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Claims  |
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What is claimed as new and desired to be secured by Letters Patent of the
United States is:
1. A system for measuring a distance between two points, which comprises:
means for generating a coherent electromagnetic first beam having a first
frequency which can be varied within a frequency range;
an interferometer coupled to said first beam and comprising plural
reflective surfaces including first and second reflective surfaces
separated by said distance, said interferometer providing an optical
output signal which is a sum of coherent electromagnetic beams that travel
different path lengths in said interferometer; and
first feedback means for producing a first feedback signal based on said
optical output signal, and feeding back said first feedback signal to said
means for generating to control the frequency of said first beam so as to
maintain constant at at least one value an optical phase difference
between at least two of said different path lengths.
2. A system according to claim 1, wherein said means for generating
comprises:
an acousto-optic modulator.
3. A system according to claim 1, wherein said means for generating
comprises:
a source which generates said first beam; and
means, coupled to said source, for varying said first frequency of said
first beam generated by said source.
4. A system according to claim 1, wherein said means for generating
comprises:
at least one of a magneto-optic modulator and an electro-optic modulator.
5. A system according to claim 1, which further comprises:
first means for frequency modulating said first beam at a first modulation
frequency.
6. A system according to claim 5, wherein said first means for frequency
modulating comprises:
an electro-optic modulator.
7. A system according to claim 5, wherein:
said means for generating comprises a source of said first beam; and
said first means for frequency modulating comprises one of an acousto-optic
modulator, a magneto-optic modulator, and a means, applied to said source,
for modulating said first frequency of said first beam generated by said
source.
8. A system according to claim 5, which further comprises:
first frequency variation control means for controlling said means for
generating to produce said first frequency; and
wherein said first feedback means further comprises means for detecting a
first amplitude modulation at said first modulation frequency, of said
optical output signal from said interferometer, and feeding back, as
negative feedback, a feedback signal corresponding to an amplitude value
of said first amplitude modulation, to said first frequency control means,
thereby maintaining a minimum first amplitude modulation.
9. A system according to claim 8, which further comprises:
a second means for frequency modulating said first beam with a second
modulation frequency.
10. A system according to claim 9, which further comprises:
means for detecting a second amplitude modulation of said optical output
signal at one of the sum and difference of said first and second
modulation frequencies;
second modulation frequency control means for controlling said second
modulation frequency; and
second feedback means for feeding back a second feedback signal
corresponding to an amplitude of said second amplitude modulation, as
negative feedback, to said second frequency modulation control means.
11. A system according to claim 10, wherein:
said second modulation frequency control means comprises auxiliary control
means for controlling a second switch means and for selectively changing
said second modulation frequency to first and second frequencies which
correspond to different optical orders of said interferometer, said second
switch means for connecting and disconnecting said second feedback signal
to the second means for frequency modulating.
12. A system according to claim 8, further comprising:
said first beam comprising first and second portions;
second means for varying frequency of the second portion which provides
said second portion with a second frequency;
monitor means for monitoring variations in frequency of the first and
second portions;
second means for frequency modulating said second portion; and
means for detecting a second amplitude modulation at said second modulation
frequency.
13. A system according to claim 12, which further comprises:
second frequency variation control means for controlling said second means
for varying frequency to produce said second frequency;
second feedback means for feeding back a signal corresponding to the
amplitude of said second amplitude modulation, as negative feedback, to
said second frequency variation control means, thereby minimizing said
second amplitude modulation.
14. A system according to claim 13, wherein:
the first frequency variation control means further comprises a first
switch means for connecting and disconnecting said first feedback signal
to said means for generating, and first auxiliary control means for
controlling said first switch means; and
the second frequency variation control means further comprises a second
switch means for connecting and disconnecting said second feedback signal
to said second means for varying frequency, and second auxiliary control
means for controlling said second switch means, whereby the first and
second frequencies may be varied to correspond to different optical orders
of the interferometer.
