Integrating Sphere for Luminan e Calibration
Peter D. His o ks
Sys omp Ele troni Design Limited
petersys ompdesign. om
First Draft: 23 August 2011
Revised: 24 Mar h 2012
Revision 2: 30 O tober 2013
Revision 4: 26 O tober 2015
Revision 5: 26 De ember 2016

Abstra t

A digital amera an be used to measure and do ument s ene luminan e, providing the amera
an be alibrated by photographing a sour e of known luminan e.
This paper des ribes a low- ost, purpose-built integrating sphere whi h reates uniform, diuseeld of light at an opening in the sphere. The illuminan e at this port an be measured using alow- ost luxmeter. The luminan e is then a simple fun tion of the illuminan e and so the luminan eof the shere port is a known value for amera alibration.
The integrating sphere has other appli ations, among them measuring the total output ux of alight sour e, and determining the ree tan e of materials.

Figure 1: Integrating Sphere, showing lat hes, base and DC power ja k for the LED light sour e.

1 Introdu tion
This proje t arose out of a need to measure the luminan e of light pollution sour es. A modern digital
amera an be used for su h measurements, but it requires alibration with a sour e of known luminan e.
1. Suitable sour es of standard luminan e are available in the standards laboratories, but a ess isexpensive1 .
2. A alibrated luminan e meter is expensive. For example the Minolta LS-100 Luminan e Meter
osts about $3300 [1℄. The Tektronix J16 Photometer with 6503 luminan e probe is sometimes
available for a reasonable pri e on the surplus market. Be prepared to repla e the power supply(whi h is NiCad battery based). The luminan e probe may require alibration.
3. A photographi spot meter an be used to measure exposure value. This an then be related toluminan e [2℄. A new spot meter is expensive, typi ally $800, but they are o asionally available
used. We obtained a used Minolta-M spotmeter for $350.
4. An illuminan e meter (measuring in lux or foot- andles) is an inexpensive instrument, osting
about $60. See for example the Maste h LX1330B [3℄. If luminan e and illuminan e an be
related, then the alibration an be done with this instrument. That turns out to be the ase.
It an be shown (see referen e [4℄ and se tion 7.2) that illuminan e and luminan e are related as :
L=

E
π

(1)

where:
EL

is the illuminan e in lux
is the luminan e in andela per metre2

For this equation to apply, the sour e of illumination must be uniform and diuse whi h, it turns
out, is available at the aperture of an integrating sphere.

2 The Integrating Sphere
The integrating sphere is a hollow sphere that isoated on the inside surfa e with a ree tive, diusing paint. The sphere is equipped with one or moremeasuring ports  in this ase, a single opening. A
light sour e is pla ed inside the sphere, shielded sothat it is not dire tly visible from the measuring
port. Light from the sour e ree ts repeatedly fromthe sphere painted surfa e, resulting in a uniform
light eld over the interior surfa e. Viewed from theport, light intensity has equal magnitude irrespe tive of dire tion, that is, the light eld is uniform
and diuse, as required by equation 1.
Figure 2: Integrating Sphere, Measuring Port LuConsequently, it should be possible to relate il- minan eluminan e and luminan e by the following:
The illuminan e meter is pla ed in the diuse light eld at the output port the integrating
sphere to measure E . The luminan e L at the port opening is predi ted a ording to equation
1. The port is then a alibrated sour e of luminan e for a digital amera or luminan e meter(gure 2).
1 The National Resear h Coun il of Canada quoted $1800 to2

alibrate a luminan e meter.

