Light-scattering heterodyne interferometer measurements in auditory organs*
for vibration
P. R. Dragsten and W. W. Webb School of Applied and EngineeringPhysics, Cornell University, Ithaca, New York 14853
J. A. Paton and R. R. Capranica Schoolof Electrical Engineeringand Sectionof Neurobiologyand Behavior,Cornell University,Ithaca, New York 14853
(Received 2 February 1976; revised 10 May 1976) An interferometric optical heterodyne technique has been developed especially for vibrational amplitude and phase measurementson auditory organs of live animals. Laser light diffusely scattered from the vibrating structure is used for the measurement.Continuous calibration and feedback compensationsystems were developed to cope with the problems of drift in interferometer alignment and small background
movements. Vibrational amplitudes frombelow0.1 • to above400• havebeendetected on theposterior tympanic membranesof live crickets. SubjectClassification:[43 ] 65.20; [43 ] 40.60; [43 ] 35.65.
sensitiveof the techniques(0.03 •k sensitivityreported)
INTRODUCTION
The desire in auditory physiology to measure small vibrations with good spatial resolution has motivated
the development of several effective techniques. Among the most sensitive methods are capacitive probes
(Wilson,1973; WilsonandJohnstone,1975), MfSssbauereffect velocity sensors (Gilad et al., 1967; Johnstone and Boyle, 1967; Johnstone, Taylor, and Boyle, 1970;
Rhode, 1971), and laser interferometry (Khanna,Tonndorf, and Walcott, 1968; Tonndorf and Khanna, 1968). We describe here a laser-scattering interferometer method that offers substantial advantages over previously available techniques. The capacitive probe originally employed by von
and has a dynamic range of around 80 dB (Khanna, Tonndorf, and Walcott, 1968). However, alignment is quite critical.
Spatial resolution is limited
to the
mirror size, whichwas reportedto be 0.1 mm•' in area, although smaller
mirrors
may be possible.
We have developed a modified laser interferometry technique that uses the light diffusely scattered from the vibrating surface. Thus, attachments that might introduce mechanical perturbations are eliminated and
alignment is simplified (Dragsten et el., 1974a, 1974b). Spatial resolution of 10 /am or less can be achieved, since it is limited only by the size of a focused laser beam.
We
have
been
able
to make
vibration
measure-
B•k•sy (1960) used a rf carrier signal which was am-
mentsbelow0.1 • in amplitudewith 3-secaveraging
plitude-modulated by the change in capacitance between the probe and the vibrating structure. The probe was
time on the opaque, diffusely scattering tympanic membranes of crickets despite slow background motion of the live subjects. Provisions to automatically correct for small background movements and drift in the interferometer alignment have been developed to facilitate
miniaturized by Wilson (1973) and Wilson and Johnstone
(1975), and used for basilar membrane studies in which
measurements below1 • in amplitudewere achieved with a detection bandwidth of 0.008 Hz. Spatial resolution, however, was limited by the probe tip diameter
whichwas150 /amin theselatter studies. Theprobe tip requires precise positioning near the vibrating structure.
The MfJssbauer method involves placement of a tiny radioactive source directly on the vibrating object. The Doppler shift of the emitted gamma radiation is then detected by resonant absorption techniques.
The ad-
vantage of this method is simple alignment. However, the useful dynamic range is only 15-20 dB, and the sensitivity is frequency dependent. Relatively long counting intervals are required for each measurement,
with a sensitivityof about10 • at 20 kHz and10-min countingtime (Johnstone,Taylor, and Boyle, 1970). The spatial resolution is limited by the size of the
radioactive source, 40x50 /•m (Rhode, 1971).
measurements
I. LIGHT
on live
SCATTERING
animals.
INTERFEROMETER
THEORY
In this section we develop the theory for vibration measurements with an interferometer using scattered light. To calculate the scattered light field and analyze its detection, we have applied the theory of quasielastic light scattering and optical heterodyne spectroscopy
(Cumminsand Swinney, 1970). For heterodynedetection the scattered light is superimposed with a reference beam on a photodetector. In this way any phase modula-
tion of the scattered light caused by the scatterer's motion can be detected in the optical heterodyne photo-
current (Khanna,Tonndorf, andWalcott, 1968; Dragsten et el., 1974a, 1974b; Deferrari, Darby, and Andrews, 1967; Deferrari and Andrews, 1966; Sizgoric, and Gundjian, 1969; Rabinowitz et el., 1962; Schmidt
et el. , 1961).
Laser interferometry requires the placement of a tiny mirror on the vibrating structure. It is by far the most
To determine the phase of the scattered light as a
665
Copyright ¸ 1976 by the Acoustical Society of America
J. Acoust. Soc. Am., Vol. 60, No. 3, September 1976
665
Redistribution subject to ASA license or copyright; see http://acousticalsociety.org/content/terms. Download to IP: 136.165.238.131 On: Sun, 21 Dec 2014 16:34:32
666
Dragsten et al.' Light-scattering heterodyneinterferometer
666 If the scatterer is vibrating sinusoidally at angular frequency cos, with amplitude and direction represented
•i =scottere2
by the vectorK andphaseby qbs,then• = • sin(co st + qb s) and
=Is+lfr+ 2e(Islr) 1/•'
FIG. 1.
