Design and Implementation of a Fiber Optic
Doppler Optical Coherence Microscopy System for
Cochlear Imaging
by
Logan P. Williams
OF TECHNOLOGY
S.B., Electrical Science and Engineering, Physics
Massachusetts Institute of Technology (2013)
JUL 15 2014
LIBRARIES
Submitted to the Department of
Electrical Engineering and Computer Science
in partial fulfillment of the requirements for the degree of
Master of Engineering in Electrical Science and Engineering
at the
Massachusetts Institute of Technology
June 2014
Massachusetts Institute of Technology 2014. All rights reserved.
Signature redacted-..
Author ..........
Department of Electrical Engineering and Computer Science
May 15, 2014
Certified by.......
Signature redacted
Dennis M. Freeman
Professor of Electrical Engineering
AhA
Signature redacted
ThessSprio
sis
Supervisor
..................
Albert R. Meyer
Chairman, Masters of Engineering Thesis Committee
A ccepted by ..........
2
Design and Implementation of a Fiber Optic Doppler Optical
Coherence Microscopy System for Cochlear Imaging
by
Logan P. Williams
Submitted to the Department of Electrical Engineering and Computer Science
on May 15, 2014, in partial fulfillment of the
requirements for the degree of
Master of Engineering in Electrical Science and Engineering
Abstract
In this thesis, the design and implementation of a fiber optic Doppler optical coherence
microscopy (FO-DOCM) system for cochlear imaging applications is presented. The
use of a fiber optic design significantly reduces system size and complexity and the
construction of a novel alignment and micropositioning apparatus increases ease of use
for the researcher performing the imaging. To enable precise measurements of tissue
motion, a time domain DOCM approach is used, utilizing an acousto-optic modulator
(AOM) based optical heterodyne system to generate a stationary interference carrier
frequency. By referencing this interference signal against the AOM drive signals,
measurements of motions with magnitude on the order of 10 pm are shown to be
possible. In addition to interferometrically measuring small amplitude motion, the
FO-DOCM system is shown to be capable of imaging with a volumetric resolution
of 10 x 9 x 9 pm. Demonstrative results of imaging cochlear tissue are presented by
using the FO-DOCM system to image and measure motion in a guinea pig cochlea
in vitro.
Thesis Supervisor: Dennis M. Freeman
Title: Professor of Electrical Engineering
3
4
Acknowledgments
Thanks to Professor Denny Freeman for welcoming me into his lab as a student and
advisee, privileging me with the power and responsibility to make my own mistakes,
and encouraging my progress whenever I felt overwhelmed.
Thanks to Scott Page, Jon Sellon, and Shirin Farrahi for their support, advice,
and unending help with everything from finding what I needed around the lab, to
debugging entire optical systems, to preparing samples and helping perform the experiments used to test the FO-DOCM apparatus.
Thanks to Rooz Ghaffari for introducing me to the Micromechanics Group.
Thanks to Janice Balzer for her help and organization around the Micromechanics
Group.
Thanks to my friends in and around MIT for their support and camaraderie. MIT
would not have been possible without all of them.
Thanks to my mother Lorie, and my brother Aaron, for their constant love and
understanding.
Finally, thanks to my father, Steve. You gave me the gift of music and mountains,
wind and water, laughter and love.
The memory of your personality, spirit, and
wisdom continues to inspire me.
5
6
Contents
1
Introduction
1.1
Motivations for a fiber optic DOCM system
. . . . . . . . . . . . . .
11
1.2
Principle of operation of time domain OCT . . . . . . . . . . . . . . .
13
1.2.1
Limits of transverse resolution . . . .... . . . . . . . . . . . .
16
OCT with acousto-optic modulators . . . . . . . . . . . . . . . . . . .
18
1.3.1
Principle of operation of an AOM . . . . . . . . . . . . . . . .
19
1.3.2
Generating a carrier wave with an AOM . . . . . . . . . . . .
20
1.4
Doppler OCT with AOMs . . . . . . . . . . . . . . . . . . . . . . . .
21
1.5
Signal processing . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
23
1.5.1
25
1.3
1.6
2
11
Analyzing motion . . . . . . . . . . . . . . . . . . . . . . . . .
Related work
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
System design
2.1
2.2
System overview
26
29
. . . . . . . . . . . . . . . . . . . . . . . . . . . . .
29
2.1.1
Incoherent light source . . . . . . . . . . . . . . . . . . . . . .
29
2.1.2
Acousto-optic modulators
. . . . . . . . . . . . . . . . . . . .
30
2.1.3
RF generation and driving . . . . . . . . . . . . . . . . . . . .
31
2.1.4
Reference path
32
2.1.5
Sample path objective
. . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . .
32
Sample alignment apparatus . . . . . . . . . . . . . . . . . . . . . . .
34
2.2.1
Mechanical device for adjusting angle and position
. . . . . .
34
2.2.2
Piezo motor stage for axial movement . . . . . . . . . . . . . .
36
2.2.3
Mounting the fiber and GRIN lens
38
7
. . . . . . . . . . . . . . .
2.2.4
Digital microscope for visual alignment . . . . . . . . . . . . .
39
2.2.5
Visible laser for assisting visual alignment
. . . . . . . . . . .
41
2.3
X-Y stage for sample movement . . . . . . . . . . . . . . . . . . . . .
42
2.4
Light detection and signal acquisition . . . . . . . . . . . . . . . . . .
43
2.5
Signal processing
. . . . . . . . . . . . . . . . . . . . . . . . . . . . .
44
2.5.1
Image generation . . . . . . . . . . . . . . . . . . . . . . . . .
44
2.5.2
Motion analysis . . . . . . . . . . . . . . . . . . . . . . . . . .
45
Theoretical performance predictions . . . . . . . . . . . . . . . . . . .
45
2.6.1
Axial resolution . . . . . . . . . . . . . . . . . . . . . . . . . .
45
2.6.2
Transverse resolution . . . . . . . . . . . . . . . . . . . . . . .
47
2.6
3
System characterization and results
49
Resolution performance . . . . . . . . . . . . . . . . . . . . . . . . . .
49
3.1.1
Measurement of axial resolution . . . . . . . . . . . . . . . . .
49
3.1.2
Measurement of transverse resolution . . . . . . . . . . . . . .
50
3.1.3
Limits of motion measurements . . .... . . . . . . . . . . . .
51
3.1.4
Resolution of motion differentiation . . . . . . . . . . . . . . .
54
3.2
Demonstrative images and motion measurements of cochlear tissue. .
55
3.3
Known issues . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
57
3.4
Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
60
3.1
8
List of Figures
1-1
A schematic drawing of tissues in the cochlea.
. . . . . . . . . . . . .
12
1-2
Block diagram of a simplified OCT system. . . . . . . . . . . . . . . .
14
1-3
Light scatters off of acoustic wavefronts in an acousto-optic modulator.
19
1-4
Basic OCT signal processing chain. . . . . . . . . . . . . . . . . . . .
24
2-1
Block diagram of the FO-DOCM system. . . . . . . . . . . . . . . . .
30
2-2
Schematic of the 1 GHz clock. . . . . . . . . . . . . . . . . . . . . . .
31
2-3
Zemax raytrace simulation of reference path. . . . . . . . . . . . . . .
32
2-4
The GRIN lens assembly . . . . . . . . . . . . . . . . . . . . . . . . .
33
2-5
Light lost to an isotropic scatterer, as a function of working distance.
34
2-6
3D model and photograph of the mechanical alignment apparatus. . .
35
2-7
Side view of the alignment apparatus. . . . . . . . . . . . . . . . . . .
36
2-8
Photograph of the piezo motion stage.
37
2-9
A close up view of the GRIN objective mounting apparatus.
. . . . . . . . . . . . . . . . .
. . . . .
38
. . . . . . . . . . .
39
2-11 A raytrace diagram of the microscope layout, simulated in Zemax. . .
40
2-12 The point spread function of the microscope, as simulated in Zemax.
40
2-10 An overview of the digital alignment microscope.
2-13 An image of a 1951 USAF Resolution Test Target, captured using the
digital m icroscope.
. . . . . . . . . . . . . . . . . . . . . . . . . . . .
2-14 An image of the visible laser spot on cochlear tissue.
41
. . . . . . . . .
42
2-15 The transverse X-Y stepper motor stage. . . . . . . . . . . . . . . . .
42
2-16 A block diagram overview of the steps necessary for image generation.
44
2-17 A block diagram overview of the steps necessary for motion analysis.
45
9
2-18 Theoretical axial point spread function. . . . . . . . . . . . . . . . . .
46
2-19 A Zemax raytrace showing the path of light through the GRIN lens. .
48
3-1
The measured axial point spread function.
. . . . . . . . . . . . . . .
50
3-2
Result of en-face scan of USAF target. . . . . . . . . . . . . . . . . .
51
3-3
Result of scan of the edge of a a glass coverslip.
. . . . . . . . . . . .
52
3-4
Transverse step function measured along the glass coverslip.
. . . . .
52
3-5
Noise floor of measured motion. . . . . . . . . . . . . . . . . . . . . .
53
3-6
Linearity of motion amplitude measurements . . . . . . . . . . . . . .
54
3-7
Motion differentiation of adjacent stationary and vibrating interfaces.
55
3-8
An annotated unfixed guinea pig cochlea, imaged with the FO-DOCM
system . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
56
A fixed guinea pig cochlea, imaged with the FO-DOCM system. . . .
