This study measures the extent to which an integrat-ing sphere’s uniformity is disrupted when the pri-mary optical system being calibrated protrudessignificantly into its interior. Previous researchershave studied larger spheres and less intrusion intothe spherical cavity.1 In the current study I reporton a map of the radiant intensity flatness of the insidesurface of a 50-cm integrating sphere characterizingthe Descent Imager–Spectral Radiometer ~DISR!, theonly optical instrument on the Huygens probe of theCassini mission to Saturn.2 In November 2004 thisprobe is planned to descend into the atmosphere ofTitan, Saturn’s largest moon, and become the firstcamera to view the satellite’s lower atmosphere andsurface from within the atmosphere. It will mea-sure upward- and downward-streaming fluxes oflight throughout the atmosphere in the UV, visible,and near-IR spectral ranges to derive an altitudinalprofile of the radiative forcing.
DISR’s subsystems are summarized in Table 1.For their calibration, a 50-cm integrating sphere pro-vides distinct advantages: ~1! a homogeneous, Lam-
B. Rizk [email protected]! is with the Lunar and Plan-etary Laboratory, University of Arizona, 1629 E. University Bou-levard, Tucson, Arizona 85721-0092.
Received 21 July 2000; revised manuscript received 26 January2001.
ertian surface for flat fielding the imagers, ~2! apectrally featureless reflectance curve for character-zing the spectral responsivity of imagers and spec-rometers, ~3! an enclosure easily purged with dryitrogen permitting detector focal planes to be cooledo their field temperatures during measurements ofbsolute responsivity, ~4! a surface that is sufficientlyomogeneous and Lambertian that its absoluterightness can be faithfully calibrated by standardnd auxiliary detectors, and ~5! an ability to accom-odate optical systems with wide fields of view.The wall brightness of a typical integrating sphere
utside the first bounce region is uniform to a highrder when the sphere is illuminated and observedhrough ports that lie flush to the sphere’s surfacend when there are no structures inside that occupyhe sphere’s internal volume as opposed to represent-ng a two-dimensional area on the inside wall surface.
Calibrating DISR violates this condition. Theront housing of the sensor head ~SH! possesses aross section of 10 cm 3 12.5 cm and protrudes somecm into the interior of the sphere, as shown in Fig.
. Its surface area is approximately 200 cm2, is cov-ered in textured black foam, and sports asymmetricalprotrusions: three bear’s-ear baffles, a shadow bar,and a sunshade for one of the imagers, as shown inFig. 2. The asymmetry of this black lopped-off co-lumnar object tends to spoil the uniformity of a spher-ical surface radiance normally achieved by the jointoperation of angle-independent scattering, the pro-jected surface area, and the inverse-square law.
An apparatus is built to quantify the radiance vari-
1 May 2001 y Vol. 40, No. 13 y APPLIED OPTICS 2095
Table 1. DISR Sybsystems
2
ations. A radiance map of the inside of the sphere isderived from data mapping the interior wall’s bright-ness variations. The discussion below describes theapparatus used to gather the brightness data andpresents the map.
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096 APPLIED OPTICS y Vol. 40, No. 13 y 1 May 2001
2. Apparatus
The integrating sphere, supplied by Labsphere, mea-sures 50 cm in diameter with one section removed tocreate a main port with a diameter of 20 cm. Itsinterior is coated with Spectraflect, Labsphere’sbarium-sulfate-textured surface. Six 5-cm ports aremounted on the sphere’s equatorial plane, three toeach side of the large central port, making a total ofseven ports on the back hemisphere and no ports onthe front hemisphere. The ports are numbered from1 to 7 starting with the leftmost port as viewed fromthe point of view of the SH and moving counterclock-wise. The location and use of each port is outlined inTable 2. Azimuths increase counterclockwise from0o at the main port to 180o on the front wall. Unusedports are capped with port covers internally coatedwith material identical to that coating the bulk of thesphere.
