Optical interferometer measurement apparatus and method

Method and apparatus for realizing unusually sensitive and stable interferometric measurement capabilities. The apparatus comprises an optical interferometer with at least two optical outputs, the ratio of whose intensities can vary with a tuning parameter; and at least one detector, each of which is optically connected to the interferometer, and producing in aggregate at least two linearly-independent signals that depend on the light intensity and the tuning parameter, which are combined to produce a first measurement whose sensitivity to light intensity changes is substantially smaller than that of either of the two linearly-independent signals, and a second measurement whose sensitivity to the tuning parameter is substantially smaller than that of either of the two linearly-independent signals.

BACKGROUND OF THE INVENTION 
This invention relates to apparatus and methodology suitable for optical 
interferometric measurement. 
INTRODUCTION TO THE INVENTION 
Our background work to the present invention subsumes optical 
interferometric measurement analysis and technique. One significant aspect 
of this background work relates to optical extinction and phase 
measurement analysis--said significance deriving from the fact that this 
work is fundamental to many measurement devices, such as absorption 
spectrometers and sol particle detectors. In particular, the sensitivity 
of these measurements may be limited by problems including available 
integration time, spurious optical signals, or laser noise. 
Our background work has identified these cited problems, to an end of 
developing methodology which can effect, with reference to pertinent prior 
art such as heterodyne interferometry, very considerable simplifications 
in ultra-high sensitivity phase and amplitude measurements. 
For example, we have invented a laser noise canceller (see U.S. Pat. No. 
5,134,276 to Hobbs), the laser noise canceller comprising a signal 
processing circuit which can make shot-noise-limited optical measurements 
possible at baseband, thereby effecting the asserted very considerable 
simplifications over earlier art techniques in ultra-high sensitivity 
phase and amplitude measurements. 
SUMMARY OF THE INVENTION 
Our present work begins with an evaluation of the laser noise canceller 
disclosed in U.S. Pat. No. 5,134,276 to Hobbs. First, shot-noise limited 
absorption spectroscopy, using this invention, has been reported. For 
example, with a 5 mW, 632.8 nm laser, the shot noise limit in a one-second 
measurement corresponds to an extinction uncertainty of 1 part in 
10.sup.8. We note, however, that this measurement only corresponds to 
measuring an intensity change in a transmitted beam, whereas for many 
purposes, such as composition determination in particle counters, it is 
useful to measure the phase of the disturbance, as well. In addition, 
higher sensitivity is always desirable. 
One known such sensitivity enhancement method centers on a use of a 
Fabry-Perot etalon. Here, an absorbing or scattering sample is placed 
inside a low-loss resonant optical cavity (etalon). When a light source 
(usually a laser) is tuned to a cavity resonance, the optical energy 
density inside the cavity is enhanced by a large factor, often 10.sup.2 to 
10.sup.5, which may be heuristically explained by the light needing many 
bounces from the cavity end mirrors to be absorbed or to escape. 
We note that important problems with the Fabry-Perot technique are the need 
for a separate servomechanism to tune the laser or the etalon to eliminate 
drift, and the continued limitations caused by laser noise. The servo 
system requires a way to measure the laser-to-cavity tuning error with 
sufficient accuracy that intensity changes due to tuning errors do not 
limit the accuracy of the measurement, which is usually difficult; the 
most common solution is to dither the laser or the cavity and use lock-in 
detection to sense the position of zero tuning error. 
Motivation for the present invention is informed by the Fabry-Perot 
technique, with a view to overcoming most of its limitations and cited 
problems, thereby advantageously realizing unusually sensitive and stable 
optical interferometric measurement capabilities. 
Accordingly, in a first aspect, the present invention discloses a method 
comprising: 
(1) providing an optical interferometer with at least two optical outputs, 
the ratio of whose intensities varies with a tuning parameter; (2) 
inputting light to the optical interferometer; (3) detecting the two 
optical outputs to yield two linearly-independent signals that depend on 
the light intensity and the tuning parameter; and (4) combining said two 
linearly independent signals to produce a first measurement whose 
sensitivity to light intensity changes is substantially smaller than that 
of either of the two linearly-independent signals, and a second 
measurement whose sensitivity to the tuning parameter is substantially 
smaller than that of either of the two linearly-independent signals. 
