1
Zero Velocity Reference Source for Fabry-Perot Determinations of Thermospheric
Wind Velocities
M. A. Biondi* and D. P. Sipler**
*Dept. of Physics and Astronomy, University of Pittsburgh
**Atmospheric Sciences Group, MIT Haystack Observatory
I. Need For Higher Precision in Thermospheric Wind Determinations
As Thermospheric General Circulation Models (TGCMs) become more
sophisticated, they employ improved modeling of the vertical flows in their transport
calculations. In the mid-, low-, and equatorial-latitude thermospheres, under quiet
geomagnetic conditions, the vertical velocities of the neutrals in the F-region are
expected to be rather small, a few m/s, yet these small drifts can have significant effects
on species transport. Thus, in experimental studies of the vertical motions via FabryPerot Interferometer (FPI) determinations of Doppler shifts in the airglow 630 nm line, it
is essential to reduce the measurement uncertainties to values commensurate with these
small velocities.
At present, various “tricks”, based on possibly dubious assumptions, are used to
determine the unshifted (zero velocity) position of the airglow 630 nm line. For example,
observations of the nightglow red line when the FPI is looking vertically are sometimes
averaged over the night and taken as the unshifted (zero velocity) position. Since,
diurnally, there can be a predominantly downward flow for half of the day and upward
for the remainder, this so-called “zero” value may well be in error.
Alternatively, in horizontal wind determinations from observations at ~600 zenith
along the 4 cardinal directions, the shifts from all directions, N, S, E, W, are sometimes
averaged together, e.g., N–S, E-W, to provide the “zero” value. The implicit assumption
here is that there are no appreciable gradients in the horizontal winds over the ~ 1000 km
diameter field-of-view of the observations, while, in practice, N-S and/or E-W gradients
are sometimes observed. Thus, while these assumptions are perhaps sufficiently accurate
for horizontal wind determinations, where velocities are often >~100 m/s, they are
suspect when dealing with vertical winds in the <~10 m/s range.
II. The Problem
As noted, FPI determinations of the Doppler shifts in the forbidden OI 630.0 nm
red line (F-region) or 557.7 nm green line (E-region) are complicated by the difficulty in
accurately determining the unshifted (zero-velocity) positions of the lines. The long
radiative lifetimes of the transitions (~100 s and ~1 s, respectively) have thwarted
attempts to develop laboratory sources of these lines to act as zero velocity references
suitable for FPI calibration purposes. As one step toward the solution to this problem, we
have developed an ultrahigh-frequency-excited afterglow source of the forbidden oxygen
2
lines [Biondi 2002].
This source produces spectral lines sufficiently free of
contaminating background for use in interferometric calibrations.
III. The Oxygen Afterglow Reference Source (OARS)
The spectrum of a discharge excited in oxygen contains numerous lines and bands
associated with allowed transitions, as well as the extremely weak 630.0 nm and 557.7
nm forbidden transitions; thus, the signal/background ratio for these forbidden lines is
very small. However, on termination of the discharge by removal of the exciting fields
(the afterglow period), the allowed transitions quickly die away, while the forbidden
transitions persist. Thus, under suitable conditions, the afterglow may provide a useful
intensity of the 630.0 nm (or 557.7 nm) line emission, with an adequately small
interfering background.
After considerable modeling and experimentation, we have found suitable
operating conditions – dilute oxygen-helium mixtures at low pressures in a large plasma
vessel excited by pulsed UHF radiation – that yield a “clean” 630.0 nm line of modest
intensity and a reasonable signal/background ratio, ~ 3/1 to 5/1 [Biondi 2002]. A
simplified schematic diagram of the OARS afterglow source in its resonant cavity is
given in Fig.1. A 445 MHz pulsed exciter creates a plasma in the large pyrex cylinder
which is filled with a high purity helium-oxygen ~300:1 mixture at a total pressure of
~0.3 Torr. The radiation is viewed by a Grating Spectrometer (not shown) and a
refractive-index-tuned Fabry-Perot interferometer, with the desired portion of the
spectrum around 630 nm (or 557.7 nm) isolated by an interference filter of 0.5 nm bandpass. Typically, five interference orders are scanned by increasing the density of argon
between the F-P plates linearly with time.
445
MHz
UHF
Pulsed
Exciter
FPI (refractive
index tuned)
OARS
Resonant
Cavity
Interference
Filter
PMT Detector
gated ON during
afterglow
Fig.1 Schematic diagram of the OARS oxygen source and the F-P interferometer
An example of five interference orders of the 630 nm line profile obtained from
the OARS afterglow is shown in Fig. 2. The diamond data points indicate a S/B ratio >3,
yielding data that can be fairly well fitted by Airy functions (solid line). However, the
uncertainty in the fit is far too large to determine “zero velocity”, i.e., the position of
theline centroid, to the desired few m/s accuracy. Therefore, an alternative approach has
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been adopted that involves finding a secondary standard source that is simple, compact,
and emits a much greater intensity of the reference line.