A general light scattering geometry.
The scatterer
is at position Y with respect to a nearby origin, and the detec-
- sin•••oJ•'"+•(•'K)sin[(2nl)(cost+qbs ' (4a)
tor is at •. •i is theincident lightpropagation vector,• is thescattered lightpropagation vector,•= •i- •s is thescatter- where J,is the Bessel functionof order n (Deferrari, ing vector,
and 0 is the scattering angle.
Darby, and Andrews, 1967). Discarding the higher harmonic terms (which can be filtered out) this becomes
= +I, + 2e function of the position of the scatterer,
we consider a
- 2 sinnJ•({. •) sin(cost + qbs) +''' }
planewavewithpropagation vector•i incidentona point scatterer (Fig. 1). Departures from this model due to the finite
areas
of scatterer
and detector
are
discussed in a later section. In the farfield limit, the scattered radiation is essentially a spherical wave emanating from the scatterer.
The scattered
electric
field Es, which is proportional to the incident field, can be expressed in complex notation:
E•-Aøs {exp[i(k• ß•- wot)]} [exp(ik I•- •1)],
(1)
where • is the position of the scatterer with respect to
a nearbyreferencelocation,the detectoris at • with R >>r, co ois the angularopticalfrequency,Asø/Ris the amplitudeof the scatteredlightfield, andk Since R >>r, this can be simplified to
E = Aøs[eikR/R]e "•otei•'• $
(2)
,
where•--[i- [s, k• beingthepropagation vectorfor the scatteredlight. Sincethescattering is elastic, [•i[ =[k•[ = kandq = 2kstn•O. ' • If the scatterer is moving, '• r will be a function of time and by Eq. (2) the scattered light will be phase modulated by the motion. This phase modulation can be detected by mixing the scattered light with a superimposed reference beam on a square law detector, such as a photomultiplier cathode or photodiode.
The reference
beam electric
field can
be writtenEr=Eø•e"•Ote m whereEø•is the amplitudeof the reference beam and 9 represents the optical phase
/ {cost&to (4b) 1
and, sincefor small argumentsJo(x)= 1 andJ• (x) = •x, I• male terms
+ 2•(/•I•)•/•'[cosf•- sin• •. • sin(cost+ qb•)] , (4c) where{. • •
for vibration
P. R. Dragsten and W. W. Webb School of Applied and EngineeringPhysics, Cornell University, Ithaca, New York 14853
J. A. Paton and R. R. Capranica Schoolof Electrical Engineeringand Sectionof Neurobiologyand Behavior,Cornell University,Ithaca, New York 14853
(Received 2 February 1976; revised 10 May 1976) An interferometric optical heterodyne technique has been developed especially for vibrational amplitude and phase measurementson auditory organs of live animals. Laser light diffusely scattered from the vibrating structure is used for the measurement.Continuous calibration and feedback compensationsystems were developed to cope with the problems of drift in interferometer alignment and small background
movements. Vibrational amplitudes frombelow0.1 • to above400• havebeendetected on theposterior tympanic membranesof live crickets. SubjectClassification:[43 ] 65.20; [43 ] 40.60; [43 ] 35.65.
sensitiveof the techniques(0.03 •k sensitivityreported)
INTRODUCTION
The desire in auditory physiology to measure small vibrations with good spatial resolution has motivated
the development of several effective techniques. Among the most sensitive methods are capacitive probes
(Wilson,1973; WilsonandJohnstone,1975), MfSssbauereffect velocity sensors (Gilad et al., 1967; Johnstone and Boyle, 1967; Johnstone, Taylor, and Boyle, 1970;
Rhode, 1971), and laser interferometry (Khanna,Tonndorf, and Walcott, 1968; Tonndorf and Khanna, 1968). We describe here a laser-scattering interferometer method that offers substantial advantages over previously available techniques. The capacitive probe originally employed by von
and has a dynamic range of around 80 dB (Khanna, Tonndorf, and Walcott, 1968). However, alignment is quite critical.
Spatial resolution is limited
to the
mirror size, whichwas reportedto be 0.1 mm•' in area, although smaller
mirrors
may be possible.
We have developed a modified laser interferometry technique that uses the light diffusely scattered from the vibrating surface. Thus, attachments that might introduce mechanical perturbations are eliminated and
alignment is simplified (Dragsten et el., 1974a, 1974b). Spatial resolution of 10 /am or less can be achieved, since it is limited only by the size of a focused laser beam.