In a second aspect, the present invention discloses a method comprising: 
(1) providing an optical interferometer with at least two optical outputs, 
the ratio of whose intensities varies with a tuning parameter; (2) 
inputting light to the optical interferometer; and (3) detecting the two 
optical outputs to yield two linearly-independent signals which are 
combined to produce orthogonal measurements of light intensity and the 
tuning parameter. 
In a third aspect, the present invention discloses an apparatus comprising: 
(1) an optical interferometer with at least two optical outputs, the ratio 
of whose intensities can vary with a tuning parameter; and (2) at least 
one detector, each of which is optically connected to the interferometer, 
and producing in aggregate at least two linearly-independent signals that 
depend on the light intensity and the tuning parameter, which are combined 
to produce a first measurement whose sensitivity to light intensity 
changes is substantially smaller than that of either of the two 
linearly-independent signals, and a second measurement whose sensitivity 
to the tuning parameter is substantially smaller than that of either of 
the two linearly-independent signals. 
In a fourth aspect, the present invention discloses an apparatus 
comprising: (1) an optical interferometer with at least two optical 
outputs, the ratio of whose intensities can vary with a tuning parameter; 
and (2) at least one detector, each of which is optically connected to the 
interferometer, and producing in aggregate at least two 
linearly-independent signals which are combined to produce orthogonal 
measurements of light intensity and the tuning parameter when light of 
appropriate wavelength and coherence is input to the optical 
interferometer.

DETAILED DESCRIPTION OF THE INVENTION 
The detailed description of the invention unfolds by first disclosing 
preferred or alternative features or limitations of the method, followed 
secondly by an analogous disclosure of preferred or alternative aspects of 
the apparatus, and concluding thirdly with an explication of the FIGS. 1 
and 2 embodiments of the present invention. 
The method is summarized above and includes three steps. 
The first step requires providing an optical interferometer with at least 
two optical outputs, the ratio of whose intensities varies with a tuning 
parameter. The tuning parameter, alternatively, may be the wavelength of 
the input light, or the optical path delay in the interferometer, or a 
combination of the optical path delay in the interferometer and the 
wavelength of the input light. The optical interferometer, in turn, may be 
selected from the group consisting of an etalon, a Michelson 
interferometer, and a Mach-Zehnder interferometer. 
The input light in step 2 preferably comes from a laser. 
The method preferably further includes an independent or distinct fourth 
step. The fourth step may comprise: 
1) making a measurement of optical extinction via the light intensity 
measurement; 
and/or 
2) making a measurement of wavelength, using an imputed change in the 
tuning parameter as measured by one of the orthogonal outputs; 
and/or 
3) making a measurement of optical phase inside the interferometer, using 
an imputed change in the tuning parameter as measured by one of the 
orthogonal outputs; 
and/or 
4) making a measurement of relative tuning of the light source and the 
interferometer; 
and/or 
5) varying the tuning parameter to stabilize at least one of the orthogonal 
measurements. 
We now turn our attention to preferred aspects of the apparatus of the 
present invention, summarized above, which is suitable for realizing the 
method steps. 
The apparatus requires at least one detector, each of which is optically 
connected to an optical interferometer, and producing in aggregate at 
least two linearly-independent signals which are combined to produce 
orthogonal measurements of light intensity and a tuning parameter when 
light of appropriate wavelength and coherence is input to the optical 
interferometer. 
Preferably, at least one detector comprises a photodiode, the photodiode 
receiving as an input one of the optical outputs of the interferometer, 
and producing one of the linearly independent signals. 
The optical interferometer may comprise a Fabry-Perot interferometer, 
wherein the optical outputs preferably are derived from light reflected 
and transmitted by it. 
The apparatus preferably further comprises feedback means whose input is a 
difference between one of the orthogonal outputs and a set point and which 
adjusts the tuning of the interferometer so as to stabilize this 
difference. For example, the set point may be chosen to be a null point 
where the tuning parameter measurement is insensitive to intensity 
changes. 
The apparatus may further comprise an electrically tunable laser for 
providing the light of appropriate wavelength and coherence for input to 
the interferometer. For this situation, the apparatus preferably further 
comprises feedback means whose input is a difference between one of the 
orthogonal outputs and a set point and which adjusts the tuning of the 
laser so as to stabilize this difference. The set point may be chosen to 
be a null point where the tuning parameter measurement is insensitive to 
intensity changes. 
Attention is now directed to FIGS. 1-2 which show, respectively, first and 
second embodiments of apparatus suitable for realizing the method of the 
present invention. The choice of a preferred realization depends on the 
availability of cost-effective tunable lasers operating at the wavelength 
of interest; if they are available, the system shown in FIG. 1, numerals 
10-32, is preferred; if not, the system of FIG. 2, numerals 34-58 is 
preferred. 
