Absolute spectral irradiance scale in the 700-2400 nmspectral range

Pedro Corredera, Antonio Corr6ns, Alicia Pons, and Joaquin Campos

An absolute spectral irradiance scale for the 700-2400 nm range has been developed. The scale is based on anabsolute radiometer and a series of interference filters, which were used to determine the spectral irradianceof quartz halogen incandescent lamps at a number of discrete wavelengths. Values at intermediate wave-lengths have been obtained by interpolation. This new scale was compared with NIST standards based onblackbody radiance. Both scales were found to agree within +1%.

I. Introduction

An absolute spectroradiometric scale covering thevisible range of the spectrum, based on an electricallycalibrated absolute radiometer and silicon detector-interference filter combinations, was developed in theRadiometry Laboratory of the Instituto de Optica deMadrid in 1980. This scale, defined for the 380-800-nm spectral range was used to realize a photometricscale to calibrate incandescent lamps as luminous in-tensity standards.",2

This paper describes the work done to expand ourfacilities for the near IR. An absolute spectroradio-metric scale for the 700-2400 nm spectral range hasbeen realized based on an absolute radiometer and aseries of interference filters. This paper also analyzesthe different sources of error and shows the resultsobtained in a comparison with another spectroradio-metric scale based on a blackbody radiator.

11. Principle of the Method

The response of a detector with known absolutespectral responsivity S(x,y,X) to the spectral irradi-ance from a radiation source filtered by means of aninterference filter having spectral transmittancer(x,y,X) is given by3

V(A,AX) = J A E(x yX)S(xyX)r(xxyX)dXdA, (1)

where E(xy,X) is the spectral irradiance in W m-2nm-1 in the test plane, AX = X2 - X, is the transmissionband of the interference filter, and A is the detectoraperture area.

If the radiation source to be measured is an incan-descent lamp, whose spectral radiance distribution is

The authors are with Institute of Optics, Daza de Valdes, CSIC121 Serrano, 28006 Madrid, Spain.

Received 9 November 1989.0003-6935/90/243530-05$02.00/0.© 1990 Optical Society of America.

continuous with no absorption and no emission lines,and we make the following assumptions:

The spectral irradiance E(x,y,X) = E(X), responsi-vity S(xy,X) = S(X), and transmittance T(x,y,X) = a(X)are uniform over the detector area, A.

The spectral irradiance E(X) and the spectral re-sponsivity S(X) are uniform over the detector area A;

The interference filters are narrow band, so that thespectral irradiance E(X) can be considered as a con-stant over an interval of width AX;

The effective wavelength for every filter is given bythe mean wavelength Xm.

r'2

Am = ̂ ., s ~~~~~~~~~~~~~(2)t r(X)dX

then we can write Eq. (1) as

V(A,AX) = AE(Xm) S(X)r(X)dX. (3)

Thus, for every filter, the spectral irradiance of thelamp at the filter effective wavelength Xm is given by

E(X,) = V(A,AX) (4)

A f S(X)r(X)dX

Thus we can determine the spectral irradiance ofincandescent lamps at a number of discrete wave-lengths by means of a set of interference filters, whosespectral transmittances are known, and a detectorwhose absolute spectral responsivity is known. Val-ues at intermediate wavelengths can be obtained by anappropriate interpolation technique.

Ill. Experimental Description

The experimental arrangement for measuring thespectral irradiance of the test lamps is shown in Fig. 1.

The components are mounted in an unpolished wall

3530 APPLIED OPTICS Vol. 29, No. 24 / 20 August 1990

RADIOMETER

ILTER WHEEL

600 1000 1400 1800 2200 2600

LAMP

Fig. 1. Experimental arrangement used in the realization of thescale.

enclosure. To minimize heating effects, there are twoisolator walls, which separate the detector and filterzone from the lamp zone. A platinum resistance ther-mometer placed near the filter wheel monitors theenvironment temperature. During the measure-ments, the temperature of detector compartment andhence the filters, is 23 + 0.2C.

