Absolute radiometers (PM06) and their experimentalcharacterization
Robert W. Brusa and Claus Frbhlich
During the late Seventies a second generation of absolute cavity radiometers based on the principle ofsubstitution of electrical power for radiative power was developed for solar radiometry. The operatingprinciple and details of the realization of this new radiometer (PMO6-type) are described. To betterunderstand these instruments and to improve their accuracy, the main effort was concentrated on thedevelopment of independent laboratory experiments to characterize them. It is demonstrated that thischaracterization allows an accuracy of solar radiometry of 0.12% from space and of 0.17% from the ground.
I. Introduction
The design and construction of modern absoluteradiometers to measure solar radiation started in thelate Sixties. The detector in these radiometers is aheat flowmeter with a cavity to absorb the radiationand with provisions for electrical calibration of itssensitivity. Although such instruments are currentlyused primarily to measure solar irradiance at theground or from space and to calibrate climatologicalradiation networks, the main reason for their originaldevelopment was radiation metrology related to space-craft testing using solar simulators.' Later develop-ments were motivated more by the need for betterradiometers for laboratory work or for solar measure-ments.2 -5 The accuracy of these first generation radio-meters was limited mainly by the uncertainties in-volved in the assumptions for the computations of thefactors to account for deviations from their ideal be-havior.
Soon after the first international comparisons ofsuch radiometers6 in 1970, it was realized that thesecomputations were inadequate to reach the goal ofhighly accurate radiometry, primarily due to the un-certainties of the underlying assumptions. The directdetermination of each individual correction factor by
Robert Brusa is with ESA, ESTEC, Space Science Department,2200 AG Noordwijk, The Netherlands, and C. Fr6hlich is with WorldRadiation Centre, Physikalisch-Meteorologisches ObservatoriumDavos, 7260 Davos Dorf, Switzerland.
specific experiments seemed to be the only feasibleway to overcome these inherent limitations. Thus, aserious effort was made during the Seventies of PMODin the development of independent laboratory experi-ments to characterize the second generation of radiome-ters developed at PMOD, the PMO6-type radiome-ters. The mutual interaction between the design ofthe radiometers, on the one hand, and the increasingexperience with the characterization experiments, onthe other hand, improved the accuracy of these instru-ments substantially and pushed the accuracy limitvery close in the 0.1% goal of room temperature radio-metry.
In the following, the present design of the PMO6-type absolute radiometer and its characterization ex-periments will be described. The results of intercom-parisons of seven fully characterized radiometers willdemonstrate the high degree of reliability of the char-acterization method adopted.
II. PMO-6 Absolute Radiometer
A. Instrument Description
The PMO6 radiometer is based on the measurementof a heat flux using an electrically calibrated heat fluxtransducer. The radiation is absorbed in a cavitywhich ensures a high absorptivity over the spectralrange of interest for solar radiometry. The heat fluxtransducer consists of a thermal impedance with resist-ance thermometers to sense the temperature differ-ence across it. A schematic drawing of the PMO6detector is shown in Figs. 1 and 2. Heat developed inthe cavity is conducted to the heat sink of the instru-ment and the resulting temperature difference acrossthe thermal impedance is sensed. The sensitivity ofthe heat flux transducer is calibrated by shading thecavity and measuring the temperature difference whiledissipating a known amount of electrical power in a
Fig. 1. Mechanical drawing of the PMO6 absolute radiometer. Infront of the detector, in good thermal contact, is the so-called muf-fler. It defines an infrared reference for the cavity, reduces scat-tered light, and protects the receiver from the effect of wind. Infront of it are the shutter and a view-limiting aperture. The dis-tance between the view-limiting and the detector aperture is 95.4mm, yielding a viewing angle of 50 and a slope angle of 10. The
weight of the instrument is 1600 g.
heater element which is mounted inside the cavity. Itis advantageous to determine the electrical powerwhich is needed to produce the same temperature dif-ference as was observed with the cavity irradiated,because in this case the heat losses are the same duringradiative and electrical heating-even if nonlinear ef-fects are involved. During practical operation of theinstrument, an electronic circuit (Fig. 2) maintains thetemperature signal constant by controlling the powerfed to the cavity heater-independent of the mode,that is, whether the cavity is shaded or irradiated.The substituted radiative power is then equal to thedifference in electrical power as measured during theshaded and irradiated periods, respectively.
