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Principles of Radiation Measurement This report presents a comprehensive summary of the terminology and units used in , , and the measurement of photosynthetically active radiation (PAR). Measurement errors can arise from a number of sources, and these are explained in detail. Finally, the conversion of radiometric and photometric units to photon units is discussed. In this report, the International System of Units (SI) is used unless noted otherwise.9

Radiometry component of plus the diffuse component of skylight received together on a horizontal surface). This Radiometry1 is the measurement of the properties of physical quantity is measured by a pyranometer such as (SI unit: , J), which is one of the many the LI-200R. Unit: W m-2. interchangeable forms of energy. The rate of flow of radi- ant energy, in the form of an electromagnetic wave, is Direct Solar Radiation is the radiation emitted from the called the radiant (unit: watt, W; 1 W = 1 J s-1). Radi- solid angle of the sun’s disc, received on a surface per- ant flux can be measured as it flows from the source (the pendicular to the axis of this cone, comprising mainly sun, in natural conditions), through one or more reflect- unscattered and unreflected solar radiation. This physical -2 ing, absorbing, scattering and transmitting media (the quantity is measured by a pyrheliometer. Unit: W m . Earth’s atmosphere, a plant canopy, etc.) to the receiving Diffuse Solar Radiation (sky radiation) is the downward surface of interest (e.g. a photosynthesizing leaf).8 scattered and reflected radiation coming from the whole hemisphere, with the exception of the solid angle sub- Terminology and Units tended by the sun’s disc. Diffuse radiation can be mea- sured by a pyranometer mounted on a shadow band, or is the amount of radiation coming from a calculated using global solar radiation and direct solar source per unit time. Unit: watt, W. radiation. Unit: W m-2. is the radiant flux leaving a point on the source, per unit solid angle of space surrounding the Photosynthetically Active point. Unit: watts per , W sr -1. Radiation is the radiant intensity emitted by a unit area In the past, there has been disagreement concerning of a source or scattered by a unit area of a surface. Unit: units and terminology used in radiation measurements W m-2 sr-1. in conjunction with the plant sciences. It is LI-COR’s pol- is the radiant flux incident on a receiving icy to adopt the recommendations of the international surface from all directions, per unit area of surface. committees, such as the Commission Internationale de Unit: W m-2. I’Eclairage (CIE), the International Bureau of Weights and Measures, and the International Committee on Radiation is the fraction of the radiant flux that is Units. The International System of Units (SI) should be absorbed by a medium. used wherever a suitable unit exists.9

Reflectance and are equivalent terms Units for the fractions of radiant flux that are reflected or transmitted. The SI unit of radiant energy flux is the watt (W). There is no official SI unit of photon flux. A mole of photons Spectroradiometry: All the properties of the radiant flux is commonly used to designate Avogadro’s number of depend on the wavelength of the radiation. The prefix photons (6.022 × 1023 photons). The einstein (E) has spectral is added when the wavelength dependency is been used in the past in plant science, however, most being described. Thus, the spectral irradiance is the irra- societies now recommend the use of the mole since diance at a given wavelength, per unit wavelength inter- the mole is an SI unit. When either of these definitions val. The irradiance within a given waveband is the is used, the quantity of photons in a mole is equal integral of the spectral irradiance with respect to wave- to the quantity of photons in an einstein (1 mole = length.8 Unit: W m-2 nm-1. Spectral measurements can 1 einstein = 6.022 × 1023 photons). be made using the LI-1800 Portable Spectroradiometer. Global solar radiation is the solar irradiance received on a horizontal surface (also referred to as the direct

2 | Principles of Radiation Measurement Note: The einstein has also been used in books on photo- chemistry, photobiology and radiation physics as the quan- 1.00 tity of radiant energy in Avogadro’s number of photons.5 This definition is not used in photosynthesis studies. Ideal 0.75 Quantum LI-190R Response Response Terminology

