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Description  |
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Within this application several publications are referenced by Arabic
numerals within brackets. Full citations for these references may be found
at the end of the specification immediately preceding the claims. The
disclosures of these publications in their entirety are hereby
incorporated by reference into this application in order to more fully
describe the state of the art to Which this invention pertains.
At present, inner ear vibration measurement techniques require opening the
cochlea. These include (i) Mossbauer, (ii) capacitive probe, and (iii)
interferometric methods. In the Mossbauer method the cohclear opening is
needed in order to place a radioactive foil on the membrane whose
vibration is to be measured [1-14]. In the capacitive probe method the
cochlea is opened in order to place the probe close to the basilar
membrane [15-17]. In the interferometric techniques the cochlea is opened
to place a mirror on the basilar membrane [18,19], or to bring the fiber
optic probe near the basilar memrane [20, 21]. In one interferometric
technique the cochlea is opened to cement a glass window [22].
There are serious problems with the use of techniques which require
surgical opening of the cochlea. Damage is incurred to the cochlea in the
opening process and once the cochlea is opened damage increases with time
[14,17,23-26]. Another problem with these techniques is that the surface
to be measured must be accessible from outside. This limits the
measurements to basilar and Reisners membrane. Due to the finite size of
the Mossbauer source, the mirrors and the capacitive probe tip,
measurements must be made on areas no smaller than (50 .mu.m).sup.2.
Conditions in the inner ear for interferometric measurements are quite
different than those encountered in other mechanical systems: (i) The
inner ear is mechanically not stable, due to blood pulsations and
breathing artifacts; (ii) access to the inner ear is limited by anatomical
constraints making it difficult to visualize the structures of interest;
(iii) vibration amplitudes to be measured in the inner ear are very low;
(v) the structures in the inner ear are nearly transparent therefore the
reflectivity is low, attempts to change this reflectivity artificially
usually alters the response characteristics; (vi) cells are subject to
light damage if the incident light intensity is too high. This limits the
laser power that can be utilized in the interferometer.
Methods have been described which apply homodyne interferometry to
vibration measurements in the middle ear [44] and in the inner ear
[45,18]. The theory, hardware and techniques of the homodyne
interferometer utilized in these methods have been recently described
[43,48]. The sensitivity of the homodyne method drops steeply with the
reduction of signal light intensity. To obtain high reflectivity, tiny
gold mirrors are placed on the basilar membrane. This method however will
not be suitable when vibration measurements are made in cochleas without
mirror placements in which case the reflectivities drop to about 0.02% of
the values obtained with mirrors placed on the basilar membrane.
The present invention can measure at low light levels, while still
retaining a measurement sensitivity of at least 10.sup.-9 cm. The
interferometry technique of the present invention utilizes the heterodyne
method in order to improve the signal-to-noise ratio in the system.
In this method, a laser beam is split into two parts. The frequencies of
the resulting beams are shifted by a fixed amount .DELTA..omega. by
frequency shifters. One beam is then directed onto the object whose
vibrations are to be measured. The reflected and/or scattered beam from
the object is mixed with the other beam in a photodetector. When the
object is stationary, the interference between the two beams results in a
detector output at the beat frequency .DELTA..omega.. When the object
vibrates, the frequency of the reflected beam is frequency modulated due
to the Doppler effect. The detector output then consists of a beat which
is frequency-modulated. The object motion can be measured by demodulating
the detector output with an FM-demodulator centered at the beat frequency.
The following advantages of heterodyne interferometry are evident in
comparison with classical (homodyne) interferometry [35,36]. First, in
contrast to homodyne techniques, the linearity of heterodyne
interferometry is not limited to small vibration amplitudes, because
optical phase variations are not converted to intensity variations
(according to a sine function) but to phase variations of an electrical ac
signal at the beat frequency. Therefore, this technique is well suited to
study nonlinear effects. Second, the familiar quadrature condition which
has to be maintained for homodyne techniques is not necessary with
heterodyning, because sensitivity is essentially independent of the phase
difference between the two interfering beams. In heterodyne
interferometry, the interference phase is completely separated from the
interference amplitude and from the other terms resulting from the
super-position of the two fields. Therefore, drifts taking the
interferometer away from the quadrature condition does not cause signal
fading. Thus, problems with the position control of the reference mirror
are avoided, and the reference beam path can be completely outside the
system under study. The property is particularly important for
investigations on biological systems. Finally, heterodyne interferometry
does not need a vibrating reference mirror for calibration, because the
interference phase, which is proportional to the displacement to be
measured depends only on the geometry of the illumination and reflection
(and of course also on the wavelength .lambda.).
