A new balanced-path heterodyne I/Qinterferometer scheme for low environmental
noise, high sensitivity phase measurements for
both reflection and transmission geometry.
Seunghyun Yoon,1 Youngkyu Park,2 Kyuman Cho1,2,*
1
Interdisciplinary Program of Integrated Biotechnology, Sogang University, 1 Sinsu-Dong, Mapo-Gu, Seoul, 121742, South Korea
2
Department of Physics, Sogang University, 1 Sinsu-Dong, Mapo-Gu, Seoul, 121-742, South Korea
*kcho@sogang.ac.kr
Abstract: A new heterodyne interferometer scheme which has open
accesses to both the geometrically balanced probe beam (PB) and reference
beam (RB) paths, for which, depending on the nature of a specific sensing
mechanism, a transmission geometry or a reflection geometry can be
employed, is presented. We will show that, because of a small separation
between the short length PB and RB running parallel to each other our
newly proposed optical arrangement allows high rejection of unlocalized
environmental perturbations. In fact, the geometrically balanced optical
arrangement provides 19dB rejection of any vibrations parallel to the
direction of beam propagation, which cannot be achieved in a conventional
interferometer scheme. Applications of this new interferometer scheme are
discussed. As an example, we will show that our newly proposed
interferometer scheme can be applied for high sensitivity measurements of
concentration dependent refractive indexes in various solutions.
©2013 Optical Society of America
OCIS codes: (120.3180) Interferometry; (120.5050) Phase measurement; (120.3930)
Metrological instrumentation.
References and links
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9 September 2013 | Vol. 21, No. 18 | DOI:10.1364/OE.21.020722 | OPTICS EXPRESS 20722
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1. Introduction
Two beam interferometry has been extensively applied for many sensor applications because
of its extremely high sensitivity in measuring the effective optical path length (OPL)
difference between the probe beam (PB) and the reference beam (RB) [1–3]. Optical
arrangements in most of two beam interferometer sensors are modifications of the Michelson
interferometer or the Mach-Zehnder interferometer. Since the PB and RB in the MachZehnder interferometer are running parallel to each other with relatively small separation, it
may be less susceptible to environmental perturbations such as atmospheric turbulence,
vibrations, acoustic noises, and so forth than a Michelson interferometer. The Jamin
interferometer [2,4] is specially designed to provide minimal beam separation between the PB
and the RB. In a Mach-Zehnder interferometer or Jamin scheme, however, since a sample cell
or a sensor head must be placed in the PB path, only a transmission geometry (TGM) is
applicable in the sensor arrangement which limits application capabilities. Refractometery
may be a typical application of the TGM [4,5]. It has been shown that the sample arrangement
becomes more flexible if PB is taken out from the interferometer and the reflected beam from
the sample is reinjected into the interferometer by using a polarizing beam splitter (PBS), λ/4plate (QWP), and the reflecting surface or the mirror [6,7], which will be referred to the
coupling mirror. This scheme can offer flexibility in the sensing arrangement: Depending on
the sample or sensing mechanism, either the reflection geometry (RGM) or the TGM can be
arranged. However, because of this extra beam path, the interferometer becomes unbalanced
and susceptible to environmental perturbations. In fact, any acoustic and/or mechanical
vibrations of the reflecting sample or the coupling mirror will be directly converted into the
corresponding phase noises. Although fiber optic or integrated waveguide interferometers
have been widely used in sensor applications [8,9], a bulk-optic interferometer is still
important in many applications such as coherent scanning microscopy [6,7,10–12], readout
sensing for a bio-CD [13] or a fluidic channel [14], and precision metrologies [15,16].
In heterodyne interferometry, the PB and the RB have different frequencies. The OPL
difference or the phase difference is then carried by intermediate frequency heterodyne beat
which is typically in the RF range. It is the big advantage of heterodyne interferometry that
state-of-the-art demodulation technologies, which have been developed in RF
communications, can be employed for extracting the phase difference. It has been shown that
the relative phase difference between the PB and RB can be directly measured by using the in
and quadrature (I/Q) demodulation scheme [6]: The exact value of the phase difference and
the amplitude change of the PB can be simultaneously measured without any rigorous
calibration procedures [6,7, 11].
