IEEE TRANSACTIONS ON INSTRUMENTATION AND MEASUREMENT, VOL. IM-23, NO. 4, DECEMBER 1974

CONCLUSIONSOf the three mechanisms thought to produce errors in

precise measurements at submillimeter wavelengths, thelight-pipe effect and diffraction effects have been shownto be negligible except at extremely long wavelengths,i.e., X > 0.5 cm. The third effect, that of reflections atinterfaces, is shown to be important where the ratio of"sample in" the beam to "sample out" is taken. However,correcting the measured values for this effect does notappear to be satisfactory and wherever possible the ratioof thick/thin samples should be taken.

ACKNOWLEDGMENT

The author wishes to thank Dr. J. Chamberlain, Dr.J. Haigh, and Dr. A. C. Lynch for helpful discussions.

REFERENCES[1] I. A. Ravencroft, and L. A. Jackson, "Proposals for a dielectric

rod transmission system.", in Proc. 1973 European MicrowaveConf., vol. 2, paper B13.2.

[2] G. W. Chantry, J. W. Fleming, G. W. F. Pardoe, W. Reddish,and H. A. Willis, "Absorption spectra of polypropylene in themillimeter and submillimeter regions." Infrared Phys., vol.11, pp. 109-118, 1971.

[3] E. M. Amrhein, and H. Heil, "Dielectric absorption of polymersfrom the millimeter to the far infrared region," J. Phys. Chem.Solids vol. 32, pp. 1925-1933, 1971.

[41 J. E. Chamberlain, J. E. Gibbs, H. A. Gebbie, "The deter-mination of refractive index spectra by Fourier spectrometry,"Infrared Phys., vol. 9, 185-209, 1969.

[5] H. A. Gebbie, and R. Q. Twiss, "Two-beam interferometricspectroscopy," Rep. Progr. Phys., vol. 26, pp. 729-756, 1966.

[6] G. J. Davies, and J. Chamberlain, "High accuracy submilli-meter-wave solution measurements," J. Phys. A, vol. 5, pp.767-772, 1972.

[7] P. E. Clegg, and J. S. Huizinga, "Improved performance ofRollin Insb electron bolometer," in Proc. IEIE Conf. InfraredTechniques, Reading, England, pp. 21-30, 1971.

[8] R. W. Ditchburn, Light. London: Blackie, p.163, 1952.[91 G. W. F. Pardoe, "Molecular absorptiont in the 1-100 cm-'

region of the electromagnetic spectrum," Ph.D dissertation,Univ. College Wales, Aberystwyth, Wales, 1969.

[10] J. E. Chamberlain, "Interface effects in Fourier transformspectroscopy," Infrared Phys., vol. 12, pp. 145-164, 1972.

[11] G. J. Davies, "Dielectric and far infrared studies of initra- arndinter-molecular motions," PhD. dissertation, Uniiv. CollegeWales, Aberystwyth, Wales, 1971.

[12] G. W. Chantry, and J. Chamberlain, Polyymer Science Ed.Amsterdam: A. D. Jenkins, North-Hollanid, p. 1371, 1972.

[13] G. W. Chantry, Submillimeter Spectroscopy, New York:Academic Press, 1971.

[14] C. H. Collie, J. B. Hastead, and D. M. Ritsoni, "The cavityresonator method of measuring the dielectric constants of polarliquids in the centimeter band," Proc. Phys. Soc., vol. 60,pp. 71, 145, 1948.

[15] J. W. Ryde, D. Ryde, Res. Lab. Rep. General Electric Co.Ltd., Wembley, England, Rep. 8670, 1945.

[161 R. W. Rampolla, R. C. Miller, and C. P. Smyth, "Microwaveabsorption and molecular structure in liquiids. XXV: Measuire-ments of dielectric constant and loss at 3*1-mm wavelengthby an interferometric method." J. Chem. Phys., vol. 30, pp.566-573, 1959.

