NREL is a national laboratory of the U.S. Department of Energy, Office of Energy 

Efficiency & Renewable Energy, operated by the Alliance for Sustainable Energy, LLC.

Contract No. DE-AC36-08GO28308

Video Scanning Hartmann 

Optical Tester (VSHOT) 

Uncertainty Analysis 

Preprint 

Allan Lewandowski and Allison Gray

National Renewable Energy Laboratory

Presented at SolarPACES 2010

Perpignan, France

September 21-24, 2010

Conference Paper

NREL/CP-5500-49305

October 2010
NOTICE

The submitted manuscript has been offered by an employee of the Alliance for Sustainable Energy, LLC 

(Alliance), a contractor of the US Government under Contract No. DE-AC36-08GO28308. Accordingly, the US 

Government and Alliance retain a nonexclusive royalty-free license to publish or reproduce the published form of 

this contribution, or allow others to do so, for US Government purposes.

This report was prepared as an account of work sponsored by an agency of the United States government. 

Neither the United States government nor any agency thereof, nor any of their employees, makes any warranty, 

express or implied, or assumes any legal liability or responsibility for the accuracy, completeness, or usefulness of 

any information, apparatus, product, or process disclosed, or represents that its use would not infringe privately 

owned rights. Reference herein to any specific commercial product, process, or service by trade name, 

trademark, manufacturer, or otherwise does not necessarily constitute or imply its endorsement, recommendation, 

or favoring by the United States government or any agency thereof. The views and opinions of authors 

expressed herein do not necessarily state or reflect those of the United States government or any agency thereof.

Available electronically at http://www.osti.gov/bridge

Available for a processing fee to U.S. Department of Energy

and its contractors, in paper, from:

U.S. Department of Energy

Office of Scientific and Technical Information

P.O. Box 62

Oak Ridge, TN 37831-0062

phone: 865.576.8401

fax: 865.576.5728

email: mailto:reports@adonis.osti.gov

Available for sale to the public, in paper, from:

U.S. Department of Commerce

National Technical Information Service

5285 Port Royal Road

Springfield, VA 22161

phone: 800.553.6847

fax: 703.605.6900

email: orders@ntis.fedworld.gov

online ordering: http://www.ntis.gov/help/ordermethods.aspx

Cover Photos: (left to right) PIX 16416, PIX 17423, PIX 16560, PIX 17613, PIX 17436, PIX 17721

Printed on paper containing at least 50% wastepaper, including 10% post consumer waste.
1 

VIDEO SCANNING HARTMANN OPTICAL TESTER (VSHOT) 

UNCERTAINTY ANALYSIS 

Allan Lewandowski

1

National Renewable Energy Laboratory, 1617 Cole Blvd, Golden CO, 80401, USA, 303-275-3779, 

allan.lewandowski@nrel.gov

1 and Allison Gray2

2

National Renewable Energy Laboratory, 1617 Cole Blvd, Golden CO, 80401, USA, 303-384-7405

Abstract

The VSHOT is a proven tool that has been used on heliostat, dish, and trough mirror facets to provide 

accurate surface slope deviations that characterize optical quality. These data are used to estimate optical 

performance within the overall system. A study of the uncertainty and sensitivity of this instrument was 

completed in 1997 and since then the hardware and software have been upgraded with new technology. To 

ensure that both industry and laboratory users understand the accuracy of the data provided by the VSHOT, 

we have conducted a new uncertainty analysis. 

This purely analytical work is based primarily on the geometric optics of the system and shows sensitivities 

to various design and operational parameters. We discuss sources of error with measuring devices, instrument 

calibrations, and operator measurements for a parabolic trough test. In this paper, we include both the random 

(precision) and systematic (bias) errors for VSHOT testing and their contributions to the uncertainty. The 

contributing factors that we considered in this study are target tilt, target face to laser output distance, 

instrument vertical offset, scanner tilt, distance between the tool and the test piece, camera calibration, and 

scanner/calibration. The results shown in this work estimate the 2σ slope error uncertainty for a parabolic 

trough line scan test to be from ±0.21 - 0.46 mrad for any given single slope error measurement. The 2σ

RMS uncertainty for slope errors for a single scan is ±0.33 mrad, ±0.6 mm (±0.01%) for focal length and 

±0.02 mrad for test article tilt. Experimental data taken on a highly accurate telescope mirror is consistent 

with these results.

