Angular‐dependent spectral responsivity—Traceable measurements on optical losses in PV devices

Angular‐dependent optical losses can have an effect on the spectral responsivity of photovoltaic devices. When these devices with differing angular‐dependent spectral responsivity are exposed to incident direct and diffuse solar spectral irradiance they will perform differently compared with direct and perpendicular beam exposure only. However, if the angular and polarization‐dependent spectral responsivity is known, optical losses can be determined for any given angular distributed solar spectrum. Here, we show the capabilities of a newly developed laser‐based calibration facility for traceable measurements on reference solar cells angular‐dependent spectral responsivity for device areas of up to 156 × 156 mm2. Our investigation is focused on a comprehensive analysis on all related measurement uncertainties. We present the results of measurements on a variety of reference solar cells as well as an industry type solar cell with and without encapsulation showing that strong differences in their optical properties occur. Additionally, we compare the results obtained with a conventional broadband characterization approach using a halogen lamp as light source. An agreement, better than 1%, was observed for the broadband measurement and the spectral measurements weighted by the spectral responsivity and the lamp spectrum. It is shown why different light sources lead to different angular‐dependent responsivities. In conclusion, validation measurements of solar simulator‐based or natural sunlight‐based angular responsivity facilities at testing and calibrations laboratories can be offered. Furthermore, by means of traceable angular‐dependent spectral responsivity measurements and multidimensional models under consideration of diffuse light components, optical losses for photovoltaic performance measurements, energy rating, and related uncertainties can be studied.

research has shown that polarization of the incident light and AOI effects are also apparent for the spectral responsivity. [3][4][5][6][7][8][9] Angular losses in PV devices can introduce differences in the short circuit current under standard test conditions I STC of up to 3.5% under global normal irradiance conditions with horizontal orientation compared with a device without losses due to angular effects. 10 In 1987, Shimokawa et al showed within a comparison of indoor and outdoor calibration methods using the same chain of traceability discrepancies ranging from 1% to 4% for short circuit calibration of reference solar cells (SCs). 11 Typical measurement uncertainties for I STC calibrations using the global normal sunlight method in that time were around 3%, dominated by the contribution of field of view and AOI effects. 12 For global measurements or energy rating with fixed PV device orientations, the AOI losses can be considerably larger (up to 15% for specific global irradiance conditions depending on the tilt angle of the device), due to diurnal and annual variations of direct and diffuse sunlight's AOI. 13,14 The IEC standard 61853-2 demands for spectral responsivity measurements in order to consider spectral mismatch for solar spectra differing from the reference solar spectrum E λ,AM1.5G (λ) defined in an international standard IEC 60904-3. 15 However, the AOI measurements demanded by the standard generally do not cover spectral effects, ie, a spectral angular mismatch correction. To fill this gap, a facility was constructed to investigate and evaluate the significance of spectral effects on AOI measurements and related uncertainties.
The laser-based differential spectral responsivity facility (Laser-DSR) at Germanys national metrology institute Physikalisch-Technische Bundesanstalt (PTB) already provides high accuracy primary calibration of the absolute spectral responsivity of reference SCs at various irradiance levels and temperatures. 16 Hence, the short circuit current of the device at any demanded solar spectrum can be derived. This facility has been upgraded to measure the AOI dependency of reference SC spectral responsivity. Consequently, AOI effects can be determined for several different spectral irradiances of light sources. The combination of an angular responsivity facility with a spectral responsivity facility was achieved by using monochromatic radiation at constant broadband bias irradiance level. The angulardependent spectral responsivity of PV reference devices with an active area of up to 156 × 156 mm 2 can be calibrated, and the angular responsivity at any given solar spectrum can be derived. Here, we show the characterization of AOI measurements including the determination of the measurement uncertainty budget. The uncertainty budget includes Type A uncertainty, nonlinearity of the current-voltage amplifier, angular-dependent uniformity of the monochromatic light field, uncertainties due to positioning of the device relative to the rotation axis, polarization dependencies, uncertainty of the rotation angle due to an expanded light source, irradiance non-linearity of the PV device, temperature-dependent effects, and wavelength uncertainty.
These uncertainty contributions were investigated exemplary for 20 × 20 mm 2 reference SCs in world photovoltaic scale (WPVS) design and for 156 × 156 mm 2 sized industrial SCs. Finally, the angular-dependent spectral responsivity s(λ, θ, φ) of different types of SCs was determined and compared. This new calibration service will be offered to calibration and testing laboratories for the validation of their own AOI facilities.