LI-COR continues to follow the lead of the Crop Science 0.50 Society of America, Committee on Terminology10 and Response (Arbitrary Units) 11 other societies until international committees put forth 0.25 further recommendations. ULTRAVIOLET VIOLET BLUE GREEN YELLOW RED INFRARED 0.00 Photosynthetically Active Radiation (PAR) is defined 300 400 500 600 700 800 as radiation in the 400 to 700 nm waveband. PAR is the Wavelength (nm) 7 general radiation term which covers both photon terms Figure 1. Typical LI-190R quantum response and and energy terms. the ideal quantum response displayed in energy units. Photosynthetic Photon Flux Density (PPFD) is defined as the photon flux density of PAR, also referred to as 120 Quantum Flux Density. This is the number of photons Ideal Quantum Response in the 400–700 nm waveband incident per unit time on 100 a unit surface. The ideal PPFD sensor responds equally LI-190R Response to all photons in the 400–700 nm waveband and has a 80 cosine response. This physical quantity is measured by a cosine (180˚) quantum sensor such as the LI-190R or 60 LI-192SA. The LI-191R Line Quantum Sensor also mea- sures PPFD. Figures 1 and 2 show the ideal quantum Response (%) Relative 40 response curve and the typical spectral response curve of LI-COR quantum sensors. Units: 1 µmol s-1 m-2 ≡ 1 20 µE s-1 m-2 ≡ 6.022 x 1017 photons s-1 m-2. ULTRAVIOLET VIOLET BLUE GREEN YELLOW RED INFRARED 0 300 400 500 600 700 800 Photosynthetic Photon Flux Fluence Rate (PPFFR). Wavelength (nm) LI-COR introduced this term which is defined as the Figure 2. Typical LI-190R quantum response and photon flux fluence rate of PAR, also referred to as the ideal quantum response displayed in photon Quantum Scaler Irradiance or Photon Spherical Irradi- units. ance. This is the integral of photon flux radiance at a point over all directions about the point. The ideal PPFFR sensor has a spherical collecting surface which Ø=0° exhibits the properties of a cosine receiver at every 0.8 point on its surface (Figure 3) and responds equally to 0.6 all photons in the 400–700 nm waveband. This physical 0.4 0.2 quantity is measured by a spherical (4π collector) quan- Ø=270° Ø=90° tum sensor such as the LI-193SA. Units: 1 µmol s-1 m-2 ≡ 1 µE s-1 m-2 ≡ 6.022 × 1017 photons s-1 m-2 ≡ 6.022 × 17 -1 -2 Ideal 10 quanta s m . LI-193SA Quantum Response Response Note: There is no unique relationship between the PPFD Ø=180° and the PPFFR. For a collimated beam at normal inci- dence, they are equal; while for perfectly diffuse radia- tion, the PPFFR is 4 times the PPFD. In practical situations the ratio will be somewhere between 1 and 4.

Figure 3. Typical Angular Response of the LI-193SA Spherical Quantum Sensor.

Principles of Radiation Measurement | 3 Photometry containing the given direction, by the product of the solid angle of the cone and the area of the orthogonal Photometry refers to the measurement of visible radia- projection of the element of the surface on a plane per- tion () with a sensor having a spectral responsivity pendicular to the given direction. Unit: cd m-2; also, lm curve equal to the average human eye. Photometry is sr -1 m-2. This unit is also called the nit. used to describe lighting conditions where the eye is the primary sensor, such as illumination of work areas, is defined as the density of the luminous interior lighting, television screens, etc. Although pho- flux incident at a point on a surface. Average illumi- tometric measurements have been used in the past, nance is the quotient of the incident on a PPFD and irradiance are the preferred measurements surface by the area of the surface. This physical quan- in plant science. The use of the word “light” is inappro- tity is measured by a cosine photometric sensor such -2 priate in plant research. The terms “ultraviolet light” and as the LI-210R. Unit: , lx. One lux is one lm m . “infrared light” clearly are contradictory.8 Measurement Errors The spectral responsivity curve of the standard human eye at typical light levels is called the CIE Standard At a Controlled Environments Working Conference in Observer Curve (photopic curve), and covers the wave- Madison, Wisconsin, USA (1979), an official from the band of 380–770 nm. The human eye responds U.S. National Bureau of Standards stated that one could differently to light of different colors and has maximum not expect less than 10 to 25% error in radiation mea- sensitivity to yellow and green (Figure 4). In order to surements made under non-ideal conditions. In order to make accurate photometric measurements of various clarify this area, the sources of errors which the colors of light or from differing types of light sources, researcher must be aware of when making radiation a photometric sensor’s spectral responsivity curve must measurements have been tabulated. Refer also to the match the CIE photopic curve very closely. specifications given with each sensor for further details.

