Research Papers

Rapid Reflective Facet Characterization Using Fringe Reflection Techniques

[+] Author and Article Information
Charles E. Andraka

e-mail: ceandra@sandia.gov

Christina Liebner

Sandia National Laboratories,
Albuquerque, NM 87185

Contributed by the Solar Energy Division of ASME for publication in the JOURNAL OF SOLAR ENERGY ENGINEERING. Manuscript received January 2, 2013; final manuscript received April 5, 2013; published online July 2, 2013. Assoc. Editor: Akiba Segal.

J. Sol. Energy Eng 136(1), 011002 (Jul 02, 2013) (11 pages) Paper No: SOL-13-1001; doi: 10.1115/1.4024250 History: Received January 02, 2013; Accepted April 05, 2013

Reflective mirror facets for concentrating solar power (CSP) systems have stringent requirements on the surface slope accuracy in order to provide adequate system performance. This paper presents a tool that can fully characterize facets quickly enough for 100% inspection on a production line. A facet for a CSP system, specifically a dish concentrator has a parabolic design shape. This shape will concentrate near-parallel rays from the sun to a point (or a line for trough systems). Deviations of surface slope from the design shape impact the performance of the system, either losing power that misses the target or increasing peak fluxes to undesirable levels. During development or production, accurate knowledge of facet defects can lead to improvements to lower cost or improve performance. The reported characterization system, SOFAST (Sandia Optical Fringe Analysis Slope Tool), has a computer-connected camera that images the reflective surface, which is positioned so that it reflects an active target, such as an LCD screen, to the camera. A series of fringe patterns are displayed on the screen while images are captured. Using the captured information, the reflected target location of each pixel of mirror viewed can be determined, and thus through a mathematical transformation, a surface normal map can be developed. This is then fitted to the selected model equation, and the errors from design are characterized. While similar approaches have been explored, several key developments are presented here. The combination of the display, capture, and data reduction in one system allows rapid characterization. An “electronic boresight” approach is utilized to accommodate physical equipment positioning deviations, making the system insensitive to setup errors. Up to 1.5 × 106 points are characterized on each facet. Finally, while prior automotive industry commercial systems resolve the data to shape determination, SOFAST concentrates on slope characterization and reporting, which is tailored to solar applications. SOFAST can be used for facet analysis during development. However, the real payoff is in production, where complete analysis is performed in about 10 s. With optimized coding, this could be further reduced.

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Grahic Jump Location
Fig. 1

Schematic of SOFAST system layout. The target is an LCD screen used to display sinusoidal fringe patterns. The camera views the fringe pattern in the reflection from the facet being measured. If the point Txyz can be determined, then the normal vector can be determined from vectors CF and FT.

Grahic Jump Location
Fig. 2

Fringe patterns with two periods, showing the 4 phase-shifted positions. The overlaid sinusoidal line indicates fringe brightness and is not included on the real target. The vertical line indicates a sample position of the return signal.

Grahic Jump Location
Fig. 3

Temporal drill-down example. The initial measurement of phase with a single fringe locates the target signal at the blue diamond at about 2.32 rad. This measurement has a positional uncertainty based on the brightness uncertainty of the four measurements. The four fringe measurement determines the final phase, and therefore the final position, as well as three aliased positions. The uncertainties shown are illustrative only.

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Fig. 4

Active pixel mask and located edges and corners. Points 1–4 are the located corners, and points 5–7 are key locations on the facet for reference. In this case, the key locations are at splits between the subfacet pieces of glass.

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Fig. 5

Typical FCS for spherical and gore facets. The origin of gore facets is not on the physical facet.

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Fig. 6

Parabolic fitting when the focal length is not correct. In this case, the facet extends from 1.5 to 4.5 m. The design curve has the correct slope and position at each location. The long focal length matches the design curve slope and position at the origin, but matches neither at the alignment point. The shifted long focal length matches the slope at the origin, but matches the position at the alignment point, selected at 4 m. Finally, the rotated and shifted long focal length matches the design facet in position and slope at the alignment point (4 m), and neither match at the origin.

Grahic Jump Location
Fig. 7

ADDS facet slope error when compared to the design shape. The very systematic horizontal errors shown by the vectors indicate a focal length error. The pixel brightness indicates the total slope error compared to the design slope, while the vectors indicate the direction and magnitude of the error at every 10th pixel. The residual slope error standard deviation of magnitude is 1.49 mrad, with 1.40 mrad in the x direction and 0.51 mrad in the y direction. The brightness scale ranges from 0 mrad (black) to 3 mrad (gray).

Grahic Jump Location
Fig. 8

ADDS facet slope error when compared to a fitted parabola. There is still some systematic error at the left end and in the center, indicating that the parabolic fit may not completely model the surface shape. The residual slope error standard deviation of magnitude is 0.78 mrad.

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Fig. 9

Slope error of the ADDS facet compared with a 3rd order (in z space, 2nd order in slope space) shape. The residual slope error appears mostly random, indicating this model fits the facet. The residual slope error standard deviation of magnitude is 0.61 mrad.

Grahic Jump Location
Fig. 10

Slope error of MDAC “Egg Crate” facet compared to parabolic fit, as determined with SOFAST. Note the print-through of the three mounts. The standard deviation of the residual is 1.5 mrad. The slope is measured at over 264,000 points on the facet. The scaling is from 0 (black) to 5 mrad (gray).

Grahic Jump Location
Fig. 11

Slope error of the same MDAC “Egg Crate” facet as determined by VSHOT. The standard deviation of the residual is 1.64 mrad. The slope is measured at 6580 points on the facet. Image courtesy of Tim Wendelin, NREL.

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Fig. 12

CIRCE2-generated flux predictions of a real parabolic dish on a flat target near the receiver plane. The image on the left is based on design facet shapes, while the image on the right is based on reflection off SOFAST-measured surface profiles of each facet. This demonstrates the impact of surface imperfections on flux profile.




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