Available online at www.sciencedirect.com

www.elsevier.com/locate/asr

Advances in Space Research 42 (2008) 1267–1275

Proposal for ionospheric tomography technique usinga new HF radio source

Lan Wang a,*, John W. MacDougall a, Rafeef Abugharbieh b

a Department of Electrical and Computer Engineering, University of Western Ontario, London, Ont., Canada N6A 5B9b Department of Electrical and Computer Engineering, University of British Columbia, Vancouver, BC, Canada V6T 1Z4

Received 9 September 2006; received in revised form 12 September 2007; accepted 13 September 2007

Abstract

Measurements of the line integral of the electron density along satellite-to-ground ray paths (i.e. TEC) using differential phase orDoppler of two coherent VHF/UHF signals transmitted from NNSS or GPS satellite networks have been used in the ionospheric tomog-raphy for mapping large-scale ionospheric images over region of interest. In this paper, we present theoretical studies of using a newsignal source HF frequency in tomographic imaging. The initial phase problem inherent in the phase measurement can be eliminatedby measuring Faraday rotations. Relative rotation on two adjacent HF frequencies is used to solve the ambiguity problem. A sec-ond-order approximation of the Faraday rotation incorporated with ray-tracing technique improves the reconstruction degradationdue to ionospheric refractions. CASSIOPE is a multi-purpose small satellite that receives HF signals from ground radar facilities andit is scheduled for launch in early 2008. Simulations have demonstrated the potential applications of the ionospheric tomography in CAS-SIOPE/e-POP satellite experiment.� 2007 COSPAR. Published by Elsevier Ltd. All rights reserved.

Keywords: Ionospheric tomography; Satellite; HF

1. Introduction

The computer tomography (CT) technique has been suc-cessfully applied in medical imaging: a sequence of X-raysis sent through a body at different angles to allow the deter-mination of body parts. Other applications of CT includeocean structures and geological formations. The conceptof ‘‘ionospheric tomography’’ came out in 1984 and waspresented in 1986 during the URSI Beacon Satellite Sym-posium (Austen et al., 1986). Experimental results and val-idation work have demonstrated the abilities of ionospherictomography in mapping and modeling ionospheric featuresfor practical applications (Andreeva et al., 1990; Kersleyet al., 1997; Pryse et al., 1998; Yeh et al., 2001). In recentstudies, the radio frequencies received by ground stations

0273-1177/$34.00 � 2007 COSPAR. Published by Elsevier Ltd. All rights rese

doi:10.1016/j.asr.2007.09.014

* Corresponding author.E-mail address: lwang28@uwo.ca (L. Wang).

for tomographic observations were from two sources: onewas the phase coherent frequencies at 150 MHz and400 MHz from the polar orbiting satellites of the NavyIonospheric Monitoring System (NIMS), previouslyknown as the Navy Navigation Satellite System (NNSS);the other was the Global Navigation Satellite Systems(GNSS: GPS and/or its Russian equivalent, GLONASS).This second source is relatively new and radio occultationdata, by a LEO satellite, is used in addition to the satel-lite-to-ground geometry. The ionospheric tomographyusing radio occultation improves the ‘‘ill-conditions’’ inthe ground-based ionospheric tomography by providingaverage vertical distribution of the ionosphere. However,the inclination of GPS (55�) and GLONASS (65�) restrictstrue tomography to regions with geographic latitudes smal-ler than the inclination (Leitinger, 1999).

The paper discusses whether we could use HF frequen-cies in the ionospheric tomography technique. HF signalsare more sensitive for probing the ionospheric disturbance

rved.

1268 L. Wang et al. / Advances in Space Research 42 (2008) 1267–1275

and are widely used for local ionospheric observations. Inearly 2008, a multi-purpose small satellite called CASSI-OPE (CASade, Smallsat and IOnospheric Polar Explorer)is scheduled for launch with a two-year operation period.It carries two payloads: one is the telecommunicationinstrument Cascade to study digital broadband courier ser-vice for commercial purposes; and the other is the e-POP(The Enhanced Polar Outflow Probe), a payload carryingeight scientific instruments to study the atmospheric andplasma flows, related wave-particle interaction, and radiowave propagation in the polar ionosphere. CASSIOPEhas a polar, elliptical orbit with an inclination angle 80�.The apogee is 1500 km and perigee is 325 km. During CAS-SIOPE operation period in selected portions of its orbit,HF signals will be received from ground radar facilities,such as CADI (MacDougall et al., 1995) and SuperDARN(Greenwald et al., 1995) networks, using a four-channelULF-HF Radio Receiver Instrument (RRI). In the rangeof 1 kHz–18 MHz, the RRI will measure electrical fieldsof waves from ground transmitters using a pair of 6 mcrossed dipoles. The receiver bandwidth will be variableup to 30 kHz and the maximum sampling rate per channelis 60 kHz. Radio wave parameters to be studied include sig-nal amplitude, group delay, direction of arrival and Dopp-ler frequency (James, 2003). Meanwhile, Cascade willprovide information storage and 100 MHz bandwidthdownlink capacity for research data with 15 GB dailytransmission volume.

