07 - sfere integratoare - teorie.pdf

8/18/2019 07 - Sfere integratoare - teorie.pdf

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Integrating Sphere

for

Luminance Calibration

Peter D. Hiscocks

Syscomp Electronic Design [email protected]

First Draft: 23 August 2011

Revised: 24 March 2012

Abstract

A digital camera can be used to measure and document scene luminance, providing the camera can becalibrated by photographing a source of known luminance.

This paper describes a low-cost purpose-built integrating sphere which creates uniform, diffuse field of light

at a port in the sphere. The luminance at the port is related by a very simple formula to the port illuminance,

which can be measured using a low-cost luxmeter.

The integrating sphere has other applications, among them measuring the total output flux of a light source,

and determining the reflectance of materials.

Figure 1: Integrating Sphere, showing latches, base and DC power jack for the LED light source.


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1 Introduction

This project arose out of a need to measure the luminance of light pollution sources. A modern digital camera canbe used for such measurements, but it requires calibration with a source of known luminance.

1. Suitable sources of standard luminance are available in the standards laboratories, but access is expensive1.

2. A calibrated luminance meter is expensive. For example the Minolta LS-100 Luminance Meter costs about$3300 [1].

3. A photographicspot meter canbe used to measure exposure value. This can then be related to luminance[3].

A new spot meter is expensive, typically $800, but they are occasionally available used. We obtained a used

Minolta-M spotmeter for $350.

4. An illuminance meter (measuring in lux or foot-candles) is an inexpensive instrument, costing about $60.See for example the Mastech LX1330B [2]. If luminance and illuminance can be related, then the calibra-

tion can be done with this instrument. That turns out to be the case.

It can be shown (see reference [4] and section 5.2) that illuminance and luminance are related as :

L =

E

π (1)

where:

E is the illuminance in luxL is the luminance in candela per metre2

For this equation to apply, the source of illumination must be uniform and diffuse which, it turns out, isavailable at the aperture of an integrating sphere.

2 The Integrating Sphere

Figure 2: Integrating Sphere, Measuring Port Lumi-

nance

The integrating sphere is a hollow sphere that is coated

on the inside surface with a reflective, diffusing paint.Thesphere is equippedwith one or more measuringports

– in this case, a single opening. A light source is placed

inside the sphere, shielded so that it is not directly visible

from the measuring port. Light from the source reflects

repeatedly from the sphere painted surface, resulting in a

uniform light field over the interior surface. Viewed from

the port, light intensity has equal magnitude irrespective

of direction, that is, the light field is uniform and diffuse,

as required by equation 1.

Consequently, it should be possible to relate illumi-

nance and luminance by the following:

The illuminance meter is placed in the diffuse light field at the output port the integrating sphere tomeasure E . The luminance L at the port opening is predicted according to equation 1. The port isthen a calibrated source of luminance for a digital camera or luminance meter (figure 2).

1The National Research Council of Canada quoted $1800 to calibrate a luminance meter.

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2.1 Construction

According to [19], to avoid significant impact on the operation of the sphere the port opening should be no more

than 5% of the total area. For the instruments in our collection, the largest illuminance meter sensor area is 2.1

inches in diameter. A port of that diameter would require a sphere diameter of 11 inches diameter, minimum.

A suitable basis for the sphere was found at the local Ikea store, a 14 inch diameter stainless steel mixing

bowl2.

Each of these bowls has a 3 inch diameter flat at the base of the bowl. The flat base of one sphere was used for

the port, which was opened with a 2.25 inch Greenlee chassis punch. The flat of the other sphere was pounded out

match the curvature of the bowl. The pounding was accomplished with a 2"x4" wooden post, rounded at one end

with a belt sander to roughly match the curvature of the bowl. The hammering was done with a sledge hammerover soft ground.

The inside of each bowl was painted with several coats of a matte white metal spray paint Cloud 33.

To align the two bowls, a 1 inch wide strip of thin sheet metal was pop-rivetted to the inside surface of the

perifery of one of the bowls. To assemble the sphere, one slides the other bowl over this skirt. Four toggle latches4

hold the bowls together.

The base was constructed using a 5.5 inch square by 0.75 inch clear pine block with furniture feet 5 implanted

and pointing upward. This arrangement keeps the sphere from rolling about on the work surface. The sphere can

be pointed at an arbitrary angle and will stay there6. Figure 1 shows the completed sphere on its base.

