Plain language summary
The VISproPT is a novel instrument useful for scientists and technicians dealing with reflective panels for parabolic-trough (PT) Concentrating Solar Power (CSP) plants. The VISproPT is an advanced laboratory instrument with high precision designed to verify the shape compliance of PT panels. Deviations of slope and height from the ideal parabolic profile are evaluated and presented in terms of 2D contour maps as well as root mean square (RMS) values; these geometrical parameters are very useful to improve the production technology. Concerning the panel effectiveness in redirecting the solar radiation onto the linear receiver tube, the most representative parameter is the so-called intercept-factor (I-F), i.e. the ratio of the geometrical intersection of the reflected solar beam with the receiver tube; the VISproPT software evaluates I-F by considering the standard divergence of the solar radiation on the Earth (4.7 mrad, half-apex angle), and the proper values of parabola focal-length and receiver-tube diameter; I-F is reported as a 2D contour map and its mean value.
1 Introduction
The Visual Inspection System (VIS) approach was patented by ENEA on 20081; it is based on the idea of placing a light source nearby the focus of the reflector and acquiring a number of images in the near-field from different positions of camera or source. On the basis of the VIS approach we developed the following instruments:
1. VISfield to verify the mutual optical alignment between receiver tube and parabolic trough reflector for modules in field2
2. VISshed, the adaptation of VISfield for the quality control in the shed, soon after the module assembling3
3. VISdish for facet-canting and 3D shape measurement of solar dish in field4
4. VISproLF for 3D shape measurements of Linear Fresnel panels in laboratory/industry5
5. VISprofile for 3D shape measurement of parabolic trough panels in laboratory
The last one was developed in 2009 at ENEA Casaccia just as demonstrative experimental set-up, alternative to the older 3D optical profilometer6; the VISprofile was scarcely engineered and unsuitable to industry. On the other hand, shape/slope deviation of the reflective surface from the ideal profile causes solar radiation leakage with reduction of efficiency. That makes the shape quality check a very important task. Therefore, under ENEA guidance, since 2012 the Italian worldwide leader in Measurement, Inspection and Testing, MARPOSS7 started to engineer a new version, named VISproPT, suitable to commercial purposes. The prototype was soon ready but because of weakness of CSP market and insufficient ENEA funding, it remained in stock until 2018 when it was delivered to ENEA Casaccia to be acquired under the umbrella of EU SFERA-III project8. The hardware commissioning was delayed to September 2021 because of the COVID-19 pandemic and the resulting shortage of electronic components. Only from that time the development of image processing software as well as calibration procedure started. The good side of such a long gestation is the relevant progress, matured in the meanwhile, of the ENEA knowhow on the use of digital cameras in 3D geometric characterization; as a result now the instrument calibration is much simpler than what initially prefigured. To exploit the new instrument we took the opportunity of WP10 Task3 of SFERA-III project8 to launch the proposal of a new round-robin (RR) on 3D shape measurements of panels for parabolic-trough (PT) solar collectors; a previous attempt, accomplished about 10 year ago in SolarPACES TaskIII framework9, did not give satisfactory results because of the difference among the results obtained by the participants were greater than the experimental error; as matter of a fact, today a dedicated guideline on the topic is still missing. The proposal was accepted by F-ISE and DLR and then has been extended to National Renewable Energy Laboratory (NREL) and Sandia National Laboratories (SANDIA) who benefit of the Transnational Access tools offered by SFERA-III to send teams in Europe for visiting research infrastructures and participating to the introductory meeting on the round robin itself.
At the time of writing this article, the round-robin is just started; the global results will be published in a next future. This paper is focused on the novel instrument VISproPT; the results achieved by ENEA are here presented just to illustrate the instrument functionality.
2 VISproPT basis
2.1 Main hardware components
In general, the VIS method1 just needs a good monochrome digital camera and a structured light source; the source type and the arrangement of these components around the object to be measured depend on the specific case.
The engineered version of the VISprofile is named VISproPT to distinguish it from the other instrument, named VISproLF5, designed for 3D shape measurements of panels for linear Fresnel collectors.
The optical sketch adopted in VISproPT is shown in Figure 1, while the hardware, manufactured by MARPOSS Italia Spa7, in Figure 2. The investigated PT panel is placed on 4 supports (1,2,3,4) aligned on the same horizontal plane and positioned accordingly to the panel design. The origin of the laboratory reference frame LabRF is about in the center of the 4 attaching points, with the Z axis aligned along the vertical and the X axis parallel to the motorized rail (and the direction of curvature of the panel).
