Dual Fabry-Perot spectrometer measurements of daytimethermospheric temperature and wind velocity: dataanalysis procedures

T. D. Cocks

Daytime thermospheric temperatures and wind velocities have been inferred from dual Fabry-Perot spec-trometer observations of the atomic oxygen emission line at 630 nm, and this paper details the analysis pro-cedures applied to the recorded spectra. Numerical simulation of the recorded spectra was used to examinethe limitations imposed by analysis assumptions and by the influence of atmospheric molecular oxygen andwater vapor absorption lines near X630 nm. The observational and analysis procedures provide a reliableground-based means of monitoring the thermal and dynamical state of the neutral thermosphere during thedaytime.

1. IntroductionThe temperature and wind velocity of the neutral

thermosphere can be inferred from ground-based ob-servations of the atomic oxygen emission line at X630nm, and extensive nighttime measurements have beenrecently reported.1"2 Daytime observations have notbeen so regularly conducted or have they been so suc-cessful. Because of the importance of monitoring thethermosphere over the full diurnal cycle, an experimentwas undertaken to develop techniques to measure theoxygen emission line during the daytime and to developreliable and efficient data analysis routines. Details ofthe experiment and the measured temperatures andwind velocities have been reported elsewhere. 3 ' 4

Some past daytime observations of the X630-nmemission line have highlighted the possibility of mis-interpretation of the observed spectra. 5'6 It is thepurpose of this paper to present details of the dataanalysis scheme and its verification. The atomic oxy-gen line of the dayglow contributes <5% of the spec-trometer signal even if the spectrometer bandpass iscomparable to the line emission width. The major partof the signal arises from the large, spectrally complex,and time-dependent background of sunlight scattered

When this work was done the author was with University of Ade-laide, Mawson Institute for Antarctic Research; he is now with CSIRO,Division of Cloud Physics, P.O. Box 134, Epping, N.S.W. 2121, Aus-tralia.

Received 14 August 1982.0003-6935/83/050726-07$01.00/0.(c) 1983 Optical Society of America.

by the earth's atmosphere. Because of the small con-tribution from the emission line, even small spectraldistortions or incomplete isolation of the line spectrumfrom the background result in a spectrum that cannotbe successfully analyzed. This paper establishes somelimits in this regard.

11. ExperimentThe emission line from atomic oxygen at X630 nm has

an intensity of a few kiloRdyleighs (kR) during the day,and the background of scattered sunlight has a typicalbrightness of -5 X 104 kR nm-1. Furthermore thespectrum of the skylight is complicated by the presenceof Fraunhofer absorption lines and atmospheric ab-sorption features due to molecular oxygen and watervapor. To determine the Doppler width and the Dop-pler shift, the line must be isolated from the backgroundof scattered sunlight. It was assumed that over a smallspectral interval around the emission wavelength thespectrum of the day sky differed from that of directsunlight by the presence of the emission line and acontinuous component which contributes a few percentto the day sky brightness generally known as the Ringeffect.7 As in other dayglow experiments, the spectrumof scattered sunlight is removed from the day skyspectrum by subtracting a suitably normalized spec-trum of direct sunlight. 8 9

The spectrometer used in this experiment was a dualetalon Fabry-Perot interferometer (FPI). A high-res-olution FPI (0.003-nm bandwidth)10 and a low-resolu-tion FPI (0.03-nm bandwidth) 11 were scanned inwavelength synchronism, with wideband isolation of thespectrum being achieved with an interference filter(0.3-nm bandwidth). The spectrometer was scanned

726 APPLIED OPTICS / Vol. 22, No. 5 / 1 March 1983

over an 0.036-nm interval, this being just sufficient toscan through the 01 Fraunhofer line at X630.03 nm,which has a width of -0.1 nm. Each spectral scan wasdigitized into 128 channels, and successive scans wereaccumulated in a multichannel analyzer. The spec-trometer was scanned over <1 order of the high-reso-lution FPI, 1 order being equivalent to 151 channels.With these parameters the Doppler shift associated witha wind velocity of 14 m sec 1 was equivalent to 0.1channels, and a 1000 K source temperature produceda linewidth equivalent to 13 channels.