Keywords: slope error, optical characterization, mirror testing, parabolic trough

1. Introduction

The VSHOT is a laser ray-trace system designed to characterize (both in the lab and field) the optical 

surfaces of solar concentrators. Originally designed to test point-focus (dish) concentrators, it was later 

modified to include characterization of line-focus (trough) concentrators and has been used to test mirror 

panels for heliostats. The VSHOT uses computer-controlled laser scanning and digital-camera image 

acquisition to provide optical surface contour data. 

The laser scans a mirror in a pattern predefined by the user. At each scanned position, the laser beam is 

reflected back to a target and the location is imaged using a camera. The surface slope is calculated at each 

position using the laser output angle and return-spot location. A Zernike Polynomial is used to 

mathematically fit the surface using the slope data.

A previous uncertainty analysis [1] used a 16-inch telescope mirror to conduct an experimental analysis. The 

distance between the mirror and the VSHOT ranged from 6.3–8.2 m and represents only a small fraction of 

the capability of the laser scanner output angles (4o vs 80o

). That study concluded the uncertainty in slope 

error was roughly 0.1 mrad (2σ) and 0.8% in focal length. Since the hardware and software have been 

significantly upgraded in the intervening years, we decided that a new analysis was needed and should 

include both analytical and experimental aspects.

The analytical study we conducted assumed a parabolic trough with a 6-m aperture and a 1.71-m focal 

length. The full 80o cone angle for the scanner ‘sees’ the entire aperture at a distance of 4.928 m from the 
2 

vertex of the trough. This arrangement was selected because it typically represents the vast majority of 

VSHOT tests conducted. For this same reason, only vertical slices across the aperture were analyzed.

The experimental work consisted of measurements on a highly accurate, parabolic mirror. The mirror 

diameter was 0.762 m with a design focal length of 3.429 m. Full mirror scans and vertical slices were 

acquired along with various mirror offsets and rotations to determine the sensitivity of calculated results.

2. Analysis

2.1. Zernike Polynomial 

A Zernike Polynomial is used to mathematically describe common optical surfaces [2]. 

z(x − ∆x, y − ∆y) = �� Bi,j(x − ∆x)j(y − ∆y)i−j

i

j=0

k

i=0

The order is k and the ∆x and ∆y terms compensate for known position offsets of the mirror vertex relative to 

the coordinate origin. These two terms are useful when fitting the data from an actual test, but for the purpose 

of this analysis, we set them equal to zero. A second order expansion is appropriate for parabolic surfaces and 

can be adapted to both axisymmetric and single axis curvatures.

z(x, y) = B0,0 + B1,0y + B1,1x + B2,0y2 + B2,1xy + B2,2x2

The meaning of each of the terms is shown in Table 1 below.

B0,0 Piston term, displacement of the optic along the z axis

B1,0 Tilt term about x axis; =tan(tiltx) ~ tiltx for small angles typical of this type testing

B1,1 Tilt term about y axis; =tan(tilty) ~ tilty for small angles typical of this type testing

B2,0 Focal length term in vertical direction; = 1

4fy

, where fy is the focal length

B2,1 Cross term indicating astigmatism

B2,2 Focal length term in horizontal direction; = 1

4fx

, where fx is the focal length

Table 1. Zernike Polynomial term definition.

We chose to conduct the analysis for a typical single axis curvature parabolic trough using simulated vertical 

slices because this is representative of the majority of VSHOT field tests. This results in a simplified Zernike 

Polynomial which is a function of y only, where the simplified Bi coefficients retain the same relative 

meaning as in the table above. 

z(y) = B0 + B1y + B2y2

The slope is the derivative with respect to y of this equation and results in a simple linear expression that can 

be easily fit to the data. 

dz

dy = B1 + 2B2y

In our analysis, the test piece has an ideal parabolic shape and oriented perfectly to the coordinate system. 

This allows us to calculate directly the value of y. When slope is plotted as a function of y position, the 

interpretation is straightforward. A linear fit yields an intercept and slope (of the fit) that correspond to the 

overall tilt and focal length. When the uncertainties described below are accounted for, this simplified 

approach allows for an estimate of slope error, focal length and tilt for fixed values of a given contributor. 

Assessing the impact of these contributors in combination as they vary stochastically is more complex.
3 

2.2. Uncertainty Contributions

Measurement error is defined as the difference between the true and measured value [3]. The measurement 

uncertainty in this analysis is applied to the calculated value of the reflective surface slope, focal length, and 

test-article tilt. The slope (or slope error) is of primary interest, so we first address the impacts of 

measurement error on it and then summarize the impacts on focal length and test-article tilt. We consider six 

random error sources and seven systematic error sources in this uncertainty analysis. These uncertainties 

(listed in Table 2) are the important variables that are associated with setting up a test and calibrating the 

system. 