58
3-10 Motion map of vibrations in a fixed guinea pig cochlea. . . . . . . . .
58
3-9
10
Chapter 1
Introduction
In this chapter, the construction of a fiber optic Doppler optical coherence microscopy
system will be motivated. Additionally, the mathematical underpinnings of the system will be introduced, and recent related work will be discussed.
1.1
Motivations for a fiber optic DOCM system
The mammalian cochlea is capable of remarkable sensory perception. It can distinguish vibratory motion as small as the radius of a hydrogen atom and discriminate
between up to 30 frequencies within a single semitone [10]. However, the mechanics
of motion in the inner ear remain poorly understood. The Micromechanics Group at
the Research Laboratory of Electronics at MIT is analyzing motion in the cochlea in
order to more fully understand what enables these remarkable sensory capabilities.
A tissue of particular interest in the cochlea is the tectorial membrane, which
is in direct contact with the sensory hair cells, as shown in Figure 1-1. This tissue's proximity to the hair cells and its interesting mechanical properties, including
frequency-sensitive acoustic wave propagation, suggest that it could play an active
role in auditory frequency discrimination and motion amplification [11].
A technique known as optical coherence tomography allows three-dimensional
imaging into and through cochlear tissues such as the tectorial membrane by making
use of the auto-correlation properties of temporally incoherent light. This technique
11
Figure 1-1: A schematic drawing of tissues in the cochlea. Adapted from a public
domain image by Oarih Ropshkow.
can image more deeply into tissues than other three-dimensional imaging methods
such as confocal microscopy. Furthermore, by measuring the Doppler frequency shift
of scattered light, OCT allows for measurement of both constant and periodic motion [5].
The Micromechanics Group at RLE currently uses a free space Doppler optical
coherence microscopy system to image the mammalian cochlea and acquire data about
the mechanical motions of tissues [15]. Optical coherence microscopy (OCM) differs
from OCT by using lenses that focus light with a narrower beam waist than that
of conventional OCT [2]. The existing system will be referred to as the FS-DOCM
system.
As the FS-DOCM system is designed around free space optics, they must be carefully aligned and positioned on an optics table. This design has several disadvantages,
chiefly that it is difficult and time consuming to align with the animal that is being
12
imaged. This process takes significant time due to the need to move the animal precisely under the DOCM objective, and the need to align the cochlea with the fixed
optical axis of the DOCM system.
The system described in this thesis, while similar in many ways to the existing FSDOCM system, primarily uses fiber optic (FO) coupled components. Therefore, it will
be hereafter referred to as the FO-DOCM system. Fiber optics can be more compact
and mobile than free space optical components. Additionally, the objective used for
imaging the actual tissue is mounted on a custom designed mechanical apparatus
that allows the angle and position of the optical axis to be easily adjusted, working
with the researcher and research animal, rather than forcing the animal to conform
to the optical system. The use of a graded index (GRIN) objective lens, rather than
a conventional microscope objective, further reduces the size of the imaging device.
These improvements should significantly improve the workflow of other researchers
in the Micromechanics Group.
Additionally, the FO-DOCM system uses a longer wavelength of light than the
FS-DOCM system, 1310 nm IR instead of 800 nm IR. While this has some disadvantages in axial and transverse resolution capability, as discussed in Section 1.2,
this wavelength also has several advantages. It is a commonly used wavelength for
communication applications, and therefore many optical components are designed for
compatibility in this region. More importantly, 1310 nm has significantly reduced
scattering through bone tissue, therefore allowing for greater light transmission and
penetration [22] [1]. This has the potential to obviate the current need to image
through either the cochlear round window or a hole cut in the cochlear apex.
1.2
Principle of operation of time domain OCT
Throughout this document, the coordinate axis parallel to the direction of light emission from the objective shall be referred to as the "axial" direction, or "z" axis. The
plane perpendicular to this axis is known as the "transverse" plane, or, sometimes,
the "x" and "y" axes.
13
Reference
mirror
I
E
OptiBeamSplitter
Photodetector
Figure 1-2: Block diagram of a simplified OCT system.
OCT functions by utilizing the principle of the Michelson interferometer. A block
diagram of a significantly simplified OCT system is shown in Figure 1-2. First, light
is split into two beams. One beam is reflected from a mirror, and the other beam is
scattered from a biological sample. The light is then recombined and the intensity
measured by a photodetector. When the optical path lengths of the two beams are
closely matched, an interference pattern may be observed. By using temporally incoherent (broadband) light, the interference pattern is capable of absolute localization,
as will now be shown.
The electric field from a temporally incoherent source can be modeled accurately
as a wide-sense stationary random process with a power spectral density (PSD) corresponding to the optical spectrum of the source [2]. In the case where the scattering
sample is replaced by a reflecting mirror, the mathematical analysis may be simplified greatly by assuming that the system is measuring the interference of this random
process with itself, delayed by the optical path length difference. With these assumptions, it is shown that the interference pattern is equivalent to the autocorrelation of
the random process and may be related to the source PSD [8].
The intensity of light with analytic (complex) amplitude V(t) is defined as
14
I(t)
=
IV(t)l 2 = V*(t)V(t)
(1.1)
.
In an OCT system, the light from a reference path is combined with the light from
a sample path after some delay. This superposition may be expressed as
VD(t; At) -VS(t)
+ VR(t + At)
.
(1.2)
As measuring instantaneous electric field amplitude is impossible, only the expected value, or the time average, of the intensity is of interest, indicated by the
notation (x(t)). The time averaged intensity of the superimposed light is
ID(At) =
IDt;A)
= (V,3(t; At) VD(t; At))
-
where
J'xy
(1.3)
(Is(t)) + (IR(t)) + 2 Re(FsR(At ))
represents the cross correlation between two random processes X and Y.
The time delay between the two signals, At, is proportional to the path length
difference between the two beams, and may be calculated as At = Az/c. When
both the sample and reference paths are illuminated from the same light source, the
cross correlation function above simplifies into an autocorrelation function of the light
source. From here, the Wiener-Khinchin theorem can be applied, which states that
the autocorrelation function of a wide-sense stationary random process is
Fxx(T) = 2
Sxx(f) exp(27rjTf)df ,
(1.4)
straightforwardly related to the process power spectral density Sxx(f) by a Fourier
transform.
Therefore, the axial resolution in an OCT system is limited by the spectral properties of the light source. The width of the envelope of the autocorrelation function,
and therefore the axial resolution, is found to be
15
n
7w AA
(1.5)
1C
=
for a source of center wavelength AO and FWHM bandwidth AA, assuming a Gaussian
PSD [8].
The autocorrelation function also has a periodic interference component, as the
PSD Sxx(f) in Equation 1.5 is not DC biased, but instead is centered around the
central optical frequency of the source. In the spatial domain, this represents itself
as a carrier wave modulating the autocorrelation envelope, with a spatial period
of one wavelength.
The time-domain frequency of this carrier as captured by the
photodetector,
fmod =
2v,/Ao ,
(1.6)
is therefore dependent both on the wavelength of the light source, A0 , and the speed of
the axial scan, v. [8]. Note that the factor of two results from the fact that changing
the length of the reference path by a distance Az changes the optical path length by
2Az.
1.2.1
Limits of transverse resolution
Unlike the axial resolution, the transverse resolution of the optical system is limited
by both the central wavelength of the optical source and the optics used to shape and
focus the light. In the case of the FO-DOCM system, these consist of an objective
lens and an optical fiber, which projects light through an air gap onto the lens. The
objective lens is a graded index (GRIN) lens, that uses glass with a continuously
varying index of refraction to focus the light onto the desired focal point.
Light travels through, and is emitted from, a single mode fiber as a Gaussian
beam, a beam of light with a transverse intensity profile approximated by a Gaussian
function. A Gaussian beam may also be described by a complex beam parameter q,
more easily defined by its inverse
16
=
_1
q(z)
-
(
R(z)
)
1
(1.7)
Z rw(z)2
where R(z) is the radius of curvature of the electromagnetic field, and w(z) is the
beam radius at a distance z from the beam waist, defined as the transverse distance
where intensity has fallen to 1/e 2 [23]. Therefore, the beam radius may be related to
the q parameter by
w(z) =
7r Im(1/q(z))
.A
(1.8)
The transverse resolution of the FO-DOCM system is determined by the minimum
spot size of the focused Gaussian beam of light.
The evolution of a propagating
Gaussian beam may be determined by matrices of the form
a
b
c
d
(1.9)
referred to as ray transfer matrices, where
q(z2 )
Aq(zi)
+ B .
Cq= i)+
(1.10)
Cq(zi) + D
The ray transfer matrix for forward propagation through free space is
(1.11)
0
1)
where 1 is the distance traveled. The ray transfer matrix for a graded index lens is
cos viAl
-(noV
(no
A)-1
sinV\/lA
,
(1.12)
cos vTA
A
) sin V4iA
where the refractive index profile of the GRIN lens is n(r)
=
no(1 - A;2 ), and the
length of the lens is 1 [23].