Changes of the temperature of the heat sink mayalso produce a temperature signal. Therefore, twoheat flux transducers with matched time constants arecombined to form a differential heat flux transducer.The temperature difference measured between thetwo tops of the thermal impedances is then-depend-ing on the quality of the matching-largely insensitiveto changes of the temperature of the heat sink.
The instrument measures irradiance, hence its re-ceiver area has to be accurately known. A precisionaperture of nominally 5-mm diameter is placed in frontof the primary cavity. A second aperture of 8.35-mmdiameter acting as a view-limiting aperture and defin-ing a field of view of 50 is placed 95.4 mm in front of theprecision aperture. This geometry puts only a moder-ate +0.75' requirement on the solar pointing. All theapertures of the so-called muffler shown in Fig. 1 are inthe shadow of the view-limiting aperture. The pur-pose of the muffler is to reduce the sensitivity to windeffects and to increase the thermal mass of the heatsink of the instrument.
The cavities are made of electrodeposited silver andare gold-plated on their outside. They are solderedonto the thermal impedances made from stainlesssteel. The thermal impendances are in turn solderedto the copper heat sink of the instrument. The heaterelement in the cavities is a flexible printed circuit. Itis etched in a 5-,gm constantan foil supported by a 20-,um Kapton foil. It is glued to the cone-shaped part ofthe cavity at the same spot as the radiation enteringthe cavity first impinges on the cavity walls. Its resist-ance is -90 Q and a four-wire terminal configuration isprovided to allow for accurate measurements of theelectrical power dissipated in the heater. All the innersurfaces of the cavity are coated with a thin layer ofspecularly reflecting black paint. The resistance ther-mometers are made from copper wire of 0.03-mm di-ameter by winding it around the joint of the thermalimpedance with the cavity and the heat sink, respec-tively. The four thermometers of the two heat fluxtransducers, each with a resistance of -100 Q, arewired in a bridge circuit to sense the difference oftemperature between the two cavities. The bridge istrimmed with a piece of the same copper wire to yieldzero response with the two cavities held at the sametemperature. The precision aperture is fabricatedfrom tempered stainless steel. Its roundness is better
Fig. 2. Schematic drawing of the PMO-6 detector with its control electronics. The detector consists of two electrically calibrated heat fluxtransducers with cavities. The cavity placed behind the precison aperture is used to substitute radiation power by electrical power. The rearcavity serves to compensate for changes of the environmental conditions. The servo loop keeps the temperature difference between the
cavities constant by controlling the square root of the current, which is proportional to the electrical power dissipated.
than 0.2 Arm and the cylindrical part of the apertureedges has a length of only 20 Arm.
B. Operation and Behavior of the Radiometer
The rear cavity is heated with a constant power of-40 mW producing a temperature difference acrossthe thermal impedance of -0.75 K. An electroniccircuit then controls the power in the front cavity tomaintain the front and rear cavities at the same tem-perature-regardless of whether the front cavity isshaded or irradiated. This 40-mW offset correspondsto an irradiance of some 2000 Wm-2. The effectivetime constant of the instrument is -2 s, hence, whenswitching between shaded and irradiated modes, the0.01% level of precision of the heater power is reachedin <20 s. In the ideal case of a perfect substitution ofelectrical for radiative power, the irradiance S wouldsimply be
S = (P. - P)1A ,(1)
where P and Pi are the electrical powers dissipatedwith the cavity when shaded and irradiated, respec-tively, and A is the area of the precision aperture.However, there are many deviations from this idealbehavior and the 1/A term will have to be replaced by a
more elaborate expression accounting for these effects.These deviations from ideal behavior, or imperfec-tions, may be grouped into four classes, the first threeof which we would like to name according to the do-main of the physical effect that leads to the corre-sponding imperfection. These are radiative, thermal,and electrical imperfections which can be determinedexperimentally and thus be corrected. The fourthclass of imperfections is due to effects of the environ-ment on the instrument. These effects are quasi-random in their nature and thus cannot be corrected.
The radiative imperfections consist of effects whichcause the substituted power to be different from thatwhich we intended to substitute. A small fraction ofthe radiation entering into the cavity is reflected andhence not substituted. On the other hand, some of theradiation falling through the entrance aperture andentering the cavity does so only because of the effect ofdiffraction or scattering in the front part of the instru-ment.
