NASA Technical Memorandum 104566, Vol. 39

SeaWiFS Technical Report Series

Stanford B. Hooker and Elaine R. Firestone, Editors

Volume 39, SeaWiFS Calibration Topics, Part 1

Robert A. Barnes, Eueng-nan Yeh, and Robert E. Eplee

October 1996
NASA Technical Memorandum 104566, Vol. 39

SeaWiFS Technical Report Series

Stanford B. Hooker, Editor

NASA Goddard Space Flight Center

Greenbelt, Maryland

Elaine R. Firestone, Technical Editor

General Sciences Corporation

Laurel, Maryland

Volume 39, SeaWiFS Calibration Topics, Part 1

Robert A. Barnes, Eueng-nan Yeh, and Robert E. Eplee

General Sciences Corporation

Laurel, Maryland

National Aeronautics and

Space Administration

Goddard Space Flight Center

Greenbelt, Maryland 20771

1996
SeaWiFS Calibration Topics, Part 1

Preface

The SeaWiFS Calibration and Validation Program consists of four primary components (see the Prologue of

Volume 38), that is, the SeaWiFS Instrument, Field Program, SeaBASS, and Calibration and Validation

Element Software. Several volumes of the SeaWiFS Technical Report Series provided detailed analyses of

prelaunch SeaWiFS sensor performance data, e.g., Volumes 22 (prelaunch acceptance), 23 (prelaunch calibration)

and 31 (stray light). This volume continues our efforts to identify and address issues associated with the SeaWiFS

sensor calibration and characterization. The considerations described herein also apply to the calibration of other

instruments with finite bandwidths including most in situ radiometers to be used in the vicarious calibration

and algorithm development for SeaWiFS.

The chapters in this volume present discussions of:

a) Calculating an equivalent blackbody temperature for the GSFC sphere;

b) The effects of source spectral shape on SeaWiFS radiance measurements;

c) Comparing the spectral responses of SeaWiFS and the SeaWiFS Transfer Radiometer;

d) The SeaWiFS center wavelengths; and

e) The SeaWiFS solar difuser.

Greenbelt, Maryland —C.R.M.

Sept. 1996 Project Scientist

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R.A. Barnes, E-n. Yeh, and R.E. Eplee

Table of Contents

Prologue .................................................................................................1

1. Calculation of an Equivalent Blackbody Temperature for the GSFC Sphere ......................... 5

1.1 Introduction ....................................................................................... 5

1.2 Instrument Model ..................................................................................6

1.3 Model Results .................................................................................... 10

1.4 Concluding Remarks ..............................................................................17

2. Effects of Source Spectral Shape on SeaWiFS Radiance Measurements .............................18

2.1 Introduction ...................................................................................... 18

2.2 Band Specifications ............................................................................... 18

2.3 Instrument Response ............................................................................. 19

2.4 On-Orbit Spectral Shape ..........................................................................33

2.5 Out-of-Band Correction ...........................................................................34

2.6 Comparison of Results ............................................................................ 37

2.7 Total Band Responses ............................................................................ 37

2.8 Concluding Remarks ..............................................................................37

3. A Comparison of the Spectral Responses of SeaWiFS and the SeaWiFS Transfer Radiometer .......39

3.1 Instrument Models ................................................................................39

3.2 SXR and SeaWiFS RSRs ......................................................................... 40

3.3 Sphere Spectral Shape ............................................................................ 40

3.4 Out-of-Band Removal .............................................................................42

3.5 In-Band Radiances ............................................................................... 42

3.6 Center Wavelengths ...............................................................................42

3.7 Radiance Conversion ..............................................................................47

4. SeaWiFS Center Wavelengths .....................................................................49

4.1 Introduction ...................................................................................... 49

4.2 Instrument Response ............................................................................. 49

4.3 Source Functions ................................................................................. 50

4.4 Calculated Wavelengths ...........................................................................50

4.5 Concluding Remarks ..............................................................................53

5. The SeaWiFS Solar Diffuser ....................................................................... 54

5.1 Introduction ...................................................................................... 54

5.2 Diffuser Description ...............................................................................55

5.3 Lab Measurements ................................................................................55

5.4 Field Measurements .............................................................................. 61

Glossary ...............................................................................................62

Symbols ................................................................................................ 62

References ............................................................................................ 62

The SeaWiFS Technical Report Series ............................................................ 64

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R.A. Barnes, E-n. Yeh, and R.E. Eplee

Abstract

For Earth-observing satellite instruments, it was standard to consider each instrument band to have a spectral

response that is infinitely narrow, i.e., to have a response from a single wavelength. The SeaWiFS bands, however,

have nominal spectral bandwidths of 20 and 40 nm. These bandwidths affect the SeaWiFS measurements on

orbit. The effects are also linked to the manner in which the instrument was calibrated and to the spectral shape

of the radiance that SeaWiFS views. Currently, SeaWiFS is calibrated such that the digital counts from each

instrument band are linked to the Earth-exiting radiance at an individual center wavelength. Before launch,

SeaWiFS will be recalibrated so that the digital counts from each band will be linked to the Earth-exiting

radiance integrated over the spectral response of that band. In this technical memorandum, the effects of the

instrument calibration and the source spectral shape on SeaWiFS measurements, including the in-band and

out-of-band responses, and the center wavelengths are discussed.

PROLOGUE

The Sea-viewing Wide Field-of-view Sensor (SeaWiFS)

measures the Earth-exiting radiance at eight nominal center wavelengths (412, 443, 490, 510, 555, 670, 765, and

865 nm). It was the practice in the retrieval of ocean

color measurements to assume that the measurements from

the satellite instrument came from individual wavelengths

and from individual wavelengths alone. The SeaWiFS

bands, however, also have nominal spectral bandwidths

(full-width at half-maximum response) of 20 and 40 nm.

The incorporation of these broad spectral responses into

the data reduction algorithms for SeaWiFS will lead to

water-leaving radiances that are different from those based

on the nominal center wavelengths alone.

For SeaWiFS, as for many other satellite sensors, the

performance specification for the instrument defines the

in-band and the out-of-band responses for each measurement band. The in-band response is defined as the response from the spectral region between the two 1% response points, that is, between the wavelengths at which

the response of the band is 1% of the maximum response.

Out-of-band is defined as the response from wavelengths

outside of those 1% points. For SeaWiFS, the out-of-band

specification allows up to 5% instrument response in the

out-of-band wavelength regions for each band (Barnes et

al. 1994a). The actual out-of-band responses for the eight

SeaWiFS bands (to a source with the spectral shape of a

5,900 K blackbody) range from 0.3–3.7% of the total band

responses (Barnes et al. 1994b). The out-of-band response

on orbit, however, will be a function of the spectral shape

of the Earth-exiting radiance that SeaWiFS actually views.

In addition, the laboratory calibration of SeaWiFS was

performed using a spherical integrating source (SIS) that

was, itself, calibrated at the nominal SeaWiFS center wavelengths. Thus, for SeaWiFS band 1, the counts from the

instrument in the laboratory corresponded to a measured

spectral radiance from the sphere at 412 nm. A similar

pairing was made for the spectral radiances from the integrating sphere and the counts from the other SeaWiFS

bands. Information from the instrument manufacturer,

who performed the laboratory calibration, indicated that

the spectral shape for the radiance from the integrating

sphere approximated that for a 2,850 K blackbody. This

type of calibration is consistent with the calibration of

other Earth-observing satellite instruments, such as the

Ocean Color and Temperature Scanner (OCTS).

As a result, it was necessary to devise a procedure for

transferring the laboratory calibration of SeaWiFS to orbit. This was done by converting the SeaWiFS laboratory

responses from those for a source with a 2,850 K spectral

shape to those for a source with a 5,900 K spectral shape

(Barnes et al. 1994b). The 5,900 K blackbody shape, which

approximates the spectral shape of the solar irradiance,

was the only spectral shape provided in the SeaWiFS performance specification (Barnes et al. 1994a).

The output of the SeaWiFS bands (in digital counts)

is linked to spectral radiances at the nominal center wavelengths. This linkage leads to dependencies between the

bands’ output and the spectral shapes of the sources

viewed. Those dependencies are a direct consequence of

the manner in which SeaWiFS was calibrated in the laboratory. There is also a connection between the response

of the instrument at wavelengths well away from the center wavelength (the out-of-band response) and the spectral

shape of the sources that SeaWiFS views.

This technical memorandum contains chapters that address aspects of the dependence of the SeaWiFS bands—as

they have been calibrated by the manufacturer—on the

source spectral shape. In general, the sources in these

studies are Planck function (blackbody) curves of different temperatures. For SeaWiFS, the spectral shape of the

laboratory source approximated that for a 2,850 K blackbody. The shape of the solar output is that for a 5,900 K

blackbody, and for the typical SeaWiFS radiances in the

instrument performance specification (Barnes et al. 1994a)

the spectral shape approximates that for a 12,000 K blackbody (Barnes et al. 1995a). For the source dependence

studies in this document, the reference spectral shapes are

1
SeaWiFS Calibration Topics, Part 1

those for blackbodies with temperatures that range from

2,000 K to 30,000 K. Those studies are explained in Chapters 1 and 2.

The upwelling Earth radiance that SeaWiFS will view

on orbit, however, does not have a spectral shape that

changes smoothly with wavelength (see Fig. 3 of Hooker et

al. 1992). There are absorption lines in that spectrum, particularly from water vapor and molecular oxygen. Oxygen

A-band absorption can remove 10–15% of the in-band radiance viewed by SeaWiFS band 7 depending on pathlengths

within the atmosphere (Ding and Gordon 1995 and Fraser

1995]. For SeaWiFS band 8, water vapor can remove up

to 1% of the upwelling radiation in its out-of-band region

for very long pathlengths within the atmosphere (Gordon

1995). It is possible to adapt the studies recounted in

this document to account for these effects. The absorption spectra for molecular oxygen and for water vapor are

available through the LOWTRAN and MODTRAN atmospheric

models. The absorption spectra for these gasses are the

kernels of the modeling studies of Ding and Gordon (1995),

Fraser (1995), and Gordon (1995).

The LOWTRAN model for oxygen A-band absorption for

two vertical passes through the atmosphere (an airmass of

2) is shown in Fig. 1. Other atmospheric transmission factors, such as absorption by water vapor and/or scattering

by aerosols, are not shown. As this figure shows, oxygen

A-band absorption occurs in the wavelength region within

which SeaWiFS band 7 responds to light best.

A similar spectrum for water vapor, with a water column amount of 3.338 g cm−2 and an airmass of 2, is shown

in Fig. 2. This figure includes the relative spectral response

for SeaWiFS band 8. Atmospheric water vapor, both as

a function of its column amount and the pathlength for

solar radiation reflected from the ocean surface, causes a

small, but significant, reduction of upwelling radiation in

the spectral wings of band 8.

SeaWiFS bands 7 and 8 form the basis for the SeaWiFS

atmospheric correction, a correction that is critical to the

calculation of SeaWiFS water-leaving radiances. As shown

in Figs. 1 and 2, oxygen and water vapor do not absorb at

individual wavelengths, but over wavelength regions that

extend from a few to more than 100 nm. Thus, based on

the modelling results of Gordon (1995), it was decided by

the Calibration Subgroup of the SeaWiFS Science Working

Group that SeaWiFS should have a laboratory calibration

which includes the response of each instrument band to

upwelling Earth radiance over its full spectral range.

This response is known as the band-weighted spectral

radiance (BSR). It is the spectral radiance of the source

integrated over the spectral response of the band. To be

useful for Earth observations, each BSR must be associated

with a band-weighted center wavelength (BCW). The calibration of SeaWiFS for BSRs has not been performed as

yet. This calibration awaits the final thermal-vacuum testing of SeaStar, the spacecraft that will carry SeaWiFS; the

calibration is currently scheduled for the fourth quarter of

1996. It will be consistent with the calibration of other

Earth-observing satellite instruments, such as the Moderate Resolution Imaging Spectroradiometer (MODIS).

Before the postthermal-vacuum calibration can occur,

three things must be known: the spectral shape of the radiance from the laboratory source; the spectral response of

the SeaWiFS bands; and the spectral shape of the bands

in the reference radiometer. The spectral response of SeaWiFS is known (Barnes 1994). The spectral shape of the

radiance from the GSFC sphere, which will be used as the

source in the calibration, is described in Chapter 1. And,

the spectral shape of the SeaWiFS Transfer Radiometer

(SXR), which will be used as the reference radiometer in

the calibration, is discussed in Chapter 3.

In addition to a calibration in terms of BSRs, the (future) postthermal-vacuum calibration of SeaWiFS can also

be interpreted in the same manner as the original laboratory calibration of SeaWiFS by the manufacturer, that is,

in terms of spectral radiances at the eight nominal SeaWiFS center wavelengths. So, before launch, SeaWiFS will

be calibrated in two ways: in terms of the BSRs from each

band, and in terms of the spectral radiances at the nominal

center wavelengths for each band. For the BSRs, a corresponding center wavelength must be determined for each

band. These center wavelengths are described in Chapter 4.

Finally, the effects of absorption by atmospheric water

vapor and oxygen on SeaWiFS bands 7 and 8 can be calculated for measurements that use the original SeaWiFS calibration. For this type of calibration, in which the counts

from the bands are linked to spectral radiances at the nominal center wavelengths for the bands, the absorption corrections require a nominal top-of-the-atmosphere spectral

radiance curve, plus models for the spectral shapes and

intensities of the molecular absorption lines. For water

vapor, which absorbs in the wings of the band responses,

LOWTRAN absorption values, with their relatively low wavelength resolution, are sufficient. For oxygen, which absorbs

in the center of the response for band 7, MODTRAN spectra,

interpolated to 0.1 nm intervals, are required. These data

sets have been compiled, and the calculated results will be

presented in a subsequent technical memorandum in this

series. A short synopsis of each chapter in this volume is

given below.

1. Calculation of an Equivalent Blackbody

Temperature for the GSFC Sphere

The SeaWiFS radiometer shares a number of fundamental characteristics with other filter-based spectrometers. Among these characteristics is a dependence of the

throughput of the interference filters on the spectral shape

of the measured radiance. This dependence varies from

band to band within the instrument and is based on the

spectral response of each individual band. Here, the measured spectral response curves for the SeaWiFS bands and

2
R.A. Barnes, E-n. Yeh, and R.E. Eplee

Fig. 1. Oxygen A-band transmittance and the spectral response for SeaWiFS band 7 are illustrated in this

figure. The scale for oxygen transmittance, as given for the LOWTRAN atmospheric model, is on the right. The

transmittance represents two vertical passes through the atmosphere, that is, an airmass of two. The scale for

the band 7 relative spectral response is on the left.

Fig. 2. The water vapor transmittance and the spectral response for SeaWiFS band 8 are shown. The scale

for water vapor transmittance, as given for the LOWTRAN atmospheric model, is on the right. The transmittance

represents two vertical passes through an atmosphere with a water vapor column amount of 3.338 g cm−2 (the

amount in the LOWTRAN tropical model). The scale for the band 8 relative spectral response is on the left.

3
SeaWiFS Calibration Topics, Part 1

a set of radiance curves to provide a model for this dependence are used. The radiance curves are normalized at

the nominal SeaWiFS center wavelengths, that is, at the

wavelengths used in the laboratory calibration of the instrument. The model results show that, as far as the eight

SeaWiFS bands are concerned, the radiance curves for the

Goddard Space Flight Center (GSFC) SIS are equivalent

to that for a 2,850 K blackbody. The model results also

show that the output from the SeaWiFS bands will have

differences of up to 5% on orbit, when compared with the

radiometric calibration in the laboratory.

2. Effects of Source Spectral Shape on

SeaWiFS Radiance Measurements

Two aspects of filter photometry on the radiances measured by SeaWiFS are examined: the dependence of the total band response, and the out-of-band response on source

spectral shape. These effects are significant contributors to

the SeaWiFS measurements on orbit. The corrections for

out-of-band response range from about 0.5% to more than

5%, depending on the SeaWiFS band. The corrections for

total band response range from near zero to about 5%.

These corrections will be used to convert the laboratory

calibration of SeaWiFS (in terms of total band response)

to orbit (in terms of in-band response). The residual uncertainty in these corrections is estimated to be small, around

0.2%. With other significantly larger error sources in the

SeaWiFS measurements, the contribution of these residual

uncertainties to the propagation of error for SeaWiFS radiance measurements at the top of the atmosphere is also

expected to be small. These corrections are prelaunch estimates and should be reexamined using flight data. In

addition, these corrections have been tailored to SeaWiFS

ocean measurements. The contributions to land measurements will be different.

3. A Comparison of the Spectral

Responses of SeaWiFS and the

SeaWiFS Transfer Radiometer

Both SeaWiFS and the SXR are filter radiometers with

finite bandwidths. The use of these instruments requires

a knowledge of the effects that finite bandwidths cause.

These effects also depend on the source’s spectral shape

which the instruments measure. For the radiometric calibration of SeaWiFS, the source is the GSFC SIS. The

BSRs and the effective center wavelengths (ECWs) for SeaWiFS and the SXR, when measuring the GSFC SIS, are

presented here. They will be needed to convert the SXR

measured spectral radiances to the SeaWiFS wavelengths.

4. SeaWiFS Center Wavelengths

With its 20 and 40 nm bandwidths, SeaWiFS does not

make measurements at individual wavelengths. Rather,

the output from each SeaWiFS band can be considered as

an integral over a finite wavelength region of the source

it measures. To make SeaWiFS measurements useful, it is

important to relate the measured radiance from the instrument to a reference wavelength. That wavelength connects

each SeaWiFS measurement to the spectral radiance from

the source at that wavelength. For the initial calibration

of SeaWiFS, the reference center wavelengths were those

from the instrument’s performance specifications. A set

of BCWs for on-orbit use are presented here. The use of

these new wavelengths will require a revision of the onorbit radiometric calibration constants for the instrument.

5. The SeaWiFS Solar Diffuser

Measurements of the solar flux with an onboard solar diffuser will provide an important check of changes in

the radiometric sensitivity of SeaWiFS over the duration

of the instrument’s on-orbit measurements of ocean color.

Although diffuser measurements do not give an absolute

determination of radiometric changes, they will identify

any rapid changes that may occur in the instrument output. The diffuser was designed to produce radiance levels

that approximate those for other SeaWiFS measurements.

This design includes an attenuator to reduce the solar radiance levels on the diffuser, and hence, the effects of photolyzed organic compounds. The BRDF, which shows the

output of the diffuser as a function of pitch and yaw angle,

has been determined. This allows the removal of angular dependencies from the long-term radiometric sensitivity data. In addition, outdoor measurements have given

the predicted output from SeaWiFS for initial on-orbit solar diffuser measurements.

4
R.A. Barnes, E-n. Yeh, and R.E. Eplee

Chapter 1

Calculation of an Equivalent Blackbody

Temperature for the GSFC Sphere

Robert A. Barnes

General Sciences Corporation

Laurel, Maryland

Abstract

The SeaWiFS radiometer shares several fundamental characteristics with other filter-based spectrometers.

Among these characteristics is a dependence of the throughput of the interference filters on the spectral shape

of the measured radiance. This dependence varies from band to band within the instrument and is based on

the spectral response of each individual band. Here, the measured spectral response curves for the SeaWiFS

bands and a set of radiance curves to provide a model for this dependence are used. The radiance curves are

normalized at the nominal SeaWiFS center wavelengths, that is, at the wavelengths used in the laboratory

calibration of the instrument. The model results show that, as far as the eight SeaWiFS bands are concerned,

the radiance curves for the GSFC SIS are equivalent to that for a 2,850 K blackbody. The model results also

show that the output from the SeaWiFS bands will have differences of up to 5% on orbit, when compared with

the radiometric calibration in the laboratory.

1.1 INTRODUCTION

The construction and calibration of SeaWiFS was completed in November 1993. The instrument was designed by

the Santa Barbara Research Center (SBRC) to meet a set

of performance specifications, including specifications for

maximum ocean radiances and maximum cloud radiances

(Barnes et al. 1994a). To determine the instrument output for these radiance levels, SBRC used a 100 cm SIS with

a calibration traceable to the National Institute of Standards and Technology (NIST). The SBRC sphere used sets

of 200 W, 45 W, and 5 W tungsten lamps. The spectral

shape for the sphere output was assumed to be equivalent

to a 2,850 K blackbody (Barnes et al. 1994b).

The output of the GSFC 106 cm SIS was characterized and calibrated by NIST in April 1995. The results

of this characterization will be published as part of a future SeaWiFS technical memorandum. The absolute calibration of the sphere will change with time as the lamps

and the reflective inner surface of the sphere age. The

use of the sphere will require frequent recalibration using

a transfer radiometer before it is viewed by the instruments under test. However, other characteristics of the

sphere—the areal uniformity of the sphere’s radiant output across its output aperture and the spectral shape of

its output—need to be checked much less frequently. As

part of the characterization of the sphere at NIST, its radiance was measured relative to a NIST-standard gold-point

blackbody, using equipment and techniques described in

Walker et al. (1987). For these measurements, the spectral

response of the GSFC sphere has a maximum radiance at

890 nm (Fig. 3a). Using the Wein displacement law (Wyatt 1978) this wavelength corresponds to a Planck function

(blackbody) temperature of 3,256 K.

The GSFC and SBRC integrating spheres were not designed to duplicate ideal flat-black radiators that emit at

specific temperatures. This non-ideal spectral output for

the GSFC sphere is shown in Fig. 3. The output from the

sphere at 890 nm is less than 1 part in 10,000 of that from

a 3,256 K blackbody, and normalization of the blackbody

curve was required to create the figure. This gives the

sphere an extremely small emissivity (), less than 0.0001.

In addition, the GSFC sphere cannot be treated as a greybody, since its emissivity changes with wavelength. This

also can be seen in Fig. 3, where the sphere output does

not follow the shape of the blackbody for wavelengths away

from 890 nm.

The data from the characterization of the GSFC sphere

are sufficient to calculate emissivity as a function of wavelength. These data can also be acquired for the SBRC

sphere. Such characterizations of the integrating spheres,

however, are not necessary. For the SeaWiFS Project, interest is limited to the manner in which the sphere output

effects the eight SeaWiFS bands. Each SeaWiFS band

has its own spectral response (Barnes et al. 1994b), and

that spectral response interacts with the spectral shape of

5
SeaWiFS Calibration Topics, Part 1

Fig. 3. Response of the GSFC sphere and a 3,256 K blackbody. Both responses have maximum radiances at

890 nm. The blackbody curve has been normalized to the sphere response at 890 nm.

the source that illuminates it. Such interactions, including

those for the output from the GSFC sphere, are presented

here. They are instrument dependent and are not readily

extrapolated beyond SeaWiFS.

