Apparatus for measuring high frequency vibration, motion, or displacement

Apparati and methods are disclosed for detecting vibrations, displacements and motions of a remote surface with high sensitivity, high frequency response and high accuracy using a laser beam with optical modulation, optical hetrodyning and phase detection. High speed digital signal processing is used. Shared aperture design is employed for utilization of a flat target, double-pass design for large lateral movement tolerance with high resolution, and dual target design for detection of displacement as well as angular changes in vibrational motion.

FIELD OF THE INVENTION 
The invention relates generally to apparati for the measurement of 
mechanical vibrations, which includes displacement, velocity, and 
acceleration, and particularly to the accurate measurement of high 
frequency vibrations in a remote object through optical techniques. 
BACKGROUND OF THE INVENTION 
Devices for measuring mechanical vibrations include the accelerometer, 
linear variable differential transformer (LDVT), laser doppler velocimeter 
(LDV), vibrometer, laser interferometer and others, as well as 
combinations of these. The accelerometer measures vibrations directly, 
being directly mounted upon the subject. Drawbacks include limited 
sensitivity and accuracy, the need for frequent calibration and the fact 
that its mass may perturb the measurement. The LDVT in measuring the 
relative displacement of vibration, has a short measurement range and it 
is highly non-linear. The LDV measures the velocity of a vibrating 
surface, is non-contacting but the signal-to-noise ratio is poor. The 
laser interferometer is non-contacting but high resolution and high speed 
cannot be obtained simultaneously so that it is useful only for low 
frequencies. None of-the prior art devices provide the ideal performance 
of remote sensing, high resolution, sensitivity and accuracy, good 
signal-to-noise ratio and being usable in both low and high vibrational 
frequency applications. 
It is noted that most prior art on the noncontact vibration measurement 
such as Foster (J. V. Foster "A Laser Device for Remote Vibration 
Measurement", IEEE Trans Aerospace and Electronic Systems, AES3(2), p.154, 
Mar. 1967), Monchalin (U.S. Pat. No. 4,633,715, 1/1987) and Khanna (U.S. 
Pat. No. 4,834,111, 5/1989), are based on the Laser Doppler Velocimetry 
technology which is quite different from the Laser Doppler Displacement 
Meter (LDDM) technology claimed here. 
Even though both use interferometers, optical heterodyne, AO-modulation, 
photodetector, etc., the basic concept, measurement and its applications 
are quite different. 
Briefly, the LDV is based on the Doppler frequency shift, 
EQU fD=fL(2V/c) (1) 
where fD is the Doppler frequency shift, fL is the laser frequency, V is 
the target velocity parallel to the laser beam, and c is the speed of 
light. The velocity can be determined by measuring the frequency shift. 
Any target with a rough surface or a diffusive reflector will scatter 
light back with the Doppler frequency shift caused by the target velocity. 
The electromagnetic field at the detector is the sum of light scattered by 
many scatter centers. As shown by Wang (C. P. Wang, "A unified Analysis on 
Laser Doppler Velocimeter", J. Phys. E, 5. p. 763,1972) 
EQU E(t)=Sum(p=1 . . . n) Ap exp{-i2pi(fL+fD) t+i Op} (2) 
where E(t) is the electromagnetic field at the detector from n scatter 
centers, Ap is the amplitude, fL is the laser frequency, fD is the Doppler 
frequency shift and Op is the phase angle. After mixing with a local 
oscillator on a square-law detector, the output spectral density has a 
term with the Doppler frequency shift fD and certain broadening. Because 
the light is scattered back, there is Doppler ambiguity (see C. P. Wang, 
"Effect of Doppler ambiguity on the measurement of turbulence spectra by 
laser Doppler Velocimeter, Appl. Phys. Lett, 22(4), p. 154, February 1973) 
which broadens the frequency shift fD and limits the detection to be above 
a certain minimum velocity of the target. Hence for LDV the 
signal-to-noise ratio is low and there is a minimum target velocity. 