The thermal imperfections are due to nonequivalentheat losses of the cavity assembly during the shadedand irradiated phases of operation. The temperaturedistribution of the cavity assembly and of the heat sinkis slightly different during the shaded and irradiated
sequences. This causes different losses during the twomodes and the substitution is thus not perfect.
The electrical imperfection arises from the heat dis-sipated in the leads to the cavity. This amount of heatis different for the shaded and irradiated sequencesand a fraction of it contributes to the heat balance ofthe cavity thus biasing the measurement of electricalpower.
The fourth class of imperfections consists of theeffects of the environmental on the instrument.These include effects such as changes of the ambienttemperature and its influence on the instrument andthe possibly disturbing effect of wind. When estimat-ing the total accuracy of a particular set of irradiancedata, one has to take these effects into account. Thiscan be done by analyzing the power readings of theshaded and irradiated sequences. As an example onemight use a linear regression of the shaded power meas-urements as a function of time to deduce informationon the possible error caused by thermal drifts of theheat sink. It has been found that for open-closedperiods of 30-120 s the contribution of these quasi-random errors is <0.01% and hence negligible.
We note that all the radiative, thermal, and electri-cal imperfections are systematic effects and, therefore,it is possible to correct for them. This requires theeffects to be known as accurately as possible. Theprocess of experimentally determining the size of theseeffects is called experimental characterization. It isimportant to note that some of these effects dependnot only on the instrument itself, but also on the envi-ronment and/or the radiation source. The correctionfor the diffraction, for example, depends on the angu-lar opening and the spectrum of the source. To giveyet another example, the nonequivalence depends onthe pressure and hence a corresponding correction forground-based measurements would be different fromthe correction for measurements obtained during aflight on a stratospheric balloon at a pressure of 3mbar. A characterization thus has to be done with theparticular application in mind.
Solar irradiance measurements will be in a rangefrom 700 to -1400 Wm-2. Within this limited rangeall the corrections may be considered to depend linear-ly on the intensity, hence we may rewrite Eq. (1) bytaking into account the above effects as follows:
s = C(P, - Pi), s(2)
where C is the instrument constant; a product of thereciprocal value of the area of the primary apertureand the correction factors for the imperfections listedabove. It may also include a calibration factor for theelectronic equipment used to measure the heater pow-er.
The measured irradiance is the difference betweenthe radiation as seen by the cavity during the open andclosed phases, respectively. With the shutter closed,this includes infrared radiation received from the muf-fler and shutter and infrared losses out of the cavity.With the shutter open, the infrared radiation balanceof the cavity is slightly different. For ground-based
measurements this change amounts to from -0.007 to0.04 Wm-2 for typical atmospheric conditions andfrom altitudes of 1 and 4 km, respectively. In spacewith the radiometer held at 300 K, the infrared loss is0.43 Wm-2. These estimates are based on the assump-tion that the cavity, the muffler, and the shutter allhave the same temperature during reference and meas-urement phases. For the cavity and muffler this con-dition is fulfilled to a very good accuracy and if theshutter is highly reflecting its temperature is no longerimportant. Solar measurements from ground includenot only the direct solar radiation but also radiationscattered by the atmosphere and radiation emitted bythe aureole. Due to a lack of information about theamount of radiation originating from the solar aureoleand the atmosphere, the results of measurements arenormally not reduced to the direct solar radiation only.However, as most radiometers have similar view-limit-ing geometries, they see similar amounts of solar andIR radiation from the sky. From stratospheric bal-loons, or in space, where the infrared correction be-comes important, it has to be applied, thereby reduc-ing the measurements to true solar irradiance.
The experimental determination of all the individ-ual correction factors also provides the basis for areliable estimate of the absolute accuracy of the instru-ment, as the uncertainty of the correction factors de-termines the accuracy of the radiometer. The errorlimits of the correction factors are estimated as abso-lute limits, that is, it is assumed that the true value fallswithin the given limits. Sometimes uncertainties aregiven as la confidence levels. In such a context ourabsolute error limits can be considered to be at the 3aconfidence level.