2.1

Constru tion

A ording to [5℄, to avoid signi ant impa t on the operation of the sphere the port opening should be
no more than 5% of the total area. For the instruments in our olle tion, the largest illuminan e meter
sensor area is 2.1 in hes in diameter. A port of that diameter would require a sphere diameter of 11
in hes diameter, minimum.
A suitable basis for the sphere was found at the lo al Ikea store, a 14 in h diameter stainless steel
mixing bowl2 .
Ea h of these bowls has a 3 in h diameter at at the base of the bowl. The at base of one sphere
was used for the port, whi h was opened with a 2.25 in h Greenlee hassis pun h. The at of the othersphere was pounded out mat h the urvature of the bowl. The pounding was a omplished with a 2"x4"
wooden post, rounded at one end with a belt sander to roughly mat h the urvature of the bowl. The
hammering was done with a sledge hammer over soft ground.
The inside of ea h bowl was painted with several oats of a matte white metal spray paint Cloud 33 .
To align the two bowls, a 1 in h wide strip of thin sheet metal was pop-rivetted to the inside surfa eof the perifery of one of the bowls. To assemble the sphere, one slides the other bowl over this skirt.
Four toggle lat hes4 hold the bowls together.
The base was onstru ted using a 5.5 in h square by 0.75 in h lear pine blo k with furniture feet
5 implanted and pointing upward. This arrangement keeps the sphere from rolling about on the work
surfa e. The sphere an be pointed at an arbitrary angle and will stay there6 . Figure 1 shows theompleted sphere on its base.
2.2

Light Sour e

Two dierent sour es were tested in the original design of the sphere: an LED point sour e and an
in andes ent lamp. Subsequently these were repla ed by an LED ring light, and then a distributed LED
strip array.
2.2.1

LED Point Sour e

The LED light sour e7 is on entrated into a small emitting area. The LED was operated from a onstanturrent sour e8 at a urrent of 360mA. The LED sour e ran quite hot (about 60◦ C) and as a onsequen e
the light output de reased by some 10% while warming up. With some help from translu ent plasti over
the LED, the integrating sphere was surprisingly ee tive in diusing this point sour e and the sphere
aperture was uniformly illuminated. If the LED is allowed to warm up, and the aperture illuminan e
is measured shortly before being used as a alibration sour e, then it would probably be a eptable.
However, we were on erned that the light output was ex essively dependent on the temperature of the
LED sour e.
2.2.2

In andes ent Lamp

The in andes ent light sour e was a 60 watt in andes ent lamp9 , nominal output 550 lumens. A sheetmetal shield blo ked dire ted light from the lamp rea hing the port. The aperture illumination wassu iently uniform.
The in andes ent lamp is operated from the AC line. Unfortunately, due to the limited thermal
inertia of the lamp lament, the in andes ent lamp output varies by some 10% at a rate of 120 times
per se ond (period, 8.3 millise onds). Figure 3 shows a re ording of a photodiode dete ting the lamp
2 Ikea #000.572.26, $17 ea h.
3 Krylon Outdoor Spa es 42904 Cloud (SHERWIN-WILLIAMS CANADA INC. KRYLON Produ ts Group Vaughan,

ON L4K 4T8. The manufa turer gives the tristimus oordinates for this paint as X:74.67, Y:79.32, Z:85.63)
4 Lee Valley Part Number 00S5590, Stainless steel Draw Lat h.
5 Lee Valley Part Number 00H5001 Levelling Glide.
6 This onstru tion might make the basis for a portaball type teles ope: http://www.mag1instruments. om/index.php.
7 LedEngin part number LZ4-40CW10, available from Newark Ele troni s, pri e $29.00 referen e [6℄.
8 Digikey DKSB1003A, $26.00
9 Philips Duramax, part #129411.

3

output, measured with a Sys omp CGR-201 os illos ope. A amera exposure that is mu h less than thisinterval will sample this variation at some random instant, introdu ing an un ertainty of 10% into themeasurement of luminan e.
The ripple will have no ee t if the shutter interval is equal to the period of the ripple waveform,in this ase, 1/120 se ond10 . Then the exposure is
integrated over one period, regardless of where theexposure begins and ends in the ripple y le. Unfortunately, that limits exposure adjustments to aperture and ISO, whi h is highly in onvenient.
The light output L of an in andes ent lamp is related to the line voltage V a ording to L ∝ V 3.4 [7℄.
Consequently a 10% hange in line voltage would
result in a 40% hange in light output. Ideally, theline voltage should be regulated or adjusted to thesame value ea h time, or the aperture needs to bealibrated for ea h use, with the hope that the line
voltage does not hange during a measurement.
Figure 3: In andes ent Lamp Fli ker
The in andes ent lamp sour e is a simple, inexpensive sour e for the integrating sphere. However,as a result of the ripple and line voltage sensitivity it is not well suited for predi table and onsistentmeasurements.
2.2.3

Ring LED Sour e

The ring illumination is provided by two rings of LEDs, 8 and 10 entimetres in diameter as shown ingure 4(a)11 . Ea h ring onsists of strings of LEDs wired in parallel. Ea h LED string onsists of 3
LEDs and a series resistor. The 8 entimeter ring ontains 8 strings of LEDs, the 10 m ring ontains 11
strings of LEDs.
The rings were mounted inside the sphere using double-sided foam tape, lo ated around the aperture,
fa ing the rear of the sphere.

