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LetterVol. 43, No. 8 / 15 April 2018 / Optics Letters

High-precision 3D surface topographymeasurement using high-stable multi-wavelength
digital holography referenced by an opticalfrequency comb
DAHI GHAREAB ABDELSALAM IBRAHIM1,2,3,* AND TAKESHI YASUI2,31

Engineering and Surface Metrology Laboratory, National Institute of Standards, Tersa St., El haram, El Giza, Egypt
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*Corresponding author: dahi.abdelsalam@nis.sci.eg
2Received 11 December 2017; revised 14 February 2018; accepted 12 March 2018; posted 16 March 2018 (Doc. ID 315397);
published 10 April 2018

High-stable, two-wavelength, digital holography referenced
by an optical frequency comb is presented. The technique isdemonstrated by using optical waves from an external cavity laser diode phase-locked to a mode-locked Er-doped
fiber comb laser light. The mixed beat signal is stabilized
at 30 MHz by a sensitive proportional integral derivativecontroller. The tunable continuous-waves stabilized withfrequency uncertainty of 5 × 10−11 are employed to investigate
large stepped structures. © 2018 Optical Society of America
OCIS codes: (120.3180) Interferometry; (090.1995) Digital holography;(120.6660) Surface measurements, roughness; (180.6900) Threedimensional microscopy; (120.0120) Instrumentation, measurement,
and metrology.
https://doi.org/10.1364/OL.43.001758

The main advantage of digital holography (DH) is that it makes
it possible to extract quantitatively the three-dimensional (3D)
information of the phase object from the numerical reconstruction of a single digitally recorded hologram [1–3]. In general, ahologram refers to the interference pattern between the lightscattered by a 3D object and a mutually coherent reference
beam. The amplitude and phase information are encoded in thefringe structure of the hologram and can be recovered and used
for many applications. Different approaches were used to retrieve the phase object based on a single wavelength. However,a serious limitation to their use is that they can only handlesmooth profiles and step heights less than half a wavelength.
One of the approaches adapted to overcome the problem ofa small dynamic range is based on two-wavelength interferometry [4]. In the two-wavelength method, a careful choice of
wavelengths enables the system to make use of long-range
measurements. If the phase of the object is measured at twowavelengths, λ1 and λ2 , then the synthetic beat wavelength
λbeat  λ1 λ2 ∕jλ1 − λ2 j. Because of the normal instability of
0146-9592/18/081758-04 Journal © 2018 Optical Society of America

the two-wavelengths used, the synthetic beat wavelength is fluctuated and, hence, an inherent phase error is produced. Since
the ambiguity range characterizes the measurement range, thisfluctuation limits the measurement range (can be achieved
with at least λ1 − λ2  1.00 nm or more). In this Letter, weincreased the measurement range (λ1 − λ2  0.08 pm) andminimized the inherent phase error to zero by using high-stable
two-wavelength DH configuration referenced to one of the optical frequency comb (OFC) lines of a commercial fiber comb
laser (FC1500-250-WG, Menlo Systems GmbH, Munich,Germany), which is phase-locked to a rubidium (Rb) atomicclock (FS725, Stanford Research Systems, accuracy  5 × 10−11and instability  2 × 10−11 at 1 s). The merits of using an OFC
include improvement of wavelength stability, reduction of laserline width, and the ability to generate two-wavelength lightwith arbitrary wavelength difference (0.08 pm < λ1 − λ2 <70 nm). This technique makes it possible to feature stepped
structures as large as 10 m depth with per minute-order resolution. To the best of our knowledge, this is the first attempt onhigh precision, wide dynamic range measurement using highstable two-wavelength DH based on OFC lines of a modelocked fiber comb laser.
In this Letter, two wavelengths λ:1  1542.7661 nm andλ:2  1534.8211 nm, yielding a synthetic beat wavelength
λbeat  298 μm, are used in a series. Using these high-stable
two wavelength signals, a beat wavelength is synthesized andallowed to measure a rough surface of a Japanese 1-yen coin.
For each high-stable wavelength, a single-shot off-axis hologram is captured by a cooled InGaAs CCD camera (GoldeyeP-008, Allied Vision Technologies GmbH, 320 × 256 pixels,pixel size  30.0 μm). The intensity distribution in the offaxis hologram formed by the interference of both object andreference beams can be formulated to Eq. (1) [2]:I k, l   jOj2  jRj2  R  O  RO ,(1)where O is the object beam, R is the reference beam,  denotes
the complex conjugate, and k, l are discrete coordinates in theVol. 43, No. 8 / 15 April 2018 / Optics LettersLetter1759