[17] I. R. Dagg, and G. E. Reesor, "Dielectric loss measuiremenitson nonpolar liquids in the microwave region from 18 to 37 G Hz."Can. J. Phys., vol. 50, pp. 2397-2401, 1972.

[18] S. K. Garg, H. Kilp, C. P. Smyth, "Dielectric relaxation, far-infrared absorption, and intermolecular forices in noiipolarliquids," J. Chem. Phys, vol. 49, pp. 2551-2562, 1968.

[19] G. J. Davies and A. C. Lynch, to be ptublished.

Submillimeter-WXfave Dielectric Measurements on Absorbing Materials

JOHN CHAMBERLAIN, M. N. AFSAR, DAVID K. MURRAY, G. DAVID PRICE, AND AM. S. ZAFAR

Abstract-A summary is given of recent developments in disper-sive Fourier transform techniques for the measurement of the fre-quency variation of the complex refractive index in the range 100GHz-9 THz. Progress in overcoming the special problems associatedwith liquid and solid specimens of medium and strong absorptionis reported and the current measurement capability is discussedwith the aid of experimental results obtained using specially con-structed equipment.

I. INTRODUCTION

MEASUREM1ENTS at discrete frequencies v of thecomplex relative permittivity e = n2 of liquid and

solid specimens can be made by "microwave" techniques

Manuscript received July 3, 1974; revised September 6, 1974.J. Chamberlain, deceased, was with Division of Electrical Science,

National Physical Laboratory, Teddington, Midd., England.1). K. Murray and G. D. Price are with D)ivision of Electrical

Science, National Physical Laboratory, Teddington, Midd., England.M. N. Afsar is with Birbeck College, London, England.M. S. Zafar was with Birbeck College, London, England. He is

Inow with the University of Punjab, Lahore, Pakistan.

up to about 300 GHz (X = 1 mm) and the complex refrac-tive index n = E1I2 can be measured beyond 600 GHz usinggas lasers as sources in free-wave "optical" techniques[1]. Time-domain spectrometry (TDS) is being developednotably by Suggett, to find the permittivity spectrumn andhas so far reached 10 GHz from lower frequencies [2]. Athigher frequencies, dispersive Fourier transforrm spec-trometry (DFTS) is being perfected to yield the complexrefraction spectrum directly.The viability of DFTS methods was established almost

simultaneously by Russell and Bell who worked in theUnited States mainly on solids [3] [-)] but also on gases[6], [7] and by Chamberlain et al. who worked in Englandon all three phases [8]-[10] but coincentrated on liquids[11]-[13] which present unique problems. As DFTS iscurrently usable from about 100 GHIz upwards, there isnow overlap between low-frequency Fourier transformspectrometry (FTS) data and high-frequency microwavemeasurements which, among other advantages, provides a

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IEEE TRANSACTIONS ON INSTRUMENTATION AND MEASURFMENT, DECEMBER 1974

useful comparison of measurement capabilities. The bulkof the basic work was on "transparent" materials. Effortis now directed towards improving accuracy and broaden-ing the techniques, especially with respect to applicationsinvolving materials with high absorption. This paper dealswith measurements on su-ch materials, with particularemphasis on finding the spectrum of the real part n (v)of the complex refractive index,

A (v) = n (v) i (ca (v) /4irv) (I)

in which a (v) is the power absorption coefficient per unitlength [Np m-']1 and c is the speed of light [m s-1].Although DFTS can yield both a (v) and n(v), it is prefer-able, if it is experimentally possible, to determine a (v)from power transmission data using conventional FTS[14]. This is now a standard and well-established pro-cedure even though it is still subject to refinement, par-ticularly in relation to systematic errors.

