Single-shot 3D profilometry using a color imaging
polarimeterYuuki Maeda ,* Shuhei Shibata, Nathan Hagen , andYukitoshi Otani
Utsunomiya University, Center for Optical Research and Education, Utsunomiya,Tochigi, Japan

Abstract. We demonstrate a single-shot uniaxial three-dimensional (3D) profilometry systemthat illuminates a sample with a color structured polarization pattern with an axial chromaticaberration. We have previously shown that real-time 3D shape measurement can be performed
without the occlusion problem using a polarization camera and a monochromatic polarized pattern. Here, we show that it is possible to double the depth range of the system, with no tradeoff indepth resolution, measurement speed, or accuracy, using color pattern projection and an RGB
polarization camera. We present the measurement principles of the system and show the resultsof a real-time 3D profilometry experiment for a sample with a deep hole. © 2021 Society of PhotoOptical Instrumentation Engineers (SPIE) [DOI: 10.1117/1.OE.60.12.124115]

Keywords: profilometry; polarization camera; fringe projection; single shot measurement;
polarization pattern.
Paper 20210867 received Aug. 11, 2021; accepted for publication Dec. 14, 2021; published
online Dec. 31, 2021.

1 Introduction
Optical methods for three-dimensional (3D) surface profile measurement are used in a wide
range of fields, such as manufacturing inspection, medical inspection, and robot vision, because
they allow noncontact and nondestructive measurement. Although stereo optical techniques,
such as the light-section method,1 the Moiré method,2 and the fringe projection method,3–7 work
well for surfaces that do not have extreme gradients, samples with deep holes or large stepheights cause difficulties for these methods because some regions are occluded from the projector or from the imager. In these cases, uniaxial profilometry methods, such as the time-offlight (TOF) method and the focus method, are more practical. The TOF method projects pulsemodulated light from a light source onto an object and measures the distance from the time ittakes for pulses to return from an object. This method is well suited to measuring large objects,
but it has difficulty resolving small feature sizes, such as in the submillimeter and millimeter
ranges.
The focus method for uniaxial profilometry obtains the surface height from changes in thecontrast (due to blurring) of a projected pattern. The 3D information of the sample can be obtainedby measuring the relationship between height and contrast in advance. This approach to profilometry appears to have been pioneered by Engelhardt and Häusler in 1988 and was refined by later
researchers.8–12 In 1997, Neil et al. used phase shifting with fringe projection methods to perform
optical sectioning through the change in fringe contrast with focus.13 However, the fringe pattern
method cannot measure the surface profile in a single snapshot because it requires multiple shifts of
the illumination pattern to measure the contrast. In 1991, Wust and Capson developed a system inwhich multiple fringes were simultaneously projected onto the object and detected separately in thered, green, and blue channels of a color camera. This allowed for snapshot profile measurement but
encountered difficulties when the object under measurement had spatially varying color.3
We have previously proposed a uniaxial 3D profilometry system that illuminates a sample
with a spatially varying polarization pattern and images the spatial distribution of contrast with a*Address all correspondence to Yuuki Maeda, cc-yuuki@mail.goo.ne.jp0091-3286/2021/$28.00 © 2021 SPIE

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December 2021 • Vol. 60(12)Maeda et al.: Single-shot 3D profilometry using a color imaging polarimeterpolarization camera.14 The aim of this system was to measure, in a snapshot, reflecting samples
with height profiles that vary within the submillimeter or millimeter range. Examples of such
samples include heat sinks and copper pillars with large step heights. For this system, the sample
to be measured needs only to have sufficient reflectance to achieve sufficient measurement SNR
at the wavelength of the light source and should have a surface that does not completely eliminate polarization. This can be either a mirror surface or a rough (diffusely reflecting) surface, but
the latter causes a loss in degree of polarization that reduces height measurement SNR.
One difficulty faced by our previous system is that since the contrast that changes with thefocus is the same for both sides of the focal plane, the profilometry system cannot determine thesign of the defocus—whether the measured height is nearer or farther from the focus. Therefore,
the monochromatic profilometry system can only measure one side of the contrast distribution.15
To increase the measurement range of the system, without sacrificing resolution, we propose aprofilometry system using a color polarization camera (CPC)16,17 and a lens system with a large
axial chromatic aberration (an extrachromatic lens). The system we show here uses different
focus positions for red, green, and blue colors, so by combining the contrast measured in two
different colors, we double the range over which we measure the 3D surface profile. In addition,
we have also introduced an additional nonpolarizing beamsplitter into the optical layout for the
purposes of canceling residual polarization effects caused by the beamsplitters and improving themeasurement accuracy. In the discussion below, we present the measurement principles of thesystem and show measurement results that demonstrate the improved range on a dynamic
sample.

