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3.7.3.1 DEVICE DISTANCE

Measuring the flat field in close distance (method A, Subsection 3.6.2.1) is based on the assumption that the EL intensity change with device distance is negligible. However, the inverse square law states that intensity ∝_distance²¹ . To analyse this dependency, four EL images (𝐼𝐼_{𝑐𝑐𝑚𝑚𝑑𝑑}, 𝐼𝐼₁₋₃)

of the same c-Si module at different distances to the camera were taken (Figure 3.79a). To extract the relative intensity differences (𝑅𝑅𝑖𝑖,𝑂𝑂), the following steps were applied:

For both examined flat field images (𝐼𝐼𝑁𝑁𝑁𝑁,1, 𝐼𝐼𝑁𝑁𝑁𝑁,2) with index (𝑖𝑖):

For all EL images (𝐼𝐼_{𝑐𝑐𝑚𝑚𝑑𝑑}, 𝐼𝐼₁₋₃):

1. Subtract the background image.

2. Divide the result by the flat field image (𝐼𝐼_{𝑁𝑁𝑁𝑁,𝑖𝑖}).

3. Remove the lens distortion.

For image 𝐼𝐼₁₋₃ with index (𝑗𝑗):

4. Obtain perspective transformation (homography) matrix

(𝐻𝐻_{𝑐𝑐𝑚𝑚𝑑𝑑→𝑂𝑂}) from a comparison of detected patterns in 𝐼𝐼_𝑂𝑂 and 𝐼𝐼_{𝑐𝑐𝑚𝑚𝑑𝑑}

and fit the perspective of 𝐼𝐼_{𝑐𝑐𝑚𝑚𝑑𝑑} to the one of 𝐼𝐼_𝑂𝑂 : 𝐼𝐼_{𝑐𝑐𝑚𝑚𝑑𝑑→𝑂𝑂} = 𝑓𝑓(𝐼𝐼_{𝑐𝑐𝑚𝑚𝑑𝑑}, 𝐻𝐻_{𝑐𝑐𝑚𝑚𝑑𝑑→𝑂𝑂}) (Subsection 4.7.2.1).

5. Calculate ratio 𝑅𝑅𝑖𝑖,𝑂𝑂 =_𝐼𝐼 ^𝐼𝐼^𝑗𝑗

𝑟𝑟𝑐𝑐𝑟𝑟→𝑗𝑗.

6. Remove the edges, created by fitting errors of both images

(𝐼𝐼𝑐𝑐𝑚𝑚𝑑𝑑→𝑂𝑂, 𝐼𝐼𝑂𝑂) by setting all areas where the edge gradient is

higher than a given threshold (𝑥𝑥) to NaN (not a number).

𝑅𝑅𝑖𝑖,𝑂𝑂��𝑠𝑠𝑅𝑅𝑖𝑖,𝑂𝑂

As Figure 3.79c,d shows, the resulting ratios range between ±10% and appear to be mostly influenced by the chosen flat field image (Subfigure b).

Figure 3.79: a-b) EL images of a Si module at different distances (LPVO);

c) Examined flat field images; d) Intensity ratio (𝑹𝑹𝒊𝒊,𝒋𝒋) from 𝑬𝑬𝟏𝟏−𝟑𝟑 to reference 𝑬𝑬𝟓𝟓 using 𝑰𝑰𝑵𝑵𝑵𝑵−𝟏𝟏; e) same, using 𝑰𝑰𝑵𝑵𝑵𝑵−𝟐𝟐

The measured intensity values within the green ROI (Figure 3.79a) are shown in Figure 3.80. If the sum of all four ROIs is plotted relative to the biggest ROI at 𝑠𝑠3 the trend follows the inverse square law. However, if the ROI averages are compared then the result remains constant. Therefore, it is concluded that the distance between camera and DUT has no influence on the specific pixel intensity.

Figure 3.80: Normalised average and sum values of ROIs, shown in Figure 3.79a,b for different LS distances.

0 0.25 0.5 0.75 1

100 140 180 220

Normalised intensity [-]

Distance d [cm]

Average Sum Inv.Square

3.7.3.2 DEVICE TILT AND ROTATION

Maintaining an orthogonal angle between camera axis and DUT is often hard to achieve - especially in outdoor or on-field imaging.