| Description of the angle of incidence facilities
We upgraded the Laser-DSR facility 16 with a fully automated goniometer that can realize any AOI in the full hemisphere within the SCs field of view (0°≤ θ ≤ 90°, −180°≤ φ ≤ 180°). An additional 3 axis translation stage (x, y, and z direction) allows AOI measurements even if the devices are mounted off-axial relative to the optical axis. It provides a positioning precision of better than 0.1 mm covering a translation range of several meters. The SC mounting plate provides Peltier-controlled sample holders for sample thermostatization and for investigations of the devices temperature dependencies. Bias lamps, producing a broadband spectrum to set the samples in a steady working point, can be mounted on the rotation stage so that the bias irradiance does not change during rotation. Hence, irradiance non-linearity effects of PV devices under test are considered to be negligible. The SC is then rotated in the uniform monochromatic light field of the Laser-DSR facility to determine the relative angular-dependent spectral responsivity s(λ, θ, φ). The spectral range of the Laser-DSR covers 250 nm ≤ λ ≤ 1600 nm. As the AOI dependence of SCs is dependent on the polarization, the angular responsivity is determined subsequently for 2 orthogonal polarization states of the monochromatic light. Afterwards, a complete calibration of the absolute spectral responsivity s(λ) at perpendicular AOI with θ = 0°was performed. Finally, the AM1.5G weighted angular-dependent responsivity s AM1.5G (θ, φ) can be derived by averaging the spectral angular responsivity curves weighted by their corresponding spectral responsivity s(λ) and the AM1.5G reference solar spectral irradiance E λ,AM1.5G (λ).
In order to validate the AOI-dependent measurements, 2 different setups were used to characterize a series of PV devices. In our first approach, we are using the setup described above and illustrated in Figure 1. In a second step, we are using a tungsten halogen lamp (1000 W FEL) as a broadband light source with a known spectrum E λ,lamp (λ).
For angular-dependent measurements, the SC is tilted relative to the light source. The axes of rotation are in the center of the device on the optical axis between SC and light source for φ-rotation (see As reference plane for the tilt-axis θ, we are using the thickness d real which is not necessarily matching with the geometrical location of the active area relative to the backside of the housing in case if the devices are encapsulated. 17

| Derivation of the modeling equation
The light (either monochromatic light or broadband light with a given spectrum) irradiating the SC, which is the PV device under test, generates a photocurrent I SC . The photocurrent is measured as a voltage V SC using a transimpedance amplifier (current-to-voltage converter with internal resistance R SC ) and a multimeter or a lock-in amplifier.
The transimpedance amplifier retains the SC operating in a short circuit state. For angular-dependent measurements, the measured current I SC (θ, φ) is normalized to the value at normal incidence I SC (θ = 0°, φ = 0°). Because the irradiance of the light source might drift over an AOI measurement cycle, it is monitored by a fixed photodiode/SC. The photocurrent of the monitor device I MD is measured as a voltage V MD using an additional transimpedance amplifier. The output voltage of the amplifier V MD can be expressed via the amplifiers internal resistance R MD for each photocurrent I MD monitored during a AOI measurement cycle with different device under test rotation φ and -tilt θ. Hence, the modeling equation for the device under test AOI dependence, which corresponds to the relative angular responsivity s(θ, φ), is then: with Q SC , the monitor corrected signals.
For the compensation of polarization dependencies of the SC, the angular-dependent measurement cycle is performed at 2 orthogonal polarisation states of the monochromatic irradiance using broadband polarization filters. Both normalized measurements were averaged to obtain an angular responsivity for unpolarized light. Thus, the modelling equation enhances to with a series of correction factors f i with individual uncertainties contributing to the total uncertainty u(s(θ,φ)) of s(θ,φ).