II. THEORYIn DFTS, n(v) is found by placing the specimen in one

arm of the two-beam interferometer which is the basis ofa Fourier transform spectrometer [14]. This gives ashifted and distorted interferogram. If the voltage inter-ferogram recorded with the specimen present is V(x) andif the reference interferogram is Vo(x), where x is pathdifference, the ratio

V(x) I/5I V (x)}I (v) - fn (A(v);position) (2)

of their full Fourier transforms it } gives the positionalinsertion loss 2(v) [15]. The resolution R is determinedby the range-D < x < D of the interferograms accordingto R l 1/(cD).The form of the relation between S (v) and hi (v) depends

on both the nature and location of the specimen. Honijket al. [16], [17] have given a full treatment with expres-sions which reduce to those given by Chamberlain in asimpler presentation [15]. Although less rigorous, theseexpressions are, nevertheless, sufficiently precise for cur-rent measurement capability.

In DETS, S (v) is complex2 anld Ai() is calculated fromit at each v via the amplitude transmiissivity t(v) for trans-mitting specimens or via the amplitude reflectivity r(v)for opaque specimens. t(v) is measured if a sufficientlythin layer d of material can be obtained to give a (v) d - 1;otherwise, a very thick layer d' is produced and r(v) ismeasured. In the case of 'r(v) measurements, the experi-mental requirements are very demanding but the calcula-

'Attention is drawn in paper to the statement of power absorp-tion per unit length in the form neper per centimeter or neper permeter. The reader is cautioned that "neper" here, by conventionin the submillimeter field, is a unit defined as the unqualified naturallogarithm of a power ratio, i.e., ln P/P2F. This unit is therefore onlyhalf the magnitude of the neper as generally used in electrical engi-neering and unambiguously defined as IIn PI/P2. Thus, in place ofthe relation 1 N = 8.686 dB, which follows from the latter definition,the appropriate conversion in this context is 1 N = 4.343 dB.

2 In conventional FTS, £(v) is real (£(v)) and yields only powerinformation (transmission or reflection); n/v) is not readily calculatedfrom this.

TABLE I

Type ofMeasurement

for n(v)

[Np.m-1 Description of Material 7(v) r(v)

< 150 very transparent V< 1500 transparent V/

1500 < a < 15 000 absorbent transmittiVigv>15 000 very absorbent ( V/)aV>>15 000 opaque

a Editing technique not usable for liquLids (see Section I1V-A).

tion of A(v) is fairly straightforward; in the case of t(v)measurements, the practical constraints are slightlyrelaxed but the calculation is more involved and a fullprocedure is, strictly, iterative [16], [17]. This calculationis, in principle, exact but it is, however, also extremelysensitive to practical shortcomings and an interim stagehas been to avoid the need for iteration wherever possible.This can be done, for example, by careful placing of thespecimen (for solids) or by editing interferograms (forliquids) to isolate structure which can be related fairlysimply to either n(v) or a (v). These procedures (particu-larly the editing) require, of course, care and skill in thepractical execution if the uncertainties and the effects ofapproximations are to be minimized.

III. CATEGORIZATION OF MATERIALSWe categorize our materials according to absorption

a (v) rather than loss e"(v). Since dielectris loss is

,, c n(v) a(v)e (v) = v

27r v (3)

the magnitude of e" varies with v for a given a and doesnot provide a good criterion for transmissioin levels inquasi-optical measurements in which the important paramn-eter is exp [-a(v)d]; thus, a transparent material canhave loss as high at low frequency as a "strong absorber"at higher frequency.Somewhat arbitrarily setting exp (-ad) to lie in the

range 0.3 (add 4 1.2) to 0.6 (ad c 0.5) for acceptablesignal levels we can define transparent and "absorbent"materials as those for which large anid small d, respectively,satisfy our criterion. Details are given in Table I.

IV. MEASUREMENT TECHNIQUESThe measurement of t(v) for transparent and absorbing

solids and for transparent liquids is established in the farinfrared and submillimeter-wave regions and is not con-sidered here [14], E18], however, the recent extension atthe National Physical Laboratory (NPL) of DFTS toabsorbing liquids is discussed and assessed as is also themeasurement of r(v) for very absorbing or opaque liquidsand solids.

