Comparisons between the Eppley radiometers and a spectroradiometer

The quantity to be measured by an Eppley radiometer is the broadband value E [Wm^-2] of the incident irradiance given by

E= E_λ

λ1

λ2

∫

^{(λ)dλ (1)}

whereE_λ(λ) [Wm^-2nm^-1] is the spectral irradiance of the incident radiation and ∆λ = λ2- λ1

[nm] is the spectral pass band of the instrument. The signal S [V] recorded by the radiometer is, however, a function of the spectral responsivity R_φ(λ) of the instrument. This quantity is determined by the properties of the receiving aperture (a diffuser of area A), the transmittance of the UV-filter and the spectral sensitivity of the detector. Thus, the signal S is related to the incident irradianceE_λ(λ) by

S(A,∆λ)= E_λ

∫

A

∆

∫

λ ^{(x,y,λ)Rφ(λ)dAdλ (2)}

where it has been assumed that the spectral responsivity is constant everywhere within the acceptance solid angle of the instrument. If the size of the receiving aperture is such that

E_λ(x,y,λ) and R_φ(λ) are constant over the aperture area, then S(∆λ)=A E_λ

∆

∫

λ ^{(λ)Rφ(λ)dλ (3)}

This relation can be further simplified if the relative spectral responsivity r(λ) of the instrument is know. If, in addition, the relative spectral distribution e(λ) of the incident irradiance is also known, then the following two relations can be introduced.

R_φ(λ)≡K₁r(λ)

E_λ(λ)≡K₂e(λ) (4)

K1 and K2 are constant for all wavelengths. By substituting (4) into Eq. (3), we obtain S(∆λ)=AK₁K_{2 λ} e

a

λb

∫

^{(λ)r(λ)dλ (5)}

where the limits of the integral include all wavelengths where R_φ(λ) is nonzero.

Measurements of the irradiance of a standard source, i.e. a source with known spectral irradianceE_λ^s(λ), can be used to evaluate the constants K1 and K2. Substituting the values obtained from such measurements into Eq. (5) yields

S^s(∆λ)= AK₁ E_λ^s

λa

λb

∫

^{(λ)r(λ)dλ (6)}

By combining Eqs. (5) and (6), we obtain the following expression for K2.

K₂ = S S^s

E_λ^s

λa

λb

∫

^(λ)r(λ)dλ

λa e

λb

∫

^{(λ)r(λ)dλ (7)}

By inspection, it is evident that all the quantities on the right hand side of Eq. (7) are known apart from S, the output signal of the instrument, which is measured. K2 can therefore be evaluated.

We recall that the quantity to be measured by the instrument is given by Eq. (1). Introducing Eqs. (4) into Eq. (1) yields

E=K₂ e

λ1

λ2

∫

^{(λ)dλ (8)}

As the integral and K2 are known, the broadband value for this particular instrument can be calculated.

Solving Eq. (8) is cumbersome as both the relative spectral responsivity r(λ) of the radiometer and the relative spectral distribution e(λ) of the incident irradiance must be known. This can be circumvented by introducing the following assumption.

For this particular case, the sun is chosen as the standard source. The absolute spectral irradiance E_λ^s(λ) is assumed to be known. If the relative spectral irradiance e(λ) of the sun is assumed to be invariant with respect to the solar zenith angles and the sky conditions (i.e. cloud conditions, ozone concentration), then

e(λ) ≅constant× E_λ^s(λ) (9)

for all wavelengths.

Comparisons of solar spectra recorded at different solar zenith angles and sky conditions have demonstrated that assumption (9) holds for the wavelength region 320 nm to 400 nm (UVA) but does not hold for the UVB region (290 - 320 nm). The spectral sensitivity of the Eppley instruments is, however, greatest in the UVA region. The UVB radiation of the solar spectrum accounts for approximately 5% of the total UV radiation (290-400 nm). The signal recorded by an Eppley radiometer will therefore be relatively insensitive to spectral changes in the UVB region. Use of approximation (9) can therefore be justified.

Introducing assumption (9) into Eq. (7) yields

E= SK where K = E_λ^s(λ)dλ

λ1

λ₂

∫

S^s (10)

K [Wm^-2/V] is a calibration factor for the wavelength interval λ₁≤λ≤λ₂. Due to the above assumption, this calibration factor is source dependent and must therefore be modified if a different source is examined. However, the broadband value E can easily be calculated as the dependence on the spectral responsivity R_φ(λ) of the instrument has been eliminated.

In the following comparison, the Eppley radiometers were compared to a Macam spectroradiometer. The spectral irradiance E_λ^M(λ) was recorded by the Macam enabling

E_M = E_λ^M

λ1

λ2

∫

^(λ)dλ to be computed. A corresponding output signal S was recorded by the Eppley radiometer. The broadband quantity E can be calculated using the calibration factor Ke

supplied by Eppley Laboratory, Inc. (E = Ke S) (see Table 5.2.1). Then,

E

E_M =κ (11)

where κ = 1 if the calibration factor Ke has been chosen correctly. By combining Eqs. (10) and (11), we can compute a corrected calibration factor (K ′ =K_e κ) which is appropriate for the conditions and source at hand.

The comparison between the radiometers and the spectroradiometer was conducted as follows.

The quantity EM was calculated from the spectral irradiance E_λ^M(λ) supplied by the Macam spectroradiometer (NRPA). Two wavelength intervals (λ₁≤λ≤λ₂) were examined. The first interval (290 to 385 nm) was chosen as the Eppley documentation specifies that the instruments are calibrated for this region. The other wavelength interval (290 to 400 nm) was chosen such that the entire UVA region was taken into account. The Eppley data was averaged over a specified time interval determined by the time taken for the spectroradiometer to scan the two intervals. The spectroradiometer used on average 11 min (13 min) to scan the interval 290 to 385 nm (290–400 nm) whereas the Eppley instruments recorded values every minute.