Two types of tungsten halogen lamp were used: the1000-W FEL type and the 1000-W conveniently agedEGT type. A stabilized power supply keeps the lampflux within ±0.08%. The lamp-detector distance isaccurately set at 500.0 + 0.1 mm.

To cover the desired spectral range, twelve interfer-ence filters, whose spectral transmittances are shownin Fig. 2, have been selected. The relative spectralirradiance of the lamps is also shown in this figure.The nominal wavelengths of the filters are 700, 800,900,1000, 1150,1200, 1300,1500,1550, 1600,2000, and2450 nm. The filters having nominal wavelength be-low 1000 nm had transmission bands at longer wave-lengths, above 1400 nm. For this reason, these filtershave been used in combination with a 20 mm thicknessdistilled water filter, which is tilted at 5° with respectto the optical axis, to avoid interreflections.

The spectral transmittance of the interference fil-ters was measured in a Cary 17D spectrophotometer at1-nm wavelength intervals, using a configurationwhich closely reproduces the actual geometry used inthe spectral irradiance measurements to avoid trans-mission band shifts. The effective wavelengths (Xm),the bandwidth (AX), and the peak transmittance[T(XM)] of these filters are shown in Table I. In thecase of 700, 800, 900, and 1000 nm filters, these valuescorrespond to the product of the filter transmittanceand the water filter transmission curve.

The best detector to be used with the describedmethod is an absolute thermal radiometer with nearlyflat spectral responsivity. Absolute radiometers alsohave the advantage of measuring irradiance directlyand accurately. In this work we used an electricallycalibrated pyroelectric radiometer manufactured byLaser Precision Corp. with a blackened and preciseaperture 0.5 cm2 in area. The reflectance of the ab-

Wavelength (nm)Fig. 2. Spectral transmittance of the selected interference filters

and relative spectral distribution of a tungsten halogen lamp.

sorbing surface of the radiometer was measured at theemission lines of a cw He-Ne laser (0.63, 1.15, and 3.39jum) and was found to be constant.

Then we can write Eq. (4) as

(5)EEXm) = AKe J r(X)dX

IA

where EA, is the total irradiance measured through thefilter and Ke is a correction factor that must be appliedto take into account the actual thickness of the filters.

IV. Measurements and Interpolation

With the experimental arrangement describedabove, we measured the spectral irradiance of eightlamps, and four FEL type and four EGT type lamps.An automatic data acquisition system, which recordsthe parameters (temperature and lamp current), thetotal irradiance measured, and the standard deviationis used in the measurement process.

As an example, the values of the power measuredwith the radiometer and the spectral irradiance ob-tained at the filter's effective wavelengths, are shownin Table II for two lamps. The lamp denoted as Z-1 isa EGT type, and F-175 denotes a FEL type lamp.

Having thus obtained the values of the spectral irra-diance at a number of discrete wavelengths, we usedthe following interpolation technique to determine thespectral irradiance values at intermediate wave-lengths.

Table 1. Effective Wavelength (Am), Bandwidth (AX), and PeakTransmittance [7(Xm)] of the Interference Filters Selected

Am AX i(\m)Filter (nm) (nm) (%)

700 701.9 16.0 40.03800 800.2 15.0 37.86900 887.9 26.0 56.41

1000 1004.4 46.0 42.191150 1151.4 63.0 38.271200 1200.0 50.0 34.201300 1294.4 48.0 38.121500 1508.4 70.0 73.001550 1532.7 71.0 25.501600 1601.2 62.0 28.302000 2014.3 111.0 72.502450 2476.5 72.0 65.50

20 August 1990 / Vol. 29, No. 24 / APPLIED OPTICS 3531

DISTI LLEDWATER FILTER

ECI

(15 Hz)

Since the radiation source to be measured is a tung-sten lamp, its spectral radiance L(X) will be close to thetheoretical spectral radiance of a blackbody LBB(TX)when it emits at the same temperature, corrected by alow order polynomial in X, B(X) (Ref. 4):

L(A) = B(X)LBB(T,X). (6)

The correction function includes the effect of thespectral emissivity of tungsten as well as the spectraltransmission of the lamp bulb.

