APPLIED PHYSICS LETTERS 112, 171101 (2018)

Multi-object investigation using two-wavelength phase-shift interferometry
guided by an optical frequency comb
Dahi Ghareab Abdelsalam Ibrahim1,2,3,a) and Takeshi Yasui2,31

Engineering and Surface Metrology Lab., National Institute of Standards, Tersa St., El haram, El Giza,
Egypt
2
Graduate School of Technology, Industrial and Social Sciences, Tokushima University, 2-1,
Minami-Josanjima, Tokushima 770-8506, Japan
3JST, ERATO, MINOSHIMA Intelligent Optical Synthesizer Project, 2-1, Minami-Josanjima,
Tokushima 770-8506, Japan(Received 30 January 2018; accepted 3 April 2018; published online 23 April 2018)
Two-wavelength phase-shift interferometry guided by optical frequency combs is presented. We
demonstrate the operation of the setup with a large step sample simultaneously with a resolution
test target with a negative pattern. The technique can investigate multi-objects simultaneously withhigh precision. Using this technique, several important applications in metrology that require highspeed and precision are demonstrated. Published by AIP Publishing.
https://doi.org/10.1063/1.5024244

Phase shift interferometry (PSI) is an optical metrology
technique used for surface micro-topography measurementswith excellent accuracy.1–4 However, the phase distribution suffers from 2p discontinuities, which set a limit to the phase measurement range of single-wavelength. Two-wavelength PSI
provides a solution to this ambiguous phase problem with theuse of a beat wavelength kbeat from two wavelengths k1 and k2.
As a result, the phase measurement range is extended to a longer kbeat. However, it involves a shortcoming of being susceptible to instability of the two wavelengths used. Instability of thetwo-wavelengths used might introduce a fluctuation in the beatwavelength, and hence an inherent phase error arises. We
expect that this error is maximized when longer kbeat is used toexamine surfaces with large steps. Also, such wavelength instability limits the minimum difference between two wavelengths,and hence the maximum kbeat.
An interesting wavelength reference to suppress the wavelength instability is an optical frequency comb (OFC).5,6 The
OFC is composed of a series of frequency spikes regularly
spaced by a repetition frequency frep with a carrier-envelopeoffset frequency fceo and can be used as an optical frequency
ruler traceable to a frequency standard by its mode-locking
nature and laser stabilization. If a tunable narrow-linewidth
continuous-wave (CW) laser, e.g., an external cavity laser
diode (ECLD), is phase-locked to one mode of OFC, the inherent characteristics of OFC (narrow linewidth, high stability,high accuracy, etc.) are transferred to the CW laser.
Furthermore, the CW laser can be tuned at a step of frep bychanging the phase-locked OFC mode. The phase-locked CW
laser, namely the optical frequency synthesizer (OFS)7 is traceable to the frequency standard via OFC, and hence largely suppresses the wavelength instability.
In this letter, we minimized the inherent phase error andexpanded the beat wavelength by introducing an OFS into
two-wavelength PSI. This technique makes it possible to feature large stepped structures as large as meter depth withnanometer resolution. We use this merit to investigate twoobjects in real-time (multi-objects simultaneously) with highprecision. This technique can be applied to test a burst ofidentical objects in real time for onsite production lines.
We here used a Mach-Zehnder interferometer to produce the interference pattern. The intensity of the interference signal is given as follows:8
Ij ¼ a þ b cos ð/ þ ðj  1Þp=2Þ;(1)where a is the so-called DC level, b is the modulation,
j ¼ 1–4 in the case of four frames, and / is the phase of theinterference signal. The interference phase is related to theoptical path difference (Dz) between the two beams of theinterferometer as follows:/ðki Þ ¼ ð2p=ki ÞDz;(2)where k is the wavelength of the illuminating light source
and i ¼ 1–2. The phase information encoded in the fringe
structure of the interferogram is recovered by the PSI technique via changing the reference arm length of the interferometer in four equal steps with a step size equivalent to thep/2 phase shift;9 for each step, the interference signal isrecorded. Using these four phase-shifted signals of Eq. (1),the phase is extracted for each point of the objects as/ ¼ tan1 ½ I4 I2 Þ=ðI1 I3 Þ:(3)A phase unwrapping algorithm to unwrap the 2p module of
the wrapped phase is applied because step heights of theobjects being tested are greater than one fringe of the interference signal.1,10 Here, we used signals of two wavelengths
k1 and k2. For each wavelength, four phase-shifted signals
are captured successively, and the single-wavelength phaseis computed by applying Eq. (3). Then, by subtracting thephase image /(k1) of k1 from the phase image /(k2) of k2, abeat phase image /beat can be written asa)