#191228 - $15.00 USD
Received 5 Jun 2013; revised 8 Aug 2013; accepted 19 Aug 2013; published 28 Aug 2013
(C) 2013 OSA
9 September 2013 | Vol. 21, No. 18 | DOI:10.1364/OE.21.020722 | OPTICS EXPRESS 20723
In this paper, we are presenting a new heterodyne I/Q-interferometer scheme, which has
the balanced PB and RB paths for both transmission and reflection measurements. As will be
shown, our new novel scheme cannot only provide versatility of sensing arrangements but
also can reject environmental noises for which characteristic lengths are larger than the
separation between the parallel PB and RB. In particular, it can provide ~19dB rejection of
any vibrations of the coupling mirror. To the best of our knowledge, no interferometer
scheme which can reject vibration noises of a sample has been published yet. As an
application example, we will demonstrate that the proposed interferometer scheme can be
used for measuring refractive index difference between the reference and sample liquids in
the homemade fluidic channel.
2. Interferometer and experimental arrangement
A schematic of the experimental arrangement is shown in Fig. 1. A homemade, stabilized,
dual frequency, dual polarization He-Ne laser is used as the light source. The laser has better
than 33dB return loss by using two optical isolators, mirrors, and polarizing beam splitters
(PBSs), which are not shown in the figure. The frequency stability is ~4MHz in the lab
environment. It has two output beams for which each beam has two orthogonally polarized
principal polarization modes with different frequencies. The principal polarization modes of
one output beam from the laser are mixed together by using a polarizer P1 oriented at 45° to
the principal polarization modes and detected by a high-speed photodiode PD1. The
heterodyne beat signal from the PD1 is used as the local oscillator for RF I/Q-demodulator
(PolyPhase Microwave, QD0511B). The principal polarization modes in the other output
beam from the laser are split into two paths by using the PBS1: the transmitted beam with
frequency ν 1 is used as the RB and the reflected beam with frequency ν 2 is used as the PB.
The plane of polarization of the PB is rotated by 90° by using the half-wave plate, HWP1, and
reflected at the right angle prism (RP). The RB and PB are transmitted through the PBS2 and
PBS3, respectively, circularly polarized by using a quarter-wave plate (QWP), and sent to the
sample. The separation between the PB and RB is 17mm in this preliminary work but it can
become much narrower if smaller optical components are closely mounted together.
Depending on a specific application, either the reflection geometry or transmission geometry
can be used. In the former case, generally used for scanning microscopy, the sample is a
reflecting surface. The PB and RB are reflected at the sample and reference surfaces,
respectively. In the latter case, the PB and RB are transmitted through the sample and
reference channel, respectively. The PB and RB are reflected back into the incident beam
paths by using a mirror. Because of the double pass in the QWP, the planes of polarization of
the returning beams are rotated by 90°. The RB is reflected back into the interferometer at the
PBS2 and the plane of polarization is rotated by 90° by using a half-wave plate HWP2. The
RB is then transmitted through the PBS3 and combined with the PB which is reflected at the
PBS3. The PB and RB are orthogonally polarized to each other and carefully aligned so that
they are propagating along the same path. The PB and RB are mixed by using the polarizer P2
oriented at 45° to the preferred axes of the PBS3 and high frequency photodiode PD2. The
output heterodyne beat signal from the PD2 carries the phase difference between the PB and
RB and drives the RF input of the I/Q-demodulator. Details of the I/Q-demodulation in
heterodyne interferometry can be found in [6,7]. Since the output signals from the I/Qdemodulator have 90° phase difference, it can be shown that [6]
vQ
vI
= tan ( Δφ )
(1)
where Δφ , vI , and vQ are the phase difference between PB and RB, low-pass filtered inphase and quadrature outputs from the I/Q-demodulator, respectively. It should be
#191228 - $15.00 USD
Received 5 Jun 2013; revised 8 Aug 2013; accepted 19 Aug 2013; published 28 Aug 2013
(C) 2013 OSA
9 September 2013 | Vol. 21, No. 18 | DOI:10.1364/OE.21.020722 | OPTICS EXPRESS 20724
emphasized that, since the phase difference can be obtained directly from arctangent
operation of Eq. (1), it does not require any calibration to extract the phase value from the
interference signal. Moreover, since the tangent function always has a large slope, it does not
require any feedback control for maintaining the optimum phase demodulation condition.
