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

Slope Error Measurement Tool 

for Solar Parabolic Trough

Collectors 

Preprint

J. Kathleen Stynes 

University of Colorado at Boulder

Benjamin Ihas 

National Renewable Energy Laboratory

To be presented at the 2012 World Renewable Energy Forum

Denver, Colorado

May 13–17, 2012

Conference Paper

NREL/CP-5500-54636

April 2012
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SLOPE ERROR MEASUREMENT TOOL FOR SOLAR PARABOLIC TROUGH
 

COLLECTORS
 

J. Kathleen Stynes 

PhD. Candidate Dpt. Mechanical Engineering
 

University of Colorado at Boulder
 

Boulder, Colorado 80301
 

Email: stynesj@colorado.edu
 

ABSTRACT 

The National Renewable Energy Laboratory (NREL) has developed an optical measurement tool for parabolic solar collectors that measures the combined errors due to absorber 

misalignment and reflector slope error. The combined absorber alignment and reflector slope errors are measured using a digital camera to photograph the reflected image of 

the absorber in the collector. Previous work using the image of the reflection of the absorber finds the reflector slope 

errors from the reflection of the absorber and an independent 

measurement of the absorber location. The accuracy of the 

reflector slope error measurement is thus dependent on the 

accuracy of the absorber location measurement. By measuring the combined reflector-absorber errors, the uncertainty in 

the absorber location measurement is eliminated. The related 

performance merit, the intercept factor, depends on the combined effects of the absorber alignment and reflector slope 

errors. Measuring the combined effect provides a simpler 

measurement and a more accurate input to the intercept factor estimate. The minimal equipment and setup required for 

this measurement technique make it ideal for field measurements. 

1 INTRODUCTION 

As we pursue efforts to lower the capital and installation 

costs of parabolic trough solar collectors, it is essential to 

maintain high optical performance. The geometric accuracy 

of parabolic trough collectors is described by the intercept 

factor, which includes the optical effects of reflector shape 

and receiver absorber alignment among others. The Distant 

Observer (DO) method, originally outlined by Wood in 1981, 

provides a means to measure optical performance of concentrating solar power plants in the field. The National Renewable Energy Laboratory (NREL) is currently developing a 

Benjamin Ihas 

Thermal Systems Group
 

National Renewable Energy Laboratory
 

Golden, Colorado, 80401
 

Benjamin.Ihas@nrel.gov
 

prototype DO system that measures the combined absorber 

alignment and reflector slope errors. The DO method uses 

digital photography of the reflection of the absorber as seen 

in the reflector to quantify the geometric alignment of the 

collector. This method is easily scalable to measure full solar 

fields at concentrating solar power plants. 

2 PREVIOUS WORK 

It was first recognized in 1981 by Wood that a great deal 

of information could be ascertained by analyzing the reflection of the absorber tube in parabolic trough collectors [1]. 

Just as parallel rays from the sun are reflected off a parabolic 

trough onto the absorber, so are the lines of sight from an 

observer reflected onto the absorber tube. Thus an observer 

aligned with the optical axis of the collector sees the reverse, 

an enlarged image of the absorber on the reflective surface. 

Wood’s method utilizes the shape of this reflected image to 

ascertain detailed information about the optical performance 

of the collector. 

The German Aerospace Center (DLR) has successfully implemented a quantitative variation of Wood’s method to measure slope errors of parabolic troughs from the reflected absorber image [2] and [3]. The method uses high-resolution 

digital photography. A series of photographs is taken of the 

collector from either the ground (first publication) or a radiocontrolled helicopter (second publication). In the original paper, the absorber location and camera position on the ground 

are measured with a laser distance meter. Most recently, the 

camera position in the air is determined using photogrammetric resection based on a series of ground control targets 

placed around the collector. The authors do not disclose their 

method for measuring the absorber position for the airborne 

technique. In all of these techniques, the uncertainty in the 

reflector slope errors depends on the uncertainty in the ab1 
sorber location measurement. In each case, the absorber location is measured independently and then used along with 

images of the reflection of the absorber to find the reflector 

slope errors. 

3 THEORY 

A parabolic trough is a type of concentrating solar thermal 

technology. Concentrating solar power (CSP) uses a reflector to focus direct-normal solar radiation onto a receiver. The 

conventional solar trough tracks the sun during the day by 

rotating about a single axis. Typical collectors track the sun 

from east to west by rotating about a north-south axis. A 

reflective surface formed in the shape of a parabola focuses 

solar rays onto a cylindrical receiver located at the focal line. 