2 Measurement Principles for Expanding Dynamic Range
Figure 1 shows the experimental setup of the uniaxial 3D profilometry system using aCPC. Starting from the white light source, the light is split into red (628  14 nm), green(530  10 nm), and blue (457  11 nm) by a multiband filter (MBF) [Edmund Optics #87245]. It is possible to improve the SNR or the depth measurement range using three color
RGB channels, but we need to use only the red and blue channels due to the small axial chromatic aberration. To partially cancel the residual polarization effects of NPBS3, we introduce anextra beamsplitter NBPS2, oriented orthogonally to NPBS3.17
The light transmitted through the MBF is linearly polarized by a linear polarizer (LP), passes
through a nonpolarizing beamsplitter (NPBS1), transmits through a quarter wave plate (QWP) toconvert the light into a circular state, and reaches the spatial light modulator (SLM). The SLM isadjusted to induce a linear phase across the face of the reflecting beam, which passes once again
through the QWP (thereby returning to being linearly polarized), returns to NPBS1, and this timeuses the reflection path. Finally, lens L1 collimates the beam coming from the SLM. With this
optical setup, an illumination polarization pattern is produced at the image plane, where the stateof polarization is everywhere linear, but the azimuth angle of polarization rotates as one goesfrom one side of the image to the other.

Fig. 1 Experimental setup: (a) perspective view, (b) side view, and (c) top view.
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The phase ϕ given by a SLM isϕðyÞ ¼

EQ-TARGET;temp:intralink-;e001;116;723

ΔnðyÞ · d;λ(1)where ϕðyÞ is the phase induced along the y direction of the SLM (the x-direction phase is held
constant), Δn ¼ nx − ny is the difference between refractive indices in the x- and y- electric field
directions, d is the liquid crystal thickness, and λ is the wavelength of light passing through theSLM. Since the phase distribution applied by the SLM is inversely proportional to the wavelength, a linear phase ramp across the SLM will induce an interference pattern at the focal planewhere the number of fringes per mm in the pattern is inversely proportional to the wavelength. As
a result, the height measurement range of the system is proportional to the wavelength.
The linear polarization pattern illumination is imaged onto the sample by lenses L1 and L2(i.e., L1 and L2 image the SLM plane onto the sample plane). The polarization pattern that isreflected from the sample is then imaged onto the CPC through lenses L2 and L3. The CPC
consists of an image sensor, a color microfilter array, and a micropolarizer array.
With this setup, the pattern illuminating the sample will appear as a field of interference
fringes when viewed through a polarizer, such that the phase of the fringe field shifts with theorientation angle of the viewing polarizer. By employing the four polarization orientation angles
available on a polarization camera, we therefore obtain four shifted fringe fields in a single snapshot. If the sample does not lie at the ideal focus of the illumination pattern, then the fringes will
become blurred, and the fringe contrast becomes lower. Therefore, using a quantitative estimateof the fringe contrast, we estimate the distance Δzðx; yÞ of the sample from the ideal focal point,
for each ðx; yÞ location in the image.
For a measurement system without the axial chromatic aberration, the dependence of thefringe contrast on sample depth is approximated by a Gaussian distribution, such that the contrast
A at height z is given as zðx; yÞ 2
Aðx; y; λÞ ¼ C · exp −
;
(2)
σðλÞ
EQ-TARGET;temp:intralink-;e002;116;416

where σðλÞ ∝ λ and C is a constant. The height zðx; yÞ is therefore estimated assﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ
Czðx; yÞ ¼ σðλÞ 2 ln:
Aðx; y; λÞ
EQ-TARGET;temp:intralink-;e003;116;360(3)