(a) Ring LEDs(b) Illuminated( ) Wiring with Driver Board

Figure 4: Ring LED Sour e
The two rings are onne ted in parallel, and operated from the onstant urrent supply des ribed
previously in se tion 2.2.112 . The total urrent is set to 360mA, giving an LED urrent of 19mA. The
10 Alternatively, one ould power the lamp from 117VDC. Unfortunately, su h a supply is not usually ready to hand in
the standard ele troni s lab.
11 These units were found in the basement ele troni s department of College Home Hardware, 290 College Street, Toronto.
Toronto ele troni s enthusiasts will re ognize this as the latest lo ation for Supremetroni sto k.
12 The LM317 integrated ir uit regulator is inexpensive and readily available, and an be ongured as a urrent sour e.

4resistors in the LED ring ensure that the urrent is distributed approximately equally in ea h string,
whi h results in equal illumination from ea h LED (gure 4(b)). The voltage a ross the LED rings isabout 10 volts at 360mA.
The suggested operation of these LED rings is from a 12 volt DC sour e. It was found in pra ti ethat the slightest variation of output voltage resulted in substantial hange in light output. Current
drive is mu h more stable. In this ase, the LED driver board regulates the urrent at 360mA, andthe driver board is fed by an 18 volt DC regulated voltage wall adaptor so the LED urrent should be
immune to hanges in line voltage or LED voltage.
In the ring illuminator, the light output is distributed over 56 LEDs, ompared to one LED in the
point sour e of se tion 2.2.1. Consequently the temperature rise in ea h LED of the ring is mu h less,about 15◦ C above ambient, ompared to 40◦ C above ambient for the point-sour e LED. The warmup
drift is then mu h less in the ring illuminator. The light output is within 1% of its nal value in 2
minutes, and 0.1% of its nal value in 6 minutes. As a onsequen e, the sour e is ready to be usedalmost immediately after it is turned on and is unlikely to drift substantially with ambient temperature.
2.2.4

LED Strip Array

With the near- ompletion of the Luma software, it be ame apparent that the non-uniformity of the sphere
illumination was aversely ae ting alibration results. The LED ring emitters des ribed in se tion 2.2.3
are not ompletely uniform and they illuminate the rear of the sphere (the area that is viewed throughthe aperture) dire tly, rather than being diused.
As a onsequen e of this non-uniform illumination a prole line measurement showed a variation of
about 25% . A temporary arrangement of ardboard and aluminum foil was then used to dee t thering illumination to the side walls of the sphere, and the variation redu ed to 9%, at the expense of lessillumination. This indi ated that diusing the LED illumination would make it more uniform, so we
onstru ted the arrangement shown in gure 5(a).

(a) Sphere Interior(b) Horizontal Prole( ) Intensity Map

Figure 5: LED Strip Sour e
The LED support stru ture is a 10 in h (25.4 m) diameter ring, one in h (2.54 m) in height.
This is held in pla e by 4 straps whi h atta h to the same bolts holding the lat hes. The LED strip(Lee Valley part 00U4108, 120 LEDs per metre) is atta hed to the ring by its adhesive ba king. With
this arrangement, the LEDs fa e the sphere wall, whi h is at a 45 degree angle to the LED output.
Consequently, illumination on the rear wall of the sphere does not ome dire tly from an LED but has
undergone at least one diuse ree tion.
Conne tion to the LED strip is brought to a onne tor on the sphere 13 . A regulated 12 volt supply(Sys omp PSM-101) operates the LEDs, whi h require a total operating urrent of 730mA.
Unfortunately, as a linear regulator, it runs quite hot and the output urrent hanges signi antly with temperature. The
Digikey DKSB1003A re ommended for this appli ation is a swit hing regulator and runs old. The output urrent does
not hange over time.
13 A 12 volt DC power supply for LED strips is also available from the Lee Valley. However, it has an output ripple of
0.5 volts at 120Hz, whi h is una eptable for this appli ation.