Therefore, the cascaded ray transfer matrix for the entire system, from fiber emission to a focused spot, is
17
cos/
CO1
1
1
cos(
-(noVA) sin /A12
-
1(no
COS2)
\/A
sin( v
cos
V12
'-1+1)o
l2)
-Ano sin(V74l 2 )
o(V_1k
1
13
0
1
123
n.)sin(v/A2
-l
+ -113
-+t-A-n
vAV
cos(VTl 2 )- VTAl 3 no sin( VAl 2
)
0
(no vA)- Sin VA12
2
(1.13)
where 13 is the distance from the end of the optical fiber to the GRIN lens, l 2 is the
length of the GRIN lens, and l1 is the distance from the end of the GRIN lens to the
focal point. By applying Equation 1.10, the new complex q parameter of the focused
beam is
13
+ qo)
)
sin(VAl 2)(Alin2(l + qo) - 1) - VAno cos(VAl 2)(li +
Ang(l + qo) sin(Vl 2 ) - V'Ano cos(V/Al 2
where qo is the complex beam parameter at the point of emission from the optical
fiber. Using Equation 1.8, and by multiplying by a scale factor, the beam radius can
be converted to an expression for the transverse FWHM distance
_ = 2In 2
1.3
-A
7r Im(
1/qi)
(1.15)
OCT with acousto-optic modulators
As derived in the previous section, the speed of the z-axis motion defines the frequency
of the interferogram carrier. For typical cases, this is on the order of 1 KHz. If the
speed of the scan is variable, this carrier is inconsistent, and if the scan stops at a
particular point, the frequency is near zero (non-zero only due to spurious mechanical
vibration).
In some cases, such as when phase recovery of the carrier frequency signal is necessary, as is the case for the FO-DOCM system, it is desirable to have an independent
carrier reference. This can also be useful for cases where the z-axis speed is zero, as
18
in en-face OCT, or when a carrier frequency independent of the speed of the z-axis
scan is desired. One method of accomplishing this is the use of an optical heterodyne,
which may be created with acousto-optic modulators (AOMs), also known as Bragg
cells [2] [14].
1.3.1
Principle of operation of an AOM
Acoustic absorber
Figure 1-3: Light scatters off of acoustic wavefronts in the quartz crystal of an acoustooptic modulator. As it scatters, it changes both frequency and propagation angle.
Acousto-optic modulators are crystals, typically quartz, that use the acoustooptic effect to shift the frequency of light.
A transducer establishes an acoustic
standing wave at radio frequencies, typically 40-200 MHz, inside the crystal. Acoustic
compression waves in the crystal can be modeled as gradients in the refractive index.
Light incident upon these refractive index gradients will be scattered, changing both
propagation angle and optical frequency. Momentum conservation of the scattered
light requires that the condition
kacoustic + kincident
kdiffracted
(1.16)
be satisfied by the wave vectors of the acoustic, incident optical, and diffracted optical
waves [13].
19
This can be solved to give a condition on the angle in the case where ki is orthogonal to k,
sin 0
Ik -=
Ikil
--
(1.17)
nA
with optical wavelength A and acoustic wavelength A. A small angle approximation
is applied as it is assumed that Ikjj> ksl.
In some crystals, higher order diffraction angles occur, however, it is difficult to
achieve high modulation efficiencies, and they are not of significant interest to this
research.
Energy conservation further requires that the frequency of scattered light be
shifted by F, the acoustic wave frequency [13]. This frequency shift is what makes
an AOM of practical interest for the creation of an optical heterodyne.
1.3.2
Generating a carrier wave with an AOM
Even with an imprecise or drifting optical center frequency, the precise shift frequency
induced by an AOM can be used to generate an extremely stable optical interference
signal [14].
The instantaneous complex electric fields for monochromatic plane waves of two
different frequencies,
f
and f + F, in a particular location, may be written as
Ea(t) = E, exp (27rftj)
Eb(t) = Eb exp (27r(f + F)tj)
The interference between the superposition of these two fields,
Ea(t) + Eb(t) =E, exp (27rftj) + Eb exp (27r(f + F)tj)
=E, exp (27rftj) + Eb(exp (27rftj) exp (27rFtj))
=E, exp (27rftj) (1 + Eb exp (27rFtj))
Ea
exp (27rFtj))
,
=Ea(t)(1 +
Ea
20
(1.19)
creates a beat frequency, with the amplitude of the optical frequency modulated by
the slower, and detectable radio frequency F.
For many applications, the radio frequency F used to drive the AOMs is a higher
frequency carrier than is desired or can be detected. In this case, it is possible to
use two AOMs to generate an even lower frequency carrier by driving them each at
slightly different frequencies, resulting in complex field amplitudes
Ea(t) = Ea exp (27rtj(f + F1 ))
(1.20)
Eb(t) = Eb exp (27rtj(f + F2 ))
It can be seen via an identical simplification to the above that the combination
of these electric field amplitudes creates a carrier wave with frequency equal to the
.
absolute value of F - F2
1.4
Doppler OCT with AOMs
Optical scattering from moving particles also induces a change in the frequency of
scattered light due to the Doppler effect. This change in frequency can be expressed
as
(t 'M0
Af~~~~
=f 2 v= )fo cos (0) sin (-) ,
c
(1.21)
2
(.1
where a is the angle between the direction of incident light propagation and the light
detector, 3 is the angle between the direction of light propagation and the direction
of motion of the media, and v(t) is the instantaneous velocity of the sample [6].
In the FO-DOCM apparatus, only backscattered light can be detected, so a is
assumed to be 7r radians. The direction of motion is assumed to be in the direction
of light propagation for simplicity, so that
#
=
0. The equation for the instantaneous
frequency change then simplifies to
Af (t)
-
2
21
v(t) fo .
C
(1.22)
Integrating the instantaneous frequency finds the phase, up to a constant term,
as
J
27rf (t)dt
= 27r
= 27r
fo(1 + 2
ft + 2
)dt
(1.23)
)
(t) =
where d(t) is the instantaneous sample displacement, the integral of the sample velocity.
In an analogous way to Equation 1.18, instantaneous field amplitudes E, and Eb,
representing the sample and reference paths respectively, may be written as
Ea(t) = E, exp
27rj(f + 2F1) t + 2d(t)
c
(1.24)
,
Eb(t) = Eb exp (27rtj(f + 2F2 ))
where Ea has scattered from media moving with velocity v(t) and has passed through
an AOM of frequency F1 , while Eb has been reflected from a stationary object and
has passed through an AOM of frequency F. Note that the radio frequencies F and
F2 have been multiplied by two, as light must make two passes through each AOM.
The electric field at the detector is the sum of the two electric field amplitudes,
Eb(t) + Ea(t)
=
E, exp (27rtj(f + 2F1 )) (exp (27rj
+
K
(f + 2F1 ))
(1.25)
exp (27rtj2(F2 - F1))
This equation may be simplified slightly to
Eb(t) + Ea(t) = Ea exp (27rtjf') exp 27rjf' 2d(t)
+
exp (-27rtj2AF))
(1.26)
.
and radio frequency difference, AF = F2 - F1
22
f'
= f + 2F1
,
by substituting two new symbols for the modified optical frequency,
The instantaneous light intensity is equivalent to the absolute value of the instantaneous electric field amplitude squared, given by
I(t)
=
E2 + Eb + 2EbE, cos 27r
2tAF + f'
(1.27)
.
The result of the frequency shift induced by the motion of the media can clearly
be seen in the instantaneous phase of the intensity oscillation,
2d(t
(1.28)
)
0(t) = 27r (2tAF + f'
.
This is equivalent to phase modulation, with the periodic change in phase of
27rf'
(1.29)
.
This oscillation can be extracted from the captured signal using the Hilbert transform, discussed in Section 1.5.1. While this derivation assumed perfectly monochromatic light sources, as would be the case in an ideal laser interferometer, the result
also generalizes to the non-monochromatic random signals used in Section 1.2.
1.5
Signal processing
Photodetector
Arplifier
Analog band
pass filter
Analog to digital
converter
Digital band pass
filter
exrcto
Downsampling
Figure 1-4: Basic OCT signal processing chain. The bandpass filter is centered around
the carrier frequency from Equation 1.6. The demodulator can be either as straightforward as an envelope follower or a Hilbert transform based analytic continuation.
A block diagram overview of a basic signal processing chain for OCT is shown in
23
Figure 1-4. After detection of the light and signal amplification, but prior to analogto-digital conversion, analog bandpass filters select for the carrier frequency and its
sidebands, in addition to bandlimiting the signal below the Nyquist frequency. The
signal is then sampled and quantized by an ADC so that it may be manipulated
digitally.
The Hilbert transform can then be used to extract the envelope from the modulated carrier signal. Assuming a signal of the following form,
x(t) = A(t) cos (wt) ,
(1.30)
the Hilbert transform can generate the approximate quadrature component,
H(x(t)) ~ A(t) sin (wt) ,
(1.31)
where A(t) is a real envelope [19].
It can therefore be seen that the envelope component of the signal can be calculated as
A(t) ~
/(x(t)) 2 + H(x(t)) 2
.
(1.32)
The envelope, which does need the high sampling rate previously required in order
to capture the carrier frequency, can then be low pass filtered and decimated to the
resolution required by the imaging application.
Additionally, it can be seen that the instantaneous phase of this arbitrary sinusoidal signal may also be estimated using the Hilbert transform as
H(x(t))
0(t) ~ tan-'
1.5.1
(1.33)
.
(X (t)
Analyzing motion
As shown in Section 1.4, the phase of the modulated light intensity scattered from
moving media, referred to as the heterodyne phase,
24
#het,
can be expressed as
Ohet(t)
2tAF + f' 2d(t)
= 27r
(1.34)
.
A reference signal must also be captured, which oscillates at a frequency equal to
the difference of the two RF drive frequencies. The phase of this reference is
Oref (t)
= 27rtAF ,
(1.35)
exactly half the phase of the carrier frequency of the heterodyne signal.