Each of these uncertainties are quantified by their random and systematic errors. Random error uncertainty 

comes from hardware vendor data on repeatability or precision. All but the camera calibration random errors 

will vary over the short time while measurements are being taken. Systematic uncertainty can be difficult to 

quantify but is associated with the operator’s ability to take the measurement. We determined those values 

based on experience, judgment or some approach specific to each uncertainty. We assumed the systematic 

errors are fixed for a given test but vary randomly over time where a large number of tests are conducted, 

each with a new setup and new set of errors. The impact of these uncertainties was calculated in a MATLAB 

program that modeled the test configuration and generated a return spot location as a function of laser output 

angle over the range of ±40o (±0.69 radian). The test configuration modeled (focal length, and distance to the 

target) clearly affects the modeled results, however we believe that these results are generally applicable 

since the typical test conditions do not vary far from the modeled one. Figure 1 shows the outgoing and 

return laser paths for the geometry modeled. 

Description Measuring Device Random (2σ) Systematic (2σ)

Target tilt Bubble level ±0.208 mrad (0.012o) ±0.416 mrad (0.024o) 

Target face to laser 

scanner output Calipers 0.0127 mm ±0.5 mm 

Instrument vertical 

location Human eye N/A ±1.59 mm 

Scanner tilt Inclinometer ±0.087 mrad (0.005o) ±0.523 mrad (0.03o) 

Distance from target 

to test piece Laser range finder ±1.27 mm +0.751 mm 

Camera calibration Prosilica GE2040 GigE 

Camera, 4.2 Mpixel 1.49 ± 0.084 mm ±0.374 mm 

Scanner/calibration Cambridge closed-loop 

galvanometer model 6220 ±8 μrad ±0.62 mrad (0.36o

) 

Table 2. VSHOT uncertainties listed as 95% confidence level (2σ).

Figure 2 shows how random error uncertainty impacts the slope error for two selected contributors: target 

distance and target tilt. The distance from the target to the test piece is the largest single random contributor 

to slope error. Figure 3 shows how systematic uncertainty impacts the slope error for two selected 

contributors: target vertical location and scanner tilt. Note that there are resolution errors in the MATLAB 

program on the order of 0.01 mrad that show as apparent noise in the data for both figures. This is not 

significant compared to the overall uncertainty. There is also a gap in the center around output angle = 0o to 

account for hole in the target for the laser ray paths.
4 

Figure 1. Left figure shows outgoing rays (magenta) and reflected rays (blue). Right figure shows 

return spot location. Circled areas show location where return spot ‘turns around’ on target. 

Figure 2. Slope error impact for fixed values of random error in selected contributors.

Figure 3. Slope error impact for fixed values of systematic error in selected contributors.

-0.2

-0.1

0.0

0.1

0.2

-0.70 -0.50 -0.30 -0.10 0.10 0.30 0.50 0.70

Slope Error Uncertainty (mrad)

Laser Output Angle (radians)

Target Tilt (-0.208 mrads)

Distance (+1.27mm)

-0.4

-0.2

0.0

0.2

0.4

-0.7 -0.5 -0.3 -0.1 0.1 0.3 0.5 0.7

Slope Error Uncertainty (mrads)

Laser Output Angle (radians)

Target Vertical Location (+1.59mm)

Scanner Tilt (+0.526mrad)
5 

As mentioned before it is not always straightforward to determine the systematic errors. In the case of the 

target tilt we assumed that the operator when measuring would be unable to be consistent to within twice the 

random error due to instrument placement by hand, target flatness, etc. The scanner output mirrors are

located just behind the target. Although the calipers used for the measurement of target face to scanner output 

are very accurate, it is difficult for the operator to place them exactly at the intended locations. Thus this 

systematic error is relatively large compared to its random error. For the instrument vertical location (laser 

output origin relative to the test piece vertex) the operator sets the laser output to its (0, 0) angular value and 

then checks the position on the test piece by eye. We estimated that this can be done to within 1/16th inch or 

1.6 mm. There is no random error for this as no quantifiable method is used for the measurement. The 

scanner apparatus (laser tilt) is leveled before each test to within 0.52 mrad establishing its systematic error. 

Distance from the target to the test piece is measured with a laser range finder with an accuracy of 1.3 mm. 