The LDDM technique (see C. P. Wang, U.S. Pat. 4,715,706, 12/19/87) is based 
on the same Doppler frequency shift, but integrates the frequency to 
obtain the relation between the phase and the displacement: 
EQU (O/2pi)=(fL/c)*(x-xO) (3) 
where O is the phase angle, x is the position and xO is the initial 
position. As shown above, in the LDV, the phase angles are lost after 
summing over many scatter centers. Hence, for the LDDM, a target with a 
flat-mirror or a specular reflector is needed. Using the same notation as 
in Wang's patent, the electromagnetic field at the detector is: 
EQU V4(r,t)=a4(r,t) exp i{(wO+wD) t+O4} (4) 
EQU V2(r,t)=a2(r,t) exp i{(wO+) t+O2} (5) 
Where V4 is the reflected field, V2 is the reference or local oscillator 
field, a4 and a2 are amplitudes, O4 and O2 are phase angles, wO is the 
laser frequency in rad/sec, is the AO-modulator frequency, wD is the 
Doppler frequency shift, r is the position and t is the time. The output 
from the square-law detector is then: 
##EQU1## 
where rp is the position of the detector, T is the averaging time, d is 
the detector diameter and A, B and O are constants. Integrating the 
Doppler frequency shift, we obtain: 
##EQU2## 
Hence, using a phase-demodulator circuit, the phase O can be measured. 
In summary, the major differences between the LDV and the LDDM are as 
follows: 
1) Signal-to-noise ratio, (S/N) 
LDV: Low, requiring averaging over time 
LDDM: High, requiring no averaging 
2) Target 
LDV: Any scattering surface or a diffusive reflector 
LDDM: Flat mirror or specular reflector 
3) Minimum Velocity 
LDV: Target must move at a minimum velocity 
LDDM: No minimum velocity 
By reference, the present invention incorporates U.S. Pat. No. 4,715,706 
issued on Dec. 29, 1987 to Charles P. Wang, the present inventor. The 
current invention builds upon the technological base established in the 
1987 patent, said patent comprising an apparatus for the precise 
measurement of the displacement of a moving cooperative target from a 
reference position, traveling over a distance of several meters with a 
measurement accuracy of a fraction of a millimeter. The doppler phase 
shift of a reflected laser beam is determined to obtain a precise 
measurement of the displacement of the target with respect to a prior 
determined reference position. 
SUMMARY OF THE INVENTION 
The invention teaches a method for optimizing the optical acquisition of 
data for measuring the vibration and displacement of a remote body. The 
technique provides the ideal performance lacking in prior art devices 
including remote sensing, high resolution, sensitivity and accuracy, good 
signal-to-noise ratio, and usefulness in both low and high frequency 
applications. A laser generated beam is used as means for detecting 
vibration in the remote body. The beam is diffracted and frequency shifted 
to act as a reference beam. Both signals are combined for detection. A 
single aperture method is employed to permit the use of a plane target 
reflector thus minimizing the mass of the target reflector and its impact 
upon the vibrating body. 
A beam expander is used in a technique permitting minimum disturbance of 
the vibrating body by employing a lightweight and physically small, planar 
mirror. The beam expander and shared aperture design permit signal 
processing with the smallest possible target reflector. Double pass 
optical arrangement is employed to improve resolution and ease alignment 
restrictions. In an alternate configuration, a double-pass design is used 
together with a large retro-reflector target to achieve a large tolerance 
for lateral movement and rotation of the target. A dual-beam design which 
includes two output laser beams and two photodetectors achieves the 
detection of both linear and angular displacement simultaneously 
The invention apparatus provides a unique method for optical measurement of 
vibration, displacement or other mechanical deflection of a target at high 
frequency. The technique uses optical modulation and heterodyning for 
phase detection of frequency shifts in a measurement laser beam as 
compared with a reference beam. The result provides information about 
displacement changes which can be differentiated once for velocity and 
twice for acceleration information. Therefore it is imperative to have a 
large signal to noise ratio and high resolution. 
As shown by the referenced U.S. patent to Wang, with respect to the Doppler 
effect, the displacement of a retro-reflector target can be expressed as: 
EQU X=[C/2F]*[N+PHI/2PI] 
where C is the speed of light, F is the laser frequency, N is the number of 
cycles (2 pi's), and PHI is the measured phase. Based upon the Wang 
apparatus both PHI and N can be measured. In the current invention an 
8-bit counter is used to record N and an 8-bit A/D converter is used to 
digitize PHI. Each data point is two bytes, one for N and the other for 
PHI. The data is recorded into solid state memory at a data rate of up to 
800,000 points per second. The data is then read by a low cost general 
purpose ze for use with microcomputer and common magnetic media. The data 
can be plotted and viewed on a monitor as displacement, velocity or 
acceleration information, and can be further processed to obtain power 
spectra density, shock response spectra or other results. Because the 
invention has the ability to accept high data rate streams and has 
resolution capabilities in the range of one nanometer, it can measure 
velocities in the range of two meters per second and mechanical 
vibrations, both transient and continuous waves, up to 100 kHz. 