hologram plane. In Eq. (1), the first two intensity terms are ofzero order, which can be directly filtered in the Fourier domain[5,6], and the last two are the interference terms which include
the interference phase. The single-wavelength phase is computed individually by the angular spectrum method [7]. Then,by subtracting the phase image of one wavelength from thephase image of the second image, an equivalent phase image
is expressed by Eq. (2):φbeat  φλ2  − φλ1 :(2)The equivalent phase image is synthesized which allows forimaging much larger axial ranges. By measuring the accurate
values of both the synthesized phase and the equivalent wavelength, the optical path difference Δz is calculated preciselyaccording to Eq. (3):Fig. 2. (a) Beat signal stabilized by PID at f beat  30 MHz, as seen
by an RF spectrum analyzer, and (b) a photograph of the investigatedrough Japanese 1-yen coin sample.

(3)
φbeat  4πΔzλ1 − λ2 ∕λ1 λ2  4πΔz∕λbeat :From Eq. (3), it is evident that by measuring the interference phase and knowing the synthetic beat wavelength, the optical path difference is obtainable. In addition, Eq. (3) showsthat any small change in the synthetic beat wavelength produces an error in the optical path difference, so it was essential tostabilize the wavelengths to one of the OFC lines of the fibercomb laser. The optical frequencies, νn , of the comb lines canbe formulated to Eq. (4) [8]:free-running beat signal is stabilized at 30 MHz by the PID
controller. The n value in Eq. (4) was determined by a wavelength meter (AQ6151, Yokogawa Test & Measurement
Corporation, wavelength accuracy  0.3 pm). The opticalfrequencies νCW1 and νCW2 were adjusted in a series by changing n and/or f rep. A representation of these frequencies νCW1and νCW2 which gives the beat signal νbeat is schematicallyshown in Fig. 1. This synthetic beat frequency is related tothe synthetic beat wavelength λbeat , according to Eq. (5):νn  f ceo  nf rep  f beat ,νbeat  νCW2 − νCW1  c∕λbeat ,(4)(5)

where n is an index the comb line, f rep is the repetition frequency, f ceo is the carrier envelope offset frequency, and f beatis the beat frequency. A representation of the output field of amode-locked fiber comb laser in frequency domain, including
the definition of the f ceo , f rep , and f beat , is shown in Fig. 1.
Frequencies f rep and f ceo , respectively, were locked at 250
and 20 MHz, whereas f beat was stabilized at f beat  30 MHz
by the proportional integral derivative (PID) controller.
Our system is presented in Fig. 3. The system is composedof two sources. The first source emits tunable continuous-wave(CW) light in the range of (1520–1590 nm) by an external
cavity laser diode (ECLD). The second is a mode-locked
Er-doped fiber comb laser light (center wavelength λc 1550 nm, spectral band width Δλ  73 nm, pulse durationΔτ  100 fs, and mean power P mean  380 mW). Two rotatable λ∕2-wave plates and a polarized beam splitter serve forsetting polarization direction, as well as the power, of the twodifferent beams. The beams diffracted from a diffraction grating are mixed to generate a beat signal. This beat signal isdetected by a high-speed photodetector (Thorlabs, InGaAS
amplified detector, 700–1800 nm) and monitored by a radio
frequency (RF) spectrum analyzer, as shown in Fig. 2(a). The

where c is the speed of light. Based on Eqs. (4) and (5), λ1 , λ2 ,and λbeat were determined.
Two wavelengths of λ:1  1542.7661 nm and λ:2 1534.8211 nm with a power of 2.5 mW were used in a series
to feed into a Michelson-type interferometer. The coin sample
was placed at one arm of the interferometer, while the otherarm was referenced by a gold mirror (suitable for near-infraredlight) of flatness λ∕10. After reflecting from the sample andreference mirror, the two beams are recombined at the nonpolarizing beam splitters (NPBS). The interfering object beam(O) and the reference beam (R) were tilted at a small angle withrespect to each other to produce an off-axis hologram and to be

Fig. 1. Representation of the output field of a mode-locked fibercomb laser in frequency domain, including the definition of thef ceo , f rep , and f beat .

Fig. 3. Experimental setup. ECLD, external cavity laser diode;
PZT, piezoelectric transducer; G, grating; M, mirror; PBS, polarizing
beam splitter; NPBS, nonpolarizing beam splitters; PD, photodetector.