1.2 INSTRUMENT MODEL

On orbit, SeaWiFS will view, on a pixel by pixel basis,

the upwelling Earth radiance. From a spectral viewpoint,

the relative spectral response of each instrument band will

be combined with the spectral shape of that upwelling radiance. The relative spectral responses of the SeaWiFS

bands have been measured. For this study, the spectral

shapes viewed by the instrument will be approximated by

a set of Planck function curves. These models are used

to give a zeroth order understanding of the instrument response on orbit.

1.2.1 Band Spectral Responses

This model for the response of SeaWiFS to source spectral shape is based on the spectral responses of the SeaWiFS bands. Those responses were described previously

(Barnes et al. 1994b) for three different types of sources: a

2,850 K blackbody, a 5,900 K blackbody, and a spectrally

flat source. The spectrally flat responses were calculated

(on a nanometer by nanometer basis) using the spectral responses of the filters, lenses, and dichroics in each band’s

optical train. For each of these components, the response

is dimensionless, that is, the response is the ratio of photons out to photons in (PO:PI). The silicon photodiode for

each band also has a spectral dependence for its response,

a response with the ratio of electrons out to photons in

(EO:PI)—or milliamperes per milliwatt. Thus, at each

nanometer interval from 380–1,150 nm, the output from

the optical train for each band has units of mA mW−1.

Here, as in Barnes et al. (1994b), the piece-part derived

response ratios have been multiplied at each nanometer by

1 mW cm−2 sr−1 μ m−1 to give the band’s response-to-unit

radiance. The output for SeaWiFS band 6 is shown in

Fig. 4a. The output for this and the other SeaWiFS bands

is the current from the photodiode. As shown in Fig. 4a for

band 6 and a spectrally flat source, the current from the

photodiode is the sum of the current at each nanometer interval; this integrated current is a few nanoamperes. This

current can be used to determine the relative response of

the instrument to sources with different spectral shapes;

however, it cannot determine the output of the instrument

on an absolute basis. There are other nonspectral factors

that are part of the instrument’s response, including the

collecting power of the fore optics and the gains of the amplifiers in the electronics that follow the photodiodes.

1.2.2 Planck Function Curves

For an idealized blackbody radiator, the radiance can

be given as a function of both temperature and wavelength

6
R.A. Barnes, E-n. Yeh, and R.E. Eplee

Fig. 4. Components in the Calculation of the Integrated Band Output. SeaWiFS band 6 (670 nm) is used

as an example. The integrated band output is calculated as the sum of wavelength-by-wavelength products

of the band spectral response and the radiance curve. a) Band 6 spectral response: this is the response to a

source with unit radiance (1 mW cm−2 sr−1 μ m−1). b) A set of Planck function (blackbody) curves normalized

at 670 nm, the nominal wavelength for SeaWiFS band 6.

7
SeaWiFS Calibration Topics, Part 1

(Wyatt 1978):

L(λ) = 2hc2

λ5



ehc/λkT − 1

, (1)

where L is the radiance (in W m−3 sr−1); λ is the wavelength (in meters); h is Planck’s constant (in J sec); c is

the velocity of light (in m sec−1); k is Boltzmann’s constant

(in J K−1); and T is the temperature (in K).

The radiance values from (1) can be converted directly

into units of mW cm−2 sr−1 μ m−1, the units for SeaWiFS

measurements. As used in the model calculations below,

these Planck function curves are normalized to the SeaWiFS typical radiances at the nominal wavelengths for

the SeaWiFS bands, which are given in Table 1. These

are the wavelengths at which SeaWiFS was calibrated in

the laboratory. The wavelength for each band in Table 1

corresponds to the radiance for each band in Table 8 of

Barnes et al. (1994b). The wavelengths in Table 1 are

embedded in the radiometric calibration of SeaWiFS. For

these fixed wavelengths, the output of the bands change

with the spectral shapes of the sources. In an alternate

approach to source spectral shape dependence, it is possible to keep the band output constant and let the reference

wavelength vary as a function of the spectral shape of the

source. However, the alternate approach lacks the security

of well-defined, fixed reference wavelengths for the instrument.

Table 1. The center wavelengths are in nanometers

and the typical (Ltypical) radiances for the SeaWiFS

bands are in units of mW cm−2 sr−1 μ m−1. These

values come from the performance specifications for

the instrument (see Barnes et al. 1994a).

SeaWiFS Nominal Typical

Band Center Radiance

Wavelength

1 412 9.10

2 443 8.41

3 490 6.56

4 510 5.64

5 555 4.57

6 670 2.46

7 765 1.61

8 865 1.09

The radiance values from the Planck function increase

at all wavelengths with increasing temperature, and the

peak of the curve shifts toward shorter wavelengths with

increasing temperature. The wavelength at which the maximum radiance occurs is given by the derivative of Planck’s

equation with respect to wavelength, also called Wein’s displacement law:

λm = 2898

T , (2)

where λm is the wavelength for maximum radiance (in

μ m). For a 2,850 K blackbody, the maximum radiance occurs at 1,017 nm; for a 5,900 K blackbody at 491 nm. These

are within the wavelength range over which the spectral responses of the SeaWiFS bands have been measured (380–

1,150 nm). Over the more restricted wavelength range of

394–908 nm, which covers the within-band responses for

the eight SeaWiFS bands (Barnes et al. 1994b), Planck

function curves with temperatures that are less than about

3,000 K have radiances that increase monotonically with

wavelength. For blackbody temperatures that are greater

than about 8,000 K, the radiances decrease monotonically

over this range. A set of blackbody curves, normalized at

670 nm is shown in Fig. 3b.

For a combination of high temperatures and long wavelengths, Planck’s law can be approximated by RayleighJeans’ law:

L(λ) = 2ckT

λ4 . (3)

The wavelength dependence for radiance in the RayleighJeans’ law is the same as that for light scattered by air

molecules (Section 1.2.4). Fig. 5a shows the response of

a 26,000 K blackbody and the Rayleigh-Jeans approximation, both normalized at the typical radiance for SeaWiFS

band 8 (1.09 mW cm−2 sr−1 μ m−1) at 865 nm. Fig. 5b

shows the difference between the blackbody curve and the

power-law approximation from the Rayleigh-Jeans law,

which appears as a straight line in log-log space.

1.2.3 GSFC Sphere Output

The radiances from the GSFC sphere were provided by

B. Carol Johnson of NIST. The data are given for four

lamp configurations: 1, 4, 8, and 16 lamps illuminated.

These data, including the spectral responses of the Fastcal

transfer radiometer (Walker et al. 1987) to a tungsten strip

lamp and to the sphere, were taken at 10 nm intervals from

380–1,100 nm. Using reference values for the radiance from

the tungsten strip lamp, the sphere radiances were calculated as ratios of the output from the transfer radiometer.

As part of the preparation of the NIST-provided data for

this study, the discontinuities in the responses of the Fastcal radiometer at 760 and 960 nm were smoothed using a

power law interpolation, that is, an interpolation in log-log

space.

Since the spectral response values for the SeaWiFS

bands cover the range from 380–1,150 nm (Barnes et al.

1994b), the NIST data were extended from 1,100–1,150 nm

using power law curve fits of the data from 1,000–1,100 nm.

The region between 1,100–1,150 nm lies at the end of the

out-of-band responses for each of the SeaWiFS bands, and

the band responses at these wavelengths are 4–5 orders of

magnitude below the peak responses (see Fig. 4a, for example). Errors of 20–30% in the radiances from the source

in this region give negligible contributions to the model

calculations. The extrapolations have been made with the

8
R.A. Barnes, E-n. Yeh, and R.E. Eplee

Fig. 5. Shown here is the spectral output of a 26,000 K blackbody and of the Rayleigh-Jeans approximation to

the Planck function. Both curves have been normalized at 865 nm to the typical radiance for SeaWiFS band 8

(1.09 mW cm−2 sr−1 μ m−1). b) Radiances shown in linear coordinates. From 380–865 nm the radiance from the

26,000 K blackbody is greater than that for the approximation. b) Radiances shown in logarithmic coordinates.

The Rayleigh-Jeans approximation appears as a straight line in these coordinates.

9
SeaWiFS Calibration Topics, Part 1

sole purpose of maintaining a uniform wavelength range

for all components of the calculations.

Finally, because the SeaWiFS spectral response values

are given at 1 nm intervals, the NIST-provided data have

been interpolated between these 10 nm intervals, again using power-law interpolation, to provide data at those wavelengths. The use of linear interpolations of the NIST data

was compared with that for power-law interpolations. Substituting one interpolation for the other caused changes of

0.05% or less in the results of the model calculations. This

difference is sufficiently small that the results from the linear interpolations are not included here.

1.2.4 Solar Flux and Rayleigh Scattering

For wavelengths above 300 nm, the solar flux has a spectral shape that is approximated by a blackbody with a

temperature of 900 K (Brasseur and Solomon 1987). As

viewed by SeaWiFS during solar diffuser measurements

(Woodward et al. 1993), the solar spectrum is essentially a

continuum, and the 5,900 K spectral shape was used in several of the SeaWiFS performance specifications (Barnes et

al. 1994a). The shape, however, is a poor approximation

for the blue sky radiance—the upwelling Earth radiance

seen by SeaWiFS on orbit. For SeaWiFS ocean measurements, the reflected light from the sea surface is a small

fraction of the sky radiance. This radiance is dominated

by scattering from air molecules.

Molecular, or Rayleigh, scattering of unpolarized light

by anisotropic air molecules has a scattering coefficient

with a dependence on wavelength (λ) which is approximated by the form λ−4 (Penndorf 1957).

σ = 8π3(n2

s − 1)2D

3λ4N2

s

, (4)

where σ is the Rayleigh scattering cross section per molecule (cm2); ns is the refractive index of air (dimensionless); D is the depolarization factor which expresses the influence of the molecular anisotropy of air (dimensionless);

and Ns is the number density of the scattering molecules

(cm−3).

There is an additional wavelength dependence in the

Rayleigh scattering coefficient, since the coefficient also

includes the refractive index of air, which has its own dependence on wavelength. Such a refinement is unnecessary

here, since the additional wavelength dependence is small,

and since the blue sky radiance is itself an approximation

to the sky radiance. The actual upwelling Earth radiance

seen by SeaWiFS also includes contributions from aerosol

scattering, absorption and emission from gasses, and reflections from the surface of the Earth.

The model calculations presented here contain three

special source spectral shapes: the measured shape for

the spectral radiance from the GSFC integrating sphere;

the spectral shape of a 5,900 K blackbody, which approximates the spectral shape of the solar flux; and a spectral shape with a wavelength dependence of λ−4, which

approximates the upwelling radiance from a molecular (or

Rayleigh) atmosphere. The model calculations also include

Planck functions with temperatures from 2,000–38,000 K.

These Planck functions encompass the three special spectral shapes.

1.3 MODEL RESULTS

The integrated output for the eight SeaWiFS bands

are listed in Table 2. The results are also shown in Fig. 6

(bands 1 and 2), Fig. 7 (bands 3 and 4), Fig. 8 (bands 5

and 6), and Fig. 9 (bands 7 and 8). For Figs. 6–9, the minimum values for the ordinates have not been set to zero.

This was done to increase resolution for the relatively small

changes in the output from the bands. To give some consistency to the vertical scales, however, the maximum values

for the ordinates have been set to about 1.2–1.25 times

the minimum values. The changes in the integrated band

output are shown in Table 3, normalized to the output for

a 5,900 K blackbody. For the prelaunch radiometric calibration of SeaWiFS (Barnes et al. 1994b), the coefficients

for the calibration equations were calculated, based on a

5,900 K blackbody.

The equivalent blackbody temperatures for the GSFC

sphere and the Rayleigh atmosphere are also shown in

Figs. 6–9. These temperatures were determined by interpolation, using the band output for the blackbody radiances. The equivalent GSFC sphere temperatures are near

3,000 K and the equivalent Rayleigh atmosphere temperatures range from 25,000–35,000 K. This consistency was

the basis for the selection of the equivalent temperature

when two possible solutions were possible.

The NIST measurements include spectral responses for

four configurations of the sphere: 1 lamp, 4 lamps, 8 lamps,

and 16 lamps illuminated. The radiances from these output cover a range of radiance levels that is sufficient for

the calibration of the SeaWiFS radiometer. The radiances

from the NIST measurements, interpolated to the nominal

SeaWiFS center wavelengths, are listed in Table 4.

The SeaWiFS integrated band output for the GSFC

sphere radiances (Table 2) contain the average values for

the four lamp settings. Table 5 gives the SeaWiFS integrated band output for each of the four NIST spectral

curves. The mean values in Table 5 have small standard

deviations. As a result, the results for the mean integrated

band output are interchangeable with those for the individual lamp settings.

It should be stressed that reality for this discussion

is based on the spectral response curves for the SeaWiFS

bands. SeaWiFS radiance measurements from the GSFC

sphere are not presented here, and, in fact, there are no

SeaWiFS radiance measurements in this report. The results are based on model radiances only.

10
R.A. Barnes, E-n. Yeh, and R.E. Eplee

Table 2. The integrated band output is shown here in picoamperes. The output is given for several Planck functions

(in kelvin) and for two special spectral shapes: the shape for the GSFC SIS output and for a Rayleigh scattering

atmosphere.

Planck Function Integrated Band Output [pA]

Temperature [K] Band 1 Band 2 Band 3 Band 4 Band 5 Band 6 Band 7 Band 8

2,000 2397.8 3570.3 4483.5 4690.5 4032.0 2059.8 2908.8 2254.2

2,500 2306.4 3514.9 4354.6 4636.5 3928.8 2065.5 2883.4 2249.1

2,850 2274.3 3492.9 4315.6 4623.7 3900.1 2069.4 2874.3 2249.0

3,000 2264.2 3485.7 4303.9 4620.5 3892.3 2071.0 2871.6 2249.4

3,500 2239.4 3468.0 4276.3 4614.3 3876.6 2075.9 2865.5 2252.2

4,000 2223.0 3456.4 4258.8 4611.9 3869.4 2080.1 2862.0 2256.3

5,000 2202.9 3442.2 4238.2 4611.3 3865.5 2087.2 2858.9 2266.0

5,900 2192.0 3434.9 4227.4 4612.4 3866.6 2092.3 2858.0 2275.3

8,000 2177.9 3425.8 4214.1 4616.0 3873.5 2101.2 2858.4 2295.5

0,000 2170.8 3421.6 4207.7 4619.1 3880.3 2107.3 2859.6 2311.9

12,000 2166.3 3419.1 4203.9 4621.5 3886.2 2111.9 2860.8 2325.6

14,000 2163.3 3417.5 4201.4 4623.5 3891.1 2115.5 2862.0 2337.0

16,000 2161.2 3416.4 4199.7 4625.1 3895.2 2118.3 2863.1 2346.7

18,000 2159.5 3415.6 4198.4 4626.5 3898.7 2120.7 2864.1 2354.9

20,000 2158.2 3415.0 4197.4 4627.6 3901.7 2122.7 2864.9 2361.9

22,000 2157.2 3414.6 4196.6 4628.5 3904.2 2124.4 2865.7 2368.1

24,000 2156.3 3414.2 4196.0 4629.3 3906.4 2125.8 2866.3 2373.4

26,000 2155.6 3413.9 4195.4 4630.0 3908.3 2127.1 2866.9 2378.1

28,000 2155.0 3413.6 4195.0 4630.6 3910.0 2128.2 2867.4 2382.3

30,000 2154.5 3413.4 4194.6 4631.1 3911.5 2129.1 2867.9 2386.1

32,000 2154.1 3413.2 4194.3 4631.6 3912.8 2130.0 2868.4 2389.4

34,000 2153.7 3413.1 4194.0 4632.0 3914.0 2130.8 2868.7 2392.4

36,000 2153.3 3412.9 4193.8 4632.4 3915.1 2131.5 2869.1 2395.2

38,000 2153.0 3412.8 4193.6 4632.8 3916.1 2132.1 2869.4 2397.7

Special Spectral Shapes

GSFC SIS 2280.2 3490.4 4305.5 4618.3 3890.8 2069.8 2869.3 2248.2

Rayleigh Atmosphere 2153.9 3413.7 4195.5 4631.5 3911.9 2126.3 2867.1 2367.6

11
SeaWiFS Calibration Topics, Part 1

Fig. 6. Instrument responses to Planck function (blackbody) curves with temperatures from 2,000–38,000 K

are shown. The vertical lines show the band responses to radiance spectra with the shape of the GSFC sphere

and of a Rayleigh scattering atmosphere. a) Response of SeaWiFS band 1 (412 nm). b) Response of SeaWiFS

band 2 (443 nm).

12
R.A. Barnes, E-n. Yeh, and R.E. Eplee

Fig. 7. Instrument responses to Planck function (blackbody) curves with temperatures from 2,000–38,000 K

are shown. The vertical lines show the band responses to radiance spectra with the shape of the GSFC sphere

and of a Rayleigh scattering atmosphere. a) Response of SeaWiFS band 3 (490 nm). b) Response of SeaWiFS

band 4 (510 nm).

13
SeaWiFS Calibration Topics, Part 1

Fig. 8. Instrument responses to Planck function (blackbody) curves with temperatures from 2,000–38,000 K

are shown. The vertical lines show the band responses to radiance spectra with the shape of the GSFC sphere

and of a Rayleigh scattering atmosphere. a) Response of SeaWiFS band 5 (555 nm). b) Response of SeaWiFS

band 6 (670 nm).

14
R.A. Barnes, E-n. Yeh, and R.E. Eplee

Fig. 9. Instrument responses to Planck function (blackbody) curves with temperatures from 2,000–38,000 K

are shown. The vertical lines show the band responses to radiance spectra with the shape of the GSFC sphere

and of a Rayleigh scattering atmosphere. a) Response of SeaWiFS band 7 (765 nm). b) Response of SeaWiFS

band 8 (865 nm).

15
SeaWiFS Calibration Topics, Part 1

Table 3. The integrated band output relative to a 5,900 K Planck function is shown in this table. The output is given

for several Planck functions and for two special spectral shapes: the shape for the GSFC SIS output and for a Rayleigh

scattering atmosphere.

Planck Function Integrated Band Output [pA]

Temperature [K] Band 1 Band 2 Band 3 Band 4 Band 5 Band 6 Band 7 Band 8

2,000 1.0938 1.0394 1.0606 1.0169 1.0428 0.9845 1.0178 0.9907

2,500 1.0522 1.0233 1.0301 1.0052 1.0161 0.9872 1.0089 0.9885

2,850 1.0375 1.0169 1.0209 1.0024 1.0087 0.9891 1.0057 0.9884

3,000 1.0329 1.0148 1.0181 1.0017 1.0066 0.9898 1.0047 0.9886

3,500 1.0216 1.0097 1.0115 1.0004 1.0026 0.9922 1.0026 0.9899

4,000 1.0141 1.0063 1.0074 0.9999 1.0007 0.9942 1.0014 0.9916

5,000 1.0050 1.0021 1.0025 0.9998 0.9997 0.9976 1.0003 0.9959

5,900 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000

8,000 0.9935 0.9974 0.9968 1.0008 1.0018 1.0043 1.0001 1.0089

10,000 0.9903 0.9961 0.9953 1.0014 1.0035 1.0072 1.0005 1.0161

12,000 0.9883 0.9954 0.9944 1.0020 1.0051 1.0094 1.0010 1.0221

14,000 0.9869 0.9950 0.9938 1.0024 1.0063 1.0111 1.0014 1.0271

16,000 0.9859 0.9946 0.9934 1.0028 1.0074 1.0125 1.0018 1.0314

18,000 0.9852 0.9944 0.9931 1.0030 1.0083 1.0136 1.0021 1.0350

20,000 0.9846 0.9942 0.9929 1.0033 1.0091 1.0145 1.0024 1.0381

22,000 0.9841 0.9941 0.9927 1.0035 1.0097 1.0153 1.0027 1.0408

24,000 0.9837 0.9940 0.9926 1.0037 1.0103 1.0160 1.0029 1.0431

26,000 0.9834 0.9939 0.9924 1.0038 1.0108 1.0166 1.0031 1.0452

28,000 0.9831 0.9938 0.9923 1.0039 1.0112 1.0172 1.0033 1.0470

30,000 0.9829 0.9938 0.9922 1.0041 1.0116 1.0176 1.0035 1.0487

32,000 0.9827 0.9937 0.9922 1.0042 1.0120 1.0180 1.0036 1.0502

34,000 0.9825 0.9937 0.9921 1.0043 1.0123 1.0184 1.0037 1.0515

36,000 0.9824 0.9936 0.9920 1.0043 1.0125 1.0187 1.0039 1.0527

38,000 0.9822 0.9936 0.9920 1.0044 1.0128 1.0190 1.0040 1.0538

Special Spectral Shapes

GSFC SIS 1.0402 1.0162 1.0185 1.0013 1.0063 0.9892 1.0040 0.9881

Rayleigh Atmosphere 0.9826 0.9938 0.9924 1.0041 1.0117 1.0163 1.0032 1.0406

Table 4. Radiances from the GSFC sphere. These are the radiances at the nominal SeaWiFS wavelengths at a distance

of 1 m from the sphere aperture.

Wavelength Sphere Radiance

[nm] 16 lamps 8 lamps 4 lamps 1 lamp

412 3.907 1.8752 0.9311 0.2358

443 6.520 3.1410 1.5620 0.3977

490 11.521 5.5780 2.7800 0.7091

510 13.954 6.7670 3.3760 0.8609

555 19.770 9.6280 4.8060 1.2251

670 33.760 16.5450 8.2780 2.1060

765 41.580 20.4200 10.2260 2.5920

865 45.020 22.1800 11.1150 2.8080

16
R.A. Barnes, E-n. Yeh, and R.E. Eplee

Table 5. The integrated band output from the GSFC sphere is shown in picoamperes. The output is given for

the individual lamp settings from the sphere, for the mean values, and the standard deviations.