15. A system according to claim 1, wherein:
said feedback means comprises detection means for detecting an amplitude
modulation of said optical output signal from said interferometer; and
control means, coupled to said detection means and to said means for
generating, for controlling said first frequency so that the intensity of
said optical output signal remains constant.
16. A system according to claim 1, which further comprises:
monitor means for monitoring a variation in said first frequency, wherein
said variation in frequency corresponds to a change in said distance.
17. A system according to claim 1, wherein the reflective surfaces of the
interferometer are arranged to form a multiple pass resonant cavity.
18. A system according to claim 1, which further comprises:
means for periodically translating one of said reflective surfaces at a
dither frequency.
19. A system according to claim 18, which further comprises:
first frequency variation control means for controlling said means for
generating to produce said first frequency having a first value; and
wherein said first feedback means further comprises means for detecting a
first amplitude modulation at said dither frequency, of said optical
output signal from said interferometer, and feeding back, as negative
feedback, a feedback signal corresponding to an amplitude value of said
first amplitude modulation, to said first frequency control means, thereby
maintaining a minimum first amplitude modulation.
20. A system according to claim 19, which further comprises:
second frequency variation control means for controlling said means for
generating to produce said first frequency having a second value;
wherein said first and second frequency variation control means control the
frequency of said first beam during first and second half-cycles,
respectively, of said hopping frequency, giving it said first and second
values;
wherein said first and second frequency variation control means control the
frequency of said first beam during first and second half-cycles,
respectively, of said hopping frequency, giving it said first and second
values;
wherein said first amplitude modulation refers to the amplitude modulation
present during said first half-cycle;
further comprising second feedback means for detecting a second amplitude
modulation of said optical output signal from said interferometer at said
dither frequency, during said second half-cycle, and feeding back, as
negative feedback, a feedback signal corresponding to an amplitude value
of said second amplitude modulation, to said second frequency control
means, thereby maintaining a minimum second amplitude modulation; and
monitor means for monitoring variations in frequency during said first and
second half-cycles.
21. A system according to claim 20, wherein:
the first frequency variation control means further comprises a first
switch means for connecting and disconnecting said first feedback signal
to said means for generating, and first auxiliary control means for
controlling said first switch means; and
the second frequency variation control means further comprises a second
switch means for connecting and disconnecting said second feedback signal
to said second means for varying frequency, and second auxiliary control
means for controlling said second switch means, whereby said first and
second values of said first frequency may be varied to correspond to
different optical orders of the interferometer.
22. A system according to claim 1, further comprising:
transducer means, coupled to said interferometer and said first feedback
means, for controlling said distance.
23. A system for measuring a distance between two points, which comprises:
an interferometer comprising plural reflective surfaces arranged to form a
resonant cavity, wherein the distance to be measured is the distance
between two of said plural reflective surfaces;
a coherent electromagnetic beam coupled to said interferometer;
means for varying a frequency of said coherent electromagnetic beam; and
means for frequency modulating said coherent electromagnetic beam.
24. A system according to claim 23, wherein:
one or more of said plural reflective surfaces of said resonant cavity are
partially transparent.
25. A system according to claim 23, wherein one of said plural reflective
surfaces of the resonant cavity comprises a flat portion and a concave
portion.
26. An interferometer for a system for measuring distance between two
points, comprising:
plural reflective surfaces arranged to form a resonant cavity, wherein the
distance to be measured is the distance between two of said plural
reflective surfaces, and wherein one of said reflective surfaces comprises
a flat portion and a concave portion.
27. A system according to claim 26, wherein:
one or more of said plural reflective surfaces of said resonant cavity are
partially transparent.