111. Analysis Scheme: Basic EquationsThe dayglow observational procedures yield three

data sets, representing the spectra of skylight, directsunlight, and a white-light source, all recorded over thesame spectral interval. This section illustrates theidentification of spectral components in the data setformed by the subtraction of a normalized solar spec-trum from the sky spectrum and outlines the analysisscheme used to estimate the temperature, wind velocity,emission intensity, and fractional Ring component.

The spectrometer is scanned over a wavelength in-terval, equivalent to N channels, from X,5 at the begin-ning of the zeroth channel to X< + NAX/NA at the endof channel number N - 1, where NA is the number ofchannels per free spectral range AX of the high-resolu-tion FPI. The spectrometer is scanned by a linear in-crease in plate separation so that the nth channel cor-responds to a small wavelength interval X + nAX/NAto Xp + (n + 1)AX/NA. The photon flux at the detectoris

O = SQp(), (1)

where X is the transmittance of the optical componentsother than the etalons, S is the area of the aperture stop,Q is the solid angle field of view at that stop, and p (X)is given by

p(X) = V(X)b(X)] * i(X), (2)

where b(X) is the spectral radiance of the source (ex-pressed as a photon flux), i(X) is the instrument func-tion of the dual FPI, and f (X) is the transmission profileof the interference filter. The asterisk denotes theconvolution operation. In a pulse counting or digitalmode the flux falls on the photocathode of the photo-multiplier giving current pulses at the anode. Thesepulses are counted and stored in the appropriatechannel of a multichannel analyzer. In the current oranalog mode, as used in the experiment, the anodecurrent is amplified by a transresistance stage, theoutput of which is digitized by a voltage-controlled os-cillator. If the response time of the amplifier is muchless than the integration time per channel, both thedigital and analog modes can be treated identically.This condition was satisfied in this experiment, andhenceforth only the digital mode will be considered.

If successive scans are cyclically accumulated into Nchannels for a total of t seconds, the total number ofcounts accumulated in the nth channel is

tn =- rSQQfp(X)dX + d + Zn' (3)

N

where Q is the photomultiplier quantum efficiency, andd is the counts from the photomultiplier dark current.The integral is evaluated over the wavelength intervalof the nth channel. The random variable Zn describesthe statistical variation of the accumulated counts andhas an expected value of zero.

Equation (3) can be simplified if p(X) is assumedlinear across a channel, that is, if X >> AX/NA, where3A is the width of features in p(X). In the dayglow ex-periment AX/NA was 3 X 10-4 nm and cA varied from.4 X 10-3 nm for observations of the emission line to

1.6 X 10-2 nm for the OI Fraunhofer line at X630 nm.Thus to sufficient accuracy, Eq. (3) becomes

P = N SQ'Q A P(Xn) + d + ZnN Na

where

Xn X + + 1) AX

(4)

(5)

The spectral radiance of the Doppler-broadenedemission line is described by the Gaussian function andin terms of channel number is given by

(6)g(n) = G exp -(n - n) 1

where

ne = 7.6 X 10-8T 2mNA, (7)

and G is the source radiance, T is the emission tem-perature, m is the order of interference of the high-resolution FPI, and np is the channel number corre-sponding to the emission wavelength Xp.A. Spectral Features of the Subtraction Set

The sky and solar spectra are sampled over an in-terval large enough to obtain information about thecontinuum on either side of the 01 Fraunhofer line.The wavelength Xc is chosen to represent the localcontinuum. The spectral shape of the solar spectrumis described by a function b(X) defined as unity at XcIf the spectral radiance of the diffuser illuminated bythe sun is L, kR nm-1 at X,, the recorded solar spectrumis described by

ya(X) = L[b(X)f(X)] * i(A)}, (8)

where the constants of Eq. (1) have been omitted forclarity.