The radiation exchange between two surfaces (camera and DUT), whereby surface1 << surface2, can be weighted using a view factor (𝜑𝜑12) [89]. 𝜑𝜑12

is a derivate of the inverse square law:

𝜑𝜑12= 1 𝜋𝜋 �

cos (𝛽𝛽₁) ∙ cos (𝛽𝛽₂)

𝑠𝑠² 𝑠𝑠𝐴𝐴2 (3.77)

� 𝜑𝜑₁₂= 1

𝑖𝑖,𝑂𝑂 (3.78)

The parameters introduced in this section are shown diagrammatically in Figure 3.81.

Figure 3.81: a) Perspective schematic of the view factor model;

b) Calculation of the differential plane area (𝑨𝑨_{𝟐𝟐𝒊𝒊}) from distance and view angle

For EL imaging the Equation 3.77 can be simplified using the following assumptions:

• All light rays enter the camera lens at a normal angle, therefore 𝛽𝛽₁ = 0 . This is valid, if vignetting (i.e. decreased light intensity for increasing 𝛽𝛽₁) has already been corrected.

• The physical area (𝑠𝑠𝐴𝐴2) is discretised for every image pixel (𝑖𝑖) and becomes 𝐴𝐴2𝑖𝑖. Using the theorem of intersecting lines (Figure 3.81b)

and noting that the effective area increases with increasing view angle, 𝐴𝐴_2,𝑖𝑖 can be described using:

𝐴𝐴_2𝑖𝑖 = �𝑈𝑈𝑑𝑑∙ 𝑠𝑠𝑠𝑠𝑑𝑑^𝑖𝑖� cos( 𝛽𝛽_2𝑖𝑖)

(3.79)

Where 𝑠𝑠_𝑑𝑑 is the focal length respective distance to plane centre [mm] and 𝑈𝑈_𝑑𝑑 is the size of one pixel in focal plane in x,y [mm]. Within the range of one pixel, 𝛽𝛽2 and 𝑈𝑈 are considered constant. This enables discretizing Equation 3.77 for every pixel (𝑖𝑖):

𝜑𝜑12 =cos(𝛽𝛽_2𝑖𝑖) ∙ 𝐴𝐴_2,𝑖𝑖

𝑠𝑠_𝑖𝑖² (3.80)

If 𝐴𝐴2,𝑖𝑖 is substituted by Equation 3.79 then the only two variable parameters 𝑠𝑠_𝑖𝑖 and cos(𝛽𝛽_2𝑖𝑖) cancel each other out. Noting Equation 3.78, the constants also cancel out. With this model and assuming a perfect Lambertian surface, 𝜑𝜑12 does not change at all for different angles!

However, at angles >60° light intensity of a PV module decreases noticeably (Figure 3.84a, b). In this experiment, the angular dependence of EL light intensity, relative to 0° was calculated (Figure 3.82).

Figure 3.82: Comparison of angular dependency of emissivity, relative to 𝜷𝜷𝟐𝟐=0°; Values for glass taken from [90]

As expected, the calculated result is almost identical to the emissivity values (𝜀𝜀) for glass, which are commonly used for thermography measurements. 𝜀𝜀 is obtained from the average EL signal of the angled module relative to the one of the module at 0° after correcting both images for vignetting, dark current and perspective. The red plot shows 𝜀𝜀 over DUT tilt angle (𝛼𝛼). In this setup, the distance between camera and device midpoint (𝑠𝑠_𝑑𝑑) is 1500 mm.

This, in comparison to the device dimension, relatively short distance causes the effective view angle (𝛽𝛽2) to vary (Figure 3.83). Since this variation is not symmetrical, the red plot in Figure 3.82 does not represent the actual situation. To correct for these variable 𝛽𝛽₂, the median of all relative images was calculated for 𝛽𝛽₂ bins of 5°. The distance of the resulting green plot even decreased relative to the emissivity of the glass.

Figure 3.83: Comparison of calculated effective view angles (𝜷𝜷_𝟐𝟐) [°] for different DUT tilt angles (𝜶𝜶) in Figure 3.84a

To correct for intensity deviation from perspective distortion, all images (Figure 3.84a) were divided by their angular dependent relative emissivity values (Figure 3.84e). The result is shown in Figure 3.84d.

In comparison to Figure 3.84b it is apparent that the intensity decrease for angles >60° is corrected. Subfigure (c) shows images (b) after division by their respective average (normalisation). For 75° and 80° light intensity slightly increases from image bottom to top. This trend is also corrected in (d). Only the last image (85°) shows inhomogeneous intensities.