The receiver is comprised of an absorber tube surrounded by 

a glass envelope. A vacuum is drawn in the annulus between 

these two tubes in order to minimize heat losses to the environment. Figure. 1 shows a cross-section of a parabolic 

trough collector. 

Fig. 1. Labeled schematic of a parabolic trough collector 

3.1 Intercept Factor 

The efficiency of a concentrating solar collector varies with 

the level of direct-normal solar radiation and the absorber 

temperature. However, due to the difficulty of measuring the 

absorber temperature directly, the efficiency is usually expressed as a function of the heat transfer fluid temperature 

with a single curve for each level of direct-normal solar radiation. As shown in Fig. 2, the optical losses far outweigh the 

thermal losses in the typical operating temperature range. 

Because the thermal and optical efficiencies behave nearly 

independently, the optical performance of a solar concentrator can be treated separately from the thermal performance. 

Fig. 2. Efficiency curve for parabolic trough solar collector comparing optical losses to thermal losses 

The optical efficiency at normal incidence is the product of 

the intercept factor γ, the mirror reflectance ρ, the glass transmittance τ, and the absorber absorptance α. 

ηo = γρτα (1) 

While the reflectance, transmittance, and absorptance are 

material properties that can be measured in a laboratory, the 

intercept factor is a purely geometric quantity that characterizes the total geometric accuracy of the system and is defined 

as the fraction of solar energy reflected from the concentrator 

that is intercepted by the absorber tube. 

The intercept factor depends on several components including the reflector’s surface profile or slope, reflector’s specularity, reflector’s alignment, absorber’s alignment, and the 

system’s solar tracking error. Additionally, factors that influence the intercept factor that are difficult to measure or 

dynamic in time include wind loading, gravitational loading, 

and sun shape. While the intercept factor is of utmost significance when evaluating the performance of a parabolic solar 

collector, it is difficult to measure due to its many contributing factors. Of all these factors, the greatest emphasis is usually placed on the reflector’s profile, characterized by surface 

slope. Several optical tools exist to measure the slope errors 

of the reflecting surface including VSHOT [4], SOFAST [5], 

photogrammetry [6], and TARMES [2]. Upon measuring the 

reflector’s slope, an estimate of the collector’s intercept factor is often presented with the results. The other parameters 

included in the intercept factor are usually estimated at the 

researcher’s discretion. There is no standard regarding the 

inclusion of specific parameters, let alone their default values. 

In order to improve the accuracy of the intercept factor estimate, the Distant Observer method is capable of measuring the combined errors in the reflector’s surface slope and 

the absorber’s alignment. This not only provides additional 

measurement data for the intercept factor estimate, but also 

2 
reduces the overall measurement uncertainty since the independent measurement of the absorber location is eliminated. 

3.2 Reflector Surface Slope Errors 

For an ideal parabola, all incoming rays parallel to the optical axis (normal rays) will be reflected through the focal 

point of that parabola. A surface slope error is defined as 

the angular difference between the measured surface normal 

and the ideal surface normal of the design parabolic surface. 

The transverse slope errors are of much greater significance 

than the longitudinal slope errors because parabolic troughs 

are linear concentrators. The Distant Observer method only 

measures transverse slope errors. The transverse slope is defined perpendicular to the length of the collector and the longitudinal slope is defined parallel to the length of the collector. The Distant Observer measurement principle for measuring only slope errors is depicted in Fig. 3. For an absorber 

aligned with the focal line of the collector, the slope error at 

each point on the collector can be measured by finding the 

angle of an incoming ray that is reflected through the focal 

point of the collector. The slope error, θr, is equal to half of 

the angular difference between the incoming ray and a normal ray. 

