LbCOR Radiation Sensors

Instruction Manual

Y

LbCOR Underwater Radiation

Sensors, Type SA

Instruction Manual

Publication No. 8609-57 November, 1986

Revised December, 1990

LI-COR, inc.4421 Superior Street

P.O. Box 4425Lincoln, NE 68504 USA

Telephone: (402) 467-3576TWX: 910-621-8116FAX: 402-467-2819

0 Copyright 1986, LI-COR, Lincoln, Nebraska USA

How to Use this ManualThis manual contains the operation and maintenance information for tiLI-COR underwater, type SA sensors.

The first section of the manual contains general information which relates toall LI-COR underwater sensors (i.e. operation, recalibration, etc).

After the general information you will find specific information about eachsensor.

When reading through the manual you should first read the generalinformation and then read the specific information for your sensor (i.e. theLI-192SA Underwater Quantum or LI-193SA Spherical Quantum Sensor).

NOTICE

The information contained in this document is subject to change withoutnotice.

LI-COR MAKES NO WARRANTY OF ANY KIND WITH REGARD TOTHIS MATERIAL, INCLUDING, BUT NOT LIMITED TO THEIMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESSFOR A PARTICULAR PURPOSE. LI-COR shall not bc liable for errorscontained herein or for incidental or consequential damages in connectionwith the furnishing, performance, or use of this material.

This document contains proprietary information which is protected bycopyright. All rights are reserved. No part of this document may bephotocopied, reproduced, or translated to another language without priorwritten consent of LI-COR, Inc.

0 Copyright 1986, LI-COR Inc.

Table of Contents y

Section 1. General Information

Type “SA” sensors ...................................................................... 1Sensor Recalibration .................................................................... 1Operation ................................................................................... 2Calibration ................................................................................. 4Cleaning Information ...................................................................2009s Lowering Frame.. ..............................................................

Section 2. LI-192SA Underwater Quantum Sensor

Use of the Underwater Quantum Sensor ........................................... 1 0Immersion Effect ......................................................................... 1 0Cosine Response ......................................................................... 11Cosine Correction Properties ......................................................... 1 2Spectral Response ....................................................................... 1 2Specifications ............................................................................. 1 3

Section 3. LI-193SA Spherical Quantum Sensor

Use of the Spherical Quantum Sensor.. ........................................... 1 4Immersion Effect ......................................................................... 1 4Angular Response ....................................................................... 1 5Azimuth Response ...................................................................... 1 5Spectral Response ....................................................................... 1 5Terminology .............................................................................. 1 5Errors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 6MathematicalDefinitions .............................................................. 1 7Bibliography .............................................................................. 20Specifications.. ........................................................................... 2 1

Appendix

Warranty . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .22

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TYPE ‘ISA” SENSORS

LI-COR SA type sensors are characterized by having the underwater cableterminated with a BNC connector. Figure 1 shows a typical SA sensor.

“SA” type underwater sensors include the LI-192SA Underwater QuantumSensor, and the LI-193SA Spherical Quantum Sensor. The type SAterrestrial sensors include the LI-190SA Quantum Sensor, the LI-191SALine Quantum Sensor, the LI-200SA Pyranometer Sensor, and theLI-210SA Photometric sensor.

Figure 1. “SA” type sensors are terminated with only aBNC connector on the end of the cable.

SENSOR RECALIBRATION

Recalibration of LI-COR radiation sensors is recommended every two years.The LI-192SA Underwater Quantum Sensor may be returned to LI-COR forrecalibration or recalibrated using the LI-COR 1800-02 Optical RadiationCalibrator. The LI-193SA Spherical Quantum Sensor must be returned toLI-COR for recalibration.

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OPERATION

The 2222UWB Underwater Cables used with LI-COR Underwater Sensorsare terminated with a BNC connector. This connector allows the sensors tobe used with the LI-189 Quantum/Radiometer/Photometer, the two currentchannels of the LI-1000 Datalogger, or with older LI-COR integrators,including the LI-5lOB and the LI-550B.