5

At a power supply setting of 12 volts, the illuminan e at the aperture is about 4000 lux.
The prole line for the LED strip illumination is shown in gure 5(b). The variation is about 4%,
a substantial improvement over previous arrangements. Figure 5( ) shows the intensity map of theaperture. The aperture false- olour is two olours only, whi h suggests reasonable uniformity.

3 Comparison of Sphere Light Sour es
Experien e with various light sour es in the integrating sphere leads to the following observations:• A single high intensity LED emitter an supply su ient light for the sphere. However, even witha heatsink, the temperature and light output hange signi antly during warm up.
• A single in andes ent lamp will work (and is the traditional sour e for an integrating sphere) but
it heats the interior of the sphere and the light output varies at the line frequen y.
• One or more LED rings have the advantage of ir ular symmetry but the LED outputs are notuniform to the degree required by this appli ation and result in a non-uniform eld when dire ted
to the rear of the sphere. However, be ause the light output is spread over a number of LEDs, itdoes not suer from the heating drift problem of a single LED emitter.
• A string of LEDs, aimed at the sphere walls, generates a uniform eld on the rear wall of the sphere.
There is no measureable drift in light output after power-on. The light output is signi antly higher
than the in andes ent lamp, single LED or ring LED sour es. The LED string an be dimmed
when the string is powered by a variable DC supply.

4 Luminan e Calibration: Results
We measured the illuminan e at the port with two luxmeters and al ulated the orresponding value ofluminan e. We also measured luminan e dire tly with a luminan e meter, and an exposure spotmeter.
The Minolta spotmeter wmeasures exposure value EV . For an ASA (lm speed) setting of 100,Minolta relates the luminan e L to the exposure value as equation 2:
2

L = 0.14 × 2EV andela/metre(2)

The measured value of EV was 11.9 Then the measured luminan e is:
L = 0.14 × 2EV = 0.14 × 211.9 = 535

andela/metre2

An exposure value of 11.9 ould be anywhere between 11.85 and 11.95, so the equivalent luminan eould be anywhere between 516 to 553 andela/metre2.
The results are summarized as follows:
Instrument

Measurement

Reading

Luminan e, d/m2

Tektronix J16 with 6511 probe
Maste h LX1330B
Tektronix J16 with 6503 probe
Minolta Model M

Illuminan eIlluminan e
Luminan eExposure Value

1596 lux
1580 lux
525 d/m2
11.9

508
503
525
535

Average517

The results for luminan e are within 3% of the average value.

65 Veri ation of Results Using SQM-LU Sky Quality Meter
The Unihedron Sky Quality Meter SQM-LU is generally intended for measuring the ba kground lightof a night sky [24℄. It an however be used as a moderate to low-level luminan e meter. This is useful
be ause the SQM-LU is inexpensive when pur hased new, and it (or a similar instrument) an often beborrowed from an astronomy lub.
The meter reads out in magnitudes per square ar se ond (MPSAS). The Unihedron web page gives
the onversion formula as follows:
L = 10.8 × 104 × 10−0.4M

where L is the luminan e in andela per square metre and M is the sky quality in magnitudes per
square ar se ond.
Measurement into the sphere port using the SQM-LU Sky Quality Meter generated a reading of 5.93
MPSAS. Converting to luminan e, using the formula given above, yeilds a luminan e of 458 d/m2 .
The illuminan e at the port entran e, using a Maste h MS6612T illuminan e meter (luxmeter) generates a reading of 1468 lux. Converting that to luminan e by dividing by π gives a result of 467 d/m2 .
This is within 2% of the result obtained using the SQM-LU.
The fa t that these two values of luminan e were obtained by ompletely dierent instruments andal ulations reates onden e that the te hniques for measuring luminan e that we des ribe here arereliable and a urate14 .