Sphere Setting Integrated Band Output [pA]

(No. of Lamps) Band 1 Band 2 Band 3 Band 4 Band 5 Band 6 Band 7 Band 8

16 2279.3 3489.7 4304.6 4618.0 3890.4 2069.9 2869.3 2248.3

8 2280.0 3490.3 4305.8 4618.5 3890.9 2069.8 2869.6 2248.2

4 2280.2 3490.6 4305.9 4618.1 3891.0 2069.7 2869.4 2248.2

1 2281.5 3491.0 4305.8 4618.4 3890.8 2069.8 2868.9 2248.1

Mean 2280.2 3490.4 4305.5 4618.3 3890.8 2069.8 2869.3 2248.2

Standard Deviation 0.8 0.4 0.5 0.2 0.2 0.1 0.2 0.0

On the average, the equivalent blackbody temperature

for the eight SeaWiFS bands is 2,980 K, with a standard

deviation of 140 K. The SeaWiFS band output, when viewing the GSFC sphere, are essentially the same as when

viewing a 2,850 K blackbody. On the average, the integrated band output for the GSFC sphere is 0.07% lower

than for a 2,850 K blackbody, with a 0.15% standard deviation. For individual bands, the differences between these

two sources are 0.25% percent or less. Thus, for SeaWiFS,

the GSFC sphere and a 2,850 K blackbody have equivalent

spectral shapes.

For the radiance source used in SBRC’s calibration of

SeaWiFS, the spectral shape of the source was assumed

to be 2,850 K, and no measurements of the source spectral

shape were provided (Barnes et al. 1994b). Such a minimal

dependence of the SeaWiFS output on spectral shape (between 2,800 and 3,000 K) shows that inaccuracies in the

manufacturer’s assumption contribute negligible error to

the instrument’s radiometric calibration.

1.4 CONCLUDINGREMARKS

Filter photometers in general, and SeaWiFS in particular, have output that vary with the spectral shape of the

source that they measure. For SeaWiFS, the transfer of

the laboratory calibration to orbit requires source shape

corrections for the eight bands that vary from near zero

(for band 4) to more than 5% (for band 8). From Table 3,

it is clear that the correction from a 2,850 K to a 5,900 K

source (Barnes et al. 1994b) does not adequately account

for the upwelling radiance that SeaWiFS will view on orbit. This said, there remain two additional factors that

must be considered.

First, Rayleigh scattering does not completely account

for the spectral shape of the Earth-exiting radiances that

SeaWiFS will view on orbit. There are absorption and

emission lines from atmospheric gasses within the wavelength region between 380 and 1,150 nm. The most important of these features are the oxygen absorption lines near

762 nm (McClain et al. 1994, Fraser 1995, and Ding and

Gordon 1995) that lie within the bandpass for SeaWiFS

band 7. These absorption lines create an oxygen notch

within band 7, and they must be treated explicitly in the

SeaWiFS data reduction algorithms.

In addition, scattered light from small atmospheric particles, i.e., Mie scattering, creates an additional source

of Earth-exiting radiance. Since Rayleigh scattering decreases as a function of wavelength to the fourth power,

Mie scattering becomes more important for wavelengths

in the red and near-infrared. As the number of small particles in the atmosphere increases, the sky loses its blue

color and turns white. Thus, the calculations presented in

this chapter cover the color range of the Earth-exiting radiances viewed by SeaWiFS during ocean measurements.

In addition, these results show the magnitude of the effects

of source spectral shape on the integrated output from the

SeaWiFS bands. This leads to the second factor that must

be considered.

For SeaWiFS band 6 (Fig. 4), the region of greatest

response, called the in-band response, occurs from 647–

678 nm (Barnes et al. 1994a). It is the in-band response

that is required from the on-orbit SeaWiFS measurements,

but it is the total band response that is measured in the

laboratory. The SeaWiFS in-band responses have source

shape dependencies, as do the SeaWiFS out-of-band responses. Together they create the source shape dependency for the total band response. Both must be accounted

for in order to convert the laboratory calibration of the instrument to the desired on-orbit values (Barnes and Yeh

1996).

17
SeaWiFS Calibration Topics, Part 1

Chapter 2

Effects of Source Spectral Shape on

SeaWiFS Radiance Measurements

Robert A. Barnes

Eueng-nan Yeh

General Sciences Corporation, Laurel, Maryland

Abstract

Two aspects of filter photometry on the radiances measured by SeaWiFS are examined: the dependence of

the total band response, and the out-of-band response on source spectral shape. These effects are significant

contributors to the SeaWiFS measurements on orbit. The corrections for out-of-band response range from about

0.5% to more than 5%, depending on the SeaWiFS band. The corrections for total band response range from

near zero to about 5%. These corrections will be used to convert the laboratory calibration of SeaWiFS (in terms

of total band response) to orbit (in terms of in-band response). The residual uncertainty in these corrections is

estimated to be small, around 0.2%. With other significantly larger error sources in the SeaWiFS measurements,

the contribution of these residual uncertainties to the propagation of error for SeaWiFS radiance measurements

at the top of the atmosphere is also expected to be small. These corrections are prelaunch estimates and should

be reexamined using flight data. In addition, these corrections were tailored to SeaWiFS ocean measurements.

The contributions to land measurements will be different.

2.1 INTRODUCTION

Barnes et al. (1994b) calculated the change in the responses of the SeaWiFS bands from those for a 2,850 K

blackbody (the spectral shape of the radiance source for

the SeaWiFS laboratory calibration) to those for a 5,900 K

blackbody (the spectral shape of the sun). This conversion

was used in the prelaunch radiometric calibration of SeaWiFS (Barnes et al. 1994b). An alternative conversion

to a spectral shape of a 12,000 K blackbody is provided

in this chapter. This spectral shape is consistent with the

SeaWiFS typical radiances in the instrument specifications

(Barnes et al. 1994a) and gives a better representation of

the radiances to be found during on-orbit ocean measurements by SeaWiFS.

Barnes et al. (1995a) presented an out-of-band correction scheme for SeaWiFS that used a combination of the

wavelength-dependent response of the instrument with the

wavelength-dependent shape of the radiance measured by

the instrument. The relative spectral responses for the

eight SeaWiFS bands were tabulated at 1 nm intervals from

380–1,150 nm (Barnes et al. 1994b and Barnes 1994). As

part of the calculations in Barnes et al. (1995a), the spectral radiances from the eight SeaWiFS bands were interpolated to 1 nm intervals and were used as the basis for the

spectral shape of the radiance measured by the instrument.

The radiances and spectral responses of the bands were

integrated from 380–1,150 nm (for the total band output

for each band) and from the lower extended band edge to

the upper extended band edge (for the in-band response).

With 771 points in the integration for each band, 8 bands

per pixel, 1,285 pixels per scan line, and 6 scan lines per

second in the on-orbit measurements, the out-of-band correction of Barnes et al. (1995a) provides a cumbersome and

time-consuming algorithm for processing SeaWiFS data.

In this chapter, the analysis method used in Barnes et al.

(1995a) is used to create simplified out-of-band calculations which run significantly faster in the SeaWiFS data

reduction.

2.2 BAND SPECIFICATIONS

The SeaWiFS specifications (Barnes et al. 1994a) define

the in-band response region for each SeaWiFS band. It is

the spectral region between the lower extended band edge

(lower 1% response point) and the upper extended band

edge (upper 1% response point). The band edges for the

eight SeaWiFS bands, taken from Barnes et al. (1994b),

are given in Table 6. With this information, it is possible

to use the model of Barnes (1996a) to calculate the inband response for each band, in addition to the total band

response.

Table 6 also gives the nominal center wavelengths for

each SeaWiFS band. These are the center wavelengths

18
R.A. Barnes, E-n. Yeh, and R.E. Eplee

Table 6. Band edges (half-maximum wavelengths) and extended band edges (1% response wavelengths) for the

eight SeaWiFS bands. The edges are given for a radiance source with the shape of a 5,900 K blackbody. The

center wavelength is calculated from the upper and lower band edges. The in-band response is the wavelength

interval between the lower and upper extended band edges.

Band Nominal Band Lower Extended Lower Band Center Wave- Upper Band Upper Extended

Number Edges [nm] Band Edge [nm] Edge [nm] length [nm] Edge [nm] Band Edge [nm]

1 402–422 395.2 403.4 413.4 423.4 433.6

2 433–453 424.1 434.2 444.0 453.8 463.7

3 480–500 470.7 480.8 491.1 501.4 511.7

4 500–520 488.1 498.9 510.1 521.2 530.7

5 545–565 536.3 545.4 554.6 563.8 577.2

6 660–680 646.7 658.3 668.2 678.1 692.5

7 745–785 727.3 744.4 764.6 784.9 813.4

8 845–885 826.4 845.5 866.1 886.7 907.5

from the specifications for the instrument (Barnes et al.

1994a). They are also the wavelengths at which SeaWiFS

was calibrated in the laboratory. The radiances from the

laboratory source [see Table 8 of Barnes et al. (1994b)] were

themselves calibrated at the nominal center wavelengths in

Table 6, using a reference source traceable to NIST. The

selection of those wavelengths for the laboratory source

embedded those wavelengths in the radiometric calibration of SeaWiFS. They are the wavelengths at which the

radiances in the source shape curves are normalized, in the

study described in this chapter.

As explained in Barnes (1996a), the model results presented here do not represent actual SeaWiFS measurements. The model examines only the spectral response

of the optical components in the instrument, including the

spectral response of the detectors. Since there are other

nonspectral components in each SeaWiFS band that are

not part of the model, the results can only be considered

in relative terms. The SeaWiFS prelaunch radiometric calibration, which converts the instrument output into radiances, was given in Barnes et al. (1994b).

2.3 INSTRUMENT RESPONSE

As described in Barnes (1996a), the instrument relative

spectral response uses the measured spectral response for

each SeaWiFS band to a spectrally flat source and combines this response with a series of sources with different spectral shapes. The model uses a series of Planck

functions with temperatures ranging from 2,000–38,000 K.

These functions cover the source spectral shapes found in

the laboratory and encompass the source spectral shapes

to be found on orbit. The effects of sources with different

color temperatures can be seen in Fig. 10.

Figure 10a shows several source spectral shapes normalized to the typical radiance for SeaWiFS band 1 (9.10 mW

cm−2 sr−1μ m−1 at 412 nm). For this band, a 2,850 K laboratory source provides orders of magnitude more radiance

in the red and the near-infrared than do the higher temperature Planck functions. For SeaWiFS band 8, the effect

is reversed, as can be seen in Fig. 10b. Higher temperature Planck functions produce more radiance in the blue

and the near-ultraviolet. The convolution of these source

shapes with the responses of the individual SeaWiFS bands

produces dependencies on source spectral shape, both outof-band and in-band, that differ from band to band.

The model results for the eight SeaWiFS bands are

listed in Tables 7–10. They are given for Planck function

temperatures from 2,000–38,000 K. These follow the temperature formats in Barnes (1996a) and include the special spectral shapes found there. Tables 7–10 also include

the total band and the in-band responses. The in-band

response is the integral between the 1% response points,

also called the extended band edges. The band edges are

listed in Table 6.

The out-of-band response is the difference between the

in-band and the total band response normalized to the total band response. For data reduction, the desired quantity

is the response of the band after the out-of-band has been

removed. Those responses, in the form of a ratio, are also

given in Tables 7–10.

The individual responses of the eight SeaWiFS bands

are shown, as a function of blackbody temperature, in

Figs. 11–18. For each of these figures, part a gives plots

of the total band response and the in-band response in

picoamperes. These correspond to the respective values

in Tables 7–10. For Figs. 11–18, the minimum ordinate

values have not been set to zero. This was done to increase the resolution for the relatively small changes in

the output from the bands. To give some consistency to

the vertical scales, however, the maximum values for the

ordinates have been set to about 1.2–1.25 times the minimums.

Part c of Figs. 11–18 divides the total band response

into three components. These components sum to unity

at each Planck temperature. The components are: the

left side out-of-band response, that is, the response for

wavelengths less than the short wavelength 1% response

point; the in-band response; and the right side out-of-band

19
SeaWiFS Calibration Topics, Part 1

Fig. 10. Planck functions are normalized at 412 nm and 865 nm. a) Functions are normalized to 9.10 mW cm−2 sr−1

μ m−1 at 412 nm, the typical radiance (Ltypical) and nominal center wavelength for SeaWiFS band 1. b) Functions are normalized to 1.09 mW cm−2 sr−1 μ m−1 at 865 nm, the typical radiance (Ltypical) and nominal center

wavelength for SeaWiFS band 8.

20
R.A. Barnes, E-n. Yeh, and R.E. Eplee

Table 7. The band responses in picoamperes for SeaWiFS bands 1 and 2 are listed here. The out-ofband response is the difference between the total response (RT ) and the in-band response (RIB). The

special spectral shapes, i.e., the GSFC SIS and the Rayleigh Atmosphere are shown at the bottom of

the table.

Planck Function Band 1 (412 nm) Band 2 (443 nm)

Temperature [K] RT RIB RIB/RT RT RIB RIB/RT

2,000 2397.752 2317.080 0.9664 3570.264 3542.373 0.9922

2,500 2306.404 2265.530 0.9823 3514.930 3494.853 0.9943

2,850 2274.303 2243.185 0.9863 3492.898 3474.751 0.9948

3,000 2264.153 2235.681 0.9874 3485.734 3468.086 0.9949

3,500 2239.354 2216.503 0.9898 3468.026 3451.334 0.9952

4,000 2223.022 2203.264 0.9911 3456.351 3440.047 0.9953

5,000 2202.907 2186.352 0.9925 3442.234 3426.076 0.9953

5,900 2192.031 2176.950 0.9931 3434.870 3418.588 0.9953

8,000 2177.883 2164.461 0.9938 3425.809 3409.077 0.9951

10,000 2170.768 2158.078 0.9942 3421.588 3404.459 0.9950

12,000 2166.343 2154.071 0.9943 3419.122 3401.671 0.9949

14,000 2163.334 2151.331 0.9945 3417.532 3399.823 0.9948

16,000 2161.158 2149.343 0.9945 3416.434 3398.511 0.9948

18,000 2159.514 2147.835 0.9946 3415.635 3397.539 0.9947

20,000 2158.228 2146.656 0.9946 3415.032 3396.789 0.9947

22,000 2157.196 2145.705 0.9947 3414.561 3396.194 0.9946

24,000 2156.349 2144.925 0.9947 3414.185 3395.714 0.9946

26,000 2155.642 2144.271 0.9947 3413.878 3395.313 0.9946

28,000 2155.043 2143.718 0.9947 3413.623 3394.982 0.9945

30,000 2154.529 2143.244 0.9948 3413.409 3394.697 0.9945

32,000 2154.083 2142.830 0.9948 3413.226 3394.450 0.9945

34,000 2153.693 2142.470 0.9948 3413.068 3394.235 0.9945

36,000 2153.348 2142.151 0.9948 3412.931 3394.047 0.9945

38,000 2153.041 2141.867 0.9948 3412.811 3393.883 0.9945

GSFC SIS 2280.169 2249.292 0.9865 3489.135 3471.437 0.9949

Rayleigh 2153.879 2142.609 0.9948 3413.669 3394.790 0.9945

21
SeaWiFS Calibration Topics, Part 1

Table 8. The band responses in picoamperes for SeaWiFS bands 3 and 4 are listed here. The out-ofband response is the difference between the total response (RT ) and the in-band response (RIB). The

special spectral shapes, i.e., the GSFC SIS and the Rayleigh Atmosphere are shown at the bottom of

the table.

Planck Function Band 3 (490 nm) Band 4 (510 nm)

Temperature [K] RT RIB RIB/RT RT RIB RIB/RT

2,000 4483.516 4316.599 0.9628 4690.465 4619.324 0.9848

2,500 4354.579 4270.518 0.9807 4636.462 4600.506 0.9922

2,850 4315.636 4250.698 0.9850 4623.705 4594.058 0.9936

3,000 4303.891 4244.067 0.9861 4620.456 4592.207 0.9939

3,500 4276.253 4227.234 0.9885 4614.326 4588.347 0.9944

4,000 4258.808 4215.722 0.9899 4611.929 4586.582 0.9945

5,000 4238.163 4201.202 0.9913 4611.322 4585.747 0.9945

5,900 4227.442 4193.247 0.9919 4612.427 4586.173 0.9943

8,000 4214.101 4182.874 0.9926 4616.010 4588.064 0.9939

10,000 4207.736 4177.680 0.9929 4619.067 4589.796 0.9937

12,000 4203.933 4174.467 0.9930 4621.536 4591.210 0.9934

14,000 4201.430 4172.297 0.9931 4623.518 4592.355 0.9933

16,000 4199.670 4170.738 0.9931 4625.126 4593.282 0.9931

18,000 4198.370 4169.565 0.9931 4626.450 4594.046 0.9930

20,000 4197.374 4168.655 0.9932 4627.557 4594.687 0.9929

22,000 4196.587 4167.920 0.9932 4628.494 4595.224 0.9928

24,000 4195.952 4167.323 0.9932 4629.297 4595.688 0.9927

26,000 4195.429 4166.828 0.9932 4629.992 4596.087 0.9927

28,000 4194.990 4166.406 0.9932 4630.600 4596.435 0.9926

30,000 4194.618 4166.049 0.9932 4631.135 4596.744 0.9926

32,000 4194.299 4165.736 0.9932 4631.610 4597.016 0.9925

34,000 4194.021 4165.464 0.9932 4632.034 4597.257 0.9925

36,000 4193.778 4165.223 0.9932 4632.416 4597.478 0.9925

38,000 4193.564 4165.010 0.9932 4632.760 4597.676 0.9924

GSFC SIS 4308.489 4248.162 0.9860 4620.657 4592.931 0.9940

Rayleigh 4195.469 4166.577 0.9931 4631.520 4596.954 0.9925

22
R.A. Barnes, E-n. Yeh, and R.E. Eplee

Table 9. The band responses in picoamperes for SeaWiFS bands 3 and 4 are listed here. The out-ofband response is the difference between the total response (RT ) and the in-band response (RIB). The

special spectral shapes, i.e., the GSFC SIS and the Rayleigh Atmosphere are shown at the bottom of

the table.

Planck Function Band 5 (555 nm) Band 6 (670 nm)

Temperature [K] RT RIB RIB/RT RT RIB RIB/RT

2,000 4031.971 3784.638 0.9387 2059.801 2041.659 0.9912

2,500 3928.768 3778.835 0.9618 2065.459 2049.506 0.9923

2,850 3900.117 3777.220 0.9685 2069.400 2053.747 0.9924

3,000 3892.322 3776.840 0.9703 2070.996 2055.322 0.9924

3,500 3876.564 3776.336 0.9741 2075.873 2059.768 0.9922

4,000 3869.381 3776.453 0.9760 2080.127 2063.262 0.9919

5,000 3865.481 3777.344 0.9772 2087.168 2068.382 0.9910

5,900 3866.629 3778.296 0.9772 2092.267 2071.637 0.9901

8,000 3873.456 3780.249 0.9759 2101.209 2076.568 0.9883

10,000 3880.281 3781.637 0.9746 2107.277 2079.433 0.9868

12,000 3886.181 3782.680 0.9734 2111.863 2081.382 0.9856

14,000 3891.117 3783.481 0.9723 2115.452 2082.791 0.9846

16,000 3895.242 3784.114 0.9715 2118.338 2083.860 0.9837

18,000 3898.714 3784.622 0.9707 2120.709 2084.695 0.9830

20,000 3901.665 3785.044 0.9701 2122.691 2085.370 0.9824

22,000 3904.199 3785.394 0.9696 2124.373 2085.921 0.9819

24,000 3906.394 3785.694 0.9691 2125.817 2086.385 0.9815

26,000 3908.312 3785.947 0.9687 2127.071 2086.778 0.9811

28,000 3910.002 3786.172 0.9683 2128.170 2087.115 0.9807

30,000 3911.501 3786.364 0.9680 2129.141 2087.408 0.9804

32,000 3912.840 3786.537 0.9677 2130.005 2087.665 0.9801

34,000 3914.042 3786.690 0.9675 2130.779 2087.893 0.9799

36,000 3915.127 3786.828 0.9672 2131.476 2088.096 0.9796

38,000 3916.111 3786.950 0.9670 2132.107 2088.277 0.9794

GSFC SIS 3890.195 3776.410 0.9708 2069.907 2054.460 0.9925

Rayleigh 3911.922 3786.190 0.9679 2126.325 2085.906 0.9810

23
SeaWiFS Calibration Topics, Part 1

Table 10. The band responses in picoamperes for SeaWiFS bands 7 and 8 are listed here. The out-ofband response is the difference between the total response (RT ) and the in-band response (RIB). The

special spectral shapes, i.e., the GSFC SIS and the Rayleigh Atmosphere are shown at the bottom of

the table.

Planck Function Band 7 (765 nm) Band 8 (865 nm)

Temperature [K] RT RIB RIB/RT RT RIB RIB/RT

2,000 2908.806 2831.298 0.9734 2254.213 2207.528 0.9793

2,500 2883.359 2823.812 0.9793 2249.117 2200.968 0.9786

2,850 2874.331 2821.321 0.9816 2248.979 2198.295 0.9775

3,000 2871.607 2820.621 0.9822 2249.414 2197.430 0.9769

3,500 2865.465 2819.219 0.9839 2252.214 2195.310 0.9747

4,000 2862.032 2818.650 0.9848 2256.286 2193.943 0.9724

5,000 2858.921 2818.539 0.9859 2266.044 2192.347 0.9675

5,900 2858.048 2818.864 0.9863 2275.286 2191.558 0.9632

8,000 2858.373 2819.874 0.9865 2295.514 2190.655 0.9543

10,000 2859.558 2820.723 0.9864 2311.900 2190.276 0.9474

12,000 2860.844 2821.398 0.9862 2325.586 2190.074 0.9417

14,000 2862.046 2821.938 0.9860 2337.030 2189.956 0.9371

16,000 2863.125 2822.371 0.9858 2346.676 2189.880 0.9332

18,000 2864.080 2822.725 0.9856 2354.884 2189.831 0.9299

20,000 2864.922 2823.020 0.9854 2361.939 2189.796 0.9271

22,000 2865.667 2823.270 0.9852 2368.057 2189.770 0.9247

24,000 2866.329 2823.480 0.9851 2373.408 2189.751 0.9226

26,000 2866.918 2823.665 0.9849 2378.124 2189.736 0.9208

28,000 2867.446 2823.824 0.9848 2382.311 2189.727 0.9192

30,000 2867.922 2823.965 0.9847 2386.050 2189.719 0.9177

32,000 2868.351 2824.087 0.9846 2389.410 2189.710 0.9164

34,000 2868.742 2824.199 0.9845 2392.444 2189.706 0.9153

36,000 2869.097 2824.299 0.9844 2395.197 2189.701 0.9142

38,000 2869.423 2824.387 0.9843 2397.707 2189.698 0.9132

GSFC SIS 2869.275 2820.374 0.9830 2248.207 2196.183 0.9769

Rayleigh 2867.115 2823.305 0.9847 2367.631 2190.131 0.9250

24
R.A. Barnes, E-n. Yeh, and R.E. Eplee

Fig. 11. Instrument responses for SeaWiFS band 1 to Planck functions with temperatures from 2,500–38,000 K.