We suggest a new method for ionospheric tomographybased on measurements of differential Faraday rotationof two adjacent HF frequencies on the CASSIOPE/e-POP satellite. Faraday rotation can be determined by usingcrossed antennas onboard and the difference of two plane-polarized HF transmitting frequencies is set at a suitablevalue in order to eliminate the 2p ambiguity. The methodovercomes the ‘‘initial phase’’ problem associated withphase measurements in conventional ionospheric tomogra-phy experiments. The effects of ionospheric refraction inthe reconstructed image can be removed in a two-step pro-cess by using a second-order Faraday rotation approxima-tion and incorporation of ray-tracing technique. Weconcluded that it is possible to use our proposed HF iono-spheric tomography combined with other observations toaddress important questions about the ionosphere in theCASSIOPE/e-POP satellite mission.

2. Methods

2.1. Faraday rotation and second-order approximation

Faraday rotation is not new to ionospheric research. Asearly as 1957, chart records of the radio signals from theSputnik I presented fine structures caused by Faraday rota-tion on frequencies 20 MHz and 40 MHz (Swenson, 1994).Many Faraday rotation experiments were conducted in1960–1970 to study ionospheric phenomena, such as sud-den ionospheric disturbances, storms, traveling ionospheric

disturbances etc. (Davis and Da Rosa, 1969; Mendillo andKlobuchar, 1973).

The basis for tomographic imaging of an ‘‘object’’ is theintegral influences of the ‘‘object’’ on the wave properties(Leitinger, 1999). In ionospheric tomography, measure-ments of the total electron content (TEC) along ray pathsfrom ground transmitter to satellite are inverted in a recon-struction algorithm to create an image of the spatial distri-bution of the density over the region of interest. TEC canbe measured using carrier phase method, differential Dopp-ler method, group delay method, and Faraday rotationmethod. The first three methods are based on the plasma’sinfluence on the phase of received signals and were adoptedby all of the ionospheric tomography campaigns. However,the ‘‘initial phase’’ of the transmitting frequencies cannotbe observed or measured.

The potential application of Faraday rotation on tomo-graphic imaging was first presented by Ganguly et al.(2001) based on simulations. They used data obtained fromthe low Earth orbiting satellites BEB (Explorer 22) withVHF frequencies at 40/41 MHz in 1967–1968 and demon-strated the improvement with the use of Faraday rotationdata compared with the use of group delay.

The Faraday rotation X can be expressed as followswhen the transmitting frequency is much higher than theplasma frequency (f >> fp) under the quasi-longitudinal(QL) approximation:

X ¼ pfc

Zs

XY L ds ¼ 2:365� 104 f �2

Zs

N eB0 cos hds ð1Þ

where c is the speed of light; f, fp and fH are the transmit-ting frequency, plasma frequency and the gyro-frequencyrespectively; X = (fp/f)2, Y = fH/f and YL = Ycosh, Ne isthe electron density; B0 is the imposed magnetic field; h isthe angle between wave propagation and the magneticfield.

Considerable error may be introduced when the trans-mitting frequency is comparable to the plasma frequencyif one uses Eq. (1). More accurate expressions for the Far-aday rotation for lower frequency (when the transmittingfrequency is closer to the plasma frequency) have beenstudied by various researchers (Garriott, 1960; Ross,1965; Titheridge and Heron, 1971). Among them, Tithe-ridge and Heron (1971) presented an improved version ofthe second-order expression as the following:

X ¼ pfc

Zs

XY Lð1� X Þ�1=2 ds ffi X0 � ð1� X Þ�1=2

¼ X0 � c ð2Þ

where X0 is denoted as the high frequency approximationas in Eq. (1); and c = (1 � X)�1/2 is the correction factorand can be brought outside the integral if a mean valuefor X is used. Example of the correction factor for a b typeChapman layer ionosphere model with a constant scaleheight given in their paper is c = (1 � 0.7Xm)�1/2, whereXm = (fc/f)

2, fc is the critical frequency of the ionosphere.