Two different sources were used in the sphere: an incandescent lamp and an LED light source. The colourtemperature of the LED source is 5500K. (For comparison, the colour temperature of sunlit sky is about 5500K

[15]). The colour temperature of the incandescent source is about 3000K, a warmer (redder) hue.

2.2 LED (Light Emitting Diode) Source and Calibration

(a) LED Light Source

Relative Light Output, %120

80

70

70

60

Case Temperature, Degrees C

0 40 60 80 100 12020

100

110

(b) Effect of Temperature

Figure 3: LED Light Source

The LED source is attractive because it is much smaller than an incandescent lamp. Until recently, LED light

sources were significantly smaller light output than an incandescent lamp, but they are now comparable.

The LED light source7 has an output flux of approximately 317 lumens at a DC current of 360mA or 635

lumens at 700mA. It is driven by a constant-current LED driver circuit8. The LED current can be jumper-selected

on the driver board as 360 or 700mA. The constant-current LED driver is in turn powered by an 18V, 1.0 amp DC

2Ikea #000.572.26, $17 each.3Krylon Outdoor Spaces 42904 Cloud (SHERWIN-WILLIAMS CANADA INC. KRYLON Products Group Vaughan, ON L4K 4T8. The

manufacturer gives the tristimus coordinates for this paint as X:74.67, Y:79.32, Z:85.63)4Lee Valley Part Number 00S5590, Stainless steel Draw Latch.5Lee Valley Part Number 00H5001 Levelling Glide.6This construction might make the basis for a portaball type telescope: http://www.mag1instruments.com/index.php.7LedEngin part number LZ4-40CW10, available from Newark Electronics, price $29.00 reference [16].8Digikey DKSB1003A, $26.00.

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power supply9 which plugs into a jack on the sphere surface. The installation in the sphere10 is shown in figure

3(a).There is an additional complication with an LED source. It generates considerable heat and the light output of

an LED source decreases with increasing temperature as shown in figure 3(b). Consequently, the heat generated

in the LED must be removed. Fortunately, the LED assembly is pre-mounted on a metallic base so that it can

be easily attached to a heat sink. In this case, the LED is machine-screw mounted to 0.030 inch thick brass

sheet stock, that then attaches to the internal surface of the sphere. The interfaces between the LED and brass,and between the brass and steel surface of the sphere, and coated with heat transfer compound to minimize the

thermal resistance. A small extension of sheet metal blocks direct view of the LED source from the integrating

sphere port.

(a) 360mA (b) 700mA

Figure 4: LED Heatsink, Thermal Response. Sampled at 10 second intervals.

Figure 4 shows the heatsink temperature as a function of time after turn-on11. The results of operating at 360and 700mA are summarized in the following table:

LED Current Time to Stablize Final Temperature Light Output Depreciation

360 mA 10 minutes 58.7◦C 90%

700 mA 25 minutes 92.3◦C 80%

We chose to operate the LED at the lower of these two currents, 360mA.

2.2.1 LED Source: Image of Sphere Port

The LED output is concentrated in a relatively narrow beam perpendicular to the chip, and this makes results in a

slightly non-uniform distribution of light in the sphere, with a variation of about 10% across the sphere aperture.

The LED was then covered in a diffuser, a single layer of translucent plastic bag material, which improved theuniformity. The LED illumination of the sphere aperture is shown in figure 5. Figure 5(a) shows an image of

the port, figure 5(b) shows a profile through the equator of the image, obtained using the ImageJ image analysis

program [12].

9CUI part number EMS180100-P5P-SZ available from Digikey for $19.00.10The installation of the driver board was complicated by the absence of mounting holes (!) and a plastic surface that does not adhere well

to heat-gun glue. It was attached to a layer of fishpaper [18] (for insulation) with contact cement. The fishpaper was then glued to the sphere

interior with contact cement.11The temperature graphs were taken with a Syscomp DVM-101 multimeter [17], connected to a netbook computer running the Microsoft

XP operating system.

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(a) Port Illumination (b) Profile

Figure 5: LED Aperture Illumination

2.3 Incandescent Lamp Source and Calibration

Figure 6: Sphere Interior, showing lamp, port and skirt

The incandescent light sourceused is a 60 watt incandes-

cent lamp12, nominal output 550 lumens. The bulb is 1.9

inches diameter with a standard ’medium’ screw base.

thas mounts in a ceramic socket. A sheet-metal shield

blocks direct light from the lamp reaching the port, as

shown in figure 6.

