1076 IEEE PHOTONICS TECHNOLOGY LETTERS, VOL. 23, NO. 15, AUGUST 1, 2011

Simultaneous Measurements of Refractive Indexand Thickness by Spectral-Domain Low Coherence

Interferometry Having Dual Sample ProbesSeong Jun Park, Kwan Seob Park, Young Ho Kim, and Byeong Ha Lee, Member, IEEE

Abstract—We propose and demonstrate the novel method thatenables simultaneous measurements of physical thickness and re-fractive group index without any prior knowledge on samples. Thesystem is based on the spectral-domain optical low coherence in-terferometry with two sample probes facing each other. Owing toboth side measurements schemes, thickness and group refractiveindex could be measured with not only transparent but also highlyabsorptive samples. The average errors were 0.06% in both thephysical thickness and the group refractive index measurements.

Index Terms—Dual sample probes, Michelson fiber-optic inter-ferometer, spectral-domain low coherence interferometry.

I. INTRODUCTION

P RECISE measurements of thickness and refractive index(RI) of an optical material or specimen have been essen-

tial in various research areas including semiconductor process,optical engineering, and biomedical imaging [1], [2]. A low co-herence interferometry (LCI), based on standardMach–Zehnderor Michelson interferometry, has been considered as one of thefundamental tools for the optical measurements. However, ingeneral, the interferometer-based measurement system does notgive the physical thickness but allows only optical thickness ofa sample [3]. Many works attempting to address this problemhave been introduced [4]–[9]. One of the preferred methods hasutilized combination of confocal optics and LCI to separate thephysical thickness and the RI of a sample [4]–[6]. Differently,Hirai et al. used a tandem configuration of LCI to measure therefractive index [7]. With a 3 3 fiber coupler, H. C. Cheng etal. implemented a simple optical coherence tomography schemefor measuring both RI and thickness [8]. Dominic F. Murphy etal. also measured the physical thickness and the group indexof a highly dispersive material by using the dispersive Fouriertransform spectroscopy applied to a tandem Michelson interfer-ometer [9]. By using a tilted mirror or two different LCIs, themeasurements could be made without mechanical scans [10],

Manuscript received October 25, 2010; revised April 22, 2011; accepted May07, 2011. Date of publication May 19, 2011; date of current version July 15,2011. This work was supported in part by the Small and Medium BusinessAdministration (SMBA) grants funded by the Korean government (S1068004)and in part by BK-21 in Gwnagju Institute of Science and Technology (GIST),Korea.The authors are with the School of Information and Communications,

Gwangju Institute of Science and Technology, Gwangju 500-712, Republic ofKorea (e-mail: leebh@gist.ac.kr).Color versions of one or more of the figures in this letter are available online

at http://ieeexplore.ieee.org.Digital Object Identifier 10.1109/LPT.2011.2155642

Fig. 1. (a) Schematic of experimental setup. : Fiber couplers.: Linear polarizers. : Collimators. SLD: Superluminescent diode.

OSA: Optical spectrum analyzer. (b) The possible optical fields at the samplearm and the reference arm. : Field amplitude of the pass-through beam.

: Amplitudes of the beams reflected at both sides of the sample anddirected to the upper probe. : The same ones but directed to the lowerprobe. : The one reflected from the reference mirror. Dotted lines denote thezero OPD positions between the sample and the reference arms.

[11]. In most reports, however, there was at least one scan-ning part, which was essential in the LCI or the confocal mi-croscopy [4]–[8]. The system, based on a specially designedsample holder, limited the size of samples [4]. The method usingseveral light sources simultaneously had problems in the mea-surement speed, stability, and repeatability also [6].In this letter, we propose a novel method, which enables

simultaneous measurements of physical thickness and grouprefractive index of a transparent or even highly absorptivesample. By utilizing dual sample probes (DSP) facing to eachother in a spectral-domain optical coherence interferometer(SDOCI), the simultaneous measurements could be possiblewithout using any moving or scanning part. Since the wholesystem is implemented by fiber-optics, we can expect a numberof advantages including flexibility, miniaturization, and alsoimmunity to external influences.