The basic assumption of the analysis is that thescattered sunlight from the day sky has the same spec-tral characteristics as the direct sunlight except for anadditional continuous component of relative magnitudea: the Ring component. For a day sky of spectral ra-diance L2 at X, and with the emission line present, therecorded sky spectrum is

yb(X) = L21[b(X)f(X) + axf(X)] * i(X)) + [g(X)f(X)] * i(X). (9)

The recorded solar spectrum is normalized so that at Xc(Fig. 1)

Yb () - Ya(c) = 0, (10)

1 March 1983 / Vol. 22, No. 5 / APPLIED OPTICS 727

the contribution from the emission line in the recordedsky spectrum was negligible; that is,

I[g(X)f(X)] * i\)IX = 0. (16)

z 099 SCD

097

630 02 630 03 630-04WAVELENGTH ( nm)

Fig. 1. Recorded sky and solar spectra normalized to unity at ,(0900 h LMT, 20 Feb. 1976).

1*0-z(DU-,

U

a.

0-5F

0.0 - vf r - - -630 02 630 03

WAVELENGTH (nm)630 04

Fig. 2. Feature resulting from subtraction of the spectra of Fig. 1,shown as a percentage of the sky signal at X,.

and the result of subtracting the normalized solarspectrum from the sky spectrum (Fig. 2) is then

y(X) = [g(X)f(X)] * i(X) + (L2 - 3L1){[b(X)f(X)] * i(X)

+ L2a[f(X) * i(A)]}. (11)

This subtraction result consists of a contribution fromthe line emission, namely, [g(X)f(X)] * i(X), and a con-tribution from the Ring effect. The recorded spectrumobtained from scanning a white-light source of spectralradiance L3 is given by

y.(X) = L3[f(X) * i(X)]. (12)

If the recorded white-light spectrum is scaled to thenormalized solar spectrum at X, so that

OYa(c) - YY.(X ) = 0, (13)

Eq. (11) is given by

y(X) = [g(X)f(X)] * i(X) + r(X), (14)+a

where

r(X) = Y.(X) - OYa(X). (15)

In the derivation of Eq. (14) two simplifying as-sumptions were made. First, it was assumed that at X,

This is only approximate because of the small but finitetransmittance between orders of the FPI, and this af-fects the value of the scaling constant 3. Second, it wasassumed that at Xc the recorded solar spectrum and therecorded white-light spectrum have the same normal-ized value, namely,

[b(X)f(X) * i(X)jx, = f(A) * i(X)lx,. (17)

This implies that the interaction of the spectrometersidebands and the Fraunhofer lines of the solar spec-trum have a negligible effect on the recorded solarspectrum at X,; i.e., b (X) = 1 over all wavelengths wheref(X) and i(X) are significant, when i(X) is centered onXs.

The consequences of these two assumptions wereexamined in a numerical simulation of the experimentand are discussed in a following section.

B. Parameter Estimation

To estimate temperature, wind velocity, and emissionintensity from the subtraction set [Eq. (14)], theGaussian line has to be recovered by a deconvolution ofthe instrument function. Recently Wilksch' 2 devel-oped a least-squares parameter estimation schemewhich used the discrete Fourier transform (DFT) toanalyze the 01 line emission in the nightglow. An ex-tension of this scheme was chosen to analyze the day-glow results. Because of incomplete knowledge of theinstrument sidebands and the possibility of ambiguityin the deconvolved spectrum, the Ring spectrum is notdeconvolved. The Ring spectrum is involved in theanalysis by way of the DFT of the function described byEq. (15).

In terms of counts accumulated, Eq. (14) is repre-sented by a set of numbers lynI defined as

aYn = t + +rn + Zn, (18)

where t represents the convolution of the instrumentfunction with the emission line profile, rn represents theRing spectrum [Eq. (15)], and z, represents the statis-tical fluctuations of the data set. In a dayglow obser-vation, the line emission contributes a few percent to thetotal signal, and so the statistical fluctuations in lyn) areessentially those present in the sky background signalwhich varies -3% across the N channels scanned.Consequently, the variance cr2 of the data set {Yn} canbe considered independent of channel and (Z_ )2 = 2.The temperature, wind velocity, emission intensity, andfractional Ring component are estimated by the gen-eration of a set t, + rn/(l + )} that results in theminimization of the x2 parameter defined as

x2=N- I-(t +an) a (19)

n=O (y2If rnI and Rn'}, tn } and TnJ), {yn and Yn} are DFT sets,minimizing x2 is the same as minimizing x2, where