Author to whom correspondence should be addressed: dahi.abdelsalam@nis.sci.eg

0003-6951/2018/112(17)/171101/4/$30.00

112, 171101-1/beat ¼ /ðk2 Þ  /ðk1 Þ;(4)

Published by AIP Publishing.

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D. G. A. Ibrahim and T. Yasui

Appl. Phys. Lett. 112, 171101 (2018)

where the beat phase image is synthesized that allows forimaging much larger axial ranges. The beat wavelength canbe formulated using
kbeat ¼ k1 k2 =ðk1  k2 Þ:(5)

By measuring the beat wavelength and the synthesizedphase, the height can be calculated precisely as
h ¼ ð/beat =4pÞkbeat :(6)From Eq. (6), it is evident that any small variation in the beatwavelength produces an error in the reconstructed height; so,
it is essential to stabilize the wavelengths employed to investigate the objects. The present OFS was achieved by phaselocking a tunable ECLD to one mode of the OFC. Figure 1
shows a description of an ECLD and an OFC in the opticalfrequency domain. The optical frequency  CW of the OFS isgiven by11
CW ¼ fceo þ nfrep þ fbeat ;(7)where n is the mode number of the OFC (typically, 106)
phased-locked by an ECLD, and fbeat is the beat frequency
between the ECLD and the n-th OFC mode.  CW can be tuned
at a step of frep by changing the n value, while maintaining thephase-locking to the frequency standard. An upper part of Fig.
2 shows an experimental setup of OFS, which is composed of atunable ECLD (LT-5001N, OptoComb, Inc., optical wavelength range ¼ 188.5 THz–197.2 THz, wavelength range¼ 1520 nm–1590 nm, mean power ¼ 30mW) and a commercialized fiber OFC laser (FC1500–250-WG, Menlo Systems
GmbH, Munich, Germany, center wavelength ¼ 1550 nm, spectral bandwidth ¼ 73 nm, and mean power ¼ 380mW). fceo andfrep were, respectively, set to 20 MHz and 250 MHz by phaselocking to a rubidium (Rb) atomic clock (FS725, Stanford
Research Systems, accuracy ¼ 5  1011 and instability ¼ 2 1011 at 1 s) using accompanying stabilization electronics.
Output lights from the ECLD and the OFC were spatially overlapped by a polarization beam splitter (PBS) and half-waveplates (k/2) together with power adjustment. After passing
through another k/2, a polarizer, and a diffraction grating, thefbeat signal was detected by a photodiode (PD). fbeat was set to30 MHz by phase-locking to the same frequency standard
using a proportional-integral-derivative (PID) controller. The nvalue can be determined by a wavelength meter (AQ6151,
Yokogawa Test & Measurement Corp., wavelength accuracy ¼ 0.3 pm). Finally,  CW can be tuned at a step of 250 MHz(¼frep) within the range of 188.5 THz to 197.2 THz. The corresponding wavelength kCW can be tuned at a step of 2 pm within
the range of 1520 nm to 1590 nm. The optical frequencies  CW1

FIG. 1. Description of the ECLD and the OFC in the optical frequency
domain.