Photons enter the sphere at port 5. They arelargely removed by absorption either by the surface ofthe SH or at one of the ports where monitoring orcalibrating detectors are positioned. Only absorp-tion at a port preserves the homogeneity of the spherewall’s radiance. Both entry and absorption on theSH’s surface contribute to nonuniformity in the radi-ance, as is well known for integrating spheres. Re-ferring to Fig. 3, given a Lambertian bright or darkarea A on the inside surface, we see that the sphericaleometry will cause the irradiance E at an arbitraryambertian point P on the sphere wall from A, which
Fig. 1. Schematic showing the relative size, orientation, andplacement of the DISR SH with respect to the 50-cm-diameterintegrating sphere used as the test station for performing many ofthe calibrations.
Table 2. Port Assignments
Fig. 2. DISR SH seen from above and below, attached to theHuygens probe.
is expressed as the product of A’s radiance, L, and theprojected solid angle V it subtends from P, oriented atangle a to the normal, to be constant for all P at anygiven wavelength l:
E 5 LV 5LA cos a cos a
d2 5LA cos2 a
d2 5LA cos2 a
4r2 cos2 a
5LA4r2 . (1)
The apparatus used to characterize the internalradiance of DISR’s calibration sphere is shown in Fig.4. It consists of five main parts: ~1! a metal shell,the dummy SH ~DSH!, covered in the same foam andblack paint and possessing the same external dimen-sions as the actual SH except for a circular 5-cm-diameter cavity at the front, voluminous enough to
Fig. 3. Diagram displaying the geometry that relates a dark orbright first-bounce region A with an arbitrary point P on thesphere’s interior wall. The various angles and line segments arelabeled.
Fig. 4. Photographs depicting the DSH, the apparatus used tomeasure the spatial dependence of radiance on location within theDISR calibration sphere. The various components of the assem-bly are described in the text.
accommodate a fork-mounted turret assembly; ~2! the4-cm-diameter turret assembly, capable of pointing a2.5-cm brass tube at different angles from the centralaxis of the integrating sphere; ~3! a broadband silicon
hotodiode mounted within the brass tube in front oflens; ~4! a 20-cm brass tube aligned with the centralxis that penetrates the DSH’s cover plate and con-ects perpendicularly to an adjusting arm that posi-ions the fork assembly at different angles around theentral axis; and ~5! a cover plate that serves as theSH’s mounting interface to the sphere itself. In-entations in the plate locate and lock the adjustingrm at different angles.The central and the auxiliary ports of the integrat-
ng sphere are all positioned on the sphere’s equator.ll dark and first-bounce bright regions of the spherere thus confined to the equator. The entrance win-ows of DISR’s various instruments are mounted onhe front of the SH and look upward and downward,ut none of them, except for the side-looking imager,nclude the equatorial region of the integratingphere within their field of view. The side-lookingmager looks toward the front of the integratingphere ~f 5 180o!, expected to be the most uniformegion of the sphere.
The port arrangement is summarized above in Ta-le 2. Attached to the ports of the integratingphere are the broadband lamp source at port 5 andtriplet of auxiliary detectors at port 1. At port 2,
n absolutely calibrated monochromator-detectorystem is mounted in a configuration identical to thaturing the DISR absolute calibrations.At port 1, mounted behind a diffuser in a common
hermal block, is a triplet of three detectors: anG&G UV-245BG silicon photodiode used in a broad-and configuration, an identical UV-245BG siliconhotodiode filtered by a 100-nm-wide bandpass filterentered at 430 nm, and an EPITAXX ETX 3000T5nGaAs photodiode ~responding from 0.8 to 1.7 mm!