12Philips Duramax, part #129411.

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2.3.1 Incandescent Source: Image of Sphere Port

(a) Port Illumination (b) Profile

Figure 7: Incandescent Aperture and Profile

Figure 7(a) shows a camera image of the illuminated sphere port. The incandescent source radiates more-

or-less equally in all directions except toward the base, and the result is reasonable uniformity across the port

aperture as confirmed in the profile measurement of figure 7(b).

2.3.2 Incandescent Source: Port Uniformity and Directivity

Figure 8: Port Uniformity and Directivity Measure-

ment

Figure 8 shows the measurement setup to verify that the

port illumation of the incandescent lamp is uniform and

diffuse.

The level of illumination at the port of the integrating

sphere was measured with a modified illuminancemeter,

mounted so it could be traversed and rotated. The usualdiffusing hemisphere was removed from the illuminance

measuring head and replaced by a narrow viewing angleport to sample the illumination field. This field sampler

meter was then moved across the integrating sphere port

to determine the uniformity, and rotated in the centre of

the sphere port opening to determine the directivity. Fig-

ure 9 shows the results of the measurements.

The port uniformity (figure 9(a)) is quite respectable.

The port directivitymeasurement (figure 9(b)) shows

two traces: the measurement of the solid trace did not

view of the lamp shield and it is reasonably consistent.

The dotted line measurement did view the lamp shield and shows a falloff of illumination at the extreme angles.

This trace is a worst case and other angles will be less affected. A more elaborate integrating sphere design couldimprove on the directivity for all angles13.

13For example, Ducharme et al [19] describe an integrating sphere in which the light first processed through smaller spheres before being

injected into the main sphere. A design based on this work is described in Czajkowski [22]

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0

5

10

15

20

25

30

35

40

0 1 2 3 4 5Position, cm

Luminance, relative units

(a) Uniformity

0

5

10

15

20

25

30

35

40

−40 −20 0 20 40

Angle, degrees

Luminance, relative units

(b) Directivity

Figure 9: Port Illumination

3 Luminance Calibration: Results

We measured the illuminance at the port with three luxmeters, with the following result:

Description Illuminance, Lux Deviation

Tektronix J16 with 6511 probe 2050 +5%

Mastech LX1330B 1818 -6%

Extech 401025 1952 +0.5%

Average 1940

Based on the average value of illuminance, the luminance of the port is:

L = E π

= 1940

3.141

= 617 candela/metre2

We then measured the luminance of the port with a Minolta model M photographic spotmeter, which measures

exposure value EV . For an ASA (film speed) setting of 100, Minolta relates the luminance L to the exposurevalue as equation 2:

L = 0.14 × 2EV candela/metre2 (2)

The measured value of EV was 12.1. Then the measured luminance is:

L = 0.14 × 2EV

= 0.14 × 212.1

= 615 candela/metre2

Assuming that a reading of 12.1 could be anywhere between 12.05 and 12.15, the measured luminance could

be anywhere between 593 and 636 candela/metre2. The value calculated from the illuminance is within this range.

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4 Summary

It is possible to create a predictable source of luminance with relatively modest equipment and minimal expense.One needs a low-cost illuminance meter (luxmeter) and an integrating sphere similar to the unit described in this

paper.The integrating sphere port then creates luminance at the port that is uniform, diffuse and reasonably pre-

dictable, that could be used for calibration of a luminance meter, spot light meter, or digital camera.

5 Notes

5.1 Integrating Sphere: Flux and Illuminance

The output luminous flux φ of the lamp undergoes a series of reflections. With each reflection, it is diminished bythe reflectance of the sphere surface ρ. Consequently the flux returned from the surface of the sphere, φint, is

φint = φ · ρ + φ · ρ2 + φ · ρ3 + . . .

= φ(ρ + ρ2 + ρ3 + . . .)

(3)

It can be shown [13] that

x + x2 + x3 = x

1 − x

Using that relationship in equation 3 we have:

φint = φ

ρ

1 − ρ

(4)

The illuminance E is equal to the flux φint given in equation 4 divided by the surface area of the sphere, As.(This assumes the area of the port is negligible, ie, under 5% of the total).

E = φ

As

ρ

1 − ρ (5)

This is the illuminance on the interior surface of the sphere, which is observed from the sphere port, quoted

as equation 11 earlier in the paper. For a source of given flux, the illuminance at the port increases with a smaller

sphere.