II. PRINCIPLE AND EXPERIMENT

Fig. 1(a) is the experimental setup of the proposed technique.It consists of a super-luminescent diode (SLD; 1310 nm centerwavelength, 40 nm 3 dB bandwidth), two Michelson fiber-opticinterferometers cascaded by two 50:50 fiber couplers ( ),two linear polarizers ( ), three beam collimators ( ), areference mirror, and an optical spectrum analyzer (OSA; Ag-ilent 86140B, 0.06 nm resolution). The light from the SLD isdivided into the reference arm and the sample arm. The lightin the reference arm is simply reflected at the reference mirror,while the light in the sample arm is divided again into two partsand illuminates both sides of a sample.The same measurements are made two times; one is without

but the other is with a sample. The dual probes in Fig. 1(a) are

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PARK et al.: SIMULTANEOUS MEASUREMENTS OF REFRACTIVE INDEX AND THICKNESS 1077

Fig. 2. Fourier spectrum of the spectral interferogram (inset) measured throughPort 1 of Fig. 1 without a sample. The displacement is resulted from theoptical path length difference (OPD) between the reference arm and the pass-through sample arm. The peak denoted by “fiber” is from the interference be-tween the beams reflected at both end facets of the DSP.

aligned so that the beam coming from one probe can be directlycoupled to the other probe. The two polarizers ( ) are ori-ented to be almost orthogonal to each other so that only a smallpart of the beam emitting from a probe can transmit to the otherprobe. If not, the directly coupled beam becomes so big thatoverwhelms the beams reflected from the sample.At first, without a sample, the spectrum was measured at port

1 of Fig. 1(a). Themeasured interferogramwas rather sinusoidalas shown with inset of Fig. 2. To analyze the interferogram inthe spatial frequency domain, Fourier transform was made withrespect to wavelength. As shown with Fig. 2, the Fourier spec-trum had three distinct peaks. The left peak near the zero dis-placement was from the spectral shape of the light source. Themiddle one, unwanted in this experiment and denoted by ’fiber’in figure, was resulted from the interference between the beamsreflected at both fiber end facets of the DSP. The right peak, fi-nally, was resulted from the interference between the referencebeam and the transmitted beam in the DSP. The location of thissignal, denoted by , means the optical path length difference(OPD) between the two arms without the sample. In Fig. 1(b),we know that the displacement is composed of three parts;, the physical thickness of a fictitious sample; , the distancefrom the zero OPD line of the upper probe to the top surfaceof the fictitious sample; , the distance from the zero OPD lineof the lower probe to the bottom surface of the sample. Or, in aword, we have

(1)

For the second step, a sample was placed between the probesof the DSP, and the same measurement was performed. De-pending on the transparency of the sample, the relative anglebetween two polarizers was adjusted.To understand the interferogramwith the sample, the possible

beam paths in the proposed system are depicted at Fig. 1(b).is the pass-through beam (top down or bottom up) of the

DSP. is the beam reflected from the reference arm. The cor-responding optical path lengths in both sample probes are de-noted with the dotted horizontal lines. and are the beamsreflected at the top and bottom surfaces of the sample and cou-pled back to the upper probe. Inversely, and are resultedfrom the sample and coupled back to the lower probe. Since the

Fig. 3. Fourier spectrum of the interferogram (inset) measured with a sampleof 0.149-mm-thick cover glass. The coplotted green dotted curve is the samemeasurement but made through Port 2 for bypassing the reference signal. Thepeaks in the dotted boxes, (b) and (c) or (d) and (e), are from the sample in thereflection mode. Peak (a) is also from the sample but in the transmission mode.Peak (A) is the autocorrelation signal of the sample.