Subtracting twice the reference phase from the heterodyne phase, and replacing c
by c/n to account for the refractive index of the media, finds the phase difference
#dif(t)
=
Ohet (t)
Because the RF frequency F <<
as f
=
f + F1
e
f,
20ref (t)
-
f,
=
27rf
2d(t)
c/n)
(1.36)
the optical frequency, it may be approximated
simplifying the equation above. Expressing the optical frequency
as a wavenumber k further simplifies the phase difference to
kdif (t)
2rtf
2d(t)
c/n
2knd(t) .
(1.37)
Using the result from Equation 1.33, the instantaneous phase difference between
the captured heterodyne signal, Vhet, and the captured reference signal Kef, may be
written as
Odif (t)
r.,tan- 1 (HVe~)
- 2 tan-
Vhet (t)
(t)
(Vref
.(rf()
(1.38)
Combining Equations 1.37 and 1.38, the periodic displacement of the sample may
be calculated as
2kn
(tan-i
2 tan-
H(Vhet)(t)
Vhet Mt
H(Vre )(t)
Vref (t
)
e1
25
(1.39)
1.6
Related work
Since the 1960s, interferometry with laser light has been used to measure vibration in
the cochlea. Early laser Doppler interferometer experiments required the placement
of reflective beads to isolate tissues of interest; however, these beads can influence the
mechanical properties of the cochlea [18]. Recent methods involving laser Doppler
interferometry have had success in measuring vibrations with a noise floor as low as
30 pm/Hz 0.5 without beads, but also require a parallel system, such as confocal microscopy, in order to produce an image of the tissues [16] [20] [21] . Furthermore, laser
interferometers are highly coherent, so without reflective beads, vibration measurements have a depth separation determined primarily by the beam divergence angle,
resulting in poor axial isolation.
Low coherence interferometry, such as OCT, is capable of solving these problems.
As mentioned in Section 1.1, the FO-DOCM system is designed to update the previous
free space system used in the Micromechanics Group. The FO-DOCM system is quite
similar to the FS-DOCM system, but is also different in several ways: the use of
fiber optic components rather than free space optics, the use of a longer wavelength
source, and the revised alignment and positioning apparatus [15]. Furthermore, the
FO-DOCM system allows for continuous scanning of lines in an image in addition to
point-by-point pixel acquisition.
Other time-domain Doppler OCT systems.
The use of acousto-optic modula-
tors is not essential for Doppler OCT, and systems similar to the FO-DOCM system
have been constructed without them. However, without a reference signal to use in
extracting phase modulation information, the system responds to vibration amplitude in a very non-linear way. Furthermore, because vibrations are not modulated
to higher frequencies by the heterodyne carrier, more interference at low frequencies,
from mechanical vibrations and electrical 1/f noise, results in a higher noise floor,
typically on the order of 30 pm/Hz 0 .5 [3].
26
Spectral-domain Doppler OCT systems.
While the FO-DOCM project uses
time-domain Doppler OCT, work has also been done in the field of spectral domain
Doppler OCT. Spectral-domain Doppler OCT systems have achieved results with an
axial resolution of 13 pm and a motion detection noise floor of 300 pm/Hz 0 5 [4] [24].
It is thought that a time domain approach can result in higher resolution motion
measurements than a spectral domain system, as monolithic photodiodes have better
noise equivalent power than a CCD line camera with a diffraction grating. Furthermore, the sampling rate of a CCD sensor is very limited compared to a photodiode,
restricting the speed and accuracy of phase recovery between sequential scans. However, the use of a time-domain system adds the considerable expense of requiring
physical motion to scan the z-axis, resulting in significantly slower image acquisition.
Trans-bone imaging.
Doppler OCT has previously been used with some success
for measuring vibrations of cochlear tissues through bone. Using a 935 nm center
wavelength, motion inside an in vivo mouse cochlea was measured with an noise floor
of approximately 100 pm/Hz 0-5 [9]. It is suspected that a 1310 nm center wavelength,
as used in the FO-DOCM system, will be even more effective at penetrating bony
tissue [22] [1].
Microangiography.
Doppler OCT is not restricted to measuring periodic vibra-
tions - one of its first applications was for angiography, measuring the velocity of
blood flow inside tissue. Current techniques with Doppler optical microangiography
are capable of isolating and measuring blood flow in a single vessel over time [7].
While low frequency motion, such as constant motion, has a significantly higher measurement noise floor, blood flow velocity amplitudes are also typically much greater
than vibrational amplitudes.
Miniaturization of OCT apparatus One of the advantages of the FO-DOCM
system to the Micromechanics Group is its smaller size, so this work may be seen as
continuing the active effort of minimizing the size of OCT apparatuses. Research in
this area includes the creation of a miniature swept frequency laser source for OCT
27
imaging [12], which could enable a higher axial resolution in a smaller form factor.
GRIN lenses, used in the FO-DOCM system, have a significant size advantage in
addition to high quality optical performance and have also been used in previous
research as endoscopic probes for OCT [25].
Overall, the FO-DOCM- system designed and constructed in this thesis builds on
previous work and ideas in optical coherence tomography to develop an apparatus that
satisfies the unique set of requirements of the Micromechanics Group, with advantages
in motion resolution, tissue penetration, mechanical adjustability, and size.
28
Chapter 2
System design
In this chapter, the major components of the fiber optic Doppler optical coherence
microscopy (FO-DOCM) system will be introduced, and the constraints that led to
their choice will be examined. The mechanical and optical design will be detailed.
Finally, predictions of system performance will be made based on component choices.
2.1
2.1.1
System overview
Incoherent light source
The choice of a light source dictates many aspects of the system performance. The
coherence length, as shown in Section 1.2, controls the axial resolution of the imaging.
The center wavelength of the source constrains the tissue penetration depth, and what
other components may be used in the system.
For this project, a super-luminescent diode, or SLD, was chosen (Exalos AG,
Switzerland, Part No: EXS210045-01). Super luminescent diodes provide the spatial
coherence of a laser with the short temporal coherence of an LED or "white" light
source. Other common broadband light sources for OCT applications include solidstate lasers, such as Ti: A1 2 0 3 lasers, lasers that sweep a frequency range in time (so
called "swept-spectrum" lasers), and femtosecond lasers. The chief advantage of an
SLD over these options is reduced cost and complexity [2].
29
1 GHz Clock
--- -
hesz
80 MHz
IF Amplifier ---
------
80.25 Mhz
-
ADC
--
250 KHz
(Difference frequency) -
-
'
-------
RF
ARFAplifiere---
Photodiode
Wx Coupler
SLD Driver
--
-JSLD
Optical
Isolator
Manual
SwtchPolarization
670n Lasr
Paddle Controller
AOM
Diode
Collimating lens
AOM
Key
----- -4 Electrical or RF connection
Collimating lens
lo SMF-28e+ single mode optical fiber
40- Free space optical transmission
Reference
Sample
mirror
Figure 2-1: Block diagram of the FO-DOCM system.
A center wavelength of 1310 nm was chosen as this is a common wavelength
for communications. It is therefore possible to find many inexpensive fiber coupled
components designed to operate in this band. Additionally, as discussed in Section
1.1, a longer wavelength could allow for deeper penetration through the bony cochlear
wall [22] [1].
An optical isolator is required after the SLD in order to prevent back reflections
from resonating and adversely impacting the spectral bandwidth of the source.
2.1.2
Acousto-optic modulators
Two fiber coupled acousto-optic modulators (Gooch & Housego, United Kingdom;
packaged by Sintec Optronics, Singapore. Part No: 23080-1-1.3-LTD-FC/APC) were
chosen, which provide a convenient, compact device and avoid the need for alignment
with the first degree deflection beam, required in free space optics. An 80 MHz drive
30
frequency was chosen for compatibility with existing hardware used in the Micromechanics Group.
2.1.3
RF generation and driving
The AOMs must be driven by an 80 MHz and an 80.25 MHz RF signal in order to
produce the beat frequency derived in Section 1.3.2. A frequency synthesizer, built
by former Micromechanics Group student Stanley Hong [15], uses a 1 GHz clock
source to synthesize a 80.25 MHz signal and an 80 MHz signal. The mixed difference
between these signals, a 250 KHz reference signal, is also generated, as it is necessary
for later signal processing steps.
Two RF amplifiers, (Mini Circuits, United States. Part No: ZHL-3A) amplify the
RF signals +29.5 dBm to +32 dBm (approximately 1.5 watts), the maximum drive
power of the AOMs.
The 1 GHz clock is generated by a small integrated oscillator (Fox Electronics,
United States. Part No: FXOPC536R-1000). An output of +13 dBm was measured
at 50Q, sufficient for driving the frequency synthesizer. This oscillator and the small
amount of supporting electrical hardware required was packaged in an enclosure and
connected to a BNC output.
vaa
0.01pF
#
E/D
Voc
R2
R1
C1FXO-PC536R-1000
13
1
NC Comp. Output
Ground
Output
R3
R4
13
130
Figure 2-2: Schematic of the I GHz clock. J1 is the I GHz output.
31
2.1.4
Reference path
The reference path uses an adjustable focus fiber optic coupled collimator, and focuses
it onto a mounted aluminum front surface mirror. A mirror was used instead of a
retroreflector as its greater parallelism resulted in higher coupling efficiency than was
achievable with a retroreflector, despite the increased difficulty in alignment. The
collimator was used with an FC/APC fiber optic terminator in order to reduce back
reflections. This setup was simulated with Zemax optical design software, as shown
in Figure 2-3, predicting a single mode fiber coupling efficiency of -0.55 dB.