| Characterization of the AOI facility and uncertainty analysis
In this section, we present a thorough characterization of the AOI facilities to determine a measurement uncertainty for measurements of the angular responsivity for the first time. A stepwise discussion of the correction factors f i is shown in detail.Contributing influences on the measurement uncertainty are • Type A uncertainty, due to statistical fluctuation in the corrected signals Q SC , • Electrical non-linearities of the current measurement • Irradiance non-uniformity within the rotation volume,  Schematic of the angular responsivity measurements using a broadband light source. The PV devices were kept attached on the same mounting plate as shown in Figure 1, while the tungsten halogen lamp is located on the same optical table next to the monochromatic setup. This setup was used to investigate the disadvantages of using an AIO facility with a given lamp spectrum E λ,lamp (λ) [Colour figure can be viewed at wileyonlinelibrary.com] • Positioning of the device under test relative to the rotational axis, • Thickness of the PV device, • Polarization, • Uncertainty of the tilt angle θ, • Irradiance non-linearity of the PV device, • Uncertainty of the temperature measurement and • Wavelength uncertainty.

| Type A uncertainty
To consider type A uncertainties, the voltage measurements at a given AOI are repeated typically n = 20 to 40 times (see Figure 3).
Type A uncertainties are individually calculated by the variance of the monitor corrected mean signal Q:

| Irradiance non-uniformity within the rotation volume
For laboratory measurements, a change of the irradiance spatial nonuniformity (nu) inclined on a device surface with a given tilt angle can be expected. The reason is the inverse-square law, which provides a 1/z 2 dependency for the irradiance in case if a divergent point light source is used. If we combine the spatial distribution of the spectral responsivity of a SC s(λ mono , x, y) at a designated monochromator wavelength λ mono and the (non-uniform) monochromatic irradiance distribution of the corresponding light field E mono (λ mono ,x, y), the generated photocurrent of the SC I nu can be expressed: For a perfect light field with uniform (uni) irradiance distribution, Equation 6 reduces to Hence, a non-uniformity correction factor f nu for a wavelength λ mono can be derived: However, the non-uniformity factor itself is not an uncertainty contribution for angle-dependent measurements. For angular-dependent measurements, only the relative change of the non-uniformity correction factor with respect to normal incidence is of importance.
Hence, we approximate the uncertainty of the angular-dependent non-uniformity u(f anu (θ)) as the relative deviation of the previously determined correction factors f nu (θ) to f nu (0°): Because f anu (θ) of a device is strongly related to the non-uniformity of the SC lateral responsivity s(λ mono ,x,y), and the lateral non-uniformity of the irradiance distribution at the given angle θ within the rotation volume of that device, an extensive characterization would be required to obtain the individual correction parameters. This is not possible within reasonable time and effort for every measurement. Later, we show such an extensive characterization in order to quantify these individual correction parameters for a general case of typical used industrial type c-Si SCs and c-Si reference SCs.
The spatial spectral responsivity s(λ mono , x, y) of a silicon SC (156 × 156 mm 2 ) was measured by using a light beam induced current   The non-uniformity of the irradiance within the rotation volume of the device E mono (λ mono , x, y, z) was calculated from the measured E mono (λ mono , x, y, z 0 ) using the E~1/z 2 law. The irradiances E mono (λ mono , x ′ , y ′ ) for varying AOI corresponding to the surface of the tilted device located at new coordinates x´and y´were obtained by applying an interpolation procedure at the designated intersection points explained in Figure 5.
As an example, the dependence of the irradiance non-uniformity E mono (λ mono , x´, y´) during a tilt of a large area device for a light field at λ mono = 800 nm and z 0 = 2500 mm is shown in Figure 6. In this case, the irradiance non-uniformity in the designated test plane calculated analog to a procedure defined in the international standard IEC 60904-9 Ed. 2 19 increases from 1.74% at θ = 0°to 7.07% at θ = 80°f or a 156 × 156 mm 2 sized field. In the case of a 20 × 20 mm 2 sized monochromatic field, the non-uniformity increases from 0.25% at θ = 0°to 0.9% at θ = 80°.
Again, these maps were determined for the wavelengths from 350 to 1150 nm in steps of 50 nm as well as for the broadband light field of a tungsten halogen lamp. Based upon these datasets of s(λ mono , x, y) and E mono (λ mono , x´, y´) u(f anu (θ)) for a large area SC (bottom). Please note, the uncertainties for the broadband light source are larger, because the non-uniformity of the irradiance distribution is higher.
As already mentioned, such a thorough analysis cannot be made for each calibration within a reasonable time and effort. Therefore, the worst-case assumptions for the uncertainty of f anu shown in Figure 7 are taken as generally assumed uncertainties for the given combination of device size and light source, so that