SUMMARY OF THE INVENTION
This invention concerns a heterodyne interferometer for measuring the
amplitude of vibration of a vibrating object. The interferometer
comprises:
(a) a laser for emitting a monochromatic light wave;
(b) a beam splitter for splitting the light wave into an object light wave
and a reference light wave, each having the same frequency;
(c) a modulator for changing the frequency of the object light wave and the
reference light wave so as to produce a predetermined offset between the
frequency of the object light wave and the frequency of the reference
light wave, said modulator being so positioned with respect to the beam
splitter that the object light wave and the reference light wave pass
through the modulator thereby changing their frequencies;
(d) means for directing the object light wave onto the vibrating object,
said means so positioned between the object and the modulator that at
least a portion of the object light wave is directed onto and reflected
off of the object;
(e) a photodetector for producing, at a frequency equal to the
predetermined offset, a beat signal varying in accordance with variations
in the interference resulting from combining at least a portion of the
reflected object light wave and the reference light wave, the
photodetector being so positioned with respect to the object and the beam
splitter that it detects and measures the interference; and
(f) means for processing the beat signal to measure variations in its phase
or amplitude, said means being electrically connected to the photodetector
in order to receive the beat signal.
The invention also provides a method for measuring the amplitude of
vibration of a vibrating object. In one embodiment, the method comprises
using the heterodyne interferometer of this invention. In another
embodiment, the method comprises:
(a) generating a monochromatic light wave;
(b) splitting the light wave into an object light wave and a reference
light wave;
(c) changing the frequencies of the object light wave and the reference
light wave by passing the object light wave and the reference light wave
through a modulator to produce a predetermined offset between the
frequencies of the object light wave and the reference light wave;
(d) directing the object light wave onto the vibrating object so that at
least a portion of the object light wave is reflected by the object;
(e) combining at least a portion of the reflected object light wave and the
reference light wave to form an interference;
(f) measuring the interference in such a manner so as to produce a beat
signal at a frequency equal to the predetermined offset having variations
corresponding to variations in the interference; and
(g) processing the beat signal so as to measure variations in its phase or
amplitude.
BRIEF DESCRIPTION OF THE FIGURES
FIG. 1. Basic elements for heterodyne interferometry. After separation by a
beam-splitter, the object beam (OB) and the reference beam (RB) are
shifted in frequency by two acousto-optical modulators (AO MOD). The
object beam frequency is .OMEGA..sub.1 and the reference beam frequency is
.OMEGA..sub.2. After reflection on the vibrating object, the object beam
is combined with the reference beam at the second beam-splitter producing
a beat signal (.OMEGA..sub.1 -.OMEGA..sub.2) which is detected by a
photodetector (DET). P.sub.OB and P.sub.RB are the light powers of the
object and reference beam, respectively, received by the detector (DET).
FIG. 2. Experimental arrangement for testing the performance of
interferometer. The system consists of (1) and HeNe-laser, (2) equipment
to generate the necessary frequency offset for heterodyne detection, viz.
acousto-optical modulators (AO MOD) and driving oscillators (OSC), (3) a
photodetector (DET) and the associated amplifier (AMP), (4) equipment to
translate the carrier frequency, viz, a balanced mixer (BAL MIXER) and a
local oscillator (LO), (5) equipment to control, demodulate and measure
the interference signal, viz. an oscilloscope (SCOPE), a RF-spectrum
analyzer (SPEC ANAL 2, HP 8553B), a FM-tuner (FM-TUNER, Revox B760) and a
LF-spectrum analyzer (SPEC ANAL 1, HP 3582A), and finally (6) equipment to
generate an artificial FM-signal (FM OSC, MOD OSC) for the calibration of
the FM-demodulator. The mirror mounted on a PZ-translator is used as the
vibrating object.