350
300
250
Signal
(c/s)
200
150
100
50
0
0
20
∆ν
400
60
800
1000
(channel no.)
Fig. 2 Five orders of the OARS afterglow 630 nm line profile
IV. Secondary Zero Velocity Standards
As noted, while the OARS source provides isolated, unshifted atomic oxygen
630.0308 nm and 557.7345 nm lines that provide zero velocity Primary Standards, its
large bulk and low forbidden line intensities make it unsuitable for use in the field. An
alternative is to develop a Secondary Standard, i.e., a spectral line of some element that
lies very close in wavelength to the OI 630 nm line. The closeness requirement has to do
with the stability of the FPI.
Suppose we have two lines, λ1 and λ2 and an FPI with a spacing t. Then nλ=2T,
where n is the order of the interference pattern. Here n can be represented by an integer
and a fraction. The integer portion of the pattern overlaps the adjacent order, so the
fractional portion of n is the part that is observed in the FPI. Consequently, the separation
of the two lines in the FPI orders will be s = (n1-n2) or
which can be written
⎛1 1⎞
s = 2T ⎜⎜ − ⎟⎟
⎝ λ1 λ2 ⎠
(1)
2T
(2)
(λ 2 − λ 1 )
λ 1λ 2
For a FPI with a 1 cm spacer observing the atomic oxygen red line, we have T=1 cm,
λ1=630.0308 nm. If we use a cerium line as a secondary reference, we have λ2=630.0210
nm. This gives us a separation of the two lines of 0.493787 orders.
s=
4
Now suppose that thermal drift changes the spacing from T to T+δT. Both lines
will shift slightly. The separation of the lines will now be
s=
2(T + δT )
(λ 2 − λ 1 )
λ 1λ 2
(3)
If δT/T is about 10-5, corresponding to about 3% of an order, then the separation
of the lines will now be 0.493792 orders, or a change of 0.000005 order. Since the free
spectral range of the FPI is ~ 10,000 m/sec with the 1 cm spacer, this introduces an error
of only ~0.05 m/sec.
The best Secondary Standard candidate appears to be the 630.0210 line of
Cerium, lying within ~0.01 nm of the Oxygen red line [Harrison, 1969; Gray, 1972]. For
a ~1 cm etalon spacing, it is displaced only ~ ½ order from the OI red line, and compact
Ce hollow cathode sources are readily available. In order to employ this standard we
must determine precisely the separation in the interference order between this line and the
OI line. (To establish the zero velocity position to ~1 m/s precision, we must know the
difference in wavelengths between the two lines to a precision of ~ 3 parts in 109, far
better than the ~1:107 accuracy of the lines’ tabulated wavelengths.)
An accurate determination of the offset between the Primary and Secondary
Standards is provided by the Comparative Interferometry technique illustrated in Fig. 3.
Shutter
Hollow K
Source
FPI (refract. index tuned)
OARS
Interference
Filter
Gated PMT
Fig. 3 Comparative Interferometry using a Ce Hollow Cathode Source
The apparatus of Fig. 1 is modified to permit introduction of the Ce line to the FPI at the
appropriate points in the interference order by opening and then closing the shutter in
front of the hollow cathode source (Ce cathode, with either Ar or Xe fill gas). The
~ 4½ interference orders of the OARS OI line, with the renormalized interposed Ce line
peaks, are shown in Fig.4. (The isolating 630.15/0.5 nm interference filter passes two Ce
lines, as well as Ar or Xe lines, within its ~0.5 nm passband, so that care must be
exercised in identifying the Ce(630.02nm) peak in the multiple peak “spectrum” of an
interferometer order.) For the nominal 1.01 cm plate spacing employed in these studies,
the Ce line and the OI line are in the same interference order and approximately ½ order
apart.
5
400
Ce/600
Signal (c/s)
300
200
100
0
0
200
400
600
800
1000
∆ν (channel #)
Fig. 4 Offset between the Ce (630.02 nm) and the OI (630.03 nm)
V. Application of the Offset to Other Interferometers
The fraction of an order offset between the OI red line and the Ce reference line
determined in the OARS experiments applies to the particular spacing of the OARS
interferometer. To translate this offset into the offset for other FPIs requires two steps.
First, the spacing of the OARS interferometer must be determined to an accuracy
of 1:104 (equivalent to ~ 1 m/s velocity accuracy). This permits the order offset for the
OARS interferometer, ~ 0.5106, to be converted to a wavelength difference, ~ 0.010024
nm.
The next step, applying the results to an FPI of different spacing, involves
determining its spacing to high accuracy (~ 1:104 for spacings of ~ 1 cm). One then
calculates the order offset through use of the wavelength offset given above.