Since the radiance is geometrically related to theirradiance, a spectral correction function of a similarform can be used to relate the irradiance from the lampto the blackbody radiance. Then the spectral irradi-ance at intermediate wavelengths can be obtained us-ing the following expression:

1.002

E 1.001

0

LUj 1.000

E 0.999

i

_-

- F - 700 nm--- F-1200 nm- F-2450 nmI _

0.998 _2500

I I I

2900 3300Temperature (K)

3700

Fig. 3. Relative variation of E(Am) vs lamp temperature for the700-, 1200-, and 2450-nm interference filters.

E(A) = k P() ,\ exp(CA/T) -1 ' (7)

where k is a constant that includes the first radiationconstant (cl) and geometric parameters; 2 is the sec-ond radiation constant, and P(X) is the polynomialfunction.

To obtain the value of T, we calculated the black-body temperature which best fits the theoretical spec-tral irradiance values to the experimental ones. (Val-ues of T = 3000 and 3100 K have been obtained forlamps denoted as Z and F, respectively.) Then bymeans of a linear least- squares fitting procedure, theparameters of the polynomial function have been cal-culated.

V. Error Analysis

The uncertainties associated with the realization ofthe absolute spectral irradiance scale by the describedmethod arise both from the theoretical assumptionsand the measurement process.

1. Uncertainties from the theoretical assumptionsThe uncertainties in the spectral irradiance values

arising from the theoretical assumptions are: (a)those due to the error related to the temperature calcu-

Table 11. Power Measured with the Radiometer Through EveryInterference Filter and rradiance Values Calculated for the Filter Effective

Wavelength for Two Different Lamps

Lamp Z-1 Lamp F-175Xm Power E(A) Power E(X)

(nm) (AW) (AW cm- 2 nm- 1 ) (AW) (AzW cm- 2 nm-1)

701.9 95.7 26.67 64.6 17.99800.2 98.8 31.49 65.1 20.75887.9 291.7 34.59 185.7 22.02

1004.4 373.7 33.55 239.8 21.531151.4 449.6 31.71 278.7 19.651200.0 299.0 29.80 184.8 18.421294.4 288.8 26.92 176.7 16.471508.4 541.3 20.78 333.7 12.811532.7 191.9 19.98 115.7 12.041601.2 195.8 19.33 117.7 11.612014.3 476.5 11.09 280.7 6.532476.5 164.8 6.17 95.8 3.60

LU.0

\Di

1.010 Ir

1.005

1.000

0.995 L500

I i I I I

1000 1500 2000 2500 3000Wavelength (nm)

Fig. 4. Ratio of irradiance calculated according to the completemeasurement equation to the irradiance calculated according to ourmeasurement equation as a function of wavelength for an interfer-

ence filter having a bandwidth of 100 nm.

lated and (b) those due to the assumption that thebandwidth of the filters was negligible.

To evaluate the uncertainties we have used a mathe-matical model5 that reproduces the spectral transmit-tance of the filter selected, considering it as either aGaussian function, or as the sum of two Gaussian func-tions depending on the shape of the transmittancecurve shape.

(a) We have considered the effect of an improperestimate of Ton the values of E(X). Figure 3 shows theratio ET(Xm)/E 3 00(m) for the interference filters at700, 1200, and 2450 nm [ET(Xm) is the spectral irradi-ance calculated for different temperatures from 2600to 3600 K]. The maximum variation is found at 700nm [as could be expected since dE(X) is greatest at thiswavelength]. In the determination of the dX tempera-ture from the experimental data, we estimated an un-certainty of ±25 K, this resulted in an error of at most0.1% in the calculated irradiance.

