COL 12(7), 071801(2014) CHINESE OPTICS LETTERS July 10, 2014
Fast pixel shifting phase unwrapping algorithm in
quantitative interferometric microscopy
Liang Xue (
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)
1+∗
, Shouyu Wang (
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, Keding Yan (
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2,4
,
Nan Sun (
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5
, Zhenhua Li (
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2
, and Fei Liu(
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3
∗∗
1
College of Electronics and Information Engineering, Shanghai University of Electric Power,
Shanghai 200090, China
2
Department of Information Physics and Engineering, Nanjing University of Science
and Technology, Nanjing 210094, China
3
Single Molecule Nanometry Laboratory, College of Veterinary Medicine, Nanjing
Agricultural University, Nanjing 210095, China
4
School of Electronic Information Engineering, Xi’an Technological University, Xi’an 710032, China
5
Institute of Quality Inspection of Electronics and Electrical Appliances, Shanghai Institute of
Quality Inspection and Technical Research, Shanghai 201114, China
+
These authors contributed equally to this work
∗
Corresponding author: xueliangokay@gmail.com;
∗∗
corresponding author: feiliu24@njau.edu.cn
Received January 2, 2014; accepted April 4, 2014; posted online June 20, 2014
Quantitative interferometric microscopy is an important method for observing biological samples such as
cells and tissues. As a key step in phase recovery, a fast phase unwrapping algorithm is proposed. By
shifting mod 2π wrapped phase map for one pixel, th en multiplying the original phase map and the shifted
one, the ph ase discontinuities could be easily determined with high speed and efficiency. The method aims
at enhancing phase retrieving efficiency without any background knowledge. We test our algorithm with
both numerical simulation and experiments, by focusing our attentions on wrapped q uantitative phase
maps of cells. The results indicate that this algorithm features fast, precise and reliable.
OCIS codes: 180.3170, 120.5050.
doi: 10.3788/COL201412.071801.
Optical microscopy
[1,2]
is a fast developing technique
in last decades since it promotes interdisciplinary re-
search in biologic al and medical sciences. Most biolog-
ical cells, including red blood cells (RBCs) and HeLa
cells, are nearly transparent under visible-light illumina-
tion and behave es sentially as phase objects. To quanti-
tatively obtain the phase image of the biological cells,
two types of phase imaging are often used. One is
noninterferometric phase imaging
[3,4]
while the other is
quantitative interferometric microscopy (QIM)
[5]
. In or-
der to obtain phase distribution of the sample, phase
extraction and phase unwrapping are needed in QIM.
There is a wealth of phas e extraction algorithms, such as
phase shifting methods
[6]
, principal component a nalysis
(PCA)
[7−9]
, fast Fourier transform method (FFT)
[10,11]
,
Hilbert transform method (HT)
[12−16]
, spatial phase-
shifting algorithm
[17,18]
and derivative algorithm
[19]
, etc.
After phase extracting, the solved phase distributions are
always wrapped from −π to π caused by tangent function
in the situation of thick phase samples or off-axis interfer-
ometry se tup. Phase unwrapping is used to eliminate the
ramps to achieve continuous phase distributions. There
are also many phase unwrapping algorithms, but some of
these methods s uch as least squares a lgorithm
[20]
, mini-
mum network flow method
[21]
, etc. ar e time-consuming
to locate the phase discontinuities which leads to low pro-
cessing efficiency. Besides, some high-s peed phase un-
wrapping methods have been proposed. Kim et al. used
two interferogra ms captured at two differe nt wavelengths
to obtain the unwrapped phase distr ibutions
[22]
. While
this method could not eliminate all the wraps in the phase
fields as the difference of these two wave lengths is obvious
or the field of view (FOV) is large where there are too
many wraps. Pham et al. developed a non-phase wrap-
ping white light diffraction phase microscopy by ca ptur-
ing one interferogram with biological samples and an-
other interferogram without samples as background
[23]
.
Though this method simplifies the phase retrieving pro-
cess, however, the phase of the tested samples could not
exceed 2π and it is difficult to obtain the accurate pha se
distribution if the sample is located in the position of
phase discontinuities. Nevertheless, both methods need
at least two interferograms to rec over final phase dis-
tributions. The limitation hinder s the developments of
real-time QIM. Moreover, much fast speed phase unwrap-
ping methods have been proposed
[24,25]
, however, some of
them need much complicated procedures which increase
the difficulty of such algorithms.
In this letter, we have proposed a fast phase unwr ap-
ping algorithm to realize high-speed QIM in low noise
condition. The new-designing high-spe e d pixel shifting
phase unwrapping algorithm, combined with phase ex-
traction methods, could be applied to recover the contin-
uous phase distr ibutions of the biological samples. Com-
pared to traditional pha se unwrapping metho ds , this
method has high calculating efficiency and easy proce-
dures.
Phase extraction includes FFT method
[10,11]
, HT
method
[12−16]
, etc., almost all of which are rapid meth-
ods. However, most phase unwrapping methods are quite
1671-7694/2014/071801(6) 071801-1
c
2014 Chinese Optics Letters