These two are the major advantages of the I/Q-interferometer scheme over the conventional
schemes. Equation (1) is switched to cotangent function if Δφ > π 4 or, equivalently, if
vI < vQ , and add or subtract π 2 to the cot−1 value to avoid the discontinuity of tangent
function at Δφ = ± π 2 .
Fig. 1. Schematic of experimental arrangement (a), and a photograph of the interferometer and
sample part of the experimental arrangement (b).
It is clear from Fig. 1 that two arms of the interferometer are almost exactly balanced, i.e.,
the corresponding OPLs of the PB and RB from the laser to the PD2 except for the roundtrip
OPL difference induced by the sample have the same lengths larm . Therefore, the phase
difference between the PB and RB is given by
Δφ =
2π
 (ν 1 − ν 2 ) larm + ΔφQ − S + ΔφNL + 2 ( nR lRν 1 − nslsν 2 ) 
c 
(2)
where nsls , and nR lR are OPLs of the sample and the reference channels, respectively. Any
other quasi-static phase drifts are included in ΔφQ-S . The periodic nonlinearity, ΔφNL , which
is a small but significant systematic error resulted from the crosstalk between principal
polarization modes caused by ellipticity on the principal polarization modes and imperfect
alignment of polarization components used in the interferometer [17]. The cross talk between
the principal modes of our stabilized laser is approximately −40dB, but, because of the
misalignment between polarization components and the principal polarizations, overall
crosstalk at the PD2 is approximately −30dB. The crosstalk has been measured by rotating the
polarizer at each output port and derived from the amplitude ratio between the maximum and
minimum beat signal. All polarization components are carefully aligned to minimize the
crosstalk between the channels and, thereby, the periodic nonlinearity. It has been shown that
the magnitude of this periodic displacement is in the nm range if the principal axes of the light
source and polarization components are properly aligned. The periodic nonlinearity may be an
important parameter for determining the accuracy of phase measurements. If it is small,
however, it may be less important in measuring a phase difference, because the phase change
caused by the nonlinearity may not be significant for a small displacement in effective OPL.
More rigorous studies about the periodic nonlinearity will be performed in the future work.
The first term in Eq. (2) is the phase difference due to the frequency difference ν 1 − ν 2
between the PB and RB which is 820MHz in our present work, which is responsible for slow
and small thermal drift caused by ambient temperature change. The center wave length of the
laser is 632.8nm. All components are fixed on top of the optical table and placed inside a
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Received 5 Jun 2013; revised 8 Aug 2013; accepted 19 Aug 2013; published 28 Aug 2013
(C) 2013 OSA
9 September 2013 | Vol. 21, No. 18 | DOI:10.1364/OE.21.020722 | OPTICS EXPRESS 20725
plexiglass enclosure on the table. In addition, as shown in Fig. 1.(b), optical components of
the interferometer part of the experimental setup are carefully aligned and firmly mounted in
a small black anodized aluminum box to isolate the sensitive components from the
environment. Characteristic sizes of atmospheric turbulences may be larger than the beam
separation in this environment for which interferences caused by environmental perturbations
can be minimized. Moreover, any longitudinal motion of the sample and/or the coupling
mirror results in the corresponding changes of larm which gives a negligible phase modulation
through the first term in Eq. (1). As a result, the interferometer becomes highly immune to
acoustic or mechanical vibrations parallel or orthogonal to the propagation directions of the
PB and RB. To prove this immunity, mirror vibrations were measured in two different
arrangements. In the first arrangement, as shown in the inset of Fig. 2(a), the PB and RB are
reflected by two independent mirrors for which one mirror, the PB mirror, is vibrated at 40Hz
by using a PZT actuator. The frequency spectrum of the vibration measurement results is
shown in Fig. 2(a). In the second arrangement, as shown in the inset of Fig. 2(b), both the PB
and RB are reflected by one vibrating mirror which is mounted on the same PZT stage as the
first arrangement with the identical driving conditions. The frequency spectrum of the
vibration measurements for the second arrangement is shown in Fig. 2(b). It is clear from
these results that our new interferometer scheme can provide almost 19dB rejection of
common mode vibrations. It can also be noted from these results that there are significant
reduction of low frequency noises which may be coupled to the mirrors by environmental
perturbations. The interferometer, however, is sensitive to tip-tilt motion of the coupling
mirror, which may be responsible for a slow drift in the measured phase. Asymmetric phase
changes due to localized environmental perturbations may be another reason for the drift
and/or noise. In our lab environment, the drift is slow enough that it can be compensated for
by eliminating the slope in the measured results if necessary. It should be noted that the
susceptibility to environmental perturbations can be significantly reduced if all of optical
components in the interferometer are aligned and glued together.