Figure 1. VISproPT optical sketch: two digital cameras (Cam1 and Cam2) acquire photos of the panel surface with the reflected images of the point source array.
Five reference frames are used in the image-processing: 1) parabola (ParRF), 2) laboratory (LabRF), 3) point source array (SourceRF), 4) Cam1 (CamRF1), 5) Cam2 (CamRF2). At the end of the image processing, the experimental values of height and partial derivatives of the surface are gridded over the sampling matrix.
Figure 2. VISproPT hardware.
The main components are: the point source array, two digital cameras and a motorized rail for moving the camera over the specimen.
The motorized rail is horizontal at about z = 1.5 m; its alignment was optimized by a Total Station Leica TDA 500510. The rail is long enough (about 3 m) to obtain that the point source images, reflected by the panel and viewed by the cameras, scan the entire panel surface during the linear translation of the cameras along a suitable range.
The light source is composed by a off-the-shelf low-cost LED strip wrapped in a metallic box where one face, made of an aluminum thick plate, has been precisely drilled by means of a computer numerical control machine; that makes our linear array of point sources with step 10.00 mm. Thanks to the chosen materials and the specific design, the array of point sources can be assumed as perfectly linear with accuracy better than 0.01 mm for each point, in anyone of the three dimensions.
The central point of the array is marked by a couple of point sources symmetrically displaced (10.00 mm) from the array central-line; as will be explained later, that detail is fundamental to allow the proper attribution of the origin point source for each one of the reflected-point images displayed in the images captured by the cameras.
By means of the Total Station the point source array is aligned parallel to the Y axis, with its center in (−0.8 , 0 , 1.5) m. In that condition only the Pitch angle is not null; it was adjusted to about -30.0 deg.
Concerning to the digital camera, the instrument makes use of two identical units composed by:
camera: Baumer VCXG-51M, 2448 px x 2048 px complementary metal-oxide semiconductor (CMOS) sensor, monochrome
objective: Opto Engineering EN5MP0816 5 Megapixel 8 mm 1:1.6 2/3”
The two cameras are fastened on a road attached to the motorized rail; the road is horizontal and parallel to the Y axis. The adoption of two cameras allows to keep constant the width of the scanned area along their linear translation; to that purpose each camera is positioned at about the same y-coordinate of the underlying curved-rims of the PT panel; the cameras are oriented in such a way to frame the entire width of the panel (in the flat direction) with the widest side of the CMOS sensor. Thanks to the procedure described in Section 2.5, the two cameras can be positioned and oriented without paying particular attention.
At author’s knowledge the VISproPT instrument is totally original for both hardware configuration (the optical sketch) and the approach adopted to evaluate the 3D shape of PT panels.
2.2 Software
The hardware provided by MARPOSS includes an industrial computer hosting a software for the basic instrument management, with commands:
go to home position
go to x
acquire a single image (one for each camera) at the given position
scan the panel surface from xmax to xmin, acquiring images with step xstep
This MARPOSS software is not provided as part of this article because proprietary; on the other hand, it is strictly related to the hardware components adopted in the VISproPT, and not useful for others. In other words, if the reader wanted to develop a similar instrument, he would have to write his own software equipped with the libraries necessary for managing the chosen hardware components (image acquisition by the cameras and motorized-rail handling). Thus the omission of the MARPOSS software does not limit the readers from replicating the methods and data processing described in this article.
The development of the software for instrument-calibration and image-processing has been totally demanded to ENEA which holds the full know-how of the VIS method. For the sake of simplicity this software is hosted on the Lab PC from which one can pilot the instrument by sending command-scripts to the industrial computer. As drawback, the sequence of acquired images must be transferred to the Lab PC before they can be processed; on the other hand, in future, the new software could be directly installed in the industrial computer.
The main features of the software developed by ENEA are:
1. C++ written;
2. provided with a Qt graphical user interface11;
3. based on the OpenCV library12 which includes a rich tool-set for computer vision;
4. equipped with nonlinear least squares offered by CMINPACK library13.