To use a type SA sensor with the LI-189 Quantum/Radiometer/Photometer,the calibration multiplier is entered by using the two calibrate keys anddialing in the calibration multiplier using the calibration screw (see LI-189manual). The calibration multiplier is given on the certificate of calibrationand on the sensor calibration tag.

When using the LI-1000 DataLogger, the calibration multiplier must beentered into the LI-1000 software as described in the LI-1000 InstructionManual.

To use a sensor with LI-COR light meters such as the LI-185B, LI-188B orLI-1776, a factory installed calibration connector is required. Other LI-CORlight meters and integrators including the LI-170, LI-185, LI-185A, LI-188,LI-510, and LI-550 require the use of the 9901-014 connector conversioncable. Contact LI-COR for further details.

When a LI-COR light meter or data logger is not used, your sensor can beused with other millivolt recorders or data loggers by connecting a millivoltadapter. Table 1 lists the millivolt adapters required for each underwatersensor and the resistance of each adapter.

Table 1. Millivolt adapters for “SA” type sensors.

SensorMillivoltAdapter Resistance

LI-192SA 2291sLI-193SA 22915:

1210 Ohm1210 Ohm

The millivolt adapter connects to the BNC connector of the underwatercable, and the wire leads of the adapter are connected to the data logger.Sensor output (in millivolts) when using the millivolt adapter can bccomputed using “Ohms law” (Voltage = Current x Resistance).

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I

sExample: Calculate the millivolt output of an LI-192SA QuantumSensor which has a calibration constant of 3.0 pA / 1000 pmol s-l me2 (inwater). Assume the 2291s millivolt adapter is used with the sensor.

3.0 pA 1A 0.00363 volts1000 l.tmol sm1rnm2

x -lo6 lrA

x 1210 Ohm =1000 pm01 se1rne2

iI = 3.63 mV / 1000 ln-r~ol s-l m-2

IMPORTANT: When using the sensor under water, the “in water”calibration constant should be used to calculate the millivolt output of thesensor. The “in water” sensor calibration includes an immersion effectcorrection.

The use of the millivolt adapter with a recorder or data logger other thanLI-COR instruments is often acceptable for radiation levels down to 10% offull sunlight. Below lo%, the recorder must be very sensitive to pick upthe small voltage signal. The recorder should have a high impedance input(>l megohm, such as potentiometric types), and the range adjustmentshould be O-10 mV, or a more sensitive range. For low light levels, theSensor should be connected directly to a LI-COR readout device (withoutusing the millivolt adapter).

In LI-COR underwater cables the white wire is positive and the black wire isnegative. The center pin of the BNC connector has a negative signal. Thisis done because the trans-impedance amplifier used in LI-COR light metersrequires a negative signal.

For data logger or millivolt applications where the millivolt adapter isneeded, the positive (green) lead should be connected to the low impedance(common terminal) when plus or minus signal capability is available on thedata logger or recorder. This will minimize noise.

If plus or minus capability is not available on the data logger or recorder,the green lead should be connected to the positive input and the blue lead tothe negative input. If noise difficulties are encountered, consult LI-COR forspecial wiring instructions.

It is recommended that the LI-COR 2009s Lowering Frame (or equivalent)be used with the sensor for underwater applications.

IMPORTANT: Do not use LI-COR 2222UWB Underwater Cable tosupport the sensor and lowering frame, as damage to the cable can result.An auxiliary cable should be used to support the lowering frame and sensor.In addition, the 2222UWB cable should not be bent sharply near the sensor.

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u LNOTE: For cable lengths over 75 m (225 ft.), care should be exercised inits use since movement of the cable within the water can cause excessivesignal noise.

CALIBRATION

LI-COR quantum sensors are calibrated using a standard radiation sourcewhich has been calibrated against a National Bureau of Standards lamp. Thephoton flux density from the standardized lamp is known in terms ofmicromoles s-t m-*, where one micromole = 6.023 x 1017 photons. Theuncertainty of the calibration is f 5%.