Fig. 3. Graphical representation of a reflector surface slope error 

using ray-tracing 

3.3 Absorber Alignment Errors 

An absorber misalignment must be modeled as a distribution 

of effective slope errors in order to combine the effects of absorber misalignment and reflector slope. For a perfect reflector with no surface slope errors, an incoming ray, assumed 

to be parallel to the optical axis, will be reflected and pass 

through the focal point of the parabola as shown in Fig. 4 

(labeled as ”ideal reflection”). For an incoming ray to pass 

through the center of an absorber that is not aligned with the 

focal point, the reflector surface must have nonzero slope error. An absorber misalignment can thus be modeled as a perfectly aligned absorber and a set of effective slope errors in 

the reflector surface. The effective slope error, θa, at each 

point across the aperture is determined by finding the surface 

slope error required for an incoming solar ray to intersect the 

center of the absorber instead of the focal point. The effective 

slope error is equal to half of the angle between the absorber 

tube, the point on the aperture, and the focal point as shown 

in Fig. 4. For a known absorber location, (Xa,Za), the effective slope error at a point on the parabolic trough reflector, 

(Xt,Zt), of a parabolic collector with focal point (0, f) is calculated using Eqn. 2. 

 1 Xt −0 Xt −Xa θa = tan−1 −tan−1 (2) 2 Zt − f Zt −Za

Fig. 4. Depiction of absorber misalignment represented with effective slope errors 

3.4 Reflector-Absorber Errors 

The reflector surface slope errors are combined with the 

effective slope errors due to absorber misalignment in the 

reflector-absorber errors. To combine the reflector surface 

slope errors with the absorber alignment errors, the absorber 

misalignment is modeled as a distribution of effective slope 

errors. The effective slope errors caused by absorber misalignment, θa, can then be directly added to the reflector 

slope errors, θr, to calculate the combined reflector-absorber 

errors, θra. The reflector-absorber errors are treated in the 

same manner as surface slope errors when estimating the intercept factor of a parabolic trough collector using ray tracing 

or convolution. 

To summarize, a reflector surface slope error is the rotation 

in the surface normal of a real parabola required for a normal 

ray to be reflected through the focal point. An effective slope 

error caused by absorber misalignment is the rotation in the 

surface normal of an ideal parabola required for a normal ray 

to be reflected through the center of the absorber. A reflectorabsorber error is the rotation in the surface normal of a real 

3 
parabola required for a normal ray to be reflected through the 

center of the absorber. 

3.5 Camera Model 

In order to use a camera as a tool to measure the absorber 

alignment, the camera must be well characterized. Traditionally, cameras are modeled using a perspective-center model 

to which both radial and tangential lens distortions are applied. The perspective-center model is based on the principle of collinearity; that is, a point in object space, the corresponding point on the image sensor (image space), and the 

focal point of the camera all lay on a straight line. Object space is the 3D space containing the objects that you 

are photographing, while image space is the 2D image sensor in the camera. The principle of collinearity allows the 

location of points in object space to be determined from 

their corresponding locations in image space. Figure 5 illustrates the perspective-center camera model. The object 

point (Xp,Yp,Zp) is imaged by the real camera on the sen­

' ' sor at point (xp,y ). This image point must be corrected by p

the lens distortion components (δx,δy) so that it is imaged 

by the perspective-center camera at point (xp, yp). The sensor 

size (sx x sy) is the length and height of the image sensor. 

The perspective center is the point through which all straight 

lines pass. The principal point (x0, y0) is the intersection of 

the image sensor and a line perpendicular to the image sensor passing through the perspective center. The focal length 

( fc) is the normal distance between the image sensor and the 

perspective center. 

Fig. 5. Perspective-center model of a camera [7] 

The lens distortion quantifies the deviation of rays from the 

ideal central-perspective model in a real camera and is expressed as deviations (δx,δy) in the image plane. The following lens distortion model is summarized from [8]. The 

primary types of lens distortion are radial distortion and tangential distortion. Radial distortion accounts for the majority 

of lens aberrations and has radial symmetry, while tangential 

distortion is mainly caused by decentering or misalignment 

of lens elements. Three radial distortion coefficients (K1, K2, 

and K3) are usually sufficient to characterize the radial components of distortion. 

2 4 δxr = x'

(K1r +K2r +K3r

6)

2 4 (3) δyr = y'

(K1r +K2r +K3r

6)

Any point (x'

,y') on the image sensor can be described as 

 r = x'2 +y'2 (4) 

Two tangential distortion coefficients (P1 and P2) are used to 

determine the tangential components of distortion. 

2 ' ' δxt = P1(r '2 +2x y ) +2P2x (5) 2 ' ' δyt = P2(r +2y'2) +2P1x y

The radial and tangential components of lens distortion are 

summed to determine the total distortion displacement in 

each direction. 