| Positioning of the photovoltaic device
The lateral positioning of the sample relative to the φ-rotation axis and optical axis (x and y direction) is made individually using an accurate laser-alignment procedure. Hence, the exact position of the device center relative to the rotation axes can be determined with an accuracy of better than ±0.1 mm. This holds both for the monochromator-based and broadband-based setups, because the same goniometer and alignment procedure is used. Hence, positioning uncertainties in x and y direction are negligibly small.

| Thickness of the solar cell
The thickness d real , ie, the exact location of the active surface of the PV device relative to the θ-axis in z direction is a more critical parameter compared with the positioning uncertainty in x and y direction. For encapsulated devices, the location of the active area relative to the backside of the housing is usually unknown. 17 This distance is defined as the thickness with an estimated uncertainty of ±0.5 mm. The exact location of the θ-axis relative to the mounting plate of the SCs has an uncertainty of d ± 0.5 mm. Hence, the conservatively estimated uncertainty of the real relative position of the active device surface to the tilt axis has a maximum value of u(d real ) ± 1 mm. Figure 8 shows the effect of an inaccurate thickness d on the angular-dependent measurements.
In case of smaller thickness values (b), the device is tilted towards the light source resulting in an overestimation of the values at increasing FIGURE 5 Schematic of the irradiance non-uniformity dependence at different AOI onto the PV device under test. By scanning the designated test area at a distance z 0 , a lateral irradiance distribution was determined for θ = 0°. For larger angles of incidence, we determined the irradiance distribution on the inclined surface at a differing distance z(x´,y´) at new coordinates by using the inversesquare law and an interpolation procedure [Colour figure can be viewed at wileyonlinelibrary.com]

| Polarization
The monochromatic irradiance of the laser-DSR facility is polarized.  surements is taken. This is shown as dotted lines in Figure 9. A conservative estimation of 10% of this maximum deviation is taken as uncertainty (rectangular) u pol (θ) for the polarization correction factor f pol :

| Uncertainty of the tilt angle θ due to an extended light source
In our setup, the light source for the angular-dependent measurements can be considered as an extended radiant area with an aperture diameter A. In our analysis, the aperture area is approximated to represent an equally distributed ensemble of point sources that irradiates the PV device with a diagonal dimension L.
Under the assumption of a Lambertian source surface, a rectangular distribution of deviating AOIs can be found within an interval of −Δθ and +Δθ. By applying a simple trigonometric law (see also Figure 10), the maximum deviation can be found in dependence of θ and the distance z: Additionally, a systematic offset θ 0 could be present if the measurement plane is not exactly perpendicular to the z-axis (ie, the optical axis). This offset was experimentally determined to be < 0.1°. The angular-dependent responsivity s(θ) is an asymmetric function within a given interval [−Δθ + θ 0 , +Δθ The average angular-dependent responsivity s([−Δθ + θ 0 , +Δθ + θ 0 ]) would lead to a systematic deviation Δs(θ i ) from s(θ i ) at each AOI θ i : The impact of this systematic deviation for an aperture of 10 mm is shown in Figure 11. (rectangular): These uncertainty contributions are individually calculated for each device visualized as dashed blue curves. Please note that the uncertainty can generally be considered higher for smaller devices, because the effect of the systematic offset outweighs the effect of the angular distribution.