728 APPLIED OPTICS / Vol. 22, No. 5 / 1 March 1983

2 =2 ql a 12Xq Z Y'+Tn' + - Rn') (20)

where q is the value of subscript n' of the transform setYn above which all components are dominated by

noise. If the instrument function is represented by aDFT set in} and {In, } and the emission line by {gn} and

2 =2 q 2 ( Xq N E- 1Yn' (InG+ 1n + Rn') . (21)

The statistical noise on rn is small compared with thatof Yn,} and is thus neglected in the analysis. The formof Eq. (21) is now amenable to a least-squares fittingroutine, and the analysis of the dayglow observationsinvolves the reconstruction of Eq. (14) in the Fouriertransform domain with the noise-dominated compo-nents being neglected. It now remains to examine thedetails of gn} and in} and their respective DFT sets {Gn'and Ins}

The spectrometer instrument function i(X) is mea-sured by scanning through the He-Ne laser line atX632.8 nm. The instrument function is recorded overa wavelength interval NA X/NA and has an area Awithin this interval. This measurement is used togenerate a set {in), which is periodic of period N channelswith the passband centered on the zeroth channel. Itis useful if {in} is defined so that

N-1

E in =1, (22)n=O

where

/An = i(Xn) A (23)NA

The Gaussian source function defined in Eq. (6) isnegligible outside the interval X,, to X + NAX/NA

0

-1

Lr

00.

CD0

-2

-3

-4

I I I I I I

0 10 20 30n'

40 50 60

Fig. 3. Normalized power spectrum of Fig. 2. Average noise powerNa 2 shown by dashed line.

when the spectrometer is tuned so that the emissionwavelength Xp occurs near the center of the scannedinterval. The interference filter bandwidth is muchgreater than both the source and instrument band-widths, and so the total number of counts accumulateddue to the emission line alone is

t N-1 X *iC=-S2rp f ng(l * i(X)]dX,N n=0 - ,)n

(24)

where TF is the peak transmittance of the interferencefilter. The quantity g(X) * i(X) can be assumed con-stant across a channel; thus

C =AX t N-C-QSTTF E 19(X *i'(X)]Xn.

NaN n=0,(25)

By the properties of convolution it can be shown that

- N-=C = -SQQAGT-TF= t,.N n=0

(26)

The normalization of the sampled instrument functionto unit area and the inclusion of integration time, solidangle, etc. into Eq. (26) can be considered, for purposesof analysis, equivalent to scaling the radiance of the linesource so that

g = H exp [-(n - np)]a e

1 1 2ne e by

and the DFT set Gn'j is then given by

(27)

Gn = H exp 2nI'2ni) exp (-2rnn) (28)

Since Tn, = GnIn', it can be seen that H equals the totalnumber of accumulated counts due to the line sourcealone and is proportional to the source radiance Gthrough Eq. (26).

The four parameters to be optimized in a least-squares sense are H, ne, np, and a, providing estimatesof source radiance, temperature, Doppler-shiftedwavelength, and the fractional Ring component, re-spectively. Having estimated H it is possible, in prin-ciple, to derive the source radiance from Eq. (26), butin practice an accurate calculation of A and is ex-tremely difficult. A calibration scheme to infer theradiance from H using an empirical relation is describedin the next section.

The DFT of the data set of Fig. 2 is implemented witha fast Fourier transform algorithm to generate thepower spectrum shown in Fig. 3. The average noisepower N 2 is computed from the high-order compo-nents, and the number of components to be analyzed isset by the first component with a ratio of power-to-noisepower of less than one. A grid search of parameterspace is used to return parameter estimates and theirassociated error. Using the estimated parameters, theset Gn,' can be calculated for all n' and multiplied by{In' to reconstruct the subtraction set of Eq. (14) bythen applying the inverse DFT and adding a Ringspectrum of the estimated amplitude, as shown in Fig.4.