Figure 3.84: a) EL images of a Si module imaged at variable tilt angles;

b-d) different corrections from (a); e) relative emissivity

As the original image in (a) shows, this is because the module edge points required for pose estimation could not be tracked precisely in this highly distorted and defocussed image.

To show their individual trends, the emission factor maps in (e) were scaled to a value, displayed on the image top. Without that scaling, a gradient within these maps would by hardly visible.

Taking this into account, as well as the fact that emissivity below 60° is almost constant, one could say intensity correction for tilted PV devices is not an issue for EL images. Depending on the imaging setup, this statement can be acceptable.

However, especially in outdoor imaging of larger areas (such as PV arrays) and under certain conditions, these deviations can become critical. In Figure 3.85, a 100x100 m PV array, as seen by a drone was simulated. The emissivity factor, shown in Figure 3.85c,d decreases in this example down to 75% at the corners of the drone’s field of view – excluding vignetting.

a) Distance [m] b) View angle [°]

c) Relative emissivity [-] d) Relative emissivity [-], as seen by the drone

Figure 3.85: Simulated optical parameters of a PV array from a drone’s perspective; Drone position xyz: -10m,50m,5m (blue dot in (c)); Camera field-of-view: 60°

An indication whether an intensity correction should be considered is given in Figure 3.86. If a maximum intensity decrease of 5% is accepted, view angles up to 50° are acceptable (Figure 3.82). As Figure 3.83 shows, the effective view angles not only depend on the objects orientation, but also its position within the image. Figure 3.86 therefore indicates areas to avoid, depending on the DUT’s rotation and tilt. For a camera field-of-view (FOV) of 30° and a DUT rotation and tilt of 40° (red line), only image areas in the top left of the image would be acceptable. For a rotation of 15° and no tilt most areas in the image will have view angles <50° and only a small area in the image (x:0-2,y:8-10) would be problematic for FOV ≥ 45°.

Figure 3.86: Image positions, where view angle 𝜷𝜷_𝟐𝟐 ≤ 𝟓𝟓𝟓𝟓° for a combination of different tilt and rotation angles of the measured PV device; a PV device imaged behind convex curves will have an intensity decrease of >5% and therefore should be avoided or corrected for; blue box: image area, if camera aspect ratio is ¾

3.7.4 SECTION SUMMARY

Flat field correction is essential for quantitative EL measurements to remove intensity distributions within EL images but also to allow inter-comparison across different imaging systems. Measured flat field images depend on the camera setup as well as orientation of the imaged DUT.

These influences are analysed in this section.

It is shown that the flat field (𝐼𝐼_{𝑁𝑁𝑁𝑁}) depends on the emitted waveband of the imaged DUT. In the examined case, 𝐼𝐼_{𝑁𝑁𝑁𝑁} differed up to 20% towards the image corners between an imaged red LCD screen and a PV module. A comparison of different aperture adjustments shows an up to 5% higher flat field at the image corner between f1.4 and f16. Therefore, it is proposed to measure 𝐼𝐼_{𝑁𝑁𝑁𝑁} for each applied aperture and waveband rather than to correct for its influence. Other influences, namely exposure time and perspective, can be corrected for.

In the examined case for exposure times shorter than 100 ms the intensity varied 200-300% due to a mechanical shutter. However, this additional

shutter vignetting decrease is inversely proportional to exposure time.

Therefore, it is proposed to only calculate the effective vignetting from base- and shutter vignetting maps for exposure times close to the opening/closing time of the shutter.

The imaged PV devices are not perfect Lambertian (diffuse) light sources.

For view angles higher than 50° their relative emissivity decreases.

Therefore, especially highly titled devices will appear darker. Depending on the imaging setup, this decrease can be corrected for by dividing the image by an emissivity factor map obtained from the DUT orientation.

Chapter Summary

When establishing an EL imaging setup, multiple calibration images should be taken in advance to reduce later measurement time and to enable image correction (Chapter 4):

If the light conditions within the imaging setup are immutable, dark current can be calculated as a function of exposure time. For this, multiple images under open circuit should be taken at a range of different exposure times. The subsequent fitting process was detailed in Subsection 3.1.2.

The current IEC draft 60904-13 in electroluminescence measurement suggests a minimum signal-to-noise ratio (SNR) of 15 for industrial and process control and a SNR of 45 for lab measurements. In order to minimise exposure time, it is suggested to calculate the SNR from two EL images and one background image (Equation 3.16). It was further shown that the noise level of an image is not constant, but rather a noise-level-function (NLF) of the EL signal intensity. A spatially resolved SNR map can be used to calculate part of the intensity-based uncertainty (Section 6.1).

