Lecture 4: The spectrum, color theory and absorption

and photogrammetry

Thursday, 14 January

Ch 2.3http://www.bway.net/~jscruggs/film.html (color film)

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Reading

Previous lecture: Spatial data - photointerpretation & basic color theory

What we covered: Image geometryColor vs. B/W, shape and compositionInterpretation of some images

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Color

Color is a sensation that can be predicted and controlled

Color has 3 dimensions and can be simulated by radiances at three different ’s

In natural color those are red, green and blue butIn remote sensing any 3 may be combined as a “false-color” image

Therefore we need to understand color

Color is created by selective absorption, so we need to understandthat first

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For SI units frequently used in Remote Sensing, see back cover of text

The electromagnetic spectrum

Light is energy - Q =hin ergsor joules (J)where h = Planck’s constant, 6.63·10-34 J s = frequency (s-1) = c/

(c = speed of light, 3.00x108 ms-1, = wavelength (µm,nm,mm,cm,m)

In remote sensing we commonly measure the flux of photons from a unit surface for a certain amount of time and by a camera or scanner a certain distance away with a lens of a particular diameter

This flux is called the radiance L and the units are W m-2 sr-1.Watts W (power) are energy per unit time (J s-1)Sr stands for steradian and is the solid angle subtended by the pixel

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On a plane, we can measure the angle q between 2 vectors sharing endpoint P, the center of a circle of radius r. A radian is defined as the angle that subtends an arc on a circle equal to the radius. It is about 57 degrees (360/2).

A circle is divided into 360 degrees, or 2 radians.

In a volume, we can measure solid angles as shown to the right, where P is the center of a sphere of radius r and q is the solid angle of a cone that intersects the sphere in a small circle of circumference *C. A sphere (area = 4r2) contains 4steradians, where a steradian (sr) is the unit of solid angle. The cone defined to the right subtends a solid angle of 1 sr.

Review On Solid Angles, class website (Ancillary folder: Steradian.ppt)

Let’s start with how humans sense color:

Cone-shaped cells within the eye absorb light in 3 wavelength ranges – RGB

They send signals to the brain proportional to how much light is absorbed

The brain turns these signals into thesensation of color

Color has three attributes – hue, saturation, and intensity or lightness

color (perception) is related to radiance (physical flux)

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Section of the eye

DAYBright light

NIGHTDim light Rods are more sensitive than cones

In bright light, the three sets of cones send strong signals to the brain that drown out the signal from the rods. The signals are interpreted as the sensation of color

In dim light, the signal from the single set of rods is dominant. It is interpreted as the sensation of black/white (gray)

1 nanometer (nm) = 10-9 m = 10-3 m6

Additive Color

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Blue Green Red

The spectrum and color

Blue Green RedBlue Green Red

Spectral yellow

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brig

htne

ss

Wavelength, (m)

Gray

Cartoon spectrum – A useful tool

Additive Color

Blue Green Red Blue Green Red

+

Blue Green Red

=

Blue Green Red

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b r

g

Additive mixtures – another framework

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0, 100, 0%

0, 0, 100%100, 0, 0%

33, 33, 33%

50, 50, 0%

ADDITIVE

MIXING

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To work with color, we use three different data “spaces”:

*Perceptual data space– how we sense color intuitively (Hue, saturation, intensity)

*Radiance data space – how the color stimulus is described by the measured image

data

*Transformed DN space – a mathematical description of color that is related to radiance

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HUE

SATURATION

INTENSITY (LIGHTNESS)

A simple perceptualcolor space (HSI)

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2) RGB radiance space

0

R

B

G

r

g

b

r=R/(R+G+B)g=G/(R+G+B)b=B/(R+G+B)

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The CIE system: characterizes colors by a brightness parameter Y plus two color coordinates x and y.

The response of the eye is best described in terms of three tristimulus coordinates rgb.

Colors that can be matched by combining a set of three primary colors (ie, Red, Green, Blue) are represented on the chromaticity diagram by a triangle joining the coordinates for the three colors.

Any H,S pair can be expressed in terms of the CIE color coordinates x and y, but intensity is not represented.

3) Transformed data space

x

y

b

r

g

r=R/(R+G+B)g=G/(R+G+B)b=B/(R+G+B)

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b r

g

Additive mixtures

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Transformation from a Cartesian XYZ radiance space to a spherical color space

Longitude = hue (H)Co-latitude = saturation (S)Radius = intensity (I)

XYZ may be any three tristimulus fluxes but are treated as RGB

0

X

Z

Y

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Natural colorIntensity

Transformed Viking Lander RGB imagesof Mars

HUE SAT

INT

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Color is created by selective Absorption

If L is the radiance from a source at strength Lo after passage through an absorbing medium such as the atmosphere, then:

L = e-kz Lo W m-2 sr-1 (Beer-Lambert-Bouguer Law)

Light must either be reflected, absorbed, or transmitted

This is the “rat” law of conservation: L= Lr + La + Lt

e-kz describes the % of light transmitted through the medium (assuming Lr =0)

k is a value characteristic of the absorptivity of the mediumz is the length of passage through the medium (which we take to be

homogeneous)

Bouguer

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0

0.2

0.4

0.6

0.8

1

0 10 20 30 40 50

Fraction of light transmitted

Fra

ctio

n of

ligh

t tra

nsm

itte

d

Thickness, mm

If it goes through z mm of medium, the total light remaining is e-kz %, where 1/k is the scale depth – that is, for every 1/k passage through the medium, 1/e = 1/2.718 % = 36.8% of the light remains.

Absorption by a homogeneous medium is a constant-rate process – for every mm of material the light passes through, a certain fraction is absorbed.

Graph of absorption as a function of medium thickness

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Absorption and color

• k is commonly different from wavelength to wavelength (k)– eg, more light might be absorbed in green than in red or blue

• When we see light having passed through such a filter, it appears magenta to us (ie, no green).

• We need to consider remote-sensing fluxes to be functions of wavelength

• Thus, radiance L (W m-1 sr-1) becomes spectral radiance L (W m-1 sr-1 µm-1)

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A word about filters…

Filters

Filter functions

, m

Tra

nsm

itta

nce

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“Subtractive” Color

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“Subtractive” Color

Blue Green Red Blue Green Red

Blue Green Red

*

=

1% 1% 100%

Red-transmitting filterInput spectrum

Filtered spectrum

Scene

Filter

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Remember: “subtractive” mixing is physically done by multiplication

white light green

filteryellowfilter

green light

dark greenlight

R: 1.0 * 0.0 = 0.0; * 0.8 = 0.0G: 1.0 * 0.9 = 0.9; * 0.8 = 0.7B : 1.0 * 0.0 = 0.0; * 0.0 = 0.0

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Next lecture: Radiative transfer & sources

we will trace radiation from its source to camera

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