We estimate that the systematic uncertainty for the operator to place and aim the rangefinder yields an error 

of 0.75 mm based on a geometric evaluation. The two uncertainties for the camera and scanner are far more 

difficult to determine.

For a given test, the camera is calibrated by placing an accurately printed grid of dots over the target and 

processing the resulting image. After reviewing data from twelve recent camera calibration files and 

recognizing that various camera positions (with different target viewing extent) were used, we calculated a 

normalized value of 0.673 ±0.038 pixels/mm for the random error corresponding to 1.49 ±0.084 mm on the 

target for a single pixel. This calculation assumes that the centroid of the return spot image can be determined 

by the software to within a pixel. Since this error does not have a zero mean, a positive error uses more pixels 

than a negative error. When combined with the discrete association of a pixel location with the corresponding 

centroid, this results in a somewhat ‘random’ looking effect. The systematic errors were based on a pooled 

calculation of the y-direction fit errors in the processing over the same twelve camera calibration files.

The laser scanner has a very high resolution so its random error is very small. There are systematic errors 

introduced during the scanner calibration. Calibration is done by manually directing the laser to specified 

positions on an accurate grid at a known distance and orientation relative to the scanner. This is done 

periodically and any time the scanner is shipped. After calibration, the VSHOT software processes the data 

and generates a fit with errors in the x and y direction. We used three recent calibration files to extract the 

pooled standard deviation representing the systematic error of ±0.62 mrad.

3. Uncertainty Estimates

3.1. Slope Error

The uncertainties are assumed to be independent of each other and have Gaussian distributions. All of the 

uncertainties, except for the camera calibration, are assumed to be symmetric about the true value. The 

random uncertainty, UR , is used to estimate the combined effect of random slope errors, UR,i. The systematic 

uncertainty, US , is used to estimate the combined effect of systematic slope errors, US,i. 

UR = ��UR,i

2

N

i=1

�

1

2

US = ��US,i

2

M

j=1

�

1

2

A first step in this analysis was to assign the 2σ values to each of the uncertainty contributors and calculate 

the resulting random and systematic slope errors, UR,i. and US,i., at each laser output angle across the aperture. 

These individual slope errors were then combined using the equations above to yield the standard 

uncertainties, UR and US , at each output angle. For the random errors, this process was done for both positive 

and negative values of each uncertainty because the camera calibration values are not symmetric. The largest 

fraction of the random standard uncertainty is from the distance from target to test piece at about 70%. The 
6 

camera calibration contributes almost 20% and the laser tilt under 10%. The remaining uncertainties have 

very little impact. For the systematic standard uncertainty, the largest contributor is the instrument vertical 

offset at about 40%. The scanner calibration contributes less than 30%, the laser tilt 20% and the distance 

from target to test piece less than 10%. These contributions vary across the aperture so these values reported 

are averages. In comparison to the random slope errors, the systematic errors are more than twice the 

magnitude and increase near the center of the scanner range. 

The overall uncertainty, URSS , combines the random and systematic uncertainties using the Root Sum Square 

uncertainty model. Although in practice the random and systematic uncertainties do not affect the test results 

in the same way, we have assumed that for the purposes of this analysis that they are equivalent.

URSS = ±[UR

2 + US2]

1

2

We again used the 2σ values for the calculation of URSS across the aperture. Figure 4 shows these results for 

both the positive and negative values of the uncertainties (the camera calibration random uncertainty is the 

only reason for the difference between positive and negative values). Thus for a single scan the individual 2σ

values range from 0.21 mrad at the turnaround points to 0.46 mrad at the vertex with an average of 0.32 

mrad. This corresponds to the combined expected uncertainty for given single measured value.

Figure 4. Overall 2σ uncertainty. 

To estimate the combined effect of the different uncertainties over a large number of tests we used a 

simplified error propagation analysis. At each output angle the positive and negative values of URSS were 

used to estimate a value for the overall uncertainty one could expect for a single scan. These values were 

used in a MATLAB program to generate a random set of slope errors. This program was run 20,000 times. A 

histogram (Figure 5) of the slope errors yields the 2σ uncertainty of 0.33 mrad. This error should be 

representative of variation between tests where vertical slices are used to characterize a single axis parabolic 

trough mirror with an RMS slope error. Although not specifically analyzed we would expect similar values 

for errors in the x direction.

0.00

0.10

0.20

0.30

0.40

0.50

-0.7 -0.6 -0.5 -0.4 -0.3 -0.2 -0.1 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7

URSS (mrad)

Laser Ouput Angle (radians)

Negative Errors

Positive Errors
7 

Figure 5. Histogram of slope error uncertaintyURSS (mrad). 