The wind velocity is determined from np. Since alaboratory source of 01 emission at X630 nm was notavailable, a zero velocity wavelength, or rather its cor-responding channel number, was obtained from actual

1 March 1983 / Vol. 22, No. 5 / APPLIED OPTICS 729

I

I

L

Pn = QSQrWAK, (30)NA

where

K = f f(X')i(X - X')dX (31)

evaluated at Xn. If both the filter and the spectrometerare tuned to Xp,

K = A f(X)dA,ma

WAVELENGTH nm)

Fig. 4. Reconstructed subtraction feature superimposed on datapoints. Analysis estimated a temperature of 1190 110 K and a 2.6

+ 0.4% Ring component.

atmospheric measurements. As the midlatitude ther-mospheric velocity field under quite geomagnetic con-ditions varies slowly as a function of latitude and lon-gitude, a reference measurement was obtained by av-eraging channel numbers obtained from pairs of N-Sand E-W observations and in the zenith where thevertical velocity is only a few meters per second. Thesecalibration measurements were made during twilightwhen the averaging time per spectrum is only a fewminutes. The errors introduced in this method of cal-ibration are significantly smaller than the statisticalerrors that occur in a daytime wind velocity measure-ment.

The advantage of the analysis procedure developedabove is that all the spectral information required isderived empirically. Analytical approximations of theinstrument function or assumptions as to the shape andintensity of the Fraunhofer lines in the solar spectrumcould have introduced serious errors into the parameterestimates, particularly as these would be needed over±0.5 nm of X630.03 nm. All the empirical data used areonly required over N channels, which is <1 order of thehigh-resolution FPI, even though the spectrometersidebands are significant outside this interval.

C. Radiance Calibration

The calibration scheme involves use of a white-lightsource of known spectral radiance and requires knowl-edge of the instrument function shape over all wave-lengths that contribute significant signal, the qualifi-cation significant being related to the desired calibrationaccuracy. This scheme does not require knowledge ofthe transmittance of the spectrometer, this being adifficult quantity to estimate analytically or to mea-sure.

If a white-light source of spectral radiance W at X630nm is scanned, the count rate in the nth channel is

Pn = QSQTW fX+l sX: f(X')i(X - X')dX'dX, (29)

where f(X) is the interference filter transmission profile.The value of the inner integral is assumed constantacross a channel; thus

(32)

where the limits Xa, Xb define the spectral intervaloutside of which there is a negligible contribution to thevalue of K. The instrument profile has a high degreeof symmetry about Xp and hence to sufficient accu-racy,

K = (1 + 2k) fX__f(X)i(X)dX,

where k is given by

L5

AN-1 j[ °N-

(33)

Little error is introduced if f(X) is considered equal toTF over the scan range, and since i(X) has an area Abetween X and XN-1,

K = (1 + 2k)TFA.

Equation (30) then becomes

P = QST AX (1 + 2k)TFA,NA

(35)

(36)

and substitution of A into Eq. (26) gives the source ra-diance as

= C(1 + 2k) WAX (37)

Pn NA

Thus that data analysis scheme yields estimates of thesource radiance by

_ = (1 + 2k) WAX (38)

Pn NAA scan of a white-light source yields a recorded

spectrum that varies by only 1% across the 128 channels,and so in practice p is a 128-channel average. Theconstant k is estimated from measurements of the nearsidebands of the instrument function and by use of anumerically generated profile extending to about ±0.6nm of Xp. For the dual FPI parameters chosen in thisexperiment, k has a value of -0.1. Consideration of theerrors involved in the spectrometer calibration and theapproximations made in the value of k, a systematicerror in the estimated source radiance of <20% is ex-pected.

IV. Numerical Simulation of Experimental Data

In view of past misinterpretation of dayglow spectra,numerical simulation of various aspects of the dayglowexperiment has been carried out to verify the validityof the data analysis scheme and to establish the limi-tations of the present experiment.

730 APPLIED OPTICS / Vol. 22, No. 5 / 1 March 1983

1-0

-j

zCD

LU 0-5:CD

LUCrC

LU0.