Because the contrast Aðx; y; λÞ is symmetric about z ¼ 0 regardless of the wavelength, it is
not possible to identify the sign of z. For a measurement system with the axial chromatic aberration, however, the contrast is given as zðx; yÞ − dðλ − λ0 Þ 2Aðx; y; λÞ ¼ C · exp −
;
(4)
σðλÞ
EQ-TARGET;temp:intralink-;e004;116;271

where dðλ − λ0 Þ represents the chromatic variation in focal length with respect to the reference
wavelength λ0 . Figure 2 shows Aðx; y; λ0 Þ and Aðx; y; λ1 Þ, the difference in the contrast versus
height curves for the reference wavelength λ0 and measurement wavelength λ1 , respectively.
Although each Aðx; y; λÞ is symmetric about its respective peak, we break the symmetry of themeasurement and determine the sign of the defocus Δz for height estimate z ¼ d  Δz.
To have a different focal plane for the illumination pattern for each color channel, lens L1 forthe illumination path is intentionally selected to produce a strong axial chromatic aberration. The
optical layout of the system and the L1 prescription data are shown in Fig. 3 and Table 1, respectively, where we use an ideal lens to represent an aberration-free objective lens L2. Both theillumination and imaging arms of the system operate at a focal ratio of f∕10. The chromatic
focal shift of this lens is shown in Fig. 4. The chromatic difference in focal length from blue
and red is 5.6 mm. We designed the optical system using commercially available lenses, so wewere unable to achieve large axial chromatic aberrations. Therefore, we used only the red andOptical Engineering

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Fig. 2 Relationship between contrast and z-distance from the focal plane, for C ¼ 1,
d ðλ1 − λ0 Þ ¼ 1.0 mm, σðλ0 Þ ¼ 4.6 mm, and σðλ1 Þ ¼ 6.4 mm.

Fig. 3 Lens layout.

Table 1 Lens data.
r (mm)d (mm)

n

ν

Glass

Object

—

95.0

—

—

—

1

—

6.35

1.6727

32.25

N-SF5

2

−33.63

0

—

—

—

3

−51.684.85

1.5168

64.17

N-BK7

4

—

90.0

—

—

—

5

f ¼ 100 mm

100.0

—

—

Image

Ideal Lens———

Note: r , radius of curvature; d , distance; n, refractive index; ν, Abbe number at d -line (587.6 nm).

Fig. 4 Chromatic focal shift.
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blue channels. If we use the green channel, misjudgments of the sign of the defocus Δz occur
because the axial chromatic aberration green light and blue light is small.
We chose lens focal lengths for L1, L2, and L3 of 100, 100, and 200 mm to measure millimeter-size samples. The ratio of focal lengths L1:L2 determines the magnification of the polarization pattern at the sample, and the ratio of focal lengths L2:L3 determines the field of view
imaged at the sample. The SLM is a liquid-crystal-on-silicon type with a 792 × 600 grid of
20 μm pixels (X10468, Hamamatsu Photonics K.K.). The CPC has a 2448 × 2048 grid of
3.45-μm pixels (BFS-U3-51S5PC-C, FLIR). The system field of view with this setup
is 4.2 mm × 3.5 mm.