28. A process for measuring a distance between two points, comprising the
steps of:
generating a coherent electromagnetic first beam having a first frequency
with a generator means;
varying the first frequency within a frequency range;.
coupling said first beam to an interferometer having plural reflective
surfaces including first and second reflective surfaces separated by said
distance, said interferometer providing an optical output signal which is
a sum of coherent electromagnetic beams that travel different path lengths
in said interferometer; and
producing a first feedback signal based on said optical output signal;
feeding back said first feedback signal to said generator means to control
the frequency of said first beam so as to maintain an optical phase
difference between at least two of said different path lengths constant at
at least one value. |
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Claims |
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Description |
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BACKGROUND OF THE INVENTION
1. Field of the Invention
This invention relates to interferometric distance measuring systems. More
particularly, this invention relates to interferometric distance measuring
systems for measurement of a change in the distance from one point to
another point, the absolute distance from one point to another point, or
for control of such distances. It also relates to interferometric distance
measuring systems for measurement of a change in the difference between
the distances from one point to each of two other points, the difference
between the absolute distances from one point to each of two other points,
for control of such distance differences, or to systems for combinations
of these functions.
DISCUSSION OF THE BACKGROUND
The market for high precision distance measuring gauges is derived from
laboratory and commercial uses. These uses are all terrestrially based.
Furthermore, all current interferometric gauges have been designed for use
in a gaseous atmosphere (e.g, air). Due to unavoidable turbulence that
occurs in air, the index of refraction of air varies from point to point
and is a function of time. The variation in the index of refraction of air
limits to approximately 10 nanometers the accuracy of devices which
measure optical path length in air except for those that make corrections
by extraordinary means.
Since ordinary interferometric devices operating in air cannot provide a
distance measurement whose uncertainty is less than the uncertainty caused
by air fluctuations, there has been little incentive to reduce the other
uncertainties in such measurements to levels which are well below the
uncertainties provided by the air fluctuations.
High quality commercial laser interferometers are used routinely to measure
distances to an accuracy on the order of 100 nanometers over distances of
up to several meters. These instruments typically do not measure the
absolute distance between the two points, but instead measure only a
distance change which occurs after the start of a measurement operation.
We call instruments which measure a distance change incremental gauges.
There are some optically-based absolute distance measuring devices
available. However, these devices are large and extremely complex.
Furthermore, these devices require a relatively accurate prior knowledge
of the distance to be measured (within 1 percent of the actual distance in
some cases). Therefore, these devices have found only limited application.
Another device of interest is an interferometric null servo, which
maintains a fixed distance between two points. In an interferometric null
servo, a laser gauge is used to measure approximately the deviation of the
controlled distance from one which would yield a null or zero output from
the interferometer, e.g., the offset from a minimum in transmission. The
measured deviation, in the form of an electrical signal, is filtered,
amplified, and applied to an actuator so as to return the distance to that
which would yield a null output.
Existing differential distance measuring gauges can be classified in two
categories. The first category includes devices which provide a relatively
low accuracy measurement limited to approximately 100 nanometers. The
second group of devices provide an accuracy which is significantly better
than 100 nanometers. Many existing devices fall into the first category.
For example, U.S. Pat. No. 3,756,722 to Wetzel discloses an interferometric
measuring system including a phase plate which produces a beam with
transversely varying phase, thereby producing sine and cosine signals. The
combination of sine and cosine signals is free of the directional
ambiguity that exist in a single signal.
Another example of a low precision system is disclosed by U.S. Pat. No.
3,452,472 to Reid Smith-Vaniz in which an AC signal is obtained by
mechanically vibrating a reference surface. This device requires a laser
having two output frequencies. The difference between the two frequencies
is varied by changing the length of the laser cavity. This device provides
an absolute distance measurement but cannot track a continuously changing
distance. Vibration of the reference surface is only provided to produce a
signal with which the measurement is made.
Conventional high accuracy interferometric distance measuring systems use
two overlapping beams that differ both in polarization and in frequency.
