RESEARCH ARTICLE

Scattering effects upon test image inside a designingsystem facing the equator

Ali A. D. Al-Zuky & Amal M. Al-Hillou &

Fatin E. M. Al-Obaidi

Received: 21 June 2010 /Accepted: 20 January 2012 /Published online: 15 February 2012# Optical Society of India 2012

Abstract This paper describes an experiment toinvestigate the influence of scattering effects upontest image. The image is located inside an opticalbuilt system facing the equator. Scattering effectshave been distinguished and tested by analyzingthe whole images that captured at regular intervals.The analyses process is performed by measuring theaverage intensity values of the RGB-bands for a certainselected line of the captured images. These measure-ments are executed in Baghdad city at a clear day. Atcertain intervals, Rayleigh and Mie scattering are thedominant effects which works individually while at otherperiods, the previous scattering types work together.

Keywords Rayleigh scattering .Mie scattering .

RGB bands . Intensity measurement

Introduction

Color of the atmosphere is much influenced by thespectrum of the sunlight, scattering/absorption effects

due to particles in the atmosphere, reflected light fromthe earth’s surface and the relationship between thesun’s position and the viewpoint (and direction). Thesunlight entering the atmosphere is scattered/absorbedby air molecules, aerosol and ozone layers. Thecharacteristics of scattering depend on the size ofparticles in the atmosphere. Scattering by smallparticles such as air molecules is called Rayleighscattering and scattering by aerosols such as dustis called Mie scattering. Light is attenuated by bothscattering and absorption [1].

Physical processes in the scene have not been astrong point of interest in the traditional line ofcomputer vision research. Recently, work in imageunderstanding has started to use intrinsic modelsof physical processes in the scene to analyze intensity orcolor variation in the image[2].

This paper presents an approach to image under-standing that uses intensity measurements andshows how the intensity varies in the image duringthe natural diurnal variation of sunlight in the caseof a clear day.

Scattering regimes

When the solar radiation in the form of electromagneticwave hits a particle, a part of the incident energy isscattered in all directions as diffused radiation. All smallor large particles in nature scatter radiation [3]. Thescattering of the incident electromagnetic wave by agas-phase molecule or by a particle mainly depends on

J Opt (January–March 2012) 41(1):54–59DOI 10.1007/s12596-012-0062-4

A. A. D. Al-Zuky :A. M. Al-Hillou :F. E. M. Al-Obaidi (*)Department of Physics, College of Science,Al-Mustansiriyah University,P.O. Box no.(46092), Baghdad, Iraqe-mail: fatinezzat@yahoo.com

A. A. D. Al-Zukye-mail: dralialzuky@yahoo.com

A. M. Al-Hilloue-mail: dr.amalhelou@yahoo.com

the comparison between the wavelength (l) and thecharacteristic size (d). We recall that, d ffi 0:1 nm for agas-phase molecule, d∈[10nm, 10μm] for an aerosoland d∈[10, 100] μm for a liquid water drop. The widerange covered by the body size will induce differentbehaviors. Three scattering regimes are usually distin-guished; Rayleigh scattering (typically for gases), scat-tering represented by the optical geometry’s laws(typically for liquid water drops) and the so-calledMie-scattering (for aerosols) [4].

Rayleigh scattering

If d<<l (the case for gases), the electromagnetic fieldcan be assumed to be homogeneous at the level of thescattering body. This defines the so-called Rayleighscattering (also referred to as molecular scattering).The scattered intensity in a direction with an angle θ tothe incident direction, at the distance r from the scat-tering body (Fig. 1), for a media of mass concentrationC, composed of spheres of diameter d and of density ρ,is then given by [4]

I θ; rð Þ ¼ I08p4

r2l4ρ2d6

C2

m2 � 1

m2 þ 2

� �2

1þ cos2θ� � ð1Þ

where I0 is the incident intensity. m is the complexrefractive index, specific to the scattered body; it isdefined as the ratio of the speed of light in the vacuumto that in the body and depends on the chemicalcomposition for aerosols. The above formula is in-versely proportional to l4[4]. This wavelength effectcan be seen in the blue color of the clear sky and thered color of the setting sun. The sky appears bluebecause the shorter wavelength blue light is scatteredmore strongly than the longer wavelength red light.The setting sun appears yellow towards red becausemuch of the blue light has been scattered out of thedirect beam [4, 5].