FIG. 3. Spectrum of the carrier frequency (beat signal) at the output of
the mixer. This spectrum was measured for an incident light power of 0.5
mW and a simulated reflectivity of the object surface of 0.002%
FIGS. 4. Demodulator output noise level as a function of CNR. The
measurement bandwidth is 1.5 Hz for the demodulator noise and 3 kHz for
the CNR. Measurements are shown for three different vibration frequencies:
500 Hz, 5 kHz and 25 kHz in FIGS. 4.1, 4.2 and 4.3, respectively. The
curves show four distinct slopes: A, B, C and D.
FIG. 5. Noise equivalent vibration amplitude versus frequency, for a 1.5 Hz
detection bandwidth. The CNR values were measured in 3 kHz bandwidth. The
curves show the lowest vibration amplitude that can be detected (S=N) by
the heterodyne system. At high frequencies, the sensitivity is essentially
limited by the CNR (horizontal dashed lines), independently of frequency.
At low frequencies, the sensitivity decreases at roughly 20 dB per decade.
FIG. 6. Amplitude response of the interferometer for a fixed vibration
velocity, i.e. for a fixed frequency excursion. The amplitude response is
extremely flat, and the 3 dB bandwidth is about 45 kHz.
FIG. 7. Phase response of the interferometer. The phase changes linearly
with the frequency. The phase lag of -6.12.degree./kHz corresponds to a
delay of 17.0 .mu.s.
FIG. 8. Effect of low frequency disturbances on the accuracy of the
amplitude measurements. Vibration amplitudes were measured at three
different frequencies (500 Hz, 5 kHz, and 25 kHz) with and without a
superimposed low frequency vibration (10 Hz). The relative difference
between the measured vibration amplitudes with and without 10 Hz vibration
is reported in dB as a function of the amplitude of the 10 Hz vibration.
FIG. 9. Linearity of the interferometer levels of the intermodulation
products (f.sub.1 +f.sub.2) and (f.sub.1 -f.sub.2) are shown as a function
of the level of the fundamental vibrations at f.sub.1 and f.sub.2 (8 and
10 kHz). A level of -15 dBV corresponds to a vibration amplitude of 8.10-8
m at each of the two frequencies.
FIG. 10. Schematic of the heterodyne interferometer used for round window
and basilar membrane vibration measurements.
A laser beam reflected by the mirror M.sub.1 is split into two parts by a
beam splitter BS.sub.1. The object beam reflected by the mirror M.sub.2 is
frequency shifted (45 mHz) by the acousto-optic modulator AOM.sub.2 and
attenuated by the attenuator ATT.sub.2. The aperture AP.sub.2 is provided
to select the correct order of the diffraction mode of the acousto-optic
modulator AOM.sub.2. The object beam is deflected downward by the beam
splitter BS.sub.2 and focused on the object by the lens L.sub.1. Light
reflected from the object goes through the beam splitter BS.sub.3 and is
reflected on the detector DET. Part of the object beam goes through the
beam splitter BS.sub.3 and is imaged by the eyepiece.sub.1. Eyepiece.sub.1
and doublet lens L.sub.1 form a low power microscope for visualizing the
object.
The reference beam is frequency shifted (44 mHz) by the acousto-optic
modulator AOM.sub.1. It is reflected by mirrors M.sub.3, M.sub.4 and beam
splitters BS.sub.2 and BS.sub.3 to fall on the detector DET and overlap
with the object beam. The eyepiece.sub.2, mirror M.sub.5 and lens L.sub.2
are provided to view the detector face through the beam splitter BS.sub.3.
This allows orientation and adjustment of the reference and object beams
at the detector so that the interference pattern has a minimum number of
fringes. The detector output at 1 mHz is shifted in frequency to 89 mHz
using the balanced mixed and the 88 mHz local oscilator so that it can be
demodulated by the FM tuner.
FIG. 11. Amplitude (top) and phase (bottom) of round window vibration as a
function of frequency. Vibration amplitude was determined at 60 dB SPL
(solid line), 40 dB SPL (dotted line) and with sound turned off (dashed
line). Phase was measured at 60 dB SPL (solid line) and at 40 dB SPL
(dotted line). The noise level (N) is frequency dependent. It is highest
at low frequencies (130 Hz) and decreases with increasing frequency up to
a frequency of 6 kHz at a rate of approximately -10 dB per octave. The
noise remains essentially flat up to a frequency of 20 kHz and then
increases in magnitude up to 33 kHz. The round window vibration amplitude
at 60 dB SPL is 1.5.times.10.sup.-8 meters between 1 and 2 kHz. The
response shows minimums near 3 kHz and 6 kHz and a peak near 20 kHz. The
response decreases between 20 and 33 kHz. S/N ratio is adequate (>20 dB)
at all frequencies between 300 Hz and 30 kHz. At 40 dB SPL the S/N ratio
is adequate only at a few selected frequencies.