Ill. Methods of Experimental Characterization
A. Aperture Area
The determination of the aperture area is based onthe measurement of length, which can in principle bedone with high accuracy. The apertures are fabricat-ed from tempered stainless steel. The edge of theaperture has a cylindrical part of 20-,um length and issufficiently hard to be measured with a sphere-shapedfeeler which exerts a force of a few tens of newtons.Measurements of the diameter are performed at stepsof 150 from 0 to 900. Only apertures with a roundnessof better than 0.2 Am are used. The absolute accuracyof the diameter determination performed by the SwissOffice of Metrology is better than ±0.4 Arm resulting inan absolute accuracy of the area of better than 0.016%.
Care has to be taken when mounting the precisionaperture to the instrument. No stress must be appliedto the aperture because it would render the measure-ment of its area invalid. In fact we first used a differ-ent aperture with a different method of mountingwhich caused us considerable problems. These aper-tures consisted of a chemically blackened copper foilwhich was placed under a clamp ring which was thenscrewed onto the heat sink. The area of each aperturewas determined after it had been mounted. However,
Fig. 3. Setup for the determination of the radiation losses of thecavity. The reflectometer is made out of PVF film coated with goldblack on its front and metallic gold on its rear face. The film issupported by a cone-shaped brass sheet and forms a pyroelectric
detector. 7
when mounting the muffler on the heat sink the conicalshape of the contact surfaces caused the whole heatsink structure, including the aperture, to be squeezed.This in turn led to inconsistent ratios among charac-terized instruments because the distortion of the aper-ture area was different for each instrument. The ef-fect could be verified by changing the torque applied tothe screws with which the muffler was attached to theheat sink and by simultaneously monitoring the fluxfalling through the aperture. It was possible to de-crease the area by up to 1%. Since 1984 we have usedthe stainless steel apertures first described in thisparagraph. They are fastened to the instrument insuch a way that no radial forces act on them (see alsoFig. 1).
B. Radiation Losses of the Cavity
The losses of radiation from the cavity are measuredwith a conical reflectometer similar to the one de-scribed by Blevin and Geist7 with a chopped laserbeam as a source (Fig. 3). The losses that interest usconsist of reflected radiation and of the part of theemitted infrared radiation that is caused by the heat-ing of the surface of the black coating of the cavity.One expects the amount of reflected radiation to beindependent of the chopper frequency and in phasewith the incident radiation. In contrast, the ampli-tude and phase of the infrared losses will depend onfrequency in a complicated manner. Moreover, thesetup shown in Fig. 3 is sensitive also to the infraredradiation that is caused by oscillations in the tempera-ture of the whole cavity assembly with the frequency ofthe chopped radiation. This latter effect, however,does not need to be corrected for because it is takeninto account by the electrical substitution and, as thetwo effects cannot be distinguished with the laser meas-urements, a supplementary experiment is needed todetermine the contribution of the black coating alone.This is done by heating the cavity with a sine waveshaped electrical power, as explained below.
The chopped laser beam should be close to a sinewave to reduce the influence of higher harmonics be-cause the cavity has a different transfer function forreflected and emitted radiation. The detector signalis the sum of reflected radiation which is inphase with
E 500a-.
Si
' 250.
E
0
E 500
' 250
E
0
4 8 1 6 32 64Frequency (Hz)
90
-90 =a.
-1 80
90
-o ,is
-90 m
-1804 8 1 6 32 64
Frequency (Hz)
Fig. 4. Results of the determination of the frequency-dependentlosses of radiation of the cavity for two instruments. Shown are thephase and amplitude of the measurements with radiative and elec-trical excitation. They are normalized to the power of the excita-tion. Positive phase means that the detector signal leads the input.As determined from the difference between radiative and electricalmeasurements, the losses of radiation amount to 250 and 425 ppmfor the two radiometers, respectively. Note that the phase of theelectrical measurement is due to the thermal excitation of the cavity,whereas the phase of the radiative measurement is dominated by the
signal of reflected radiation.
the incident beam and an infrared part of unknownphase and amplitude. The phase and amplitude aredetermined from a quadrature measurement with twophase-sensitive detectors. The fraction of infraredradiation that is caused by the thermal oscillations ofthe cavity can be measured directly by heating thecavity with a sine wave shaped electrical power of thesame amount and frequency as the laser beam in theprevious measurement. As the dissipated power is attwice the frequency of the excitation voltage, possiblecapacitive coupling to the detector does not bias themeasurement. The difference between the radiativeand electrical measurements is almost identical to thereflected radiation plus the emitted radiation due tothe thermal impedance of the black coating. Resultsof such measurements for two instruments are shownin Fig. 4. At frequencies above 40 Hz the amount ofemitted infrared becomes small. This is true for thesetwo radiometers but could be quite wrong for a radio-meter where the quality of the gluing of the cavityheater is poor. This would lead to a considerableoverestimation of the radiative losses from the cavity ifone were to perform the experiment with only thechopped laser beam.