L. Wang et al. / Advances in Space Research 42 (2008) 1267–1275 1269

Titheridge and Heron (1971) found that Eq. (2) improvesthe accuracy of Faraday rotation by 0.1% as comparedto the analytic expression for the correction factor c givenby Garriott (1960).

Utilizing the HF measurements in the CASSIOPE/e-POP experiment, relative rotation on two adjacent frequen-cies f and f + df is suggested in order to eliminate ambigu-ity. Differentiation of Eq. (1) gives

dX0 ¼ �4:73� 104 f �3 dfZ

sN eB0 cos hds

¼ Cðf ÞZ

sN eBL ds ð3Þ

where BL = B0 cosh is the longitudinal component,C(f) = � 4.73 · 104 f�3 df is a frequency dependent con-stant when the two transmitting frequencies aredetermined.

The integration value in Eq. (3) depends on the density ofthe ionosphere. The correction factor c for each transmittingfrequency is almost the same when mean value of X is usedand df is relatively small. It is safe to assumedX = X01 · c � X02 · c = dX0 · c. dX will be in the range0–2p if df is carefully selected when HF frequencies are used.

2.2. Reconstruction algorithms

The equation for using a finite set of basis functions toapproximate Eq. (3) in a discrete form for a reconstructedionospheric image with N pixels is given by

dX0 ¼ F i ¼ Cðf ÞXN

j¼1

Aijxj ð4Þ

where Fi is denoted as the differential Faraday rotation foreach ray path; xj is the electron density within jth(j = 1, . . . N) pixel; Aij = pij · B0 cosh (i = 1, . . . ,M raypaths) is a variable in each pixel and pij is the part of thepath Pi traversing the jth pixel. Actually, B0 cosh acts asweighting function for the path segment pij. With M raypaths, the reconstruction problem becomes solving the sys-tems of linear equations (SLE):

F ¼ CAX ð5Þ

where C is the constant, F is M by 1, A is M by N; X is N

by 1.The discrete inverse theory provides versatile solutions

for minimizing the residual iCAX � Fi and solving theSLE problems. The first published reconstruction algo-rithm using an iterative method for ionosphere imagereconstruction is ART (Algebraic Reconstruction Tech-nique) (Austen et al., 1986). MART (Multiplicative Alge-braic Reconstruction Technique) is similar to ART and ithas found the widest practical application as a general pur-pose tomography algorithm for its computational efficiency(Leitinger, 1999).

We therefore revised the ART and MART algorithmsbased on the paper presented by Pryse et al. (1998) using

the differential Faraday rotation measurement instead ofTEC measurement shown in the form given in Eqs. (6)and (7) respectively.

xkþ1j ¼ xk

j þ kF i � hCAi; xkihCAi;CAii

CAij

xkj

maxðxki Þ

ð6Þ

xkþ1j ¼ xk

j �F i

< CAi; xk >

� � kAij

Amax

ð7Þ

where hU ; V i ¼PN

j¼1U jV j is a scalar product for any vec-tors U, V 2 RN; the relaxation parameters k is a real num-ber, usually confined within the interval: e1 6 k 6 2 � e2

and e1, e2 > 0. Note, a positiveness of data and matrix ele-ment is not required in Eqs. (6) and (7). The exponent inEq. (7) is normalized by the maximum element in matrixA and bounded such that 0 <j kAi

j=Amax j6 1.

2.3. Ray-tracing adjustment

We look at the discrete form of the differential Faradayrotation in Eq. (4) and expand the matrix A into the follow-ing form:

A ¼

A11 A12 � � � A1N

A21 A22 � � � A2N

� � � � � � � � � � � �AM1 AM2 � � � AMN

26664

37775 ð8Þ

where M is the number of ray paths and N is the number ofpixels; and Aij ¼ pij � B0 cos hij � 1ffiffiffiffiffiffiffiffiffi

1�X ij

p ; pij is the same; hij

is angle between the phase direction of ith ray path andthe magnetic field at jth pixel; Xij is the value of X at jthpixel. All these parameters are related to the coordinatesof the wave front and these coordinates can be predictedby using a ray-tracing program. The application of theray-tracing technique allows for the estimation of the cor-rection factor (1 � X)�1/2, the angle h and even the projec-tion of the magnetic filed B onto the plane of interest if anadditional static magnetic field B model is provided alongeach ray path. In this way, one should be able to determinethe correct matrix A in Eq. (8).