6 Summary
It is possible to reate a predi table sour e of luminan e with relatively modest equipment and minimal
expense. One needs a low- ost illuminan e meter (luxmeter) and an integrating sphere similar to theunit des ribed in this paper.
The integrating sphere port then reates luminan e at the port that is uniform, diuse and reasonably
predi table, that ould be used for alibration of a luminan e meter, spot light meter, or digital amera.

7 Notes
7.1

Integrating Sphere: Flux and Illuminan e

The output luminous ux φ of the lamp undergoes a series of ree tions. With ea h ree tion, it isdiminished by the ree tan e of the sphere surfa e ρ. Consequently the ux returned from the surfa eof the sphere, φint , isφint=

φ · ρ + φ · ρ2 + φ · ρ3 + . . .

=φ(ρ + ρ2 + ρ3 + . . .)(3)
It an be shown [8℄ thatx + x2 + x3 =x
1−xUsing that relationship in equation 3 we have:φint = φ

14 Alert readers will noti e that the port luminan e has

ρ
1−ρ



(4)

hanged from 503 d/m2 to 458 d/m2 between se tions 4 and5. The time between these two sets of measurements is at least two years, so we attribute the dieren e to aging of the
LED ring. This hange in values emphasizes the importan e of measuring the luminan e on a regular basis.

7

The illuminan e E is equal to the ux φint given in equation 4 divided by the surfa e area of thesphere, As . (This assumes the area of the port is negligible, ie, under 5% of the total).
E=

φ ρ
As 1 − ρ(5)This is the illuminan e on the interior surfa e of the sphere, whi h is observed from the sphere port.
For a sour e of given ux, the illuminan e at the port in reases with a smaller sphere.
The quantityρ1−ρ
is known as the sphere multiplier and given the symbol M . A larger value of multiplier results in greater
illuminan e at the output port and improves the uniformity of the light eld in the sphere. However,with a large multiplier a small hange in ree tivity (due to dust, deterioration of the paint oating, or
hange in wavelength of the light sour e) then has a large ee t on the sphere alibration [9℄.
7.2Integrating Sphere: Illuminan e and Luminan e.......................................
...................
...........
.........
...........
........
.........
.......
........
.
.
.
.
.
.
......
....
.
.
......
.
.
.
......
....
.
.
.
.
.....
...
.
.
.....
.
.
...
....
.
.
....... ..... ..... ..... ..... ..... ..... ..... ..... ..... ..... ..... ..... ..... ..... ..... ..... ..... ..... ............
.
.
.. . . θ.
.
.
dφ . . .......
..
dA ......
...
.
.
...
..
..
..
...
..
...
...
..
...
...
..
.
..
.
...
.
.
.
..
...
.
..
...
..
..
.
..
.
...
.
.
.
.
...
.
.
....
r
..
...
..
...
..
..
.
...
.
...
.
.
..
...
..
...
..
..
.. ..
...
....
.
...
...
....
...
...
....
...
...
..
..
...
...
...
...
...
..
....

Referring to gure 6, onsider that there is an emitting area dA on the inside of the sphere. Then by Emitting ♣♣ ♣♣♣ ♣Area ♣ ♣Lambert's Law of Cosines [10℄, the intensity of thelight emitted isdI = dA L cos(θ)(6)

where:♣♣♣♣♣ Re eiving♣♣♣♣ Area

RadiusIntegrating Sphereis the intensity of light emitted byarea dA, andela (lumens per steradian)Figure 6: Illuminan e and Luminan e in thedA is small pat h of area on the interior
Spheresurfa e of the sphere, metres2
L is the luminan e of the pat h, andela per metre squaredθis the angle between the emitted lightand the normal to the surfa e, as
shown in gure 6.
At the re eiving area, the illuminan e is equal to the in ident intensity divided by the distan esquared (a ording to the inverse square law) and again subje t to Lambert's Law of Cosines:
dI

dE =

dI cos(φ)d2(7)

where:
dE is the illuminan e on the re eiving area, lumens per metre2 (lux)dI is the light intensity emitted from area dA, lumens per steradian ( andela)φis the angle between the re eived light and the normal to the surfa e, as shown in gure 6.
By geometry, sin e this is the interior of a sphere the angles θ and φ are equal. As well, the distan ed is given by equation 8:
d = 2r cos(θ)

where r is the sphere radius.
Collapsing equations 6,7 and 8, we nd for the illuminan e:

8

(8)

LdA
(9)
4r2
This is the illuminan e at any point in the sphere interior, reated by the luminan e of the pat harea. Noti e that this is a onstant value of illuminan e, independent of position or angle.
To relate the illuminan e and luminan e, integrate equation 9 over the area of the sphere. Then thein remental area da is repla ed by the total sphere area, 4πr2 .
dE =

E

LdA
2
sphere 4r

Z=

L(4πr2 )
4r2
= πL
=

7.3

(10)

Measuring Luminous Flux of the Sour es

The integrating sphere is ommonly used to measure the total output luminous ux of a light sour e. A
light sour e will likely produ e an output that varies by dire tion. To determine the total light output,
one ould plot the output of the light sour e, generate a three-dimensional fun tion for the light output,
and then integrate (average) that fun tion over the surfa e of the sphere.
The integrating sphere makes that unne essary. The illuminan e at the port may be shown (seese tion 7.1) to be related to the total output ux of the lamp by equation 11:E=

φ ρ
As 1 − ρ(11)where:EφAs
ρ

is the illuminan e at the sphere port in lux
is the total luminous output ux of the lamp, in lumens
is the total surfa e area of the sphere in metres2 , equal to 4πrs 2 , where rs is theradius of the sphere in metres.
is the ree tan e of the surfa e.

If the ree tan e ρ is known, then the total output ux φ of the lamp, in lumens, is determined by
the illuminan e at the port E , in lux.
For example, in the ase of the LED point sour e (se tion 2.2.1) without its diusing lter theilluminan e E at the sphere port is 3260 lux. The surfa e area As of the sphere is 0.397 metres2 . The
ree tan e ρ under LED illumination is 0.77. Rearranging equation 11 to solve for ux φ and plugging
in these values, we have:

φ =

As E



1−ρ
ρ



=

0.397 × 3260 ×=

386 lumens

1 − 0.77
0.77

A ording to the data sheet, the output of the LED sour e will be between 228 and 446 lumens.
With known values of output ux for a given sour e, we ould rearrange equation 11 to enter the valuesof illuminan e and sphere surfa e area, and solve for the ree tan e of the sphere interior. However, thenameplate values of lamp and LED sour e an be dramati ally dierent from their true output. (At one
point, we experimented with a ompa t uores ent lamp (CFL) whi h had a nameplate rating of 600
lumens. A measurement of the total ux output showed 863 lumens, an in rease over the nameplate9value of 140%15 .) Furthermore, measuring the total ux output is not simple, sin e most sour es do nothave a spheri al distribution.
7.4

Appli ations for the Integrating Sphere

The integrating sphere was useful in this appli ation be ause it produ es a uniform, diuse light eld ofpredi table luminan e. There are many other appli ations:
Helmlinger [12℄ shows how to build an integrating sphere for demonstration of mixing
olours from red, green and blue LEDs.

Mixing Colours

Referen e [13℄ des ribes onstru tion of a small integrating sphere, used to measure the light output of LED ashlights.

Luminous Output from LED Flashlight

Referen e [14℄ des ribes a number of appli ations, among them the measurementof laser opti al power, measurement of transmittan e and ree tan e, and the testing of imaging
systems.

Laser Power Output

7.5

A knowledgements

Spe ial thanks to my olleagues Gabriel Guillen, who parti ipated in helpful dis ussions on this topi ,and Axel Ja obs, who pointed out the luminan e ripple ee t and a formula error in the rst draft ofthis paper.