FIG. 2. Experimental setup. ECLD, external cavity laser diode; PZT, piezoelectric transducer; G, grating; M, mirror; PBS, polarizing beam splitter;
NPBS, non-polarizing beam splitter; PD, photodetector; S1, first object ofstep height of around 7.201 mm (employed also as a reference); and S2, second object of a USAF resolution target with a negative pattern.

and  CW2 of the OFS were adjusted in series by changing n.
The optical beat frequency  beat between them is related to thebeat wavelength kbeat bybeat ¼ CW2  CW1 ¼ ckCW1  kCW2
c¼;
kCW1 kCW2kbeat(8)

where c is the speed of light and kCW1 and kCW2 are wavelengths corresponding to  CW1 and  CW2. The present OFS
has the ability to generate two-wavelength light with an arbitrary wavelength difference (2 pm < k1- k2< 70 nm), corresponding to the beat wavelength from 35 lm to 1.2 m.
An experimental setup of two-wavelength PSI is shownin the lower part of Fig. 2. Output light from the OFS wasfed into the Mach-Zehnder interferometer. After recombining both beams, the off-axis holograms were captured at two
different wavelengths by a cooled InGaAs CCD camera(Goldeye P-008, Allied Vision Technol. GmbH, 320  256
pixels, pixel size ¼ 30.0 lm), and then reconstructed with afour-step PSI algorithm.3 The variations in the optical pathlength of one arm were done by a piezoelectric transducer(PZT).
A reflection object S1 and a transmission object S2 wereused as samples. S1 is a step height of around 7.201 mm(measured roughly by a digital micrometer) positioned atreflection in the reference arm of the interferometer, while S2
is a USAF (United States Armed Forces) resolution test target with a negative pattern positioned at transmission in theobject arm of the interferometer. In order to image the twoobjects S1 and S2 in the imaging plane of the camera, the second object S2 was placed in a suitable distance in the object
arm related to the power of the imaging lens L (NA ¼ 0.4).
A schematic drawing of S1is shown in Fig. 3(a). Photographsof both S1 and S2 taken with the proposed setup with blocking of the two arms of the interferometer mutually are shownin Figs. 3(b) and 3(c), respectively. The two objects wereinvestigated simultaneously by using two different wavelengths at k1 ¼ 1540.403 nm and k2 ¼ 1541.403 nm.

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Appl. Phys. Lett. 112, 171101 (2018)FIG. 3. (a) Representation of thereflected type object, (b) a photographof 12 mm of (a), and (c) a photographof the transmissive USAF object.