Fig. 2. Frequency spectra of vibration measurements: (a) the RB and PB are reflected by the
two independent mirrors of which a 40Hz vibration is applied to one mirror by using a PZT,
and (b) the PB and RB are reflected by one mirror which is driven by the same PZT with the
identical driving signal with (a).
3. Applications of the proposed interferometer
One potential application of our new interferometer scheme in TGM may be readout sensing
of fluidic channels in which a sample and reference fluid are flowing. As a feasibility study, a
homemade dual-channel fluidic cell is used for measuring refractive indexes of various
solutions with different concentrations. For this purpose, the sample in Fig. 1(a) bis replaced
by the fluidic cell for which a schematic diagram is shown in the inset of Fig. 3(a). The fluidic
cell is constructed by inserting properly tailored silicon pads in between the glass window and
mirror. It has two channels in which the reference and sample liquids are flowing. We will
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Received 5 Jun 2013; revised 8 Aug 2013; accepted 19 Aug 2013; published 28 Aug 2013
(C) 2013 OSA
9 September 2013 | Vol. 21, No. 18 | DOI:10.1364/OE.21.020722 | OPTICS EXPRESS 20726
refer to these two channels as the sample channel (SCH) and reference channel (RCH),
respectively. The gap between the mirror and window is ~.5mm and the width of each
channel is approximately 1mm. The RB and PB are reflected at the mirrored back plane of the
corresponding fluidic channels. The phase difference between the PB and RB can be directly
measured by using our interferometer scheme without any calibration procedure, from which
the refractive index of the liquid in the SCH can be derived.
Fig. 3. Experimental results on RI measurements: (a) Phase measurements for various
concentrations of ethylene glycol solution. The phase was modulated by altering flow of the
water and the ethylene glycol solutions in the SCH. (b) Measurement results for concentration
dependent ΔRIs for various solutions. The solid lines are extrapolations of the corresponding
linear fitting results of previous measurements in [18–20].
The second term in Eq. (2) represents the phase difference induced by the OPL difference
between the SCH and RCH, which can be rewritten as
ΔφFC =
4π
( nRν 1 − nsν 2 ) lFC ,
c
(3)
where ns , nR , and lFC are refractive index of sample liquid, reference liquid, and the
thickness of the fluidic channels, respectively. Therefore, the RI difference (ΔRI) between the
sample and reference liquids can be derived from the phase measurements. The absolute
value of the RI of a sample liquid can be obtained if the RI of reference liquid is known. In
this study, deionized water was used as the reference liquid, for which we use 1.33 as the RI
at 633nm and at room temperature [18]. The RCH is filled with the DI water all the time
during the measurements. Different concentrations of ethylene glycol, sodium chloride, and
ethanol solutions were carefully prepared and used as sample liquids. Resulting phase
difference is then determined by the solute and its concentration. The reference liquid and the
sample liquids are alternately flowing through the SCH to modulate the phase of the PB.
Phase differences between the sample liquids and the reference liquid are measured from
these modulated signals. For example, the measurement results for various concentrations of
ethylene glycol solutions are shown in Fig. 3(a), in which, if necessary, the slope due to a
slow drift was removed. An enlarged view of the measurement results for 0.003wt% is shown
in another inset specified as dotted ellipse in Fig. 3(a). Since the RI does not change abruptly
because of the diffusion at the boundary between water and liquids under test in the SCH,
there may be no upper bound for measuring concentration dependent RIs of sample liquids by
employing a standard fringe counting algorithm. Measurement results for various
concentrations of ethylene glycol, sodium chloride, and ethanol are shown in Fig. Theoretical
plots based on the corresponding empirical law for ethylene glycol given in the literature [19]
is shown as solid line in Fig. 3(b). The corresponding best fits of the published data on
measurements of concentration dependent refractive indexes for ethyl alcohol [20] and
#191228 - $15.00 USD
Received 5 Jun 2013; revised 8 Aug 2013; accepted 19 Aug 2013; published 28 Aug 2013
(C) 2013 OSA
9 September 2013 | Vol. 21, No. 18 | DOI:10.1364/OE.21.020722 | OPTICS EXPRESS 20727
sodium chloride [21] solutions to the linear function are extrapolated to low concentrations
and plotted as the corresponding solid lines in Fig. 3(b). It can be seen in the figure that our
measurement results show good agreement with the previous measurement results, for which
we can make sure that our new interferometer scheme is ideal for precision measurements of
the RI difference between the reference and sample liquids.
