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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

2junzhang@uci.edu

3z2chen@uci.edu

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

[1], digital holographic microscopy [2], Fourier phase

microscopy [3], Hilbert phase microscopy [4], and op-

tical coherence tomography (OCT) [5], 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 [8], 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

Fig. 1.

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

150 mm.

(Color online) Schematic of the spectral domain

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0146-9592/09/213442-3/$15.00© 2009 Optical Society of America

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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 + ??,

?1?

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.

Theprocessofnarrow-bandpass

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

signal as

I˜?k? = 2S?k??RRRSexp?j?2k?d + ???.

filteringwas

?2?

The phase term of I˜?k? can be retrieved as

??k? = 2k?d + ?.

?3?

In our setup with a 2048 pixel spectrometer, the

phase term is a discrete function:

??ki? = 2ki?d + ?

?i = 0 ? 2047?.

?4?

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

?0

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

??ki?

2ki

2??/4???, while the displacement error with the

?d =

+

?

ki?floor?

??

2???,

?5?

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-

Fig. 2.

space with the top surface of a coverslip as the sample. (a)

Wrapped phase, (b) unwrapped phase.

(Color online) Measured phase in wavenumber

Fig. 3.

phase variations with a microscope coverslip as the sample.

(Color online) Probability distribution of measured

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retical phase sensitivity is determined by the signal-

to-noise ratio (SNR) of the phase measurement sys-

tem as [6,7]

???2? ?

1

SNR.

?6?

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

cells.Theimage covering

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.

asamplearea of

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

Institute Endowment.

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Fig. 5. (Color online) Image of human neonatal dermal ke-

ratinocyte cells.

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-

wrappedinwavenumber

changed phase shift. (c) 3D phase image of the patterns.

space.(b) Discontinuously

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