A. Amplitude Transmissivity of Absorbing LiquidsCurrently, for liquid measurements, the interferometer

is arranged with the fixed-mirror (specimen) arm vertical:

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CHAMBERLAIN et al.: MEASUREMENTS ON ABSORBING MATERIALS

175' A n (v)1-525

Oct15520

1 70

1.515

1 65 _1 510

n (v) X 1 1(5 2 2 5 3

1*0 v [THz]

1-60

1j55 -.

Oct

1-50E. i 1

2-0 - : . EtOH

19 _

n{v)17_

16_

1.5 _A II

1. 1.

0102 005 01 02v [THZ]

005 2 3

Fig. 1. Upper: Refraction spectrum n(v) of liquid chlorobenzene at-22°C. Data from inset shown as solid line ; DFTS datataken from earlier work [28] -.-.-; estimate ....; various micro-wave points referenced in [28]. Inset: Comparison of editing(---) and subtraction (-) techniques, and laser data (@,03).Resolution 60 GHz. Lower: Refraction spectrum n(v) of liquidethanol at -22°C. Solid line ( ) from DFTS using subtractiontechnique; laser result 0; estimate ....; various spot data refer-enced in 119]. Resolution 60 GHz.

0-B

06

04~

02

IDDr

F5Z

S °

0)I51 l15 2 25 3 35 4

v [THz]

Fig. 2. Modulus rWL(v) and phase OWL(V) of amplitude reflectivityof a window-liquid interface averaged from three independentmeasurements for TPX and liquid water. Resolution 60 GHz.

downwards for i(v) and upwards for r$(v). For the t(v)measurements, the liquid is not contained against rigidflat windows because of materials and other problems[11], [15] but rests as a gravity-held plane-parallel layeron a stainless steel mirror in a chamber separated fromthe main body of the evacuated interferometer by a

polyester window. In general, the interferogram is the

v [THzlFig. 3. (a) Modulus r(v) and phase 0(v) of amplitude reflectivity of

a crystal (KBr) averaged from ten independent sets of measure-ments. Resolution 120 GHz. (b) Standard deviation of 7r - 0(v).

sum of a number of interference signatures [17], [19]:

V(X) = VR(X) + VT(X) + VM(X) (4)which represent, respectively, radiation reflected (R)from the first (upper) surface of the specimen, transmitted(T) through it (twice) via reflection from the interferom-eter mirror, and multiply reflected (M) within it. Thecenters of R and T are about 2nid apart, where ni is a meanrefractive index, and the center of R is a distance 2d-afrom x = 0, where a is due to phase shift on reflection andis, in general, not determinable. Calculations indicate thatit is typically a few micrometers. Use of the completeexpression (4) in (2) requires iterative procedures for thecalculation of n(v) (and a(v) ). However, the T term alonecan be simply related to n(v) through

n(v) 1-1- phT(V)47rvd (5)

where

(V) .1 VTV() (v) exp -47riv[E(v) 1]d/c}.

(6)

In (6), S(v) is a reflection-loss term which is a functionof n(v) but, being real (to a good approximation), it doesnot affect ph T(m(V). It follows from (6) that

(v)(v) 4 d-IEln S (v)-lIn """T(v ) ]

At NPL we have concentrated on techniques for iso-lating VT (X) from V(x) in order to enable (5) to be usedfor liquids. Initially, for transparent liquids, simple editingand smoothing to the noise level were used to remove

from V(x) all structure other than that believed to beassociated with VTW(X [12]. This procedure was aided bymaking d sufficiently large to prevent VR(x) and VT (X)from overlapping significantly. For small d (essential forabsorbing liquids), VR(x) overlaps VT (x) amd cannot beremoved by simple editing. The principle of our new

TPX - H20I_O

-0.

- rWL(V)

___ I i I i

1- 4 .f

1-0. JA

0.