amplitude of the pass-through beam is much bigger than theother beams from the sample, as was mentioned earlier, the twopolarizers ( ) in Fig. 1(a) are utilized. Interferogram (inset)was measured with a sample of 0.149 mm thick cover glass andits Fourier spectrum was calculated as shown with Fig. 3. Theinterferogram looked very complicated and the Fourier spec-trum had 8 distinct peaks.In Fig. 3, the peak (a), located at the center, has the same

origin as the right peak of Fig. 2; the interference between thereference beam and the sample pass-through beam . Dueto the group index of the sample, its displacement isgiven as

(2)

The peaks in the dotted boxes are resulted from the sample. Thetwo peaks (b) and (c), of the left box, were measured with theupper probe of the DSP, thus originated from the interferencebetween and , respectively. With the configuration ofFig. 1, the locations of the peaks are given by

(3)

Similarly, the peaks (d) and (e) were measured with the lowerprobe of the DSP, which were originated from the interferencebetween and , respectively. Thus, we have

(4)

Of course, the locations of boxes can be exchanged dependingon the location of the sample within the DSP.With these peaks, the physical thickness of the sample is

simply obtained as

(5)

And the group refractive index is also simply extracted from (3)as

(6)

1078 IEEE PHOTONICS TECHNOLOGY LETTERS, VOL. 23, NO. 15, AUGUST 1, 2011

TABLE ISIMULTANEOUSLY MEASURED PHYSICAL THICKNESSES AND REFLECTIVEINDICES OF SEVEN SAMPLES. THE LAST SAMPLE NG9 IS HIGHLY

ABSORPTIVE

Of course, it can be obtained with using (4) also.The other left-most three peaks in Fig. 3 are originated from

only the sample arm without interfering with the referencebeam. The first and the third peaks are the same as the left twopeaks of Fig. 2; from the source spectrum and from the fiberend facets, respectively. The second peak, denoted by ’A’ inthe figure, is from the interference between the beams reflectedat the top and bottom surfaces of the sample. To confirm thesepeaks, the measurement was made through port 2 of Fig. 1(a),thus bypassing the reference beam. The result is depicted withthe dotted green line in Fig. 3; the left three peaks are exactlyoverlapped with the ones measured through port 1.With an absorptive sample, instead of transparent ones, the

beam reflected from the bottom of the sample hardly reachesto the top probe due to absorption. Therefore, in this case, itis helpful to use the transmitted beam and align the polarizersparallel to each other. From , , and of Fig. 1, we canget the group reflective index of an absorptive sample as

(7)

Further, when the sample is so much absorptive or opaque thateven the transmission beam cannot be detected, only from thereflected beam, and of Fig. 1, we can have the thicknessby using (5).Owing to the both side measurements scheme, it is less sen-

sitive to the absorption of the sample and thickness can be de-termined even with an opaque sample. Since the input beam isnormal to the sample surface, there is no appreciable polariza-tion related problem. The wavelength dependency of fiber andfiber coupler can affect the resolution of the system, but is not asevere problem [14]. However, only uniform and slab-like sam-ples can be successfully measured by this system. The max-imum measurement thickness, , of SDOCI is basicallylimited by the resolution of the spectrometer [9], [10]. In oursystem, was mm (with ). The spatial reso-lution of the system was 18 m also. The measurements madewith seven samples, including one opaque sample, are summa-

rized in Table I with the reference values calculated from properSellmeier equations.

III. CONCLUSION

By utilizing spectral-domain low coherence interferometry(SDLCI) we could measure the physical thickness and the grouprefractive index of a sample simultaneously. With utilizing dualsample probes (DSP), aligned to face each other, the simulta-neous measurements could be made without using any movingpart or any prior knowledge on the sample. The both side mea-surements scheme allowed the measurements even with highlyabsorptive, including opaque, samples. The average measure-ments errors obtained with seven samples were in thethickness and in the group refractive index. By usingfocusing elements and a customized spectrometer, it is expectedthat the proposed scheme would find applications in the mea-surements of rough-faced samples and biomedical specimensalso.

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