| Irradiance non-linearity of the photovoltaic device
The irradiance non-linearity of the PV device leads to systematic deviations when changing the incident angle and hence the irradiance. This could either be corrected for when the non-linearity is known or otherwise an uncertainty has to be assigned. In the case of the monochromatic AOI facility, the angular-dependent spectral responsivity is measured with constant bias irradiance E. This is realized using bias lamps mounted on the rotation stage (see Figure 1). Hence, the non-  The situation changes for broadband of the AOI facility used for this work. In this case, the irradiance changes upon rotation by 1 order of magnitude. In the present case of a 1000 W tungsten halogen lamp at a distance of 2500 mm is less than 10 W/m 2 and no additional bias lamps are used (see Figure 2). For AOIs larger than 80°, irradiance decreases to values below 1 W/m 2 .
Because the uncertainty due to the irradiance non-linearity is device dependent, it should be investigated and corrected individually for each device and each AOI θ. However, for the broadband AOI setup, the uncertainty due to non-linearity u E (θ) is estimated to be a function of θ and of the maximum influence of the individual irradiance non-linearity. The maximum influence was previously determined with the DSR method.

| Uncertainties due to the device temperature
The spectral responsivity of the SC is temperature dependent. It is assumed that the temperature coefficient is not influenced by the angular-dependent excitation. Hence, only temperature fluctuations during the measurement remain as a source for uncertainties. The Peltier element-based temperature control keeps the device temperature constant at 25°C with insignificant fluctuations around ± 0.05 K.
In case of the monochromatic facility, we use steady-state bias lamps which are kept in a fixed position during rotation related to the PV device (see Figure 1). The bias irradiance represents the dominant heat load. Therefore, the heat load on the SC does not change significantly during rotation. We conclude that uncertainties introduced by temperature effects are assumed to be negligible for the angular-dependent spectral responsivity measurements.
In case of a broadband setup without additional bias irradiance, the heat load changes up to 15% across the rotation volume for a 156 × 156 mm 2 SC at a distance z 0 = 2500 mm if the 1/z 2 distance law is assumed. Because the serially connected Peltier elements theoretically provide uniform cooling at for a given uniform heat load, a non-uniform heat load can affect the device temperatures non-uniformity, resulting in differences in the temperature ΔT(x,y) for varying AOI. However, we assume that at distances >2 m, the effect of the positive temperature difference in the surface area with a higher heat load is compensated by the effect of the negative temperature difference in the surface area with lower heat load for tilted devices.
Asymmetries in the device temperature non-uniformity ΔT(x,y) seem to be negligible for larger distances. Hence, uncertainties due to temperature effects are assumed to be negligible also for the investigated broadband AOI facility.

| Wavelength uncertainties
The light source is a laser setup generating the desired wavelength by using a tunable mode-locked Titan:Sapphire laser and different nonlinear optics. Furthermore, a monochromator reduces the spectral bandwidth. The wavelength uncertainty is smaller than 0.3 nm and hence negligible in our study.

| Calculation of a combined uncertainty for the angular-dependent measurements
All relevant uncertainty contributions described earlier can now be incorporated into the modelling equation 3 leading to the final equation for the angular-dependent spectral responsivity: ·f el ·f anu ·f d ·f pol ·f θ : (17) In analogy, the equation for the integral angular-dependent responsivity using a broadband light source can be written as The calculation of the uncertainty of the angular-dependent spectral responsivity u(s(θ, φ)) is performed using Monte Carlo methods.
The calculation is done for every single measurement because the uncertainty contributions are partly dependent on the measurement result itself (ie, Type A, f pol , f θ ). Furthermore, most uncertainty contributions are functions of the AOI. Therefore, the uncertainty budget individually changes dependent on device, device size, wavelength, and AOI. Because the creation of a classical tabulated uncertainty budget cannot cover all these dependencies, we only show a selected example in Figure 12 in order to visualize the magnitude of the  (s(θ, φ)).
In the upper graph, the relative standard uncertainties of the individual uncertainty contributions are shown for an angular-dependent measurement of the spectral responsivity at 450 nm of an encapsulated reference SC. The black curve donates the combined standard uncertainty. It can be seen that the uncertainty increases with increasing AOI. This is related to the uncertainty contribution from the non-uniformity and the AOI θ. In the lower graph, the contribution of the individual uncertainty components to the combined standard uncertainty is shown as percentage values. This graph visualizes the dominating uncertainty components for the respective AOI in our example.