Absolute Calibration Error

1.0 Absolute calibration error depends on the source of the lamp standard and its estimated uncertainty at the time 0.75 of calibration, accuracy of filament to sensor distance, alignment accuracy, stray light, and the lamp current 0.50 measurement accuracy. Where it is necessary to use a Relative Response transfer sensor (such as for solar calibrations) additional 0.25 error will be introduced. LI-COR quantum and photo- metric sensors are calibrated against a working quartz 0.0 400 500 600 700 halogen lamp. These working quartz halogen lamps Wavelength (nm) have been calibrated against laboratory standards Figure 4. Typical spectral response of LI-COR traceable to the National Institute of Standards and photometric sensors. This response is very close Technology (NIST). Standard lamp current is metered to the CIE photopic curve. to 0.035% accuracy. Microscope and laser alignment in the calibration setup reduce alignment errors to less than 0.1%. Stray light is reduced by black velvet to less

4 than 0.1%. The absolute calibration accuracy is limited Terminology and Units to the uncertainty of the NIST traceable standard lamp. Luminous Flux is the amount of radiation coming from The absolute calibration specification for LI-COR a source per unit time, evaluated in terms of a standard- sensors is ± 5% traceable to the NIST. ized visual response. Unit: , lm. Relative Error (Spectral Response Error) is the luminous flux per unit solid angle in the direction in question. Unit: , cd. One This error is also called actinity error or spectral correc- candela is one lm sr -1. tion error. This error is due to the spectral response of the sensor not conforming to the ideal spectral is the quotient of the luminous flux at an response. This error occurs when measuring radiation element of the surface surrounding the point and prop- from any source which is spectrally different than the agated in directions defined by an elementary cone calibration source.

4 | Principles of Radiation Measurement The quantum and photometric sensor spectral response Spatial Error conformity is checked by LI-COR by the use of a com- - This error is caused by a sensor not responding to radi- ious sources due to non-ideal spectral response are ation at various incident angles. Spatial error consists of checked by actual measurement and a computer pro- the cosine error (or the angular error) and azimuth error. gram which utilizes the source spectral irradiance data and the sensor spectral response data. Cosine Error

The relative error specifications given for LI-COR quan- A sensor with a cosine response (follows ’s tum and photometric sensors are for use in growth chambers, daylight, greenhouses, plant canopies and aquatic conditions. When used with sources that have When a parallel beam of radiation of given cross-sec- strong spectral lines such as gas lamps or lasers, this error could be larger depending on the location of the the area that it covers is inversely proportional to the lines. cosine of the angle between the beam and a plane nor- mal to the surface. Therefore, the irradiance due to the The LI-COR pyranometer measures irradiance from the beam is proportional to the cosine of the angle. A radi- sun plus sky. The LI-200R is not spectrally ideal (equal - spectral response from 280–2800 nm, Figure 5). There- ent directions follows the same relationship, is said to fore, it should be used only under natural, unobstructed be “cosine-corrected”.6 daylight conditions. NOAA states in a test report that for clear, unobstructed daylight conditions, the LI-COR pyranometer compares very well with class one ther- mopile pyranometers.3 The LI-200R is a WMO (World Meteorological Organization) class two pyranometer.