Note: From these data an effective loss has been calculated for asolar spectrum and is shown in the last column. Numbers are given inparts per million (ppm).
For a freshly painted cavity a value for the reflectiv-ity of 0.008-0.010% at 514 nm is found. During thefirst year this value normally degrades to -0.03% andthen remains constant. The uncertainty of the reflec-tivity measurement is of the order of 0.005% (o level).
To estimate the losses of radiation of the cavity forsolar radiation, measurements were performed at sev-eral wavelengths using an argon and a krypton laserbetween 367 and 797 nm. Table I summarizes theresults of these experiments. The value quoted forsunlight was obtained by weighing the measured val-ues with the solar spectrum. Below 367 nm and above797 nm, respectively, the values were assumed to stayconstant. This explanation seems justified because ameasurement of the black coating on a spectrometerrevealed no significant change of its characteristics upto a wavelength of 9 ,um. The accuracy of the valuequoted for solar radiation is estimated to be betterthan 0.02% (3a level).
C. Diffraction
As the experimental determination of the correctionfor diffraction is very difficult, the result of a numeri-cal calculation is used. Recently, Brusa8 has shownthat the effect of diffraction at the view-limiting aper-ture for the PMO6-type radiometers is 0.13%, the in-strument reading too high. The spectrum of the radi-ation entering the instrument changes with absoluteair mass and atmospheric conditions. The resultingchanges in the correction for diffraction are <0.005%and can therefore be neglected. Additional diffrac-tion occurs at the primary aperture causing some of theradiation falling through it to be diffracted out of thecavity opening. This effect amounts to -0.02% (Ref.9) resulting in a total correction for diffraction of 0.11%with an estimated uncertainty of 0.01% (3c level).
D. Scattered Radiation
Radiation reflected from the precision aperture tothe muffler and back into the cavity (scattered light) ismeasured with a silicon diode in place of the cavity andwith a collimated laser beam as a source. By scanningthe beam across the polished surface of the aperture weobtain the data needed to estimate the correction forscattered light in measurements with the sun as asource. The deduced values are between 0.02 and0.03%. The uncertainty of the determination is 0.03%(3ca level).
E. Nonequivalence
The nonequivalence is due to the effect of a differ-ence in the temperature distribution in the cavity andthe heat sink during the shaded and irradiated se-quences. The main effect is due to radiation which isreflected from the conical part of the cavity to itscylindrical wall causing a rise of temperature relativeto the value prevailing during the shaded phase. Thisleads to an additional loss of heat by conduction andconvection in air during the irradiated phase. A simi-lar effect exists because of the additional heating of theprimary aperture during the irradiated phase. Again,due to conduction and convection in air, this effectmay be coupled to the cavity. Because the outer sur-faces of the cavity are gold-plated, the cavity would belargely decoupled from the surrounding heat sink ifoperated in vacuum where only radiative losses arepresent and hence only a negligibly small nonequiva-lence would exist. Thus the air-to-vacuum ratio of thesensitivity of an instrument as measured with the sunas a source minus the air-to-vacuum ratio measuredwith electrical heating is equivalent to the correctionfor nonequivalence. The PMO-6 radiometers have anonequivalence of the order of 0.15-0.45%. The un-certainty of the determination is 0.05% (3o- level).
F. Heating of Leads
The correction for the heating of the leads is de-duced from the following experiment: The radiome-ter is operated in the active mode and the heater cur-rent is monitored. An additional current, drawn froma floating source, is then fed through the current feed-ing wire and the potential sensing wire attached toeach side of the heater element. Its effect on theheater current tells one how much of the heat dissipat-ed in the wires to the heater flows into the cavity. Theexperiment is performed for both sides of the heaterelement. The method is only applicable if the currentfeeding wire and the potential sensing wire are of thesame kind, thereby avoiding the need for a specialthird terminal on each side, only to be used for themeasurement of this effect.10 The measurements ac-cording to our method show a very high precision of-0.001% (1 level). The uncertainty of the correction,however, is influenced by a possible asymmetry be-tween current feeding and potential sensing wire, be-cause during normal operation of the instrument nocurrent is flowing through the potential sensing termi-nals of the heater element. Taking this into account,we estimate the correction thus determined, which istypically 0.02-0.05%, to be accurate within 0.01% (3alevel).