The overlapped beams are separated into first and second polarization
beams by a polarization-dependent beam splitter. The first separated beam
traverses a length to be measured and is then rejoined with the second
beam. However, the polarization separation is imperfect. Therefore, some
fraction of each of the first and second beams is always intermixed with,
and travels the path intended for, the second and first beams,
respectively, leading to measurement errors. These measurement errors
principally provide a signal bias that is a periodic function of the
measured distance.
For example, U.S. Pat. No. 3,458,259 to Bagley et al and U.S. Pat. No.
3,656,853 also to Bagley et al disclose systems using two frequencies. In
the '259 patent, a two frequency single mode laser (Zeeman-split) produces
two copropagating beams of different polarization and frequency. Bagleys'
patents both require polarization separating components. The limitations
in the alignment of the polarization directions introduce a cyclic bias in
the amplitude of the signal output from the interferometer. The bias
corresponds to a systematic error on the order of one nanometer.
In the article by de Groot, in Applied Optics, Vol. 30, No. 25, dated Sep.
1, 1991, an absolute distance gauge design is disclosed which uses a pair
of laser diodes. Use of very small laser diodes allows a compact and an
inexpensive gauge to be built. In the use of this device, the absolute
length must be known a priori to the order of 1 mm because of the limited
frequency resolution of the grating used to distinguish between
closely-spaced diode laser wavelengths.
SUMMARY OF THE INVENTION
One object of the present invention is to provide a compact and low cost
high precision optical distance measurement system.
Another object of the present invention is to provide precise measurement
of relative and absolute distances from between 0.01 and 100 meters.
Another object of the present invention is to provide a precise measure of
relative and absolute distances between spacecraft.
Another object of the present invention is to provide continuous and/or
extremely rapid distance measurements.
Another object of the present invention is to provide for an absolute
measurement of distance.
Another object of the present invention is to provide for extremely
accurate measurements of distances in vacuum.
Another object of this invention is to provide extremely accurate
measurement of distances within satellites and stations in space and
between satellites and stations.
Another object of the present invention is to provide a fiber optic
coupling system, useful for coupling optical signals into and out of
optical fibers, which has extremely low internal reflection.
These objects may be accomplished by a system and a process for using the
system for measuring distance between two points, which comprises an
interferometer through which a coherent electromagnetic beam passes and a
means for varying the frequency of the coherent electromagnetic beam
frequency.
These objects may also be accomplished by a system and a process for using
the system for measuring distance between two points, which comprises an
interferometer through which a coherent electromagnetic beam passes and a
means for frequency modulating the coherent electromagnetic beam before
passing the beam through the interferometer.
These objects may also be accomplished by a system and a process for using
the system for measuring distance between two points which comprises an
interferometer which comprises a resonant cavity.
These objects may also be accomplished by a system and a process for using
the system for maintaining, at a fixed value, a distance between two
points, which comprises an interferometer and means for coupling a
coherent electromagnetic beam to said interferometer, wherein said means
for coupling comprises a first means for frequency modulating at a first
frequency, said coherent electromagnetic beam.
These objects may also be accomplished by a fiberoptic coupler and process
of using the coupler, which comprises a single mode optical fiber having
at least one end thereof, a surface that is at an angle with respect to
the optical axis; and a transparent cap which is joined to the end of the
fiber and which has a larger diameter than the fiber core.