FIG. 12. Round window vibration amplitude (S) and noise (N) measured as a
function of frequency. Note that noise level has been averaged over ten
frequencies around each measuring frequency. The noise level shows a
frequency dependence similar to that illustrated in the previous figure
except that the shape of the curve is slightly different due to averaging.
Round window vibration amplitude was measured for a 40 dB S/N ratio. The
amplitude varied from 5.times.10.sup.-9 m at 0.4 kHz to about
3.times.10.sup.-10 meters at frequencies between 10 and 30 kHz.
FIG. 13. Round window vibration amplitude (S) and noise (N) measured as a
function of frequency. Measurements were made at the same spot used for
measurements in FIG. 12 after readjustment of the interferometer, and as a
consequence the noise floor is slightly higher.
FIG. 14. Sound pressure level required to produce 10.sup.-10 m round window
vibration amplitude as a function of frequency (top) and vibration phase
as a function of frequency (bottom). The two amplitude curves have been
calculated from the data shown in FIGS. 12 and 13. The close agreement
between the two sets of data (solid line and dashed line) shows excellent
repeatability. Similar close agreement is shown for the phase data (bottom
curves).
FIG. 15. Amplitude (top) and phase (bottom) of basilar membrane vibration
as a function of frequency. Vibration amplitude and phase was determined
for 60 dB SPL (solid line) and nose with sound turned off (dashed lines).
The noise level varies with frequency in a manner similar to that shown
for the round window membrane in FIG. 11. The S/N ratio is about 17 dB at
frequencies below 0.7 kHz and much higher (up to 66 dB) at frequencies
between 0.7 kHz and 33 kHz.
DETAILED DESCRIPTION OF THE INVENTION
This invention concerns a heterodyne interferometer for measuring the
amplitude of vibration of a vibrating object. The interferometer
comprises:
(a) a laser for emitting a monochromatic light wave;
(b) a beam splitter for splitting the light wave into an object light wave
and a reference light wave, each having the same frequency;
(c) a modulator for changing the frequency of the object light wave and the
reference light wave so as to produce a predetermined offset between the
frequency of the object light wave and the frequency of the reference
light wave, said modulator being so positioned with respect to the beam
splitter that the object light wave and the reference light wave pass
through the modulator thereby changing their frequencies;
(d) means for directing the object light wave onto the vibrating object,
said means so positioned between the object and the modulator that at
least a portion of the object light wave is directed onto and reflected
off of the object;
(e) a photodetector for producing, at a frequency equal to the
predetermined offset, a beat signal varying in accordance with variations
in the interference resulting from combining at least a portion of the
reflected object light wave and the reference light wave, the
photodetector being so positioned with respect to the object and the beam
splitter that it detects and measures the interference; and
(f) means for processing the beat signal to measure variations in its phase
or amplitude, said means being electrically connected to the photodetector
in order to receive the beat signal.
Essentially any modulator for changing the frequency of a light wave may be
used in the practice of the subject invention. Presently, the preferred
modulator is an acousto-optical modulator. In the preferred embodiment of
the invention, one acousto-optical modulator is employed on the reference
light wave and a second acousto-optical modulator is on the object light
wave. The acousto-optical modulators are driven by predetermined
frequencies which differ by the predetermined offset.
The means for directing the object light wave onto the object whose
vibration is to be measured may comprise a variety of optical devices.
Suitable devices are those which are capable of directing a light wave,
such as mirrors, lens, combinations of lens (e.g. a microscope), etc. In
the preferred embodiment, the means for directing the object light wave
comprises a microscope or a part thereof, i.e. the objective lens.
Suitable photodetectors are those which do not suffer a loss of sensitivity
when the level of light reaching the photodetector is low. Merely by way
of example suitable detectors include a photomultiplier tube, a
photoconductive device, and a PN Junction device. Since PN junction
devices, such as a reverse-biased silicon PN photodiode, are small,
rugged, and readily available at low cost, they are presently the
preferred photodetectors for use in the heterodyne detection system of the
subject invention.