(b) The correct measurement equation for a black-body radiator without considering narrowband filterswould be

Eb(Xm) = (8)K A5 [xp(C2/Any) 1] X., T(X)dXKeM[xpczxm) X

5[exp(C 2IXT - 1]

where subscript b denotes a broadband filter.Figure 4 shows the ratio Eb(Xm)/E(Xm) [E(Xm) being

3532 APPLIED OPTICS / Vol. 29, No. 24 / 20 August 1990

. I

1 .015r

1.0051-

LU

U

1.000 0 o o 0 O 0 cP a 0

1.0101

E< 1005

'LU""1.000

E-< 0.995

0.9900.995 t

o.99o 600

I l , t I I , I

1000 1400 1800 2200 2600

Wavelength (nm)

Fig. 5. Ratio of irradiance calculated according to the completemeasurement equation to the irradiance calculated according to our

measurement equation for the interference filters used.

the value given by Eq. (5)] for a filter having a hypo-thetical bandwidth of 100 nm. It can be seen that thiserror can be significant if such broadband-width inter-ference filters were used for wavelengths below 1000nm. In this work, we used the interference filtersspecified in Table I. The ratio Eb(G\m)/E(Xm) has beenevaluated again for these interference filters (see Fig.5), resulting in an error of <0.1%.

2. Uncertainties from the measurement processThe uncertainties of the spectral irradiance values

arising from the measurement processes are those re-lated to the spectral transmittance measurement ofthe interference filters, to the radiant power measure-ment, and to the lamp positioning and power supplyvariations. A description and estimate of each aregiven below.

(a) Spectral Transmittance MeasurementUncertainties

Two kinds of error may be distinguished in thismeasurement. One is the uncertainty in the spectraltransmittance value, and the other is the uncertaintydue to wavelength shifts. The first is the main errorsource in this experimental technique due to the accu-racy and precision of the spectrophotometer used inthis work. This error produces a maximum uncertain-ty of ±1.5% in the calculated irradiance value.

To evaluate the second one, we calculated the ratioEm/Exm', where Em is the spectral irradiance value ofa blackbody radiator through the transmission band ofan interference filter, and E~m is the value that wouldbe obtained if the transmission band of the filter wasshifted over a range of -5 to +5 nm. The results areshown in Fig. 6 for three interference filters, the filter700 nm presenting the highest deviation. Consideringthat the measured transmission band will not be shift-ed by more than 41 nm, which has been determinedtaking into account changes due to temperature, beamgeometry, and spectrophotometer wavelength accura-cy, the uncertainty in the calculated spectral irradi-ance values will be lower than 40.5%.

0.985k

- F 700 nm--- F 1200 nm-- F 1600 nm

_ - -

-4.0 -2.0 0.0 2.0 4.0 6.0

Wavelength Shift ( nm)

Fig. 6. Ratio of calculated irradiance to true irradiance as a func-tion of the wavelength shift error in the spectral transmittance of the

filter.

(b) Radiant Power Measurement UncertaintyThis is limited by the electrically calibrated pyro-

electric radiometer (ECPR) accuracy (±1%)6 and mea-surement precision (+0.2%).

(c) Positioning and Power Supply UncertaintiesThe uncertainties in lamp positioning and the elec-

trical power supply (experimentally evaluated) pro-duce the following errors in the spectral irradiancevalues. Lamp-radiometer distance = +0.2%, lamporientation = ±0.1%, and power supply variations =±0.1%.

All of the uncertainties described in this section aresummarized in Table III, where the mean quadraticerror is also given. This is considered to be the overalluncertainty of our absolute spectral irradiance scale,and its value is approximately ±2%.

Table IV compares the spectral irradiance valuesobtained using the method described in this paperwith the reported calibration values reported by theNational Institute for Standards and Technology(NIST) (formerly NBS) for two lamps of type FEL.For each lamp, the average difference between the twosets of values is 0.5%, and the maximum difference is0.77%.