used in a broadband mode. The temperature of thedetector block is stabilized to a temperature just afew degrees above room temperature by resistiveheaters. Of these three auxiliary detectors, thebroadband silicon photodiode monitors the generallevel of luminance inside the integrating sphere. Itprovides a temporal reference for an identical detec-tor mounted in the turret, under the expectation thatfluctuations in a quartz–tungsten–halogen ~QTH!lamp output cause variations in the average radi-ance. It is estimated that an additional source ofvariation in the radiant uniformity, the changing ge-ometry of the DSH and its solid angle V caused by the
ovement of the turret in its fork mount through thewo-degrees-of-freedom range, introduces little addi-ional error; however, the auxiliary detectors alsoonitor this variation and are used to correct it.he turret detector used to gather the homogeneityata is an EG&G UV-245BG silicon photodiode usingroadband, identical to the silicon broadband detec-or used in the auxiliary triplet of detectors mountedt port 1.At port 5 the source of light for the integrating
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sphere is a condensing-focusing system fed by a150-W broadband QTH bulb. The beam of light isdirected at a baffle mounted 5 cm within the inte-grating sphere aligned to the port. The baffle ispositioned at an angle of 45o to the normal of theport so as to direct first-bounce light toward theback of the integrating sphere, i.e., next to wherethe DISR SH or DSH is mounted, but away from thesubsystem windows. The QTH source is shut-tered.
The spatial homogeneity apparatus achieves ageneral pointing accuracy of a few tenths of a de-gree. The field of view of the detector–lens config-uration possesses a FWHM responsivity of some10o. The center of rotation of the two-axis systems located at a distance of 8.6 cm from the edge of thephere along the central axis, running normal to thearge central port. The back of the sphere is de-ned to be the side containing the large centralort, the front the side toward which the SH andSH look.The angles a and b that characterize the different
positions of the fork-mounted turret assembly aredefined in Fig. 5. The detector fork-mounted as-sembly rotates about the central axis manually, us-ing the adjustment arm. The hollow brass tubethat penetrates the 20-cm-diameter cover plateguides the wires conducting the detector signal to aconnector outside the integrating sphere. The ad-
Fig. 5. Schematic defining the angles a and b.
098 APPLIED OPTICS y Vol. 40, No. 13 y 1 May 2001
justing arm can be placed at any angle and can belocked into position at any one of 36 detent posi-tions, spaced at 10o intervals to within 0.1o. Thefork-mounted assembly rotates about an axis per-pendicular to the central axis of the sphere to orientthe 4-cm brass tube containing the detector andlens assembly to different angles with respect to thecentral axis. As with the cover plate and adjustingarm, detents are accurately placed at 10o intervalson the body of the fork assembly turret, allowing thedetector barrel to be locked into positions fromstraight ahead ~a 5 0o! to a 5 110o, which points thebarrel toward the rear of the integrating sphere butnot all the way to the axis. The turret is preventedfrom turning to examine the DSH by the DSH’s ownshell.
3. Data Analysis
The data consists of ;5300 turret and simultaneousauxiliary-silicon detector signals mediated by similartransimpedance amplifying circuits and then digi-tized and recorded with a computer interface. A to-tal of 316 distinct directions within the sphere aresampled, each with a between 0 and 110o in 10o in-crements and b between 0 and 360o at increments inmultiples of 10o. Measurements at each directionare performed in sets of ten and then averaged. Thepointing angles of the fork-mounted detector assem-bly are chosen to achieve as uniform a density ofpoints as possible. The measurement locations areindicated with asterisks in Fig. 6.
The 150-W QTH FDS broadband source illumi-nating the integrating sphere during the measure-ments is identical in characteristics and injectiongeometry to lamps used during DISR absolute cal-ibrations and flat-fielding. The lamps are drivenat their design current of 6.25 A. At this currentthey typically last 100 h. The lamp used has beenrun for 5 h when the measurements begin and isthen used for 22 h. It is powered by an OptronicLabs OL-65S dc supply.