This software now covers all the steps of 3D shape measurements:
Camera-lens calibration, for image undistortion
Instrument calibration
Image-processing for evaluating: i) 3D shape (slopes dz/dx, dz/dy and height z), ii) deviations from the ideal shape and, last but not least, iii) evaluation of the intercept factor at a given longitudinal angle.
To add value to the work done so far, believing in knowledge sharing, we took the opportunity offered by Open Research Europe to make the VISproPT software available for everyone as open source software under the GNU General Public License as published by the Free Software Foundation version 3. Code source files and data of one exemplary measurement can be freely downloaded from Software availability and Data availability14,15.
Although already described in 5, in order to make fully understandable the image processing we developed for VISproPT, the next three paragraphs shortly recall some well assessed arguments, such as: pinhole camera model, camera calibration, transformation rules between two reference frames, and determination of position and attitude of the camera.
2.3 Pinhole camera model and camera calibration
The pinhole camera model12, shown in Figure 3, is commonly used for 3D reconstruction from 2D images. Let us consider the camera reference frame (CamRF) depicted in the figure: the 3D point P = (ξ, η, ζ) is imaged in the point Pimg = (u, v) on the sensor (commonly, CCD or CMOS) which is set on the plane ζ = f orthogonal to the optical axis, i.e. the ζ-axis; the origin of CamRF is the lens center; the ζ-axis crosses the sensor at the principal point with pixel coordinates (cξ, cη); the sensor is unrealistically set between lens-center and object to take into account of the image straightening provided by the sensor electronic; ξ-axis (η-axis) is parallel to sensor rows (columns). In the pinhole camera model, source (P), image (Pimg) and lens-center (the origin of CamRF) are on the same straight line, thus
where fξ and fη are the focal lengths, and (cξ, cη) are the coordinates of the principal point; all these parameters are expressed in pixel units and stored in the so-called camera matrix. If the pixel is a perfect square, like for the here adopted cameras, fξ = fη = f. It must be noted that the principal point is close to the sensor center, but generally it is not coincident with it.
Figure 3. Pinhole camera model.
Source point P, image point Pimg, and lens center (the origin of the camera reference frame CamRF) are aligned along the same straight line.
Unfortunately any real lens usually induce some distortions (mostly radial) in the image. In order to make the pinhole camera model valid, one has first to undistort the image on the basis of camera matrix and distortion coefficients; those are obtained by calibrating the camera-lens system; please note that the evaluation of focal length f and principal point (cξ, cη) is part of that calibration. Noteworthy, camera matrix and distortion coefficients are strictly related to the specific camera-lens system, so that even if only the focus is slightly changed, one must repeat the whole calibration procedure. Procedure and functions for camera calibration and image correction are part of the rich OpenCV library12 to which we refer the reader for further information. Here we just recall that calibration is obtained by processing a sequence of images of the same chessboard differently oriented. Such a chessboard has to be printed and stitched on a rigid flat substrate by the user. We used a black and white chessboard composed by 54 × 46 squares with 10.0 mm side.
2.4 Transformation rules
As shown in Figure 1, five reference-frames play an important role in VISproPT:
the first two, named CamRF1 and CamRF2, are related to the cameras (as detailed in Figure 3)
the third is the Laboratory frame (LabRF), which origin is set in the center of the four attaching points, with the z-axis aligned along the vertical, and the x-axis parallel to the motorized rail
the fourth reference-frame, named SourceRF, is related to the point source array: it is centered between the two special central points, with the y-axis along the array, and z-axis orthogonal to the drilled-face of the metallic box
the fifth (ParRF) is the natural reference frame of the ideal parabola, where with fp parabola focal length
The 3D coordinates of a point in one of these reference-frames can be expressed in those of any other by translation and rotation. The translation rules are well known; conversely for rotations there are dozen of different conventions, depending on the considered angles and the sequence of rotations around the axes16. Among them we chosen the one normally used for aircraft, where the association between angle and axes is: Yaw → ζ, Pitch → η and Roll → ξ. They are applied in that order.
The transformation of the coordinates (ξ, η, ζ) from CamRF, SourceRF or ParRF (the plane) to LabRF (x, y, z) (the Earth) are
where sj and cj are respectively sin and cos with argument j = 1 → Yaw, j = 2 → Pitch, j = 3 → Roll.
With the same symbolism, the opposite transformation from Earth (LabRF) to plane (CamRF, SourceRF or ParRF) are
Equation 3 and Equation 4 represents only the rotation; the translation is applied after the rotation.