The Planck functions are normalized at 412 nm, the nominal center wavelength for the band. a) The total band

response and the in-band response are given for band 1. The in-band wavelength range is given in Table 6. b)

The total band response and the in-band response are given for band 1. The responses are normalized to the

total band response at 5,900 K to show response changes from the band in relative terms. c) The components

of the band response are given in relative terms. The out-of-band responses have been added to unity to place

all three components on the same graph. The left side out-of-band response includes all wavelengths that are

shorter than the in-band and the right side out-of-band includes all wavelengths that are longer.

25
SeaWiFS Calibration Topics, Part 1

Fig. 12. Instrument responses for SeaWiFS band 2 to Planck functions with temperatures from 2,500–38,000 K.

The Planck functions are normalized at 412 nm, the nominal center wavelength for the band. a) The total band

response and the in-band response are given for band 2. The in-band wavelength range is given in Table 6. b)

The total band response and the in-band response are given for band 2. The responses are normalized to the

total band response at 5,900 K to show response changes from the band in relative terms. c) The components

of the band response are given in relative terms. The out-of-band responses have been added to unity to place

all three components on the same graph. The left side out-of-band response includes all wavelengths that are

shorter than the in-band and the right side out-of-band includes all wavelengths that are longer.

26
R.A. Barnes, E-n. Yeh, and R.E. Eplee

Fig. 13. Instrument responses for SeaWiFS band 3 to Planck functions with temperatures from 2,500–38,000 K.

The Planck functions are normalized at 412 nm, the nominal center wavelength for the band. a) The total band

response and the in-band response are given for band 3. The in-band wavelength range is given in Table 6. b)

The total band response and the in-band response are given for band 3. The responses are normalized to the

total band response at 5,900 K to show response changes from the band in relative terms. c) The components

of the band response are given in relative terms. The out-of-band responses have been added to unity to place

all three components on the same graph. The left side out-of-band response includes all wavelengths that are

shorter than the in-band and the right side out-of-band includes all wavelengths that are longer.

27
SeaWiFS Calibration Topics, Part 1

Fig. 14. Instrument responses for SeaWiFS band 4 to Planck functions with temperatures from 2,500–38,000 K.

The Planck functions are normalized at 412 nm, the nominal center wavelength for the band. a) The total band

response and the in-band response are given for band 4. The in-band wavelength range is given in Table 6. b)

The total band response and the in-band response are given for band 4. The responses are normalized to the

total band response at 5,900 K to show response changes from the band in relative terms. c) The components

of the band response are given in relative terms. The out-of-band responses have been added to unity to place

all three components on the same graph. The left side out-of-band response includes all wavelengths that are

shorter than the in-band and the right side out-of-band includes all wavelengths that are longer.

28
R.A. Barnes, E-n. Yeh, and R.E. Eplee

Fig. 15. Instrument responses for SeaWiFS band 5 to Planck functions with temperatures from 2,500–38,000 K.

The Planck functions are normalized at 412 nm, the nominal center wavelength for the band. a) The total band

response and the in-band response are given for band 5. The in-band wavelength range is given in Table 6. b)

The total band response and the in-band response are given for band 5. The responses are normalized to the

total band response at 5,900 K to show response changes from the band in relative terms. c) The components

of the band response are given in relative terms. The out-of-band responses have been added to unity to place

all three components on the same graph. The left side out-of-band response includes all wavelengths that are

shorter than the in-band and the right side out-of-band includes all wavelengths that are longer.

29
SeaWiFS Calibration Topics, Part 1

Fig. 16. Instrument responses for SeaWiFS band 6 to Planck functions with temperatures from 2,500–38,000 K.

The Planck functions are normalized at 412 nm, the nominal center wavelength for the band. a) The total band

response and the in-band response are given for band 6. The in-band wavelength range is given in Table 6. b)

The total band response and the in-band response are given for band 6. The responses are normalized to the

total band response at 5,900 K to show response changes from the band in relative terms. c) The components

of the band response are given in relative terms. The out-of-band responses have been added to unity to place

all three components on the same graph. The left side out-of-band response includes all wavelengths that are

shorter than the in-band and the right side out-of-band includes all wavelengths that are longer.

30
R.A. Barnes, E-n. Yeh, and R.E. Eplee

Fig. 17. Instrument responses for SeaWiFS band 7 to Planck functions with temperatures from 2,500–38,000 K.

The Planck functions are normalized at 412 nm, the nominal center wavelength for the band. a) The total band

response and the in-band response are given for band 7. The in-band wavelength range is given in Table 6. b)

The total band response and the in-band response are given for band 7. The responses are normalized to the

total band response at 5,900 K to show response changes from the band in relative terms. c) The components

of the band response are given in relative terms. The out-of-band responses have been added to unity to place

all three components on the same graph. The left side out-of-band response includes all wavelengths that are

shorter than the in-band and the right side out-of-band includes all wavelengths that are longer.

31
SeaWiFS Calibration Topics, Part 1

Fig. 18. Instrument responses for SeaWiFS band 8 to Planck functions with temperatures from 2,500–38,000 K.

The Planck functions are normalized at 412 nm, the nominal center wavelength for the band. a) The total band

response and the in-band response are given for band 8. The in-band wavelength range is given in Table 6. b)

The total band response and the in-band response are given for band 8. The responses are normalized to the

total band response at 5,900 K to show response changes from the band in relative terms. c) The components

of the band response are given in relative terms. The out-of-band responses have been added to unity to place

all three components on the same graph. The left side out-of-band response includes all wavelengths that are

shorter than the in-band and the right side out-of-band includes all wavelengths that are longer.

32
R.A. Barnes, E-n. Yeh, and R.E. Eplee

Fig. 19. Typical input radiances from SeaWiFS plotted with three blackbody radiance curves.

response, that is, the response for wavelengths greater than

the long wavelength 1% response point. The terms “left

side” and “right side” refer to locations on a plot of the

band spectral response [see Fig. 2a of Barnes (1996a), for

example]. In that type of plot, wavelength increases from

left to right along the abscissa. Part c gives the out-of-band

components after they have been added to unity. This

allows the presentation of each of the three components

on the same plot with the same vertical resolution. Thus,

Fig. 11c shows the right-side out-of-band response for band

1 to be 1.033 at a Planck temperature of 2,000 K. With the

subtraction of unity, the right-side out-of-band response for

band 1 is about 3.3% of the total response at 2,000 K. At

this blackbody temperature, the in-band response is 0.966.

For SeaWiFS bands 1, 2, 3, 4, and 7, Figs. 11c, 12c,

13c, 14c, and 17c, respectively, show that for Planck temperatures from 10,000–38,000 K, the in-band response is a

constant fraction of the total response. For these bands

and for these blackbody temperature ranges, changes in

the left-side and right-side out-of-band responses are small,

equal in magnitude, and opposite in sign, creating a summation for out-of-band that is a constant fraction of the

total band response. For on-orbit SeaWiFS measurements,

the out-of-band responses for bands 1, 2, 3, 4, and 7 can

be considered as constant fractions of the total band responses.

For SeaWiFS bands 5, 6, and 8, Figs. 15c, 16c, and 18c

show less constancy for the in-band output for Planck function temperatures from 10,000–38,000 K. For band 5, the

fractional in-band decrease is 0.7% from 10,000–38,000 K;

for band 6, 0.7%; and for band 8, 3.4%. For comparisons of Figs. 15c (band 5), 16c (band 6), and 18c (band

8), it should be noted that the ordinates for these figures

range from 0.92–1.08, 0.96–1.04, and 0.90–1.10, respectively. With significant band-to-band differences in the

band responses, it was not practical to place all of the

plots on the same vertical scales.

Band 8 is the keystone for the SeaWiFS atmospheric

correction (Gordon and Wang 1994). As a result, an accurate and well-defined out-of-band correction for this band

is crucial for SeaWiFS data reduction. Band 8 also shows

the greatest change in the size of its out-of-band with

source spectral shape. The out-of-band correction for band

8 cannot be based on Planck function curves alone, but

must be based on the spectrum of the on-orbit radiance

viewed by SeaWiFS.

2.4 ON-ORBIT SPECTRAL SHAPE

For SeaWiFS ocean measurements, the spectral shape

of the upwelling radiances will resemble that for the typical (Ltypical) radiances from the SeaWiFS specifications

(Barnes et al. 1994a). Those Ltypical are shown in Fig. 19,

33
SeaWiFS Calibration Topics, Part 1

Table 11. The initial out-of-band correction factors are listed here. For bands 1–4 and band 7, these are also

the final correction factors. The calculation of the final correction factors for bands 5, 6, and 8 uses these initial

values as input data.

Band Nominal Center k(b) Comments

Number Wavelength [nm]

1 412 0.9943 Final value, also taken from Table 7, 12,000 K

2 443 0.9949 Final value, also taken from Table 7, 12,000 K

3 490 0.9930 Final value, also taken from Table 8, 12,000 K

4 510 0.9934 Final value, also taken from Table 8, 12,000 K

5 555 0.9734 Final value calculated using (9)

6 670 0.9856 Final value calculated using (12)

7 765 0.9844 Final value, also taken from Table 10, 12,000 K and corrected

for oxygen absorption (Section 2.5.2, below)

8 865 0.9417 Final value calculated using (14)

along with a set of three Planck function curves. Although

not a perfect fit, the Ltypical radiances are approximated

by a 12,000 K blackbody. As shown in Tables 7–10, the

responses of the SeaWiFS bands are nearly identical for

Planck function curves of 10,000 K; 12,000 K; and 14,000 K.

For the purposes here, it is assumed that the typical SeaWiFS radiances for ocean measurements have the spectral

shape of a 12,000 K blackbody.

2.5 OUT-OF-BAND CORRECTION

2.5.1 Bands 1–4

Tables 7 and 8 show the ratios of the in-band to the

total-band responses (for bands 1–4) to be about 0.990–

0.995 for blackbody spectral curves between 12,000 K and

38,000 K. For each of these bands, the change in the outof-band correction factor is negligible—between 12,000 K

and 38,000 K; thus, for bands 1–4 the 12,000 K correction

factor is used in the simplified correction scheme proposed

here (Table 11). As shown for band 1 (412 nm), the outof-band correction is applied using the formula:

Lo(412) = kb(412)Li(412), (5)

where Li(412) is the input radiance to the correction

scheme for band 1 (412 nm); kb(412) is the out-of-band

correction factor for band 1 (412 nm); and Lo(412) is the

output radiance from the correction scheme for band 1

(412 nm). It is the kb correction factor for each SeaWiFS

band that this simplified calculation scheme provides. For

bands 1–4, kb is a constant value, listed in Table 11.

For the SeaWiFS Project, there is a naming convention

for the radiances from the eight bands. In this convention,

the bands are not described in terms of their number (1

through 8) but in terms of their nominal center wavelength

(412, 443, 490, 510, 555, 670, 765, and 865 nm). This

convention is also applied in the equations used here.

2.5.2 Band 7

For SeaWiFS band 7 (the 765 nm band), there is an

atmospheric oxygen absorption feature in the center of the

pass band response (McClain et al. 1994, Fraser 1995, and

Ding and Gordon 1995). This oxygen A-band absorption

does not effect the out-of-band response for the 765 nm

band. Using the same technique, McClain et al. (1994)

and Fraser (1995) both estimated the reduction in the output of band 7 from this absorption feature to be 12% for

an air mass of 2, and 13% for an air mass of 3. Ding and

Gordon (1995) used a separate calculation to estimate the

reduction in Rayleigh scattered light at the top of the atmosphere from oxygen absorption to be 7% for an air mass

of 2, and 11% for an air mass of 5. Because the out-ofband contribution to the output of band 7 is close to zero

(about 1.5%), the error in the calculated effect of oxygen

absorption on the out-of-band correction is also small. For

the calculations here, oxygen absorption is assumed to decrease the in-band response of SeaWiFS band 7 by 12%.

The modification of band 7’s correction factor, kb(765),

is shown in Table 12. In this table, the total band, the inband, and the out-of-band responses (for a 12,000 K blackbody) were taken from Table 10. The effect of oxygen absorption was calculated by removing 12% from the in-band

response (338.568 pA) and by removing the same number

of picoamperes from the total band response. The out-ofband response remains constant. The revised out-of-band

correction factor is calculated as the ratio of the revised

in-band response to the revised total response. That ratio

is 0.9844, and this value is given in Table 11 for the band

7 correction, kb(765). Thus, the out-of-band correction for

band 7 is:

Lo(765) = kb(765)Li(765), (6)

where Lo(765) is the output from this correction scheme

for band 7. The correction to this band for oxygen A-band

absorption is applied as part of the atmospheric correction algorithms in the SeaWiFS data reduction process.

34
R.A. Barnes, E-n. Yeh, and R.E. Eplee

Lo(765) provides the input to that process for band 7.

However, for use with the band 8 (865 nm) out-of-band

correction below, the oxygen notch is replaced, using the

equation

Lc(765) = 1.12

Lo(765)(7)

where Lc(765) is the band 7 spectral radiance corrected for

oxygen A-band absorption.

Table 12. The band 7 out-of-band correction factor, modified for the out-of-band response is presented. The effect of this modification is minimal.

The total band response values are taken from Table 10. The units are in picoamperes [pA]. In the

second row, 338.658 pA are removed from the RT

and RIB to account for oxygen absorption.

RT RIB ROB kb(765)

Values Values Values

2860.844 2821.398 39.446 0.9862

2522.296 2482.830 39.446 0.9844

2.5.3 Band 8

The simplified, out-of-band calculation for SeaWiFS

band 8 uses the relative spectral response of the band divided into six components (Fig. 20). Each component gives

the output of the band for a spectrally flat source over a

wavelength subset of the band’s relative spectral response.

Component S5 gives the in-band response for the 865 nm

band, covering the wavelength range from 827–907 nm (Table 13). For a spectrally flat source, the out-of-band correction for band 8 is the response of component (S5) divided by the summed response for all six components (S1

through S6). For on-orbit calculations, the measured radiances from the SeaWiFS bands are included in the band 8

out-of-band correction. In addition, an estimate of the radiance to be paired with component S6 is obtained before

the correction can be calculated.

In these calculations, each component of the band 8

spectral response is associated with the radiance from a

SeaWiFS band: component S1 with band 1, Lo(412); component S2 with band 4, Lo(510); component S3 with band

5, Lo(555); component S4 with band 7, Lo(765); component S5 with band 8, Lo(865); and component S6 with an

estimate for the radiance at 965 nm, Lo(965).

The calculation scheme starts with initial output radiances for the SeaWiFS bands, Lo(412) through Lo(865),

calculated using the form of (5). For band 7, Lc(765) is

used. Finally, the radiance at 965 nm is calculated using

an extrapolation based on the radiances at 765 nm and

865 nm as in,

Lo(965) = 2

Lo(865)− Lo(765). (8)

The selection of 965 nm for the radiance associated with

component S6 was made to correspond with the 100 nm

spacing between bands 7 and 8. This selection is arbitrary

and is based on the judgement of the authors.

With these values, it is possible to calculate the revised out-of-band correction factor, which is the in-band

response divided by the sum of the responses for all six

components. The new kb(865) replaces the initial kb(865)

from Table 11,

kb(865) = Lo(865)S5

W (9)

where W represents the denominator to (9),

W = Lo(412)S1 + Lo(510)S2 + Lo(555)S3

+ Lc(765)S4 + Lo(865)S5 + Lo(965)S6

, (10)

and a new output radiance is calculated for band 8

Lo(865) = kb(865)Li(865). (11)

2.5.4 Bands 5–6

The correction calculations for bands 5 and 6 (555 nm

and 670 nm) are simplified versions of that for band 8.

For these bands, the corrections are calculated, using only

three components. Those components are listed in Tables 14 and 15. For bands 5 and 6, the out-of-band correction factors vary by less than 1% for blackbody curves

between 12,000 K and 38,000 K. This is less than a third

of the change in the correction factor for band 8. In addition, the relative magnitudes of the out-of-band responses

for these bands are one-third to one-half those for band 8.

For bands 5 and 6, the relative spectral response is

divided into a short wavelength (left-side) out-of-band, an

in-band, and a long wavelength (right-side) out-of-band

response. Figures 11 and 12 show the right-side out-ofband to contribute a nearly constant fraction of the band

response for these bands for Planck function temperatures

from 12,000–38,000 K. The variability in the out-of-band

correction comes from the left-side, or shorter wavelength,

contribution.

For band 6, the spectral response is shown in Fig. 23 of

Barnes et al. (1994b), and the tabulated values are given

in Barnes (1994). The three components of the band 6

spectral response are separated at the extended band edges

(Table 6). The components for this band (Table 14) are

associated with three SeaWiFS bands: component S7 with

band 3, Lo(490); component S8 with band 6, Lo(670); and

component S9 with band 8, Lo(865). The calculation of the

out-of-band correction for band 6 provides a new kb(670)

to replace the initial value from Table 11:

kb(670) = Lo(670)S8

Lo(490)S7 + Lo(670)S8 + Lo(865)S9

(12)

and the calculation of a new output radiance for the band.

Lo(670) = kb(670)Li(670). (13)

35
SeaWiFS Calibration Topics, Part 1

Fig. 20. Six components of the spectral response for SeaWiFS band 8 are shown. The component S5 contains

the in-band response.

Table 13. The spectral response of band 8 is divided into six components. The spectral responses are

given for a spectrally flat source, that is, a source with a radiance of 1 mW cm−2 sr−1μ m−1.

Symbol Value Description

S1 0.583 Out-of-band spectral response (380–466 nm)

S2 0.829 Out-of-band spectral response (467–532 nm)

S3 6.251 Out-of-band spectral response (533–669 nm)

S4 13.533 Out-of-band spectral response (670–826 nm)

S5 1013.592 In-band spectral response (827–907 nm)

S6 9.374 Out-of-band spectral response (908–1,150 nm)

Table 14. The spectral response of band 6 is divided into three components. The spectral responses

are given for a spectrally flat source, that is, a source with a radiance of 1 mW cm−2 sr−1μ m−1.

Symbol Value Description

S10 2.592 Out-of-band spectral response (380–646 nm)

S11 491.802 In-band spectral response (647–692 nm)

S12 2.112 Out-of-band spectral response (693–1,150 nm)

Table 15. The spectral response of band 5 is divided into three components. The spectral responses

are given for a spectrally flat source, that is, a source with a radiance of 1 mW cm−2 sr−1μ m−1.

Symbol Value Description

S7 5.261 Out-of-band spectral response (380–536 nm)

S8 488.215 In-band spectral response (537–577 nm)

S9 7.475 Out-of-band spectral response (578–1,150 nm)

36
R.A. Barnes, E-n. Yeh, and R.E. Eplee

The calculation of the out-of-band correction for band

5 follows the pattern for band 6. For band 5, the spectral

response is also shown in Fig. 23 of Barnes et al. (1994b),

and the tabulated values are also given in Barnes (1994).

The three components of the band 5 spectral response are

also separated at the extended band edges (Table 6), and

the components for this band (Table 15) are associated

with three SeaWiFS bands: component S10 with band 2,

Lo(443); component S11 with band 5, Lo(555); and component S12 with band 6, Lo(670). The calculation of the

out-of-band correction for band 5 provides a new kb(555)

to replace the initial value from Table 11:

kb(555) = Lo(555)S11

Lo(443)S10 + Lo(555)S11 + Lo(670)S12

, (14)

and the calculation of a new output radiance for the band.

Lo(555) = kb(555)Li(555). (15)

2.6 COMPARISON OF RESULTS

For comparison, out-of-band corrections were calculated using the SeaWiFS typical radiances. The calculations were done in two ways: using the method of Barnes

et al. (1995a) and using the simplified method presented

here. The results of the two sets of calculations are presented in Table 16. The two sets of corrections should be

nearly identical, since they are based on the same set of

radiances. The agreement in the comparison is good, with

corrections for seven of the eight bands that agree within

0.1%.

For band 1, the difference is 0.2%. This is due, in

part, to the estimate of the spectral source shape for the

wavelength range from 380–412 nm in the two calculations.

This difference can be seen in Figs. 8 and 9 of Barnes et

al. (1995a). The method of Barnes et al. (1995a) assumes

a constant source radiance for wavelengths shorter than

412 nm. The simplified method assumes a source radiance

that increases with decreasing wavelength below 412 nm.

This tends to give the simplified method slightly more outof-band response from the left side (shorter wavelengths).

For such a small difference, the authors feel it is appropriate to split the difference and use an out-of-band correction

for band 1, i.e., 0.9953, for the simplified technique.

For band 7, the calculations using the method of Barnes

et al. (1995a) do not include oxygen A-band absorption.

Such an atmospheric effect was not a consideration in that

paper; thus, the comparison in Table 16 uses the result

from the simplified method without the correction for oxygen absorption. The difference is small; however, it is recommended that when using the correction technique of

Barnes et al. (1995a), a correction of 0.0018 should be

added to the result for band 7.

Table 16. Out-of-band corrections for the SeaWiFS typical using the method of Barnes et al.

(1995a) and those using the simplified method presented here. Note that the corrections for band 7

have been applied without the oxygen absorption

notch.

Band Barnes et al. Simplified

Number (1995a) Method

1 0.9963 0.9943

2 0.9946 0.9949

3 0.9928 0.9930

4 0.9928 0.9934

5 0.9729 0.9721

6 0.9843 0.9842

7 0.9863† 0.9862†

8 0.9414 0.9418

† Calculated without oxygen absorption.

The two recommendations in this section are small and

of little consequence; however, they are easy to apply and

take very little time in the data reduction. Overall, the

simplified calculation method reduces computation time

by more than two orders of magnitude, compared to the

method of Barnes et al. (1995a).