0.25

Solar irradiance curve outside the atmosphere

0.20 Curve for blackbody at 5900 ºK -1

Å Solar irradiance curve at sea level -2 0˚: Light received 60˚: Light received by 0.15 Atmospheric absorption by CO2, H2O and O3 ) - W m λ by the top surface the edge of the eye, LI-200R relative response (right axis) of the sensor eye. compensating for 0.10 100 from the top. Spectral Irradiance (S e Response 0.05 50 v

0 0 LI-200R Relati 0 500 1000 1500 2000 2500 3000 Wavelength (nm)

Figure 5. The LI-200R Pyranometer spectral response is illustrated along with the energy distribution in the solar spectrum.6 80˚: The rim begins 90˚: The rim completely to block some light, blocks the eye, in preventing too much keeping with a proper from striking the cosine response. The LI-200R should not be used under spectrally edge. chambers, greenhouses, and plant canopies. Under Figure 6. LI-COR sensor creating the proper cosine - response at various angles of incidence. nometer should be used.

Principles of Radiation Measurement | 5 A sensor without an accurate cosine correction can give a severe error under diffuse radiation conditions within 0° a plant canopy, at low solar elevation angles, under flu- 340° 2% 20° orescent lighting, etc. 320° 1% 40°

Cosine response is measured by placing the sensor on 0% 300° 60° a platform which can be adjusted to rotate the sensor -1% about an axis placed across the center of the measuring surface. A collimated source is directed at normal inci- 280° -2% 80° dence and the output of the sensor is measured as the -3% angle of incidence is varied. The cosine error at angle 260° 100° 0 is the percent difference of the ratio of the measured output at angle 0 and normal incidence (angle 0°) as compared to the cosine of angle 0. This is repeated for 240° 120º various azimuth angles as necessary. 220° 140° The LI-190R, LI-200R and LI-210R are fully corrected 200° 160° cosine sensors. These sensors have a typical cosine 180° error of less than 5% up to an 82° angle of incidence. Figure 7. Azimuth error for a set of five LI-COR Totally diffuse radiation introduces a cosine error of sensors at a 45˚ angle of incidence. approximately 2.5%. For sun plus sky at a sun elevation of 30° (60° angle of incidence), the error is ≈2%. The LI-192SA sensor has a slightly greater cosine error since Displacement Error this sensor has a cosine response optimized for both air and water. The LI-191R uses uncorrected acrylic dif- In highly turbid waters, the LI-193SA Spherical Sensor fusers and has a greater error at high angles of inci- will indicate high PPFFR values due to the displacement dence. For totally diffuse radiation, the LI-191R error is of water by the sensor sphere volume. This is because ≈8%. For conditions within canopies, the error is less the point of measurement is taken to be at the center because the radiation is not totally diffuse. of the sphere, but the attenuation which would have been provided by the water within the sphere is absent. Angular Error This error is typically + 6% for water with an of 3 m-1.2 A spherical PPFFR sensor measures the total flux incident on its spherical surface divided by the Tilt Error cross-sectional area of the sphere. Angular error is measured by directing a collimated source at normal Tilt error exists when a sensor is sensitive to orientation incidence and rotating the sensor 360° about an axis due to the effects of gravity. This exists primarily in ther- directly through the center of the sphere at 90° from mopile type detectors. Silicon type detectors do not have normal incidence. This is repeated for various azimuth this error. All LI-COR sensors are of the latter type and angles as necessary to characterize the sensor. have no tilt error. This error in the LI-200R Pyranometer is nonexistent and has an advantage over thermopile The LI-193SA angular error is due to variations in den- type detectors for solar radiation measurements.3 sity in the diffusion sphere and the sphere area lost because of the sensor base (Figure 3). This error is less than -10% for total because the upwelling radiation is Linearity Error much smaller than the downwelling radiation. Linearity error exists when a sensor is not able to follow proportionate changes in radiation. The type of silicon Azimuth Error detectors used in LI-COR sensors have a linearity error This is a subcategory of both cosine and angular error. of less than ± 1% over seven decades of dynamic range. It is specified separately at a particular angle of inci- dence. This error is the percent change of the sensor Fatigue Error output as the sensor is rotated about the normal axis at a particular angle of incident radiation. This error is Fatigue error exists when a sensor exhibits hysteresis. less than ± 1% at 45° for the LI-190R, LI-192SA, LI-200R, This is common in selenium-based illumination meters and LI-210R sensors (see Figure 7). The error is less and can add a considerable error. For this reason, than ± 3% for the LI-191R and LI-193SA sensors.