2.5 Position and attitude of cameras
Position and attitude of each camera in LabRF are fundamental parameters. They can be easily obtained by analyzing the image of a chessboard placed on the specimen holder (see Figure 4). The chessboard is precisely positioned by means of the Total Station.
Figure 4. View of the chessboard 15 × 9 = 135 corners from Cam1 (left) and Cam2 (right).
Our chessboard consists of 16 × 10 squares, resulting in 15 × 9 corners, i.e. the points where the corners of 4 squares (2 white and 2 black) are touching one to each other; the step along columns and rows is the same, 70.0 mm.
Each one of the two images shown in Figure 4, is analyzed for evaluating the pixel-coordinates (u, v) of each 15×9 = 135 corners in the proper CamRF. This job can be automatically accomplished by using the function findChessboardCorners of the OpenCV library12.
On the other hand the coordinates of these corners can be easily computed in LabRF because the chessboard is: i) aligned on the horizontal plane defined by the X Y axes; ii) centered in the origin (0, 0, 0); iii) oriented with rows (columns) parallel to Y (X) axis. Under these conditions the coordinate of the corner at row i = 1, 2, .., Ni − 1 and column j = 1, 2, .., Nj − 1 are
where Δ = 70.0 mm.
When corner-coordinates, lens-center-position (xc, yc, zc) and camera-attitude (Yaw,Pitch,Roll) are known in LabRF, one can evaluate the expected position of each corner in the acquired image by means of the pinhole camera model: in LabRF the corner ( j, i) is located at the end of the vector
applied to the camera lens-center. By means of Equation 4 the components of in LabRF (given in Equation 6) can be transformed in CamRF, obtaining (ξj,i, ηj,i, ζj,i). Then, according to the pinhole camera model, the image of the corner (i, j) is expected in
where (uj,i, vj,i) are its pixel coordinate.
The comparison between experimental and expected values of the corner pixel-coordinates is a powerful method for optimizing the values of (xc, yc, zc) and (Yaw,Pitch,Roll). More precisely we adopted the modified Levenberg Marquardt non linear least square algorithm, offered by CMINPAK library13 on the differences between calculated and experimental corner pixel coordinates. The best fit procedure is launched starting from a rough (but realistic!) initial evaluation of position and attitude of the camera. The procedure is separately applied to each camera.
2.6 Instrument calibration
Unfortunately we realized that the evaluation of principal point (cξ, cη) and focal length f by the chessboard, explained in Section 2.3, is not precise enough for our purposes: we found that as the number of images considered for the camera calibration increases, the succession of estimated values does not seem to converge because at each step the result is affected by the portion of the visual field occupied by the chessboard in the new added image. This weak point has a cascade effect on the accuracy of the evaluation of lens-center position and camera-attitude described in Section 2.5.
To overcome this problem we enriched the software with the final instrument-optimization: principal point, focal length, lens-center position and attitude of each camera are optimized with the modified Levenberg Marquardt non linear least square algorithm, by minimizing the slope deviations of the 3D shape measurement of a perfectly flat surface as that of a calm body of water. Thanks to the laboratory’s remoteness from busy streets, undergrounds and railways, once calm, the water surface remains totally unperturbed. As shown in Figure 5 a basin (1.2 × 0.8 m2) is placed on the attaching points of the VISproPT; once again the z coordinate of the interface air|water was evaluated by means of the Total Station. Moreover, said xcj and zcj two of the three coordinates in LabRF of the lens center of the j-camera, the difference Δx21 = xc2 − xc1 and Δz21 = zc2 − zc1 can be directly measured by the Total Station and used as constrains in the best-fit by setting xc2 = xc1 + Δx21 and zc2 = zc1 + Δz21; thus xc2 and zc2 are derived parameters.
Figure 5. Basin with water and corner cube reflector for z measurement by Leica Total Station.
After the instrument calibration, the measured shape of the water surface results to be flat for better than 0.1 mrad and 0.3 mm (RMS values), respectively for slope and height of the surface with area 1.2 × 0.8 m2, about.
2.7 Evaluation of the 3D shape
Once lens-center position, camera-attitude and point-source-array deployment are known in LabRF, the instrument is ready to perform 3D shape measurements. This section describes the original procedure we are proposing.