At each point on the interior surface of the inte-grating sphere, ten bright ~shutter open! detectoreadings are recorded in a group at a specific a and betting before the adjusting arm is moved to a new betting. At the end of the group of b settings, theort cover is unmounted from the integrating spherend the fork-mounted assembly moved to a new aetting. At the beginning and end of each circle of beadings, a group of four dark ~shutter closed! mea-urements are recorded.All turret and auxiliary-silicon signals are dark
ubtracted by an average of the most nearly coinci-ent darks and then the turret readings divided byhe simultaneous auxiliary-silicon signals to take outariations in the general brightness level inside thephere that are due to lamp fluctuations and geome-ry shifts. The normalized signals are transformedrom the apparatus’ ~a, b! system to a sphere-
wambl9
gacbtbmdrdibortt
centered ~u, f! Mercator system by use of the follow-ing relations
x 5 2@r2 2 ~r 2 d!2sin2 a]1y2 cos a 1 ~r 2 d!sin2 a,
y 5 @r2 2 ~r 2 d!2sin2 a#1y2 sin a cos b
1 cos a~r 2 d!sin a cos b,
z 5 @r2 2 ~r 2 d!2sin2 a#1y2 sin a sin b
1 cos a~r 2 d!sin a sin b,
u 5 cos21~ zyr!,
f 5 tan21~ yyx!, (2)
here r is the radius of the sphere and d is the offsetlong the central axis of the pivot point for the fork-ounted turret. In the sphere-centered system the
ack center of the sphere, where the DISR SH isocated, is at u 5 90o, f 5 0o, the front center is at u 50o, f 5 180o, the top is at u 5 0o, and the bottom is
at u 5 180o.The percentage difference between a typical nor-
malized signal and the average of those at thesphere’s front center is computed. The resulting iso-photic contour is displayed in Fig. 6. Each contourline is labeled with the percentage deviation inbrightness from the front center of the sphere, wherethe deviation is defined to be zero. Positive devia-tions represent brighter regions. Also displayed arethe 316 points where measurements occur, denotedby asterisks, and the outlines of the fields of view ofthe various DISR instruments. Refer to Table 1 for
Fig. 6. Spatial radiance profile of the interior of the DISR calibraapproximates the radiance field when the DSH is replaced withmarked in percentage ~%! deviation relative to the front center of tmarked with asterisks. The boundaries of the fields of view of th
the specifications of the pointing and fields of view ofthe various DISR instruments.
The data presented in Fig. 6 is used to construct agray-scale image of the inside of the DISR calibrationsphere as seen in a piecewise fashion by the DSHapparatus. It is displayed in Fig. 7. The scale ofsignificant variations in integrating sphere derivedbrightness over the front half of the sphere is found tobe several factors larger than the sampling area ofthe detector, indicating that the general results arelargely independent of the detector sampling area.
The main correctable sources of error in the mea-surement are ~1! drift in the lamp, ~2! the changingeometry of the fork-mounted turret assembly as thengle b is varied around a full circle, and ~3! thehanging geometry of the fork-mounted turret assem-ly as the angle a is varied through its range. Allhese effects are essentially corrected by division ofy the reference silicon detector measurements. Ainor source of error, the nonzero settling time of the
etector and differences in brightness caused byeadings occurring at different relative times, is re-uced to a negligible magnitude by means of averag-ng each set of ten measurements. The integratedrightness of the integrating sphere drifts by ;3%ver the 22-h period over which measurements areecorded, as determined by the auxiliary-silicon de-ector. The brightness variation over a full cycle ofhe angle b is typically ;0.7%.
The major uncorrectable error in the isophotic con-tours displayed in Fig. 6 is caused by the extent towhich the exact shape of the DSH differs from that ofthe DISR SH as viewed from various points on the
sphere subject to the absorbing region of the DSH. It accuratelyctual DISR SH. Relative brightness contours, or isophotes, aretegrating sphere. The locations of the actual measurements are
rious DISR instruments are indicated.
tionthe ahe ine va
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sphere’s interior. The main morphological dissimi-larity is the existence of the fork turret on the front ofthe DSH. The cross section of the fork turret is some15 cm2, compared with the typical 155-cm2-frontcross section of the SH’s main structure or to its61-cm2-side cross section. The error is basically neg-igible on the front wall, where the turret’s cross sec-ion is lost against the larger solid angle of the SH.t begins to become noticeable starting at points morehan ;75o away from the front center of the sphere,here the turret can be seen as a silhouette protrud-
ng outward from the front of the SH. Toward theide, top, and back of the sphere, the error incurred athese locations may approach 25% of the recordedelative brightness deviations. In between, the er-or is generally of the order of 10%. In any case, it isn unavoidable error, correctable only by modeling ofhe sphere’s internal brightness in a detailed fashion,omething not performed in this study.