BRIEF DESCRIPTION OF THE DRAWINGS
A more complete appreciation of the invention and many of the attendant
advantages thereof will be readily obtained as the same becomes better
understood by reference to the following detailed description when
considered in connection with the accompanying drawings, wherein:
FIG. 1 shows a distance gauge of the present invention;
FIG. 2 shows a tracking frequency gauge (TFG) of the present invention;
FIG. 3 shows a null gauge, and a system for maintaining a fixed distance
between two points;
FIG. 4 shows a system for measuring an absolute distance between two points
of the present invention;
FIG. 5a shows a tracking frequency gauge with a resonant cavity
interferometer of the present invention;
FIGS. 5b-5d show exemplary resonant cavities for a tracking frequency
gauge;
FIGS. 6a and 6b show in detail, a tracking frequency gauge of the present
invention;
FIGS. 7a-7e show, as a function of optical frequency, signals useful in
explaining FM to AM conversion in the present invention;
FIG. 8 shows an AM detection and control circuit of the present invention;
FIGS. 9a-9c show a detailed version of an absolute distance gauge of the
present invention;
FIGS. 10a and 10b show, as a function of optical carrier frequency, signals
useful in understanding operation of the absolute distance gauge shown in
FIGS. 9a-9c;
FIGS. 11a and 11b show a detailed version of an embodiment of a tracking
frequency gauge of the present invention having alternating frequency
modulation;
FIG. 11c shows an alternative arrangement for a tracking frequency gauge
with alternating frequency modulation;
FIG. 12 shows an absolute distance gauge of the present invention having
dual frequency modulation;
FIGS. 13a and 13b show, as a function of optical carrier frequency, signals
useful in understanding operation of the absolute distance gauge with dual
frequency modulation shown in FIG. 12;
FIG. 14 shows an FM side band locking null gauge of the present invention;
FIGS. 15a and 15b show, as a function of optical carrier frequency, signals
useful in understanding a resonant cavity interferometer of the present
invention;
FIGS. 16a-16d show exemplary resonant cavities of a resonant cavity
interferometer of the present invention;
FIG. 17a-17c show reflective elements of a resonant cavity of the present
invention and symmetry operations which may be performed thereon;
FIGS. 18a and 18b show systems for terminating an optical fiber, and
launching a low-distortion beam into free space, with greatly reduced
reflection back along the fiber; and
FIG. 19 shows another laser gauge system of the invention.
DESCRIPTION OF THE PREFERRED EMBODIMENTS
Referring now to the drawings, wherein like reference numerals designate
identical or corresponding parts throughout the several views, and more
particularly to FIG. 1 thereof, which shows a beam 1a emitted by laser 1.
The function of the laser indicated in FIG. 1 is to provide a coherent
optical beam.
Preferably, the laser is of a type which provides a beam of optical waves
of a single frequency or very narrow band of frequencies, wherein the
frequency or average frequency is stable in time. Instead of a laser beam,
any coherent electromagnetic beam may be used, such as any coherent beam
with a frequency between radio frequencies and the high end of the
ultraviolet light wave frequencies. Such a beam may be provided by a
MASER, or a high frequency oscillator such as a Gunn diode, an impact
device, a double barrier diode, a crystal oscillator or similar devices.
The beam 1a is frequency modulated by frequency modulator 2. Frequency
modulator 2 may be any device which provides a modulation to the frequency
of the coherent optical beam.
In particular, the frequency modulator 2 may be an acousto-optic device, an
electro-optic device or a magneto-optic device. Furthermore, the frequency
modulation represented by frequency modulator 2 may be provided by
actually frequency modulating the laser, by modulating properties of the
laser material, the cavity or a power source for the laser.
A preferred frequency modulator is an electro-optic modulator cell. Varying
an applied voltage to an electro-optic cell varies the index of refraction
of the cell, thereby varying the effective optical length of the cell. If
the electro-optic cell is driven at a radio frequency, a beam passed
therethrough has its phase modulated at the modulation radio frequency due
to the voltage-driven variation in optical path length. The phase
modulation of the beam after passing through the electro-optic cell is
equivalent to frequency modulation of the beam, as will be discussed in
more detail below. The modulation depth is proportional to the peak of the
radio frequency voltage applied to the cell. A good review of the
mathematics of frequency modulation is provided in the book, "REFERENCE
DATA FOR RADIO ENGINEERS", sixth edition, Library of Congress card number
75-28960, in Chapter 23.