LAYOUT
R-375
TUE MAR 18 2014
TOTAL AXIAL LENGTH:
422.77124 MM
VERTICAL SCALE STRETCHED BY 20000 X
REFERENCECOUPLING. ZMX
CONFIGURATION I OF 1
Figure 2-3: Zemax raytrace simulation of reference path. Note that the vertical axis
is enlarged by 20x, and that the mirror is represented by duplicating and reversing
the optical system about the center.
The mirror was mounted on a non-motorized, single axis micropositioning stage,
allowing the reference path length to be adjusted so that it matches the distance to
the sample path objective focal point.
2.1.5
Sample path objective
A graded index (GRIN) lens (Thorlabs, United States. Part No: GRIN2313A) was
used to focus light onto the sample under examination. The GRIN lens is sold as a
package that can be assembled to focus to a desired distance. An 8 degree angled
face is used to reduce back-reflection. This was fixed in place with a UV cured optical
adhesive (Norland Products, United States. Part No: NOA68).
32
r*Face Angle
01.800 MM
Fiber
GRIN23 Series
SMPFO1 Series
Figure 2-4: The GRIN lens assembly. Adapted from an image by Thorlabs.
The physical distance from the GRIN objective lens to the sample under examination, referred to as the working distance (W), is determined by balancing the
achievable penetration depth, the amplitude of scattered light, the transverse resolution, and the complexity of positioning the lens near the sample.
The solid angle Q subtended by the GRIN lens is equal to
Q = 27r(1 - cos 0) ,
where 6 = arctan
r
(2.1)
, or equivalently,
Q = 27r
1-
(2.2)
W2
W2+ r2ri
Assuming an isotropic scatterer, the fraction of optical power that will be recollected by the GRIN lens is equal to -.
As the GRIN lens used in this thesis has a
radius of 0.9 mm, this fraction may be written numerically as
1
2
W2
.(2.3)1
W2 +0.81)
-
A plot of this scattering loss for working distances between 0 and 5 mm is shown
in Figure 2-5.
A working distance of approximately 2.5 mm was chosen, as it provided the minimum sufficient distance between the lens and sample, while avoiding unnecessary
scattering loss or resolution limitations.
33
0
I
-5
U)
0
0)
-10
-15
U)
-20
0
1
2
3
4
5
Working distance (mm)
t
Figure 2-5: Light lost to an isotropic scatterer, as a function of working distance.
2.2
Sample alignment apparatus
The sample alignment apparatus, pictured in Figure 2-6, is a mechanical device designed to accomplish several goals:
* Securely hold the GRIN objective lens
" Move the GRIN objective along the direction of the optical axis with a precise
motorized stage
" Allow the GRIN objective lens to be rotated a certain angle around its focal
point
" Allow adjustments for height and horizontal distance
" Provide a visible alignment aid beam
" Hold a small digital microscope for visual inspection of alignment
2.2.1
Mechanical device for adjusting angle and position
To control the angle of the optical axis, the z-axis stage is mounted on a horizontal
aluminum cantilever, with two circularly concentric slots cut out.
By screwing the
stage mounting block into the slots, the angle can be adjusted around a fixed point.
When the system is configured such that it is focused on this point, the operator is
34
/
4
Figure 2-6: A 3D model and a photograph of the mechanical alignment apparatus.
1) Vertical adjustment slider. 2) Horizontal adjustment slider. 3) Angular adjustment slider. 4) GRIN objective lens. 5) Z-axis piezo stage. 6) Digital microscope.
7) Microscope illumination source.
35
FI
Figure 2-7: Side view of the alignment apparatus, with arrows indicating mechanisms
for adjusting position and angle.
able to change the angle of axial movement without changing the current focal point,
a helpful feature for alignment.
The cantilever part was designed in SolidWorks and then milled on a CNC machine
in the Edgerton Center Student Shop. An 'L'-shaped part was designed to hold
the horizontal cantilever.
Later, a vertical part was added to enable continuous
adjustment of cantilever height and to allow for a higher maximum height, necessary
as a result of the clearance requirements of the 2D transverse stage. These parts were
milled by hand at the Edgerton Center Student Shop.
2.2.2
Piezo motor stage for axial movement
To control z-axis scanning, a piezo-electric motorized stage was used (Newport, Inc.,
United States.
Part No: CONEX-AG-LS25-27P). This stage uses an "inchworm"
drive method to control motion in discrete steps. Quadrature position encoders with
closed loop feedback provide movements repeatable of up to a manufacturer specification of 200 nm.
36
Figure 2-8: A photograph of the piezo motion stage. 1) Piezoelectric motorized stage.
2) 'L'-backet to mount piezo stage. 3) 'S'-bracket to mount GRIN lens. 4) GRIN lens
'V'-clamp.
Unfortunately, this stage also has some drawbacks for an OCT application. Though
the closed loop feedback allows for the stage to move precisely to any location, the
speed of movement is not consistent.
As a result, it is necessary to either collect
data pixel-by-pixel or to re-interpolate the data collected based on the actual position of the stage as it scans. These methods, and their advantages and drawbacks,
are discussed further in the signal processing section, Section 2.5.
To capture information about the real time position of the stage, two approaches
were used. The first involved repeatedly querying the stage driver over a serial connection.
While this was straightforward to accomplish and within the bounds of
normal operation of the stage, it (lid not provide high enough time resolution of
the position of the stage. The second approach required adding analog output from
the stage encoders that could be captured directly by the analog-to-digital converter
simultaneously with the interferoinetric signal. This involved extracting the quadrature encoder signal from the controller circuit board and soldering additional BNC
outputs.
The piezo stage was mounted to the angle adjustment apparatus by fabricating
37
a custom mounting bracket designed for the unique hole spacing on the stage. The
bracket is also designed as an 'L' shape, so that the GRIN lens points in the radial
direction of the angle adjustment arc.
2.2.3
Mounting the fiber and GRIN lens
q)
(z
Figure 2-9: A close up view of the GRIN objective mounting apparatus. 1) GRIN
objective. 2) Brass extension rod used to lower the GRIN lens. 3) V-clamp. 4) Digital
microscope. 5) Optical fiber (truncated in image.) 6) 'S' bracket.
To hold the GRIN lens at a sufficient distance from the stage with minimal bulk,
a small brass rod was adhered with a UV-cured optical adhesive to the outer glass
tube in the GRIN lens assembly. A V-clamp was used to firmly hold the brass rod
in place. A custom 'S'-shaped mounting bracket was designed and milled to connect
to the piezo stage, allow the V-clamp to be mounted, and also to allow the digital
microscope to be installed such that it could image the focal point of the GRIN lens.
Note that without the brass extension rod, the focal point of the GRIN lens would be
blocked from the view of the microscope by the V-clamp and supporting hardware.
The narrow profile of the brass tube and GRIN lens also allow the objective to be
positioned more easily near the sample under examination.
38
2.2.4
Digital microscope for visual alignment
Figure 2-10: An overview of the digital alignment microscope. 1) LED illumination
source. 2) Mounting bracket (position and angle adjustment). 3) Lens tube. 4) USB
web camera CCD.
In order to aid the alignment process, an optical microscope with a digital CCD
viewfinder was constructed to observe the region imaged by the OCT process.
The design required a relatively large working distance, and correspondingly low
numerical aperture, in order to allow the microscope to have an angle as close to the
optical axis of the OCT objective lens as possible.
A CCD sensor from a USB web camera (Microsoft, United States. Part No: Xbox
Live Vision) was used, due to its compact size, low cost, and use of the standard USB
Video Class protocol, compatible with MATLAB and other image capture applications. As the CCD has a quite small size, approximately 3x5mmn
(actual dimension
specifications are not available), a low magnification was sufficient.
A MATLAB script was used to optimize the working distance using a simple
paraxial lens approximation, while keeping the overall optical length within reasonable
limits, and while working with a set of easily obtainable lenses. From this MATLAB
program, a Zemax simulation model was created, using accurate models of the real
lenses from which the microscope would be constructed.
The microscope is composed of three lenses in two groups: a 15 mm1 spherical
doublet (Edmund Optics, United States. Part No: 45209) and a 20 mm spherical
singlet (Thorlabs, United States.
Part No: LA1074).
a 1/2 inch diameter lens tube. A 4 mn
The lenses are mounted in
diameter aperture, laser cut from opaque
39
acrylic, was used to further reduce spherical aberrations, improving image quality
at the expense of light intensity. A raytrace diagram of the microscope is shown in
Figure 2-11, and the predicted point spread function in Figure 2-12.
I
LAYOUT
TUE MAR 25 2014
159,72000 MM
TOTAL AXIAL LENGTH:
VERTICAL SCALE STRETCHED BY 5.0000 X
MICROSCOPE
CONFIGURRTION
' ZMX
I OF
L
Figure 2-11: A raytrace diagram of the microscope layout, simulated in Zemax.
9
8.2
0.3
-8
-32
-29
--t6
-9
0
X-POSITIDN IN
P
16
24
32
V
Pm
PSF CROSS SECTION
TUE MAR 25 2019
M
L
FIELI 0
WRVE=LENGTH:0POLYOIROMRTIC
LIN X SECTION, CENTER ROW.
MICROSCOPE.