2.7 TOTAL BAND RESPONSES

The SeaWiFS prelaunch radiometric calibration (see

Barnes et al. 1994b) provided an adjustment to the laboratory calculation of the instrument. In the laboratory,

SeaWiFS was calibrated using a source with the spectral

shape of a 2,850 K blackbody, while measurements on orbit will have a spectral shape that is much more blue. The

adjustment in Barnes et al. (1994b) was based on a 5,900 K

blackbody, the only spectral shape given in the SeaWiFS

specifications (Barnes et al. 1994a).

Figure 19 shows the on-orbit spectral shape to be close

to that for a 12,000 K blackbody. It is the adjustment for

this spectral shape that should be included in the SeaWiFS

radiometric calibration. The appropriate adjustments for

total band response are given in Table 17. For band 1,

the adjustment in Table 17 differs from that in Barnes et

al. (1994b) by 1%. For the other bands, the differences

in the adjustments are less. A 1% factor is significant,

if the calibrations of the SeaWiFS bands are to be made

consistent at the 2% level.

2.8 CONCLUDINGREMARKS

For SeaWiFS, the conversion of the spectral shape dependence in the SeaWiFS laboratory calibration to orbit is

done in two steps. First, the total band responses are converted to those for a source spectral shape representative

of the Earth-exiting radiances viewed during ocean measurements on orbit. Second, the residual in-band response

is calculated after the removal of the out-of-band response.

37
SeaWiFS Calibration Topics, Part 1

The first step is described in Section 2.7, and the second

step in Section 2.5. Both conversions are done in relative

terms. There are no absolute values in the spectral shape

dependencies calculated here.

Table 17. Shown here are the model results of

the band responses to a 2,850 K blackbody and a

12,000 K blackbody (in picoamperes) for the SeaWiFS bands. The ratio gives the total band output

on orbit relative to that in the laboratory. Thus, on

orbit, SeaWiFS band 1 will produce fewer counts

per unit radiance than it will in the laboratory.

Band 2,850 K 12,000 K Ratio

Number Blackbody Blackbody

1 2274.303 2166.343 0.9525

2 3492.898 3419.122 0.9789

3 4315.636 4203.993 0.9741

4 4623.705 4621.536 0.9995

5 3900.117 3886.181 0.9964

6 2069.400 2111.836 1.0205

7 2874.331 2860.844 0.9953

8 2248.979 2325.586 1.0341

The calculations presented here use the actual spectral responses of the SeaWiFS bands and Planck functions

as simplified models of the Earth-exiting radiances to be

viewed on orbit. For example, the Planck functions do

not include the absorption and emission lines from atmospheric gasses, including the oxygen A-band absorption

lines at 761 and 763 nm. The effect of this absorption feature on the out-of-band response of band 8 was examined,

since band 8 has the greatest out-of-band response of the

SeaWiFS bands and since the oxygen absorption lines occur in a region of maximum out-of-band response for band

8 (Fig. 20). For air masses of five or less, the fractional

decrease in the response of band 8 is 0.1% or less. For

the other SeaWiFS bands, the effects of atmospheric oxygen A-band absorption are much smaller. Atmospheric

absorption and emission features do not expand the residual uncertainties in the corrections presented here. They

remain at about 0.2%, both for total and out-of-band response.

Studies of atmospheric effects on ocean color imagery,

e.g., Ding and Gordon (1995), used detailed models of the

atmospheric and oceanic contributors to the top-of-theatmosphere radiances, but used a simplified model of the

response of the instrument. For Ding and Gordon (1995),

SeaWiFS band 7 was assumed to have a square wave response with wavelength, with the band response outside of

the band edges (the 50% response points) set to zero and

the response inside the band edges set to a constant value.

It is now possible to combine the actual response of

the SeaWiFS instrument with detailed models of the atmosphere and ocean, since ocean color imagery from SeaWiFS is an amalgam of the top-of-the-atmosphere radiances and the instrument. In the concept of Evans and

Gordon (1994), however, the imagery derives from the

ocean atmosphere instrument system.

38
R.A. Barnes, E-n. Yeh, and R.E. Eplee

Chapter 3

A Comparison of the Spectral Responses of SeaWiFS

and the SeaWiFS Transfer Radiometer

Robert A. Barnes

General Sciences Corporation

Laurel, Maryland

Abstract

Both SeaWiFS and the SXR are filter radiometers with finite bandwidths. The use of these instruments requires

a knowledge of the effects that finite bandwidths cause. These effects also depend on the source’s spectral shape,

which the instruments measure. For the radiometric calibration of SeaWiFS, the source is the GSFC SIS. The

BSRs and the ECWs for SeaWiFS and the SXR, when measuring the GSFC SIS, are presented here. They will

be needed to convert the SXR measured spectral radiances to the SeaWiFS wavelengths.

3.1 INSTRUMENT MODELS

Six of the SeaWiFS bands have bandwidths (full-width

at half-maximum) of 20 nm; the other two have bandwidths of 40 nm (Barnes et al. 1994a). These bandwidths

are sufficiently wide to cause the output from SeaWiFS to

be dependent on the spectral shape of the source it measures. On orbit, the measurements from each SeaWiFS

band involve a range of wavelengths:

Le =

 ∞

0

Le(λ)R(λ)dλ, (16)

where Le(λ) is the Earth-exiting spectral radiance at wavelength λ, and R(λ) is the spectral response of the band at

wavelength λ. By this definition, Le is the Earth-exiting

spectral radiance integrated over the SeaWiFS spectral response.

For the SeaWiFS Project, spectral radiance is expressed

in mW cm−2 sr−1 μ m−1. For SeaWiFS measurements on

orbit, the spectral shape of the Earth-exiting radiance is

never known exactly. The calibration of the instrument

is forced to use approximations to that on-orbit spectral

radiance. A study of several spectral approximations can

be found in Barnes and Yeh (1996).

The output from each SeaWiFS band is the solution

of the integral in (16), plus the inclusion of several multiplicative constants that have no spectral dependence. For

the SeaWiFS Project, radiance, i.e., the solution to (16),

is expressed in mW cm−2 sr−1. For most uses of the SeaWiFS measurements, the radiance for each band must be

expressed in a form that represents the spectral radiance

from the source at a given wavelength. This representation

will be discussed below.

The spectral response of each band is given in terms of

milliamperes of current from the photodiode in the detector per unit of spectral radiance. The photodiode performs

the integration for the instrument. It converts the integral

in (15) into an electric current. The electronics within the

instrument convert this current into volts and then into

digital counts. These conversions are multiplicative with

no spectral dependence.

There are practical limits to the wavelength ranges of

the spectral responses of the SeaWiFS bands. Outside of

those wavelength limits, the responses of the bands are

next to zero. For example, there is a limited wavelength

range over which the silicon photodiodes respond to incoming flux (see Fig. 11 of Barnes et al. 1994b). In the

laboratory characterization of SeaWiFS, the wavelength

interval over which the band spectral responses have been

determined extends from 380–1,150 nm. For most of this

interval, the responses of the individual bands are effectively zero (Barnes et al. 1994b).

For the laboratory calibration of SeaWiFS, the spectral

shape of the radiance from the source, i.e., from the GSFC

SIS, is known (Barnes 1996a). In the laboratory, therefore,

the measurement of the sphere radiance by a SeaWiFS

band can be expressed as

Ls =

 1150

380

Ls(λ)R(λ)dλ, (17)

where Ls(λ) is the spectral radiance from the integrating

sphere at wavelength λ. As used here, Ls(λ) and R(λ) are

normalized values—normalized to unity at their maximum

values. Ls is the sphere spectral radiance integrated over

the SeaWiFS spectral response.

39
SeaWiFS Calibration Topics, Part 1

For SeaWiFS and for several other satellite instruments

managed at GSFC, there is a distinction made between inband and out-of-band response from the instrument. The

in-band response is defined as the integrated response between the 1% transmission points for each band (Barnes

et al. 1994a). Since the spectral shape of the source and

the spectral response of the individual SeaWiFS bands are

known, it is possible to calculate the fraction of the instrument response that comes from outside of the 1% transmission points. In this manner, it is possible, for a given

source spectral shape, to calculate the fraction of the total

response for a given band that is in-band and the fraction that is out-of-band (see for example, Barnes and Yeh

1996). The in-band and out-of-band distinction is made

here. With the removal of the out-of-band response, that

is, with the removal of a few percent of the total band

response, the measurement of the integrating sphere by

SeaWiFS is given by:

Ls =

 λ2

λ1

Ls(λ)R(λ)dλ, (18)

where λ1 and λ2 are the lower and upper 1% transmission

points for the band, respectively.

Using (18), it is possible to calculate the BSR, using

R(λ) as the weighting function:

LB(λB) =

 λ2

λ1 Ls(λ)R(λ)dλ

 λ2

λ1 R(λ)dλ , (19)

where LB(λB) is the BSR for the band.

In a similar manner, the BCW associated with this

spectral radiance can be calculated, using Ls(λ)R(λ) as

the weighting function.

λB =

 λ2

λ1 λLs(λ)R(λ)dλ

 λ2

λ1 Ls(λ)R(λ)dλ , (20)

where λB is the BCW.

Alternately, it is possible to define an ECW for each

band, λeff, which is the wavelength where Ls(λ) equals

LB(λB). The ECW can be applied to sources that are well

behaved spectrally, that is, to sources whose spectral radiance increases or decreases monotonically between the 1%

response points for each band. In this regard, the GSFC

sphere is a well behaved source.

For an instrument that measures with infinitely narrow bandwidths, λB and λeff are the same; however, for

SeaWiFS and the SXR, the spectral bandwidths are finite.

The calculated center wavelengths are different for the two

methods. For the SXR, the differences are very small. The

results from both calculation methods are given below.

The comparisons presented here will use the relative

spectral response (RSR) for the SXR, the RSR for SeaWiFS, and the relative source spectral shape for the GSFC

SIS. Each of these will be described briefly in the sections

that follow.

3.2 SXR AND SEAWIFS RSRS

The relative spectral responses of the six SXR bands

are also shown in Fig. 21. The responses were provided

by B. Carol Johnson at NIST. These are system level responses, measured using a source with a bandwidth of less

than 0.5 nm. The technique for the measurement of the

system level response of the SXR is similar to that used

for the system level response measurement of SeaWiFS (see

Sect. 10 of Barnes et al. (1994b). The SXR responses were

normalized by NIST to a maximum of unity.

The spectral responses of the eight SeaWiFS bands are

shown in Fig. 21. The curves for SeaWiFS were previously

compiled at 1 nm intervals from 380–1,150 nm (Barnes et

al. 1994b and Barnes 1994). For the comparisons presented

here, the spectral responses were also normalized to a maximum of unity.

3.3 SPHERE SPECTRAL SHAPE

The radiance curves for the GSFC sphere were provided

by NIST. The complete characterization of the sphere by

NIST will be described in a future SeaWiFS technical memorandum. The spectral shape of the sphere output is described in Barnes (1996a). For the comparison here, the

output of the sphere has been normalized to unity at its

maximum radiance level. There are no actual radiance

measurements in this comparison—the radiance measurements will come later. The spectral shape comparison

presented here was performed to allow the conversion of

the SXR measurements to the wavelengths which SeaWiFS

measures.

The normalized response curve for the GSFC sphere

is shown in Fig. 22. This curve shows the shape of the

output when the full complement of 16 lamps are lit. For

the radiometric calibration of SeaWiFS, the sphere will be

operated in four configurations with 16, 8, 4, and 1 lamp

illuminated. The spectral response curves for these lamp

configurations are not identical to the curve in Fig. 22,

but they are very close duplicates. For the comparisons

presented here and for the recalibration of SeaWiFS, the

spectral curve for each lamp configuration is treated independently. The differences between lamp configurations,

although slight, can be seen in the results below.

Changes in the spectral shapes of the sphere radiances

do occur over time. The changes are most evident in the

blue wavelengths from the sphere, that is, in the spectral

radiances near 412 nm in this comparison. These changes

result from the aging of the lamps and of the reflective surface on the interior of the sphere. These changes are greatest for new lamps and for a fresh coating on the sphere’s

interior. Over time, the rate at which these changes occur approaches zero. For the GSFC sphere, the output in

the blue appears to have been stable during the most recent SeaWiFS Intercomparison Round-Robin Experiment

(SIRREX) comparison (Johnson et al. 1996). Although

40
R.A. Barnes, E-n. Yeh, and R.E. Eplee

Fig. 21. The RSRs are shown for the bands in the comparison. The responses are normalized to a maximum

of unity. For each band, responses that are less than 1% of the maximum have been eliminated; the out-of-band

responses are not shown. a) Responses of the SXR. b) Responses of the SeaWiFS instrument.

41
SeaWiFS Calibration Topics, Part 1

Fig. 22. The relative spectral output from the GSFC sphere is shown in this figure. The response is shown for

the full complement of lamps (16 lamps) illuminated. The relative spectral output for other lamp configurations

are very similar.

changes from the source spectral shapes presented here

are not expected for the SeaWiFS recalibration, changes,

if they do occur, could require a revision of these results

before they are applied to the laboratory measurements.

3.4 OUT-OF-BAND REMOVAL

For SeaWiFS and for several other satellite instruments

managed at GSFC, there is a distinction made between the

in-band and out-of-band responses from the instrument.

The in-band response is defined as the integrated response

between the 1% transmission points (Barnes et al. 1994a).

The remaining response is out-of-band. The out-of-band

responses for SeaWIFS and the SXR, given as percentages

of the total band responses, are listed in Table 18. The inand out-of-band responses are calculated from the products of the GSFC sphere output and the band response,

that is, for Ls(λ)R(λ) in (17), over the wavelength intervals

for the spectral characterization of the instruments. For

SeaWiFS, the spectral characterization was made over the

wavelength interval from 380–1,150 nm. The wavelengths

for the 1% response points for each band in both instruments are listed in Table 19.

The out-of-band responses for the SeaWiFS instrument

in Table 18 are very close to those previously calculated for

a 2,850 K blackbody (Barnes et al. 1994b and Barnes and

Yeh 1996). This is not surprising, since the GSFC sphere,

as viewed by SeaWiFS, has an equivalent blackbody temperature of 2,980 K (Barnes 1996a). For the same reason,

the out-of-band responses for the SXR in Table 18 should

also be very close to those for a 2,850 K blackbody.

3.5 IN-BAND RADIANCES

The band-weighted responses for the SeaWiFS and SXR

bands are listed in Table 18. The responses were calculated

using output from the GSFC SIS normalized to unity at

890 nm. For SeaWiFS band 8, which has a center wavelength near 865 nm, the BSR is within 0.5% of unity.

The BSRs were calculated, using a set of summations

that approximate (19). The calculation of the spectral radiance for SXR channel 1, viewing the GSFC sphere output

with 16 lamps illuminated, can be found in Table 20. The

contributors to the summations are listed at 0.5 nm intervals from 402.0–419.5 nm. The band responses at the end

wavelengths are just below 1% of the maximum response.

The spectral radiances for each band in Table 18 are

accompanied by an ECW (λeff). This wavelength has been

calculated for the 16 lamp sphere configuration. A sample

calculation of λeff for SXR band 1 is given in Table 20 and

illustrated in Fig. 23. As shown below, the ECWs for the

other lamp configurations very closely agree with those in

Table 18.

3.6 CENTER WAVELENGTHS

The ECW, λeff, ties the BSR from the band to the

spectral radiance from the sphere. At λeff, both spectral

42
R.A. Barnes, E-n. Yeh, and R.E. Eplee

Table 18. The ECWs and BSRs [LB(λB)] from the GSFC sphere for SeaWiFS and the SXR are shown here.

For each band, the weighting is made over the wavelength range between the band’s 1% response points. The

GSFC sphere radiances have been normalized to unity at the maximum spectral radiance (i.e., the spectral

radiance at 890 nm). The center wavelengths are calculated for the sphere output with 16 lamps illuminated.

Band ECW λeff BSRs LB(λB) Out-of-Band

Number [nm] 16 Lamps 8 Lamps 4 Lamps 1 Lamp Response [%]

SXR 1 411.26 0.085180 0.082925 0.082125 0.082334 0.50

2 441.42 0.141042 0.137828 0.136701 0.137806 0.19

3 486.97 0.247171 0.242745 0.241247 0.243699 0.42

4 547.88 0.416733 0.411506 0.409644 0.413591 0.38

5 661.63 0.727251 0.722906 0.721130 0.726807 1.48

6 774.70 0.932858 0.929945 0.928896 0.932218 0.70

SeaWiFS 1 413.78 0.089553 0.087212 0.086381 0.086612 1.37

2 444.09 0.146546 0.143257 0.142106 0.143294 0.52

3 491.19 0.258126 0.253620 0.252091 0.254651 1.50

4 510.10 0.309091 0.304265 0.302594 0.305630 0.64

5 554.91 0.437253 0.432014 0.430128 0.434211 3.15

6 668.33 0.743251 0.739068 0.737314 0.742960 0.76

7 764.85 0.919969 0.916657 0.915525 0.918936 1.84

8 862.74 0.995819 0.995166 0.994892 0.995347 2.25

Table 19. In this table, the center wavelengths for measurements of the GSFC sphere by SeaWiFS and the

SXR are shown. The upper and lower integration wavelengths are the 1% response points for the bands.

Band ECW λeff BCW λB Lower Integration Upper Integration

Number [nm] [nm] Wavelength λ1 [nm] Wavelength λ2 [nm]

SXR 1 411.26 411.39 402.0 419.5

2 441.42 441.55 431.5 450.0

3 486.97 487.09 476.0 496.0

4 547.88 547.96 538.0 556.5

5 661.63 661.67 650.0 671.0

6 774.70 774.80 760.5 786.0

SeaWiFS 1 413.78 414.48 394.0 433.0

2 444.09 444.62 423.0 464.0

3 491.19 491.59 470.0 512.0

4 510.10 510.51 488.0 531.0

5 554.91 555.19 536.0 578.0

6 668.33 668.69 646.0 693.0

7 764.85 765.76 727.0 815.0

8 862.74 866.29 826.0 909.0

radiances are the same. The calculation of the effective

wavelength for SXR band 1 is shown in Table 20. The

wavelength for Ls(λ) is obtained using interpolation between the sphere spectral radiances that bracket the BSR,

LB(λB), for the band. The sphere output at 411.26 nm is

the same as the BSR for SXR band 1. As shown in Fig. 23,

the spectral radiance from the sphere increases monotonically with wavelength over the in-band response range of

the band.

The BCW, λB, is calculated in the same manner as the

BSR, as in (20). A sample calculation of λB is given in

Table 21. This calculation is made for the sphere output

with 16 lamps illuminated. Clearly, LB(λB) and λB are

also tied together uniquely. For an instrument with infinitely narrow bandwidths, λB and λeff will be identical.

For SeaWiFS, and to a much lesser extent for the SXR,

the two types of calculated center wavelengths are different. The two types of center wavelengths for all SeaWiFS

and SXR bands are listed in Table 19, along with the upper

and lower integration limits for the calculations.

Table 22 shows the spectral radiances from the sphere

at the effective and BCWs for the SeaWIFS and SXR

bands. It shows the differences in spectral radiance that

correspond to the differences in wavelength. For the SXR,

43
SeaWiFS Calibration Topics, Part 1

Table 20. Shown is the calculation of the BSR [LB(λB)=0.085180] for SXR band 1 when measuring

the output of the GSFC sphere with 16 lamps illuminated. LB(λB) is calculated by the summation of

Ls(λ)R(λ)=1.805337 [which approximates the integral in (18)] divided by the summation of R(λ) =

21.194483. The ECW, which equals 411.26, is calculated by interpolation. It is the wavelength at which

Ls(λ) = LB(λB). The calculated spectral radiances and ECWs for each of the SeaWiFS and SXR bands

can be found in Table 18.

λ Normalized Band Normalized Sphere Product

[nm] Response R(λ) Response Ls(λ) Ls(λ)R(λ)

402.0 0.006211 0.070502 0.000438

402.5 0.010747 0.071283 0.000766

403.0 0.020770 0.072065 0.001497

403.5 0.042285 0.072846 0.003080

404.0 0.098298 0.073628 0.007237

404.5 0.145084 0.074409 0.010796

405.0 0.259889 0.075191 0.019541

405.5 0.390215 0.075972 0.029646

406.0 0.536661 0.076754 0.041191

406.5 0.704143 0.077535 0.054596

407.0 0.814871 0.078317 0.063818

407.5 0.904308 0.079098 0.071529

408.0 0.935774 0.079880 0.074749

408.5 0.938132 0.080661 0.075671

409.0 0.958579 0.081443 0.078069

409.5 0.972649 0.082224 0.079976

410.0 0.979553 0.083006 0.081309

410.5 0.987429 0.083872 0.082817

411.0 0.985067 0.084737 0.083472

411.5 0.980620 0.085603 0.083944

412.0 0.984612 0.086468 0.085138

412.5 1.000000 0.087334 0.087334

413.0 0.993836 0.088200 0.087656

413.5 0.983767 0.089065 0.087620

414.0 0.989480 0.089931 0.088985

414.5 0.942185 0.090797 0.085547

415.0 0.895148 0.091662 0.082051

415.5 0.816659 0.092528 0.075564

416.0 0.667959 0.093393 0.062383

416.5 0.544351 0.094259 0.051310

417.0 0.345317 0.095125 0.032848

417.5 0.200552 0.095990 0.019251

418.0 0.105112 0.096856 0.010181

418.5 0.031104 0.097722 0.003040

419.0 0.013452 0.098587 0.001326

419.5 0.009666 0.099453 0.000961

Totals 21.194483 1.805337

44
R.A. Barnes, E-n. Yeh, and R.E. Eplee

Table 21. The calculation of the BCW (λB = 411.39) is given for the SXR band 1. The summations

approximate the integral in (21) and are arrived at by taking the summation of λLs(λ)R(λ) (equals

742.693515) divided by the summation of Ls(λ)R(λ) (equals 1.805337). The calculations are made for

the sphere output with 16 lamps illuminated.