δx = δxr +δxt (6) δy = δyr +δyt 

To correct for lens distortion the pixel positions are shifted 

by the total distortion displacement values. This transforms 

the image to emulate one obtained by a central perspective 

camera. 

' x = x +δx (7) ' y = y +δy 

Therefore, a point in object space (X,Y,Z) will appear on 

' the real camera’s sensor in image space at (x , y'

). Once the 

camera is modeled as a perspective-center camera, where the 

point in object space, the focal point, and the point in image space are collinear, the point in image space is corrected 

to be located at (x, y). A photograph that appears as though 

it were taken with a perspective-center camera is called an 

ideal photograph. Real photographs can be corrected to ideal 

photographs after a camera calibration is used to quantify the 

camera geometry. 

4 METHOD 

A reflector-absorber error is defined as the rotation in the surface normal of a real parabola at a point on the collector required for a normal ray (parallel to the optical axis) to be 

4 
reflected through the center of the absorber. The reflectorabsorber errors can be calculated by determining the angle 

of an incoming ray that passes through the center of the 

absorber. The reflector-absorber error at any point on the 

collector is equal to half the angular difference between an 

incoming ray that is reflected through the center of the absorber and the optical axis of the collector. To calculate the 

reflector-absorber errors, a series of photographs of the collector showing the reflected image of the absorber are taken. 

Each photograph is analyzed to determine where on the aperture the center of the reflection of the absorber is located. The 

location of the camera relative to the collector is determined 

using photogrammetry and provides the angles of the incoming rays. 

4.1 Taking the Photographs 

The Distant Observer measurement consists of taking a series 

of photographs of a parabolic trough solar collector at different angles with respect to the optical axis of the collector. 

In general, each photograph should show the entire collector 

module. The photographs should begin with the reflection of 

the absorber not visible in the collector, as the angle of the 

camera with respect to the collector changes the reflection of 

the absorber should appear on one side of the aperture and 

move across the entire aperture until it is no longer visible. 

Ideally, the angles at which the photographs are taken should 

be evenly spaced. There are two options for obtaining the 

required images: move the camera across the aperture of a 

stationary collector or hold the camera stationary and rotate 

the collector. 

4.2 Camera Calibration 

In order to use the camera as a measurement device, the camera must be calibrated. A complete camera calibration quantifies the focal length, sensor size, principal point of the camera, and both the radial and tangential lens distortion coefficients (as described in Section 3.5). Specifications provided 

by the camera manufacturer for sensor size and focal length 

are approximations and should not be used in calculations; 

these values should always be determined with a camera calibration. Once the camera calibration has been performed, 

the images can be corrected for lens distortion. 

The camera is calibrated by taking images of a calibration 

target. A grid of dots or a black and white checkerboard, 

as shown in Fig. 6, are convenient targets for calibration. 

A camera calibration toolbox for Matlab developed by CalTech is available online [9], or a commercial software package, such as PhotoModeler [10], can be purchased to perform 

the calibration. Other commercial photogrammetry software 

packages exist that are capable of performing camera calibrations, but the authors’ experience is limited to the previously 

mentioned options. Specific guidelines for each of the aforementioned camera calibration platforms are provided with 

each software package. Once the camera has been calibrated, 

each photograph can be corrected for lens distortion as described in Section 3.5. 

Fig. 6. Photographs of example calibration targets 

4.3 Locating the Camera 

The camera location is determined using photogrammetry. 

Photogrammetry uses the concept that a point in object space, 

the perspective center of the camera, and the corresponding 

point in image space all lie on the same line. Identifiable 

points in object space that are visible in multiple photographs 

are used as the targets. Targets are classified either as intentional targets which are designed for maximum accuracy and 

placed on and around the collectors specifically for this measurement or natural targets which are any naturally occurring 

distinguishable features on the collector. Intentional targets 

are typically black circular targets mounted on a white background. Manufacturer identifying stickers that can often be 

found on many of the mirror panels make good natural targets as do the corners of the mirror panels. 