Note that Rayleigh scattering is an increasing func-tion of the size (d) and a decreasing function of thedistance (r). Moreover, Rayleigh scattering is symmetricbetween the backward and forward directions [4]:

I θ; rð Þ ¼ I p � θ; rð Þ ð2Þ

Mie scattering

If d ≈ l (the case for most of atmospheric aerosols), thesimplifications used above are no longer valid. Adetailed calculation of the interaction between theelectromagnetic field and the scattering body is re-quired; this is given by Mie theory. The intensity ofthe scattered radiation in the direction with an angle θto the incident direction, at a distance r, is [4]

I θ; rð Þ ¼ I0l2 i1 þ i2ð Þ4p2r2

ð3Þ

Where i1 and i2 are the intensity Mie parameters,given as complicated functions of d/l, θ and m. Theparameters i1 and i2 are characterized by a set ofmaxima as a function of the angle θ. Note that theforward fraction of the scattering intensity is dominant(Fig. 2).

Optical geometry

If d >> l (this is the case of liquid water drops withrespect to the solar radiation), the laws of optical geom-etry can be applied, leading to the understanding ofmany physical phenomena (e.g. rainbow formation).The scattering weakly depends on the wavelength [4].

Color descriptions

There are three attributes usually used to describe aspecific color. The first of these attributes specifies oneof the colors of the spectral sequence or one of the non-spectral colors such as purple, magenta, or pink. Thisattribute is variously designated in different descriptivesystems as hue, dominant wavelength, chromatic color,or simply but quite imprecisely as color [6].

A second attribute of color is variously given assaturation, chroma, tone, intensity, or purity. This

I0

r

θ

I (θ,r)

Fig. 1 Scattering of an incident radiation (I0) [4]

J Opt (January–March 2012) 41(1):54–59 55

attribute gives a measure of the absence of white, gray,or black whichmay also be present. Thus the addition ofwhite, gray, or black paint to a saturated red paint givesan unsaturated red or pink, which transforms ultimatelyinto pure white, gray, or black as the pure additive isreached; with a beam of saturated colored light, whitelight may also be added but the equivalent of addingblack is merely a reduction of the intensity [6].

For a color having a given hue and saturation, therecan be different levels variously designated as brightness,value, lightness, or luminance completing the threedimensions normally required to describe a specificcolor. It should be noticed that these terms do not haveprecisely the same meaning and therefore are not strictlyinterchangeable [6].

Blue sky

The blue color of the sky is caused by the scattering ofthe sunlight off the molecules of the atmosphere. Thisscattering, called Rayleigh scattering as mentioned

Fig. 2 Scattering of an incident radiation of wavelength l by anaerosol (gray sphere) of diameter d. The size of the vectorsoriginating from the aerosol is proportional to the scatteredintensity in the vector direction [4]

Scene

Window's Aperture

Camera

32.8º

SN

120 cm

40 cm

60 cm

(a) (b)

Fig. 3 Schematic diagram of experimental setup

tilted box's angle=32.80

0

20000

40000

60000

80000

100000

120000

140000

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

Time (Hours)

Illu

min

ance

(L

ux)

Fig. 4 Illuminance variation upon an inclined wooden boxtowards South direction with time

56 J Opt (January–March 2012) 41(1):54–59

before is more effective at short wavelengths. There-fore the light scattered down to the earth at a largeangle with respect to the direction of the sun’s light ispredominantly in the blue end of the spectrum. Notingthat the blue of the sky is more saturated when youlook further from the sun. The almost white scatteringnear the sun can be attributed to Mie scattering, whichis not very wavelength dependent. The mixture ofwhite light with the blue gives a less saturated blue [7].

Intensity image measurement

An image is an array of measured light intensities andit is a function of the amount of light reflected from theobjects in the scene [8]. The color of the a pixel isdefined by the intensities of the red (R), green (G) andblue (B) primaries. These intensity values are calledthe display tristimulus values R, G and B [6].

In order to measure the intensity, we have beenused the following equation [9–11].

