Work on the development of an interferometric system for the purpose of absolute length determination commenced in January of this year. Our goal is to develop a system capable of measurements on the order of one meter with an accuracy of 1 part in 10 or greater. A modified Michelson bread board with stabilized laser diode source was assembled. Some preliminary measurements began using the tunable Santek laser in an FM modulation scheme. During this same period a literature search yielded a paper by Suematsu and Takeda which discusses a promising fourier transform technique for real time data analysis. We are in the process of evaluating this technique while we continue to change and upgrade the system configuration

Kay, Richard B.

English

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NASA-CR-194133
NASA Grant NAG 5-1319: Solid State Laser Systems for
Space Appllcatlon
Forth Semi-Annual Report, Summer '93
Richard B. Kay, Principal Investigator
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Introduction
Work on the development of an interferometrlc system for the
purpose of absolute length determination commenced in January of
this year. Our goal is to develop a system capable of measurements
on the order of one meter with an accuracy of 1 part in 109 or
greater. A modified Michelson bread board with stabilized laser
diode source has been assembled. Some preliminary measurements
have begun using the tunable Santek laser in an FM modulation
scheme 1'2 During this same period a literature search yielded
a paper by Suematsu and Takeda which discusses a promising fourier
transform technique for real time data analysls 3. We are in the
process of evaluating this technique while we continue to change
and up grade the system configuration.
Research
First we decided on a schematic for the Michelson breadboard,
which is shown in Fig. I. Next a list of required components was
drawn up and those not available in the Photonics Branch were
ordered. The Santek stabilized laser had been previously procured
by NASA for interferometric experiments. Basic specifications for
this laser are:
Tunable wavelength: I. 28-I. 36_tm,
linewidth -< 200kHz,
frequency fluctuation <- +- 5MHz
frequency stability -_ _+lOOkHz over a I0 sec time period
(NASA-CR-194133) SOLID STATE LASER
SYSTEMS FOR SPACE APPLICATION
Semiannu_| Report No. 4 (American
Univ.) 7 p
N94-13420
Uncl as
G3/36 0182838
https://ntrs.nasa.gov/search.jsp?R=19940008947 2020-06-16T21:51:44+00:00Z
The configuration shown in Fig. 1 comprises three Mlchelson
interferometers in one, using one source and one detector. The
Santek diode source is optically coupled from its fiber optic
output to the interferometer by a conventional lens. Light from
the three lees that reflect from corner cubes I, 2 and 3 is
brought to interfere at the single photodiode detector. Signals
from this detector can be recorded on disc in the computer which
is additionally used for data analysis. The signals can also be
displayed on a digital oscilloscope.
As has been explained by Kikuta et al. I, and Seta and Ward 2, and
others, if one modulates the laser diode output frequency by
changing the drive current in a linear ramp, a beat frequency fb
will be created between a reference beam and any beam that has
traveled a distance L greater than the length of the reference
arm:
fb = L/c.[Af/At] = L'AX/CA2-At) I]
where Af/At is the change in the diode output frequency with time
and c the speed of light. In Fig. l and ignoring corner cube 3, L
could be 2[dl-d 2] for example. With the addition of corner cube
3, two additional interference patterns are obtained. The most
important of these is that due to the path between dland d 3, which
can be used as a reference path difference.
Multi-beam Interferometry
In the work of Suematsu and Takeda, it is explained how non
linearities in the frequency scan can be removed by using two or
more frequencies and/or two or more reference interferometers, one
of which provides a very precisely known optical path, LR
(reference length). 3 If the non linear behavior of the wavelength
+ A_(t)].At, where
change with time is expressed as AA = [ao o
gives the linear portion and A_(t) the non-linear portion, then
Eg.I becomes:
• + A_Ct)] 2]fb = L/_2 [_o
2
In the work of Suematsu and Takeda,
L/A2m f
o s'
a constant carrier frequency produced by a perfectly
wavelength scan.
3]
linear
If for a moment we assume, no nonlinearities, then the second term
of Eq. 2 would be zero. If there were two interferometers
observing the same diode scanned radiation, then there would be
two frequencies of the type in Eq. 3 present at the detector, one
for each path difference. The frequency associated with the
would be f =
interferometer with a know path difference L R R
L /A 2. Taking the ratio of the frequencies for the two
o R
interferometers yields:
4]
L = [fs/fR]'LR.
Ideally, one can determine the length of an unknown optical path
difference from a known or reference path using this technique.
The additional interferometric paths shown in Fig. I are there by
explained where twice the path difference between legs d 2 and d 3