The reconstruction process is conducted in two steps: inthe first step, differential Faraday rotation dX is put into areconstruction algorithm to generate ionospheric imagebased on a few assumptions: straight ray paths when calcu-lating the pij, unity correction factor c = 1 and a constantBLij = B0 coshij along the ray paths. In the second step,the first reconstructed image is used as the ionosphericbackground model in the ray tracing program to obtainnew sets of pij, correction factor cij = (1 � Xij)

�1/2 and BLij;These are weighting parameters for the electron density ineach pixel in the second application of the reconstructedalgorithm. This time Aij = pij · B0 coshij · cij. After the sec-ond step, the degradation of the first reconstructed imagedue to ionospheric refraction effects for HF signals willbe corrected (the ray paths of HF signals will bend whereasray paths of VHF/UHF signals can be considered to be

1270 L. Wang et al. / Advances in Space Research 42 (2008) 1267–1275

straight lines). Furthermore, the correction factor cimproves the accuracy when Faraday rotation of HF sig-nals is used. Key points in the reconstruction process areas follows: the differential Faraday rotation with a correc-tion factor is used as the measurement quantity in thereconstruction algorithm; The correction factor is not afixed number as Garriott (1960) and Titheridge and Heron(1971) used in their studies, but varies along the ray paths;The ray tracing program plays an important role to get theray path segments and the correction factor.

3. Simulation

Current ionospheric tomography campaigns utilize mea-surements of total electron content of the ionosphere byrecording group delay or differential phase of transion-spheric satellite signals for ionospheric image reconstruc-tions. These measurements are difficult for VHF andhigher frequencies and require reasonably sophisticatedinstruments (Ganguly et al., 2001). On the other hand, Far-aday rotation measurements need relatively simple instru-ments. In our studies, a new radio source HF frequencyfor the ionospheric tomography is proposed and resultsare simulated. Differential Faraday rotations of two closeHF frequencies (18 MHz and 17.985 MHz) were calculatedusing the ray-tracing technique with ionospheric modelscontaining irregular structures. A 5-transmitter-geometrywas used to cover around 7� latitude horizontal range.These ground transmitters are evenly spaced in the simula-tions for simplicity. The CASSIOPE satellite is assumed tobe passing over the chain of transmitters at the altitude of850 km.

The derivation of Faraday rotation is based on the QLapproximation. The rotation angle X varies during a satel-lite passage due to the effects of the slant TEC along thepath and the component of imposed magnetic field B par-allel to the ray direction BL = B0 cosh. In the North hemi-sphere, the rotation angle is relatively large because coshand slant TEC are large when the satellite is south of theground facility. As the satellite flies to the north, the rota-tion angle decreases because B0 cosh decreases to a verysmall value and overwhelms the increase of slant TEC.Finally, it may fall into the quasi-transverse (QT) region,in which the polarization is found to be elliptical at mosttimes (Davies, 1969) and should be avoided in the tomo-graphic reconstruction. If the transmitting frequency is18 MHz, high electron density is 2.0 · 106 el/cm3, and

Table 1Descriptions of the irregular models

Irregular models Maximum deviation withrespect to the background

Width of Gaussiandisturbance (km)

Mafreq

Model-1 +75% 600 5.1Model-2 +75% 600 5.1Model-3 +75% 600 11.3Model- Trough �55% 100 5.1

gyro-frequency is 1.5 MHz, the ratioY 4

T

4ð1�X Þ2Y 2L

in QLapproximation (where YT = Y sinh) is less than 1% whenthe elevation angle is between 40� and 140� at most partsof Canada, which will provide a reference for the size ofreconstructed image. For example, the horizontal span ofthe image will be 1000 km if the satellite orbit is at850 km altitude. The resolution for the reconstructionimage is 20 km for altitude and 50 km for horizontal dis-tance which is around 0.5� latitude. The value of the hori-zontal resolution is chosen because it can provide goodindications about the irregular features in the reconstructedimage without increasing the sampling rates of the receiverand the computation time.

Our irregular ionospheric models contain large-scalestructures, such as blobs and troughs and are describedin Table 1. The background electron density obtains itskey parameters (hmF2 & NmF2) based on a typical IRImodel with mathematical expressions for a cosine layerand a Chapman layer below and above the height ofhmF2. Irregular features have a Gaussian shape distributionas a function of horizontal distribution with different hor-izontal locations and various maximum plasmafrequencies.