485S

5

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IEEE TRANSACTIONS ON INSTRUMENTATION AND MEASUREMENT, DECEMBER 1974

procedure is to record a third interferogram V'(x) for athick layer d' (>d) of liquid to obtain an R signature only(since Vr'(x) and VM'(x) are negligible), shift its centerthrough p = 2(d' - d) from x -2d' to x -2d togive

V'(x) * 6(x - p) VR'(x) *(X - P) VR"(X) (7)

edit the very small VM(x) from V(x) if it can be discerned,and use the relation

V (X) - VR" (X) C V (X) - VR (X) = VT (X) (8)

to find VT(x). The procedure is, in practice, more com-plicated because of incoherent sampling of the R and R'signatures in the digital interferogram records and it hasto be performed, using transforms, in the frequencydomain. This procedure is also applicable to transparentliquids and is more acceptable than editing since, inprinciple, all the R structure is removed from V(x); theprice paid is the addition of noise introduced with the thirdinterferogram.We have constructed a new modular interferometer for

t(v) measurements on liquids which is more precise andmore versatile than earlier instruments [19]. It can beused with wire-grid beam dividers or with dielectric beamdividers [1]. These alternatives permit the range 70-6GHz (wire grid) or 3-12 THz (6-/um polyester dielectric)to be covered. Usually only wire grids are used as thesegive a high virtually featureless passband below cutoff.For 10-,um tungsten wires with 25-,um spacing, cutoffnear 6 THz gives a band covering the range ofgreatest current interest in liquid studies. The radiationwithin the interferometer is collimated and amplitude orphase modulated, AM or PM [20], by choice at a fre-quency fo appropriate to either the Golay cell or InSbRollin detector. PM is preferable because of the advantageit affords in the accurate recognition signature centers.The interferometer is compensated to give no change ofpath difference with change of temperature (at x = 0)and is temperature controlled to 1 or 2°C to reduce thermalchanges in x away from x = 0. A special stepped path-difference (increments ,B = 2m ,um, m = 1,2,--. by selec-tion) has minimal periodic error and high reproducibility(-0.3 tim). The thickness d is found (to within an un-known 23) from the interferogram V(x) in terms of ,B andfractions thereof. The minimum usable value of d is setby the surface tension and viscosity of the liquid and is ofthe order 0.2 mm. This restricts the technique to materialswith a(v) less than about 15000 Np*m-1 Eexp (-ad)0.05].The subtraction and editing procedures have been com-

pared over the submillimeter-wave range 1-3 THz forchlorobenzene whose refractive index has been measuredpreviously. Using the same interferograms Vo(x) andV(x), we find agreement of n(v) to within better than0.001 with more noise on the subtracted index, as expected,due to the use of V'(x). The spectra (R = 60 GHz) havethe same shape as earlier results, pass through the laser

point at 891 GHz and show continuity with literaturemicrowave data.3The technique has now been applied at millimeter and

submillimeter wavelengths to absorbing liquids like thealcohols to give spectra not otherwise obta riable. For suchsystems, comparison with microwave and laser data iscurrently the only way to obtain an assessmient of thesenew spectra. The indications are that they are satisfactoryalthough there are differences which lie outside the esti-mated uncertainties (up to O0.04 depending on a(v)).An error in d alters both the level and shape of n(v)

and is revealed by lack of reproducibility for differentthicknesses d and by discontinuity with other data (micro-wave and laser [1]). It is clear that for practical thick-nesses, 6 << d and a can be legitimately neglected in rela-tion to currently attainable noise levels. A phenomenonwhich alters d and distorts the interferogram is evaporationof the liquid; this is minimized by allowing the vapor andliquid to come to equilibrium. Further problems are pro-duced by an abzorbing vapor. They can be lessened byfiushing the space above the liquid with dry air, but thisaccelerates the reduction of d. Confinement of the liquidagainst a suitable flat rigid window would eliminate theevaporation problems. Until recently, no suitable materialof sufficient size (-50-mm diameter) was available, butthere are now very transparent (but highly reflecting)semiconductors and a variable-thickness cell is underconstruction.4