The lamp used in LI-COR’s calibration is a high intensity standard ofspectral irradiance (G.E. 1000 Watt type DXW quartz halogen) supplied witha spectral irradiance table.

The following procedure was used to calculate the quantum flux outputfrom the lamp. The lamp flux density (AE) in watts me*, in an incrementat wavelength L\3L can be expressed as

AE = E(h)&

where E(h) is the spectral irradiance of the lamp at wavelength h.

The number of photons s-lrn-* in & is

Photons s-‘rn-’ =

where h is Planks constant and c is the velocity of light. This can besummed over the interval 400-700 nanometers (nm) to give

The result is adjusted to micromoles s-*m-* by dividing by 6.023 x 1017.

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CI YCLEANING INFORMATION

DO NOT use alcohol, organic solvents, abrasives, or strong detergents toclean the diffusor element on LI-COR light sensors.

The acrylic material used in LI-COR light sensors can be crazed by exposureto alcohol or organic solvents, which will adversely affect the cosineresponse of the sensor.

Clean the sensor only with water and/or a mild detergent such asdishwashing soap. LI-COR has found that vinegar can also be used toremove hard water deposits from the diffusor element, if necessary.

2009s &ERING FRAME

The 2009s Lowering Frame provides for the placement of two cosinesensors, one each for upwelling and downwelling radiation, or a singleunderwater spherical sensor (Figure 2). Each LI-COR underwater sensor hasthree 6-32 tapped mounting holes on the underside of the sensor forconnection to the mounting ring. Corrosion resistant mounting screws areincluded with each sensor.

Suspension Ring

Q

Shaft

Downwelling orSpherical SensorMounting Ring

LFin

Upwelling Sensor

0 Mounting Ring

mI

Weight Ring

Figure 2. 2009s Lowering Frame.

When two sensors are used, the frame is well balanced and will work well inmild currents without twisting the cables. The sensor for downwellingradiation is always attached using the mounting ring on the fin. Likewise,the sensor for upwelling radiation is attached to the opposite mounting ring.Depending on the speed of the current the frame will tilt a few degrees, butthis can be minimized by hanging a compact weight from the weight ring.Moderate weights will often suffice (4 kg). Weights over 25 kg should beavoided

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IIThe use of a single cosine sensor will require a small weigr(0.2 kg)attached at the empty mounting ring or a moderate weight from the weightring, or possibly both, depending upon the speed of the current.

The underwater cable(s) should be attached to the frame such thatapproximately 25 cm of cable forms a smooth arc to the underwater sensorconnector and is restrained from being flexed or supporting any weight.

LI-COR underwater cable is not recommended as a support cable, althoughit can be used as a lowering cable providing it is properly attached and theattached weights do not exceed 5 kg. The cable(s) must be attached asdescribed above. Additionally, the cable must be securely attached to theshaft of the lowering frame at multiple points so that the cable does not slipand put strain on the sensor connector. However, the cable cannot beclamped so tightly as to damage it. Possible methods to use are numerousnylon cable clamps along the length of the shaft, or a tight wrap of lightcord around the shaft and cables, starting at the suspension ring andextending downward at least 25 cm.

Underwater Cable for Sensor

Tight, Non-slipWrap of Cord

Cosine Sensor

Cosine Sensor

Oceanographic Cable 1Supporting the Frame

Underwaterfor Sensor

LI-193SB SphericalQuantum Sensor

Cable

Moderate Weight (dense)

For long-term immersion or use in heavily ionic water, it may be necessaryto provide electrical insulation between the underwater sensor(s) and thelowering frame to prevent galvanic corrosion. This is accomplished byslipping an insulating flat washer over the mounting screws down to theheads, followed by a l/2” (13 mm) length of thin tubing over the screwthreads. This tubing insulates the screws from the mounting ring.

Next, place a large flat insulating washer between the sensor and themounting ring (with three holes for the screws). Use the “insulated” screwsto attach the sensor in place. In this way neither the screws nor sensor haveelectrical contact with the frame.