6 | Principles of Radiation LI-COR sensors incorporate only silicon detectors a greater ratio of indices of refraction than the water-dif- which exhibit no fatigue error. fuser interface. LI-COR provides a typical immersion effect correction factor for the underwater sensors. Temperature Coefficient Error Immersion effect error is the difference between this typical figure and the actual figure for a given sensor in Temperature coefficient error exists when the output of a particular environment. Since LI-COR test measure- a sensor changes with a constant input. This error is ments are done in clear water, the error is also typically less than ± 0.1% per °C for the LI-190R, dependent on other variables such as turbidity, salinity, LI-191R, LI-192SA, LI-193SA, and LI-210R sensors. This etc. Immersion effect error is typically ± 2% or less. A error is slightly higher for the LI-200R. complete report on the immersion effect properties of LI-COR underwater sensors is available from LI-COR. Response Time Error Surface Variation Error This error exists when the source being measured changes rapidly during the period of measurement. In general, the absolute responsivity and the relative spectral responsivity are not constant over the radia- Averaging: tion-sensitive surface of sensors. This error has little effect in environmental measurements except for spatial Large errors can exist when measuring radiation under averaging sensors such as the LI-191R. This error is rapidly changing conditions such as changing cloud < ± 7% for the LI-191R. cover and wind if measuring within a crop canopy, and waves if measuring underwater. The use of an integrat- User Errors ing meter to average the reading will eliminate this error. Spatial User Error Instantaneous: This is different than sensor-caused spatial error. Spatial When radiation measurements are desired over a user error can be introduced by using a single small period of time (much less than the response time of the sensor to characterize the radiation profile within a crop system), large errors can exist. For example, if one were canopy or growth chamber. The flux density measured to measure the radiation from a pulsed source (such as on a given plane can vary considerably due to shadows a gas discharge flash lamp) with a typical system and sunflecks. To neglect this in measurements can designed for environmental measurements, the reading introduce errors up to 1000%. Multiple sensors or sen- would be meaningless. Such a measurement should sors on track scanners can be used to minimize this not be made with LI-COR instruments without consul- error. If track scanners are used, the output of the sen- tation with LI-COR. sors must be integrated.

Long-Term Stability Error The LI-191R Line Quantum Sensor, which spatially aver- ages radiation over its one meter length, minimizes this This error exists when the calibration of a sensor changes error and allows one person to easily make many mea- with time. This error is usually low for sensors using high surements in a short period of time. Another method, quality silicon photovoltaic photodiodes and glass filters. although not as accurate, is to use an integrating meter LI-COR uses only high quality components. The use of and the LI-190R Quantum Sensor and physically scan Wratten filters and/or inexpensive silicon or selenium the sensor by hand within the canopy while integrating cells add significantly to long-term stability error. the output with the meter.

Important: Customers should have their sensors Another type of spatial user error can be caused by recalibrated every two years. misapplication of a cosine-corrected sensor where a spherical sensor would give a more accurate measure- Immersion Effect Error ment. An example is in underwater photosynthetic radi- ation measurements when studying phytoplankton. A sensor with a diffuser for cosine correction will have an immersion effect when used under water. Radiation entering the diffuser scatters in all directions within the diffuser, with more radiation lost through the water- diffuser interface than in the case when the sensor is in the air. This is because the air-diffuser interface offers