λ Normalized Band Normalized Sphere Product Product

[nm] Response R(λ) Response Ls(λ) Ls(λ)R(λ) λLs(λ)R(λ)

402.0 0.006211 0.070502 0.000438 0.176041

402.5 0.010747 0.071283 0.000766 0.308355

403.0 0.020770 0.072065 0.001497 0.603209

403.5 0.042285 0.072846 0.003080 1.242906

404.0 0.098298 0.073628 0.007237 2.923942

404.5 0.145084 0.074409 0.010796 4.366813

405.0 0.259889 0.075191 0.019541 7.914198

405.5 0.390215 0.075972 0.029646 12.021256

406.0 0.536661 0.076754 0.041191 16.723439

406.5 0.704143 0.077535 0.054596 22.193241

407.0 0.814871 0.078317 0.063818 25.973972

407.5 0.904308 0.079098 0.071529 29.148187

408.0 0.935774 0.079880 0.074749 30.497788

408.5 0.938132 0.080661 0.075671 30.911619

409.0 0.958579 0.081443 0.078069 31.930407

409.5 0.972649 0.082224 0.079976 32.749987

410.0 0.979553 0.083006 0.081309 33.336591

410.5 0.987429 0.083872 0.082817 33.996470

411.0 0.985067 0.084737 0.083472 34.306926

411.5 0.980620 0.085603 0.083944 34.542898

412.0 0.984612 0.086468 0.085138 35.076814

412.5 1.000000 0.087334 0.087334 36.025319

413.0 0.993836 0.088200 0.087656 36.201945

413.5 0.983767 0.089065 0.087620 36.230671

414.0 0.989480 0.089931 0.088985 36.839731

414.5 0.942185 0.090797 0.085547 35.459323

415.0 0.895148 0.091662 0.082051 34.051282

415.5 0.816659 0.092528 0.075564 31.396705

416.0 0.667959 0.093393 0.062383 25.951327

416.5 0.544351 0.094259 0.051310 21.370620

417.0 0.345317 0.095125 0.032848 13.697699

417.5 0.200552 0.095990 0.019251 8.037327

418.0 0.105112 0.096856 0.010181 4.255551

418.5 0.031104 0.097722 0.003040 1.272032

419.0 0.013452 0.098587 0.001326 0.555676

419.5 0.009666 0.099453 0.000961 0.403249

Totals 1.805337 742.693515

45
SeaWiFS Calibration Topics, Part 1

Fig. 23. The BSR and ECW for SXR band 1 are shown here. These factors are tied together by the spectral

radiance from the source. In this case, the source is the GSFC sphere with 16 lamps illuminated. The data for

this figure come from Table 20.

Table 22. The sphere spectral radiances at the ECWs [Ls(λeff)], and BCWs [Ls(λB)], are shown in

this table for the SeaWiFS and SXR bands. The calculations are made for the sphere output with 16

lamps illuminated. The ratio gives Ls(λB)/Ls(λeff).

Band λeff Sphere Spectral λB Sphere Spectral Ratio

Number [nm] Radiance Ls(λeff) [nm] Radiance Ls(λB)

SXR 1 411.26 0.085180 411.39 0.085409 1.0003

2 441.42 0.141042 441.55 0.141302 1.0003

3 486.97 0.247171 487.10 0.247495 1.0003

4 547.88 0.416733 547.96 0.416972 1.0002

5 661.63 0.727251 661.67 0.727339 1.0001

6 774.70 0.932858 774.80 0.932977 1.0001

SeaWiFS 1 413.77 0.089553 414.48 0.090763 1.0135

2 444.09 0.146546 444.62 0.147627 1.0074

3 491.19 0.258126 491.59 0.259192 1.0041

4 510.10 0.309091 510.51 0.313017 1.0127

5 554.91 0.437253 555.19 0.438068 1.0019

6 668.33 0.743251 668.69 0.744111 1.0012

7 764.85 0.919969 765.76 0.921223 1.0014

8 862.74 0.995819 866.29 0.996629 1.0008

46
R.A. Barnes, E-n. Yeh, and R.E. Eplee

Table 23. The ECWs (λeff) for the SeaWiFS and SXR bands are shown for all lamp configurations (16, 8, 4,

and 1) for the GSFC sphere. All units are in nanometers [nm].

Band Sphere Average Standard

Number 16 Lamps 8 Lamps 4 Lamps 1 Lamp Deviation

SXR 1 411.2555 411.2541 411.2523 411.2517 411.2534 0.0015

2 441.4250 441.4258 441.4266 441.4262 441.4259 0.0006

3 486.9690 486.9700 486.9694 486.9695 486.9695 0.0004

4 547.8817 547.8814 547.8816 547.8815 547.8816 0.0001

5 661.6315 661.6309 661.6298 661.6314 661.6309 0.0007

6 774.7044 774.6911 774.6846 774.6675 774.6869 0.0133

SeaWiFS 1 413.7820 413.7813 413.7800 413.7439 413.7718 0.0186

2 444.0919 444.0938 444.0960 444.0943 444.0940 0.0017

3 491.1895 491.1952 491.1920 491.1921 491.1922 0.0023

4 510.1038 510.1121 510.1034 510.1124 510.1079 0.0050

5 544.9090 544.9086 544.9074 544.9089 544.9085 0.0007

6 668.3344 668.3443 668.3355 668.3392 668.3384 0.0045

7 764.8503 764.8856 764.8420 764.7767 764.8386 0.0454

8 862.7743 863.0759 863.1742 862.9470 862.9854 0.1857

with its narrow bandwidths, the spectral radiance differences are very small, 0.03% or less. For SeaWiFS, the radiance differences are greater, particularly with the shorter

wavelength bands. Thus, the choice of the appropriate

center wavelength for the SeaWiFS bands becomes important, when the SXR is used as a calibration standard for

SeaWiFS with both instruments viewing the GSFC sphere.

For that comparison, λeff has been chosen, since LB(λB)

and Ls(λeff) are identical by definition.

Table 23 shows the ECWs for each SeaWiFS and SXR

band for each sphere configuration. The center wavelength

differences are essentially insignificant. For example, Table 22 shows that a 0.7 nm difference in center wavelength

causes a 1.35% difference in the sphere spectral radiance

for SeaWiFS band 1. This corresponds to a 0.2% difference per 0.1 nm. The 0.04 nm range in the ECWs for

SeaWiFS band 1 in Table 23 would cause a difference of

less than 0.1% in sphere spectral radiance. For SeaWiFS

band 8, a 3.5 nm change in center wavelength causes only

an 0.08% change in sphere output (Table 23). Thus, the

0.3 nm range in ECWs for SeaWIFS band 8 in Table 23

causes a negligible difference in sphere spectral radiance.

Barnes (1996b) made a similar comparison, using the

shape of a 12,000 K blackbody to approximate the spectrum of the Earth-exiting radiance that SeaWiFS will view

on orbit. Those results show that, on orbit, the differences

in the source radiances at λeff and λB will be 0.12% or less

for each of the SeaWiFS bands.

3.7 RADIANCE CONVERSION

For measurements of the GSFC sphere, the BSRs for

the SeaWiFS bands can be calculated directly from the

BSRs measured by the SXR. These calculations, using

band pairs, require no information about the center wavelengths for the bands. The steps in this calculation are

simple. They start with a measured radiance from an SXR

band of the sphere output.

1. Remove the out-of-band response from the SXR

measured radiance. The percent out-of-band response for each SXR band is given in Table 18.

2. Convert the SXR in-band radiance to the SeaWiFS

in-band response using the ratios of the BSRs in

Table 18. The conversion factors for measurements

of the GSFC sphere with 16 lamps illuminated is

given in Table 24. A similar use of the conversion

factors from Table 18 can be made for the other

sphere configurations.

3. Restore the out-of-band response to the SeaWiFS

band to calculate the total band response. Depending on the use for the results, this step may not

be necessary. The percent out-of-band response for

each SeaWiFS band is listed in Table 18.

There are other conversion techniques that can use the

set of SXR BSRs to calculate the spectral radiances from

the sphere at the SeaWiFS wavelengths. These techniques

require a clear and consistent understanding of the center wavelengths for the bands. For example, by using the

spectral radiance from each SXR band and the values in

Table 18, it is possible to calculate the sphere output at

890 nm, that is, at the wavelength where the sphere output

is normalized to unity. From the six resulting values for the

spectral radiance at 890 nm, a best value for the radiance

at that wavelength can be determined. This combination

uses the entire set of SXR measurements so that effects in

measurement errors by any one band will be minimized.

47
SeaWiFS Calibration Topics, Part 1

Table 24. The factors for converting the SXR spectral radiances to SeaWiFS are given in this table. These

values (dimensionless) are for measurements of the GSFC sphere with 16 lamps illuminated; these factors are

derived from values in Table 18. Spectral radiances are given as mW cm−2 sr−1 μm−1. There are no SXR bands

that correspond to SeaWiFS band 4 (510 nm); conversions for SeaWiFS band 4, however, can be made using

SXR bands 3 and 4.

SeaWiFS SXR SeaWiFS SXR Conversion

Band λeff Band λeff Spectral Spectral Factor

Number [nm] Number [nm] Radiance Radiance

1 413.77 1 411.25 0.089553 0.085180 1.0513

2 444.10 2 441.43 0.146546 0.141042 1.0390

3 491.21 3 486.97 0.258126 0.247171 1.0443

4 510.10 3 486.97 0.309091 0.247171 1.2505

4 510.10 4 547.88 0.309091 0.416733 0.7417

5 554.91 4 547.88 0.437253 0.416733 1.0492

6 668.38 5 661.63 0.743251 0.727251 1.0220

7 764.91 6 774.69 0.919969 0.932858 0.9862

8 862.95 6 774.69 0.995819 0.932858 1.0675

Using the sphere output at 890 nm and the SeaWiFS

factors in listed in Table 18 (which are based on the knowledge of the wavelength dependence of the spectral radiance from the sphere), the radiances at the SeaWiFS center wavelengths can be calculated. If the spectral shape

of the sphere output is very well determined, then using

the technique, such as the one outlined in this chapter,

should reduce the scatter in the spectral radiances at the

SeaWiFS wavelengths, compared to those calculated from

the SeaWiFS–SXR band pairs. This should reduce the

relative, or band-to-band, differences in the calibration of

SeaWiFS.

48
R.A. Barnes, E-n. Yeh, and R.E. Eplee

Chapter 4

SeaWiFS Center Wavelengths

Robert A. Barnes

General Sciences Corporation, Laurel, Maryland

Abstract

With its 20 and 40 nm bandwidths, SeaWiFS does not make measurements at individual wavelengths. Rather,

the output from each SeaWiFS band can be considered as an integral over a finite wavelength region of the

source it measures. To make SeaWiFS measurements useful, it is important to relate the measured radiance

from the instrument to a reference wavelength. That wavelength connects each SeaWiFS measurement to the

spectral radiance from the source at that wavelength. For the initial calibration of SeaWiFS, the reference center

wavelengths were those from the instrument’s performance specifications. A set of BCWs for on-orbit use are

presented here. The use of these new wavelengths will require a revision of the on-orbit radiometric calibration

constants for the instrument.

4.1 INTRODUCTION

For the development of the initial SeaWiFS calibration equations (Barnes et al. 1994b), the instrument was

assumed to have a set of eight fixed center wavelengths,

one for each band. For SeaWiFS bands 1–8, these wavelengths are 412, 443, 490, 510, 555, 670, 765, and 865 nm,

respectively. These wavelengths come from the instrument

specifications (Barnes et al. 1994a), and they are the wavelengths at which the laboratory source for the SeaWiFS

radiometric calibration was itself calibrated. These center

wavelengths are embedded in the radiometric calibration

of SeaWiFS. For the current calibration of the instrument,

they are the de facto center wavelengths for the instrument. Since the development of the original SeaWiFS calibration equations, studies were performed to investigate

the effects of different source spectral shapes on the output

of the SeaWiFS bands (Barnes 1996a, and Barnes and Yeh

1996). In addition, these studies used the de facto center

wavelengths for each band and calculated changes in the

output from the bands for different source spectral shapes

normalized at those wavelengths. Those studies were particularly instructive in developing an approach for calculating the out-of-band responses of the SeaWiFS bands for

different source spectral shapes.

It is also possible, however, to examine the effects of

source spectral shape in terms of fixed radiometric output

from the SeaWiFS bands, accompanied by changes in their

center wavelengths with changes in source spectral shape.

The groundwork for this approach was presented in a comparison of the spectral responses of SeaWiFS and the SeaWiFS Transfer Radiometer (SXR) (Barnes 1996c). That

comparison centered on the in-band responses of the two

instruments for the spectral shape of the GSFC sphere—

the source to be used in the recalibration of SeaWiFS.

In spectral terms, the output from the GSFC sphere

varies smoothly with wavelength over the extended bandpasses of the SeaWiFS bands (Barnes 1996a). This allows the calculation of the wavelength at which the spectral radiance from the sphere equals the BSR from each

instrument band. The same smooth changes with wavelength are found in the Planck function curves that were

used as approximations to the spectral shapes of the Earthexiting spectral radiance which SeaWiFS will view on orbit (Barnes 1996a and Barnes and Yeh 1996). Eventually,

these approximations to the Earth-exiting spectral radiances may be replaced with spectral shapes based on atmospheric radiometric transfer models. The adoption of

these more realistic spectral shapes will require a modification of the results presented here.

4.2 INSTRUMENT RESPONSE

As part of a comparison of the spectral responses of

SeaWiFS and the SXR, Barnes (1996c) examined the effects of the finite bandwidths of the two instruments. The

discussion in this section has been extracted from that report.

For a SeaWiFS band, it is possible to calculate the

BSR, using the band’s spectral response as the weighting

function:

LB(λB) =

 λ2

λ1 λLs(λ)R(λ)dλ

 λ2

λ1 R(λ)dλ , (21)

49
SeaWiFS Calibration Topics, Part 1

where LB(λB) is the BSR for the band; λ1 and λ2 are

the lower and upper 1% transmission points for the band,

respectively; Ls(λ) is the source spectral radiance at wavelength λ; and R(λ) is the spectral response of the band at

wavelength λ. The integration limits, λ1 and λ2, mark the

wavelength range for the in-band response of the band.

Examples of Ls(λ) for a 12,000 K Planck function and of

R(λ) for SeaWiFS band 7 are shown in Fig. 24. The Planck

function has been normalized to unity at 380 nm.

For the discussions here, the term spectral radiance

refers to the radiant flux (in watts or photons per second) per unit wavelength. For the SeaWiFS Project, the

units of spectral radiance are mW cm−2 sr−1 μ m−1. The

SeaWiFS instrument measures the integral of spectral radiance (Barnes 1996c). This integral is the numerator of

(21). Again, for the discussions here, the integral that

SeaWiFS measures is called “radiance” and does not have

the term per micron (μ m−1). To make SeaWiFS measurements useful, it is important to relate the measured

radiance from the instrument to a reference wavelength.

That wavelength connects the SeaWiFS measurement to

the spectral radiance from the source at that wavelength.

For the vast majority of discussions of SeaWiFS measurements in the literature, the terms radiance and spectral

radiance are used interchangeably. In those presentations,

radiance means the same as spectral radiance here.

In a similar manner, the BCW associated with this

spectral radiance can be calculated, using Ls(λ)R(λ) as

the weighting function.

λB =

 λ2

λ1 λLs(λ)R(λ)dλ

 λ2

λ1 Ls(λ)R(λ)dλ , (22)

where λB is the BCW.

Alternately, it is possible to define an effective wavelength for each band, λeff, which is the wavelength where

Ls(λ) equals LB(λB). The ECW can be applied to sources

that are well behaved spectrally. In this regard, the Planck

function curve in Fig. 24 is well behaved. For the source

function and the band response in Fig. 24, the ECW is

765.0 nm.

For an instrument that measures with infinitely narrow

bandwidths, λB and λeff are the same; however, for SeaWiFS the spectral bandwidths are finite. The calculated

center wavelengths are different for the two methods. The

center wavelength results from both calculation methods

are given below. As the calculations will show, on orbit

differences in the source spectral radiance at λeff and λB

will be 0.12% or less, for each of the SeaWiFS bands.

4.3 SOURCE FUNCTIONS

Fig. 25 shows the typical SeaWiFS spectral radiances,

as found in the performance specifications for the instrument (Barnes et al. 1994a). The figure also shows three

Planck function curves normalized at 412 nm to the typical

spectral radiance for SeaWiFS band 1. These three curves

provide approximations to the Earth-exiting spectral radiances that SeaWiFS will view on orbit. Of the three, the

12,000 K Planck function is considered to have the best

overall fit to the typical spectral radiances. The BCWs

and ECWs are calculated below using these source spectral

shapes. Because the calculation of the center wavelengths

depends solely on the spectral shapes of the source functions and those of the band responses, the absolute values

of the source functions are unimportant. For the calculations presented here, the Planck functions have been normalized to unity at 380 nm.

The center wavelengths are also calculated below using

the spectral shape of the output of the GSFC sphere. In

Barnes and Yeh (1996), each lamp setting for the sphere

was considered as having an independent spectral shape.

In that study, the minor differences between lamp settings

were important because the results were a fundamental

part of the recalibration of SeaWiFS. For the purposes of

this report, the spectral shapes from the four lamp settings

have been combined into one representative shape for the

sphere, since for this report, the sphere’s spectral shape is

used only for comparisons with the Planck functions.

Finally, a constant source function of unity is used below for calculations of BCWs for each band. These BCWs

can be compared with the system level center wavelengths

for SeaWiFS from Table 13 of Barnes et al. (1994b). The

system level center wavelengths, in turn, were calculated

as the center point of the full-width at half-maximum for

each band. The BCWs in this chapter differ from the system level values in Barnes et al. (1994b) by up to 0.6 nm.

4.4 CALCULATED WAVELENGTHS

The BSRs for the SeaWiFS bands were calculated, using a set of summations that approximate (21). The details of such a calculation were demonstrated in Table 20

of Barnes (1996c). The calculation of a BCW, λB, using

(22) was demonstrated in Table 21 of Barnes (1996c).

The SeaWiFS BCWs, using the source spectral shapes

described above, are listed in Table 25. The spectral shape

of the GSFC sphere is given as 2,920 K—the sphere’s equivalent blackbody temperature (Barnes 1996a). For SeaWiFS ocean measurements on orbit, the spectral shape of

the Earth-exiting spectral radiance is expected to be close

to that for a 12,000 K Planck function. For the 10,000 K;

12,000 K; and 14,000 K spectral shapes, the BCWs in Table 25 are nearly identical. For each of the bands, the

center wavelengths for the 12,000 K spectral shape is less

than 0.06 nm from those for the adjacent blackbody temperatures. As a result, the BCWs should remain essentially constant throughout the range of spectral shapes

that SeaWiFS will encounter during its measurements of

water leaving spectral radiances.

Table 25 also lists the ECW, λeff, for each SeaWiFS

band and for each source spectral shape, except for the

50
R.A. Barnes, E-n. Yeh, and R.E. Eplee

Fig. 24. A 12,000 K Planck function source curve and the relative spectral response for SeaWiFS band 7 are

illustrated. The Planck function has been normalized to unity at 380 nm. The calculations of the BCWs and

ECWs depend solely on the shapes of the source functions and those of the band spectral responses. a) The

blackbody curve. b) The band 7 response curve.

51
SeaWiFS Calibration Topics, Part 1

Fig. 25. Typical spectral radiances from the SeaWiFS specifications plotted with three blackbody curves are

shown here.

Table 25. This table gives the calculated center wavelengths (in nanometers) for the eight SeaWiFS Bands.

ECWs are given for four spectral shapes—the GSFC sphere and three Planck function curves that approximate

the source spectral shape which SeaWiFS will view on orbit. The BCWs are given for the same spectral shapes

and for a spectrally flat source.

Spectral Shape BCW (λB)

[K] Band 1 Band 2 Band 3 Band 4 Band 5 Band 6 Band 7 Band 8

2,920 (Sphere) 414.49 444.62 491.59 510.52 555.19 668.70 765.76 866.30

Spectrally Flat 413.62 443.97 491.10 510.03 554.91 668.55 765.49 866.25

10,000 413.46 443.80 490.91 509.81 554.75 668.36 764.79 865.62

12,000 413.41 443.75 490.87 509.77 554.72 668.34 764.74 865.58

14,000 413.37 443.72 490.84 509.74 554.71 668.33 764.70 865.55

ECWs (λeff)

2,920 (Sphere) 413.77 444.09 491.19 510.11 554.91 668.34 764.84 862.99

10,000 413.61 443.93 491.02 509.93 554.83 668.44 765.08 865.87

12,000 413.53 443.87 490.98 509.89 554.81 668.42 765.03 865.84

14,000 413.49 443.84 490.95 509.86 554.79 668.41 765.00 865.82

52
R.A. Barnes, E-n. Yeh, and R.E. Eplee

Table 26. The spectral radiances at the ECWs and BCWs are shown for the eight SeaWiFS bands. The source

for these calculations is a 12,000 K Planck function normalized to unity at 380 nm.

Band λeff Spectral Radiance λB Spectral Radiance Ratio

Number [nm] Ls(λeff) [nm] Ls(λB)

1 413.53 0.857363 413.41 0.857863 1.0006

2 443.87 0.743143 443.75 0.743547 1.0005

3 490.98 0.594213 490.87 0.594521 1.0005

4 509.89 0.543435 509.77 0.543740 1.0006

5 554.81 0.440746 554.72 0.440916 1.0004

6 668.42 0.266086 668.34 0.266183 1.0004

7 765.03 0.179003 764.74 0.179215 1.0012

8 865.84 0.122143 865.58 0.122260 1.0010

spectrally flat source. The calculation of an ECW was

demonstrated in Table 20 of Barnes (1996c). As with the

BCWs, the ECWs in Table 25 are nearly identical for the

10,000 K; 12,000 K; and 14,000 K spectral shapes. In addition, as with the BCWs, the ECWs should remain essentially constant for SeaWiFS ocean measurements.

For the 10,000 K, 12,000 K, and 14,000 K source spectral shapes, the ECWs are shorter than the BCWs. These

differences are very small. Table 26 shows the effects of

these wavelengths differences in terms of differences in the

spectral radiance from the source. In Table 26, the spectral radiances from a 12,000 K source are listed for each

of the center wavelengths. For the SeaWiFS bands with

20 nm bandwidths (bands 1–6), the differences between the

BCWs and ECWs average 0.05%. For SeaWiFS bands 7

and 8 (with 40 nm bandwidths), the differences average

0.11%. Clearly, the choice between BCWs or ECWs to

represent SeaWiFS on-orbit measurements makes no appreciable difference in the results of the measurements.

For measurements of the GSFC sphere, there is a larger

difference between the effective and BCWs (Table 25).