| RESULTS AND DISCUSSION
In the following section, exemplary results of the angular-dependent spectral responsivity of different types of SCs are shown in order to demonstrate the strong differences that can occur. Subsequently, it is shown that the angular responsivity measured by any broadband light source (natural sunlight, solar simulator, etc.) can be mathematically derived from the measured angular-dependent spectral responsivity, the measured spectral responsivity of the device at normal incidence and the spectral irradiance. Subsequently, a validation of the spectral measurements is shown by calculating the angular responsivity for a broadband light source using the spectral data and then comparing it with the actual experimental measurement using this (previously described) broadband light source. Finally, based on these data sets an angular-dependent spectral mismatch referring to reference conditions is discussed as well as the occurrence of additional measurements uncertainty due to azimuthal asymmetry of a PV device. Figure 13 shows the angular-dependent responsivities at different wavelengths of a non-encapsulated c-Si reference SC (left-hand side), an encapsulated c-Si reference SC (middle), and an encapsulated c-Si reference with an IR-filter as cover glass (right-hand side) that is typically used as a reference for calibration of amorphous Si SCs. In the upper graphs, the angular-dependent responsivity for different wavelengths is shown together with the ideal cosine response (black dotted line). In the lower graphs, the relative deviation from this ideal cosine response is shown.

| Measurement results
From these graphs, significant differences in the angular-dependent spectral responsivity can be observed. For the non-encapsulated reference SC, there is a strong deviation from cosine at incidence angles larger than 25°apparent. This deviation is enhanced with were previously described by Geisemeyer et al. 9 For the bare SC, the deviation from cosine is large even at low angles of incidence for short wavelengths below 500 nm. In the VIS-IR region from 500 to 1200 nm, the deviation from cosine is very low even for high angles of incidence up to 60°. After encapsulation of such a SC in a module package, this spectral and angular characteristic significantly changes. The cosine response significantly improves for all wavelengths and even lead to a relative super-cosine response for the infrared region at angles below 65°. Hence, we conclude that the spectral responsivity of typical PV devices can significantly vary for different AOI.  angle-dependent spectral responsivities. The latter can generally be expected when 1 device is encapsulated and the other is not.

| Validation
For validation of the measurements and the determined measurement uncertainties, the 2 described methods for angular-dependent measurements will be compared. The angular dependence of the previously described IR-filtered device was measured using the broadband 1000 W FEL tungsten halogen lamp and the spectral facility. From the spectral data, an artificial broadband data set was derived by weighting the spectral angular data with the measured spectral responsivity of the device at normal incidence and the spectral irradiance of the 1000 W FEL tungsten halogen lamp. The results are shown in  Figure 15 for each AOI. Hence, we conclude, that both measurements are consistent within the stated expanded uncertainties. Furthermore, it can be concluded that the angular-dependent responsivity for any spectral irradiance can be derived from the spectral data by calculating the weighted average using the spectral responsivity at normal incidence and the spectral irradiance.

| Discussion of spectral mismatch effect
From the previous section, we can conclude that the measurement of the angular-dependent spectral responsivity allows the analysis of spectral and angular effects under any given spectrum including diffuse irradiance components. While spectral mismatch errors can be neglected for monochromator-based AOI measurements, they have to be considered for measurements taken with broadband setups providing a fixed spectrum. The angular-dependent spectral mismatch factor SMM(θ) due to the spectral irradiance of the broadband light source E λ,lamp (λ) and due to the angular-dependent spectral responsivity s(λ, θ) of the individual PV device can be expressed as analog to the definition in 22 : As a reference spectral responsivity, we used for this computation the devices spectral responsivity under normal incidence (θ = 0°). E λ (λ) We calculated the spectral mismatch factors in dependence of the AOI θ for 3 different PV devices (see Figure 16). In our example, we refer to the global solar reference spectrum under air mass 1.5 defined in the IEC standard 23 by using it in Equation 19 for E λ (λ) and the spectral irradiance of a 1000 W tungsten halogen lamp E λ,lamp (λ) used in the previously described broadband AOI-facility.
In analogy to the conventional need for spectral mismatch correction when either the spectral irradiance of the solar simulator differs significantly from the AM1.5G spectrum or the spectral responsivity of reference and DUT differ significantly also a need for spectral mismatch correction can be observed for AOI-dependent measurements. In this case, the spectral irradiance of the halogen lamp differs significantly and can be considered to be a poor performing solar simulator. Hence, this scenario can be considered as a worst-case scenario. For the encapsulated device, the angular-dependent change of spectral responsivity (shown in Figure 13 middle) is less pronounced.
Hence, spectral mismatch correction of less than 0.5% is needed, even at larger AOI. For the non-encapsulated device, angle-dependent change of spectral responsivity (shown in Figure 13 left) is more pronounced, especially in the UV-VIS region above 30°. This leads to a needed spectral mismatch correction up to 1.2%. The most pronounced angular-dependent change of spectral responsivity was observed for the IR-filtered reference device (shown in Figure 13 right-hand side). The resulting spectral mismatch correction is up to 6%.
Hence, we conclude that an angular-dependent spectral mismatch can be considered to be of major importance and should be included in any uncertainty budget for a broadband light source AOI facility. If the angular-dependent spectral responsivity is not known, a larger uncertainty should be estimated.