The measurement is based on the analysis of the two sequences of images acquired by the two cameras along their translation xmax → xmin; the range of the translation is properly set to maximize the scan area of the specimen surface, but taking care to avoid any loss in the sequence of the imaged point sources. As matter of fact, avoiding discontinuity between one point source and its neighborhoods is essential for the right association between imaged and origin point source, as will be clarified shortly.
Differently to conventional deflectometry17, VISproPT adopts a fully binary method. As an example Figure 6 shows the relevant part of a couple of images acquired for the instrument calibration. The images are monochrome with 8 bit pixel-depth, i.e. the luminosity ranges in [0, 255].
Figure 6. Point source array reflected by water and viewed by Cam1 (left) and Cam2 (right).
The automatic detection of the point sources contained in the image is fundamentally based on grey thresholding around a suitably set value (in this case 30): the luminosity of the pixels forming the point source image (technically named “blob”) is above the threshold, while all the pixels around have lower luminosity. Anyway additional constrains, as minimal blob area, minimal distance from two blobs, etc, can be set if necessary. To avoid false blob-detection, the laboratory must be sufficiently darkened.
Initially, the software performs two operations for any image of each sequence:
1. automatic detection of the blobs framed in the image by means of the SimpleBlobDetector Class offered by the OpenCV library (the luminosity threshold is one of the input parameters)
2. for each detected blob, the corresponding values of camera-number, frame-number, origin-point-source-number and (j, i) pixel coordinates of the blob centroid are stored in the array
double results[550000]; /*
results[i*6+ 0] = N. frame
results[i*6+ 1] = N. Camera
results[i*6+ 2] = N. source
results[i*6+ 3] = /
results[i*6+ 4] = column blob-coordinate (px)
results[i*6+ 5] = row blob-coordinate (px) */
where i is the progressive number of the detected blob, and N.source is the index of the point source from which the blob originates; the software takes care of the association
starting from the recognition of the special doublet marking the center of the point source array (see Figure 6); from that, the proper point-source index is sequentially assigned to all the other surrounding blobs.
At the end of the images processing, the array results is populated with the data of all the blobs detected. Note that, unless one modify the distortion coefficients, the data stored in results do not depend on focal, central point, lens-center position and camera-attitude. This fact greatly reduces the computing time of the instrument calibration algorithm because the image-analysis has not to be repeated at each iteration of the best-fitting.
Then the second stage of the processing starts; it consists in the use of the data already stored in results to evaluate the parameters of the surface at each point of reflection; the new parameters are computed and stored in the multidimensional array
double S[Nj][Ni][12]={}; /*
S[j][i][0] = vn[0] \
S[j][i][1] = vn[1] - normal unit vector
S[j][i][2] = vn[2] /
S[j][i][3] = z_ideal (height) (mm)
S[j][i][4] = N. of independent evaluations
S[j][i][5] = dz/dx (partial y-derivative)
S[j][i][6] = dz/dy (partial x-derivative)
S[j][i][7] = z_exp (height) (mm)
S[j][i][8] = dz/dx_ideal
S[j][i][9] = dz/dy_ideal
S[j][i][10]= intFat
S[j][i][11]= z_exp rms */where the indices [j][i] give the cell position (j-column and i-row) of the sampling matrix drawn in Figure 1, while the third index is used to store the several parameters associated to the cell.
More precisely the data-set of each blob stored in results is processed as follow:
In CamRF, computing of the reflected unit vector by the knowledge of the pixel coordinate of the blob (u, v) and the central point (cξ, cη) of the system camera-lens (see Equation 7)
Transformation of in LabRF by Equation 3 using the knowledge of the lens-center coordinates and camera-attitude
Calculation of the intersection between the straight line driven by applied to the lens-center (with xc actualized to the proper frame-number) and the specimen surface represented by the z-data stored in S[j][i][7]; the knowledge of the reflection-point position allows one to determine the coordinate [j][i] of the cell containing it
Calculation of the incidence unit vector in LabRF by the knowledge of the position of the origin point source and the one of the point of reflection (as determined in the previous step)
Calculation of the unit vector normal to the surface ∝ –( – ) and, consequently, the partial derivatives along X and Y axis
We use to set the size of S matrix cell to the step-value used for the image acquisition during the camera translation, typically 10.0 mm. Generally each cell is filled with more than one point; the mean value of the normal unit vector is finally stored. Then the sub-region of S matrix really populated by experimental data is delimited and processed with an inpainting routine to fill the few cells not containing data.
