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Library of Congress Cataloging-in-Publication Data

Names: Yellowhair, Julius E., author.Title: Field guide to solar optics / Julius Yellowhair.Description: Bellingham, Washington : SPIE Press, [2020] | Includesbibliographical references and index.

Identifiers: LCCN 2020009994 | ISBN 9781510636972 (spiral bound) |ISBN 9781510636989 (pdf)

Subjects: LCSH: Solar collectors–Optical properties. | Solar energy.Classification: LCC TJ812 .Y45 2020 | DDC 621.47/2–dc23LC record available at https://lccn.loc.gov/2020009994

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Copyright © 2020 Society of Photo-Optical Instrumentation Engineers(SPIE)

All rights reserved. No part of this publication may be reproduced ordistributed in any form or by any means without written permission of thepublisher.

The content of this book reflects the thought of the author. Every effort hasbeen made to publish reliable and accurate information herein, but thepublisher is not responsible for the validity of the information or for anyoutcomes resulting from reliance thereon.

Printed in the United States of America.First printing.For updates to this book, visit http://spie.org and type “FG47” in the searchfield.

Table of Contents

Glossary of Symbols and Notation xiii

Background on Energy and Solar Technologies 1Energy Usage and Needs 1Energy Resources 2Solar Resource 3Concentrating Solar Technologies 4Photovoltaic Solar Technologies 5Other Solar Technologies 6

Solar Radiation 8Sun Properties 8Earth Orbit 9Earth Celestial Sphere 10Earth–Sun Angles 11Sun Angular Subtense 12Sun Position 13Sun Movement 14Solar Radiation Energy 15Blackbody Radiation 16Solar Spectral Irradiance 17Terrestrial Solar Spectrum 19Direct and Diffuse Radiation 20Solar Radiation Data 21Solar Radiation Metrology 22Radiometry Quantities 23Radiometry Basics 24Geometrical Considerations 26Energy Transfer Example 27Etendue 28Sources and Surfaces 29

Fundamentals of Solar Optics 30Principles of Reflection and Refraction 30Vector Reflection and Refraction 31Reflection Coefficients 32Transmission Coefficients 33Flat Mirrors 34Curved Mirrors 35

Field Guide to Solar Optics

vii

Other Curved Surfaces 36Aberrations in Mirrors 37Astigmatism 38Solar Collector Basics 39Solar Glass 41Reflective Coatings 42Concentration Ratios 43Concentration Limit 44

Collector Optics for Solar Technologies 45Flat Plate Collector 45Linear Collectors 46Parabolic Trough System 47Linear Fresnel Collector 48Parabolic Collectors 49Heliostat Collector 50Heliostat Field 51Aimpoint 52Dish Concentrator 53Sizing a Parabolic Trough Collector Field 54Sizing a Power Tower Collector Field 55Fresnel Lens Concentrator 56Solar Furnace 57Solar Simulator 58Another Concentrator Type: Cassegrain 59Solar Multiple 60

Optical Characterization and Analysis 61Mirror Surface Slope Error 61Mirror Shape Error 62Mirror Specularity 63Mirror Facet Canting-Alignment Error 64Facet Canting Adjustment 65On-Axis Canting Strategy 66Off-Axis Canting Strategy 67Tracking and Pointing Errors 68Sunshape 69Gravity and Wind Impacts 70Combined Optical Errors 71

Table of Contents


viii

Shading and Blocking 72Cosine Losses 73Intercept Factor 74Mirror Soiling 75Atmospheric Attenuation 76Collector Optical Efficiency 77

System Modeling Approaches 78Cone Optics 78Hermite Polynomials 79Ray Tracing 80Systems Performance Modeling 81

Metrology Tools 82Deflectometry Method 82Deflectometry Surface Determination 84Laser Scanning System 85Target Imaging Metrology 86Beam Characterization System 87Radiometer and Flux Gauge 88Reflectometer 89Emissometers 90