| Azimuthal asymmetry of a photovoltaic device
Angle of incident-dependent measurements using a broadband light source or even monochromatic light can be considered as a very time-consuming measurement. Furthermore, the parameter space that should be covered (θ, φ, λ) is very large; hence, often a full characterization is not possible. The energy rating standard IEC 61853-2 1 demands measurements to be taken along 2 orthogonal azimuthal directions with respect to the module normal. Rotational symmetry should be verified at θ = −80°and θ = 80°AOI. We tested the azimuthal symmetry for several devices in order to evaluate the measurement uncertainty if only measurements along 2 orthogonal azimuthal directions are performed compared with measurements in the full half space using the previously described broadband light source facility. Figure 17 shows the result for the non-encapsulated reference SC (see also Figure 13 left-hand side). This example was found to have the FIGURE 15 Comparison of angular responsivity measurements of the IR-filtered reference device using the broadband light source (tungsten halogen lamp) and the monochromatic light source. From the spectral data shown in Figure 13 (right-hand side), the weighted average was calculated using the measured spectral responsivity of the device at normal incidence and the spectral irradiance of the halogen lamp as weighting functions. The upper graph shows the absolute value of the E n number according to ISO17043. Because the absolute value of the E n number is smaller than 1 for all angles, the 2 measurements can be considered to be consistent within the respective expanded uncertainties [Colour figure can be viewed at wileyonlinelibrary.com] tion observed for all other azimuthal orientations. For this example, the asymmetry at 80°along the φ = 0°and φ = 90°direction is 3.5% and 5.6%, respectively. Hence, this non-encapsulated WPVS reference SC must be considered to be non-symmetrical according to the standard. However, the maximum azimuthal deviation shown as the grey area in Figure 17 is 12%. Therefore, we conclude that the azimuthal symmetry in the studied reference PV device is not apparent. If such dependence is found, the procedure defined in the energy rating standard 1 cannot be applied properly. Please note that a measurement error related to a systematic offset of the AOI θ can lead to asymmetric measurements. A systematic offset of only 1°leads to a measured asymmetry of 22% at 80°AOI.

| SUMMARY
We have improved PTB's primary calibration facility for reference SCs with the capability to measure optical losses in dependence of the spectrum and AOI of PV devices, such as reference SCs and mini-modules with active areas of up to 156 × 156 mm 2 . By means of a comprehensive characterization of the setup and measurement method, we were able to derive a detailed measurement uncertainty budget for the angular-dependent spectral responsivity measurement.
We show measurement results of angular-dependent spectral responsivities for a diversity of different PV devices. Dependent on the device, we observed strong differences in the responsivities particularly in the UV and IR wavelength regions for varying AOI. We validated the measurement results obtained with our primary setup with a comparison against a broadband facility, providing a fixed lamp spectrum. The impact of an angular-dependent spectral mismatch problem was outlined. Finally, we have shown the significance of PV devices azimuthal symmetry for angular-dependent PV device characterization. As a result of this study, PTB offers the calibration of the angular-dependent spectral responsivity of reference SCs and will transfer these findings to standardization bodies. Furthermore, based on this characterization method, a variety of investigations regarding the impact of diffuse light components on high accuracy PV device performance measurements and energy rating is now feasible. 20,24