5.2.4.2 Daylight measurements

UV data collected on 7.06.1995 (Day 158) was found to be suitable for comparison between the Eppley radiometers and the Macam spectroradiometer. All instruments were in operation from 8:30 to 13:00 (UTC). The UV data was compared at approximately one hour intervals.

The results are shown in Tables 5.2.5 and 5.2.6. As can be seen, the ratios κ between the Eppley and Macam instruments were relatively constant regardless of zenith angle. The ratios obtained at 8:30 were higher than the others and may be due to disturbances in the vicinity of the instruments.

According to the Eppley documentation, the instruments were calibrated for the wavelength interval 290–385 nm. As can be seen from Table 5.2.5, there was good correspondence between instruments E-15728 and E-30072 and the Macam spectroradiometer. The other two Eppley instruments deviated considerably.

Table 5.2.5. Ratio (κ =E E_M) between the broadband irradiance provided by the Eppley instruments and the Macam spectroradiometer for daylight measurements on 7.06.1995 (Day 158). The wavelength interval (λ₁≤λ≤λ₂) is 290 to 385 nm.

Table 5.2.6. Ratio (κ =E E_M) between the irradiance provided by the Eppley instruments and the Macam spectroradiometer for daylight measurements on 7.06.1995 (Day 158). The wavelength interval (λ₁≤λ≤λ₂) is 290 to 400 nm.

UTC TUVRxxxx/Macam (λ-interval: 290–385 nm)

E-13814 E-13815 E-15728 E-30072

8:30 2.5 2.3 1.5

9:00 1.7 1.6 1.0 0.9

10:00 1.7 1.6 1.1 0.9

11:00 1.8 1.7 1.1 0.9

12:00 1.7 1.6 1.1 0.9

13:00 1.8 1.7 1.1 0.9

5.2.4.3 Lamp measurements

A similar comparison was conducted using SSI's lamps as light sources. The results for the two wavelength intervals are shown in Tables 5.2.7 and 5.2.8. The ratios κ between the Eppley instruments and the Macam spectroradiometer for a given wavelength interval were on the whole the same for both lamps. On average, the ratios found for the lamp measurements were slightly lower than those found for the daylight measurements. Again, for the wavelength interval 290–385 nm, there was good correspondence between instruments 15728 and E-30072 and the spectroradiometer whereas the other two Eppley instruments deviated considerably.

Table 5.2.7. Ratio (κ =E E_M) between the irradiance provided by the Eppley instruments and the Macam spectroradiometer for the lamp measurements. The wavelength interval (λ₁≤λ≤λ₂) is 290 to 385 nm.

Table 5.2.8. Ratio (κ =E E_M) between the irradiance provided by the Eppley instruments and the Macam spectroradiometer for the lamp measurements. The wavelength interval (λ₁≤λ≤λ₂) is 290 to 400 nm.

5.2.4.4 Conclusions

From the above comparison, it appears that of the Eppley instruments, E-15728 and E-30072, provide the most reliable measurements of broadband incident irradiance if the factory provided calibration factors are used. Good correspondence was found between these two instruments and the Macam spectroradiometer for both daylight and lamp measurements. The broadband irradiance provided by instruments E-13814 and E-13815, deviated considerably from the irradiance provided by the Macam spectroradiometer when the factory provided calibration factors were used. However, with a proper choice of calibration factor, these instruments should be able to provide reliable measurements.

UTC TUVRxxxx/Macam (λ-interval: 290–400 nm)

E-13814 E-13815 E-15728 E-30072

8:30 2.0 1.9 1.2

9:00 1.3 1.2 0.8 0.7

10:00 1.4 1.3 0.9 0.7

11:00 1.4 1.3 0.9 0.7

12:00 1.3 1.3 0.8 0.7

13:00 1.4 1.3 0.9 0.7

Lamp TUVRxxxx/Macam (λ-interval: 290–385 nm)

E-13814 E-13815 E-15728 E-30072

100 W 1.6 1.7 1.0 0.8

150 W 1.6 1.6 1.0 0.8

Lamp TUVRxxxx/Macam (λ-interval: 290–400 nm)

E-13814 E-13815 E-15728 E-30072

100 W 1.1 1.2 0.7 0.5

150 W 1.1 1.1 0.7 0.6

If corrected calibration factors are to be calculated, it is advantageous if the ratio κ be approximately constant for measurements of the same source under different conditions. For the Eppley instruments included in this comparison, the ratio κ was stable for different zenith angles as well as for different lamps. This enables corrected calibration factors for both wavelength intervals to be calculated.

Corrected calibration factors for each Eppley instrument can be estimated from the ratios κ given in Tables 5.2.5-8 using K′ = K_e κ where Ke is the factor provided calibration factory (see Table 5.2.1). As can be seen from Eq. (10), these calibration factors are source dependent. It is estimated that an uncertainty of approximately 10% will be inherent in these corrected calibration factors particularly for the daylight measurements. This uncertainty is to a large extent due to the unstable weather conditions. The cloud conditions changed considerably during the 11 to 13 min required to complete a scan on the Macam spectroradiometer. These changes were reflected in the large variation in the broadband values collected in the same time interval by the Eppley radiometers. It is therefore advisable to repeat these measurements under stable weather conditions.

In document The 1995 intercomparison of UV-and PAR instruments at the University of Oslo. (sider 59-64)