for example could be the reference length.
Fourier Transform Technique
In any real system, the wavelength change with time will not be
purely linear, and the second term in Eq.2 will be important. The
same information in the beat frequency is carried in the phase
difference at the detector and it can be readily shown that A#/_t =
2xf b or _(t)- #o = 2xfb'(t - 0)= 2x'L/A2"[_o + A_(t)].t. Then
t + e(t) 5]
#(t) = #o + 2_fs
where e(t) = 2_LA_(t)t/A 2 6]
and carries the nonlinear information. These equations are Eq. 7
and 8 in the work of Suematsu and Takeda 3. The remaining
3
development follows directly from their work.
If the waveform in each lee of a Mlchelson interferometer is of
i(2=ft+#i) then the interference fringe pattern
the form E = Eie
will have the form E2 = E2 + E2 + 2E E cos(¢ 2 - _I). Masakazu and1 2 I 2
Takeda there for write the interference signal g(t) at the
interferometer as
g(t) = a(t) _+ c(t)e 2_ifst + c*(t)e-2_ifst 7]
where a(t) is the intensity sum for the two beams and the
additional and non-linear information is carried in c(t):
i[eCt) + _o ] s]
oct) = E E e
I 2
If the nonlinearities in the wavelength sweep are relatively small
so that a ) _(t) and if L • A2/AA - A the so called "synthetic
o
wavelength", the fourier transform of g(t) separates into three
regions. The region centered around f=O contains the amplitude
information which is of no importance. Two other spectra on either
side centered around ± f contain the nonlinear phase information.
s
Filtering out one of these regions and re- transforming retrieves
c(t), [Eq. 8] from the frequency spectra. The phase information
is separated from the amplitude information in Eq. 8 by taking the
natural logarithm and pulling out the imaginary part.
This technique has thereby isolated the phase #(t) given in Eq.5
above. If there is a second leg in the interferometer to provide
a reference phase:
CR = _RO + 2_fRt + eR(t) 9]
where f = _ L /A2and e (t) = 2nL Aa(t)t/A 2. [9a,9b]
R 0 R R R
To get rid of the constant phases in Eqs. 5 and 9, time
derivatives of the phases are taken and defined as angular
frequencies:
+ d{n_(t)t}/dt],(t) = d_ /dt = 2nf + 6 (t) = 2nL/l" _o
S S S S
10]
4
+ e (t)= 2_L IA'[_ + d{A_(t)t}/dt].
_R (t) = d#R/dt = 2_f R R R o
Taking the ratio of Eq I0 to Eq 11 and solving for L yields:
11]
L = [_s(t)/_BCt)]'LR.
12]
Thus the optical path difference can be computed once the angular
frequencies have been obtained. Note that the nonlinearities in
A_(t) cancel out in this technique.
Discussion
Suematsu and Takeda have made measurements using two and three
beam interference patterns. They find laser noise, noise in the
different arms and mechanical vibrations to be limiting in their
measurements. They also show that the nonlinearities in _i
increase with increased ramp drive frequency. However they gave
no numerical limits to the accuracy of which the unknown length L
could be determined relative to a reference length.
Currently we are configuring our optical breadboard to reproduce
their results while looking into ways to improve the concept. We
plan to add a high finesse (s 10,000) Fabry-Perot Interferometer
to monitor the primary radiation from the Santek laser while at
the same time maintaining three Michelson path differences. The
Fabry-Perot will also give us an additional point of reference.
The method by which the angular frequencies are retrieved from the
phases using computer analysis is of present concern. We must un
wrap the phase information which is currently being presented as a
periodic output at the frequencies fs and fB"
The results of Suematsu and Takeda are for modulation of the laser
diode between mode-hop regions. We plan to reproduce these
results and then push the technique to include mode-hops. In this
case the assumptions on the small deviation in A_(t) from _ may0
5
no longer be quite true. This may or may not limit the fourier
transform scheme of retrieving the phase information and we can
learn this only by experimental investigation.
As the nonlinear portions in the derivatives of the phases cancel
out of the ratio used in length determination [Eq. 12], the
technique may still work across mode hop regions. This would allow
length ratio determinations to be limited primarily by the
fundamental stability of the source laser diode.
During the coming months we will be investigating the above
concepts, looking into different methods to analyze and process
our signals, improving on the experimental setup and determining
the limitations of the system.
References
1) H. Kikuta, K lwata and R Nagata, "Distance measurement by the
wavelength shift of laser diode light", Applied Optics 25,
2976,(1991).
2) K.Seta and B. K. Ward, "Interferometric Absolute Distance
Measurement Utilizing a Mode-Jump Region of a Laser Diode", Opt.
Comm. 77, 275, (1991).
3) Suematsu, M. and Takeda, M.,"Wavelength-shift interferometry
for distance measurements using the Fourier transform technique
for fringe analysis", Appl. Optics 30, 4046, (1991).
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Solid state laser systems for space application

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