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t

"Insulated Screw" (one of three)

I

Large Insulating Washer

Cosine Sensor

II

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(;,.,,,,,IUSE OF THE UNDERWATER QUANTUM SENSOR

The LX-192SA Underwater Quantum Sensor is used for measuringPhotosynthetically Active Radiation (PAR) in aquatic environments. Withits 400-700 nanometer (nm) quantum response it is a valuable tool forresearching primary productivity or other projects of environmental concern.The sensor can be used in the air with accuracy similar to that of theLI-190SA Quantum Sensor. Prior to obtaining atmospheric readings, thesensor must be dried.

The sensor connector should be lubricated with a silicone grease beforeinstalling it in the mating connector of the underwater cable. The yellowdots on the connector and the underwater cable should be aligned beforepushing them together in order to obtain the proper pin connection. If thedots are not aligned this can result in a negative reading on the readoutdevice due to the change in polarity of the conductors. The connector pinsare small and care should be taken when mating the connectors.

The quantum sensor has three 6-32 tapped holes on the underside of thesensor which are used for mounting the sensor to the 2009s LoweringFrame.

To maintain appropriate cosine correction the vertical edge of the diffusermust be kept clean. Periodically inspect the sensor for foreign deposits onthe upper surfaces during prolonged submerged operation. See page 5 ofthis manual for detailed cleaning instructions.

IMMERSION EFFECT

A sensor with a diffuser for cosine correction will have an immersion effectwhen immersed in water. The radiation entering the diffuser scatters in alldirections within the diffuser with more of the radiation lost through thewater-diffuser interface than in the case where the sensor is in air. Thisresults because the air-diffuser interface offers a greater ratio of the indexes ofrefraction than the water-diffuser interface. Thus, a greater percentage ofradiation entering the diffuser in air reaches the photodiode than in the casewhere the LI-192SA is in water. Therefore, a normal underwater readingwould need to be multiplied by this effect if the sensor is used in water.

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vThe LI-192SA calibration certificate contains calibration mxpliers forboth in air and in water operation. The in water multiplier includes theimmersion effect correction.

COSINE RESPONSE

Measurements intended to approximate radiation impinging upon a flatsurface (not necessarily level) from all angles of a hemisphere are mostaccurately obtained with a cosine corrected sensor.

A sensor with a cosine response (follows Lambert’s cosine law) allowsmeasurement of flux densities through a plane surface. This allows thesensor to measure flux densities per unit area (m2). A sensor without anaccurate cosine correction can give a severe error under diffuse radiationconditions within a plant canopy, at low solar elevation angles, underfluorescent lighting, etc.

The cosine relationship can be thought of in terms of radiant flux linesstriking a flat surface. Lambert’s Cosine Law is explained by illustratingradiant flux lines impinging upon a surface normal to the source (Figure3A) and at an angle of 60” from normal (Figure 3B). Figure 3A shows 6rays striking the unit area, but at a 60” angle only 3 rays strike at the sameunit area. This is illustrated mathematically as

S = (I) (cosine 60”) per unit area3 = (6) (0.5) per unit area

where S = vertical component of solar radiation; I = solar radiationimpinging perpendicular to a surface and cosine 60” = 0.5.

Figure 3. Lambert’s Cosine Law.

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COSINbORRECl+ION PROPERTIES

A comparison of the sensor’s cosine response curve in air and in water canbe found in the “Immersion Effect of LI-COR Underwater Sensors” Report(available from LI-COR). Engineering requirements result in differentcorrection characteristics for air and water. Overcompensation in air andundercompensation occurs in water. The better response was selected for airbecause in water the direct incident solar radiation does not exceed the criticalangle of 48.6” (a result of the air-water interface).

SPECTRAL RESPONSE

The spectral response is similar to that of the LI-190SA Quantum Sensor(Figure 4).

Figure 4. Spectral Response of the LI-190SA Quantum Sensor.