CONFIGURATION
I
ZMX
OF
I
Figure 2-12: The point spread function of the microscope, as simulated in Zemax.
The performance was tested by imaging a backlit 1951 USAF Resolution Test
Target, demonstrating that the microscope is capable of resolving features as small
as 7.8 pm wide, and has a field of view of 1.16 mm x 0.87 mm, for a magnification
of approximately 4x.
40
Figure 2-13: An image of a 1951 USAF Resolution Test Target, captured using the
digital microscope.
Due to the nature of the microscope's intended application, the sample is not
illuminated by transillumination but instead by viewing the light scattered by the
sample from a bright LED source mounted near the end of the microscope. While
the performance of this microscope is too limited for most imaging applications (in
particular, the contrast is quite poor, as evidenced by the "haze" around the bright
regions in Figure 2-13), it is sufficient for performing basic alignment of the FODOCM system and is therefore sufficient for the system design requirements.
2.2.5
Visible laser for assisting visual alignment
The spectral responsivity of a silicon photosensor, like that used in the digital microscope CCD, falls sharply above 1000 nm. As the optical source in this system is
centered at 1310 nm, it is difficult to view the spot produced by the focused infrared
light. To solve this, a second optical source can be coupled into the GRIN lens.
For this purpose, an inexpensive 650 nm laser diode is used. The output of the
diode is collimated and coupled into an optical fiber, which can be attached through
an FC/APC connector directly to the GRIN lens. This produces a highly visible laser
spot that is helpful for aligning the start of an OCT scan.
41
Figure 2-14: An image of the visible laser spot on cochlear tissue, captured by the
digital microscope.
2.3
X-Y stage for sample movement
Figure 2-15: The transverse X-Y stepper motor stage. 1) Laser-cut mounting platform, with aluminum stand-offs. 2) Prior H101 two-axis stage. 3) Laser-cut mounting
plate.
To move in the transverse plane, the sample is placed on a stepper motor driven
two axis stage (Prior Scientific Ltd., Japan. Part No: H101BX), pictured in Figure 242
15. While this stage is designed for use with a conventional upright microscope,
custom mounting hardware was designed and fabricated to allow it to stand freely.
The stage is driven by a stepper controller, which accepts commands over a serial
connection (Prior Scientific Ltd., Japan. Part No: H128V). The stage has a 1 im step
size, but poor repeatability, making it suitable only for 2D scanning in the x-z or y-z
planes.
2.4
Light detection and signal acquisition
The light is detected by a photodiode with an integrated transconductance amplifier
(New Focus, Inc., United States.
Part No: 2117-FC). This photodetector has a
sensitivity range of 800-1700 nm and a transimpedance gain of up to 18.8 x 106 V/A,
with responsivity near 1A/W at 1310 nm.
As the interference carrier signal is set at 500 KHz, the analog photodiode lowpass and high-pass filters in the photodetector are configured to pass signals between
300 KHz and 1 MHz.
The output from the photodiode is digitized by using a two input PCI DAC/ADC
card (Interface Co., Japan. Part No: PCI-3525). Multiple DAC/ADC cards are daisy
chained together to be able to capture greater than two signals simultaneously. This
is useful, as up to five signals may be of interest to capture: the photodiode output,
the RF synthesizer difference frequency, the acoustic stimulus signal, and the two
z-stage quadrature encoders.
To capture these signals, a program was written in C to communicate with the
DAC/ADC. As the photodiode filters frequencies above 1 MHz, a sampling frequency
of 2.5 MHz was chosen to avoid frequency aliasing. The capture program allows for
application-specific flexibility and may be used with imaging interfaces in MATLAB
and Python.
43
2.5
Signal processing
The FO-DOCM system is capable of performing two distinct tasks. The first is image
generation, where a static 2D or 3D image of the sample is made. The second is motion
analysis, capturing information about the movement of one specific area of a sample.
The primary difference between these two tasks is that motion analysis requires a
segment of data to be sampled from one stationary point while image generation can
use a continually scanning axis.
2.5.1
Image generation
An overview of the signal processing steps necessary for continuous scan image generation from acquired data, for a single z-axis sweep, is shown in Figure 2-16.
Digital BPF
Hilbert transform
signalI
e i sri t
z-a is tago
encoder signal
Position reinterpolation
ro
I
Decirmation
extract thioe
envelope oftesga.Uigdtrmtexuaratur n coesoh
Figure 2-16: A block diagram overview of the steps necessary for image generation.
First, the captured signal is bandpassed using a digital FIR filter with a smaller
passband than is practical with analog filters. Next, the Hilbert transform is used to
extract the envelope of the signal. Using data from the quadrature encoders of the
z-axis stage, this envelope is reinterpolated to be a function of space instead of time.
As the envelope is much more slowly varying than the original 500 KHz signal, it can
be decimated to the size desired for the final image. This process is repeated for each
captured line to assemble the full 2D or 3D image. A function to implement these
steps was written in MATLAB.
44
2.5.2
Motion analysis
An overview of the signal processing steps necessary to perform on acquired data to
estimate motion parameters, for a single pixel, is shown in Figure 2-17.
------ Fibr tasfr
Interference
l
BPF
+
Cosine fit - Scaling 10
phase extractionMotion
parameters
signal
RF synthesizer
Digital
BPF
Hilbert transform
phase extraction
x(2
x (-2)
reference
Figure 2-17: A block diagram overview of the steps necessary for motion analysis.
This process is the same as that derived mathematically in Section 1.5.1. First,
the Hilbert transform is used to estimate the instantaneous phase of the photodiode
interference signal, and of the 250 KHz reference output from the RF synthesizer.
The difference between the 500 KHz phase signal and twice the 250 KHz phase signal
is periodically varying when the phase of the 500 KHz signal varies periodically, as is
the case when light is scattered from a moving sample excited at a known frequency.
A sinusoid of this known frequency is fit by linear least squares to this periodically
varying phase, as a noise-resistant method of estimating both the amplitude and
the phase offset of the oscillation. This process provides an estimate of the motion
parameters at a single point in the sample and can be repeated for as many points
are desired, or for an entire array of points, in order to generate an image of motion
amplitude and phase in a sample. This analysis is also implemented as a function in
MATLAB.
2.6
2.6.1
Theoretical performance predictions
Axial resolution
Axial resolution is limited by the coherence length of the optical source, derived in
Equation 1.5 in Chapter 1 as
45
6Z = 1C =
21n2 A2
.
7r A
(2.4)
The specifications for the optical source used in this project were not precisely
equivalent to the measured performance of the actual source. The actual -3dB bandwidth was 86.3 nm, whereas the specified bandwidth was 100 nm.
Additionally,
the actual power output was 7.00 mW, whereas the specified power was 10 mW.
The slightly smaller bandwidth results in an axial resolution of 9.94 Jrm, inferior to
the prediction in Section 1.2. The optical spectrum measurements also showed that
bandwidth, and therefore resolution, is not adversely impacted by any other optical
components in the system.
From the optical power spectral density, the point spread function can be numerically predicted by calculating the Fourier transform, as derived in Section 1.2. Using
the Discrete Fourier Transform, the measured optical spectrum analyzer results may
be used to estimate the axial point spread function.
The result of this analysis is
shown in Figure 2-18.
1
0.9
0.8
0.7
C
0.6
C
0.5
0.4
E
0.3
0.2
0.1
'
-25
-20
-15
-10
-5
0
5
Distance (pm)
10
15
20
25
Figure 2-18: Theoretical axial point spread function. Computed from optical spectrum analyzer measurements of the SLD source.
46
2.6.2
Transverse resolution
As previously discussed in Section 1.2.1, the maximum achievable resolution is determined by the objective optics used to focus the light as well as the central wavelength
of the light itself. Light emitted from the optical fiber propagates as a Gaussian
beam, so by solving for the evolution of the parameters of the Gaussian beam, the
minimum beam waist may be calculated. The complex beam parameter q, defined in
Equation 1.7, may be used to describe the Gaussian beam. Light is emitted from an
optical fiber with infinite radius of curvature, and with a waist defined by the fiber
mode diameter, so the initial q parameter of the beam is the purely imaginary value
2
q =i
.
(2.5)
From Equation 2.6, the complex beam parameter after propagation is
sin(VAl 2 )(Alinr2(l + qo) - 1) - V/'no cos(V1A 2 )(l1 + 13 + qo)
An(l 3 + qo) sin(vrAl 2 ) - V/iAno cos(v,/Al 2
(2.6)
)
qi =
The mode field diameter of the SMF-28e+ optical fiber used by the FO-DOCM
system is 9.2 pm. For the objective GRIN lens,
1/A
= 0.327 mm- 1 ,
12 =
4.42 mm,
and no = 1.5916. From these values, the numerical value of the new complex beam
parameter is calculated to be
(0.242 - 0.051i)l1 + (3.692 + 0.012i) - 1113 + 0.24213
(0.242 - 0.051i) - l3
(2.7)
where l 3 is the distance from the fiber to the GRIN lens and 11 is the working distance
from the GRIN lens to the focal point. To achieve a working distance of approximately
2.5 mm, the GRIN lens was assembled approximately 2 mm away from the optical
fiber. Using this value for 13, and Equation 1.8, the new beam diameter is
47
Wi =
-A
,
)v
w Im(1/qi
(2.8)
= 0.047/(4.176 - 1.75811) 2 + (0.0123 - 0.0511h)
2
which has a minimum at a working distance of 11 = 2.374 mm away from the GRIN
objective lens. At this distance, the beam radius at 1/e 2 intensity was 5.07 pm. This
corresponds to a transverse FWHM resolution of 5.97 pm.