There are a number of variations in the configuration of useful PN junction
photodiodes: the abrupt or graded junction, the PIN structure, and the
avalanche device. In the PIN structure, an intrinsic, high-resistivity
layer is sandwiched between the P and N regions; hence the acronym PIN. It
is constructed so that the potential drop occurs mainly across the
intrinsic layer. This layer is sufficiently long to insure that most of
the incident photons are absorbed within it, thereby minimizing the travel
distance for the carriers and maximizing the charge flow in the external
circuit (responsivity). By increasing the reverse bias across a PN
junction, the field in the depletion layer can increase to a point where
the carriers eject new electrons from the valance to the conduction band,
while still traversing the layer. The result is a multiplication effect
(avalanche) of the current, which creates gain in the manner that a
photomultiplier tube does. The gain (M) can reach a factor of several
hundred.
Unfortunately, carrier avalanche gain is not quite as noise-free as that
provided by the photomultiplier secondary-emission process, principally
because of the contribution of two kinds of carriers (electrons and holes)
to the multiplication process. The avalanche device is, nevertheless,
particularly useful in direct (video) detection where the gain provides an
increase in the SNR by enhancing the shot noise contribution (along with
the signal) while the thermal (amplifier) noise remains constant. By
optimally adjusting the gain, the minimal detectable power is improved
over the ordinary photodiode by a factor that is approximately equal to
the gain.
In the heterodyne configuration, however, it has already been pointed out
that optimal detection is available with the reverse-biased PN junction
photodiode without avalanche multiplication, when the local oscillator
(LO) signal is sufficiently strong and the beams are aligned parallel to
each other. In this case, the avalanche gain provides a stronger signal
(by a factor of M.sup.2), but it also provides an even stronger shot noise
(by a factor of Mn where 2<n<3). Thus it is contemplated that the
avalanche device will be useful in the heterodyne mode only when there is
insufficient LO power to swamp the thermal (amplifier) noise.
The means for processing the beat signal may utilize phase-demodulation or
frequency-demodulation techniques. Presently the preferred approach is to
use a standard FM-demodulator. Such demodulators are readily available in
the form of FM-receivers.
The invention also provides a method for measuring the amplitude of
vibration of a vibrating object. In one embodiment, the method comprises
using the heterodyne interferometer of this invention. In another
embodiment, the method comprises:
(a) generating a monochromatic light wave;
(b) splitting the light wave into an object light wave and a reference
light wave;
(c) changing the frequencies of the object light wave and the reference
light wave by passing the object light wave and the reference light wave
through a modulator to produce a predetermined offset between the
frequencies of the object light wave and the reference light wave;
(e) combining at least a portion of the reflected object light wave and the
reference light wave to form an interference;
(f) measuring the interference in such a manner so as to produce a beat
signal at a frequency equal to the predetermined offset having variations
corresponding to variations in the interference; and
(g) processing the beat signal so as to measure variations in its phase or
amplitude.
Essentially the amplitudes of vibrations of any vibrating object may be
measured by the method of this invention. This invention is particularly
useful when the amplitudes of vibration are submicroscopic in magnitude,
i.e. below about 10.sup.-7 cm, or when the vibrating object has low
reflectivity, i.e. below about 0.02%. Presently, it is contemplated that
the subject inventions will be used to measure the vibration of biological
tissues, such as the vibrations of structures of the inner ear or of the
eye. In one embodiment of the invention, the vibrations of the basilar
membrane is measured. In another embodiment, the vibrations of the hair
cells of the organ of Corti are measured. Certain embodiments of this
invention are exemplified in the Examples and Experimental Discussion
which follow. The Examples and Experimental Discussion are set forth to
aid in an understanding of the invention but are not intended to, and
should not be construed to, limit in any way the invention as set forth in
the claims which follow thereafter.