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c”.

Y *

The spectral response of the quantum sensor is obtained by use of a lightsource and a monochromator. A thermopile which has a known spectralresponse over the spectral range of interest is used to determine themonochromator output in energy flux density, W(h). at the wavelengthsetting h. If Q(h) is the sensor output at wavelength h when exposed to themonochromator output, W(h), then Q(h) can be approximated by

Q(h) = R(h) WV

where R(h) is the sensor spectral response at the wavelength setting 1. Theabove approximation assumes that the monochromator bandwidth, Ah, ismuch less than the wavelength setting 1. The normalized sensor spectralresponse r(h), is determined by

r(h) = R(X)/Rm

where Rm is the maximum value of Q&)/W(h) over the range ofwavelengths measured.

SPECIFICATIONS

Absolute Calibration: + 5% in air traceable to NBS.Sensitivity: Typically 3 pA per 1000 l.trnol s-l me2 in water.Linearity: Maximum deviation of 1% up to 10,000 pmol s-l rnw2.Stability: < * 2% change over a 1 year period.Response Time: 10 pS.Temperature Dependence: + 0.15% per “C maximum.Cosine Correction: Optimized for both underwater and atmospheric use.Azimuth: < f 1% error over 360” at 45” elevation.Detector: High stability silicon photovoltaic detector (blue enhanced).Sensor Housing: Corrosion resistant metal with acrylic diffuser for bothsaltwater and freshwater applications. Waterproof to withstand 800 psi (54bars).Size: 3.18 Dia. x 4.62 cm H (1.25” x 1.81”).Weight: 227 g (0.50 lb.).Mounting: Three 6-32 holes are tapped into the base for use with the2009s Lowering Frame or other mounting devices.Cable: Requires 2222UWB Underwater Cable.

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USE OF THE SPHERICAL QUANTUM SENSOR

The LI-193SA Spherical Quantum Sensor is used for measuring Photo-synthetically Active Radiation (PAR) in aquatic environments, andspecifically the Photosynthetic Photon Flux Fluence Rate (PPFFR). TheLI-193SA gives an added dimension to underwater PAR measurements inthat it measures PAR from all directions. The LI-193SA Sensor can also beused in air.

Because PPFFR can be defined as those photons having a wavelengthbetween 400 and 700 nm that are incident per unit time on the surface of asphere divided by the cross-sectional area of the sphere, the LI-193SASpherical Quantum Sensor is designed to respond equally to photonsbetween 400 and 700 nm. Because the energy of a photon is inverselyproportional to its wavelength, a sensor which responds equally to photonswill have a linear energy response with wavelength. Therefore, an idealPPFFR sensor would have a linear energy response between 400 and 700nm, and would have a slope of 1% per 7 nanometers (nm) if it werenormalized to 100% at 700 nm.

IMMERSION EFFECT

Because of the difference of index of refraction between air and water, thecalibration constant of the LI-193SA when used in water will be differentthan the calibration constant when used in air. This phenomenon is knownas the immersion effect. The air/water ratio of the calibration constants isequal to the sensor output in air divided by the sensor output in water for thesame PPFFR. This ratio is greater than one, and the approximate air/waterratio for normal incident radiation (0’) can be calculated by dividing the “inwater” cal constant (listed on the calibration certificate) by the “in air”calconstant. The ratio for an 180” incident radiation is about 5% higher thanthe ratio for 0” incident radiation.

For an explanation of the immersion effect as well as methods that can bcused to determine it, a report entitled “Immersion Effect and CosineCollecting Properties of LI-COR Underwater Sensors” is available fromLI-COR.

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)I wANGULAR RESPONSE

The LI-193SA sensor uses an acrylic diffuser to obtain an angular responseerror of less than f 4% for angles of incidence up to 90” from the normal.Testing is done with a collimated beam of radiation to verify these limits.

AZIMUTH RESPONSE

With a collimated beam of radiation at an angle of incidence of 90” fromnormal, the sensor is rotated about its normal axis. The maximumacceptable variation in response under these conditions is f 3%.