G. Summary
The total error limit of a PMO6-type radiometer asobtained by summing the above-stated 3c error limitsfor the individual corrections amounts to 0.14%. Tak-ing into account an additional 0.02% uncertainty in themeasurement of the difference of electrical powersbetween open and closed states, and allowing for a0.01% uncertainty due to quasi-random errors, the to-
Table I. Correction Factors for Seven PM06-Type Radiometers Determined by Experimental Characterization and the Results of Comparisons with thePMO-2 Radiometer with the Sun as a Source
Instrument Cavity Scattered Lead Total Ratio toIdent. Nonequivalence losses light heating charact.a PMO-2
Uncertainty r level 0.00017 0.00007 0.00010 0.00003 0.00056b
a Includes a factor of 0.9989 for the correction of diffraction.b Includes also the uncertainties for the aperture area (0.016% at 3a),
electrical power, and environmental effects (0.01% at 3a).
tal error limit for ground-based solar total irradiancemeasurements with a PMO6-type radiometer is typi-cally <0.17%. The corresponding rms error limit,which is obtained by adding the squares of all theuncertainties and taking the square root of the sum,amounts to 0.07% (3cr level).
IV. Discussion and Results of Comparisons
The characterization procedure was applied to sevenPMO6-type radiometers. As a necessary, albeit notsufficient condition for the characterization results tobe correct, one expects that simultaneous solar irradi-ance measurements performed with these instrumentsshould agree within the stated error bounds of thecharacterized instruments. The instruments werecompared to the PMO-2 radiometer with the sun as asource and the results (Table II) show that indeed theyall fulfill the condition stated above. Moreover, fromthese results it becomes evident that the accuracy issubstantially improved by the characterization, be-cause the variability of the correction factors is-withthe exception of the cavity losses-more than twice ashigh as the variability of the results of the radiometriccomparisons. The lc uncertainty of the radiometersas obtained by adding up all 1a uncertainties of thecharacterizations is just equal to the la standard devi-ation of the results of the comparison. This verystrongly supports the validity of both the characteriza-tion methods and the error analysis.
From the results of the comparisons given in TableII we may also deduce the ratio of the PMO6-typeradiometers to the World Radiometric Reference(WRR). The WRR is the base for all solar measure-ments within the meteorological community. It wasestablished in 1977 as a result of comparisons of manydifferent types of absolute radiometer. It was official-ly accepted by the World Meteorological Organizationin 198111 and is realized by a group of absolute radio-meters. The PMO-2 radiometer is part of this groupand it is according to the definition of WRR thatreadings taken by the PMO-2 instrument must belowered by 0.14% to refer its measurements to theWRR. Taking this into account we find that the
the correction for diffraction (0.01% at 3a), the measurement of the
PMO6 scale of irradiance as represented by the meanof the seven PMO6-type radiometers is 0.22 lower thanthe WRR. This is within the estimated ±0.3% uncer-tainty of the WRR, but outside the +0.17% uncertaintyof the PMO6-type radiometers. Due to the fact thatnone of the radiometers used to define the WRR wascorrected for diffraction, the WRR is -0.1% too high.Thus correcting the WRR for diffraction would place itwithin the uncertainty of the PMO6-type radiometers.
V. Conclusions
The results demonstrate that experimental tech-niques of characterization of absolute radiometers canlead to a rms accuracy at the 3c level for ground-basedsolar radiometry of better than 0.07%. The sum of allthe individual uncertainties (3 level) amounts to0.17%. Experimental characterization also leads to atransparent and hence more reliable error analysis.Furthermore, the characterization may be repeatedwhen the instrument shows any degradation, and thecause of the degradation can be more easily identified.Repair and recharacterization will always allow its fullaccuracy to be reestablished. Experimental charac-terization may thus be regarded as a method whichallows one to maintain the radiometric accuracy de-scribed above over long periods of time.
Part of this work was supported by the Swiss Na-tional Science Foundation which is gratefully acknowl-edged. The authors are indebted to Ch. Wehrli and S.Tuor of PMOD for many helpful discussions. Most ofthis work was done while R. W. Brusa was still withPMOD/WRC.
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