Once S1 and the gold mirror (in the absence of S2) constitute the off-axis interferogram, S2 is introduced in theother arm. The obtained off-axis hologram is deformed inaccordance with the patterns of S2. For each wavelength,
four phase-shifted off-axis interferograms were recorded
successively. The change in the optical pathlength was doneby actuating S1 using a closed-loop PZT with a linearityof up to 0.15%. Figures 4 and 5 show four phase-shiftedimages at two different wavelengths k1 ¼ 1540.403 nm andk2 ¼ 1541.403 nm, respectively. For each wavelength, the3D phase map is computed in accordance with Eq. (3). As
seen in Figs. 4 and 5, the off-axis fringes appear clearly
inside the yellow and red rectangles of both objects shown inFigs. 3(b) and 3(c).
Since the arctan function produces values only in therange of [p/2, p/2], as shown in Fig. 6, the wrapped phasefor each wavelength is unwrapped9,10 to remove the ambiguity in the phase. Figures 7(a) and 7(b) show the unwrapped
phases of Figs. 6(a) and 6(b), respectively. By subtracting
the phases of Figs. 7(a) and 7(b), an equivalent phase image
is synthesized, as shown in Fig. 7(c).
As seen in Fig. 7(c), all the illuminated patterns of S1and S2 are extracted into a single image. Based on the synthesized phase image of Fig. 7(c) and the beat wavelength,
the step-height of S1 as well as the heights of the patterns inS2 are precisely obtained using Eq. (6). The phase profile
extracted horizontally along the red line (S1) in the synthesized phase of Fig. 7(c) is shown in Fig. 7(d), indicating thecross-sectional profile of 320 pixels. Here, the X-axis isreversed to see the phases from different angles of view.12
Based on Fig. 7(d), the /beat ¼ 38 rad (the difference
between the blue lines). The beat wavelength is calculatedusing Eq. (5) to be kbeat ¼ 2.3744eþ6 nm. By substituting thevalues of /beat and kbeat in Eq. (6), the step height is estimated to be 7.180 mm [no image enhancement technique
was applied to Fig. 7(d)], which is in excellent agreementwith the nominal value.
The heights of the patterns of S2 can also be extracted
from the same synthesized phase image of Fig. 7(c). The
phase profiles extracted vertically along both blue and blacklines of Fig. 7(c) were corrected from noise by applying thehigh pass filter,13 and the corrected phase profiles are shownin Figs. 8(a) and 8(b), respectively. The benefit of this filter
is to mitigate the coherent noise to some amount. The beatphase along the blue and black lines of Fig. 7(c) before correction with a high pass filter was estimated to be(/beat ¼ 5.9 rad), while after correction, it is estimated to be(/beat ¼ 3.2 rad) as shown in Fig. 8. By substituting the values of /beat and kbeat in Eq. (6), the step height is estimatedto be 0.605 mm.
We claim that image enhancement techniques such asflat fielding with apodization may improve the edges inFig. 8,14–16 and this will be the next step of our futureresearch. Here, the measurement precision of the object
surface depends on the wavelength stability and therobustness of the interferometer to surrounding external
disturbances such as air turbulence or vibration. Although
the optical comb largely enhances the stability of the frequency and the phase of two-wavelength light, surrounding external disturbances essentially limits the phase noise
to k/100–k/1000. For that reason, we expect that using
single-shot parallel four-step PSI will minimize the error
in measurement, and this will also be the next step of ourfuture research.

FIG. 4. Four phase-shifted images of one wavelength k1 ¼ 1540.403 nm
captured by a cooled In-GaAs camera.

FIG. 5. Four phase-shifted images of one wavelength k1 ¼1541.403 nm captured by a cooled In-GaAs camera.

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D. G. A. Ibrahim and T. Yasui

FIG. 6. (a) Wrapped phase map of Fig. 4 and (b) wrapped phase map of Fig. 5.

Appl. Phys. Lett. 112, 171101 (2018)secured by the frequency standard via the OFC. The technique
is fully operable for samples having large step heights as largeas meter depth with nanometer resolution. Merit of this technique is that it can be used onsite in a production line to test
identical objects in real time. The mechanism can be done asfollows: a calibrated object is positioned at reflection in the reference arm of the interferometer and a burst of same objects
being tested are positioned in the object arm in the interferometer. From the difference in the phase between the calibrated
object and the object being tested, the performance of the object
being tested is assigned. If the difference in the phase equals
zero, this means a perfect tested object, if not, means a reconditioning is needed. Future improvement of the system
includes use of this technique with a single-shot parallel fourstep, dual-wavelength PSI interferometry, which is expected toincrease the SNR and improve the accuracy of measurement.
Funding was provided by Exploratory Research for
Advanced Technology (ERATO), Japanese Science andTechnology Agency (MINOSHIMA Intelligent Optical
Synthesizer Project, JPMJER1304) and Mitutoyo Associationfor Science and Technology.

FIG. 7. (a) Unwrapped phase map of Figs. 6(a) and (b) the unwrapped phasemap of Fig. 6(b). (c) Difference between (a) and (b). (d) 1D phase profile
along the red line of (c).

FIG. 8. (a) 1D phase profile along the blue line of Fig. 7(c) and (b) a 1D
phase profile along the black line of Fig. 7(c). The profiles shown here areafter application of the high pass filter process.

In conclusion, we have presented an optical metrology
technique for measuring the 3D surface profiles of many
objects simultaneously with high precision. Excellent results
were extracted with all featured patterns in a single shot. The
term high precision here refers to the highly stable wavelengths

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