In all of the embodiments described herein, it is preferable to transport
the beam from the modulator or modulators to the interferometer by passing
it through a single mode optical fiber. In this case it is also preferable
to use a polarization-preserving fiber; this allows better control of the
polarization of the light emerging from the fiber. The use of such an
optical fiber allows precise, stable alignment of beams injected into the
interferometer without rigid mechanical connections which might transmit
vibrations; produces a beam at the entrance to the interferometer which
has a simple, smooth profile and stable position and orientation which are
independent of the alignment of beams between the laser source and the
fiber input coupler; and affords the convenience of transporting the beam
through a narrow flexible waveguide over distances which may be large. The
use of an optical fiber also risks introducing errors associated with
polarization changes, variations in transmission due to variations in beam
alignment at the fiber input, and spectral modification of the light due
to weak interferometric effects within the fiber.
If an optical fiber is used, it may advantageously be inserted between the
frequency modulator 2 and the interferometer. In this case, the beam
leaving the frequency modulator 2 is coupled to the optical fiber 4
through input coupler 3; this input coupler tightly focussed the beam onto
the tiny core of the fiber. The beam is transmitted through the optical
fiber and exits through the output coupler 5; this output coupler captures
the beam diverging from the end of the fiber and focussed it into a beam
which is suitable collimated for injection into the interferometer.
If an optical fiber is not used, it may be advantageous to transport the
beam from the frequency modulator 2 to the interferometer using some
combination of mirrors and lenses so that the alignment and focussing of
the beam may be adjusted easily.
The beam output from the output coupler 5 enters an interferometer, which
may be a two-beam interferometer with dihedral or cornercube retro
reflectors as shown by the example in FIG. 1; this common type of
interferometer is closely related to the Michelson interferometer, which
uses flat mirrors instead of dihedrals or cornercubes. The interferometer
includes retroreflectors 8 and 9 and partial reflector 6. The entering
beam intersects partial reflector 6 at position 7 where the beam is split
into two components denoted E.sub.l and E.sub.2. The first component
E.sub.l propagates toward retroreflector 9 which returns the first
component E.sub.1 to partial reflector 6 at position 10. Similarly the
second component E.sub.2 propagates toward retroreflector 8 and is
returned to the partial reflector 6 at position 10.
The distance which second component E.sub.2 travels from partial reflector
6 to retroreflector 8 and back to partial reflector 6 is denoted by L2.
The distance which first portion E.sub.1 travels from partial reflector 6
to retroreflector 9 and back to partial reflector 6 is denoted by L1.
The beams E.sub.l and E.sub.2 are each split into two components again when
they return to partial reflector 6 at position 10; the first component of
beam E.sub.1 overlaps and combines with the first component of beam
E.sub.2 to form beam E.sub.3, and the second components of each beam
similarly combine to form beam E.sub.4. Note that as the retroreflector 9
is moved, the length L1 is changed by twice as much distance, since it
includes the distances to and from the retroreflector 9. Similarly, the
rate of change of L1 is twice the rate of change of the distance between
retroreflector 9 and partial reflector 6. The two output beams E.sub.3 and
E.sub.4 contain useful information regarding the difference of the lengths
of the interferometer arms, as discussed below.
The interferometer converts the frequency modulation of the optical carrier
beam to an amplitude modulation as will now be described with reference to
FIGS. 7a-7d. As with all two-beam interferometers, the interferometer
shown in FIG. 1 provides an output 10 whose intensity varies sinusoidally
with the difference between the optical path lengths in the two arms. In
particular, the intensities of beams E.sub.3 and E.sub.4 vary as
I.sub.3 =I.sub.0 [1-cos (2.pi.L/.lambda.)]/2 (Equation 1)
I.sub.4 =I.sub.0 [1+cos (2.pi.L/.lambda.)]/2 (Equation 2)
where L=L1-L2. As the path difference L changes by one optical wavelength,
the intensities vary through one complete cycle, returning to the same
values. The arguments of the cosine function in Equations 1 and 2 may be
written
##EQU1##
Here we have used .lambda.=c/.nu., where c is the speed of light and .nu.
is the optical frequency; N is an integer; and .theta. is an increment
between zero and 2.pi. to account for a possible non-integer ratio between
the path difference L and the wavelength .lambda.. We may then temporarily
consider the integer N to be a fixed constant (which may be very large),
and turn our attention to the small increments represented by .theta..