Finally, 2D integration is accomplished starting from each one of the attaching point (where z is known); then the mean value is stored in S[j][i][7] while the RMS value in S[j][i][11].
At the first run the panel-shape is assumed to be the ideal one, that is S[j][i][7] = S[j][i][3]; then the whole procedure is repeated by using each time the refreshed value of S[j][i][7] obtained by the 2D integration; when the maximum difference between one iteration and the following is less than a threshold value (as an example 0.03 mm) the loop ends. Generally the convergence is reached after few tens of iterations.
Once the 3D shape of the panel is known, the intercept factor can be computed; the software consider the standard solar divergence of 4.7 mrad (half apex-angle) and the longitudinal incidence angle θL set by the user.
As final step the software builds and saves as JPEG images the 2D contour maps representing the deviation of dz/dx, dz/dy, height z as well as the one of the intercept factor; here for deviation we refer to the difference between experimental and ideal values.
It is noteworthy that the above procedure is not restricted to parabolic trough panels: as a matter of fact it was successfully used to measure the water surface. Anyway the movement limited to the cameras, with the source in steady position, greatly limits the maximum size of the measurable area of flat specimens. On the other hand, the VISproPT hardware could be easily implemented by adding a linear translator to move the specimen along the x-axis, and scan the specimen with cameras and point source array in steady position. This alternative configuration could be useful for linear-Fresnel panels.
2.8 Ideal parabola reference frame
For evaluating the compliance of height z and slopes, dz/dx and dz/dy, observed in LabRF with the values expected for the ideal parabola, the knowledge of the relationships between LabRF and ParRF (where the profile is described by the canonical equation ) is fundamental.
Referring to Figure 7, the angle θ between the x axis of LabRF and ξ axis of ParRF is given by
where (ξb1, ηb1) and (ξb2, ηb2) are the coordinates in ParRF of the inner (b1) and outer (b2) supporting points.
Let Δx and Δz the signed increments to reach the LabRF origin from the center of b1; in ParRF the origin of LabRF is at
Figure 7. ParRF (parabola reference frame) and LabRF (lab reference frame); the center of the four supports (see Figure 1) lie over an horizontal plane parallel to the X Y plane of LabRF.
Let (x, y, z) the coordinate of the measured point P of the panel surface. In order to compare z with the value expected for the ideal parabola, one needs to know the value of ξP, i.e. the abscissa of P in ParRF. Developing the reasoning in the plane y = 0, the point (x, 0, 0) in ParRF has coordinates
The coordinate of P (ξP, ηP) are the solution of the equation system
having solution
where .
Finally, in LabRF
where .
Concerning the ideal slopes at point P in LabRF
Finally, the compliance of the measured 3D shape with the ideal one is given by the deviation, i.e. the difference between experimental and ideal values in LabRF already discussed in the end of Section 2.7.
3 Validation experiment
VISproPT was designed for measuring Italian style PT panels; they are characterized by the use of 1 mm thick solar mirrors glued to rigid parabolic-shaped sheet moulding compound substrates, 1200 mm wide; so that a PT module (12 m long) is composed by 40 panels, 20 inner and 20 outer; the focal length is 1810 mm.
Conversely the panels adopted in RR are for collector type LS3 with focal length 1710 ± 1 mm. The panel width is 1700±1 mm while the chord is 1624 and 1501 mm for inner and outer type, respectively; that width value is a bit over the limit of the actual VISproPT hardware: although the two cameras can be spaced 1.7 m apart (each one flying over one of the two curved-rims), the source array is not sufficiently long to be viewed reflected over more than half-width of the panel surface when the cameras are close to xmax; therefore a small triangular area with base centered in the middle of the farthest rim from the vertex is not sampled; in the 2D contour maps that not-sampled area is gray painted. VISproPT was calibrated in the modified arrangement by minimizing the slope deviations of a perfectly flat surface as that of a calm body of water (see Section 2.6), keeping fixed the parameters listed in Table 1 to the value measured with the Total Station; here xcj and zcj are two of the three coordinates in LabRF of the lens center of the j-camera.