4. Discussion
As Fig. 6 implies, most of the variation in relativeradiance over the area of the integrating sphereseems to be related to three effects: ~1! the locationof a point either within a dark region such as theports where auxiliary detectors, the monochromator,or the DISR itself is mounted; ~2! the location of apoint within the bright first-bounce region of thelamp injection port and baffle; or ~3! the proximity ofa point to the region of the DISR SH at port 4 and theinjection baffle at port 5. The degree of variation ishighly nonlinear: little variation is seen over a widerange for distant points, whereas much more rapidvariation occurs over small distances for points nearthe SH. The first and the second effects would hold
Fig. 7. Gray-scale image constructed of the inside of the 50-cm-dibased on the DSH.
100 APPLIED OPTICS y Vol. 40, No. 13 y 1 May 2001
true for any integrating sphere with dark or brightregions. The third effect holds because of the exis-tence of the DISR SH within the volume of thesphere. The shape and the magnitude of its solidangle for nearby points versus distant ones does fol-low the cosine dependence necessary to achieve auniform field. The source injection baffle also con-tributes to the nonhomogeneity though to much lessa degree.
The variation in brightness over the integratingsphere’s front surface is minor, attaining a maximumof 12% and a minimum of 22%, both located near theequator and thus out of the field of view of most DISRinstruments. The asymmetry of the radiance profilereflects the change in the shape of the DSH, espe-cially the shadow bar, as seen from those two loca-tions. Within the fields of view of most of the DISRinstruments, the variation is 1–2% and only at theedges of the hemispherical instruments does this in-crease to 6–8%. Even in the downward-looking in-struments whose fields of view are right under port 4,the variation from the front of the sphere is no morethan 2–3%.
Much of the brightness variation within the sphereoccurs on the equator, where all the ports are located,where the light is injected and where the main ab-sorbing surface—the DISR itself—is positioned.This aspect of the brightness variation is achieved byconfinement the ports to the equator of the back halfof the sphere. But most of the DISR’s instrumentsdo not look at the equator; the only instrument whosefield of view includes the equator—the side-lookingimager—looks only at the front half of the sphere,where the variation is slightest.
er DISR calibration sphere derived from the spatial radiance map
amet
5. Conclusions
An integrating sphere of 50-cm diameter used forradiometric calibration provides an internal radiancefield flat to less than 2% over two-thirds of the inte-rior including the entire front wall even when theprimary optical system being calibrated possesses asubstantial surface area and protrudes significantlyinto its interior. Even an instrument with a field ofview approaching that of p, looking either upwardand downward, is able to assume the sphere’s inter-nal radiance field to be uniform.
As might be expected, significant variations fromhomogeneity, ranging from 10% to 100%, occur nearthe objects that protrude into the sphere’s internalvolume and in the first-bounce regions of photon in-jection and removal. At distances comparable withthe radius of the sphere or greater, the three-dimensional relief associated with these objects is not
as detectable, and the object’s cross section from onepoint is similar from many points of view. At thesepoints, departures from homogeneity are 0–2%.
The author thanks David Buchhauser, Mike Bush-roe, and Chuck Fellows for their superlative engi-neering of the measurement hardware and softwareand Martin Tomasko for his helpful comments aboutthe manuscript.
Reference and Note1. W. A. Hovis and J. S. Knoll, “Characteristics of an internally
2. M. G. Tomasko, D. Buchhauser, M. Bushroe, L. E. Dafoe, L. R.Doose, A. Eibl, C. Fellows, E. McFarlane, G. M. Prout, M. J.Pringle, B. Rizk, C. See, P. H. Smith, and K. Tsetsenekos arepreparing a manuscript to be called “The descent imageryspec-tral radiometer ~DISR! experiment on the Huygens entry probeof Titan.”
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