Other features and advantages of the present invention will become apparent 
from the following more detailed description, taken in conjunction with 
the accompanying drawings, which illustrate, by way of example, the 
principles of the invention.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENT 
FIG. 1 illustrates an apparatus for detecting vibration or motion of a 
first reflective target 11. The apparatus comprises a laser source 10, 
which may be any readily available laser such as a 1 mw HeNe laser or a cw 
semiconductor diode laser, for producing a source light beam 1 of 
frequency f1. The source beam 1 strikes the reflective target 11 and 
returns as reflected beam 1A; beams 1 and 1A sharing a first common path 
20. After leaving laser 10, source beam 1 enters a frequency modulator 25, 
such as an acustic-optical modulator, thereby producing a diffracted 
reference beam 2 of frequency f2, diffracted from the source beam 1, where 
f2 is shifted relative to frequency f1 of the source. A reflector 8 steers 
reference beam 2 to intersect reflected beam 1A at first beam combiner 6, 
whereby the first combined beam 3 (1A+2) is directed into first detector 9 
by second reflector 8A. In order to enhance the signal-to-noise ratio, 
assure acquisition of the first target 11 by the source beam 1, and reduce 
the required alignment precision, first beam expander 12 may be used to 
broaden source beam 1. 
FIG. 2 describes an alternate embodiment similar to that of FIG. 1 but with 
large tolerance for both lateral and angular movement of the second 
reflective target 11A. For the setup shown in FIG. 1, either a flat mirror 
or a corner-cube may be used as the target 11. Although the use of a 
flat-mirror as a target is insensitive to lateral movement, it is very 
sensitive to the rotation of the target. The corner cube as a target is 
insensitive to rotation, but is very sensitive to lateral movement. The 
arrangement in FIG. 2 provides tolerance, simultaneously, for both 
relatively large lateral target movement, on the order of one-half the 
size of the third reflector 8B, which is preferrably a flat mirror, as 
well as relatively large rotational angles, but typically less then 30 
degrees. In this case the second reflective target 11A is a corner cube 
set approximately in line with the source beam 1. The third reflector 8B 
is preferrably an extended plane reflector mounted opposite the second 
reflective target 11A and having a fixed angular relationship with respect 
to the laser source 10, reflector 8B being positioned to receive the 
reflected beam 1A from the target 11A, producing second reflected beam 1B 
projected back along the second common path 20A of the reflected beam 1A, 
to be again reflected by the target 11A producing third reflected beam 1C 
passing back along the first common path 20, whereby the total path length 
of beams 1, 1A, 1B and 1C is approximately doubled with respect to the 
optical path of the apparatus of FIG. 1. Reflector 8B is typically larger 
than the beam width (alpha) in order to accommodate significant 
misalignment and movement of target 11A. As in FIG. 1, reflector 8 steers 
reference beam 2 into intersection with third reflected beam 1C at 
combiner 6, whereby the combined beam 3A (1C+2) is directed into first 
detector 9 by reflector 8A. 
FIG. 3 describes an alternate embodiment of the invention similar to that 
of FIG. 2. The requirement for the target 11 of FIG. 1 is that it has to 
be typically perpendicular to beam 1 within about 30 arcsec, which is very 
difficult to achieve in the field. It was noted that the lateral tolerance 
of the return beam is about 1/2 beam diameter. The purpose of the 
arrangement in FIG. 3 is to trade lateral tolerance for angular tolerance. 
The angular tolerance of target 11 becomes a few degrees instead of a few 
arcsec. Hence it makes the use of a flat-mirror in the field practical 
except that the normal 13 to reflective target 11 is not parallel to the 
path of source light beam 1. The fourth reflector 8C is a corner cube 
reflector having a fixed angular relationship with the laser 10. The 
corner cube is positioned to receive, on axis, first reflected beam 1A 
from the target 11, thereby generating the second reflected beam 1B which 
is reflected back along the second common path 20A, to target 11, 
generating third reflected beam 1C in common path 20 in the opposite 
direction of source beam 1, whereby the total path length of beams 1, 1A, 
1B and 1C is approximately doubled with respect to the optical path of the 
apparatus of FIG. 1. 
FIG. 4 describes an alternate embodiment similar, in part, to that of FIG. 