Synthetic differential Faraday rotation and TEC valueswere obtained using ray-tracing technique in the presenceof the irregular models described above. The transmittingfrequencies for the differential Faraday rotation are at17.985 MHz and 18 MHz (HF) in the upper band of RRIon CASSIOPE/e-POP satellite. For comparison of HFand VHF/UHF tomography, simulations were also con-ducted by using TEC measurement at 150 MHz and400 MHz. Reconstruction algorithms in Eqs. (6) and (7)were applied on HF ionospheric tomography; On the otherhand, MART algorithm presented by Pryse et al. (1998)was used for conventional ionospheric tomography usingthe simulated VHF/UHF signals. Sets of differential Fara-day rotation and TEC measurements were then insertedinto corresponding reconstruction algorithms to create ion-ospheric images after 10 iterations. The first reconstructedimage were smoothed by applying a three-point movingaverage filter along the vertical direction in order to removesharp artifacts and then put into the ray tracing program toobtain ray path coordinates, h and the correction factor(1 � X)�1/2 along each path for the second application ofthe reconstructed algorithm. The resolution degradationdue to ionospheric refraction for HF ionospheric tomogra-phy is thereby solved.

ximum criticaluency (MHz)

Center of the irregularityrelative to the zero point (km)

Background electrondensity profile

200 Night-time�180 Night-time�180 Day-time100 Night-time

L. Wang et al. / Advances in Space Research 42 (2008) 1267–1275 1271

We started our simulation on Model Trough and thereconstructed images are shown in Fig. 1. A stratified ion-ospheric background with a Chapman layer as the topsideprofile and a cosine layer as the bottom side profile wasused as the ‘‘initial guess’’. The importance of peak heightand Hscale of the Chapman layer in the initial guess hasbeen demonstrated in various studies (Heaton et al.,1995; Raymund et al., 1990) and required additional crite-ria for determining the right values and computation time.The topic is beyond the focus of this paper so values ofNmf2, hmf2 and Hscale in the background of the originalmodels were simply used.

The original Model Trough is shown in Fig. 1a and thereconstructed image using VHF/UHF/TEC measurementby MART algorithm is shown in Fig. 1b. Fig. 1c and dpresent the second reconstruction results using HF/differ-ential-Faraday-rotation measurement by MART andART for this model respectively. The unit of the numberson the contour lines is 105 el/cm3. Triangles in the plot indi-cate the locations of the five transmitters at horizontal dis-tance �400 km, �200 km, 0 km, 200 km, and 400 km. Thereconstructed images differ in detail but successfully recon-struct the Model-Trough and detect the two enhancementsbeside the trough.

The examples of the reconstructed images for blobModel-3 are presented in Fig. 2 with the original modelshown in Fig. 2a. Fig. 2b presents the reconstructed resultusing TEC measurements at VHF/UHF frequencies andFig. 2c and d present the first reconstruction results usingHF method by MART and ART algorithms respectively.

Fig. 1. (a) Model trough (b) reconstructed image using VHF/UHF method bMART (d) second reconstructed image using HF method by ART. The unit

Model-3 has a more intensive electron density profiles:the maximum critical frequency is 11.3 MHz which is justa few Megahertz lower than the transmitting frequencies.Although the radio wave can penetrate the intense regionit must travel a longer distance to reach the satellite dueto the refraction. The first reconstruction results havehigher electron density profiles than the model, the maxi-mum density reached as high as 2 · 106 el/cm3. Theassumptions in the first reconstruction make matrix A havesmall value in the reconstruction algorithm and thereforegenerate a more intensive reconstructed image. Fortu-nately, this first reconstructed image will be put into theray-tracing program to obtain the new matrix A which con-tains higher value in each element and will correct the biasin the second run. The second reconstructed images forModel-3 are shown in Fig. 2e and f and contain somedistortion.

Fig. 3a–d present the reconstructed measurements usingboth VHF/UHF and HF method in the presence of Model-Trough and Model-3 respectively. The projection measure-ment for Fig. 3a and b is TEC, and the projection measure-ment for Fig. 3c and d is the differential Faraday rotation.The solid curves are the original synthetic projection mea-surement obtained by the ray-tracing technique andmarked by the location of the transmitters; the dash-dottedcurves are the reconstruction results. Both reconstructedTEC values and differential Faraday rotation values havegood agreement with their corresponding original values.One can see that the slant TEC values are 2–11 TEC Units(1TEC unit is 1 · 1016 el/m2) in the presence of Model-

y MART algorithm (c) second reconstructed image using HF method byof the numbers on the contour lines is 105 el/cm3.

Fig. 2. (a) Original Model-3; (b) reconstruction result for VHF/UHF method; (c) first reconstruction for HF method using MART; (d) first reconstructionusing ART; (e) second reconstruction using MART; (f) second reconstruction using ART. The unit of the numbers on the contour lines is 105 el/cm3.

