material inspection. Quantitative phase micro-
copy based on interferometric techniques are widely
developed, including phase shifting interferometry
, digital holographic microscopy , Fourier phase
microscopy , Hilbert phase microscopy , and op-
tical coherence tomography (OCT) , etc. The recent
application of spectral domain phase microscopy with
the Fourier domain OCT (FDOCT) technique for
phase measurement has resulted in excellent phase
stability, high sensitivity, and imaging speed, because
FDOCT does not require mechanical reference scan-
ning and is able to reject common mode noise with
common path configuration [6,7].
In phase measurement with FDOCT, the oscilla-
tion of the fringes in spectral domain due to optical
path difference (OPD) between the reference and
sample arms is detected. The phase information is
extracted from the complex depth-resolved profile,
which is obtained by Fourier transformation of the
spectral fringes. Since the phase oscillates 2? rad at
every shift of half a wavelength of the OPD, high-
sensitivity phase measurement of the fringes can
provide an ultrahigh accuracy measurement of the
OPD. However, the measurement of OPD with
FDOCT systems is restricted to less than half a
wavelength owing to the 2? ambiguity. To measure
OPD longer than half a wavelength, phase unwrap-
ping algorithms are needed. Conventional phase un-
wrapping algorithms require that the phase shift
varies slowly and gradually , which limits the dy-
namic range of the phase measurement in the case of
large phase discontinuity. Phase unwrapping by syn-
thesizing a beat wavelength between two wave-
lengths was demonstrated for correction of the 2?
ambiguity [9,10]. However, additional phase noise or
spikes were generated.
In this Letter, we demonstrate a spectral domain
phase microscopy technique that is capable of high-
dynamic-range quantitative phase-contrast imaging
by overcoming the limitation of 2? ambiguity. Unlike
conventional spectral domain phase microscopy, the
presented technique retrieves phase information in
spectral domain instead of depth domain by Hilbert
transformation of the detected fringe signal. The dis-
continuous phase change in depth domain can be con-
verted to a gradually varying phase shift in spectral
domain with this approach.
Figure 1 shows the setup of the spectral domain
phase microscopy. A superluminescent diode (SLD)
with a center wavelength of 890 nm and an FWHM
bandwidth of 150 nm was used as the light source.
The light was focused by a 20? objective lens on the
sample, which rested on the top surface of a cover-
slip. The backreflected light from the bottom surface
of the coverslip acted as the reference for common
path configuration to eliminate phase turbulence due
phase microscopy system. SLD, superluminescent diode; L,
lens; OB, 20? objective lens; G, transmission grating with
1200 groves/mm; LG, lens group with focusing length of
(Color online) Schematic of the spectral domain
OPTICS LETTERS / Vol. 34, No. 21 / November 1, 2009
0146-9592/09/213442-3/$15.00© 2009 Optical Society of America
to environment variation. The interference fringe
was detected by a high-performance 2048 pixel spec-
trometer which was set at 20,000 A lines/s.
In a spectral domain phase microscopy system, the
detected intensity can be expressed as
I?k? = S?k?RR+ S?k?RS+ 2S?k??RRRScos?2k?d + ??,
where k is the wavenumber; S?k? is the spectral den-
sity of the light source; RRand RSare the reflectivi-
ties from the reference surface and the sample, re-
spectively; ?d denotes the OPD between sample and
reference arms; and ? is the arbitrary phase. The first
and second terms in Eq. (1) represent the reflected
intensities from the reference surface and the
sample, respectively, and the last term represents the
interference between the reference and the sample
beams. In a conventional spectral domain phase mi-
croscopy, the phase information ? is extracted by
Fourier transformation of the detected spectral in-
tensity and by taking the argument of the trans-
formed depth-resolved complex function. The OPD
was calculated to be ?d=?0?/?4??, where ?0is the
center wavelength of the source. This method directly
retrieves phase shift and, therefore, experiences the
limitation of 2? ambiguity. In this Letter, the spec-
tral fringe I?k? was first transformed from wavenum-
ber to depth space by fast Fourier transformation.
adopted to select the positive term of the complex
depth function and reject the noise from the dc term
and multiple reflections. The subsequent inverse fast
Fourier transform step acquired the complex spectral
I˜?k? = 2S?k??RRRSexp?j?2k?d + ???.
The phase term of I˜?k? can be retrieved as
??k? = 2k?d + ?.
In our setup with a 2048 pixel spectrometer, the
phase term is a discrete function:
??ki? = 2ki?d + ?
?i = 0 ? 2047?.
The spectral range ?? of the spectrometer is 200 nm.
