One of the main hologram characteristics is the diffraction
efficiency . In the general case, the diffraction efficiency
is determined by the ratio of the power of the diffracted light
beam
to the incident power of the beam
given by this relation:
(23)
The power of the beam is determined by the integral of the light
intensity over the surface of the detector :
(24)
In the case of lasers with Gaussian light beams, the relation
between the mean light intensity and power is
described by:
(25)
where is the Gaussian radius of the beam. If the light
intensity of the subject and reference beams are and
and the diffracted beam intensities are ,
then the diffraction efficiency is given by:
(26)
The diffraction efficiency depends on the wavelength as well as on
the thickness of the recording medium. For different elementary
holographic gratings the diffraction efficiency is summarized in
Table 1. The diffraction efficiency depends on whether
the hologram is 3-D or 2-D, phase or amplitude, and on the type of
grating profile. Note that the brightness of the images made in
amplitude holograms does not depend very strongly on the thickness
of the medium, the maximum for 3-D holograms is 3.7%, which is
significantly smaller than for 2-D, 6.25%, Table 1.
Amplitude recordings have a much lower diffraction efficiency than
phase holograms which, of course, makes them less attractive. The
diffraction efficiency can be used to determine the type
(amplitude/phase, thick/thin) of hologram being investigated.
Table 1:
Diffraction efficiency for different transmission grating types [2]
diffraction efficiency; amplitude
transmittance; modulation factor ;
amplitude of modulated index of absorbtion; mean index
of absorbtion after exposure; thickness;
angles of incidence in a vacuum and in a medium, respectively.
Dim
Profile
Equation for diffraction efficiency
Amplitude holograms
3-D
sinusoidal
3.7
2-D
sinusoidal
6.25
2-D
rectangular
10.1
Phase holograms
3-D
sinusoidal
100
2-D
sinusoidal
33.0
2-D
rectangular
40.5
In general, however, the real time recording almost always leads
to mixed amplitude/phase holograms. For high efficiency hologram
recording the absorption of the medium (at the recording
wavelength ) must be sufficiently strong. The
properties of the recorded hologram depend on the wavelength used
during reconstruction, . Upon reconstruction with
light of the same wavelength
, the
hologram is usually an amplitude and during readout the
holographic properties can be changed by the photoactive light.
Therefore, it is more common for the reconstruction light to be of
longer wavelength
. In such a case,
the hologram is usually a phase hologram with a higher diffraction
efficiency and the readout process would not change the properties
of the recorded hologram (i.e., the light of is not
photoactive). However, for optimal reconstruction efficiency at
, the angle of incidence for the
reference beam during readout must be changed from to
. According to (17), is
given by:
(27)
Grating period is determined by and
. For light sensitive
films, the
optimal wavelengths for recording and readout are
nm ( laser) and
nm
(He-Ne laser). For grating periods of 0.5-1.0 m and
, the angle correction
is approximately 20%. Under such conditions, in 10
m thick films, diffraction efficiency of 80% was reached
which is close to the theoretical limit (Table 1). The
diffraction efficiency is decreased from the theoretical maximum
(100% for 3-D phase holograms) when the amount of reflected light
increases. Thus, materials with very high refractive indices like
films , which makes a reflection
coefficient of 18% must be coated with antireflection layers.
This is particularly important for optoelectronic devices
[10,6].
Note that is a function of the amplitude of the induced
holographic grating
, Table 1,
Fig. 8) which depends on the length of exposure
and its intensity .
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2002-05-23