1/13/2008
21
ECE
415
EXPERIMENT NO. 2
LENSPINHOLE SPATIAL FILTERS AND BEAM EXPANDERS
PURPOSE
:
To study the operations of beam expanders and lenspinhole spatial filters and to
practice alignment of simple optical components.
REFERENCES
:
1.
C. L. Chen,
Elements of Optoelectronics & Fiber Optics
, Irwin, (1996), Sections 2.4
and 2.8, pp. 4955 and 6874.
2. A. Nussbaum and R. A. Philips,
Contemporary Optics for Scientists and Engineers
,
PrenticeHall, Inc.,
Englewood, NJ (1976), Chapter 10.
3.
E. Hecht,
Optics
, AddisonWesley, 4th edition, (2002), Chapter 11.
4.
F. L. Pedrotti and L. S. Pedrotti,
Introduction to Optics
,
Second edition, Prentice
Hall, (1993), Section 163.
5.
B. J. Pernick, "Irradiance uniformity and power loss with a spatially filtered
laser beam,"
Rev. Sci. Instrum
., Vol. 45, pp. 134447, (1974).
6.
Notes on "Autocollimation of convex lens." (Attached)
7.
M. E. Cox, "The lenspinhole spatial filter,"
Physics Education
, Vol. 14, pp. 56
57, (1979).
(Attached)
8.
J. M. Yaeli, "Method for designating the optical axis of a refracting system,"
Opt. Eng.
, Vol. 19, pp. 438439 No. 3, (1980)
REMARKS
:
The beams emitted by typical HeNe lasers may be approximated accruately as
Gaussian beams.
A detailed discussion of the properties of Gaussian beams can be
found in Section 2.4 of Ref. [1]. We briefly discuss the key properties of Gaussian beams
here. The irradiance distribution of a Gaussian beam is:
)
z
(
w
/
r
2
2
2
2
e
w
P
2
)
z
,
r
(
I
−
∞
π
=
(1)
where I(r,z) is the irradiance (W/m
2
) at a distance r from the beam axis and at a
distance z from beam waist,
P
∞
is the total beam power (W), and w(z) is the beam
radius at which the irradiance reduces to e
−
2
of the onaxis value. The beam diameter at
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z is to 2w(z).
A derivation of (1) is given in p. 52 of Ref. [1]. In fact, (1) is exactly (2.60)
of Ref. [1].
Outside the Rayleigh range, a Gaussian beam diverges or spreads at a half angle
(Figure 1),
θ
h
=
λ
π
w
o
(2)
where 2
θ
h
is the full cone angle to the e
−
2
irradiance points and w
o
is the beam waist
radius. (Also see (2.62) of Ref. [1]).
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