I i; jð Þ ¼ 0:3Rþ 0:59Gþ 0:11B ð4Þ

Image acquisition setup

The setup for acquiring images is shown in Fig. 3. Theimaging system consists of advanced HDD CCD (SonyHandycamDCR-SR85) which is rigidly mounted insidean inclined wooden box fixed at 32.8° to the surfacenormal toward the south direction, the wooden box waspainted by gray paint with an aperture 40×40 cm2. Alight meter (LX801) used to measure the illuminanceupon box’s face. The scene is a color test image locatedin the end of the wooden box facing window’s aperture.The captured images for the colored test image are ofsize (323×229) pixels.

Fig. 5 One of the captured images at solar noon time for thecolored test image with the selected line upon itT

able

1Weather

inform

ationsupp

liedby

[12]

Tim

e(A

ST)

Tem

p.°C

Dew

point°C

Hum

idity

Sea

levelpressure(hpa)

Visibility

Winddir

Windspeed

Gustspeed

Precip

Events:cond

ition

s

5:55

AM

10.0

0.0

50%

1020

.510

.0km

NNW

5.6km

/h/1.5

m/s

–N/A

Clear

6:55

AM

10.0

0.0

50%

1020

.910

.0km

NW

7.4km

/h/2.1

m/s

–N/A

Clear

7:55

AM

13.0

−2.0

36%

1021

.010

.0km

North

9.3km

/h/2.6

m/s

–N/A

Clear

8:55

AM

15.0

−2.0

31%

1021

.010

.0km

NNW

13.0

km/h/3.6

m/s

22.2

km/h/6.2

m/s

N/A

Clear

9:55

AM

18.0

−2.0

26%

1020

.710

.0km

North

13.0

km/h/3.6

m/s

24.1

km/h/6.7

m/s

N/A

Clear

10:55AM

21.0

−4.0

18%

1020

.110

.0km

NNW

18.5

km/h/5.1

m/s

29.6

km/h/8.2

m/s

N/A

Clear

11:55AM

22.0

−5.0

16%

1019

.610

.0km

North

18.5

km/h/5.1

m/s

35.2

km/h/9.8

m/s

N/A

Clear

12:55PM

23.0

−5.0

15%

1019

.610

.0km

NNW

31.5

km/h/8.7

m/s

31.5

km/h/8.7

m/s

N/A

Clear

13:55PM

23.0

−4.0

16%

1017

.910

.0km

NNW

16.7

km/h/4.6

m/s

35.2

km/h/9.8

m/s

N/A

Clear

14:55PM

24.0

−5.0

14%

1017

.210

.0km

North

18.5

km/h/5.1

m/s

29.6

km/h/8.2

m/s

N/A

Clear

J Opt (January–March 2012) 41(1):54–59 57

1PM1(5)

0

50

100

150

200

250

0 100 200 300 400

x

I(x,

y1)

R-Band G-BandB-Band

2PM1(5)

0

50

100

150

200

250

0 100 200 300 400

x

I(x,

y1)

R-Band G-BandB-Band

3PM1(5)

0

50

100

150

200

250

0 100 200 300 400

x

I(x,

y1)

R-Band

G-Band

B-Band

4PM1(5)

0

50

100

150

200

250

0 100 200 300 400

x

I(x,

y1)

R-Band G-BandB-Band

5PM1(5)

0

50

100

150

200

250

0 100 200 300 400

x

I(x,

y1)

R-Band G-Band

B-Band

6PM1(5)

0

50

100

150

200

250

0 100 200 300 400

x

I(x,

y1)

R-Band G-BandB-Band

BRIS1(5)

0

50

100

150

200

250

0 100 200 300 400

x

I(x,

y1)

R-Band G-BandB-Band

7AM1(5)

0

50

100

150

200

250

0 100 200 300 400

x

I(x,

y1)

R-Band G-Band

B-Band

8AM1(5)

0

50

100

150

200

250

0 100 200 300 400

x

I(x,

y1)

R-Band G-Band

B-Band

9AM1(5)

0

50

100

150

200

250

0 100 200 300 400x

I(x,

y1)

R-Band G-BandB-Band

10AM1(5)

0

50

100

150

200

250

0 100 200 300 400

x

I(x,

y1)

R-Band G-BandB-Band

11AM1(5)

0

50

100

150

200

250

0 100 200 300 400

x

I(x,

y1)

R-Band G-Band

B-Band

12PM1(5)

0

50

100

150

200

250

0 100 200 300 400

x

I(x,

y1)

R-Band G-BandB-Band

BNOON1(5)