Barnes (1996c) calculated differences in sphere spectral radiances for these pairs of wavelengths to be up to 1.3%. For

that study, the ECWs were deemed to better represent the

spectral radiance from the sphere. For measurements on

orbit, the two types of center wavelengths are equivalent.

4.5 CONCLUDINGREMARKS

The current center wavelengths for the SeaWiFS bands

(1–8) are 412, 443, 490, 510, 555, 670, 765, and 865 nm,

respectively. These are the wavelengths from the SeaWiFS specifications (Barnes et al. 1994a), and these are

the wavelengths at which the instrument was calibrated

in the laboratory. A more representative set of SeaWiFS

wavelengths, the BCWs, are listed in Table 25. These

center wavelengths are tied to the BSRs from the SeaWiFS

bands. These BCWs have not been incorporated into the

current calibration of SeaWiFS (Barnes et al. 1994b). It is

possible, however, to derive a revised on-orbit calibration

of SeaWiFS at the BCWs, using the spectral comparison

of SeaWiFS and the SXR (Barnes 1996c), along with the

out-of-band results from Barnes and Yeh (1996).

It is also possible to convert the SeaWiFS measured

spectral radiances to wavelengths other than those in this

study. This is important, because SeaWiFS’s measurements will be compared with those from other satellite instruments; these other instruments will measure at wavelengths different from, but close to, SeaWiFS. OCTS, on

board the Advanced Earth Observation Satellite (ADEOS1) was launched in August 1996, and MODIS on board the

Earth Observing System’s morning platform (EOS-AM) is

scheduled for launch in 1998. Both of these instruments

have ocean color bands at wavelengths similar to SeaWiFS.

If the measurements of Earth-exiting spectral radiances

from each of these instruments are to be compared for uniformity, then the wavelengths at which the measurements

are made must be clearly determined. For SeaWiFS, it will

be possible to convert the measured spectral radiances on

orbit to the spectral radiances at the wavelengths of the

other instruments.

Finally, it is possible to provide a better source spectral shape than a 12,000 K Planck function for corrections

to SeaWiFS measurements on orbit. This can be done by

means of an atmospheric radiative transfer model, which is

outside the scope of this study. Alternately, it will be possible to use initial flight data from the instrument to provide

an updated set of typical spectral radiances as the basis for

a better model of the source spectral shape, which will be

viewed during SeaWiFS ocean color measurements.

53
SeaWiFS Calibration Topics, Part 1

Chapter 5

The SeaWiFS Solar Diffuser

Robert A. Barnes

Robert E. Eplee

General Sciences Corporation, Laurel, Maryland

Abstract

Measurements of the solar flux with an onboard solar diffuser will provide an important check of changes in

the radiometric sensitivity of SeaWiFS over the duration of the instrument’s on-orbit measurements of ocean

color. Although diffuser measurements do not give an absolute determination of radiometric changes, they will

identify any rapid changes that may occur in the instrument output. The diffuser was designed to produce

radiance levels that approximate those for other SeaWiFS measurements. This design includes an attenuator

to reduce the solar radiance levels on the diffuser, and hence, the effects of photolyzed organic compounds. The

BRDF, which shows the output of the diffuser as a function of pitch and yaw angle, has been determined. This

allows the removal of angular dependencies from the long-term radiometric sensitivity data. In addition, outdoor

measurements have given the predicted output from SeaWiFS for initial on-orbit solar diffuser measurements.

5.1 INTRODUCTION

The SeaWiFS design requirements were based on the

National Aeronautics and Space Administration (NASA)

experience with the operation of the Nimbus-7 Coastal

Zone Color Scanner (CZCS), since SeaWiFS is the successor instrument to CZCS. SeaWiFS is considered an improved replacement instrument for its predecessor. Among

the improvements are the incorporation of lunar and solar

measurements on orbit.

Lunar measurements are the single source of SeaWiFS

measurements to directly monitor the long-term drift in

the radiometric sensitivity (or responsivity) of the instrument (McClain et al. 1992 and Woodward et al. 1993). The

sun is considered a stable, unchanging light source. The

surface of the moon is also considered as unchanging over

the lifetime of the SeaWiFS measurements. Geometric

factors, such as the Earth-sun and Earth-moon distances,

can be calculated, and differences in the lunar reflectance

caused by small changes in the lunar phase angle and by

lunar libration can be removed using empirically-based lunar models (Hapke 1986, Helfenstein and Veverka 1987,

and Kieffer and Wildey 1996). To eliminate errors due to

uncertainty in the locations of the measured pixels on the

face of the moon, the lunar measurements will be used as

integrated images of the entire surface of the moon (Woodward et al. 1993). With these corrections, measurements

of the lunar reflectance can be used directly by SeaWiFS to

detect changes in the sensitivity of the instrument, since

SeaWiFS views the Earth and the moon in an identical

fashion.

For solar measurements that use a diffuser to bring the

solar irradiance within the SeaWiFS dynamic range, it is

not possible to separate changes in the instrument sensitivity from changes in the reflectance of the diffuser plate

in an a priori fashion. All that can be derived from these

measurements is the product of the change in the instrument and the change in the diffuser; however, there is an

assumption that can be used to tie solar diffuser measurements with lunar measurements. Basically, the change in

the reflectance of the diffuser is assumed to be linear over

periods of a few months. Over longer periods, from one to

several years, the change may be exponential with gradually decreasing changes over time; however, this exponential change can be treated as a series of many linear

segments. Experience with diffusers on previous satellite

instruments (Frederick et al. 1986 and Herman et al. 1990)

led to the assumption that diffuser degradation was caused

by the coating of the diffuser with photolyzed organic materials that outgassed from the spacecraft. This accumulation of organic materials is generally temporally smooth

and does not cause step functions in the reflectivity of the

diffuser.

Using virtually simultaneous lunar- and solar-diffuser

measurements, it is possible to separate changes in the

sensitivity of the instrument, using lunar measurements,

from changes in the reflectance of the diffuser. With the

time series of diffuser measurements normalized by lunar

measurements, it is possible to use the assumption of a

short-term linear change in diffuser reflectivity to identify

54
R.A. Barnes, E-n. Yeh, and R.E. Eplee

step changes in instrument sensitivity between lunar measurements. Such step changes were found in CZCS measurements (Evans and Gordon 1994).

Determining these changes waits for the launch of SeaWiFS and the initiation of on-orbit operations. This chapter reports on the design of the diffuser and its prelaunch

characterization and calibration.

5.2 DIFFUSER DESCRIPTION

Overviews of the operation of the SeaWiFS scanner

were presented in Barnes and Holmes (1993) and in Barnes

et al. (1994b). This section concentrates on a description

of the solar diffuser, itself. Figure 26 shows the SeaWiFS

instrument, the coordinate system for the instrument, and

the spacecraft. The flat plate at the top of the instrument

is mounted to the SeaStar spacecraft (not shown), and

nadir is the +x direction. Using the coordinate system in

Fig. 26, SeaWiFS and SeaStar both fly in the −y direction,

and SeaWiFS scans west-to-east in the xz plane, or normal

to the instrument’s y axis. The solar diffuser (also called

the solar calibrator) points in the +y direction, that is,

to the aft of the spacecraft. On the sunlit side of the

Earth, the spacecraft moves from north to south; it has

a descending equatorial crossing. As a result, the diffuser

views the sun as the spacecraft passes over the Earth’s

South Pole.

Figure 27 is a drawing of the diffuser assembly mounted

to the sensor. With the sun to the right of the drawing,

sunlight passes through the attenuator, is scattered off the

diffuser, and enters the instrument to the left. The diffuser

plate itself is part of the diffuser housing. It is painted on

the inside surface of the housing, behind the diffuser cover

in Fig. 27. The figure shows the back of the diffuser cover;

the back of the diffuser cover is also painted and acts as a

second diffuser. The cover has a spring-loaded hinge at its

bottom and is held in the vertical position by a solenoid

actuator. When the one-time actuator releases the cover,

the diffuser cover rotates into the page and comes to rest

on the bottom of the diffuser housing, held in place by the

spring on the hinge. A schematic of the diffuser assembly,

as seen from above the instrument, is shown in Fig. 28.

The figure shows the assembly without the diffuser cover.

The diffuser has a nominal illumination angle of 60◦

to avoid possible specular glints from its surface and to

reduce the flux density on the diffuser plate by a factor of

two. The plate and diffuser covers have coatings of YB71

paint. This paint provides a durable flat white coating with

proven orbital stability, as shown in the results from the

Long Duration Exposure Facility (LDEF) flown by NASA.

The wavelength dependence of the reflectivity of a YB71

coated plate, as measured at SBRC, is shown in Fig. 29.

The attenuator is a flat black anodized aluminum aperture plate with holes which reduce the solar flux on the

diffuser (Fig. 30). The small hole size (4.32 mm diameter)

and the close spacing of the holes (6.35 mm centers) in the

attenuator ensures that images of the sun partially overlap

on the diffuser, providing a uniformly illuminated surface.

The aperture holes were drilled in a pattern that was rotated 35◦ to prevent striping of the diffuser by photolyzed

organic compounds over the 5-year life of the SeaWiFS

mission. The spacing between the diffuser and the attenuator is such that reflections from the back of the attenuator

onto the diffuser account for less than 1% of the total illumination.

The attenuator has a uniform thickness of 2.54 mm and

is tilted by 30◦ about the x axis. This design prevents

attenuator glints from reaching the diffuser. It also reduces

illumination variations as the incidence angle of the sun

varies over the seasons. Over each SeaWiFS orbit, the

instrument rotates (pitches) about the z axis (Fig. 26).

However, because of the inclination of the Earth’s axis to

the plane of the Earth’s orbit and the inclination of the

satellite’s orbit about the Earth, there is also a relative

motion of the solar incidence angle with respect to the

instrument’s xz plane over each year. This motion has a

range of ±5◦ about the x axis. It is the effect of this angular

change that the tilted attenuator reduces (Fig. 31).

5.3 LAB MEASUREMENTS

The SeaWiFS diffuser acts to convert the input irradiance from the sun into an output radiance to be measured by the instrument. The input irradiance has units

of W cm−2 μ m−1 and the output radiance has units of

W cm−2 μ m−1 sr−1, where sr is the SI unit symbol for

steradian (which is a unit of solid angle). A radiance measurement is made of a source that is large enough that

the solid angle of its surface is greater than the solid angle

viewed by the instrument. For example, SeaWiFS has been

designed so that each radiance measurement has a solid

angle equivalent to an area of 1.1×1.1 km at the Earth’s

surface at nadir. For SeaWiFS, the diffuser is measured as

a radiance source, but the sun is an irradiance source. The

solar flux is not parsed into individual units of solid angle,

but is used as the flux from the entire surface area of the

sun.

The ratio of the output radiance to the input irradiance

is known as the BRDF, with units of inverse steradians. A

perfect, 100% reflective Lambertian diffuser has a BRDF

of π−1, or 0.318. For SeaWiFS, the instrument gains were

set to measure the ocean, which is a relatively dark light

source, compared with the sun. As a result, the SeaWiFS

diffuser required a smaller BRDF, corresponding to 10%

of a perfect Lambertian diffuser. This requirement determined the diffuser design, with the diffuser plate tilted at

an angle of 60◦ to the solar illumination and with the attenuator containing an array of small holes.

5.3.1 Reflectance at Normal Incidence

In order to properly test the SeaWiFS diffuser, it was illuminated with a source having an angular subtense similar

55
SeaWiFS Calibration Topics, Part 1

Fig. 26. The on-orbit coordinate system is shown here for SeaWiFS and for the SeaWiFS diffuser (solar

calibrator). The diffuser points away from the direction of the spacecraft motion. The sun is viewed as the

spacecraft passes over the South Pole.

Fig. 27. This figure shows a detailed view of the diffuser assembly. The diffuser is painted on the inside of the

diffuser housing, behind the diffuser cover. When the solenoid is actuated, the diffuser cover rotates into the

drawing and lies on the bottom of the diffuser housing. The diffuser cover is also painted to create a second

diffuser.

56
R.A. Barnes, E-n. Yeh, and R.E. Eplee

Fig. 28. This figures shows a schematic of the diffuser assembly as viewed from above. The diffuser cover is not shown.

Fig. 29. Shown here is the reflectivity of YB71 paint as a function of wavelength.

57
SeaWiFS Calibration Topics, Part 1

Fig. 30. The pattern of the holes in the attenuator was rotated 35◦ to prevent striping of the diffuser.

Fig. 31. This is the diffuser’s response to the rotation of solar flux about the y axis. This rotation is a seasonal

effect due to the inclination of the Earth’s axis to the Earth-sun plane and the inclination of the satellite’s orbit

around the Earth. The tilted SeaWiFS attenuator greatly reduces this effect.

58
R.A. Barnes, E-n. Yeh, and R.E. Eplee

Table 27. The calculation of the solar diffuser reflectance is shown in this table. The data were taken

using a lock-in amplifier to measure the signals from the preamplifiers. The instrument output was

measured using the SeaWiFS diffuser and the amplifier output was measured using the halon diffuser.

(The reflectance of the halon diffuser was 0.99/π sr−1.) There are eight SeaWiFS bands, and each band

has four channels.

Band Channel Instrument Output Amplifier Output SeaWiFS Diffuser

[μ V] [μ V] [sr−1]

1 1 65.00 773.0

2 65.40 778.0

3 66.10 769.0

4 68.80 804.0

Average 66.33 781.0 0.0268

2 1 46.00 1,640.0

2 145.00 1,660.0

3 143.00 1,620.0

4 143.00 1,620.0

Average 144.25 1,635.0 0.0279

3 1 366.00 4,270.0

2 364.00 4,210.0

3 373.00 4,230.0

4 374.00 4,240.0

Average 369.25 4,237.5 0.0275

4 1 531.00 6,020.0

2 523.00 5,890.0

3 525.00 5,920.0

4 536.00 5,970.0

Average 528.75 5,950.0 0.0281

5 1 726.00 8,420.0

2 712.00 8,170.0

3 738.00 8,410.0

4 716.00 8,150.0

Average 723.00 8,287.5 0.0276

6 1 1,120.00 12,700.0

2 1,090.00 12,300.0

3 1,130.00 12,700.0

4 1,120.00 12,600.0

Average 1,115.00 12,575.0 0.0280

7 1 2,750.00 30,800.0

2 2,850.00 31,700.0

3 2,780.00 30,500.0

4 2,790.00 30,600.0

Average 2,792.50 30,900.0 0.0285

8 1 3,420.00 36,100.0

2 3,640.00 38,200.0

3 3,520.00 36,800.0

4 3,400.00 35,500.0

Average 3,495.00 36,650.0 0.0301

59
SeaWiFS Calibration Topics, Part 1

Table 28. This is the normalized angular response table for band 4. The azimuth angles were measured in relation

to the elevation angle with both the door deployed and the door shut.

Elevation Azimuth Angle with Door Deployed

Angle −12.40 −10.32 −8.24 −6.17 −4.11 −2.05 0.00 2.05 4.09 6.13 8.16 10.18 12.10

−0.5 96.96 99.09 98.35 97.78 99.29 99.42 99.45 100.73 101.28 100.41 100.36 100.37 99.43

0.0 98.18 98.12 98.13 98.67 100.17 99.90 100.00 100.30 99.76 100.26 99.91 101.08 99.19

0.5 97.24 97.83 98.57 98.79 98.29 98.87 99.24 101.42 100.79 100.82 100.18 101.09 100.58

1.0 96.05 98.75 97.81 98.71 98.82 100.38 101.27 100.59 100.09 99.94 101.07 100.72 100.60

2.0 95.73 98.48 98.23 98.08 99.74 99.96 99.96 101.41 100.66 101.45 100.16 100.61 100.18

3.0 94.53 97.11 98.22 99.02 98.71 99.66 100.06 100.03 101.21 100.76 100.32 99.72 99.23

4.0 97.11 96.98 97.76 97.84 98.84 98.07 99.11 101.00 100.59 100.30 100.38 100.66 98.06

4.5 95.23 97.93 96.93 98.38 99.20 99.07 98.68 99.58 99.77 101.36 100.51 100.46 99.17

5.0 95.01 97.89 97.97 98.25 98.96 99.62 99.55 101.16 100.34 100.30 99.96 101.12 99.27

5.5 95.56 97.06 97.76 98.69 98.69 99.67 99.60 99.66 100.27 101.49 101.09 100.78 100.80

Azimuth Angle with Door Shut

−0.5 100.81 99.03 99.59 98.52 99.43 99.39 100.08 99.50 99.09 99.97 98.88 99.58 92.13

0.0 100.49 97.15 99.24 98.67 100.68 100.06 100.00 100.68 100.24 99.31 99.19 100.15 92.89

0.5 97.95 97.36 97.95 98.60 99.59 99.63 98.78 101.06 99.88 100.36 99.62 99.97 91.28

1.0 98.74 97.85 98.01 98.35 98.16 100.52 100.39 99.36 101.06 100.50 99.02 99.69 94.54

2.0 98.30 97.62 97.93 98.05 98.91 99.55 100.07 100.85 101.91 100.12 99.72 99.27 93.94

3.0 99.07 96.87 97.79 98.97 99.12 99.59 98.87 99.24 100.68 100.46 100.51 98.92 91.68

4.0 100.63 96.90 97.50 98.09 99.14 98.96 100.12 100.15 101.17 99.87 98.43 99.26 91.57

4.5 101.13 97.40 97.67 98.74 98.52 98.89 100.18 99.01 99.19 100.29 99.50 97.71 92.65

5.0 102.36 98.84 96.90 98.41 98.39 99.82 99.11 99.37 99.51 98.77 99.87 97.34 90.04

5.5 102.50 98.58 97.34 97.88 98.16 98.56 100.39 99.75 99.98 99.94 100.45 97.81 90.82

Table 29. This is the normalized angular response table for band 8. The azimuth angles were measured in relation

to the elevation angle with both the door deployed and the door shut.

Elevation Azimuth Angle with Door Deployed

Angle −12.40 −10.32 −8.24 −6.17 −4.11 −2.05 0.00 2.05 4.09 6.13 8.16 10.18 12.10

−0.5 76.92 86.15 91.43 95.59 97.63 99.87 99.87 99.50 97.78 94.32 89.54 83.89 73.59

0.0 78.57 86.33 91.07 94.81 97.50 99.68 100.00 99.76 97.94 94.27 89.92 83.16 73.97

0.5 80.20 86.59 91.58 95.07 97.99 99.71 100.08 99.42 97.65 94.40 89.84 83.62 74.41

1.0 80.07 86.56 91.63 95.17 98.23 99.32 99.53 99.45 97.78 94.32 89.68 83.41 73.10

2.0 80.84 86.74 91.32 94.97 97.34 99.27 99.79 99.19 96.86 93.84 89.33 83.30 72.45

3.0 78.70 86.33 91.09 95.04 97.60 99.13 99.48 99.26 96.35 93.34 88.71 83.05 72.78

4.0 76.23 86.33 90.84 94.71 96.98 99.13 99.63 98.44 96.46 93.10 88.50 82.06 71.78

4.5 74.32 84.98 90.76 94.22 96.88 98.90 99.16 98.26 96.17 92.48 87.80 82.11 70.69

5.0 72.51 83.85 90.37 93.98 96.64 98.17 99.00 98.13 96.09 92.40 87.56 81.44 69.17

5.5 70.27 82.60 89.94 93.44 96.20 98.12 98.40 98.28 95.66 92.06 87.02 80.55 67.79

Azimuth Angle with Door Shut

−0.5 103.62 100.01 100.02 99.80 99.96 99.63 100.10 100.09 99.76 99.53 100.09 100.23 94.30

0.0 102.42 100.74 100.42 99.87 100.20 99.76 100.00 99.54 100.18 99.87 99.64 100.49 94.71

0.5 101.21 100.35 100.05 100.07 100.01 100.00 99.95 99.53 99.84 99.53 99.70 99.58 94.52

1.0 101.66 100.14 99.66 99.93 99.51 100.13 100.37 99.93 99.65 99.64 99.88 99.80 94.25

2.0 101.05 100.71 99.71 100.55 100.55 100.08 100.02 99.93 99.94 99.49 99.60 99.28 94.53

3.0 103.44 100.23 99.82 99.79 99.96 99.86 99.91 99.28 100.89 99.86 99.62 98.81 92.37

4.0 104.52 99.96 100.16 100.03 100.33 99.70 99.60 100.22 99.86 99.51 99.19 99.51 92.71

4.5 105.30 101.12 100.13 100.33 99.81 99.62 99.94 100.16 100.16 100.69 100.61 98.78 92.93

5.0 106.00 101.80 99.98 100.44 100.38 99.87 99.45 99.45 99.46 99.46 99.57 97.76 93.24

5.5 107.47 102.65 100.41 100.44 100.59 99.66 100.20 99.24 99.62 99.52 100.06 97.79 92.45

60
R.A. Barnes, E-n. Yeh, and R.E. Eplee

to the sun (0.5◦). The illumination source was a 1,000 W

calibrated lamp placed as far as possible from the diffuser

inlet (about 305 cm), yielding a divergence of 1.45◦ across

the aperture. Determining the reflectance at normal incidence required two measurements. For the first measurement, the light from the 1,000 W lamp was measured

using the SeaWiFS diffuser. For the second measurement,

the entire instrument was rotated to measure the reflected

light from a second diffuser as if it were viewing the Earth.

In the second measurement, the light from the 1,000 W

lamp was reflected off a pressed halon diffuser of known reflectance (99%). The ratio of the two measurements (SeaWiFS:halon) was used to calculate the diffuser reflectance.

These calculations are given in Table 27. For the calculations, the reflectance of the pressed halon diffuser plate

was 0.99/π at normal incidence.

5.3.2 BRDF

Normal incidence for the SeaWiFS diffuser lies along

the +y vector, that is, normal to the xz plane, facing aft

(see Fig. 26). On each orbit, SeaWiFS rotates once about

its z axis. For the BRDF measurements of the SeaWiFS

diffuser by the manufacturer, this rotation was called “a

change in elevation angle.” Over the course of a year, the

direction of the sun, relative to the xz plane, changes as

a rotation about the x axis. For the SeaWiFS calibration,

this rotation was called “a change in azimuth angle.”