From Equation 3 we can see that, in general, the interferometer output
intensity varies sinusoidally with both the distance and the optical
frequency. It is periodic in L with period .lambda.; this is the distance
change necessary to change N by one. It is periodic in optical frequency
with a period equal to the free spectral range, or FSR, given by
FSR=c/L (Equation 4)
If the path difference L is small, then the FSR is large, and the
interferometer is insensitive to changes in optical frequency. However, if
L is thousands of wavelengths or more (large N), then the interferometer
output can be a sensitive function of the optical frequency. For small
fractional changes in .nu. and L, we can write
##EQU2##
where .delta. denotes a small increment to the indicated quantity. This
expression shows that if the path difference is large enough, we may use
optical frequency changes and distance changes interchangeably to return
the intensity I.sub.3 or I.sub.4 to some desired value, such as its
minimum or maximum. Thus to maintain the interferometer at this target, we
may push one endpoint with an actuator to change the path difference L, or
we may tune the optical frequency until L is an integer multiple of the
new wavelength. Furthermore, if we use both an optical frequency change
and a distance actuator, we may control the path difference to follow a
target which may be arbitrarily selected by the tuning of the laser.
A null servo may be constructed if a signal may be derived which is zero at
the target condition, negative for errors or detuning to one side, and
positive for errors or detuning to the other. This signal may then be used
in a servo which minimizes the deviation from the target condition. One
way to produce such a signal from the interferometer output signals is to
measure the difference in the intensities of the output beams E.sub.3 and
E.sub.4 ; this signal is zero for .theta.=.+-..pi./2, and changes sign
with deviations of .theta. near these points. This is a simple method of
deriving a signal for the servo, but is more susceptible to drift than the
frequency modulation methods which we will describe.
The transmission intensity transmitted to each of the outputs of the
interferometer varies sinusoidally as a function of the optical carrier
frequency as shown in FIG. 7a. For L=1/2 meter, the nodes are separated by
about 300 MHz. This is indicated in an exemplary fashion by the 300 MHz in
FIG. 7a between two maxima. The so-called orders of the interferometer
correspond to the different allowed values of the integer N.
In a spectrometer which measures only the intensity of the coherent optical
beam passed through an interferometer, the intensity versus optical
frequency corresponds to the graph shown in FIG. 7a.
Frequency or phase modulation of the carrier adds sidebands to the optical
signal. The first pair of sideband frequencies are offset from the carrier
frequency by the modulation frequency. The modulation frequency may be
less than, approximately equal to, or greater than the FSR.
FIG. 7b shows the spectral components of a frequency modulated beam in
which the optical carrier frequency CAR is centered at the node shown in
FIG. 7a, and the upper sideband USB and lower side band LSB are denoted.
The sidebands are separated by a frequency .nu..sub.2, the modulation
frequency, from the optical carrier.
Phase modulation and frequency modulation are very closely related. The
instantaneous frequency is just the rate of accumulation of phase. This
rate includes a large constant rate, known as the carrier frequency, and a
small varying increment to the rate, which we may describe as either a
frequency increment or the rate of change of a phase increment. Because
the resulting waves are essentially the same, frequency and phase
modulation need not be considered separately.
The modulation depth is defined as the peak phase increment, usually given
in radians. For a sinusoidal frequency modulation waveform, the phase
varies cosinusoidally, and the modulation depth is equal to the peak
deviation of the instantaneous frequ | | |