Experimental Discussion
The heterodyne laser interferometer described herein was specifically
designed for vibration measurement of biological tissue. One application
is for the study of the vibration of individual cellular elements of the
organ of Corti. In order to successfully measure vibration of single
cellular elements, the interferometer had to designed to work under unique
conditions:
(i) The size of the surfaces whose vibration is to be measured is small (A
hair cell diameter is between 5 and 15 .mu.m [27-31]; the surface is also
not flat);
(ii) The reflectivity of the cells is very low, as they are nearly
transparent;
(iii) The vibration amplitudes to be measured are very low (The mechanical
response of the cochlea is nonlinear even at modest levels of sound
pressure; therefore, in order to measure responses at threshold sound
pressure levels, the vibration sensitivity of the interferometer has to be
at least 10.sup.-11 meters [18,9-14]);
(iv) The frequency response of the interferometer has to be wide (In the
basal region of the cat cochlea accessible through the round window
opening, characteristic frequencies are expected to be in the region of 35
kHz [33]; accordingly, to observe the complete response, the frequency
response of the interferometer should extend to at least 50 kHz);
(v) The mechanical characteristics of the inner ear structures are
nonlinear [12,13,34], therefore, the linearity of the interferometer must
be high;
(vi) The sensitive vibration measurements are to be made on living animals
(Low frequency noise due to breathing, blood circulation of the animal and
muscle movements will be superimposed on the vibrations to be measured);
and
(vii) The incident light level should be kept below 0.5 watts/cm.sup.2
since there is evidence that high intensity of incident light may damage
the cochlear cells.
The principle of heterodyne interferometry is very simple in concept. It is
illustrated in FIG. 1. The basic idea is to introduce (by means of two
acousto-optical modulators) a small frequency shift .DELTA..omega. between
the optical frequencies and .omega..sub.1 and .omega..sub.2 of the two
interfering beams. Due to this frequency difference
(.DELTA..omega.=.OMEGA..sub.1 -.OMEGA..sub.2), the interference between
the reference beam (RB) and the object beam (OB) reflected from the
vibrating object produces an intensity modulation of the light field at
the beat frequency .DELTA..omega.. This intensity modulation is detected
by a photodetector (DET). Displacement of the object changes the optical
path length and therefore the phase of the object beam. This is converted
directly into a change of phase of the beat frequency. As long as
.DELTA..omega. is chosen small enough to be resolved by the photodetector,
the photocurrent is given by
i(t)=a+b cos [.DELTA..omega.t+.PHI.(t)], (1)
where a is the dc and b the ac amplitude of the photocurrent and .PHI.(t)
is the phase difference between the two interfering beams. The information
about the object movement is contained in the phase .PHI.(t) of the beat
frequency .DELTA..omega.. This phase can be measured electronically. An
advantage of the heterodyne system is that the phase angle is not affected
by intensity fluctuations of the interfering beams.
In case of vibration analysis, the interference phase in Eq.(1) is a
periodic function of the form
.PHI.(t)=.beta.u cos(.OMEGA.t+.psi.)+.PHI., (2)
where u is the amplitude, .OMEGA. the frequency, .psi. the phase of the
vibration, .PHI. is a constant phase, and .beta. is a geometrical factor.
If 2 .alpha. represents the mutual angle between the illumination and
observation directions (see FIG. 1) and the .lambda. wavelength or the
laser, .beta. is given by
.beta.=(4.pi./.lambda.) cos .alpha.. (3)
Combination of Eqs. (1) and (2) shows that the detector output is a phase
or a frequency-modulated signal with carrier frequency .DELTA..omega. and
modulation frequency .OMEGA.. The corresponding spectrum of such a signal
is a discrete Bessel spectrum, centered at .DELTA..omega.. For small
vibration amplitudes, this spectrum consists essentially of three lines:
the carrier and the first upper and lower sidebands. Thus, small
vibrations amplitudes are readily found from the power ratio of the
carrier (P.sub.0) and the first sideband (P.sub.1) by the relation
(P.sub.0 /P.sub.1).sup.1/2 =J.sub.0 (.beta.u).perspectiveto.2/(.beta.u) (4)
where J.sub.0 and J.sub.1 are Bessel functions of integer order [37]. The
power P.sub.0 and P.sub.1 can be measured with a spectrum analyser.