SPECTRAL RESPONSE

The spectral response is comparable to that of the LI-190SA QuantumSensor, (Figure 4), as both use computer-tailored filter glasses to closelyapproximate the ideal linear energy response (flat photon response) from 400to 700 nm. This response ideally produces an equal output for equalPPFFR even if the spectral irradiance varies within the cutoff points of 400and 700 nm.

Measurement of the spectral response requires a stabilized light source,monochromator, and calibrated reference detector. Measurements taken withthe test sensor and reference detector at many wavelengths yield data pointsused to plot a relative spectral response. For details, the “Description ofCalibration Procedures” applications note is available from LI-COR.

TERMINOLOGY

The terminology associated with radiation measurements has not beenconsistent. The following terms have been used to describe the samephysical quantity:

1) Photon Flux Density2) Photon Irradiance3) Quantum h-radiance

The physical quantity described is the number of photons incident on anelement of a surface in an element of time. This physical quantity ismeasured by a cosine-corrected quantum sensor such as the LI-CORLI-192SA Underwater Quantum Sensor. When the wavelength range of thephotons measured is limited to the 400-700 nm range, the termPhotosynthetic Photon Flux Density (PPFD) has been used.

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The follozg terms have been used to describe the integral of the PhotonFlux Radiance at a point over all directions about the point:

1) Photon Flux Fluence Rate2) Scalar Photon hradiance3) scalar Quantum Irradiance4) spherical Photon Irradiance5) Spherical Quantum b-radiance6) Photon Flosan

This physical quantity can also be described as the number of photonsincident on the outer surface of a spherical element of volume in an elementof time divided by the cross-sectional area of the sphere. When thewavelength range of photons measured is limited to the 400-700 nm range,the term Photosynthetic Photon Flux Fluence Rate (PPFFR) can be used.The LI-193SA Spherical Quantum Sensor measures PPFFR.

An ideal PPFFR sensor placed in a uniform radiance distribution (perfectlydiffuse radiation) would indicate a PPFFR that is four times higher than thePPFD measured by an ideal cosine-corrected sensor also placed in such auniform radiance distribution.

An ideal PPFFR sensor placed in a uniform radiance distribution (perfectlydiffuse radiation) would indicate a PPFFR that is four times higher than thePPFD measured by a spherical collecting surface which exhibits theproperties of a cosine-corrected collector at every point of its surface whensuch a sensor is also placed in a uniform radiance distribution.

An ideal PPFFR sensor placed in a spatially uniform collimated beam ofradiation will indicate a PPFFR that is the same as thePPFD measured byan ideal cosine-cone&d sensor.

ERRORS

The spatial error of the LI-193SA Sensor is due to variations in thediffusing sphere, (negligible), and the sphere area “lost” because of thesensor base. This error is less than -10% for totally diffuse radiation, but isusually smaller than this because the upwelling radiation is smaller than thedownwelling radiation.

In highly turbid waters the sensor will indicate high quanta values due to thedisplacement of water by the sensor sphere volume. This is because thepoint of measurement is taken to be at the center of the sphere, but theattenuation which would have been provided by the water within the sphereis absent. This error is typically +6.3% for water with an attenuationcoefficient of 3 m-l.

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w wMATHEMATICAL DEFINITIONS

The mathematical definition of photon flux fluence rate (PFFR) isL

PFFR= LdQI4R

where L is the photon flux radiance and CJ is the solid angle. Sinced = sin@ d6 d$, this can be rewritten as

The mathematical definition of photon flux density (PFD) as measured by acosine-corrected sensor is

PFD = L( +, Q) sinOcos@ d@ d#

If 0’ = 20, then sinQcos@ = 1/2sinO’ and d@ = l/2 dQ’. Also, the limits of6’ are 0 to 7r. Then

PFD=1/4 L( qb, 63’) sin@’ dO’ dq?r

In a uniform radiance distribution, L($,O) = L($,O’) = L (a constant). Then

PFFR = 4xLPFD=?rLor PFFR = (4)(PFD)

A small spherical collecting surface which exhibits the properties of acosine collector at every point of its surface would measure the limit of theratio of total photon flux onto a spherical surface to the area of the surface,as the radius of the sphere tends toward zero. Mathematically, the “photonflux I(@,$) per unit solid angle” in the direction (O,$) that is intercepted bya spherical surface using the cosine law is

where w is the angle between the normal of dA and the direction (O,Q).