Other Nonimaging Optics and Solar Collectors 91Secondary Concentrator 91Other Compound Parabolic Surfaces 92Waveguides 93Free-Form Surfaces 94Metasurfaces 95Spectral Splitting Optics 96

Special Topics 97Solar Glint and Glare 97Solar Technology Interference 98

Equation Summary 99

Cited References 108

Bibliography of Further Reading 109

Table of Contents


ix

Online Resources 113

Index 114

Table of Contents


x


The Field Guide to Solar Optics consolidates and sum-marizes optical topics in solar technologies and engineeringthat are dispersed throughout literature. It also attemptsto clarify topics and terms that could be confusing or attimes misused.

As with any technology area, optics related to solartechnologies can be a wide-ranging field. The topicsselected for this field guide are those frequently encoun-tered in solar engineering and research for energy harvest-ing, particularly for electricity generation. Therefore, theselected topics are slanted toward solar thermal power, oras it is commonly called, concentrating solar power.

The first section provides background on energy needs andusage, and explains where solar technologies fit into theenergy mix. Section 2 covers properties of the sun andpresents our basic understanding of solar energy collection.The third section introduces optical properties, concepts,and basic components. In Section 4, the various opticalsystems used in solar engineering are described. Opticalsystems used for solar energy collection are commonlyreferred to as collectors (e.g., a collector field)—a term thatis frequently used in this field guide. Another termcommonly applied in solar collectors is nonimaging optics.The fifth section introduces concepts for characterizingoptical components/systems and analysis approaches.Lastly, the measurement tools commonly used in solarengineering and research are described in Section 6.

The fundamentals of each topic are covered. Providingmethods or approaches to designs was not the goal of thisfield guide. However, the fundamental understanding thatcan be gained from the book can be extended and used fordesign of components and systems.

Julius YellowhairJune 2020


xi

Energy Usage and Needs

The world needs energy to function and move societiesforward. Access to adequate and reliable energy resourcesis crucial for economic growth and for maintaining thequality of our lives. As our need for energy continues togrow, one important question to ask is whether currentlevels of energy consumption and production aresustainable. The United States (U.S.) Energy InformationAdministration (EIA) publishes energy data periodically.The graph shows the world energy consumption fromdifferent energy sources, starting from 1990 and projectedto 2040. This includes all of the energy consumed (fuel fortransportations, electricity, etc.).

Oil continues to be the largest resource for our energyneeds. However, oil supplies are finite, and it is believedthat its use contributes to climate change. Coal usage hasseen an increase in recent years. Coal is also finite insupply and also could be contributing to climate change.

Renewable energy sources have been growing rapidlyin the last decade and, according to the figure above, willcontinue to grow in the future and outpace other energysources.

Developed countries, including the U.S., have plans toincrease renewable sources into their energy portfoliosto meet some of our growing demands for energy and toproduce cleaner energy.


1Background on Energy and Solar Technologies

Concentrating Solar Technologies

Concentrating solar power (CSP), sometimes calledsolar thermal power, utilizes the thermal energy of thesun, which is converted into mechanical energy to produceelectricity. Solar energy is collected and concentrated onreceivers using large collectors (i.e., mirrors or otherreflective surfaces). Receivers composed of metal tubesflow a heat transfer fluid (HTF) that is heated by theconcentrated solar power. The hot fluid (water, oil, ormolten salt) is transferred to the power block, wherewater is heated to generate steam, which then runs aturbine to generate electricity. Some of the hot fluid can bestored for later use or cloudy days. This is calledthermal energy storage. There are three main types ofCSP technologies: parabolic trough, power tower, and dish-engine systems. A schematic of each type is shown below.

The Solar Energy Generating Systems (SEGS) powerplants near Barstow, California utilize the parabolictrough technology and are the longest-running CSP plantsin the world (commissioned in the mid-1980s). There arenine plants in total, generating 361 MW.