Carrier-to-noise ratio in heterodyne detection:
The sensitivity is essentially determined by the carrier-to-noise ratio
(CNR), or in other words, by the power ratio of the beat signal and the
noise after detection. To estimate the CNR value, two noise sources have
to be considered: first, the shot-noise which is due to the quantum nature
of the light, and second, the thermal-noise (or Johnson-noise) of the
electronics. The electrical power of the thermal-noise at the output of
the detector amplifier, which is used as current-to-voltage converter, is
given by [38]
P.sub.TN =4 kT B R.sub.0 /R, (5)
where k=1.38.10.sup.-23 J/K is the Boltzmannn constant, T the absolute
temperature, R.sub.0 the feedback resistance, R the load resistance, and B
the bandwidth. Equation (5) shows that the thermal-noise is independent of
the detected optical power, in contrast to the shot-noise, which is known
to be essentially determined by the average light power (P.sub.O) (falling
on the detector [38]. The electrical power corresponding to the shot-noise
at the output of the detector amplifier is given by
P.sub.SN =2(R.sub.0.sup.2 /R) e B S P.sub.0, (6)
where e is the electron charge and S=.eta.e/h.nu. is the spectral
sensitivity of the photodetector. It is determined by the quantum
efficiency .eta., the electron charge e and the photon energy h.nu.. It
the detector aperture is sufficiently large in comparison with the beams
sizes, P.sub.0 is the sum of the light powers in the reference (P.sub.RB)
and object (P.sub.OB) beams, both measured after the beam-splitter
BS.sub.2 shown in FIG. 1, (P.sub.0 =P.sub.RB P.sub.OB).
On the other hand, the electrical power or the heterodyne signal is given
by
P.sub.ac =2(R.sub.0.sup.2 /R) m.sup.2 S.sup.2 P.sub.OB P.sub.RB, (7)
where m represents the relative interference amplitude. This factor is
maximum and equal to 1 when the interference is maximum, i.e. when the two
interfering beams are well superimposed. From Eqs. (6) and (7), it is now
possible to find the carrier-to-noise ratio CNR for shot-noise-limited
detection, namely
CNR=P.sub.ac /P.sub.SN =(.eta./h.nu.)(m.sup.2 /B) [P.sub.OB P.sub.RB
/(P.sub.OB +P.sub.RB ]. (8)
Assuming that m=1 (maximum interference) and P.sub.RB is much greater than
P.sub.OB, this equation becomes
CNR=(.eta. P.sub.OB /h.nu.)/B. (9)
Equations (6) and (7) show that both the electrical power of the shot-noise
P.sub.SN and the electrical power of the signal P.sub.ac increase with
increasing optical power P.sub.RB of the reference beam. However, Eq.(9)
indicates that the shot-noise-limited CNR becomes independent of the
reference beam power P.sub.RB if P.sub.RB dominates the object beam power
P.sub.OB. In fact, Eq. (9) corresponds to the maximum CNR value that can
be obtained with a given light power in the object beam. In order to
attain this most favorable situation of shot-noise-limited detection, one
has to make sure that the shot-noise (Eq.(6)) dominates the thermal-noise
of the electronics (Eq. (5)). This is always possible by sufficiently
increasing the reference power P.sub.RB (which is supposed to be free of
excess noise). The resulting improvement of the CNR is known as
"heterodyne gain".
Shot-noise-limited sensitivity:
Since the incident light power of the living cells must be kept below 0.5
W/cm.sup.2 and since the reflectivity of these cells is very low (less
than 2.10.sup.-4), the power in the object beam P.sub.OB is very low too.
Thanks to the heterodyne gain described above, one can overcome the
thermal noise of the detection system even for a photodiode (see Eqs. (5),
(6), (7) and (8)). Therefore, one is not constraint to use a
photomultiplier which has inherent low noise amplification but poor
quantum efficiency. A silicon photodiode will provide a considerably
better CNR value than a photomultiplier, because the quantum efficiency of
photodiodes is typically 80%, whereas it is only between 5% to 10% for
photomultipliers.
An important quantity is the minimum reference power P.sub.RB for which the
detection begins to be shot-noise-limited. Using Eqs. (5) and (6) and
assuming that P.sub.RB is greater than P.sub.OB, one gets
P.sub.RB,min =2 kT/(eR.sub.O S). (10)
For example, with a feedback resistance R=56 k .alpha., and a temperature
T300.degree. K., this limit is found to be P.sub.RB,min =2.3 .mu.W. As a
consequence, the reference power must be greater than this value to be
sure that the detection is really shot-noise-limited. Practically, one can
test in a simple manner whether the shot-noise is the dominant noise
contribution or not, by blocking the light in detector amplifier. If the
noise level goes down when blocking the light, the detection is
shot-noise-limited and has maximum CNR.