Principles of Radiation Measurement | 7 User Setup and Application Errors The total error = Square Root (5 × 5 + 5 × 5 + 2 × 2 + 1 × 1) = 7.4%. All of the above errors are minimized by These errors include such causes as: LI-COR through design and calibration. While this error seems reasonably low, it must be remembered that no § § Reflections or obstructions from clothing, user error has been added, and that statistically it is buildings, boats, etc. possible that all the errors could be of the same polarity. §§ Dust, flyspecks, seaweeds, bird droppings, etc. The sum of the errors (less the user error) could equal 21% in the worst case. The absolute error is conserva- §§ Shock, causing permanent damage of optics tively stated and is more typically ± 3%. User error in within the sensor. vegetation canopies where shadows and sunflecks exist §§ Submersion of terrestrial sensors in water for an can be very large (1000%) and one of the methods extended period (partial or total). Rain doesn’t described under Spatial User Error should be employed. affect the sensors since they are weatherproof. §§ Use of the incorrect calibration constant. When purchasing a radiation measuring system, it is necessary to insure that the spatial (cosine, etc.) and §§ Incorrect interpolation of analog meters. relative spectral response errors are as low as possible. These two errors depend upon the skill and expertise Total Error of the designer and manufacturer. Some manufacturers deliberately do not give specifications for these errors The errors given are largely independent of each other and the user can expect large errors. The absolute error and are random in polarity and magnitude. Therefore, is largely dependent on the NIST lamp standard. Mini- they can be summed in quadrature (the square root of mization of this error can be achieved by the more expe- the sum of the squares). The total error is shown below rienced companies through the use of precise for an LI-190R Quantum Sensor and LI-COR meters techniques and expensive capital equipment. In order when used for measuring lighting in a typical growth to ensure long-term stability, it is necessary that the chamber or natural daylight over a temperature range manufacturer use the highest quality silicon photovol- of 15° to 35°C. taic/photodiodes and only the best glass filters. Modern Typical Error electronic readout instruments virtually eliminate read- Absolute Error 5% max., 3% typical out error. Relative (spectral response) 5% The user should be aware of all the types of errors that Error can occur, particularly the relative and spatial errors, Spatial (cosine) Error 2% since these can add considerably to the total error. Displacement Error 0% LI-COR has and continues to put forth a considerable Tilt Error 0% effort to insure that the spectral and cosine response Linearity Error 0% Fatigue Error 0% of all quantum and photometric sensors are as nearly Sensor Temperature 1% (0.1% per °C) ideal as optically possible. This assures LI-COR custom- Coefficient Error ers of the best possible accuracy. Response Time Error 0% Immersion Effect Error 0% Surface Variation Error 0%

8 | Principles of Radiation Measurement Conversion Of Units Then: N Δλ ∑ λi 17 i Conversion of Photon Units to WT = 6.022 × 10 (Rhc) (6) λN Δ λ Radiometric Units ∑ i λi i Conversion of quantum sensor output in µmol s-1 m-2 where Δλ is any desired wavelength interval, λi is the -2 (400–700 nm) to radiometric units in W m (400–700 center wavelength of the interval and N is the normal- λi nm) is complicated. The conversion factor will be ized radiant output of the source at the center different for each light source, and the spectral distri- wavelength. In final form this becomes: bution curve of the radiant output of the source (W ; W m-2 nm-1) must be known in order to make the λ ∑ Nλ i conversion. The accurate measurement of Wλ is a dif- i -2 WT ≈ 119. 8. (R) W m (7) ficult task, which should not be attempted without λ N ∑ i λi adequate equipment and calibration facilities. The i radiometric quantity desired is the integral of W over λ -1 -2 the 400–700 nm range, or: where R is the reading in µmol s m . The following procedure should be used in conjunction 700 WT = Wλ dλ (1) with Eq. (7). ∫400 1. Divide the 400–700 nm range into ‘i’ intervals At a given wavelength λ, the number of photons per of equal wavelength spacing Δλ. second is: 2. Determine the center wavelength (λi) of each -1 Wλ interval. photons s = (2) hc/λ 3. Determine the normalized radiant output where h = 6.63 • 10-34 J•s (Planck’s constant), c = 3.00 of the source (N ) at each of the center λi • 108 m s-1 (velocity of light) and λ is in nm. hc/λ is the wavelengths. energy of one photon. Then, the total number of pho- 4. Sum the normalized radiant tons per second in the 400–700 nm range is: N outputs as determined in Step 3 to find ∑ λi i 700 Wλ 5. Multiply the center wavelength by the dλ (3) normalized radiant output at that wavelength ∫ 400 hc / λ for each interval.