VI. Interferometer Spacing Determination
We use 3 lines that lie close to the OI 630 nm line and that are separated by
several orders from each other in order to determine the spacing of the FPI. These are:
Ne 630.47866 nm; Ar 630.7662 nm, and Ar 629.6876 nm. The Ne line is specified to the
highest precision and is listed as a secondary spectroscopic standard by the AIP
Handbook, 3rd ed. (1972). Since this line lies between the Argon lines, it is used as a
reference in our analysis. For convenience, these lines have been obtained from 2 hollow
cathode sources containing, respectively, Ne and Ar fill gases and using Ba cathodes
(there are no interfering barium lines around 630 nm). In these studies a broader
interference filter (630.2 / 2 nm) is used to isolate the lines.
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cb
100000
80000
Sig 60000
(c/s)
40000
20000
0
0
a
100
500
1000
Channel #
Fig.5 Spacing determination. Lines: a) Ne 630.47866 nm,
b) Ar 630.7662 nm, c) Ar 629.6876 nm. Filter: 630.3/2 nm
The apparatus of Fig.3 is used, with the shutter permanently opened and the
OARS plasma not excited. As the interferometer is scanned through the several orders,
the Ba(Ar) and Ba(Ne) sources are alternated to get the peak patterns indicated in Fig.5.
The three line profiles are fitted by Airy functions and their centroids determined in order
to locate, as accurately as possible, the positions of the different lines, and also to
calculate the free spectral range (from the Ne line positions). We then find the offset
between the Ne reference line position and the two Ar line positions, expressed as a
fraction of the free spectral range. These two numbers are used to find the interferometer
spacing.
From the wavelengths of the Neon reference line and the nominal spacing value,
we find the nominal order of interference. We then bracket that value with a set of
spacings corresponding to integer values of the order of interference. All of these
spacings will result in a Neon line at the same position in the interference pattern (since
the order of interference is an integer). However, since the Argon lines are at a different
wavelength, the positions of the two lines relative to the Neon line will vary as a function
of order. We calculate the expected position for each line relative to the Neon reference at
each assumed spacer value. We then have three lines: the Neon reference position, which
lies along the x-axis; and the two Argon lines, which have some slope relative to the xaxis.
In order to find the best value for the spacing, we subtract the observed offsets
from the calculated offsets. This is shown in Fig. 6, with the dots of the rising curve
Fig. 6 Determination of the FPI spacing using 3 spectral lines
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corresponding to the offsets from the Ar 629.6876 nm line at sequential spacer values
(one order apart) and the dots of the falling curve the results for the Ar 630.7662 nm line.
If all the line wavelengths were infinitely accurate, the two Argon curves would cross the
x-axis at the same point, corresponding to the spacing. Since this not the case, we need a
criterion to find the best spacer value.
We do not have sufficiently accurate knowledge of the uncertainties in the
wavelengths of the three lines; for convenience, we have assumed that they are equal.
Accordingly, we define the best spacing value as the one that intersects a point that is
equidistant from the three sets of points. To find that point, we construct bisectors to the
angle defined by each of the argon offsets and the x-axis. The intersection of the bisectors
is the center of the inscribed circle in the triangle defined by the two sets of Argon offsets
and the x-axis. The x-value of the center of this inscribed circle is then taken as the best
value for the spacing, i.e., t = 1.00988 ± 0.0001 cm.
Note that this is the “true” spacing of the plates, not a physical spacing such as is
provided by a mechanical spacer. It takes into account the index of refraction of the
medium between the plates and the effective reflection point in the multi-layer dielectric
coatings, which are several wavelengths thick. (In this analysis we have assumed that the
effective reflection point is the same for all these wavelengths around 630 nm, a
reasonable assumption, since the wavelengths involved differ by only a small amount.)
VII. Conclusion
Success in employment of a Secondary Standard in thermospheric velocity
determinations hinges on how accurately we are able to determine the offset between that
standard and the OI 630.0 nm line from the OARS studies. Analysis of ~300 of the
OARS comparison runs obtained to date yields the value 0.010024 ± 0.000068 nm for the
wavelength difference between the OI and the Ce 630.02 nm line. This uncertainty in the
wavelength difference corresponds to an equivalent velocity uncertainty of ~34 m/s.
Analysis of the substantial data base and acquisition of additional OARS comparison runs
continues, with a view to reducing the statistical error in the offset value.
Support for some of the research reported in this paper was provided by the
National Science Foundation under grant ATM-0221920.
References
Biondi, M. A., “Oxygen 630.0 nm and 557.7 nm line source for thermospheric dynamics
studies”, Applied Optics 41, 6499 – 6506, 2002.
Gray, D. E., Ed., American Institute of Physics Handbook, 3rd edition, McGraw-Hill,
New York (1972)
Harrison, G., Ed., MIT Wavelength Tables, MIT Press, Cambridge MA (1969)