This chapter presented the simple, yet effective Tenengrad parameter to measure relative image sharpness (Equation 3.3). This can be used to find best focus level. The expression of absolute image sharpness as standard deviation of a Gaussian blur kernel or as factor on the image resolution

was presented in Subsection 3.4.3. The latter parameter can be directly used to determine the minimum resolvable object size. This knowledge enables determination of the ability to resolve features (such as cracks and fingers) in EL images.

A novel way to measure the point spread function (blur) using a commercially available compact disc (CD) is presented in Subsection 3.4.4.6. A programmatically simpler method to obtain a radially invariant PSF using a V-shaped mask or a printed spoke pattern was shown in Subsection 3.4.4.3 and 3.4.4.4.

Several methods are discussed in literature to measure the image flat field (𝐼𝐼_{𝑁𝑁𝑁𝑁}). The methods often rely on the assumption that the calibration device is spatially homogenous. As was shown, this can cause erroneous results.

Section 3.6 therefore proposed different methods to measure and functionally fit 𝐼𝐼𝑁𝑁𝑁𝑁. Even without any calibration 𝐼𝐼𝑁𝑁𝑁𝑁 can be estimated to a certain extent. A method imaging a PV device in the image plane at multiple random positions (Subsection 3.6.2.5) was found to give best results in a quantitative comparison.

The last Section 3.7 further described 𝐼𝐼_{𝑁𝑁𝑁𝑁} as function of exposure time, aperture, wave band and perspective orientation. Correction for exposure time and perspective were discussed in Subsection 3.7.2 and 3.7.3. It was shown that a PV device can be described as a diffuse Lambertian surface up to an angle of 50°. This reduces effort when rectifying perspective in EL images.

The source code, used to calculate the signal-to-noise ratio, to measure and validate sharpness, flat field, lens- and perspective distortion is made publicly available and is embedded in the image processing software dataArtist (Appendix 3).

4 I ^MAGE C ^ORRECTION

To correct EL images, related distortions must be removed. This chapter covers the implemented image correction routine (Figure 4.1) using two EL images as well as a dedicated camera calibration file. The routine sequence is chosen for distortions to not impair subsequent steps.

Figure 4.1: Overview of Chapter 4

First, temporal imaging artefacts (single-time-effects) are removed through evaluating changes in two EL images (Section 4.1). Using results from camera calibration (Chapter 3), the dark current which offsets the EL signal is removed (Section 4.2). Spatial image distribution is corrected for in the following Section 4.3. The removal of remaining artefacts is described in Section 4.4. Methods to sharpen images and to remove lens distortion are detailed in Section 4.5 and 4.6. Position and orientation of PV devices in EL images is detected and corrected for in Section 4.7.

Precise alignment of two EL images is described in Section 4.8. Finally, intensity normalization (Section 4.9) ensures equal image contrast and brightness.

Single-time-effects

This section discusses the statistics and removal of specific EL image artefacts, called single-time-effects (STE). STE are caused by cosmic particles such as heavy ions, along with neutrons and protons with energies above 10 MeV [91]. When these mainly space-born particles cross the sensitive region of the CCD matrix, they cause effects of ionisation and lead to spots, which are only visible once after signal readout.

STE increase the intensity of affected pixels. Depending on whether STE occur in the EL image or in the background image, they are visible in the background-corrected EL image as bright or dark spots. In the latter case, the small spots or straight to curvy lines caused by STE can be conceivably confused with cell defects. In this section the intensity offset due to STE as well as their occurrence over time is evaluated. For the examined setup, it is shown that the disruptive influence of STE is visible for cell voltages under 0.65 V. For this case, a robust STE removal method is proposed using an additional EL image taken in series.

STE can be distinguished from hot pixels [92] by comparing two images taken in series with the same exposure time (Figure 4.2). Whilst hot pixels will remain constant in place and intensity, the probability of STE to occur

twice at the same time is negligible. STE saturate CCDs bit by bit. For space-borne CCDs Hill et al. reported that an exposure time of 1000 s would affect already 2.5% of the image [93].

Figure 4.2: Selection of STE with different size and intensity;

hot pixels are visible as single bright pixels

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3.7.4 SECTION SUMMARY

Chapter Summary

4 I MAGE C ORRECTION

Single-time-effects

4 I ^MAGE C ^ORRECTION