1272 L. Wang et al. / Advances in Space Research 42 (2008) 1267–1275

Trough at night and 40–95 TEC units in the presence ofModel-3 during the day. On the other hand, Fig. 3c andd show that the differential Faraday rotations in the pres-ence of Model-Trough and Model-3 are 0.1–0.7 rad and2–6 rad respectively. The differential Faraday rotation isless than 2p so ambiguity is eliminated.

4. Discussion

Two iteration reconstruction algorithms ART in Eq. (6)and MART in Eq. (7) were applied in our simulations.Without a priori data, a stratified ionospheric profile wasused as initial guess for both methods. The relaxationparameter in the algorithm was carefully chosen to satisfya certain convergence rate. Both algorithms aim to mini-mize the residual iCAX � Fi tending to zero with increas-ing iterations. The estimated projection measurement andthe reconstructed image can be obtained after applyingiteration algorithms. However the behavior of the recon-struction error is very complicated and is defined both bythe number of iterations and measurement errors. Theerror r for the projection measurement is given by

r ¼ jjMP�RPjjjjMPjj ð9Þ

where MP is the measured projection such as TEC or dif-ferential Faraday rotation measurement and RP is recon-structed projection.

The image error d(l2) in the Euclidean l2 space is givenby

dðl2Þ ¼

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiPiðMIi �RIiÞ2

qP

iMI2i

ð10Þ

where MI is the Model image and RI is the reconstructedimage.

Table 2 compares the statistics of the projection errorsand image errors after 10 iterations using the VHF/UHFmethod and the HF method. In reality one does not havea reference model for comparison so that the number ofiterations has to been chosen by experience. With increas-ing iterations, the residual iCAX � Fi is always towardzero due to the nature for solving SLE, i.e. r alwaysdecreases. Qualitatively, the projection error will reach toless than 3% after 10 iterations. However, the image recon-

Fig. 3. (a, b) Comparisons of the simulated TEC and reconstructed TEC for different transmitter locations in the presence of Model-Trough and Model-3respectively. The solid curves are simulated TEC and the dashed curves are reconstructed TEC. The triangles show the locations of the 5 transmitters. (c,d). Comparisons of the simulated differential Faraday rotation and corresponding reconstructed values in the presence of Model-Trough and Model-3.

Table 2Statistics of the projection errors and image errors

Method Error types Model-1 Model-2 Model-3 Model-Trough

VHF/UHF (MART) TEC error (%) 2.58 2.69 2.73 3.13Image error (%) 6.98 8.03 8.99 9.81

HF (MART) Differential Faraday rotation error (%) 2.96 2.54 2.07 3.10Image error (1st reconstruction %) 9.25 9.78 23.50 11.63Image error (2nd reconstruction %) 7.56 7.57 9.04 10.61

HF (ART) Differential Faraday rotation error (%) 2.34 3.04 2.25 2.75Image error (1st reconstruction %) 10.21 9.34 23.4 13.27Image error (2nd reconstruction %) 7.50 7.28 8.52 13.29

L. Wang et al. / Advances in Space Research 42 (2008) 1267–1275 1273

struction error d(l2) may diverge as iteration numberincreases. Factors such as the hm F2, NmF2, and the scaleof the Chapman layer (Hscale) in the initial guess affectthe accuracy of the reconstruction result. Simulation resultsshowed that 7–15% reconstruction error can be reached in3–10 iterations. Comparable image reconstruction errorsfor VHF/UHF method and HF method after ray-tracingadjustment are presented in Table 2. When the transmittingfrequency is around 3 times the critical frequency (such asin the cases of Model-1, Model-2 and Model-Trough), thesecond reconstruction results have 1–2% less image errorsthan the first ones because of almost straight ray paths. Sig-nificant improvement after ray-tracing adjustment can befound in the case of Model-3 when the transmitting fre-quency is 1.5 times the critical frequency (the image errordecreased by more than 10%).