Using Zemax with lens files provided by the manufacturer of the GRIN lens, a
more accurate simulation was created of the objective lens performance. A geometric
ray trace approximation to the Gaussian beam is shown in Figure 2-19. When the
imaged object was on the optical axis, as is the case when light emerges from an
optical fiber in the GRIN lens assembly, Zemax found the 1/e 2 Gaussian beam radius
to be 5.08 pm, almost identical to the value calculated theoretically above.
3D LAYOUT
SW-180-0313
GRIN LENS
OB,~ECTI[VEGR1N
.ZMX
CONFIGURRAT ION I DF I
Figure 2-19: A Zemax raytrace showing the geometric ray optics approximation of
the path of the Gaussian beam through the GRIN lens. Light emerges from the
SMF-28e+ single mode fiber (NA = 0.14) on the left, and is focused to a point on
the right.
48
Chapter 3
System characterization and results
In this chapter, efforts to characterize the performance and capabilities of the FODOCM system will be detailed. Results obtained with the FO-DOCM device using
actual cochlear tissues will be shown. The shortcomings and successes of the system
will be discussed, and conclusions will be drawn.
3.1
3.1.1
Resolution performance
Measurement of axial resolution
In Section 2.6.1, predictions were made about the axial resolution achievable by the
FO-DOCM system. Here, these predictions are tested and limitations are explained.
To verify the axial resolution, the sample was replaced by an aluminum frontsurface mirror.
The z-axis stage was moved in increments of 100 nm over a 60
pm range around the interference maximum.
A small 0.1 second segment of the
500 KHz carrier wave was sampled for each z position, from which the envelope could
be extracted at each point.
The axial point spread function (PSF) measured by this process and a comparison
to the PSF predicted by optical spectrum analyzer measurements- in Section 2.6.1 are
shown in Figure 3-1. The measured FWHM resolution is 9.9 jim, extremely close to
the predicted FWHM resolution of 9.94 jim.
49
1
-
0.9
Measured PSF
Predicted PSF
0.8
(D 0.7
70
0.6
E
\/-
0.5
CO
0.4
0
z
0.3
0.2
/\
0.1
0
-25
-20
-15
-10
-5
0
E
10
15
20
25
Distance (pm)
Figure 3-1: The measured axial point spread function of the FO-DOCM system. The
measured PSF is shown as a solid line, and the predicted PSF as a dashed line.
3.1.2
Measurement of transverse resolution
The FO-DOCM system is not designed for en-face (transverse) scanning, so measuring
the transverse resolution was significantly more difficult than measuring the axial
resolution. To measure the transverse resolution, two methods were used: an en-face
scan of a standard 1951 USAF resolution test target and a cross-sectional scan of the
edge of a microscope coverslip.
Shown in Figure 3-2, the USAF resolution test target was imaged by holding the
FO-DOCM system at a constant z-axis depth, and recording the photodiode signal
while moving the y-axis continuously. Then, the x-axis was incremented by 1 pm, and
the process repeated. Because the transverse stage was not chosen for suitability for
this type of scanning, severe distortion is visible in the result due to the acceleration
and deceleration of the stage during the y-axis scan. Point-by-point scanning was
not possible due to the slow speed of the transverse stage. Vertical re-alignment of
each column was performed to correct for poor stage repeatability in the y-axis, and
a median filter was applied to reduce noise. Despite the clear unsuitability of this
method of scanning for imaging applications, the visibility of all elements of group
50
50' 11
'04
Figure 3-2: Result of en-face scan of 1951 USAF target. Note the distortion caused
by the variable speed and low repeatability on the transverse stepper motor stage.
Despite the distortion, all of the elements of Group 6 are distinguishable, indicating
a transverse resolution of approximately 8.8 pin.
6 within the USAF resolution test target in this experiment indicates a transverse
resolution of approximately 8.8 pm.
To obtain a less distorted measure of the transverse resolution of the FO-DOCM
system, a second experiment was performed. In this experiment, shown in Figure 3-3,
the edge of a microscope coverslip, resting on a microscope slide, was imaged in the
x-z plane. The lateral transition between the coverslip and air is the transverse step
function of the system. Theoretically, this step function could be differentiated to
obtain the transverse point spread function. However, differentiation increases noise,
which renders this PSF unsuitable. Instead, the integral of a Gaussian function, a
scaled error function, can be fitted to the step function, as shown in Figure 3-4. The
best fit parameters correspond to a transverse FWHM resolution of 9 + 0.7 pm, which
corroborates the results obtained with the USAF target image.
3.1.3
Limits of motion measurements
To measure the noise floor of motion measurements, the sample path was focused onto
a fixed aluminum front-surface mirror. To more accurately simulate the reflectivity of
51
200
200
250
250
300
300
1
0.9
0.8
0.7
350
350
0.6
c8400400
0.5
450
9450
500
500
0.3
0.2
550
550
0
10
20
30
40
50
X-axis distance (pm)
60
70
0.1
0 204060
X-axis distance (pm)
Figure 3-3: Result of scan of the edge of a a glass coverslip, with major features
labeled. On the right is the same image, with 1:1 scaling between the x and z axes.
Error function fit
of cover slip reflectivity
-. . . .. . -..
--..
. .. .
-... '
.-..
-.
E
N
0.8
-
-
..
.
-..
-
.
0.6
0 .4
-
-- -
------
-
-Q)
~~Magnitude
.
-- ~.
0
0
10
20
30
40
50
60
70
80
X-axis distance (pm)
Figure 3-4: Transverse step function measured along the glass coverslip. This corresponds to a single horizontal line in Figure 3-3. The best fit error function (the
integral of a Gaussian function) corresponds to a FWHM resolution of 9 0.7 Pm,
corroborating the USAF target experiment.
tissues, a 10-2 attenuator was inserted into the optical path, attenuating the sample
signal by 10- . The acquired photodiode signal was analyzed according to the process
outlined in Section 2.5.2. The spectral density of the resulting displacement signal is
shown in Figure 3-5. Above 3 KHz, a noise floor of approximately 1 pm/HzO. 5 was
52
measured.
The strong impulsive frequencies present above 10 KHz are caused by electromagnetic interference in the analog-to-digital converter, originating from within the
computer that hosts the converter card, and are not the result of any inherent issues
with the FO-DOCM system. Below 3 KHz, the harmonic noise could be the result
of mechanical vibrations in the apparatus, air movement caused by building HVAC
systems, or sidebands produced by the RF synthesizer. An effort to further explain
the presence of these frequencies is made in Section 3.3. To avoid this interference,
stimulus frequencies of 1 KHz, 4 KHz, and 16 KHz were used in further testing.
102
E
10
10
Frequency (Hz)
Figure 3-5: Noise floor of measured motion with sample reflectivity of approximately
10-4. The noise floor above 3 KHz is approximately 1 pm/Hz0 5 . The impulsive peaks
in this range are the result of electromagnetic interference between the ADC and the
computer hosting it.
To verify the linearity of the motion measurements, a piezo-electric actuator was
imaged while excited at a range of voltages. As the response of the piezo-electric
actuator is very linear [17], the motion amplitude should increase linearly with increasing stimulus. The response of the FO-DOCM system was shown to be linear
over motion amplitudes ranging from approximately 200 pm to 80 nm. Measured
amplitude values and the best zero-intercept linear regression for each are shown in
Figure 3-6. Maximum deviation from the linear regression was < 2% above 10 nm of
motion, and for the 4 KHz stimulus was < 5% over the entire range. The root mean
53
square error from the linear regression, for all frequencies, was 0.06 nm for amplitudes
less than 10 nm, and 0.1 nm over the entire amplitude range.
o
7n
~
760
8
1 KHz stimulus
4 KHz stimulus
16 KHz stimulus
*
X
6
E
4
.2
-.
0
E
-00
0.2
0.2
0.15
0.15
0.1
0.1
0.05
0
~30
Jr.7
~20
0
0
0.2
0.4
0.6
0.8
1
i
I
I
I
1.2
1.4
1.6
1.8
2
Piezoelectric stimulus voltage (V)
Figure 3-6: Linearity of motion amplitude measurements, for three stimulus frequencies over two orders of magnitude.
3.1.4
Resolution of motion differentiation
The ability of the FO-DOCM system to resolve the difference in vibrational amplitude
between closely spaced objects, referred to as "motion differentiation resolution," is
another important system characteristic for analysis of cochlear motion.
For this
experiment, a glass coverslip was held just above a small ball-bearing glued to a piezo
electric crystal. A sequence of reflectance and motion magnitude images were made,
with an axial step size of 1 pm and no transverse step, while the distance between
the ball bearing and the coverslip was gradually reduced. The motion amplitude at
the center of the ball bearing interference peak and at the center of the coverslip
interference peak is plotted in Figure 3-7. Motion measurements were taken as the
median over a 3 x 1 pixel area, of the peak-to-peak amplitude of the oscillation in
the analyzed distance signal. It should be noted that the reflected amplitude from
the coverslip was approximately 10% that of the reflected amplitude from the ball
54
bearing, and that the motion differentiation resolution may be finer for more closely
matched reflectivities.
25
-
-
--
-
-
2 0 - --
E
Ca
_0a 15
.
..
0'
0
10
20
30
40
50
60
70
80
Coverslip - ball bearing separation (pm)
Figure 3-7: Motion differentiation of adjacent stationary and vibrating interfaces
(coverslip and ball-bearing, respectively), as measured with the FO-DOCM system.