00 _

0 -2630-02

z0C)ur

z

a-

v)

J

(n

00z

C. Normalization Factor1.0

0-5

0-0L6295

0 56nmIIII0-03nm

630-0WAVELENGTH (nm)

630 5

Fig. 5. High- and low-resolution (thick line) FPI profiles over a1.2-nm wavelength range centered on Xp.

A. Instrument and Source ProfilesTo numerically simulate recorded spectra, an in-

strument profile must be generated over a wavelengthinterval of 1.2 nm (30 orders of the high-resolutionFPI). This exceeds the scan range of the dual FPI, andso the instrument profile was generated from empiricalprofiles of the two FPIs, each measured over 1 order.The dual FPI profile was approximated by multiplyingthe individual profiles. This is not a rigorous formu-lation but is adequate for the tests described below.Figure 5 illustrates the two individual FPI profiles, andto emphasize the sidebands of the dual FPI, Fig. 6 ispresented as the logarithm of the dual FPI profile. Theinterference filter is used to suppress the near coinci-dent sidebands of the individual profiles, and its effecthas been included in Fig. 6. If both FPIs were ideal, thedual FPI profile would be the product of two Airyfunctions. The increase in the relative transmittanceof the sidebands is due to departures in parallelism ofthe etalons and the use of a finite field of view.

A data set representing the solar spectrum was gen-erated at a resolution of 5.6 X 10-4 nm over the samespectral interval using published tables. The skyspectrum, excluding the dayglow emission line, wasidentical, except that the atmosphere absorption linedepths could be varied and a Ring component added.

B. Recorded Spectra

The recorded sky and solar spectra were generatedby discrete integration of the product of sky or solarspectrum, the spectrometer profile, and the interferencefilter profile as the central band of the dual FPI wassuccessively positioned at channels corresponding to X0through XN-1. The emission line was convolved withthe same instrument profile used in the data analysisand added to the numerically derived scan of the skyspectrum. Figure 7 shows an example of the numeri-cally derived sky and solar spectra with a 1200 K emis-sion line present. Both spectra have been normalizedto unity at X, and the emission line contributes 1.2%of the signal at Xp. Comparison with actual recordedspectra (Fig. 1) indicates that the numerically derivedspectra give a good representation.

At wavelengths (Xp - ) from the central maxi-mum the spectrometer has a transmittance of 0.4%relative to the central maximum. When convolved withthe emission line the signal at Xc is 0.7% of that at Xp.The analysis scheme assumed that the signal from theline at X, was zero [Eq. (16)]. Although the line signalis small at Xc compared with the sky signal (typically -7X 10-3%), it has a measurable effect. Using numericallygenerated sky and solar spectra, the analysis schemeoverestimated the temperature by 20 K and returneda Ring component of -0.6% instead of zero. This errorwas caused by underestimation of the factor by whichthe solar spectrum is scaled before subtraction. Theanalysis returns correct values if the scaling factor isadjusted by an amount dependent on the percentagesignal from the line source at Xp.

D. Ring Component

In generating a Ring component from recordedspectra of direct sunlight and a white-light source, theassumption of Eq. (17) was required. This is notstrictly valid for this experiment or can it be easily takeninto account. However, using numerically generatedspectra, it was found that for Ring components up to 6%,

0 5

LUz

-2

Z -3

Cr

0

-5

-6 p629-5 630-0 630-5

WAVELENGTH (nm)

Fig. 6. Dual FPI profile used in numerical simulation of the exper-iment. Product of two Airy functions shown by dots.

z(D

n 0.99LUN

cr0 9z 098

630-02 630-03 630-04

WAVELENGTH (nm)

630-05

Fig. 7. Numerically generated sky and solar spectra normalized tounity at X,.

1 March 1983 / Vol. 22, No. 5 / APPLIED OPTICS 731

- l l

the temperature was estimated to within 20 K and thewind velocity to within 5 m sec 1. In comparison withthe statistical errors in the observational data, theanalysis scheme was of sufficient accuracy.