3 Calibration
We characterize the calibration of NPBS quantitatively using Mueller calculus. Passing the input
Stokes vector Sin from the light source (which we assume to be unpolarized) through each of the
optical elements in turn gives the output Stokes vector Sout imaged onto the CPC given as
EQ-TARGET;temp:intralink-;e005;116;549

Sout ¼ N TV · M · N RV · N TH · N RH · Qð−45 degÞ · Lðϕ; 0 degÞ· Qð45 degÞ · N TH · Pð0 degÞ · Sin ;(5)where N, M, Q, L, and P represent the Mueller matrix of NPBS, sample, QWP, SLM, and LP,
respectively. The subscripts T and R represent the transmission and reflection, respectively. The
subscripts H and V represent a fast axis azimuth of 0 deg and 90 deg. Since the NPBS has a linear
retardance and a linear diattenuation, the Mueller matrix of the NPBS is given as2

pT þ sT
16
6 pT − sT
N TH ¼ 6
0
24
0

EQ-TARGET;temp:intralink-;e006;116;451

2

sT þ pT
16
6 sT − pT
N TV ¼ 6
0
24
0

EQ-TARGET;temp:intralink-;e007;116;3612

pR þ sR
16
6 pR − s R
N RH ¼ 6
0
24
0

EQ-TARGET;temp:intralink-;e008;116;293

2

sR þ pR
16
6 sR − pR
N RV ¼ 6
0
24
0

EQ-TARGET;temp:intralink-;e009;116;225

pT − sTpT þ sT00

00
pﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ
2 pT · sT · cos δT
pﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ−2 pT · sT · sin δT

3
0
7
0
7
pﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ;
2 pT · sT · sin δT 7
5
pﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ
2 pT · sT · cos δTsT − pTsT þ pT00

00
pﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ
2 pT · sT · cos δT
pﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ
2 pT · sT · sin δT

3
0
7
0
7
pﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ;−2 pT · sT · sin δT 7
5
pﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ
2 pT · sT · cos δT

pR − sR
pR þ sR0000pﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ
2 pR · sR · cos δR
pﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ−2 pR · sR · sin δR

3
0
7
0
7
pﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ;
2 pR · sR · sin δR 7
5
pﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ
2 pR · sR · cos δRsR − pR
sR þ pR0000
pﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ
2 pR · sR · cos δR
pﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ
2 pR · sR · sin δR

3
0
7
0
7
pﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ;−2 pR · sR · sin δR 7
5
pﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ
2 pR · sR · cos δR

(6)

(7)

(8)

(9)

where pT and sT are the transmittance of p- and s-polarizations, respectively; pR and sR are thereflectance of p- and s-polarizations, respectively; and δT and δR are the retardance of transmission and reflection, respectively. The Mueller matrix of the mirror is given as
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2

EQ-TARGET;temp:intralink-;e010;116;735

1
60
M¼6
40
0

3
0 0
0
1 0
0 7
7:
0 −1 0 5
0 0 −1(10)

We obtain the following equation:
EQ-TARGET;temp:intralink-;e011;116;663

Sout ∝ M · Qð−45 degÞ · Lðϕ; 0 degÞ · Qð45 degÞ · Pð0 degÞ · Sin :(11)Thus, we see that the polarization state at the camera, Sout , does not depend on the linear
retardance or linear diattenuation of any of the NPBS’s in the system. If the sample is a partial
depolarizer such as a diffuser or a metal surface, the retardances of the NPBS’s will cancel out,
but the NPBS’s diattenuation will not. Thus, it is important to select NPBS’s with as small adiattenuation as possible. Previous studies14 have shown that, for a polarization invariant sample,
the degree of linear polarization (DOLP) of the linear polarization pattern illumination is equal tothe modulation contrast. Thus, we estimate the contrast by measuring the DOLP, but the presenceof any unwanted retardance or diattenuation in the NPBS or the sample will alter the DOLP. This
introduces an error in the contrast measurement and therefore the estimated surface height.
To confirm that NPBS2 is successfully minimizing unwanted polarization effects from thebeamsplitters, we measured the relationship between the SLM phase and the azimuth angle ofpolarized light at the sample, with and without NPBS2. Figure 5 shows the results. When NPBS2
is in place, the azimuth angle of polarized light changes linearly with SLM phase [Fig. 5(a)].
When NPBS2 is not present, the polarization azimuth no longer follows a simple line.
The relationship between the maximum fringe contrast and the SLM phase is shown in Fig. 6.
Although the residual polarization effects of NPBS3 have been reduced, they have not quite beenFig. 5 Azimuth angle of polarization at the sample versus SLM phase: (a) NPBS2 present and(b) NPBS2 absent.