Table Ill. Uncertainties Associated in Developing the Absolute SpectralIrradlance Scale

(%)Filter bandwidth +0.1Temperature +0.1Wavelength shift ±0.5Transmittance +1.5Radiometer accuracy +1.0Measurement precision +0.2Radiometer-lamp distance +0.2Lamp flux variations +0.1Lamp orientation +0.1

Mean quadratic error ±1.9

20 August 1990 / Vol. 29, No. 24 / APPLIED OPTICS 3533

1.010

, , , I , , I I I I Il l I I Il

Table IV. Comparison of Calculated Spectral Irradiance Values with Those Reported by NIST

Lamp F-1 Lamp F-178I0 NIST I0 NIST

X E(X) A E(X) A Diff E(A) A E(X) A Diff(nm) (,uW cm- 2 nm- 1 ) (%) (AW cm- 2 nm- 1 ) (%) (%) (/W cm- 2 nm'1) (%) (,UW cm- 2 nm-1) (%) (%)

700 17.88 1.6 17.92 1.2 +0.22 17.72 1.6 17.81 1.2 +0.51800 20.82 1.6 20.94 1.2 +0.57 20.58 1.6 20.70 1.2 +0.58900 21.84 1.4 22.00 1.2 +0.73 21.53 1.4 21.60 1.2 +0.32

1050 20.90 1.6 21.03 1.2 +0.62 20.55 1.6 20.65 1.2 +0.481150 19.38 1.7 19.53 1.2 +0.77 19.03 1.7 18.99 1.2 -0.211200 18.50 1.7 18.57 1.2 +0.38 18.15 1.7 18.15 1.2 0.001300 16.63 1.5 16.69 1.2 +0.36 16.31 1.5 16.31 1.2 0.001540 12.38 1.8 12.43 1.2 +0.40 12.13 1.8 12.12 1.2 -0.081600 11.44 1.8 11.46 1.2 +0.17 11.22 1.8 11.16 1.2 -0.54

VI. Conclusions References

We have described a method for determining the A. Corrons, "Absolute Spectroradiometric and.. , . l ............. 1. C. Carreras and A orn,"boueSetoaimti nabsolute spectral irradiance values of an incandescent Photometric Scales Based on an Electrically Calibrated Pyroelec-lamp in the near IR spectral range. This method is tric Radiometer," Appl. Opt. 20, 1174-1177 (1981).based on an absolute radiometer (ECPR) used in con- 2. C. Carreras y A. Corrons, "Escala Espectroradiometrica Abso-junction with a series of interference filters. luta. Realizacion practica de la unidad basica de Fotometria"

We have performed the analysis of the errors to be (Publicaciones del Instituto de Optica 43, Madrid, 1980).expected. This shows that the radiometer accuracy 3. H. J. Kostkowski and F. E. Nicodemus. "An Introduction to theand the measurement of the interference filters trans- Measurement Equation." Self-Study Manual on Optical Radia-mittance are the highest sources of uncertainty. tion Measurement. Chap. 5. NBS Technical Note 910-2. 58-92.

Finally, we have measured the absolute spectral ir- 1978.radiance of eight 1000 W tungsten halogen lamps, at 50 4. J. C. De Vos, "A New Determination of the Emissivity of Tung-cm, in the 700-2400 nm spectral range, two of them sten Ribbon," Physica 20, 690-714 (1954).spectralher700-2400 standardsafromnthe twoTowith e- 5. L. P. Boivin, "Calibration of Incandescent Lamps for Spectralspectral irradiance standards from the NIST with re- Irradiance by Means of Absolute Radiometers," Appl. Opt. 19,ported calibration from 250 to 1600 nm referred to the 2771-2780 (1980).blackbody primary standard. Our measurements 6. W. M. Doyle, B. C. McIntosh, and J. Geist, "Implementation of aagree with the NIST calibration within 0.8%, well with- System of Optical Calibration Based on Pyroelectric Radiome-in our estimated uncertainty. try," Opt. Eng. 15, 541-548 (1976).

3534 APPLIED OPTICS / Vol. 29, No. 24 / 20 August 1990