Finally, using Eq.(4), one finds for the minimum detectable vibration
amplitude
##EQU1##
For example, with a quantum efficiency .eta.=77%, a photon energy
h.nu.=3.1.multidot.10.sup.19 Ws (.lambda.=633 nm) and P.sub.OB =50 nW, the
shot-noise-limited CNR for 1 Hz bandwidth is equal to 111 dB, or 76 dB for
3 kHz bandwidth. For normal incidence (.alpha.=0.degree., .beta.=19.9
.mu.m.sup.-1), the corresponding minimum detectable amplitude, or in other
words, the noise equivalent vibration amplitude is then equal to u.sub.min
=0.28.multidot.10.sup.-12 m (for 1 Hz bandwidth).
Effects of the optical properties of the structure under study:
It was assumed so far that the surface of the objects under study was
optically flat. For a given incident light power, it is evident that the
curvature and the roughness of the vibrating surface have a strong
influence on the CNR. In case of specular reflection on distorted surfaces
for example, the optical power which is relevant for the CNR if given by
the power of the back-reflected portion of light which corresponds to the
same optical mode as the reference. The power of this portion can be
considerably smaller than the total power of the reflected beam. In the
extreme case of diffusely scattering surfaces, the reflected beam shows
speckles. Since the interference within each speckle is statistically
independent of the others, the contributions from all speckles add up only
incoherently. Therefore, P.sub.OB in Eqs.(8) and (9) for the CNR has to be
replaced by the optical power within one speckle, i.e. within one
correlated cell of the back-scattered light 37,39].
Signal processing:
The final step of heterodyne detection consists in the extraction of
.PHI.(t) from a signal of the form given by Eq. (1). Two different methods
can be used, namely phase- or frequency-demodulation techniques. The
simplest approach is to use a standard FM-discriminator. FM-demodulation
of the detector output would produce a signal which is proportional to the
instantaneous velocity of the mechanical movement versus time, as it is
well known from laser Doppler velocimetry [40]. For vibration frequencies
between 10 Hz and 100 kHz, such demodulators are readily available for
carrier frequencies in the range of 87 MHz to 108 MHz in the form of
standard FM-receivers. From the beat frequency, which has to be adapted to
the detector response, a suitable carrier frequency is easily obtained by
frequency translation using a mixer and local-oscillator (see FIG. 2).
FM-demodulation has several advantages: first, FM-receivers are readily
available; second, no external reference oscillator is needed for the
demodulation; finally, FM-demodulation allows high phase excursions at low
frequencies, which is particularly important when measuring vibrations in
living animals. On the other hand, FM-demodulators displacement
sensitivity decreases with frequency. The most serious drawback is the
well known "threshold effect" which characterizes FM-demodulators [41].
When the carrier-to-noise ratio equals about 10 dB for the full receiver
bandwidth (typically 150 kHz), the signal-to-noise ratio at the
demodulator output shows a rapid deterioration. This threshold (which
corresponds to 27 dB for 3kHz bandwidth) determines the minimum CNR for
which the FM-demodulator works properly. Nevertheless, a conventional
FM-receiver is a powerful demodulation system for heterodyne detection.
EXAMPLE 1
Method:
The experimental arrangement used to determine the performance of the
heterodyne interferometer is shown schematically in FIG. 2. The most
common method to produce the necessary frequency offset for heterodyne
detection consists in using two acousto-optical modulators (one in each
beam, see FIG. 1) driven at .omega..sub.1 and .omega..sub.2, respectively.
Several diffracted beams are produced by these modulators. The first order
beams (which are selected by an appropriate mask) are shifted in
frequency, due to the Doppler effect, by either +.sub..omega.1,2 or
-.sub.107 1,2, depending on whether the diffraction is in the direction of
the travelling acoustic wave or opposite to it. The net frequency shift
between the two interfering beams is then given by .DELTA.w=w.sub.1
.+-.w.sub.2. The operation bandwidth of such modulators is typically 10
MHz and centered at 40 MHz. The diffraction angle is typically 5 mrad,
which is about 15 times the diffraction limited divergence of a 1 mm
diameter laser beam. In order to get maximum optical power in the
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