B. Amplitude Reflectivity of Very Absorbing Liquids

When the absorption of the material is so strong that animpracticably thin layer would be required for trans-mission measurements, reflection from a flat surface of abulk specimen can be used to yield the amplitude reflec-tivity.5 A fixed reference plane for the surface is essentialas measurement of VR (x) from a free surface of the liquid,while adequate for a correction procedure in i(v) measure-ments has proved incapable of giving ni(v). The liquid isplaced against an optically polished rigid tranisparentwindow which terminates one arm of the interferometer.The reference reflector is also a liquid (mercury). Thecollimated radiation falls at normal incidence on thewindow. For a sufficiently thick window dt, the signatureV1, (x) due to reflection from its front face lies outside therange x < D of the interferogram used (2ii,dw > D isa useful criterion). Then, V(x) = VR(x), where R refersto the back (upper) face of the window [the window-liquid interface (WL) ], and, using (2),

_S(v=-rWL(V) nt(v) - ii-(v)-C(V) = -' L (V) =

-A V+it(V (9)

3A direct comparison with new microwave data is under waywith R. Finsy and R. van Loon, Free University of Brussels, Bel-gium, using chlorobenzene as test material.4In conjunction with D. D. Honijk and W. F. Passchier, Uni-

versity of Leiden, The Netherlands. The same chamber would beused for rv) measurements (see Section IV-B).6Note that for a free layer dmin 0.2 mm, whereas for a con-fined layer dmi. can be an order of magnitude less.

486

CHAMBERLAIN et al.: MEASUREMENTS ON ABSORBING MATERIALS

In (9), f,i (v) is the complex refractive index of the windowwhich is found also from DFTS from t(v). For a trans-parent window this index is real and varies little with v.The center of VR(x) is displaced from x = 0 by a small

amount AWL and the phase ph 2 (v) of 2 (v) is directlyrelated to this. As the values calculated for A (v) (par-ticularly a (v)) are very sensitive to ph Z (v) an extremelystable interferometer with an accurate and reproduciblemirror drive is required. This requirement is much morestringent thani in t(v) measurements where the phase of2(v) depeinds on 2 (nh- l)d = x which can be two ormore orders of magnitude greater than 5WL. Thus, anerror Ax gives Ax/6WL >>Ax/x. No assessment of theeffect on ph £2 (v) is realizable for a Ax which varies withx, but a simple shift Ax of the center of V(x) to simulatean error in 5WL can be used and for Ax = 0.5 ,.m this leadsto an error of about 0.04 rad at 4 THz and 0.08 rad at8 THz, which is near the maximum that can be tolerated.We have constructed a modular interferometer for

?r(v) imeasurements on liquids which is an improvementon an earlier setup [21]. The drive and temperaturecontrol are similar to that described for the t(v) systembut the r(v) instrument is flushed with dry air sinceevacuation would distort the window. Only PM is usedbecause it is essential in WL (v) measurements to eliminatethe relatively large background voltage V that wouldotherwise accompany V(x) [20]. Currently, the liquidsrest on a 60-mm-diameter 10-mm-thick TPX polymerwindow but this material limits the technique to speci-mens for which n(v) - n,(v) n-1.46 is notnegligible and for which TPX is chemically inert. Thiseliininates most organic systems of interest and we haveso far been confined to aqueous systems which have large,but slowly-varying, absorption. For water, we find that?WL (v) varies little over the range 1 to 4 THz and has avalue near 0.25 with an uncertainty of about :b0.02;