Ivanpah and Crescent Dunes plants in Nevada are largepower tower plants commissioned in 2014 and 2015. Ivanpahhas three power tower units producing at a capacity of392 MW. Crescent Dunes has one central tower producing ata capacity of 110 MW with 10 h of thermal energy storage.

The last parabolic dish project in the U.S. was a 1.5 MWplant in Maricopa, Arizona in 2009.


4 Background on Energy and Solar Technologies

Earth Orbit

The earth orbits the sun in an elliptical path at a speed of108,000 km/h (67,108 mph) and with eccentricity of0.0167. It completes one orbit every 365.256 days (1sidereal year). The extra partial day accumulates to a fullday every four years, creating what is known as a leap year.

The planet’s distance from the sun varies as it orbits. Atperihelion, around 3 January, the earth is closest to thesun when the distance is about 147,098,074 km. Ataphelion, around 3 July, it is farthest from the sun whenthe distance is about 152,097,701 km. The average dis-tance between the earth and the sun is about 149.6 millionkm, or one astronomical unit [AU]. The changing seasonsare determined by the tilt of the earth’s rotation axis, notits distance from the sun. Because of the axial tilt of theearth, the highest solar energy is incident at 23.4 deg northof the equator at the summer solstice (Tropic of Cancer)and 23.4 deg south of the equator at the winter solstice(Tropic of Capricorn).

As seen from Earth, the planet’s orbital progrademotion (i.e., earth’s rotation direction) makes the sunappear to move with respect to other stars at a rate ofabout 1 deg (or a sun or moon diameter) every 12 heastward per solar day based on the earth’s orbital speed.


9Solar Radiation

Solar Radiation Energy

Radiation is emitted at the speed of light but can beemitted at different energy levels. The photon energy Qe

can be defined in terms of the radiation frequency n orwavelength l:

Qe 5 hn 5 hcl

where h is Planck’s constant, and c is the speed of light.To find the photon energy in electronvolts [eV], thefollowing approximation can be used with the wavelengthspecified in microns (mm):

Qe 51.2398l ½mm� eV

The different energy regimes are usually depicted on theelectromagnetic (EM) spectrum, as shown below, wherethe frequency, and therefore the energy, increases to theleft. The wavelength, however, reduces to the left since it isinversely proportional to the energy.

From the solar spectrum most of the sun’s energy onEarth is between 280 nm and 2.5 mm (ultraviolet toinfrared), marked by the shaded region in the EMspectrum diagram above. Over the solar spectrum, thesun emits mostly in the visible region (400 to 700 nm).


15Solar Radiation

Solar Radiation Metrology

Two instruments are primarily used to measure solarradiation for direct normal irradiance (DNI), globalhorizontal irradiance (GHI), and global tilted irradi-ance (GTI). A pyrheliometer is an instrument formeasuring direct beam solar irradiance. Sunlight entersthe instrument through a window and is directed onto athermopile or thermocouple, which converts heat to anelectrical signal that can be recorded. The signal voltage isconverted via a formula to measure irradiance [W/m2].A pyrheliometer is used with a solar tracking system tokeep the instrument aimed at the sun.

Similarly, a pyranometer uses thermopiles or thermocouplesto measure solar irradiance [W/m2] on a planar surface over ahemisphere. Direct sunlight and diffuse sunlight enter theglass hemispheric dome and arrive at an array of temperaturesensors. The temperature is then converted to an electricalsignal, and the signalis calibrated to pro-vide an irradiancemeasurement. Whenthe pyranometer isplaced on a level sur-face, it measures GHI.When placed on atilted surface, it mea-sures GTI.


22 Solar Radiation

Radiometry Basics

Radiant exitance M [W/m2] is the radiation emitted by asource of area A, whereas irradiance E [W/m2] isradiation incident on a target surface of area A.

Irradiance E can be written as

E 5dFdA

Radiant exitance is defined in the same way. The differenceis in the direction of the radiation.