6. Sum the products determined in Step 5 to find λ N This is the integral which is measured by the sensor. If ∑ i λi R is the reading of the quantum sensor in µmol s-1 m-2 i 7. Use Eq. (7) to find W in W m-2, where R is the (1 µmol s-1 m-2 ≡ 6.022 • 1017 photons s-1 m-2), then: T quantum sensor output in μmol s-1 m-2.

The following approximation assumes a flat spectral 17 700 Wλ 6.022× 10 (R) = ∫ dλ (4) distribution curve of the source over the 400–700 nm 400 hc/λ range (equal spectral irradiance over the 400–700 nm Combining Eq. (1) and Eq. (4) gives range) and is shown as an example.

700 Given: ∫ Wλ dλ W= 6.022 × 1017 (Rhc) 400 (5) T 700 i = 1 ∫ λW d λ 400 λ Δλ = 300 nm To achieve the two integrals, discrete summations are λ = 550 nm necessary. Also, since Wλ appears in both the numer- i ator and the denominator, the normalized curve Nλ may be substituted for it. ⎛ N(550) ⎞ 119. 8 (R) -2 WT ≈ 119.8 (R)⎜ ⎟ = = 0. 22 (R) W m ⎝ 550× N(550)⎠ 550

Principles of Radiation Measurement | 9 Or, e) Replace Step 4 with:

1W m-2 ≈ 4.6 μmol s-1 m-2

4a) Multiply the coefficient (yλ) of the This conversion factor is within ± 8.5% of the factors center wavelength by the normalized radiant output 8 determined by McCree as listed in Table 1. (Nλ) at the wavelength for each interval.

4b) Sum the products determined above to find: Conversion of Photon Units to Photometric Units yλ N λ ∑ i i i To convert photon units (µmol s-1 m-2, 400–700 nm) to photometric units (lux, 400–700 nm), use the above The following approximation assumes a flat spectral procedure, except distribution curve of the source over the 400–700 nm range (equal spectral irradiance over the 400–700 nm a) Replace Eq. (1) with range) and is shown as an example.

Given: 700 Lux = 683 yλ W λ dλ ∫400 i = 1 to 31

Δλ = 10 nm where yλ is the luminosity coefficient of the standard

CIE curve with yλ = 1 at 550 nm and Wλ is the spectral -2 -1 = 400, = 410, = 420.... = 700 irradiance (W m nm ). λ1 λ2 λ3 λ31 N = 1 for all wavelengths b) Replace Eq. (5) with λ 700 y = 0.0004, y = 0.0012, y = 0.004....y = 0.0041 yλ W λ d λ λ1 λ2 λ3 λ31 × 17 ∫400 Lux = 683 (6.022 10) (Rhc) 700 yλ λ ∑ i Wλ d λ i ⎛ 10.682⎞ ∫400 Lux = 8.17× 104 (R) = 8. 17× 104 (R) λ ⎝ 17050 ⎠ c) Replace Eq. (6) with ∑ i i

y N Δλ Lux = 51.2 R, where R is in μmol s-1 m-2 ∑ λi λ i × 17 i Lux = 683 (6.022 10) (Rhc) Or, λN Δ λ ∑ i λi i 1000 lux = 1 klux = 19.5 μmol s-1 m-2 d) Replace Eq. (7) with

y N ∑ λi λ i Lux = 8.17× 104 (R) i λ N ∑ λi i

Table 1. Approximate conversion factors for various light sources. (8) (PAR waveband 400–700 nm) Light Source Daylight Metal Sodium Mercury White Incand. Halide (HP) Fluor. To Convert Multiply By W m-2 (PAR) to µmol s-1 m-2 (PAR) 4.6 4.6 5.0 4.7 4.6 5.0 klux to µmol s-1 m-2 (PAR) 18 14 14 14 12 20 klux to W m-2 (PAR) 4.0 3.1 2.8 3.0 2.7 4.0

10 | Principles of Radiation Measurement Radiation Measurement References

1. CIE (Commission Internationale de l’Eclairage). 7. McCree, K.J. 1972. Test of current definitions of 1970. International lighting vocabulary, 3rd photosynthetically active radiation against leaf edition. Bureau Central de la CIE. Paris. photosynthesis data. Agric. Meteorol. 10:443–453.

