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A. Approximation of the Inclination Factor
During the derivation of the Fresnel and the Fraunhofer diffraction
formulae (4.14) and (4.15), respectively,
the inclination factor occurring in (4.10) has been
approximated under the assumption that the source
x_{s} as well as the
observation point
x_{o} are located near the optical axis
(cf. Figure 4.1).
We will now explain how this approximation is obtained.
First we define three angles , , and
guided by Figure 4.1 and shown in
Figure A.1:

(A.1) 
The approximation of the inclination
factorcompare (4.12)
with (4.14) or (4.15)thus writes to

(A.2) 
Furthermore we introduce the two auxiliary angles
and
as illustrated in Figure A.1.
In the situation of interest the two points
x_{s} and
x_{o} are
near the optical axis and thus
,
1
yielding

(A.3) 
By noting that the sum of the angles of the two triangles
{x_{o},x^{},x} and
{x_{s},x,x^{}} equals ,
we get^{a}

(A.4) 
With these two expressions for
and
and the approximations
listed in (A.3), the derivation of (A.2)
is straight forward:
Figure A.1:
Approximation of
the inclination factor. The dashed lines indicate the two
auxiliary triangles used throughout the derivation.

Footnotes
 ... get^{a}
 The terms
forming one common triangleangle are indicated by delimiters
(cf. Figure A.1).
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Up: PhD Thesis Heinrich Kirchauer
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Heinrich Kirchauer, Institute for Microelectronics, TU Vienna
19980417