The BRDF for the SeaWiFS diffuser was measured for

elevation and azimuth angles from the normal incidence

vector (+y axis). These values are shown for SeaWiFS

bands 4 (Table 28) and 8 (Table 29). The values are normalized to 100% at zero azimuth and zero elevation. Those

100% values can be converted to reflectances using the corresponding SeaWiFS diffuser reflectances at normal incidence from Table 28.

5.4 FIELD MEASUREMENTS

At the instrument manufacturer’s (SBRC) facility, two

outdoor measurements of the solar flux using the SeaWiFS

instrument and diffuser (Biggar et al. 1994 and 1995) were

performed. In the interim between the two outdoor measurements, there were modifications to SeaWiFS to ameliorate the effects of instrumentally-based stray light (Barnes

et al. 1995b). The experiments were made to simulate the

solar flux on the diffuser on orbit using measurements on

the ground.

The concept for the experiment is simple. The simulation requires only the direct solar beam, and the beam

must illuminate the diffuser at the same incidence angle

used during on-orbit measurements. Atmospheric effects

on the direct beam in the ground measurements must be

determined, and corrections for these effects must be applied to the ground results. A discussion of this correction

procedure is given by Biggar et al. (1994).

The experiment after corrections for stray light in the

instrument (Biggar et al. 1995) provided a set of predicted

top-of-the-atmosphere digital counts from SeaWiFS. These

values will be compared with digital counts from on-orbit

diffuser measurements during the initial check of the instrument. In addition, the experiment after corrections

for stray light in the instrument provided a comparison

between the outdoor (solar radiation-based) and the indoor (integrating sphere-based) determinations of the radiometric sensitivity of SeaWiFS. In this comparison, the

differences between the two methods were less than 3% for

all eight SeaWiFS bands.

61
SeaWiFS Calibration Topics, Part 1

Glossary

ADEOS Advanced Earth Observation Satellite (Japan)

BCW Band-Weighted Center Wavelength

BRDF Bidirectional Reflectance Distribution Function

BSR Band-Weighted Spectral Radiance

CHORS Center for Hydro-Optics and Remote Sensing

CZCS Coastal Zone Solor Scanner

ECW Effective Center Wavelength

EO Electrons Out

EOS-AM Earth Observing System’s morning platform

GSFC Goddard Space Flight Center

GUI Graphical User Interface

HRPT High Resolution Picture Transmission

LDEF Long Duration Exposure Facility

MODIS Moderate Resolution Imaging Spectroradiometer

NASA National Aeronautics and Space Administration

NIST National Institute of Standards and Technology

NOAA National Oceanic and Atmospheric Administration

NRT Near-Real Time

OSC Orbital Sciences Corporation

OCTS Ocean Color and Temperature Scanner

PI Photons In

PO Photons Out

RSR Relative Spectral Response

SBRC (Hughes) Santa Barbara Research Center

SeaBASS SeaWiFS Bio-Optical Archive Storage System

SeaWiFS Sea-viewing Wide Field-of-View Sensor

SIS Spherical Integrating Source

SXR SeaWiFS Transfer Radiometer

UCSBUniversity of California at Santa Barbara Laboratory.

Symbols

Lc(λ) Radiance corrected for oxygen A-band absorption.

Le Earth-exiting spectral radiance integrated over the

SeaWiFS spectral response.

Le(λ) Earth-exiting spectral radiance at a given wavelength.

Li(λ) Input radiance to the correction scheme for a given

SeaWiFS band.

Lo(λ) Output radiance from the correction scheme for a

given SeaWiFS band.

Ls Sphere spectral radiance integrated over the SeaWiFS spectral response.

Ls(λ) Spectral radiance from the integrating sphere at a

given wavelength.

Ltypical Typical radiances from the SeaWiFS specifications.

LB(λB) Band-weighted spectral radiance for the band.

ns Refractive index of air (dimensionless).

Ns Number density of the scattering molecules.

R(λ) Spectral response of the band at a given wavelength

Si Components of the spectral response for SeaWiFS

band 8.

T Temperature.

W Represents the denominator in (9).

x Abscissa or longitudinal coordinate.

y Ordinate or meridional coordinate.

z Component of orbit position.

 Emissivity.

λ Wavelength.

λB Band-weighted center wavelength.

λeff Effective center wavelength, that is, the wavelength

where Ls(λ) equals LB(λB).

λm Wavelength for maximum radiance.

λ1 Lower 1% transmission points for the band.

λ2 Upper 1% transmission points for the band

σ Rayleigh scattering cross section per molecule.

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The SeaWiFS Technical Report Series

Vol. 1

Hooker, S.B., W.E. Esaias, G.C. Feldman, W.W. Gregg, and

C.R. McClain, 1992: An Overview of SeaWiFS and Ocean

Color. NASA Tech. Memo. 104566, Vol. 1, S.B. Hooker

and E.R. Firestone, Eds., NASA Goddard Space Flight

Center, Greenbelt, Maryland, 24 pp., plus color plates.

Vol. 2

Gregg, W.W., 1992: Analysis of Orbit Selection for SeaWiFS:

Ascending vs. Descending Node. NASA Tech. Memo.

104566, Vol. 2, S.B. Hooker and E.R. Firestone, Eds.,

NASA Goddard Space Flight Center, Greenbelt, Maryland, 16 pp.

Vol. 3

McClain, C.R., W.E. Esaias, W. Barnes, B. Guenther, D. Endres, S.B. Hooker, G. Mitchell, and R. Barnes, 1992: Calibration and Validation Plan for SeaWiFS. NASA Tech.

Memo. 104566, Vol. 3, S.B. Hooker and E.R. Firestone,

Eds., NASA Goddard Space Flight Center, Greenbelt,

Maryland, 41 pp.

Vol. 4

McClain, C.R., E. Yeh, and G. Fu, 1992: An Analysis of GAC

Sampling Algorithms: A Case Study. NASA Tech. Memo.

104566, Vol. 4, S.B. Hooker and E.R. Firestone, Eds.,

NASA Goddard Space Flight Center, Greenbelt, Maryland, 22 pp., plus color plates.

Vol. 5

Mueller, J.L., and R.W. Austin, 1992: Ocean Optics Protocols

for SeaWiFS Validation. NASA Tech. Memo. 104566, Vol.

5, S.B. Hooker and E.R. Firestone, Eds., NASA Goddard

Space Flight Center, Greenbelt, Maryland, 43 pp.

Vol. 6

Firestone, E.R., and S.B. Hooker, 1992: SeaWiFS Technical

Report Series Cumulative Index: Volumes 1–5. NASA

Tech. Memo. 104566, Vol. 6, S.B. Hooker and E.R. Firestone, Eds., NASA Goddard Space Flight Center, Greenbelt, Maryland, 9 pp.

Vol. 7

Darzi, M., 1992: Cloud Screening for Polar Orbiting Visible

and IR Satellite Sensors. NASA Tech. Memo. 104566, Vol.

7, S.B. Hooker and E.R. Firestone, Eds., NASA Goddard

Space Flight Center, Greenbelt, Maryland, 7 pp.

Vol. 8

Hooker, S.B., W.E. Esaias, and L.A. Rexrode, 1993: Proceedings of the First SeaWiFS Science Team Meeting. NASA

Tech. Memo. 104566, Vol. 8, S.B. Hooker and E.R. Firestone, Eds., NASA Goddard Space Flight Center, Greenbelt, Maryland, 61 pp.

Vol. 9

Gregg, W.W., F.C. Chen, A.L. Mezaache, J.D. Chen, J.A.

Whiting, 1993: The Simulated SeaWiFS Data Set, Version 1. NASA Tech. Memo. 104566, Vol. 9, S.B. Hooker,

E.R. Firestone, and A.W. Indest, Eds., NASA Goddard

Space Flight Center, Greenbelt, Maryland, 17 pp.

Vol. 10

Woodward, R.H., R.A. Barnes, C.R. McClain, W.E. Esaias,

W.L. Barnes, and A.T. Mecherikunnel, 1993: Modeling

of the SeaWiFS Solar and Lunar Observations. NASA

Tech. Memo. 104566, Vol. 10, S.B. Hooker and E.R. Firestone, Eds., NASA Goddard Space Flight Center, Greenbelt, Maryland, 26 pp.

Vol. 11

Patt, F.S., C.M. Hoisington, W.W. Gregg, and P.L. Coronado,

1993: Analysis of Selected Orbit Propagation Models for

the SeaWiFS Mission. NASA Tech. Memo. 104566, Vol.

11, S.B. Hooker, E.R. Firestone, and A.W. Indest, Eds.,

NASA Goddard Space Flight Center, Greenbelt, Maryland, 16 pp.

Vol. 12

Firestone, E.R., and S.B. Hooker, 1993: SeaWiFS Technical

Report Series Cumulative Index: Volumes 1–11. NASA

Tech. Memo. 104566, Vol. 12, S.B. Hooker and E.R. Firestone, Eds., NASA Goddard Space Flight Center, Greenbelt, Maryland, 28 pp.

Vol. 13

McClain, C.R., K.R. Arrigo, J. Comiso, R. Fraser, M. Darzi,

J.K. Firestone, B. Schieber, E-n. Yeh, and C.W. Sullivan, 1994: Case Studies for SeaWiFS Calibration and Validation, Part 1. NASA Tech. Memo. 104566, Vol. 13,

S.B. Hooker and E.R. Firestone, Eds., NASA Goddard

Space Flight Center, Greenbelt, Maryland, 52 pp., plus

color plates.

Vol. 14

Mueller, J.L., 1993: The First SeaWiFS Intercalibration RoundRobin Experiment, SIRREX-1, July 1992. NASA Tech.

Memo. 104566, Vol. 14, S.B. Hooker and E.R. Firestone,

Eds., NASA Goddard Space Flight Center, Greenbelt,

Maryland, 60 pp.

Vol. 15

Gregg, W.W., F.S. Patt, and R.H. Woodward, 1994: The Simulated SeaWiFS Data Set, Version 2. NASA Tech. Memo.

104566, Vol. 15, S.B. Hooker and E.R. Firestone, Eds.,

NASA Goddard Space Flight Center, Greenbelt, Maryland, 42 pp., plus color plates.

Vol. 16

Mueller, J.L., B.C. Johnson, C.L. Cromer, J.W. Cooper, J.T.

McLean, S.B. Hooker, and T.L. Westphal, 1994: The Second SeaWiFS Intercalibration Round-Robin Experiment,

SIRREX-2, June 1993. NASA Tech. Memo. 104566, Vol.

16, S.B. Hooker and E.R. Firestone, Eds., NASA Goddard

Space Flight Center, Greenbelt, Maryland, 121 pp.

Vol. 17

Abbott, M.R., O.B. Brown, H.R. Gordon, K.L. Carder, R.E.

Evans, F.E. Muller-Karger, and W.E. Esaias, 1994: Ocean

Color in the 21st Century: A Strategy for a 20 -Year Time

Series. NASA Tech. Memo. 104566, Vol. 17, S.B. Hooker

and E.R. Firestone, Eds., NASA Goddard Space Flight

Center, Greenbelt, Maryland, 20 pp.

Vol. 18

Firestone, E.R., and S.B. Hooker, 1995: SeaWiFS Technical

Report Series Cumulative Index: Volumes 1–17. NASA

Tech. Memo. 104566, Vol. 18, S.B. Hooker and E.R. Firestone, Eds., NASA Goddard Space Flight Center, Greenbelt, Maryland, 47 pp.

64
R.A. Barnes, E-n. Yeh, and R.E. Eplee

Vol. 19

McClain, C.R., R.S. Fraser, J.T. McLean, M. Darzi, J.K. Firestone, F.S. Patt, B.D. Schieber, R.H. Woodward, E-n. Yeh,

S. Mattoo, S.F. Biggar, P.N. Slater, K.J. Thome, A.W.

Holmes, R.A. Barnes, and K.J. Voss, 1994: Case Studies

for SeaWiFS Calibration and Validation, Part 2. NASA

Tech. Memo. 104566, Vol. 19, S.B. Hooker, E.R. Firestone,

and J.G. Acker, Eds., NASA Goddard Space Flight Center,

Greenbelt, Maryland, 73 pp.

Vol. 20

Hooker, S.B., C.R. McClain, J.K. Firestone, T.L. Westphal,

E-n. Yeh, and Y. Ge, 1994: The SeaWiFS Bio-Optical

Archive and Storage System (SeaBASS), Part 1. NASA

Tech. Memo. 104566, Vol. 20, S.B. Hooker and E.R. Firestone, Eds., NASA Goddard Space Flight Center, Greenbelt, Maryland, 40 pp.

Vol. 21

Acker, J.G., 1994: The Heritage of SeaWiFS: A Retrospective on the CZCS NIMBUS Experiment Team (NET) Program. NASA Tech. Memo. 104566, Vol. 21, S.B. Hooker

and E.R. Firestone, Eds., NASA Goddard Space Flight

Center, Greenbelt, Maryland, 43 pp.

Vol. 22

Barnes, R.A., W.L. Barnes, W.E. Esaias, and C.R. McClain,

1994: Prelaunch Acceptance Report for the SeaWiFS Radiometer. NASA Tech. Memo. 104566, Vol. 22, S.B. Hooker, E.R. Firestone, and J.G. Acker, Eds., NASA Goddard

Space Flight Center, Greenbelt, Maryland, 32 pp.

Vol. 23

Barnes, R.A., A.W. Holmes, W.L. Barnes, W.E. Esaias, C.R.

McClain, and T. Svitek, 1994: SeaWiFS Prelaunch Radiometric Calibration and Spectral Characterization. NASA

Tech. Memo. 104566, Vol. 23, S.B. Hooker, E.R. Firestone,

and J.G. Acker, Eds., NASA Goddard Space Flight Center,

Greenbelt, Maryland, 55 pp.

Vol. 24

Firestone, E.R., and S.B. Hooker, 1995: SeaWiFS Technical

Report Series Cumulative Index: Volumes 1–23. NASA

Tech. Memo. 104566, Vol. 24, S.B. Hooker and E.R. Firestone, Eds., NASA Goddard Space Flight Center, Greenbelt, Maryland, 36 pp.

Vol. 25

Mueller, J.L., and R.W. Austin, 1995: Ocean Optics Protocols

for SeaWiFS Validation, Revision 1. NASA Tech. Memo.

104566, Vol. 25, S.B. Hooker, E.R. Firestone, and J.G.

Acker, Eds., NASA Goddard Space Flight Center, Greenbelt, Maryland, 66 pp.

Vol. 26

Siegel, D.A., M.C. O’Brien, J.C. Sorensen, D.A. Konnoff, E.A.

Brody, J.L. Mueller, C.O. Davis, W.J. Rhea, and S.B.

Hooker, 1995: Results of the SeaWiFS Data Analysis

Round-Robin (DARR-94), July 1994. NASA Tech. Memo.

104566, Vol. 26, S.B. Hooker and E.R. Firestone, Eds.,

NASA Goddard Space Flight Center, Greenbelt, Maryland, 58 pp.

Vol. 27

Mueller, J.L., R.S. Fraser, S.F. Biggar, K.J. Thome, P.N. Slater,

A.W. Holmes, R.A. Barnes, C.T. Weir, D.A. Siegel, D.W.

Menzies, A.F. Michaels, and G. Podesta, 1995: Case Studies for SeaWiFS Calibration and Validation, Part 3. NASA

Tech. Memo. 104566, Vol. 27, S.B. Hooker, E.R. Firestone,

and J.G. Acker, Eds., NASA Goddard Space Flight Center,

Greenbelt, Maryland, 46 pp.

Vol. 28

McClain, C.R., K.R. Arrigo, W.E. Esaias, M. Darzi, F.S. Patt,

R.H. Evans, J.W. Brown, C.W. Brown, R.A. Barnes, and

L. Kumar, 1995: SeaWiFS Algorithms, Part 1. NASA

Tech. Memo. 104566, Vol. 28, S.B. Hooker, E.R. Firestone,

and J.G. Acker, Eds., NASA Goddard Space Flight Center,

Greenbelt, Maryland, 38 pp., plus color plates.

Vol. 29

Aiken, J., G.F. Moore, C.C. Trees, S.B. Hooker, and D.K.

Clark, 1995: The SeaWiFS CZCS-Type Pigment Algorithm. NASA Tech. Memo. 104566, Vol. 29, S.B. Hooker

and E.R. Firestone, Eds., NASA Goddard Space Flight

Center, Greenbelt, Maryland, 34 pp.

Vol. 30

Firestone, E.R., and S.B. Hooker, 1996: SeaWiFS Technical

Report Series Cumulative Index: Volumes 1–29. NASA

Tech. Memo. 104566, Vol. 30, S.B. Hooker and E.R. Firestone, Eds., NASA Goddard Space Flight Center, Greenbelt, Maryland, 43 pp.

Vol. 31

Barnes, R.A., A.W. Holmes, and W.E. Esaias, 1995: Stray

Light in the SeaWiFS Radiometer. NASA Tech. Memo.

104566, Vol. 31, S.B. Hooker, E.R. Firestone, and J.G.

Acker, Eds., NASA Goddard Space Flight Center, Greenbelt, Maryland, 76 pp.

Vol. 32

Campbell, J.W., J.M. Blaisdell, and M. Darzi, 1995: Level-3

SeaWiFS Data Products: Spatial and Temporal Binning

Algorithms. NASA Tech. Memo. 104566, Vol. 32, S.B.

Hooker, E.R. Firestone, and J.G. Acker, Eds., NASA Goddard Space Flight Center, Greenbelt, Maryland, 73 pp.,

plus color plates.

Vol. 33

Moore, G.F., and S.B. Hooker, 1996: Proceedings of the First

SeaWiFS Exploitation Initiative (SEI) Team Meeting.

NASA Tech. Memo. 104566, Vol. 33, S.B. Hooker and

E.R. Firestone, Eds., NASA Goddard Space Flight Center, Greenbelt, Maryland, 53 pp.

Vol. 34

Mueller, J.L., B.C. Johnson, C.L. Cromer, S.B. Hooker, J.T.

McLean, and S.F. Biggar, 1996: The Third SeaWiFS Intercalibration Round-Robin Experiment (SIRREX-3), 19–

30 September 1994. NASA Tech. Memo. 104566, Vol. 34,

S.B. Hooker, E.R. Firestone, and J.G. Acker, Eds., NASA

Goddard Space Flight Center, Greenbelt, Maryland, 78 pp.

Vol. 35

Robins, D.B., A.J. Bale, G.F. Moore, N.W. Rees, S.B. Hooker,

C.P. Gallienne, A.G. Westbrook, E. Mara ̃n ́on, W.H.

Spooner, and S.R. Laney, 1996: BAOPW-1 Cruise Report

and Preliminary Results. NASA Tech. Memo. 104566, Vol.

35, S.B. Hooker and E.R. Firestone, Eds., NASA Goddard

Space Flight Center, Greenbelt, Maryland, 87 pp.

Vol. 36

Firestone, E.R., and S.B. Hooker, 1996: SeaWiFS Technical

Report Series Cumulative Index: Volumes 1–35. NASA

Tech. Memo. 104566, Vol. 36, S.B. Hooker and E.R. Firestone, Eds., NASA Goddard Space Flight Center, Greenbelt, Maryland, (in press).

65
SeaWiFS Calibration Topics, Part 1

Vol. 37

Johnson, B.C., S.S. Bruce, E.A. Early, J.M. Houston, T.R.

O’Brian, A. Thompson, S.B. Hooker, and J.L. Mueller,

1996: The Fourth SeaWiFS Intercalibration Round-Robin

Experiment (SIRREX-4), May 1995. NASA Tech. Memo.

104566, Vol. 37, S.B. Hooker and E.R. Firestone, Eds.,

NASA Goddard Space Flight Center, Greenbelt, Maryland, 65 pp.

Vol. 38

McClain, C.R., M. Darzi, R.A. Barnes, R.E. Eplee, J.K. Firestone, F.S. Patt, W.D. Robinson, B.D. Schieber, R.H.

Woodward, and E-n. Yeh, 1996: SeaWiFS Calibration and

Validation Quality Control Procedures. NASA Tech.

Memo. 104566, Vol. 38, S.B. Hooker and E.R. Firestone,

Eds., NASA Goddard Space Flight Center, Greenbelt, Maryland, 68 pp.

Vol. 39

Barnes, R.A., E-n. Yeh, and R.E. Eplee, 1996: SeaWiFS Calibration Topics, Part 1. NASA Tech. Memo. 104566, Vol.

39, S.B. Hooker and E.R. Firestone, Eds., NASA Goddard

Space Flight Center, Greenbelt, Maryland, 66 pp.

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Laboratory for Hydrospheric Processes

Goddard Space Flight Center 97B00004

Greenbelt, Maryland 20771

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NSN 7540-01-280-5500 Standard Form 298 (Rev. 2-89) Prescribed by ANSI Std. 239-18, 298-102

 SeaWiFS Technical Report Series

Volume 39–SeaWiFS Calibration Topics, Part 1

 Code 970.2

 October 1996 Technical Memorandum

Elaine R. Firestone, Robert A. Barnes, Eueng-nan Yeh, and Robert E. Eplee: General Sciences Corporation, Laurel, Maryland

 -

SeaWiFS, Oceanography, Calibration, Validation, Blackbody Temperature 66

Spectral Shape, Radiance Measurements, Spectral Responses, Center Wavelengths,

Solar Diffuser

6. AUTHOR(S)

 Robert A. Barnes, Eueng-nan Yeh, and Robert E. Eplee

 Series Editors: Stanford B. Hooker and Elaine R. Firestone

National Aeronautics and Space Administration

Washington, D.C. 20546–0001 TM–104566, Vol. 39

13. ABSTRACT (Maximum 200 words)

For Earth-observing satellite instruments, it was standard to consider each instrument band to have a spectral response that

is infinitely narrow, i.e., to have a response from a single wavelength. The SeaWiFS bands, however, have nominal spectral

bandwidths of 20 and 40 nm. These bandwidths affect the SeaWiFS measurements on orbit. The effects are also linked to

the manner in which the instrument was calibrated and to the spectral shape of the radiance that SeaWiFS views. Currently,

SeaWiFS is calibrated such that the digital counts from each instrument band are linked to the Earth-exiting radiance at an

individual center wavelength. Before launch, SeaWiFS will be recalibrated so that the digital counts from each band will be

linked to the Earth-exiting radiance integrated over the spectral response of that band. In this technical memorandum, the

effects of the instrument calibration and the source spectral shape on SeaWiFS measurements, including the in-band and

out-of-band responses, and the center wavelengths are discussed.