The corresponding spectral space ?k=ki+1−kiof the
spectrometer is about 8 cm−1. With the sample re-
sides on the top surface of a coverslip, the typical
OPD ?d is around 210 ?m. Therefore, the phase step
??=??ki+1?−??ki? is 0.34 rad. Figure 2 shows the
phase term as the function of a wavenumber with the
top surface of a coverslip as the sample. With a phase
step of 0.34 rad, the phase function can be easily un-
wrapped as shown in Fig. 2(b). A least-square algo-
rithm was used to calculate the slope of the phase
function, which is proportional to the OPD. By cali-
bration with a standard thickness sample, an OPD
can be determined precisely. This approach is capable
of absolute OPD determination; however, it suffers
from a larger displacement error compared with the
direct phase retrieval method. Suppose phase stabil-
ity of the system is ??, the displacement error by cal-
culating the slope of the phase function will be
direct phase retrieval method will be ?0??/4?.
Hence the displacement error is amplified by a factor
of ?0/??, which is around 5 in our setup. In our ex-
periment, the slope of the phase function was used as
the reference for removal of 2? ambiguity, while the
OPD was determined with one of the phase compo-
nents ??ki?, as
2??/4???, while the displacement error with the
where kiis one of the discrete wavenumbers and ?? is
the phase determined with the slope of the phase
function, which is used for the determination of the
integer multiple of 2?.
The minimum detectable displacement is depen-
dent on the phase error in the system. To evaluate
the phase stability of the system, a stationary micro-
scope coverslip with a thickness of 210 ?m was used
as the sample. 1024 A-scans were averaged to deter-
mine the phase difference between adjacent A-lines
of the interference between the top and bottom sur-
faces. The phase variations are demonstrated in Fig.
3 showing a phase stability of 0.48 milliradians. The
corresponding displacement sensitivity of the system
was calculated to be 34 pm in free space. The theo-
space with the top surface of a coverslip as the sample. (a)
Wrapped phase, (b) unwrapped phase.
(Color online) Measured phase in wavenumber
phase variations with a microscope coverslip as the sample.
(Color online) Probability distribution of measured
November 1, 2009 / Vol. 34, No. 21 / OPTICS LETTERS
retical phase sensitivity is determined by the signal-
to-noise ratio (SNR) of the phase measurement sys-
tem as [6,7]
The signal-to-noise ratio of our system was measured
to be 70 dB. The corresponding theoretical phase sta-
bility was calculated to be 0.32 milliradians, which is
consistent with our measured value.
To evaluate the capability of the system to remove
2? ambiguity, we imaged patterns with thickness
steps of more than half a wavelength. Standard SU-8
photolithography technique was used to fabricate the
patterns on a glass slide. A coverslip was placed in
front of the target as the reference and adjusted to be
parallel to the surface of the sample. The OPD be-
tween the surfaces of the sample and the coverslip
was measured as shown in Fig. 4. Figure 4(a) illus-
trates the profile of the OPD of the target in one di-
rection measured with the phase unwrapped in
wavenumber space in comparison with the OPD cal-
culated with the conventional direct phase retrieval
approach. The discontinuously changed phase shift
shown in Fig. 4(b) reveals that the 2? ambiguity can-
not be corrected with the conventional phase un-
wrapping algorithm. Figure 4(c) shows 3D phase im-
ages of the pattern. The residual spikes in the image
were due to scratches during fabrication with photo-
lithography. With the phase retrieval approach per-
formed in wavenumber space, the spectral domain
phase microscopy system could measure a large
range of displacements, ranging from the minimum
measurable displacement of 34 pm to the maximum
measurable displacement of 2 mm, which is the im-
aging range of the system and determined by the
spectral resolution of the spectrometer.
To demonstrate the performance of the system in
cell imaging, living human neonatal dermal kerati-
nocyte cells were used as samples. Figure 5 shows
two-dimensional quantitative phase imaging of the
150 ?m?150 ?m was acquired in 0.3 s.
In summary, a spectral domain phase microscopy
capable of high-dynamic-range quantitative phase-
contrast imaging was developed. The phase stability
of the system was measured to be 0.48 mrad corre-
sponding to a minimum measurable displacement of
34 pm in free space. 2? ambiguity was corrected by
retrieving the phase in spectral domain. A phase ob-
ject pattern with discrete displacements was imaged,
demonstrating the high-dynamic-range capability of
the system. Two-dimensional quantitative phase im-
aging of human neonatal dermal keratinocyte cells
was also presented to evaluate the performance of
the system for cell imaging.
This work was supported by the National Insti-
tutes of Health (NIH) (EB-00293, NCI-91717, RR-
01192), National Science Foundation (NSF) (BES-
86924), Air Force Office of Scientific Research
(AFOSR) (FA9550-04-0101), and the Beckman Laser
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Fig. 5. (Color online) Image of human neonatal dermal ke-
Fig. 4. (Color online) Measured OPD of patterns on a glass
slide. (a) Cross-sectional profile of the OPD in one direction.
Lower red curve, OPD calculated with the wrapped phase;
upper blue curve, OPD calculated with the phase un-
changed phase shift. (c) 3D phase image of the patterns.
OPTICS LETTERS / Vol. 34, No. 21 / November 1, 2009