1

Contrast

Red

Blue
0.8

0.6

0

50

100

150

200

SLM phase

Fig. 6 Fringe contrast at the sample versus SLM phase.
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December 2021 • Vol. 60(12)Maeda et al.: Single-shot 3D profilometry using a color imaging polarimeter(b)Ay (mm)y (mm)

(a)

1.0

1.0 B
x (mm)

0

90

A

(deg)

1.0
0

1.0 B
x (mm)

0

2.0

2.0

-90

(c)

y (mm)

Fig. 7 (a) Azimuth angle of polarization at the sample for blue light and (b) red light; (c) crosssections (A-B) through (a) and (b).

completely compensated for, as we can see from the contrast that changes depending on the SLM
phase. Manufacturing variations in each NPBS produce different wavelength-dependent linear
retardances (δT and δR ) and different linear diattenuations (pT , sT , pR , and sR ). We analyze
Eq. (5) to show that the DOLP of illumination pattern decreases as the retardance and diattenuation variations increase. When the SLM is adjusted to generate a linear phase ramp along the y
direction, the result is to create a linearly polarized pattern with an azimuth that varies linearlywith the y direction along the sample. The azimuth angle of polarization calculated from theimage captured by the CPC is shown in Fig. 7.
To calibrate the mapping of contrast to the sample height, we insert a plane mirror at the
sample position and measure the contrast at each pixel while changing the mirror height, withthe results shown in Fig. 8. The measurement height range is 36 mm, from −18 to þ18 mm.
From this calibration measurement, we can see that the difference in the peak positions of thecontrast distributions between blue and red light is 2.8 mm. This 2.8 mm corresponds to an axial
chromatic aberration of 5.6 mm. Figure 9 shows the results of 40 independent measurements of
0.8
RedContrast

0.7
0.6
0.5

0.4
0.3
-20

Blue
Focus position (red)Focus position (blue)-10-2.8 01020Height : z (mm)Fig. 8 The measured contrast (open squares) as a function of the sample height, and the fitted
Gaussian function (solid curves), for red and blue lights.
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2.00

Error (mm)

1.00

0.00

-1.00

-2.00

0

10

20

30

40

Measurement number
Fig. 9 A series of measurements for the height, at a single pixel, of a mirror placed at the focus.
The standard deviation of the measurement is 0.2 mm.

the mirror height when the mirror is placed at the focus. Since the standard deviation of a singleframe measurement is 0.2 mm at the center position, we estimate the resolving power of thesystem’s depth measurement to be 36 mm∕0.2 mm ¼ 180. The resolving power represents thenumber of resolvable elements (measurement range/accuracy).

4 Experimental Results
For an experimental demonstration of the system, we imaged a stepped sample (Fig. 10) to
confirm the increased dynamic range of the 3D profile measurements due to our use of twocolors. The stepped sample is placed so that z ¼ 0 lies between the top surface of mirror-1 andthe top surface of mirror-2. We used a ceramic gauge with a thickness of 8.0 mm as the spacer.
The thickness of mirror-2 measured by a height gauge is 8.0 mm. Therefore, the step height ofthe stepped sample is 16.0 mm. The in-plane standard deviation of the height measurements in
Fig. 10 is 0.9 mm. This error is larger than the 0.2 mm standard deviation measured in Fig. 10
because our setup cannot fully compensate for manufacturing variations in NPBS polarization(a)z (mm)

(c)

10

10

A

(mm)

(b)
2

2.5
x (mm)0y (mm)

B-10

Fig. 10 Profile measurements of the step sample: (a) the sample shape, (b) measured profile
image, (c) a cross section (A-B) through the measured profile.
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Fig. 11 Results of the real-time 3D profile measurements of the sample with the deep hole:(a) sample cross-section, (b) measured 3D profiles, (c) a cross section (A-B) through the measured profiles. (See Videos 1 and Video 2.) (Video 1; MP4, 141 KB [URL: https://doi.org/10.1117/1.OE.60.12.124115.1]; Video 2; MP4, 216 KB [URL: https://doi.org/10.1117/1.OE.60.12.124115.2).