To find the camera location, the method of least squares bundle adjustment is used as described in The Manual of Photogrammetry 4th ed. [11]. The bundle adjustment technique 

uses photographs that have already been corrected for lens 

distortion through a camera calibration. The camera locations and target locations in object space are found simultaneously using the collinearity equations (Eqn. 8) in order to 

minimize the residuals in target locations in image space. 

r11(X −Xc) +r12(Y −Yc) +r13(Z −Zc) x−x0 = −fc 

r31(X −Xc) +r32(Y −Yc) +r33(Z −Zc) (8) r21(X −Xc) +r22(Y −Yc) +r23(Z −Zc) y−y0 = −fc 

r31(X −Xc) +r32(Y −Yc) +r33(Z −Zc)

When solving a system of equations it is important to keep 

track of the number of unknowns and the number of equations to make sure that the system is not under speci5 
 

 

fied. Each photograph introduces six unknowns: the external orientation parameters, which are the camera location (Xc,Yc,Zc) and the Euler angle rotation of the camera 

(θα,θβ ,θγ ). Each object point introduces three unknowns: 

the three point coordinates (Xp,Yp,Zp). Two observation 

equations can be written for each point on each photograph. 

For M photographs and N points, there will be 6M +3N unknowns and 2MN equations. If there are more unknowns 

than equations, the additional required equations must come 

from constraint equations. A constraint equation provides 

measured values for known locations of targets in object 

space, known distances, and other known geometric constraints. 

Regardless of the number of photographs and object points, 

it is necessary to define the coordinate system with constraint 

equations. A minimum of seven constraint equations are required for this task. Three constraints define the origin or 

translation of the coordinate system, three constraints define 

the axes or rotation, and the seventh constraint defines the 

scaling. A minimum of three object points are used in the 

constraint equations to specify the coordinate system. For 

example, Fig. 7 shows a parabolic collector with three object 

points on the corners of the collector. With the object points 

labeled j = 1,2,3, we specify (X1,Y1,Z1), (X2,Z2), (Z3), and 

the distance between points 1 and 2. Typically, the design 

conditions give Z1 = Z2 = Z3 and X1 = X2. The distance 

between points 1 and 2 is measured with a laser distance meter to provide the final scaling constraint. The accuracy of 

Fig. 7. Schematic of Parabolic Collector with three object points 

on the corners 

the camera location depends primarily on the accuracy of the 

distance measurement, the number of targets visible in each 

photograph, and the accuracy to which each target can be located in the photographs. 

4.4 Reflection of the Absorber 

Once the camera locations are known, the surface of the reflector must be found in each photograph. The surface of the 

design parabola is discretized with a regular grid of points 

as shown in Fig. 8. The regular grid of points can be projected onto a photograph by solving the collinearity equaFig. 8. Regular grid of points discretizing the design parabolic 

collector 

Fig. 9. Ideal photograph with regular grid of point projected onto 

the collector 

tions (Eqn. 8) explicitly for the corresponding image points 

on the sensor (xp, yp). Points in image space can be converted to pixel space (xI, yI) by shifting them by half the sensor length and then scaling by the ratio of the number of pixels (Np) to the length of the sensor (s) (Eqn. 10). 

 sx Npx xI = xp + (9) 2 sx 

 sy Npy yI = yp + (10) 2 sy 

Figure 9 shows a photograph of a collector with the reflector 

discretization superimposed. The intensity values at the location of each point on the reflector are determined by interpolating the intensity values in the photograph. Re-sampling 

the photograph along the grid of points corrects for the ef6 
 

fects of parallax and results in an image of the reflector where 

the location of each image pixel is known in object space. 

Figure 10 shows the resulting image of the reflector. The 

reflection of the absorber can be seen clearly near the bottom of the collector. The location of the reflected image of 

the absorber on the aperture can be found directly from this 

parallax-corrected image. 

Fig. 10. Parallax corrected photograph of the reflector surface 

with centerline of the absorber superimposed in red 

4.5 Reflector-Absorber Errors 

The reflector-absorber errors are calculated from the location of the camera and the location of the reflection of the 

absorber. The intersection point on the reflector of an incoming ray that is reflected through the center of the absorber 

is found in the parallax-corrected image as the center of reflected image of the absorber (shown in red in Fig. 10). The 

reflector-absorber angle (θra) is equal to the half of the angle 

between the incoming ray that is reflected through the center 

of the absorber and a normal ray (Eqn. 11). 

Xc −Xr θra = 1 

tan−1 (11) 2 Zc −Zr 

where Xr is found on each parallax-corrected image as a 

function of length (Yr) and Zr is calculated from the design 

parabola. The camera location corresponding to that photograph (Xc,Zc) was found previously using least squares bundle adjustment. By locating the center of the reflection of 

the absorber on each photograph, the reflector-absorber errors can be found across the entire collector. 