2. Combs, W.S., Jr., 1977. The measurement 8. McCree, K.J. 1981. Photosynthetically active and prediction of available for radiation. In: Physiological plant ecology. Lang, photosynthesis by phytoplankton in lakes. Ph.D. O.L., P. Novel, B. Osmond and H. Ziegler (ed). Thesis, Univ. of Minnesota, Limnology. Vol. 12A, Encyclopedia of plant physiology (new series). Springer-Verlag. Berlin, Heidelberg, New 3. Flowers, E.C. 1978. Comparison of solar radiation York. sensors from various manufacturers. In: 1978 annual report from NOAA to the DOE. 9. Page, C.H. and P. Vigoureux (ed). 1977. The international system of units (SI). Nat. Bur. of 4. Illuminating Engineering Society of North Stand. Special Publ. 330, 3rd edition. U.S. Govt. America. 1981. Nomenclature and definitions Printing Office, Washington D.C., U.S.A. for illuminating engineering. Publication RP-16, ANSI/IES RP-116-1980. New York. 10. Shibles, R. 1976. Committee Report. Terminology pertaining to photosynthesis. Crop Sci. 16:437–439. 5. Incoll, L.D., S.P. Long and M.A. Ashmore. 1981. SI units in publications in plant science. In: 11. Thimijan, R.W., and R.D. Heins. 1983. Commentaries in Plant Sci. Vol. 2, pp. 83–96, Photometric, radiometric, and quantum light Pergamon, Oxford. units of measure: a review of procedures for interconversion. HortScience 18:818–822. 6. Kondratyev, K. Ya. 1969. Direct solar radiation. In: Radiation in the atmosphere. Academic Press, New York, London.

Your comments on the subjects addressed in this Excerpted from: Advanced Agricultural Instrumentation. Proceed- report or any other measurement problems are always ings from the NATO Advanced Study Institute on “Advanced welcome and will be treated as valuable inputs. Agricultural Instrumentation”, 1984. W.G. Gensler (ed.), Martinus Nijhoff Publishers, Dordrecht, The Netherlands. - William W. Biggs, Author

Principles of Radiation Measurement | 11 LI-COR Biosciences

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LI-COR GmbH, Germany Serving Andorra, Albania, Cyprus, Estonia, Germany, Iceland, Latvia, Lithuania, Liechtenstein, Malta, Moldova, Monaco, San Marino, Ukraine, and Vatican City. LI-COR Biosciences GmbH Siemensstraße 25A 61352 Bad Homburg Germany Phone: +49 (0) 6172 17 17 771 Fax: +49 (0) 6172 17 17 799 [email protected] [email protected]

LI-COR Ltd., United Kingdom LI-COR is an ISO 9001 registered company. © 2015 LI-COR, Inc. Specifications subject to change. LI-COR is a registered Serving Denmark, Finland, Ireland, Norway, Sweden, and UK. trademark of LI-COR, Inc. in the United States and other coun- LI-COR Biosciences UK Ltd. tries. For patent information, visit www.licor.com/patents. St. John’s Innovation Centre The LI-COR board of directors would like to take this opportu- Cowley Road nity to return thanks to God for His merciful providence in Cambridge allowing LI-COR to develop and commercialize products, CB4 0WS through the collective effort of dedicated employees, that United Kingdom enable the examination of the wonders of His works. “Trust in Phone: +44 (0) 1223 422102 the LORD with all your heart and do not lean on your own understanding. In all your ways acknowledge Him, and He will Fax: +44 (0) 1223 422105 make your paths straight.” —Proverbs 3:5,6 [email protected] [email protected] P/N 980-15606 8/15 2nd Edition