In order to minimize the uncertainty, the full set of RR specimens (5 inner + 5 outer) was measured in the same session with the scan-parameters reported in Table 2; here the parameter x4set is the value of xmotor to which move the motorized rail to observe the center image of camera #1 on x = 0 of the chessboard used for the initial evaluation of position and attitude (see Figure 4). The introduction of x4set is due to the unsatisfactory accuracy of the motorized rail initialization based on searching xmotor = 0 by means of the limit switch detector; conversely the initialization made by the setting of x4set is better than 0.1 mm.
Table 1. Parameters measured by the Total Station.
PSA=point source array. The error is 0.3 mm for coordinates and 0.1 deg for angles.
| Parameter | Experimental value | unit |
|---|
| Center of PSA | (−760.0 , 0.0 , 1483.7) | mm |
| Yaw Pitch Roll of PSA | (0.0 ,−30.6 , 0.0) | deg |
| Δx21 = xc2 − xc1 | -3.2 | mm |
| Δz21 = zc2 − zc1 | 1.6 | mm |
Table 2. Main VISproPT parameters used to measure the round-robin specimens.
| Parameter | Inner | Outer |
|---|
| xmax (mm) | 1960.0 | 2070.0 |
| xmin (mm) | 340.0 | 110.0 |
| xstep (mm) | 10.0 | 10.0 |
| x4set | 1095.6 | 1095.6 |
| Gray threshold | 50 | 55 |
The validation of the VISproPT results with those obtained with another independent technique is difficult. The most immediate solution might seem the Total Station, but unfortunately its Corner Cube Reflector accessory10 cannot be placed freely on the surface because its weight-force deforms the panel surface itself, altering the result. Another approach, completely safe but limited, is the evaluation of the rim-shape by the analyses of its photography acquired by the side. Because of the VISproPT collocation in the Lab Hall, only two rims of the panel can be properly photographed. We use a Nikon D800 equipped with a Nikkor 24-120mm f3.5-5.6D. In each photography, the rim was manually sampled by reading the pixel-coordinates in several points, then transformed in millimeters by scaling with the total length of the rim, or the chord for the curved one. Finally the deviation from the ideal profile (linear for the edge close to the vertex and parabolic for the other) was calculated and compared with the ones obtained by VISproPT: as shown in Figure 8 the agreement is perfect although the VISproPT data-deviation refer to a section 10 mm far from the rim. Please note that, because of the shadowing by one of the four columns of the VISproPT structure, a small part of the curved rim is not visible; there deviation-data by photograph are missing.
Figure 8. z deviation at two rims of Outer#100 obtained by VISproPT (grey band) and photograph (red error-bars).
In order to show the instrument effectiveness, in the following the results we achieved on the RR specimen set are reported. In particular, the results of the 3D shape measurement are here reported as deviation from the ideal values (see Section 2.8): Table 3 reports the RMS value of the deviation, while Figure 9 and Figure 10 show the 2D contour-maps, respectively for inner and outer panel. Those 2D contour-maps are directly built using the multidimensional array S[j][i][k] introduced in Section 2.7 by assigning at the pixel of the map with coordinates [j][i] the color from blue to red proportionally to the experimental value in the range [-5,+5] mrad and [-2, 2] mm for Δdz/dx or Δdz/dy and Δz, respectively; in white (black) the value above (below) the considered range; in gray the not sampled area.
Table 3. Root mean square deviation from the ideal shape.
| Panel | Δdz/dx
(mrad) | Δdz/dy
(mrad) | Δz
(mm) |
|---|
| Inner#58 | 2.1 | 2.7 | 0.40 |
| Inner#59 | 2.1 | 2.7 | 0.40 |
| Inner#60 | 2.6 | 2.7 | 0.47 |
| Inner#61 | 2.6 | 2.7 | 0.49 |
| Inner#62 | 2.1 | 2.7 | 0.40 |
| Outer#093 | 1.6 | 2.1 | 0.71 |
| Outer#097 | 1.6 | 2.0 | 0.68 |
| Outer#099 | 1.6 | 2.1 | 0.79 |
| Outer#100 | 1.6 | 2.3 | 0.70 |
| Outer#101 | 1.5 | 2.1 | 0.73 |
Figure 9. 2D contour-maps of Δdz/dx (1st column), Δdz/dy (2nd column), and Δz (3rd column) of the inner panels #58, #59, #60, #61, and #62 (sorted by rows).