5 UNCERTAINTY 

The uncertainty in the measurement of the reflector-absorber 

errors depends on the interaction of many different variables. 

To evaluate the uncertainty for typical testing conditions, a 

detailed model was constructed in order to perform a Monte 

Carlo uncertainty analysis. The model uses ray tracing to 

create photographs of the reflector, absorber, and reflection 

of the absorber for known camera positions, collector geometry, and reflector-absorber errors. The photographs are analyzed with random errors in the collector geometry, camera calibration, target locations, and constraint parameters 

to determine the reflector-absorber errors. The calculated 

reflector-absorber errors are then compared to the initial input reflector-absorber errors to determine the measurement 

error. The whole photograph generation and analysis process 

is repeated to find the measurement uncertainty as a function 

of the random errors. 

The camera selected is a CCD camera that takes high definition video at 1920x1080 pixels. The camera is moved virtually across a stationary collector with photographs generated 

every 5 cm. To locate the camera using least squares bundle 

adjustment, six target coordinates are provided as constraints 

as described in section 4.3. The collector design is typically 

used to determine values for these target constraints; however, if the collector does not conform perfectly to design 

there will be errors in the target constraints. The target constraint errors are estimated to be σ = ±5 mm. The difference 

between the focal length of the collector used to generate the 

images and the focal length of the collector used to analyze 

the images is σ = ±5 mm. Using intentional targets, the target centroid location can be found to within σ = ±0.1 pixels 

and when using natural targets, the target centroid error is 

limited to σ = ±1 pixels. 

The input reflector-absorber errors used to generate the photographs consist of an absorber that is misaligned from the 

focal line by 3 mm towards the rim of the collector (Xa = 3 

mm) and 5 mm towards the vertex of the collector (Za = −5 

mm). The sinusoidal pattern given in Eqn. 12 was used as 

the input reflector slope errors. 

θr = 0.003[sin(4Yt)sin (4Xt)] (12) 

Figure 11 shows the cumulative probability plot of the errors 

in the calculation of the reflector-absorber errors. That is, 

the plot shows the absolute value of the difference between 

the input reflector-absorber errors used to generate images 

and the reflector-absorber errors calculated during the image 

analysis. Each line in the cumulative probability plot represents the average of 30 model runs for a different value of 

error in the target image points. Figure 11 shows the differ7 
ence in measurement accuracy when using intentional targets 

(σ = 0.1 pixels) and natural targets (σ = 1 pixel). The uncertainty in the reflector-absorber errors for intentional targets is ±0.78 mrad and ±0.90 mrad for natural targets with 

95% confidence. While using intentional targets provides 

a slightly more accurate measurement, both intentional and 

natural targets can be used to measure the reflector-absorber 

errors to within ±1 mrad (95% confidence). 

Fig. 11. Cumulative probability of the uncertainty in the calculated reflector-absorber errors (averaged over 30 model runs) using 

typical random errors described above and noted target image point 

location errors 

6	 Conclusions 

The Distant Observer Method has been adapted to measure 

the combined errors due to reflector slope errors and absorber 

misalignment errors. The combined errors are termed the 

reflector-absorber errors and are defined as the rotation of the 

surface normal in the transverse direction required for an incoming ray parallel to the optical axis to be reflected through 

the center of the absorber. The reflector-absorber errors are 

measured by taking a series of photographs of the reflected 

absorber image at incremental locations across the aperture 

of the collector. The images are analyzed to find the camera 

location using photogrammetric bundle adjustment. The calculated camera location is used along with the location of the 

reflection of the absorber to determine the reflector-absorber 

errors. The uncertainty in the reflector-absorber errors for 

typical measurement conditions was found using a detained 

model. Under typical measurement conditions the reflectorabsorber errors can be found to within ±0.78 for intentional 

targets that are placed on the collector and ±0.90 for natural 

targets such as the mirror edge corners. The Distant Observer 

measurement technique can be applied in the field to improve 

the estimate of optical intercept factor. 

ACKNOWLEDGMENT 

This work was supported by the U.S. Department of Energy 

under Contract No. DE-AC36-08-GO28308 with the National Renewable Energy Laboratory. 

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