3.2 Focal Length and Tilt

The same basic process was used to determine the uncertainty on calculated focal length and test article tilt. 

These 2σ values are calculated using a fit to the simplified linear equation with slope error as a function of y. 

The resulting linear coefficients yield the focal length and tilt as described earlier. Neither the focal length 

nor the tilt are very sensitive to any of the uncertainty contributions. Only the distance measurement from the 

target to the test piece had a small effect, ±0.6 mm, on the focal length. All of the uncertainties have a 

relatively small effect on the calculated tilt term and all are less than 0.2 mrad. For field testing, a practically 

achievable tilt error of 1 mrad is considered low. 

The same type of error propagation analysis was used the estimate the combined effect of the uncertainties on 

focal length and tilt. This process was identical to that for slope error but required the additional step of 

fitting the slope error as a function of y to the simplified linear equation. The resulting focal length 

uncertainty was ±0.6 mm and the tilt uncertainty is ±0.02 mrad. These values are extremely small compared 

to both desired errors in focal length to maintain good optical performance and acceptable errors in test set up 

for tilt.

4. Reference Mirror Testing

We procured a custom-made, axisymmetric parabolic mirror of very high quality to test using our laboratory 

VSHOT apparatus. This mirror has a diameter of 0.762 m with a design focal length of 3.419 m. We assume 

there is essentially zero slope error for its parabolic contour. A number of tests of the full mirror surface were 

conducted to determine the calculated slope errors, focal length and tilt. The mirror was set 4.74 m from the 

VSHOT vertex so the scanner output angle required was only 5o (0.08 radian). 

A number of tests scanning the full mirror surface were conducted with very consistent results in slope error, 

focal length and tilt returned by the VSHOT software. This indicates good repeatability, although there were 

insufficient trials for statistically significant results to be quantified. The range of 2σ slope error was from 

0.1-0.2 mrad. However, the calculated focal length was consistently about 0.7% less than the design value. 

Since the focal length was not independently verified it is possible that the actual value was slightly shorter 

than the design specification. Calculated values for tilt were in the 0.1-0.2 mrad range, well within the 

expected ability of the operators to align the test piece during set up. Two tests were conducted after 

purposely tilting the mirror, first about the x axis and then about both x and y axes. The actual tilt of the 

mirror was not accurately measured so a comparison with the calculated values (~30 mrad) is not possible. 

The calculated slope errors and focal length were well within the range of values from the other full mirror 

scan results indicating this level of tilt had no effect on those results.

0.0

0.2

0.4

0.6

0.8

1.0

Normalized Frequency Distribution

-0.80 -0.60 -0.40 -0.20 0.00 0.20 0.40 0.60 0.80

Uncertainty Bin (mrad)
8 

Following the last full mirror scan a series of vertical slice data were acquired. The slices were spaced at 

about every 5 cm along the width of the mirror. These data were compared with the last full mirror scan and 

analyzed using the same Zernike coefficients. Figure 6 shows the full mirror scan results for dz/dx and dz/dy

slope errors with the slice data superimposed. It is clear that the slice data matches very well with the full 

mirror data with variations not exceeding about 0.02 mrad. However, if the slice data are analyzed 

individually to obtain Zernike coefficients, those new coefficients will result in smaller slope errors. If this is 

true for a reference mirror it is likely to be magnified for parabolic trough mirrors with presumably greater 

surface contour variations. To avoid this potential underestimation of slope errors slice data should be 

analyzed against a consistent focal length, either the design value or overall best fit value.

Figure 6. VSHOT generated slope errors in x direction (left) and y direction (right). Slice data has been 

superposed over full mirror scan. Center hole corresponds to circular hole in target. Every 3rd data 

point in the slice is shown to enhance visual interpretation. 

5. Summary

We completed an uncertainty analysis for the VSHOT assuming the typical test configuration simulating a 

single axis parabolic trough taking vertical slices. For an individual slope error measurement the 

2σ uncertainty ranges from ± 0.21 to ± 0.46 mrad depending on the laser output angle. The 2σ uncertainty in 

the RMS slope error for a full line scan is ±0.33 mrad. . The corresponding calculated focal length 

uncertainty was ± 0.6 mm and the tilt uncertainty was ± 0.2 mrad. Although slightly higher than the results 

from the previous experimental uncertainty analysis, we must remember that the current study was purely 

analytical. These values are well within the desired tolerances for parabolic troughs and thus we can conclude 

that VSHOT remains a viable and valuable tool for measurement of parabolic trough mirrors and for solar 

concentrator mirrors in general.