Color-range: [blue,red]= [-5,+5] mrad or [-2, 2] mm; black (white) below (above) that range; gray not sampled.
Figure 10. 2D contour-maps of Δdz/dx (1st column), Δdz/dy (2nd column), and Δz (3rd column) of the outer panels #93, #97,#99, #100, and #101 (sorted by rows).
Color-range: [blue,red]= [-5,+5] mrad or [-2, 2] mm; black (white) below (above) that range; gray not sampled.
The panels belonging to the same kind (inner and outer) resulted to be affected by very similar deviations; probably they are a consequence of the good systematic nature of the production process which is affected by some imperfections. Once the 3D shape of the panel is known, one can evaluate the intercept factor, i.e. the fraction of the reflected radiation which is geometrically intercepted by the receiver. The computation is made by considering the standard value of the solar radiation divergence, 4.7 mrad (half-apex angle) and three different values for the longitudinal incidence angle (θL): 0, 35 and 70 deg.
Table 4 summarizes the intercept-factor mean-value, while Figure 11 shows the intercept factor as 2D contour-map at 70 deg; here white color is assigned for full interception, while colors from blue to red are used to index values from 0 to 1.
Table 4. Mean intercept factor.
| Panel | θL = 0° | θL = 35° | θL = 70° |
|---|
| Inner#58 | 1.000 | 1.000 | 0.976 |
| Inner#59 | 1.000 | 0.999 | 0.969 |
| Inner#60 | 0.999 | 0.999 | 0.966 |
| Inner#61 | 0.999 | 0.998 | 0.966 |
| Inner#62 | 1.000 | 1.000 | 0.973 |
| Outer#093 | 0.993 | 0.982 | 0.826 |
| Outer#097 | 0.998 | 0.994 | 0.844 |
| Outer#099 | 0.993 | 0.987 | 0.825 |
| Outer#100 | 0.992 | 0.985 | 0.824 |
| Outer#101 | 0.993 | 0.983 | 0.815 |
Figure 11. 2D contour-maps of intercept factor at θL = 70° for inner (left) and outer (right) panels, sorted by rows.
Color-range: [blue,red] = [0,1); white full interception; gray not sampled.
As expected the intercept factor mainly depends on Δdz/dx deviation, but for outer panels, at oblique incidence, also Δdz/dy deviation reduces the intercept factor.
4 Conclusions
The VISproPT instrument is the engineered version of the older VISprofile6. The hardware was manufactured by MARPOSS Italia Spa7 and funded by SFERA-III EU project8, while ENEA developed the image processing software as well as the calibration procedure.
Differently from VISproLF5, the instrument is not completely self-calibrating because some components have to be aligned and positioned with high accuracy; to that aim we used a Total Station.
The instrument is designed for indoor measuring the 3D shape of PT panels, but the outlined image processing method is also effective for differently curved specimens. As an example, in the current configuration, VISproPT can also measure flat specimens, like those for linear Fresnel plants, as long as their length does not exceed 1 m about; however this limit could be easily overcome by improving the hardware to accomplish the scan by only moving the specimen, keeping source point array and cameras in steady position.
The fine-calibration of the instrument is based on the shape measurement of a calm body of water. After that, the instrument accuracy resulted to be better than 0.1 mrad and 0.3 mm (RMS value over an area 1.2×0.8 m2), respectively for slope and height of the surface. In a next paper dealing with the results of the round-robin, the accuracy of all the adopted instruments will be compared and discussed.
The VISproPT was exploited by measuring ten panels (5 inner + 5 outer) used in the round-robin (RR) on 3D shape measurements organized in the framework of the SFERA-III EU project, with the participation of F-ISE, DLR, NREL and SANDIA. The scansion of a specimen and the following image-processing typically take less than 90 s by a PC with Intel Xeon CPU E5-1620 v4 @ 3.50GHz; the duration of the measurement would be shorter using a more modern and performing PC.
For the sake of RR reliability, ENEA developed a simple supporting system which was proved to ensure a satisfactory reproducibility of the specimen-placing; supporting system and instructions will circulate together with the panels.
The deviation from the ideal parabolic profile are quite similar among the panels belonging to the same type, inner and outer; typically the slope deviation is better than 3 mrad and 2 mrad, respectively for inner and outer. The intercept factor at θL = 0° is better than 99.9% and 99.2%, respectively for inner and outer kind.