The radiant flux or power F [W] is calculated as theintegration of irradiance (or radiant exitance) over thecollection area:

F5

ZEdA

Radiation (emitted or incident) canbe bounded by a surface of area A.

Radiation can also be defined over asolid angle v. A solid angle isdefined as

dv 5dAr2

5 sin ududf

v 5

Zf

Zu

sin ududf

The projected solid angle V is theprojection of the solid angle v ontothe observer plane and is defined as

dV5 cos udv


24 Solar Radiation

Solar Collector Basics

In solar thermal systems, solar collectors (i.e., mirrors)are the fundamental components needed to collect andconcentrate solar radiation onto a receiver or heat-absorbing element(s).

A typical solar collector mirror facet has the so-calledsandwich construction.

This refers to the waythe mirror facets areconstructed. Two glasssheets “sandwich” thereflective film. Oneglass sheet serves asthe substrate, and theother serves as thefront cover. The glasssheets are on the orderof 1–5 mm thick. Thereflective film is typi-cally silver because sil-ver reflects well over the solar spectrum (discussed onpage 41).

The mirror, which is on the order of 1–3 m2 in size, cannominally be flat or curved, depending on the solartechnology application. The glass assembly is bonded to asupport structure that can be a metal framework, stampedsheet metal, honeycomb panels, or another stiff structure.Mounting points are then bonded to the structure and serveas the interface points to the large collector frame. Threemounting points are ideal if two-axis mirror facet angleadjustments are needed. Additional mounting pointscan induce stress on the mirror facet. During facet angleadjustments, or canting, one mounting point serves as thepivot point, while the other mounting points are adjustedwith actuators to tilt the mirror into alignment. A rigidcollector frame, such as a heliostat frame, can hold an arrayof the mirror facets. The mirror array is arranged such thatit will concentrate the sunlight onto a target or receiver.


39Fundamentals of Solar Optics

Linear Collectors

Linear collectors are curved in one direction and usuallyhave a rectangular aperture. Because they are curved only inone direction, they focusthe incident sunlight to aline. The parabolictrough concentrator isan example of a linearcollector. The curvedcross-section follows aparabolic shape of theform

y5x2

4fwhere f is the focal length ofthe parabolic shape. The rimangle can be calculated as

fr 5 tan�1

�8ðf=DÞ

16ðf=DÞ2 � 1

�

5 sin�1

�D2r

�

The concentration C on aflat surface at the focal point perpendicular to the opticalaxis can be determined by considering only the angle beamspread from the sun:

C 5aD

51

2 sinðusÞwhich shows half the maximum solar concentration Cmax

possible for an ideal linear concentrator. A circular receiveris shown as a dashed circle. The size is just big enough tointercept rays from an ideal concentrator. Imperfectionsfrom the reflector (i.e., slope errors) will cause the reflectedbeam to spread farther, which will require a slightly largerreceiver size to minimize light spillage.

Linear Fresnel concentrators also fall into the linearconcentrator category.


46 Collector Optics for Solar Technologies

Combined Optical Errors

The collector tracking error can be defined as

stracking 5ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiDu2 þ Da2

p

where the errors in the azimuth and elevation axes arecombined. All optical errors are assumed to follownormal or Gaussian distributions. That is, when the errorsfrom all of the collectors (e.g., heliostats) are combined, thedistribution of the errors will tend to follow Gaussiandistributions. The probability distribution function for eacherror source can be defined as

p5 e�ðx�x0Þ2

2s2

The different error sources can be combined through aconvolution calculation:

P 5 p1�p2�: : :

The error sources can be combined as a root sum square:

soptical total

5ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffis2surface þ s2

canting þ s2tracking þ s2

wind þ s2gravity

q

The beam reflected from the collectors will spread due tothese error sources and the sun angular spread.