Referen es[1℄ Luminan e Meter
http://www.koni aminolta. om/instruments/produ ts/light/luminan e-meter/
ls100-ls110/index.html[2℄ Exposure Value EV as a measure of luminan e and illuminan e
http://en.wikipedia.org/wiki/Exposure_value#EV_as_a_measure_of_luminan e_and_illuminan e[3℄ Illuminan e Meter (Luxmeter)
http://www.multimeterwarehouse. om/luxmeter.htm[4℄ Derivation of the relationship between illuminan e E and luminan e L for a Lambertian ree tive
surfa e, L = Eρ/π.
Yi Chun Huang
http://www.yi hunhuang. om/files/tea hing/landa/lambertian_luminan e.pdf[5℄ Design of an Integrating Sphere as a Uniform Illumination Sour e
Alfred Du harme, Arnold Daniels, Eri Grann, Glenn Boreman
IEEE Transa tions on Edu ation, Vol 40, No. 2, May 1997, pp 131-134[6℄ Datasheet: High Luminous E a y Cool White LED Emitter LZ4-00CW10
LedEngin, In .
De ember 2009http://www.ledengin. om/files/produ ts/10wLZ/LZ4-00CW10.pdf[7℄ In andes ent Light Bulb
http://en.wikipedia.org/wiki/In andes ent_light_bulb
15 A ording to the Wikipedia entry on CFL's [11℄: CFLs produ e less light later in their lives than when they are new.
The light output de ay is exponential, with the fastest losses being soon after the lamp is rst used. By the end of theirlives, CFLs an be expe ted to produ e 70 to 80% of their original light output. Assuming a light depre iation of 70%, an
initial output of 140% of the nameplate value would ensure a light output of 100% of the nameplate value at the end of
the lamp life.

10[8℄ Geometri Series
Wikipedia
http://en.wikipedia.org/wiki/Geometri _series[9℄ Integrating Sphere, Design and Appli ations
SphereOpti s
http://www.sphereopti s. om/assets/sphere-opti -pdf/sphere-te hni al-guide.pdf[10℄ Lambert's osine law
Wikipedia
http://en.wikipedia.org/wiki/Lambert%27s_ osine_law[11℄ Compa t uores ent lamp
Wikipedia
http://en.wikipedia.org/wiki/Compa t_fluores ent_lamp[12℄ How to make an LED Illuminated Integrating Sphere for Demonstration of Color, Vision andWavelength

Mark Helmlinger
http://do uments. lubexpress. om/do uments.ashx?key=SsTKdeybVjXFSS73wyC6v0MOb5G8fbN\\1fYRxub3BHqMRYU50O2RsGR12PYo FYdGTz9RF8\%2FXUHdeCJtewgxuJQ\%3D\%3D
Note: Lengthy URL has been broken by a double ba kslash. Remove that before using.
[13℄ A home-made integrating sphere
sixty545
http://budgetlightforum. z.

/node/1763[14℄ A Guide to Integrating Sphere Theory and Appli ations
Labsphere
http://www.labsphere. om/uploads/te hni al-guides/a-guide-to-integrating-sphere-theory\\-and-appli ations.pdf
Note: Lengthy URL has been broken by a double ba kslash. Remove that before using.
[15℄ Measuring Ree tan ePeter D. His o ks, August 2011
http://www.ee.ryerson. a/~phis o k/
[16℄ Ja k O'Lanterns and integrating spheres: Halloween physi s
Lorne A. Whitehead and Mi hele A. Mossman
Ameri an Journal of Physi s 74 (6), June 2006, pp537-541[17℄ Issues in Ree tan e Measurement
David L.B.Jupp
http://www. ossa. siro.au/millwshop/ref_ al.pdf[18℄ ImageJ: Image Pro essing and Analysis in Java
http://rsbweb.nih.gov/ij/[19℄ Color Temperature
Feit Ele tri
http://www.feit. om/feit olortemperature.html[20℄ Digital Multimeter DVM-101
http://www.sys ompdesign. om/DVM101.html[21℄ Wikipedia: Fishpaper
http://en.wikipedia.org/wiki/Fishpaper11[22℄ Light Measurement Handbook
Alex Ryder
http://files.intl-light. om/handbook.pdf[23℄ Controlling Veiling Glare in an Opti al Imaging System
Amber Czajkowski
http://www.opti s.arizona.edu/optome h/Spr09/523L/523L_Final%20Report_A.
Czajkowski.pdf[24℄ Sky Quality Meter - LU
Unihedron
http://unihedron. om/proje ts/sqm-lu/

12