The motion amplitude between adjacent surfaces is shown to be differentiable for
distances greater than approximately 7 pm. This is expectedly close to the axial
FWHM resolution of 9.94 pm.
3.2
Demonstrative images and motion measurements of cochlear tissue
A guinea pig (Cavia porcellus) cochlea was used to test the ability of the FO-DOCM
system to image biological tissues of interest for the Micromechanics Group. Care
and use of the animal was approved by the MIT Committee on Animal Care. A
female guinea pig was euthanized by urethane overdose and decapitated. The left
temporal bone was removed and placed in a low calcium, low chloride solution of
artificial perilymph (7 mM NaCl, 163.4 mM sodium gluconate, 3 mM KCl, 0.1 mM
CaCl 2 -2H 2 0, 0.1 mM MgCl 2 , 2.0 mM Na2 SO 4 , 0.5 mM NaH 2 PO 4 , 5 mM HEPES, 5
mM dextrose, 4 mM L-glutamine). The cochlea was extracted from the bulla and
anchored to a Petri dish using dental cement (Durelon) with its apical side up. Using
55
a #11 scalpel blade, a small rectangular hole was scored into the apical bone. The
bone was then penetrated and force exerted upward from the bottom of the rectangle
to pop out the scored section. The cut was made such that scala vestibuli of the
apical turn was exposed, leaving the Reissners membrane almost completely intact.
Imaging was performed in immersion, using the continuous scanning method described in Section 2.5.1, with a transverse step size of 2 pm. The image in Figure 3-8
shows a cross section of the exposed apical turn, near a small tear in the Reissner's
membrane. Several cochlear tissues are visible in the image, including the Reissner's
membrane, the basilar membrane, the organ of Corti, the tectorial membrane, the
spiral lamina, and the surrounding bone. The intensity of back-scattered light is
shown on a logarithmic scale.
0
0
100
-2
200
-4
-8
E
L 400
-
-6
300
-10 E
Cc 500
-12
0D
-14
700
-16
800
-18
900
-20
-600
-400
-200
0
200
400
600
X-axis distance (pm)
Figure 3-8: An annotated unfixed guinea pig cochlea, imaged with the FO-DOCM
system. The transverse (x-axis) step size is 2 pm, arid the z-axis is a continuous scan.
Several distinct cochlear tissues are visible and labeled.
The cochlea was later fixed in a 2% gluteraldehye solution, and re-imaged sev56
eral days after isolation. The fixation process results in changes to the tissues in
the cochlea; an increase in reflectivity, caused by polymerization of tissue, is clearly
visible, as is the delamination of tissue from the spiral lamina.
To test the ability of the FO-DOCM system to measure vibrations in cochlear
tissues, the sample was excited by placing a piezo-electric actuator with an attached
titanium tip against the exterior of the cochlea. The piezo induced a 10 KHz motion
throughout the isolated cochlea including the organ of Corti. The sample was then
imaged by the FO-DOCM system in a pixel by pixel manner, collecting data for
analyzing reflected intensity and the motion of the sample at each point, as described
in Section 2.5.2. The size of the image was 1200 x 800 lim, with a pixel size of 3 x 5
pm. The motion analysis showed a much larger range of motion than was expected,
spanning almost two orders of magnitude. However, it is not believed that this is the
result of noise or poor measurements, as the calculated phase of the motion is locally
coherent. The measured reflectivity and motion parameters are shown in Figures 3-9
and 3-10. As the motion induced by the piezo-electric actuator has an amplitude on
the order of 1-100 nm, it does not result in visible artifacts in either image. Due to
the large variation in motion amplitude, it is shown on a logarithmic scale in units of
dB nm.
3.3
Known issues
Scanning speed.
As a result of the long settling times of the z-axis piezo motor
stage, the FO-DOCM system is slower than the FS-DOCM system when scanning
pixel by pixel. However, when using the continuous scanning method discussed in
Section 2.5.1, scans can be significantly faster, though the system is unable to analyze
motion. This suggests that a different paradigm of imaging may be more useful for
the FO-DOCM system. Rather than performing an entire motion map scan at once,
an interface could be developed to allow the motion at specific points of interest in
the continuously scanned image to be measured.
57
0
0
-2
-2
200
-4
-4
-6
-8
10
40
-a
-8
U
-V
-12
-14
-16
1000
-1
-18
-1200
-1000
-800
-00
0
-200
-400
400
200
-2
X-axis distance (pm)
X-axis distance (pm)
Figure 3-9: A fixed guinea pig cochlea, imaged with the FO-DOCM system. On the
left is a large area scan performed with continuous z-axis motion and a 10 Pm transverse pixel size, and on the right is a smaller reflectivity map that was captured
simultaneously with the motion map in Figure 3-10, with a 3 x 5 Pm pixel size. The
cross section is slightly different between the two scans, and they were separated by
several hours.
Motion amplitude (dB nm)
Motion phase (radians)
20
6
15
20
10
ID
U
10
C
"0
to
~0
5
U)
CN
0
-5
100
i
I
-10
-400
-200
0
200
400
0
-400
-200
0
200
400
X-axis distance (pm)
X-axis distance (pm)
Figure 3-10: Motion map of vibrations in a fixed guinea pig cochlea, phase shown
on the left in radians and amplitude on the right in dB nm, captured simultaneously
with the reflectivity map on the right side of Figure 3-9. A 3 x 3 median filter was
used to reduce noise.
58
Stage repeatability.
The transverse stepper motor stage has quite poor repeata-
bility, as became apparent during the en-face experiment to measure transverse resolution limits.
While this is not a problem for unidirectional x-z or y-z scans, it
prevents the use of the apparatus for en-face scanning or for accurate three dimensional scanning.
The z-axis piezo motor stage was also shown to have less reliable repeatability
than originally intended. While the manufacturer's quoted bi-directional repeatability specification was 0.2 pm, in practice a repeatability of 2 um is achieved. The
cause of this order of magnitude disparity between quoted specifications and apparent performance is currently unknown. While this repeatability is sufficiently below
the resolution limit of the FO-DOCM device to allow it to be functional for scanning,
improving the repeatability of this stage would improve the resulting image quality.
Transverse resolution.
The measured transverse resolution of the FO-DOCM sys-
tem was significantly worse than the predicted value from theory and Zemax, by approximately a factor of two. This performance degradation must be caused by a problem with the GRIN lens assembly used for focusing the optical sample path. As shown
in Figure 2-4, the GRIN lens has an 8 degree face angle to reduce back-reflections.
If this face angle were axially misaligned, it could result in optical aberrations that
would degrade performance. Furthermore, any uncleanliness on interior surfaces of
the assembly might degrade performance and would be impossible to clean after the
optical adhesive has set. It is therefore theorized that some combination of the above
issues is responsible for the degraded transverse resolution performance and that the
issue would be resolved by the construction of a new GRIN lens assembly.
Signal-to-noise ratio.
The motion measurement noise floor shows significant in-
terference at particular frequencies, though the broadband noise floor is quite low. It
is believed that much of the harmonic noise at frequencies above 10 KHz results from
electromagnetic interference between the analog-to-digital conversion PCI card and
the host computer. To test this assumption, a signal was acquired from the analog59
to-digital converter while the converter was connected only to a 50 ohm terminator.
This power spectrum shows frequency peaks explaining the 16 KHz, 19 KHz, and
higher peaks in Figure 3-5. As the signal was acquired with the inputs immediately
terminated, the most likely origin of this interference is within the host computer
itself and would require a different analog-to-digital converter to eliminate.
The lower frequency peaks in noise, at 380 Hz, 760 Hz and 1950 Hz, are still of
unknown origin. Mechanical noise and vibration are more probable sources of interference at lower frequencies. To limit mechanical vibration, vibration damping washers
could be employed on the fasteners in the alignment apparatus. Air movement caused
by building HVAC systems could also increase noise at low frequencies. This could
be mitigated by the use of physical baffles around the system. The peaks could also
be the result of sidebands produced by the RF synthesizer or distortion caused by
the RF amplifier. Further investigation and debugging is required if the FO-DOCM
system is to become useful for measuring small amplitude motion at frequencies less
than 3 KHz.
3.4
Conclusion
The design and implementation a fiber optic Doppler optical coherence microscopy
(FO-DOCM) system for use in cochlear imaging was presented. The FO-DOCM system uses a fiber optic design to reduce system size and complexity over the previous
FS-DOCM system in use at the Micromechanics Group. Additionally, a novel alignment and micropositioning apparatus was created to increase the ease of use for the
researcher performing the imaging. To enable precise measurements of subnanometer
tissue motion, a time domain DOCM approach is used, utilizing an acousto-optic
modulator (AOM) based optical heterodyne system to generate a stationary interference carrier frequency.
This system is shown to be capable of measuring motion with a noise floor of
1 pm/Hz' 5 above 3 KHz, a significant improvement over the results of most published Doppler optical coherence tomography systems. In addition to interferomet60
rically measuring small amplitude motion, the FO-DOCM system is shown to be
capable of imaging with a volumetric resolution of 10 x 9 x 9 pm. Results of imaging
cochlear tissue in vitro using the FO-DOCM system have been presented, showing
its suitability for cochlear imaging. The FO-DOCM system will continue to be used
and developed by the Micromechanics Group for use in researching the mechanical
properties of structures inside the mammalian cochlea.
61
62
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