Proceedings of 1st International Symposium for Color Science and Art 2019

A Common-Path Phase-Shifting Interference-Microscope
Using RGB Lasers
Jun Chen and Junji Endo*
Tokyo Polytechnic Univ., 1583 Iiyama, Atsugi, Kanagawa 243-0297, Japan* FK Optics Laboratory, 1-13-4 Nakano, Niiza-shi, Saitama 352-0005, Japanthe outputs of these fibers are then combined using a multiplexer
to form a quasi-white light source. A polarizer is used to obtain alinearly polarization at 45°. This light beam is then used toilluminate the sample placed in half of the incident beam. Thesample is imaged using a microscopic objective lens (Olympus,20X, NA0.45). The WP splits the incident beam into two
orthogonally polarized components. These two components arethen interfere with each other after passing through an analyzer.
By adjusting the sample position, the wavefront that modulatedby the sample can be arranged to overlap with the wavefront
unaffected by the sample. The interference fringe pattern is thendetected with a C-MOS color camera (Mako G-507C, alliedVision), and then fed to a computer. The WP is mounted on aPZT stage controlled with a computer through GPIB interface.
In this way, the WP can be moved in a direction perpendicular tothe optical axis to introduce the phase shifts required in phaseextraction procedure.

ABSTRACT
We present a near-common-path phase-shifting
interference-microscope using RGB lasers for quantitative
measurement of living biological cells. In this system, aWollaston prism is used as both a beam splitter and a phaseshifter. Since the object and reference waves pass throughalmost the same path, the developed system has an extremely
high stability. By using RGB lasers as a light source, the sample
can be measured at different wavelengths not only one by one
but also at the same time. Experimental results for evaluating
the system error and for measuring an onion cell are shown.
1. INTRODUCTION
Recently, quantitative measurement of living biological cells
is becoming more and more important in biology and medical
diagnosis[1]. However, conventional optical transmittancemicroscopes do not work for a transparent biological cellwithout a staining procedure that may change the property of thesample. Even a phase-difference optical microscope does notprovide quantitative information about the samples. On the other
hand, phase-shifting interferometry (PSI) [2] proved to be avery powerful tool for extracting the phase information from aseries of interferograms with phase shifts introduced between
the object and reference waves. Various type of interference
microscope [3, 4] using PSI have been proposed. However,interference microscopes based on Mach-Zehnder or Michelson
type interferometers are extremely sensitive to vibration and air
turbulence. Moreover all of those systems use a single laser aslight source, the color information loses.
In order to make both quantitative measure and microscopic
observation with white light illumination possible, we havedeveloped a common-path phase-shifting interference
microscope using RGB lasers as quasi-white light source[5~7].
In this system, a Wollaston-prism (WP) located between theobjective lens and an imaging lens is used as both a beam splitterand a phase shifter. The WP is laterally moved by a piezoelectrictransducer (PZT) to introduce a relative phase shift between theobject and reference waves. This interference microscope
enables us to measure a living biological cell at RGB
wavelength.

Fig.1. Schematic of the optical system
2.2 The theory of phase measurement
The phase shifting interferometry is used for phasemeasurements. The intensity of the detected interference fringe
pattern is given by
I ( x, y)  a( x, y)  b( x, y)cos 2 f 0 x   ( x, y)    .  (1)Where a( x, y) and b( x, y ) are bias and modulation, and2 f 0 x is tilt wavefront between the object and reference waves.
 ( x, y) denotes the phase under the measurement. For a sampleof thickness t and refractive index n(x,y),  ( x, y) is given by2 ( x, y)t  n( x, y)  nr  .
     (2)2. OPTICAL SYSTEM AND THEORY
2.1 Optical system
A schematic configuration of optical system is shown in Fig.1.
The optical system consists of a transmission optical microscopewith a WP (CaCO3, separation angle 2°). RGB lasers lasing at
671nm, 532nm, and 453nm wavelengths are used as the lightsource. The output of the lasers is coupled to optical fibers, and

In Eq. (1),  is phase shift introduced by a small movement of theprism. The phase shiftintroduced by moving WP by y is givenby



354



(n0  ne ) tan   y .