0

50

100

150

200

250

0 100 200 300 400

x

I(x,

y1)

R-Band G-BandB-Band

BSET1(5)

0

50

100

150

200

250

0 100 200 300 400

x

I(x,

y1)

R-Band G-BandB-Band

(a) (b)

(i)

(l)

(h)

(f)(d) (e)

(c)

(g)

(j) (k)

(m) (n) (o)

Fig. 6 The RGB-bands values measurements for the selected line upon the captured images from sunrise to sunset

58 J Opt (January–March 2012) 41(1):54–59

Acquisition data

At Monday, March 22, 2010, images were captured atregular intervals (from sunrise to sunset) in Baghdadcity (Latitude 33.2°N, Longitude 44.2°E). The illumi-nance measurements upon box’s face is shown inFig. 4, weather information obtained from [12] andis shown in Table 1.

Experimental results

Figure 5 shows one of the captured images with theselected line location upon it. The line was selected ina white region to analyze the illuminance distributionfor a homogeneous region upon the image. Figure 6shows the corresponding intensities to the previousselected line from sunrise to sunset. The x in intensityfigures denotes line’s position upon the color testimage while I(x,y1) is line’s corresponding intensity.

Conclusions

Due to the scattering effects, it is clear to the eye that theprogression in daytime leads to give us different sunlightcolors. Measurements of the color were made at eachtime based on the presence of amounts of red, green andblue. Figure 6a & o are the measured intensities atsunrise/sunset times with enough dark exposure, i.e.,the light from the sun does not saturate the CCD detector(Rayleigh scattering). The green was significantlybrighter than the red and the blue is the brightest one.This is consistent with Rayleigh scattering whichemphasizes the shorter wavelengths. The highest satu-ration occurred at early morning hour due to Rayleighscattering intensity value for B-band ≈ 250 as shown inFig. 6b. The color after that becoming less saturated.This can be interpreted as blue mixed with an increasingfraction of white light, which is consistent with the lightbeing a combination of Rayleigh and Mie scattering in

intermediate times to the solar noon shown in Fig. 6c, d,e, j, k, l, m, n. As we approach the normality state of thesun’s direction to the acqusition system (at solar noonexplained in Fig. 6g & h), Mie scattering accounts for alarger fraction of the total light and the Mie scatteredlight is essentially white (intensity value ≈ 50 for allbands at solar noon).

Thus, our measurement for intensity gives us anessential tool to explain the physical phenomenaaround us (i.e. scattering effects).

References

1. T. Nishita, T. Sirai, K. Tadamura, E. Nakamae, “Display ofthe earth taking into account atmospheric scattering”, Inter-national Conference on Computer Graphics and InteractiveTechniques Proceedings of the 20th Annual Conference onComputer Graphics and Interactive Techniques, (1993)

2. G.J. Klinker, S.A. Shafer, T. Kanade, A physical approachto color image understanding. Int. J. Comput. Vis. 4, 7–38(1990)

3. Z. Şen, “Solar energy in progress and future researchtrends” (Elsevier Ltd., 2004)

4. B. Sportisse, “Fundamentals in air pollution from processto modelling” (Springer Science + Business Media B. V.,2010)

5. R. H. B. Exell, “The intensity of solar radiation” (KingMongkut’s University of Technology Thonburi, 2000)

6. K. Nassau, “Color for science, art and technology” (ElsevierScience B. V., 1998)

7. R. Nave, “Characterizing color” (HyperPhysics, Depart-ment of Physics and Astronomy, Georgia State University,2001)

8. J. R. Parker, “Algorithms for image processing and computervision” (John Wiley & Sons, Inc., 1997)

9. C. B. Neal, “Television colorimetry for receiver engineers”(IEEE Trans. Broadcast Tele. Receiver, 1973)

10. F. E. M. Al-Obaidi, “A study of diurnal variation of solarradiation over Baghdad City” (Ph.D thesis, Department ofPhysics, College of Science, Al-Mustansiriyah University,2011)

11. H.Maruyama,M. Ito, F. Arai, T. Fukuda, “On-chip fabricationof optical multiple microsensor using functional gel-microbead”. IEEE. (2007)

12. Weather Underground home page. (web site: http://www.wunderground.com)

J Opt (January–March 2012) 41(1):54–59 59