The intention of HF ionospheric tomography for theCASSIOPE/e-POP mission is to produce observations oflarge-scale ionospheric features and contribute to theunderstanding of plasma process in the ionosphere. How-ever, the reversed position of transmitter and receiver inthe CASSIOPE/e-POP mission is unique to ionospherictomography campaigns. Questions arise regarding thesatellite’s ability to distinguish the source from each trans-mitter without increasing the complexity of the receiver.We solve this problem in a straightforward way based ontime-multiplexing techniques. Each ground transmitter is‘‘ON’’ during a set interval and ‘‘OFF’’ otherwise. Suffi-cient time between ON/OFF states have to be left so thatthe received signals will not interfere with each other.Fig. 4 shows one example of a 5-transmitter-timing scheme.On the satellite, the RRI receiver will receive a series of

Tran1 0ms 125ms

Tran2

25ms Tran3

50ms Tran4

75ms Tran5

Start point 100ms

Fig. 4. An example of timing scheme for a 5-transmitter-arrangement.Pulse width is 10 ms and the repetition frequency is 8 Hz for eachtransmitter.

1274 L. Wang et al. / Advances in Space Research 42 (2008) 1267–1275

pulses with 10 ms width at a repetition frequency 40 Hz.On the ground, each transmitter waits for a time delay, rel-ative to a fixed start time, which depends on the position ofthe transmitter in the row: 25 ms · (No. of Transmit-ter � 1). It then transmits pulses with 10 ms width at a rep-etition frequency that depends on the total number of thetransmitters (for a 5-transmitter-geometry it is 40 pps/5 = 8 Hz). The GPS system will be used for synchroniza-tion. This arrangement allows identifying the informationfrom each transmitter by determining its relative delay inlater processing.

The Faraday rotation angle, X, can be easily determinedby the ratio of the signal amplitude received by two crosseddipoles, one varies with cosX and the other varies withsinX. In the simulations, the transmitting frequencies arechosen at 18 MHz and 17.985 MHz. The differential

Fig. 5. Map of the positions of dual-frequency ionospheric tomography tr80.56�W), Sudbury (46.37�N, 80.48�W) and Timmins (48.34�N, 81.22�W); ThRabbit Lake (53.06�N, 107.52�W) and Rankin Inlet (62.52�N, 93.11�W).

Faraday rotation angle of the two frequencies falls in therange of 0–2p for a typical ionosphere and this eliminatesany ambiguity in the measurements. The 15 kHz frequencydifference turns out to be an advantage in that the two closefrequencies can be received together using one digital recei-ver channel with 20 kHz bandwidth on RRI and separatedby filtering out each of them in the later processing.

In the future, four transmitters will be deployed in Lon-don (42.59�N, 81.14�W), Owen Sound (44.34�N, 80.56�W),Sudbury (46.37�N, 80.48�W) and Timmins (48.34�N,81.22�W) in Canada for testing the performance of the pro-posed HF tomography. Fig. 5 is the map showing the fourtransmitter locations and the sites of three CanadianAdvanced Digital Ionosondes at London (42.59�N,81.14�W), Rabbit Lake (53.06�N, 107.52�W) and RankinInlet (62.52�N, 93.11�W). The whole system can be relo-cated to an auroral region if our local HF tomographymeasurements work well during the initial CASSIOPEoperational period. Although the transmitters and thesatellite orbit may not be exactly in the same plane, alarge-scale tomographic ionospheric image can be derivedafter projecting the measurements to one plane. Significanterrors will be introduced in the final tomographic imagefrom a misplaced estimation of the peak height in the initialguess. Key parameters such as NmF2 and peak height canbe obtained from nearby CADI in real experiment. There-fore the coordinated observations from CADI in the e-POPexperiment will play a key role in the tomographicreconstructions.

ansmitters (+) at London (42.59�N, 81.14�W), Owen Sound (44.34�N,ree Canadian Advanced Digital Ionosondes (CADI) sites (#) at London,

L. Wang et al. / Advances in Space Research 42 (2008) 1267–1275 1275

5. Conclusions

Experiments of ionospheric tomography have been con-ducted using radio sources at VHF/UHF coherent frequen-cies transmitted from NISS satellite networks or using GPSsignals with radio occultation data. Unfortunately, co-locations in time and in space for verification purpose usingground radar facilities were never completely satisfied.With the launch of the CASSIOPE/e-POP satellite, a newHF radio source for ionospheric tomography will be avail-able. Differential Faraday rotations measurements of twoclose HF frequencies will be used in a reconstruction algo-rithm to generate a large-scale ionospheric image for thefirst time instead of the phase measurements of VHF/UHF coherent signals. The second-order approximationof the Faraday rotation is integrated into the reconstruc-tion process to improve the precision. It was found thatthe effects of path bending using HF frequencies on thereconstructed image can be removed by ray-tracing tech-nique based on the reconstructions of various ionosphericmodels. Two iterative reconstruction algorithms wereapplied and both generated satisfactory results. Recon-structed images using the HF method gave comparableresults with the VHF/UHF method.