Fig. 12 Conceptual diagram of the contrast change that occurs when part of the lens pupil isblocked.

properties. Figure 11 shows a 10-fps video measurement of a cylinder moving within a deephole. The image size at the sample is 3.5 mm × 1.5 mm. Because the cylinder lies deep inside
the narrow hole, part of the illumination is blocked near the edges of the hole. This causes achange in the calibrated relationship between the contrast and the object height, as illustrated
with the conceptual diagram given in Fig. 12. Without a separate height-to-contrast calibration
measurement, the measured height will suffer from the error near the edges of the hole.

5 Conclusion
The real-time uniaxial 3D profilometry approach that we demonstrate here, using a lens systemwith a large axial chromatic aberration and a CPC, is used to double the height range over which
the 3D surface profile of a sample can be measured. Using a 100-mm focal length objective lens,
we demonstrated that it is possible to measure sample depth ranges over 20 mm. This corresponds
to a real-time depth resolving power (measurement range divided by resolution) of 720. This realtime coaxial 3D profilometry system has the advantages of being able to measure inside deepholes and other samples with large step heights, such as when measuring heat sinks and copper
pillars. Not only are these features difficult for stereo projection systems but also the snapshot
capability of the system that we present here allows the measurement to be adapted for inline use,
in which the measurement speed is critical to capturing dynamic changes and motion.
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The system that we demonstrate here is suited to samples with height variations in the millimeter range, but this can be adjusted for larger height ranges using larger projection optics or forsmaller height features using a higher numerical aperture objective lens. Our overall approach ofcolor polarization pattern projection is well suited to evaluating shapes of samples composed of asingle material. Samples composed of different materials with different depolarizations cancause problems because the contrast depends on the degree of depolarization. It may also prove
possible to increase the depth measurement range beyond what we have achieved here using all
three color RGB channels while using an illumination lens with a much larger axial chromaticaberration such as a Fresnel lens or other diffractive optical element.

Acknowledgments
This work was supported by JSPS KAKENHI Grant Nos. JP 20K04516 and 20H05702. The
authors declare no conflicts of interest.

Code, Data, and Materials Availability
Data underlying the results presented in this paper are not publicly available at this time but may
be obtained from the authors upon reasonable request.

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Yuuki Maeda is an engineer at Optics R&D Center, Canon Inc., Japan. He received his master’s
degree from the University of Tokyo in 2006 and his doctor’s degree from Utsunomiya
University in 2021. His interests include projection technology, polarization technology, andoptical three-dimensional measurement technology.
Shuhei Shibata is a postdoctoral researcher at Center for Optical Research and Education(CORE), Utsunomiya University, Japan. He received his doctor’s degree from Utsunomiya
University in 2019. He was the first president of the SPIE student chapter of Utsunomiya
University in 2014. His current interests include polarization engineering and bioscience.
Nathan Hagen is an associate professor of optical engineering at Utsunomiya University inJapan. He received his PhD in optical sciences from the University of Arizona in 2007.
After working as a postdoc at Duke University and Rice University, in 2011 he became thelead scientist for the successful startup company Rebellion Photonics. In 2016 he joined thefaculty of Utsunomiya University. He is a senior member of SPIE and Optica (OSA), andan associate editor of Optical Engineering.
Yukitoshi Otani is a professor in the Department of Optical Engineering and a vice director ofCenter for Optical Research and Education (CORE), Utsunomiya University, Japan. He received
his master’s degree from Tokyo University of Agriculture and Technology in 1990 and his doctor’s degree from the University of Tokyo in 1995. After working for a brief period at HOYA
Corp., he was an associate professor at Tokyo University of Agriculture and Technology until
2010. He was a visiting professor at College of Optical Sciences, the University of Arizona from2004 to 2005. He joined CORE in April 2010. His current research interests include polarizationengineering and optomechatronics. He is a fellow of SPIE and Optica (OSA) and an associate
editor of OSA Continuum.

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