Fig. 4. Phase noise measurements when both channels are filled with water for 10 minutes (a),
and RMS noises for 20 same consecutive measurements.
Typical output signal from the interferometer when both channels are filled with water in
a lab environment for 10 minutes is shown in Fig. 4(a). RMS phase noise,
( Δφ −
where ⋅⋅ stands for average, for this particular measurements is 1.58 × 10
−4
Δφ
)
2 1/2
,
rad. Same
measurements were made for 20 times and the corresponding RMS phase noises for these
measurements are shown in Fig. 2(b). A slope due to slow drift is removed for each
measurement if necessary. Our preliminary results show that the average RMS noise for 20
measurements is 2.2 × 10−4 rad. There may be better way to claim the sensitivity for RI
measurements, but we think that it is reasonable to assume that the average RMS phase noise
or the average standard deviation is the system noise for our measurements. Based on this
assumption, we may say that the minimum ΔRI which can be measured in our new scheme is
2.3 × 10−8. We are now in the process of constructing a better quality fluidic channel and we
will return to this issue in the near future. We believe that the measurement speed can be
increased significantly if professionally fabricated micro-fluidic channels are used. Noise
characteristics may be improved for short-time measurements and, thereby, improve the
sensitivity.
The RGM scheme also has many applications such as scanning microscopy, wafer
inspection, readout sensing for a biochip, and so forth. In these applications, vibration modes
perpendicular to the scanning directions can be excited on the sample mount during the
scanning, which results in the corresponding phase noises in a conventional interferometer
scheme, which limits the scanning speed and the depth resolution. In our new interferometer
scheme, however, both the sample surface and the reference surface can be mounted on the
same scanning stage, which can reject phase noises caused by vibrations of the scanning
stage. Therefore, we believe that our newly proposed interferometer is ideal for these
applications utilizing the RGM. We are now doing researches on applying the proposed
interferometer scheme to a scanning microscopy and will not be discussed in this paper.
4. Summary and conclusions
In summary, a new heterodyne interferometer scheme has been introduced. The
interferometer was specially designed so that the PB and RB have the geometrically balanced
#191228 - $15.00 USD
Received 5 Jun 2013; revised 8 Aug 2013; accepted 19 Aug 2013; published 28 Aug 2013
(C) 2013 OSA
9 September 2013 | Vol. 21, No. 18 | DOI:10.1364/OE.21.020722 | OPTICS EXPRESS 20728
paths. Moreover, depending on the nature of a specific application, our new optical design
allows for choosing either the TGM or RGM, which gives flexibilities in interferometric
measurements. We showed that, because of the geometrical balance and small separation
between the PB and RB, 17mm in this preliminary study, the interferometer was inherently
immune to environmental perturbations. The phase difference between the PB and RB was
measured without calibration procedure by using the I/Q-demodulation scheme. Since the
output signal is proportional to the tangent of the phase difference and the tangent function
has a large slope with respect to a phase change, it does not require any additional feedback
control for maintaining optimum phase demodulation condition. As an application example,
we applied our new scheme for measuring RIs of the liquids flowing through the SCH of the
fluidic cell. In general, for RI measurements in SCH, because of diffusion at the boundaries
between water and the other solutions, RIs or OPLs do not change abruptly, for which a
standard fringe counting or a phase unwrapping algorithm can be used for wide dynamic
range measurements. In all, by using our new scheme, we were able to achieve both very high
sensitivity and wide dynamic range measurements of RI difference between the reference and
sample liquids. It should be noted that we can use any combinations of reference and sample
liquids, which may offer flexibility and versatility for designing a biosensor.
Acknowledgment
This research was supported by National R&D Program through the National Research
Foundation of Korea (NRF) funded by Ministry of Education, Science and Technology
(NRF-20120005921).
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Received 5 Jun 2013; revised 8 Aug 2013; accepted 19 Aug 2013; published 28 Aug 2013
(C) 2013 OSA
9 September 2013 | Vol. 21, No. 18 | DOI:10.1364/OE.21.020722 | OPTICS EXPRESS 20729