6. Acknowledgements

This work was supported by the U.S. Department of Energy’s Concentrating Solar Power Program under 

Task Number CP091001.

7. References

[1] S.A. Jones, J.K. Gruetzner, R.M. Houser, R.M. Edgar, and T.J. Wendelin, VSHOT Measurement 

Uncertainty and Experimental Sensitivity Study. IECEC-97: Proceedings of the Thirty-Second 

Intersociety Energy Conversion Engineering Conference, 27 July–1 August 1997, Honolulu, Hawaii. 

Volume 3: Energy Systems, Renewable Energy Resources, Environmental Impact and Policy Impacts on 

Energy, American Institute of Chemical Engineers, New York, NY, vol. 3, 1997, pp. 1877–1882.

[2] J. Ojeda-Castaneda, Optical Shop Testing, 2nd Edition, edited by Malacara, 1992.

[3] R. Dieck, Measurement Uncertainty Methods and Applications, 4th Edition. Research Triangle Park: The 

Instrumentation, Systems, and Automations Society, 2007.
F1147-E(10/2008) 

REPORT DOCUMENTATION PAGE Form Approved

OMB No. 0704-0188

The public reporting burden for this collection of information is estimated to average 1 hour per response, including the time for reviewing instructions, searching existing data sources, 

gathering and maintaining the data needed, and completing and reviewing the collection of information. Send comments regarding this burden estimate or any other aspect of this 

collection of information, including suggestions for reducing the burden, to Department of Defense, Executive Services and Communications Directorate (0704-0188). Respondents 

should be aware that notwithstanding any other provision of law, no person shall be subject to any penalty for failing to comply with a collection of information if it does not display a 

currently valid OMB control number.

PLEASE DO NOT RETURN YOUR FORM TO THE ABOVE ORGANIZATION.

1. REPORT DATE (DD-MM-YYYY)

October 2010

2. REPORT TYPE

Conference Paper

3. DATES COVERED (From - To)

4. TITLE AND SUBTITLE

Video Scanning Hartmann Optical Tester (VSHOT) Uncertainty 

Analysis: Preprint

5a. CONTRACT NUMBER

DE-AC36-08GO28308

5b. GRANT NUMBER

5c. PROGRAM ELEMENT NUMBER

6. AUTHOR(S)

Allan Lewandowski and Allison Gray

5d. PROJECT NUMBER

NREL/CP-5500-49305 

5e. TASK NUMBER

CP09.1001

5f. WORK UNIT NUMBER

7. PERFORMING ORGANIZATION NAME(S) AND ADDRESS(ES)

National Renewable Energy Laboratory

1617 Cole Blvd.

Golden, CO 80401-3393

8. PERFORMING ORGANIZATION

REPORT NUMBER

NREL/CP-5500-49305 

9. SPONSORING/MONITORING AGENCY NAME(S) AND ADDRESS(ES) 10. SPONSOR/MONITOR'S ACRONYM(S)

NREL

11. SPONSORING/MONITORING

AGENCY REPORT NUMBER

12. DISTRIBUTION AVAILABILITY STATEMENT

National Technical Information Service

U.S. Department of Commerce

5285 Port Royal Road

Springfield, VA 22161

13. SUPPLEMENTARY NOTES

14. ABSTRACT (Maximum 200 Words)

This purely analytical work is based primarily on the geometric optics of the system and shows sensitivities to various 

design and operational parameters. We discuss sources of error with measuring devices, instrument calibrations, and 

operator measurements for a parabolic trough test. In this paper, we include both the random (precision) and 

systematic (bias) errors for VSHOT testing and their contributions to the uncertainty. The contributing factors that we 

considered in this study are target tilt, target face to laser output distance, instrument vertical offset, scanner tilt, 

distance between the tool and the test piece, camera calibration, and scanner/calibration. 

15. SUBJECT TERMS

slope error; optical characterization; mirror testing; parabolic trough

16. SECURITY CLASSIFICATION OF: 17. LIMITATION 

OF ABSTRACT

UL

18. NUMBER 

OF PAGES

19a. NAME OF RESPONSIBLE PERSON

a. REPORT

Unclassified

b. ABSTRACT

Unclassified

c. THIS PAGE

Unclassified 19b. TELEPHONE NUMBER (Include area code)

Standard Form 298 (Rev. 8/98)

Prescribed by ANSI Std. Z39.18