Now, dA = nr2 where r = radius of the hemisphere (hemi).

Therefore, the total photon flux (F) intercepted by the sphere is

I7

This spherical collecting surface would then measure h

-4:2 = (1 / 4)(PFFR)

that is, PFFR = 4 times the associated quantity measured by a smallspherical collecting surface which exhibits the properties of a cosinecollector at every point of its surface in a uniform radiance distribution.

From this fact and also the fact that the cross-sectional area of a sphere = l/4the surface area, one could define PFFR as the limit of the ratio of totalphoton flux onto a spherical surface to the cross-sectional area.

In a uniform collimated beam of radiation, the following conditions ofphoton flux radiance hold

L(@,O<O*) = L (a constant)

L(@,o>o*) = 0

whcrc O* is small such that sin@ E 0 and co& z 1.

Then

PFFR =

18

bdAlso,

Therefore, PFFR z PFD

Photon flux fluence rate = photon flux density in a uniform collimated beamif the beam is normal to the cosine collector. One might also note that ifthe beam is perfectly collimated (O*=O), then the radiance L must be infinitein order for flux to be transmitted.

One could use an alternate approach. The total flux (does not need to becollimated) impinging onto a sphere is

F = rrr2 PFFR

where r is the radius of the sphere, and PFFR is the photon flux fluencerate. If the flux is collimated and covers the entire sphere, then the fluxdensity of the beam would be F/rrr2, where xr2 is the cross-sectional area ofthat portion of the beam that is intercepted by the sphere, and F is the totalflux in the beam that is intercepted by the sphere. If the beam is uniform,then the flux density is F/rrr2 every-where in the beam. If a cosine-correctedcollector is put into the beam, it will measure the flux density times thecosine of the angle between the beam and the normal of the collector. Ifthat angle is zero, then the cosine-collector will measure the flux density(F/rrr2) even if its cross sectional area is less than rrr2. Therefore, thecosine-collector will measure the photon flux density to be equal to thephoton flux fluence rate measured by the sphere in a uniform collimatedbeam of radiation.

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Combs, W.S., Jr. 1977. The measurement and prediction of irradianceavailable for photosynthesis by phytoplankton in lakes. University of 5Minnesota Ph.D. Thesis, Limnology.

Incoll, L.D., S.P. Long and M.R. Ashmore. 1977. SI units in publicationsin plant science. Commentaries in Plant Science (No. 28). Published in:Current Adv. Plant Science 9: 33 l-343.

,

Jerlov, N.G. 1968. Optical Gceanography.Elsevier.

McCree, K.J. 1979. Radiation.

NBS Technical note 910-1, 1976. Self-study manual on optical radiationmeasurements.

Shibles, R. 1976. Committee Report: Terminology pertaining tophotosynthesis. Crop Sci. 16: 437439.

Tyler, J.E., and R.W. Preisendorfer. 1962. Light in the sea, p. 399-400.In M.N. Hill (ed.), The Sea, V.I. Interscience.