We
have
been
able
to make
vibration
measure-
B•k•sy (1960) used a rf carrier signal which was am-
mentsbelow0.1 • in amplitudewith 3-secaveraging
plitude-modulated by the change in capacitance between the probe and the vibrating structure. The probe was
time on the opaque, diffusely scattering tympanic membranes of crickets despite slow background motion of the live subjects. Provisions to automatically correct for small background movements and drift in the interferometer alignment have been developed to facilitate
miniaturized by Wilson (1973) and Wilson and Johnstone
(1975), and used for basilar membrane studies in which
measurements below1 • in amplitudewere achieved with a detection bandwidth of 0.008 Hz. Spatial resolution, however, was limited by the probe tip diameter
whichwas150 /amin theselatter studies. Theprobe tip requires precise positioning near the vibrating structure.
The MfJssbauer method involves placement of a tiny radioactive source directly on the vibrating object. The Doppler shift of the emitted gamma radiation is then detected by resonant absorption techniques.
The ad-
vantage of this method is simple alignment. However, the useful dynamic range is only 15-20 dB, and the sensitivity is frequency dependent. Relatively long counting intervals are required for each measurement,
with a sensitivityof about10 • at 20 kHz and10-min countingtime (Johnstone,Taylor, and Boyle, 1970). The spatial resolution is limited by the size of the
radioactive source, 40x50 /•m (Rhode, 1971).
measurements
I. LIGHT
on live
SCATTERING
animals.
INTERFEROMETER
THEORY
In this section we develop the theory for vibration measurements with an interferometer using scattered light. To calculate the scattered light field and analyze its detection, we have applied the theory of quasielastic light scattering and optical heterodyne spectroscopy
(Cumminsand Swinney, 1970). For heterodynedetection the scattered light is superimposed with a reference beam on a photodetector. In this way any phase modula-
tion of the scattered light caused by the scatterer's motion can be detected in the optical heterodyne photo-
current (Khanna,Tonndorf, andWalcott, 1968; Dragsten et el., 1974a, 1974b; Deferrari, Darby, and Andrews, 1967; Deferrari and Andrews, 1966; Sizgoric, and Gundjian, 1969; Rabinowitz et el., 1962; Schmidt
et el. , 1961).
Laser interferometry requires the placement of a tiny mirror on the vibrating structure. It is by far the most
To determine the phase of the scattered light as a
665
Copyright ¸ 1976 by the Acoustical Society of America
J. Acoust. Soc. Am., Vol. 60, No. 3, September 1976
665
Redistribution subject to ASA license or copyright; see http://acousticalsociety.org/content/terms. Download to IP: 136.165.238.131 On: Sun, 21 Dec 2014 16:34:32
666
Dragsten et al.' Light-scattering heterodyneinterferometer
666 If the scatterer is vibrating sinusoidally at angular frequency cos, with amplitude and direction represented
•i =scottere2
by the vectorK andphaseby qbs,then• = • sin(co st + qb s) and
=Is+lfr+ 2e(Islr) 1/•'
FIG. 1.
A general light scattering geometry.
The scatterer
is at position Y with respect to a nearby origin, and the detec-
- sin•••oJ•'"+•(•'K)sin[(2nl)(cost+qbs ' (4a)
tor is at •. •i is theincident lightpropagation vector,• is thescattered lightpropagation vector,•= •i- •s is thescatter- where J,is the Bessel functionof order n (Deferrari, ing vector,
and 0 is the scattering angle.
Darby, and Andrews, 1967). Discarding the higher harmonic terms (which can be filtered out) this becomes
= +I, + 2e function of the position of the scatterer,
we consider a
- 2 sinnJ•({. •) sin(cost + qbs) +''' }
planewavewithpropagation vector•i incidentona point scatterer (Fig. 1). Departures from this model due to the finite
areas
of scatterer
and detector
are
discussed in a later section. In the farfield limit, the scattered radiation is essentially a spherical wave emanating from the scatterer.
The scattered
electric
field Es, which is proportional to the incident field, can be expressed in complex notation:
E•-Aøs {exp[i(k• ß•- wot)]} [exp(ik I•- •1)],
(1)
where • is the position of the scatterer with respect to
a nearbyreferencelocation,the detectoris at • with R >>r, co ois the angularopticalfrequency,Asø/Ris the amplitudeof the scatteredlightfield, andk Since R >>r, this can be simplified to
E = Aøs[eikR/R]e "•otei•'• $
(2)
,
where•--[i- [s, k• beingthepropagation vectorfor the scatteredlight. Sincethescattering is elastic, [•i[ =[k•[ = kandq = 2kstn•O. ' • If the scatterer is moving, '• r will be a function of time and by Eq. (2) the scattered light will be phase modulated by the motion. This phase modulation can be detected by mixing the scattered light with a superimposed reference beam on a square law detector, such as a photomultiplier cathode or photodiode.
The reference
beam electric
field can
be writtenEr=Eø•e"•Ote m whereEø•is the amplitudeof the reference beam and 9 represents the optical phase
/ {cost&to (4b) 1
and, sincefor small argumentsJo(x)= 1 andJ• (x) = •x, I• male terms
+ 2•(/•I•)•/•'[cosf•- sin• •. • sin(cost+ qb•)] , (4c) where{. • •
