Chemical Engineering January 2016 - 56

FIGURE 6. When the source of light is small compared to the illuminated object, the light produced is
hard. When the source of light is large compared to the illuminated object, the light produced is soft [4].
Note the differences in the shadow patterns on the subjects
Phong Reflection Model
When an optic reflection model -
called the Phong Reflection Model
(box, p. 56) - is applied, then the
mechanism for how undiffused light
and diffused light behaves becomes
more clear. The Phong Reflection
Model is an empirical model for light
reflection, which calculates the intenT
sity
of light using a number of inputs
(see sidebar, below, for details). It is
commonly used in reflection calculations
for computer rendering [1].
Because no surface is perfectly
smooth - even highly polished stainless
steel has tiny hills and valleys on
its surface - these imperfections
affect the angle at which the light
PhonG REFlEctIon ModEl
he Phong Reflection Model (Equation 1) calculates the intensity of light at any
point (Ip) using the material's specular reflection constant (ks), diffused reflection
constant (kd), ambient reflection constant (ka), and shininess constant (), along
with the direction vector of the light source (Lˆ m
*
), the normal vector of reflection (Nˆ ), the
ideal reflection vector (Rˆm ), and the viewer vector (Vˆ ). The inputs to the Phong Reflection
Model are the ambient lighting intensity (ia), the specular intensity (is), and the diffused
intensity (id) [1].
Ip = ka
ia
+
m lights kd Lˆ m
()im,d
Nˆ
+ ks Rˆ m
() im,s
Vˆ
(11)
In the Phong Reflection Model, the light from an undiffused LED light source can be assumed
to be only specular light (light that reflects at a consistent angle), while the light from
a diffused LED can be assumed to be entirely diffused light [2]. Assuming that the intensity
of the light source is the same for both LEDs, the intensity of light reflected for the undiffused
light is dependent on the dot product of Rˆm and Vˆ , while the intensity of diffused
light is dependent on the dot product [Note: A dot product is an algebraic operation used
to describe the resulting magnitude of two different vectors. When the vectors are perpendicular
to each other, the dot product is 0; when the vectors are parallel to each other, the
dot product is equal to A*B].]
For undiffused light, the dot product of Rˆm and Vˆ
creates a large variation of intensities
that a surface is capable of producing. Since no surface is perfectly smooth, there are hills
and valleys present that will affect the angle that the light will reflect [3] (Figure 8). The smaller
the angle between the vectors, the more intense the light. However, due to the way light
deflects off of surfaces, only a small range of surface angles will result in the difference between
the vectors being small. While most of an object's surface will have a lower intensity,
areas with the proper angle will be noticeably more intense. And importantly, the intensity of
the light will also change based on how the user orients his or her view, so features on the
surface can appear and disappear based on the angle at which they are viewed [5].
For diffused light, the dot product of Lˆ m and Nˆ will result in less variable light compared
with the undiffused dot product. While the natural roughness of an object will result in a wide
variation in Nˆ , Nˆ
will not change unless the surface is modified (Figure 9). This means that
the only way to affect the intensity of diffused light is to change Lˆ m .
This is in contrast to the undiffused light source, where the intensity of the reflected spectral
light will be affected by changes in both Lˆ m and Vˆ . This makes the intensity of the
diffused light constant for any viewer angle. Additionally the Nˆ of a flat surface will average
out to be perpendicular to the surface, unlike the Rˆm which can vary widely based on many
factors of the surface roughness.
56
FIGURE 9. When diffused light reflects off of an
uneven surface, the difference between the light
vector and the normal vector affects the intensity
of the reflected light
reflects [2]. The smaller the angle between
the vectors, the more intense
the reflection. The model predicts
that the intensity of the diffused light
will be constant for any viewer angle,
and that undiffused light will reflect
light more intensely in some areas
when viewed at certain angles.
ChemiCal engineering www.Chemengonline.Com january 2016
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FIGURE 7. Figure 7a (left): Shadowing occurs on a
rough surface. The light is unable to reach certain
areas of the surface. Figure 7b (right): Masking occurs
on a rough surface. The light is reflected off
the geometry of the surface in such a way that the
region will gain increased intensity
V
R
FIGURE 8. When spectral light reflects off of an uneven
surface the difference between the reflection
vector and the viewer vector affects the intensity
of the reflected light
N
L
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Chemical Engineering January 2016

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