(3)Proceedings of 1st International Symposium for Color Science and Art 2019a generalized phase extraction algorithm was then used to used.
The experimental results for measuring an onion cell at RGB
wavelengths are shown in Fig. 4.

An amount of 15.10m movement of the prism corresponds to a2 phase shift for light of 532nm. Four interference fringe
patterns with every /2 phase shift were captured. These fourinterferograms were used to calculate the phase distribution
using a 4-step phase extraction algorithm[1] 
2 fx   ( x, y) tan 1  I 4 I 2  mod 2 .    (4) 
 I1 I3
The tilt wavefront can then be removed by using least-squares
method and a subtraction procedure. For measure the phase
distribution at different wavelengths at the same time, ageneralized phase extraction algorithm[1] was used.

(a)㻌

3. EXPERIMENTS AND RESULTS
Several experiments were carried out to demonstrate theperformance of the developed system.
3.1 Linearity of phase measurement and system error
To check the linearity of the proposed system, the tilt
wavefront were measured. The results for the red laser is shownin Fig. 2, where line profiles of the tilt wavefront and the phasenoise were plotted against pixel across the horizontal direction.
Since the object and reference beams pass through the almost
the same path, the developed system can measure the phase witha very extremely stability. Therefore, the system error can beremoved by subtraction of the background phase error. Aftersuch a procedure, the rms phase error was evaluated as small
as/1000.

100m㻌

(c)㻌

(b)㻌

(d)㻌

Fig. 3 Experimental results for measuring the nucleus of anonion skin cell: (a)a color interferogram, (b) green-channel
image, (c) masked interferogram, (d) 3D plot of themeasured phase(a)㻌

20m㻌 (b)㻌(c)㻌Fig. 4 Experimental results of simultaneously measuring anonion living cell: (a)~(c) show the phase image at red, green,
and blue laser respectively.
4. Conclusions
A common path phase shifting interference microscope using
RGB lasers is presented. Since the object and reference beams
pass through almost the same path, this system is insensitive tovibration and air turbulence, and the rms phase error is as small
as/1000 . This method enables us to quantitatively measure thephase distribution of transparent objects such as a biological cellat RGB laser wavelengths. The usefulness of the developed
system has been demonstrated by measuring the index
distribution of living cell. This system may be used for cancer
cell identification.

Fig. 2 Experimental results for evaluating the linearity andthe residual noise of phase measurements
3.2 Measurement of biological cells
To demonstrate the ability of the developed system forquantitatively measuring the small phase objects such as a living
biological cell, an onion-skin cell was measured. To prepare thespecimen, a small piece of epidermis was peeled from an onion,
and then was put on a slide glass.
For the phase measurement, 4 color interference fringe
patterns were taken with every /2 phase shift. The obtained
experimental results are shown in Fig.3. Fig. 3(a) is an RGB
interference pattern. (b) extracted green channel image, (c)masked interferogram, (d) 3D plot of the measured phase
distribution. The phase distribution can be easily transformed to
the refractive index distribution.
The developed system can also be used to measure abiological sample at red, green, blue laser wavelength at thesame time. Four color interferograms with phase shifts weretaken with the color camera, and then separated to RGB
channels. Since the phase shift has different value for eachwavelength, a phase shift estimation method was developed and5. Acknowledgment
This work was supported by “FY2016 MEXT Private
University Research Branding Project”.
6. REFERENCES[1] E. Watanabe, et al., Opt. Lett. P.1319, Vol.38(2013)[2] K. Creath, in Progress in Optics, p. 349, Vol. 26(1988)[3] J. Endo, J. Chen, et al., Appl. Opt., p. 1308, 41(2002)[4] Y. Ishii, J. Chen, et al., Opt. Engineering, p.60, 42(2003)[5] J. Chen, and J. Endo, OPJ 2017, 2aB3(2017)[6] J. Chen, et al. The 65th JSAP Spring Meeting, 20a-p2-6(2018)[7] J. Chen, et al., ODF’18, Technical Digest, p188, (2018)36