-- OWL(v) rises slightly with increasing v with valuesaround 0.75 rad (uncertainty ±0.05 rad). The valuesdeduced for a (v) are strongly dependent on OWL (v) (muchmore so than n (v)) and are very sensitive indicators of theperformance of the instrument. Currently, we find a (v)in acceptable agreement with laser values recorded at891 GHz and 2.54 THz [22] and with values calculatedfromnmeasurements of the power transmitted by verythin (e.g., 60-,um) cells. Our uncertainty, for an a(v)rising from 20 000 to over 80 000 Np *m-1 between 1 and4 THz, is about i2500 Np m-l.The refraction spectrum n (v) falls slowly with increasing

v from 2.20 to 1.98 between 1 and 3 THz and shows goodcontinuity with microwave results and agreement withthe rather sparse data available at submillimeter wave-lengths. A shift Ax -+2.5 ,um raises n(v), for example,by 0.10 at 3 THz, anid provides further evidence for theimportance of accurate OWL (v).

C. Amplitude Reflectivity of Very Absorbing SolidsA flat surface of the specimen exactly replaces one of the

interferonmeter mirrors in the technique devised by Bell

[23]. The arrangement for handling and interchangingthe mirror and specimen6 needs to be highily reproducibleand stable as does the interferometer itself, because of thegreat importance of phase stability. The interferogramV(x) contains only one signature VR(x) and the comnplexrefractive index is found (without iteration) from (1)with V(x) = VR(x) and

t(v) -'(v) -(? 1IIC()= v) nt(v) + I(10)

We have perfected a modular interferoIneter for r(v)measurements oni solids (outlined in [27]). It is funda-mentally similar to those used for liquids (but currentlyhas only a dielectric beamn divider and amplitude modula-tion of the radiation). The instrument is evacuated. Thevertical arm supports a chamber which houses a speciallyconstructed mechanical arrangement for handling up tofour reflectors aind placing each in turn in a reproduciblemanner (to within 0.25 Mrm) on three rigid supportslocated in a well-defined and stable plane. Beam-balancedevices reduce the (equal) net weighits of mirror orspecimen to minimize sinkage onto the three supports.This aspect is specially important for soft specimens (e.g.,like KBr or KDP). The method is nondestructive butcurreintly operates only at ambient temperature.KBr has a strong reststrahlen band itear 3.3 THz and

is a favorite test material for r (v) nmeasuremenlts [24],[25]. The phase 7r - 0(v) varies conisiderably from nearlyzero to 2.2 rad and the peak, which is structured, occurswhere r (v) is least (and where [r(r) ]2 is only 0.0015). It isnoteworthy that such detailed (and very important)structure can be recorded in a region where the reflectivityis so low. The reproducibility of the phase is about ±t0.03rad below 6 THz and two or three tinmes -larger above(where the signal in our interferoineter was low). It isimportant that the phase be nowhere negative; a dis-placement Ax --2.5 Am makes 0(v) negative helow3 THz and above 6.5 THz in the wing regionls and rendersa (v) and e" (v) negative similarly; it also decreases themagnitude of the dispersion. On the other hand, a shiftAx = +2.5 Am increases the mnagnitude and alters themaximum value of a (v) from 670 000 to 925<) 000 Np. m-1and that of e"(v) from 35 to 74.

V. DISCUSSIONThe foregoing demonstrates that there have been real

advances in DFTS which enable a wider variety of mate-rials to be studied than hitherto. There is, however, stillneed for improved accuracy, particularly at longer wave-lengths (X > 1 mm), need for extension to 5-mm wave-length, and need to obviate some of the present probleinsand limitations such as those, for example, which prevent

6In a recent development by Parker et al. [24], part of the speci-men is metallized for reference purposes. However, the technique isinot nondestructive and four interferograms are nieeded for thecalculation of n(v). The specimen may be cooled with greater easethan in the replacement method of Bell [231, Johnsoin and Bell 1251,Gast and Genzel [26], and ourselves.