E. Atmospheric AbsorptionThe dayglow spectra are analyzed on the assumption

that the only spectral difference between the sky andsolar spectra is the presence of an emission line and aRing component. However, in the region of X630 nmthere exists several atmospheric absorption features dueto 02 and H2 0 vapor. The depths of these absorptionfeatures depend on the optical path through the atmo-sphere and will be different in the sky and solar spectra.Sidebands of the dual FPI result in leakage of infor-mation from the spectral region of the absorption fea-tures into the wavelength interval scanned by the cen-tral maximum, and the difference in absorption depthsis apparent in the residuals of the subtraction.

In the generation of the numerical sky and solarspectra, the amount of 02 absorption in the solar spec-trum was made 30% greater than in the sky spectrum.From observations of the X629.92-nm line of 02, thisrepresents a realistic upper limit for the conditions ofthis experiment. Upon subtraction, the residuals hada magnitude of 2 X 10-2% of the sky spectrum at Xp.The analysis scheme returned temperatures underes-timated by 30 K, Ring components overestimated by0.6%, and wind velocities in error by 10 m sec 1.

V. SummaryThe analysis scheme chosen for the dayglow experi-

ment is best suited to the analysis of simple spectraobtained with high-resolution high-contrast spec-trometers, and the least-squares parameter estimationcarried out in the Fourier transform domain is very ef-ficient. The numerical simulation of the experimenthas shown that it is possible to successfully isolate andanalyze the OI emission line during the daytime andthat the approximations made in the formulation of theanalysis scheme are valid for the experimental param-eters chosen.

The numerical simulations have also shown that evensmall spectral distortions of the order of 5 X 10-2% ofthe recorded sky spectrum can result in significant er-rors in the estimated temperature and to a lesser extentthe wind velocity. With the present experiment, the

interaction of far sidebands and the atmospheric 02

absorption features provide the most serious limitation.This can be improved in future experiments by usinghigher finesse, higher contrast FPI (particularly thelow-resolution FPI), and a narrower bandpass inter-ference filter. There is nothing to be gained by at-tempting to suppress the near sidebands by using athird FPI. The resulting loss of transmission (by afactor of -3) would far outweigh any benefits.

Considering all the sources of systematic error in thedayglow experiment it is expected that the temperatureis correct to within 50 K and the wind velocity to within10 m sec 1. For a single measurement, typical statis-tical errors are 130 K and 40 m sec 1, respectively.Reduction of the 02 absorption effects would result insystematic errors in temperature measurements towithin 20 K. Using higher transmission FPI it is pos-sible to reduce the statistical errors to -40 K and 15 msec 1 for an observational period of 90 min. Theequipment, observational procedures, and data analysisdescribed in this paper and in Ref. 4 provide a reliableground-based means of monitoring the thermal anddynamical state of the neutral thermosphere during thedaytime.

This work had support from the Australian ResearchGrants Committee. The contributions of F. Jacka andP. A. Wilksch were greatly appreciated.

References1. F. Jacka, A. R. D. Bower, and P. A. Wilksch, J. Atmos. Terr. Phys.

41, 397 (1979).2. G. Hernandez and R. G. Roble, J. Geophys. Res. 81, 2065

(1976).3. T. D. Cocks and F. Jacka, J. Atmos. Terr. Phys. 41, 409 (1979).4. T. D. Cocks D. F. Creighton, and F. Jacka, J. Atmos. Terr. Phys.

42, 499 (1980).5. L. L. Cogger and G. G. Shepherd, Planet. Space Sci. 13, 1163

(1965).6. G. Henderson and P. N. Slater, Planet. Space Sci. 14, 1035

(1966).7. J. F. Grainger and J. Ring, Nature London 193, 762 (1962).8. A. R. Bens, L. L. Cogger, and G. G. Shepherd, Planet. Space Sci.

13, 551 (1965).9. F. E. Barmore, Planet. Space Sci. 25, 185 (1977).

10. F. Jacka, A. R. D. Bower, D. F. Creighton, and P. A. Wilksch, J.Phys. E 13, 562 (1980).

11. T. D. Cocks, Ph.D. Thesis, U. Adelaide (1977).12. P. A. Wilksch, Ph.D. Thesis, U. Adelaide (1975).

732 APPLIED OPTICS / Vol. 22, No. 5 / 1 March 1983