The total reflected beam angular spread can be calcu-lated as

sbeam−spread−total 5 soptical−total þ ssunshape

The sunshape is sometimes included in the convolutioncalculation. Here, it is merely added to the result of theconvolution calculation since sunshape is a systematic“error” source. Also, soptical_total is one standard deviationwide. To include more of the beam spread from the opticalerrors, Nsoptical_total can be used, where N is the number ofstandard deviations (N5 1, 2, or 3).


71Optical Characterization and Analysis

Laser Scanning System

A laser scanning system was developed and implemen-ted by Sandia and NREL8 for reflector surface characteri-zation. The system uses a laser to scan the reflectorsurface; the laser beam is reflected back to a target, and acamera is used to detect the location of the laser spot.Individual mirror facets or entire collector systems can bemeasured with this method.

A test is performed by placing the reflective surface atroughly twice its focal length from the laser scanner andtarget board so that the reflected laser beam lands on thetarget board. The laser is steered by scanning mirrors. Thelocation of the return spot is measured with a CCDcamera. This process is repeated across the surface of thetest article in a user-defined pattern. From the scanneraiming angles and return spot locations, the slope at eachpoint and theshape of themirror surfaceare computedusing prede-fined coordinatedefinitions. Sur-face slope devia-tions from theideal surfacecan be deter-mined.

To test flat reflective surfaces, the target board size mustbe increased to slightly larger than twice the size of themirror under test to capture all of the reflected light.

The camera calibration involves temporarily mounting arectangular grid of spots with known spacing on the targetboard, and collecting images of the target grid with thecamera. The centroids of each circular spot are determinedto a fraction of a pixel, and a fit of the surface is performed.This surface fit is possible because the actual grid spacingin both X and Y directions is known.


85Metrology Tools

Emissometers

An emissometer works according to the same principlesas a reflectometer but measures the in-band reflectance onsamples that are all in the IR, which it then uses tocalculate the thermal emittance of the samples. Theconservation of energy states that the sum of thetransmitted, reflected, and absorbed light in all directionsand at all wavelengths must equal unity, or

tþ rþ a 5 1

The directional emittance becomes

εd 5 1� rd � ts

for transmissive surfaces, where rd is the measureddirectional reflectance. For opaque surfaces, the transmit-tance component ts is zero. The total directional emittanceof an opaque surface at a given temperature is

εTðu;fÞ5 1�R∞0 rdðlÞuðl;T ÞdlR∞

0 uðl;TÞdlwhere u is Planck’s function in terms of spectral energydensity at a given temperature:

uðl;TÞ5 8phcl5ðehc=lkT � 1Þ

When the sample reflectance is measured over severalincidence angles, the total hemispherical emittance canbe estimated by

εH 5 2Z

p=2

0εTðuÞ sin u cos udu

Emissometers provide measurements at room temperaturebut calculate the emittance at the specified temperature.Like commercial reflectometers, portable emissometers arealso commercially available.


90 Metrology Tools

Equation Summary

Atmospheric attenuation (Schmitz):

hatm5

�0.99321�0.0001176Rþ1.97 ⋅10�8R2 R≤ 1kmexpð�0.000106RÞ R. 1km

Cassegrain system parameters (radii of curvature):

R1 52DFF � B

R2 52DB

F � B�D

Circle surface equation:

ðy� rÞ2 þ x2 5 r2

Collector field efficiency:

hfield 5

PNhi51 hðiÞNh

where Nh is the total number of heliostats in the field.

Collector optical efficiency:

hopt 5 hsb ⋅ hcos ⋅ hint ⋅ href ⋅ hatm

hðiÞ5P365

n51

R t1t0 hðtÞdtP365

n51

R t1t0 dt

hEðiÞ5P365

n51

R t1t0 EðtÞhðtÞdtP365

n51

R t1t0 EðtÞdt

Concentration limits:

Linear concentrators : Cmax 5Rrs

51

sin us

Point concentrators : Cmax 5

�Rrs

�25

1sin2 us


99

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