The quantityρ

1 − ρ

is known as the sphere multiplier and given the symbol M . A larger value of multiplier results in greater illu-minance at the output port and improves the uniformity of the light field in the sphere. However, with a large

multiplier a small change in reflectivity (due to dust, deterioration of the paint coating, or change in wavelength

of the light source) then has a large effect on the sphere calibration [7].

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5.2 Integrating Sphere: Illuminance and Luminance

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θ φ

Radius r

Integrating Sphere

ddAArea

EmittingAreaReceiving

Figure 10: Illuminance and Luminance in the Sphere

Referring to figure 10, consider that there is an emitting

area dA on the inside of the sphere. Then by Lambert’sLaw of Cosines [14], the intensity of the light emitted is

dI = dA L cos(θ) (6)

where:

dI is the intensity of light emitted byarea dA, candela

dA is small patch of area on the interiorsurface of the sphere, metres 2

θ is the angle between the emittedlight and the normal to the surface,

as shown in figure 10.At the receiving area, the illuminance is equal to the incident intensity divided by the distance squared (ac-

cording to the inverse square law) and again subject to Lambert’s Law of Cosines:

dE = dI cos(φ)d2

(7)

where:

dE is the illuminance on the receiving area, lumens per metre2 (lux)dI is the light intensity emitted from area dA, candelaφ is the angle between the received light and the normal to the surface, as shown in figure 10.

By geometry, since this is the interior of a sphere the angles θ and φ are equal. As well, the distance d is givenby equation 8:

d = 2r cos(θ) (8)

where r is the sphere radius.Collapsing equations 6,7 and 8, we find for the illuminance:

dE = LdA

4r2 (9)

This is the illuminance at any point in the sphere interior, created by the luminance of patch area. Notice that

this is a constant value of illuminance, independent of position or angle. The patch of luminance illuminates the

interior of the sphere.

To relate the illuminance and luminance, integrateequation 9 over the area of the sphere. Then the incremental

area da is replaced by the total sphere area, 4πr2.

E =

sphere

LdA

4r2

= L(4πr2)

4r2

= πL (10)

which was originally given as equation 1.

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5.3 Measuring Luminous Flux of the Sources

The integrating sphere is commonlyused to measure the total output luminousflux of a light source. A light source

will likely producean output that varies by direction. To determine the total light output,one could plot the output

of the light source, generate a three-dimensional function for the light output, and then integrate (average) that

function over the surface of the sphere.

The integrating sphere makes that unnecessary. The illuminance at the port may be shown (see section 5.1) to

be related to the total output flux of the lamp by equation 11:

E = φ

As

ρ

1 − ρ (11)

where:

E is the illuminance at the sphere port in luxφ is the total luminous output flux of the lamp, in lumens

As is the total surface area of the sphere in metres2, equal to 4πrs2, where rs is the radius of the sphere in metres.

ρ is the reflectance of the surface.

If the reflectance ρ is known, then the total output flux φ of the lamp, in lumens, is determined by the illumi-nance at the port E , in lux.

For example, in the case of the LED source (without its diffusing filter) the illuminance E at the sphere port is3260 lux. The surface area As of the sphere is 0.397 metres

2. The reflectance ρ under LED illumination is 0.77.Rearranging equation 11 to solve for flux φ and plugging in these values, we have:

φ = AsE

1 − ρ

ρ

= 0.397 × 3260 ×1 − 0.77

0.77= 386 lumens

According to the data sheet, the output of the LED source will be between 228 and 446 lumens.

With known values of output flux for a given source, we could rearrange equation 11 to enter the values of

illuminance and sphere surface area, and solve for the reflectance of the sphere interior. However, the nameplate

values of lamp and LED source can be dramatically different from their true output. (At one point, we exper-

imented with a compact fluorescent lamp (CFL) which had a nameplate rating of 600 lumens. A measurement

of the total flux output showed 863 lumens, an increase over the nameplate value of 140% 14.) Furthermore,

measuring the total flux output is not simple, since most sources do not have a spherical distribution.

5.4 Applications for the Integrating Sphere

The integrating sphere was useful in this application because it produces a uniform, diffuse light field of pre-

dictable luminance. There are many other applications:

Mixing Colours Helmlinger [9] shows how to build an integrating sphere for demonstration of mixing coloursfrom red, green and blue LEDs.