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SPECIFICATIONS

Absolute Calibration: k 5% in air traceableto NBS.Sensitivity: Typically 3 pA per 1000 t.tmol s-l mm2 in water.Linearity: Maximum deviation of 1% up to 10,000 mmol s-l mm2.Stability: < 912% change over a 1 year period.Response Time: 10 p.s.Temperature Dependence: f 0.15% per “C maximum.Cosine Correction: Acrylic diffuser.Angular Response: < + 4% error up to f 90” from normal axis.Azimuth: < f 3% error over 360” at 90” from normal axis.Detector: High stability silicon photovoltaic detector (blue enhanced).Sensor Housing: Corrosion resistant metal for both saltwater andfreshwater applications with an injection molded, impact resistant, acrylicdiffuser. Units have been tested to 500 psi (34 bars) with no failures.SizeGlobe: 6.1 cm Dia. (2.4”).Housing: 3.18 cm Dia. (1.25”).Overall Height: 10.7 cm (4.2”).Weight: 142 g (0.31 lb.).Mounting: Three 6-32 mounting holes are tapped into the base for usewith the 2009s Lowering Frame or other mounting devices.Cable: Requires 2222UWR Underwater Cable.

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War&tyL

Each LI-COR, inc. instrument is warranted by LI-COR, inc. to be free fromdefects in material and workmanship; however, LI-COR, inc.% soleobligation under this warranty shall be to repair or replace any part of theinstrument which LI-COR, inc.‘s examination discloses to have beendefective in material or workmanship without charge and only under thefollowing conditions, which are:

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2 .

3 .

4 .

5 .

6 .

The defects are called to the attention of LI-COR, inc. in Lincoln,Nebraska, in writing within one year after the shipping date of theinstrument.The instrument has not been maintained, repaired or altered by anyonewho was not approved by LI-COR, inc.The instrument was used in the normal, proper and ordinary manner andhas not been abused, altered, misused, neglected, involved in an accidentor damaged by act of God or other casualty.The purchaser, whether it is a DISTRIBUTOR or direct customer ofLI-COR or a DISTRIBUTOR’S customer, packs and ships or deliversthe instrument to LI-COR. inc.at LI-COR inc.‘s factory in Lincoln,Nebraska, U.S.A. within 30 days after LI-COR, inc. has receivedwritten notice of the defect. Unless other arrangements have been madein writing, transportation to LI-COR, inc. (by air unless otherwiseauthorized by LI-COR, inc.) is at customer expense.No-charge repair parts may be sent at LI-COR, inc.% sole discretion tothe purchaser for installation by purchaser.LI-COR, inc.% liability is limited to repair or replace any part of theinstrument without charge if LI-COR, inc.‘s examination disclosed thatpart to have been defective in material or workmanship.

There are no warranties, express or implied, including butnot limited to any implied warranty of merchantability offitness for a particular purpose on mderwater cam or on

.expendables such as battertes, lamDs, thermocouDles, and.

Other than the obligation of LI-COR, inc. expressly set forthherein, LI-COR, inc. disclaims all warranties ofmerchantability or fitness for a particular purpose. Theforegoing constitutes LI-COR, inc.‘s sole obligation andliability with respect to damages resulting from the use orperformance of the instrument and in no event shall LI-COR,inc. or its representatives be liable for damages beyond theprice paid for the instrument, or for direct, incidental orconsequential damages.

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The laws of some locations may not allow the exclusion or limitation onimplied warranties or on incidental or consequential damaged, so thelimitations herein may not apply directly. This warranty gives you specificlegal rights, and you may already have other rights which vary from state to

I state. All warranties that apply, whether included by this contract or bylaw, are limited to the time period of this warranty which is a twelve-monthperiod commencing from the date the instrument is shipped to a user who isa customer or eighteen months from the date of shipment to LI-COR, inc.‘sauthorized distributor, whichever is earlier.

This warranty supersedes all warranties for products purchased prior to June1.1984. unless this warranty is later superseded.

DISTRIBUTOR or the DISTRIBUTOR’s customers may ship theinstruments directly to LI-COR if they are unable to repair the instrumentthemselves even though the DISTRIBUTOR has been approved for makingsuch repairs and has agreed with the customer to make such repairs ascovered by this limited warranty.

Further information concerning this warranty may be obtained by writing ortelephoning Warranty manager at LI-COR, inc.

IMPORTANT: Please return the User Registration Card enclosed with yourshipment so that we have an accurate record of your address. Thank you.

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