By using HF ionospheric tomography, the sensitivityto ionospheric disturbance and the additional informa-tion from coordinated HF measurements in the missioncan be used to improve the reconstruction accuracy.However, it may suffer serious resolution degradationdue to the missing data during extremely rare intensiveionospheric activities when the critical frequency of theionosphere is close or even above the transmittingfrequencies.

References

Andreeva, E.S., Galinov, A.V., Kunitsyn, V.E., Mel’nichenko, Y.A.,Tereshchenko, E.D., Filimonov, M.A., Chernyakov, S.M. Radiotomographic reconstruction of ionization dip in the plasma near theEarth. J. Exp. Theoret. Phys. Lett. 52, 145–148, 1990.

Austen, J.R., Franke, S.J., Liu, C.H., Yeh, K.C. Application ofcomputerized tomography techniques to ionospheric research, in:

Tauriainen, A. (Ed.), Proc. Beacon Satellite Symposium. University ofOulu, Finland, pp. 5–35, 1986.

Davies, K. Ionospheric Radio Waves. Blaisdell Publishing Company,1969.

Davis, M.J., Da Rosa, A.V. Traveling ionospheric disturbances originat-ing in the auroral oval during polar substorms. J. Geophys. Res. 74(24), 5721–5735, 1969.

Ganguly, S., Brown, A., DasGupta, A., Ray, S. Ionospheric reconstruc-tion using Faraday rotation data: a new technique. Radio Sci. 36 (4),789–800, 2001.

Garriott, O.K. The determination of ionospheric electron content anddistribution from satellite observations, Part 1: Theory of the analysis.J. Geophys. Res. 65 (4), 1139–1150, 1960.

Greenwald, R.A., Baker, K.B., Dudeney, J.R., Pinnock, M., Jones, T.B.,Thomas, E.C., Villain, J.-P., Cerisier, J.-C., Senior, C., Hanuise, C.,Hunsucker, R.D., Sofko, G., Koehler, J., Nielsen, E., Pellinen, R.,Walker, A.D.M., Sato, N., Yamagishi, H. DARN/SuperDARN: aglobal view of the dynamics of high-latitude convection. Space Sci.Rev. 71, 761–796, 1995.

Heaton, J.A.T., Pryse, S.E., Kersley, L. Improved background represen-tation, ionosonde input and independent verification in experimentalionospheric tomography. Ann. Geophys. 13, 1297–1302, 1995.

James, H.G. High-frequency direction finding in space. Rev. Sci. Instrum.74 (7), 3478–3486, 2003.

Kersley, L., Pryse, S.E., Walker, I.K., Heaton, J.A.T., Mitchell, C.N.,Williams, M.J., Willson, C.A. Imaging of electron density troughs bytomographic techniques. Radio Sci. 32, 1607–1621, 1997.

Leitinger, R. Ionospheric tomography. Rev. Radio Sci., 581–623, 1999.MacDougall, J.W., Grant, I.F., Shen, X. Ionosonde Networks and

Stations, Rep. UAG-104, 21–27, World Data Cent. A for Sol. – Terr.Phys., Boulder, CO, 1995.

Mendillo, M., Klobuchar, J.A. Preliminary results of a multi-stationanalysis of total electron content variations during geomagneticstorms. EOS Trans. Am. Geophys. Union 54 (4), 386, 1973.

Pryse, S.E., Kersley, L., Mitchell, C.N., Spencer, P.S.J., Williams, M.J. Acomparison of reconstruction techniques used in ionospheric tomog-raphy. Radio Sci. 33 (6), 1767–1779, 1998.

Raymund, T.D., Austen, J.R., Franke, S.J., Liu, C.H., Klobuchar, J.A.,Stalker, J. Application of computerized tomography to the investiga-tion of ionospheric structures. Radio Sci. 25, 771–789, 1990.

Ross, W.J. Second-order effects in high frequency transionosphericpropagation. J. Geophys. Res. 70 (3), 597–612, 1965.

Swenson Jr., G.W. Reminiscence: at the dawn of the space age [satelliteradio missions]. IEEE Antenna Propagat. Mag. 36 (2), 32–35, 1994.

Titheridge, J.E., Heron, M.L. Second-order effects in the Faraday rotationof satellite signals. Radio Sci. 6 (5), 567–577, 1971.

Yeh, K.C., Franke, S.J., Andreeva, E.S., Kunitsyn, V.E. An investigationof motions of the equatorial anomaly crest. Geophys. Res. Lett. 28,4517–4520, 2001.