47

IEEE TRANSACTIONS ON INSTRUMENTATION AND MEASUREMENT, DECEMBER 1974

solutions from being studied (evaporation problems) orthe temperature of the specimen from being varied(especially acute for solids where a wide temperaturerange accompanied by nondestructive mounting of thespecimen is desirable). So far as liquid measurements areconcerned, the construction of a special chamber for bothr(v) and t(v) measurements should solve many of theproblems and should enable full iterative calculations tobe employed where they are applicable.

Direct comparisons of differing techniques, alreadystarted in a limited way, need to be made for as many dif-ferent methods as possible, preferably with the samespecimen. These would be especially important in themicrowave-optical overlap region around X = 2 to 4 mm.The purpose would be to discern systematic errors in thevarious methods and, if possible, to establish standardmaterials for the testing and calibration of equipment.

REFERENCES

[1] J. Chamberlain, "Submillimetre-wave techniques," in HighFrequency Dielectric Measurement, J. Chamberlain and G. W.Chantry, Eds. Guildford: IPC, 1973, pp. 104-116.

[2] A. Suggett, "Time domain spectroscopic measurements," inHigh Frequency Dielectric Measurement, J. Chamberlain andG. W. Chantry, Eds. Guildford: IPC, 1973, pp. 98-103.

[3] E. E. Russell and E. E. Bell, "Measurement of the far infraredoptical properties of solids with a Michelson interferometerused in the asymmetric mode-the vacuum interferometer,"Infrared Phys., vol. 6, pp. 75-84, 1966.

[41 , "Measurement of the optical constants of crystal quartzin the far infrared with the asymmetric Fourier transformmethod," J. Opt. Soc. Amer., vol. 57, pp. 341-348, 1967.

[5] , "Optical constants of sapphire in the far infrared,"J. Opt. Soc. Amer., vol. 57, pp. 543-544, 1967.

[6] R. B. Sanderson, "Measurement of rotational line strengths inHCI by asymmetric Fourier transform techniques," Appl. Opt.,vol. 6, pp. 1527-1530, 1967.

[71 W. H. Robinette and R. B. Sanderson, "Dipole moment ofHBr from far infrared dispersion measurements," Appl. Opt.,vol. 8, pp. 711-712, 1969.

[8] J. Chamberlain, J. E. Gibbs, and H. A. Gebbie, "Refractometryin the far infrared using a two-beam interferometer," Nature,vol. 198, pp. 874-875, 1963.

[9] J. Chamberlain and H. A. Gebbie, "Submillimetre rotationalline strengths in the hydrogen halides," Nature, vol. 208, pp.480-481, 1965.

[10] J. Chamberlain, J. E. Gibbs, and H. A. Gebbie, "The determina-

tion of refractive index spectra by Fourier spectrometry,"Infrared Phys., vol. 9, pp. 185-209, 1969.

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[191 J. Chamberlain, M. N. Afsar, and J. B. Hasted, "Direct meas-urement of refraction spectrum of ethanol at submillimetrewavelengths," Nature Phys. Sci., vol. 245, pp. 28-30, 1973.

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[22] M. S. Zafar, J. B. Hasted, and J. Chamberlain, "Submillimetrewave dielectric dispersion in water," Nature Phys. Sci., vol. 243,pp. 106-109, 1973.

[23] E. E. Bell, "Measurement of the far infrared optical propertiesof solids with a Michelson interferometer used in the asym-metric mode," Infrared Phys., vol. 6, pp. 57-74, 1966.

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[26] J. Gast and L. Genzel, "An amplitude Fourier spectrometer forinfrared solid-state spectroscopy," Opt. Commun., vol. 8, pp.26-30, 1973.

[27] J. Chamberlain, "Measurement in the submillimeter-wave-length region," IEEE Trans. Instrum. Meas., vol. IM-21, pp.438-442, Nov. 1972.

[28] M. Davies, G. W. F. Pardoe, J. Chamberlain, and H. A.Gebbie, "Character of absorption in the far infrared by polarmolecules in the liquid state," Trans. Faraday Soc., vol. 64, pp.847-860,1968.

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