Luminous Output from LED Flashlight Reference [8] describes construction of a small integrating sphere,

used to measure the light output of LED flashlights.

14According to the Wikipedia entry on CFL’s [21]: CFLs produce less light later in their lives than when they are new. The light output

decay is exponential, with the fastest losses being soon after the lamp is first used. By the end of their lives, CFLs can be expected to produce

70 to 80% of their original light output. Assuming a light depreciation of 70%, an initial output of 140% of the nameplate value would ensurea light output of 100% of the nameplate value at the end of the lamp life.

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Laser Power Output Reference [6] describes a number of applications, among them the measurement of laser

optical power, measurement of transmittance and reflectance, and the testing of imaging systems.

5.5 Acknowledgements

Special thanks to my colleagues Gabriel Guillen, who participated in helpful discussions on this topic, and Axel

Jacobs, who pointed out an error in the first draft of this paper.

References

[1] Luminance Meter http://www.konicaminolta.com/instruments/products/light/

luminance-meter/ls100-ls110/index.html

[2] Illuminance Meter (Luxmeter)http://www.multimeterwarehouse.com/luxmeter.htm

[3] Exposure Value EV as a measure of luminance and illuminancehttp://en.wikipedia.org/wiki/Exposure_value#EV_as_a_measure_of_

luminance_and_illuminance

[4] Derivation of the relationship between illuminance E and luminance L for a Lambertian reflective surface,L = Eρ/π.Yi Chun Huang

http://www.yichunhuang.com/files/teaching/landa/lambertian_luminance.

pdf

[5] Measuring Reflectance

Peter D. Hiscocks, August 2011http://www.ee.ryerson.ca/~phiscock/

[6] A Guide to Integrating Sphere Theory and ApplicationsLabsphere

http://www.labsphere.com/uploads/technical-guides/a-guide-to-integrating-sphere-theory-and-applications.pdf

[7] Integrating Sphere, Design and Applications

SphereOptics

http://www.sphereoptics.com/assets/sphere-optic-pdf/

sphere-technical-guide.pdf

[8] A home-made integrating spheresixty545

http://budgetlightforum.cz.cc/node/1763

[9] How to make an LED Illuminated Integrating Sphere for Demonstration of Color, Vision and WavelengthMark Helmlinger

http://documents.clubexpress.com/documents.ashx?key=SsTKdeybVjXFSS73wyC6v0MOb5G8fbN1fYRxub3BHqMRYU50O2RsGR12PYocFYdGTz9RF8\

%2FXUHdeCJtewgxuJQ\%3D\%3D

[10] Jack O’Lanterns and integrating spheres: Halloween physicsLorne A. Whitehead and Michele A. Mossman

American Journal of Physics 74 (6), June 2006, pp537-541

[11] Issues in Reflectance Measurement

David L.B.Jupphttp://www.cossa.csiro.au/millwshop/ref_cal.pdf

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[12] ImageJ: Image Processing and Analysis in Java

http://rsbweb.nih.gov/ij/

[13] Geometric SeriesWikipediahttp://en.wikipedia.org/wiki/Geometric_series

[14] Lambert’s cosine lawWikipediahttp://en.wikipedia.org/wiki/Lambert%27s_cosine_law

[15] Color Temperature

Feit Electric

http://www.feit.com/feitcolortemperature.html

[16] Datasheet: High Luminous Efficacy Cool White LED Emitter LZ4-00CW10LedEngin, Inc.

December 2009http://www.ledengin.com/files/products/10wLZ/LZ4-00CW10.pdf

[17] Digital Multimeter DVM-101http://www.syscompdesign.com/DVM101.html

[18] Wikipedia: Fishpaper

http://en.wikipedia.org/wiki/Fishpaper

[19] Design of an Integrating Sphere as a Uniform Illumination SourceAlfred Ducharme, Arnold Daniels, Eric Grann, Glenn Boreman

IEEE Transactions on Education, Vol 40, No. 2, May 1997, pp 131-134

[20] Light Measurement Handbook

Alex Ryderhttp://files.intl-light.com/handbook.pdf

[21] Compact fluorescent lamp

Wikipediahttp://en.wikipedia.org/wiki/Compact_fluorescent_lamp

[22] Controlling Veiling Glare in an Optical Imaging SystemAmber Czajkowski

http://www.optics.arizona.edu/optomech/Spr09/523L/523L_Final%20Report_

A.Czajkowski.pdf

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07 - sfere integratoare - teorie.pdf

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