FIG. 1 shows the tunable-laser version. A beam from a tunable laser 12 
(e.g., a diode laser) passes through beam splitter 14, 16, then into an 
etalon 18. Inside the cavity is a scatterer 20, which causes an extinction 
.epsilon. and a phase perturbation .delta..o slashed. in one pass of the 
beam. A transmitted (T) beam and reflected (R) beam, together with a 
sample of the laser output (S) are detected and fed to a signal processor 
30. This signal processor 30 consists of a differential version of the 
noise canceller already cited (Hobbs, 1990), and puts out two voltages 
which are related to the ratio of the sum (R+T) and difference (R-T) of 
the reflected and transmitted beams to the sample beam. This processor 30 
can eliminate the effect of laser noise and spurious signals above the 
shot noise level, allowing the system to operate right at the shot noise 
limit. The R-T output is integrated (32) and fed to the tunable laser 12 
as its tuning current; this stabilizes the operating point of the system 
half way up the resonance curve of the etalon, where R-T is zero. 
In the absence of absorption, the sum of the reflectance R and 
transmittance T is unity; any phase change inside the cavity will 
redistribute the total beam power between the transmitted and reflected 
beams, resulting in a nonzero R-T signal; this will persist for a short 
time, during which the servo loop adjusts the operating wavelength of the 
laser to zero it out. An extinction signal unaccompanied by any phase 
shift will cause optical loss inside the cavity; by conservation of 
energy, the sum signal T+R must decrease. For small extinctions, where the 
total reduction in R+T is several percent or less, the operating point is 
stable; R and T decrease by almost exactly the same amount, so the 
amplitude perturbation does not cause any apparent phase perturbation. In 
this way, the amplitude and phase of the scatter signal can be measured 
separately, to great accuracy. 
If there is significant excess loss in the cavity already, the stability of 
the operating point will be degraded somewhat. It can be restored by 
taking a slightly different linear combination of R and T (e.g., T-0.9R 
for one particular value of extinction) as the phase signal. The exact 
factors required will depend on the excess loss encountered. 
A Fabry-Perot interferometer with a finesse of 1000 has high selectivity; 
the rate of change of its reflected and transmitted beam intensity as a 
function of frequency, dR/df and dT/df, are of the order of 1000/f0. 
Similarly, both depend linearly on the input beam intensity. The 
logarithmic output of the laser noise canceller described in U.S. Pat. No. 
5,134,276 to Hobbs provides the ratio of the beam powers incident on its 
two photodetectors, and suppresses the laser intensity information by a 
factor of at least 20 dB and as much as 60 dB, even when the two beams are 
unequal in power. 
Thus the logarithmic output provides an amplitude-insensitive measure of 
the relative tuning of the laser and the Fabry-Perot. Alternatively, 
choosing the set point so that R-T=O will produce a zero baseline 
measurement in which an intensity shift produces a change of slope but not 
of offset, much like a balanced mixer used as a phase detector in a 
phase-locked loop. In both cases, amplitude shifts do not cause the null 
point to move, so that the tuning set point is not disturbed. 
If the two photocurrents are added together instead (with a slight 
modification to the circuitry, both can be done at once), after being 
linearly scaled (with an optical neutral density filter before detection 
or a resistor network after detection, for example) so that dR/df=-dT/df 
at the chosen set point, then small changes in the tuning parameter will 
make one signal increase and the other decrease, producing very much 
smaller relative changes in their sum. Thus, we can make a 
tuning-insensitive measurement of the light intensity alone. A third 
detector, sampling the laser beam alone, can be used as in the patent just 
cited, to provide a comparison current to cancel the laser noise down to 
the shot noise level, leaving only signals due to transient extinction 
events in the cavity. This noise cancellation will in principle be as 
effective as that of the difference or logarithmic output. 
The sensitivity of this approach is very high. With a 5 mW laser at 632.8 
nm, the shot noise is equivalent to an absorption uncertainty of 1 part in 
10.sup.8 in 1 second, so with an etalon with an energy density enhancement 
of a factor of 10.sup.3, a 1-second measurement could in principle measure 
an extinction of 10.sup.-11. It could also measure phase perturbation as 
small as 10.sup.-12 radians. 
The advantages of this technique are its high sensitivity, and the accuracy 
and simplicity of its control and measurement systems.