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Vol. 43, No. 8 / 15 April 2018 / Optics Letters

LetterFig. 4. (a) Original off-axis hologram at a wavelength1542.7661 nm, (b) correction of (a), and (c) the difference between(a) and (b).

transferred via an imaging lens LNA  0.4 to the cooled IR
InGaAs camera.
To minimize the background noise produced by the ambient medium, a single-shot off-axis hologram is captured at eachwavelength. The captured off-axis holograms were corrected bya flat fielding method to reduce the speckle noise [9–11]. The
corrected off-axis holograms were further corrected by using
4 × 4 median filters. Figure 4(a) shows the off-axis hologram
captured at λ:1  1542.7661 nm. Figure 4(b) shows the corrected off-axis hologram of Fig. 4(a) by using both a flat fielding
method and a 4 × 4 median filter. The intensity and phase of
the corrected off-axis hologram was numerically retrieved byusing the angular spectrum method. Figures 5(a)–5(c) show the3D pseudo-color reconstructed amplitude-contrast images of
the red circles of Fig. 4. Figures 5(d)–5(f ) show the corresponding 3D pseudo-color reconstructed phase-contrast images. It is
worth mentioning that using flat fielding in reconstruction of
scattering objects is preferable; otherwise, the structure of theobject is partially lost, as shown in Fig. 5.
Figure 6(a) shows the 3D pseudo-color reconstructed phasedifference (reversed direction of the x-axis) map of two off-axis
holograms captured at wavelengths λ:1  1542.7661 nm andλ:2  1534.8211 nm.
To measure clearly the depth of the pattern one (number 1)
on the front face of the Japanese coin, a grafting process has
been done. In this process, the phases of an array of pixels(125 × 195) along the x-axis and (5 × 150) along the y-axis
are converted to maximum phases. Cut lines before and aftergrafting along the red and blue lines in the phase-contrast images of Figs. 6(a) and 6(b), respectively, are shown in Fig. 6(c),indicating the cross-sectional profile of 164 pixels. Based on
Fig. 6(c), the step height is calculated to be 139.9995 μm,Fig. 5. 3D pseudo-color reconstructed amplitude-contrast image ofa single wavelength of (a) Fig. 4(a), (b) Fig. 4(b), (c) Fig. 4(c), and(d) the corresponding phase-contrast images.

Fig. 6. (a) 3D pseudo-color synthesized phase of two off-axis holograms captured at the two wavelengths λ:1  1542.7661 nm andλ:2  1534.8211 nm, (b) grafting of (a), and (c) 1D phase profiles
along both the red and blue lines of (a) and (b).

which matches very well with the nominal value measured withthe confocal microscope. In Fig. 6, the 3D reconstructed phasemaps were flipped upside down to see the surface from a different side [12]. An experiment on another step height object wasperformed to demonstrate the effectiveness of our approach.
A representation of the step sample of surface height of around7.00 mm measured roughly by a digital micrometer is shown inFig. 7(a). The sample was tested by two super-stable wavelengths at λ:1  1540.4010 nm and λ:2  1541.4015 nm.
The captured off-axis holograms at each wavelength werecorrected by a flat fielding method to reduce the speckle noise
and then were numerically reconstructed by using the angularspectrum method.
The retrieved phase maps of the two wavelengths are thensubtracted, and a 1D phase profile along the X -axis is shown in
Fig. 7(b). The phase is then converted to height and, as seen in
Fig. 7(b), the step height is in the range of 7.1800 mm.
In conclusion, we have presented a new method utilizing
high-stable, two-wavelength, DH referenced by an OFC. The
merits of using an OFC are high accuracy, high stability, andlarge range ambiguity which, as whole, are unavailable inexisting approaches, which makes it adequate for metrology
applications. The presented method was effectively applied

Fig. 7. (a) Representation of the step sample of a 7.00 mm stepheight measured at super-stable two wavelengths λ:1  1542.7661 nm
and λ:2  1534.8211 nm. (b) 1D phase profile along the X -axis of thereconstructed phase difference.

Letter
for testing two different stepped structures of 140 μm and7.00 mm, and the results showed excellent matching with
the nominal values. We claim that this method can be used
for stepped structures as large as 10 m depth with high precision, and this will be the next step of our research work. The
high precision is mainly due to the high stability of wavelengths
that are referenced by an OFC lines of a fiber comb laser, whichis stabilized to the (Rb) atomic clock with frequency uncertainty of 5 × 10−11 .
Funding. Ministry of Education, Culture, Sports, Scienceand Technology (MEXT) (26246031); Exploratory Researchfor Advanced Technology (ERATO); Japanese Science andTechnology Agency (MINOSHIMA Intelligent Optical
Synthesizer Project, JPMJER1304); Mitutoyo Association for
Science and Technology (MAST).

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