1. Based on the same concept as shown in FIG. 1, beam 1 strikes the third 
reflective target 11B', typically a composite target made up of two corner 
cube reflectors 11B' and 11B", and returns as first reflected beam 1A, 
where it is combined with first reference beam 2 at the fourth beam 
combiner 6c before entering first detector 9. The output of detector 9 
contains the information on the displacement of the target 11B', 11B". 
Additionally, a portion of the first reference beam 2 is directed to 
target 11B" by beam splitter 7, is returned as second reflected beam 2A to 
be combined first reflected beam 1A at second beam combiner 6A and is then 
directed into second detector 9A. The output of the second detector 9A 
contains the information on the displacement of the third target 11B', 
11B". 
The first combined beam 3 (1A+2) contains the doppler frequency shift 
information from motion of the third reflective target 11B', 11B". The 
output 50 therefore contains information on the displacement of the third 
target. The second combined beam 3A (1A+2A) is detected by second detector 
9A so that output 51 contains the information on the difference of the 
displacement of the two corner cubes of the third reflective target 11B', 
11B". This is proportional to the rotation or angular displacement of the 
target. Hence both linear displacement (detector 9) and angular 
displacement (detector 9A) can be measured simultaneously. 
The electrical signal outputs 50, 51 of the detectors are amplified and 
introduced to a phase demodulator. The detection and signal processing 
scheme is disclosed in the referenced 1987 patent to Wang. The modulator 
25 serves three functions including the generating and frequency shifting 
of the reference beam 2 and isolating the laser cavity from any reflected 
or stray laser light. This later function prevents laser instability and 
permits the use of the shared aperture design employed, whereby both the 
source/reference light beams and the target reflected light beams travel 
on the same path. The laser beams are not polarized so reflectors may be 
first surface devices and all beam handling components including beam 
splitters and combiners can be very small in size. 
For vibration measurement it is important that the vibrating reflective 
target be as small as possible, and that it be attached rigidly to the 
vibrating body. These constrants are required so that the resonance 
frequency of the mirror-system be much higher than the vibration frequency 
to be measured. Typically the resonance frequency F (r) can be expressed 
as: 
EQU F(r)=1/2pi* SQR(k/m) 
where k is the equivalent spring constant and m is the mass of the 
mirror-system. It is clear from this equation that a large spring constant 
is necessary or that the reflective target have a very small mass in order 
to achieve high resonance frequency. This is achieved in the configuration 
of FIG. 1 where the reflective target can be a very lightweight mirror or 
a polised specular reflective surface on the vibrating body itself. 
FIG. 2 is a double pass light beam arrangement used where large lateral 
alignment tolerances must be tolerated. Here an extended plane reflector 
8B is properly aligned and fixed to the laser head box 4. The source beam 
1 is reflected by the reflector 11A to the extended plane reflector 8B. 
Beam 1B is passed through exactly the same path but in the reverse 
direction as beam 1A. Although the alignment of the reflector 8B is 
critical, it is prealigned and fixed to the laser head 4. 
The alignment requirements of the reflector 11A, in this case, are very 
much relaxed. The retro-reflector can be rotated up to 30 degrees, limited 
only by its size, and can be laterally moved up to a distance of (D-d)/2, 
where D is the diameter of the flat mirror and d is the laser beam 
diameter, without loss of alignment. Because the laser beam is reflected 
by target 11A twice, displacement changes produces twice the phase shift 
when compared to single pass. Hence resolution is doubled. It is noted 
that the total displacement of a flat reflector is limited due to narrow 
alignment limits. The tolerence for displacement is a function of 
measurement distance, off-angle magnitude and other geometric 
considerations specific to the application. A typical setting might have a 
distance of 50 cm and an angle of 2-3 degrees, whereby the displacement 
range of a flat mirror is a few centimeters which is more than enough for 
the measurement of vibrations. 
The advantages of the double-pass arrangement shown in FIG. 3 are the 
ability to use a thin and light weight flat mirror for the reflective 
target instead of a more massive corner cube, the alignment tolerance is 
much larger and the resolution is doubled due to the double pass of the 
light beam. 
The embodiment shown in FIG. 4 provides a method for measuring both pitch 
(yaw), and displacement simultaneously. Detector 9 measures the phase 
shift due to the displacement of the target 11A while detector 9A measures 
the relative phase shift between the retro-reflectors 11B' and 11B". 
In practical vibration measurement, it is important to record the data at a 
high date rate. The techniques of the present invention permit the use of 
relatively low cost, common microcomputer equipment and interface circuits 
capable of 800,000 bits/sec.