Download FILTERS AND BEAM SPLITTERS Several of the applications of

FILTERS AND BEAM SPLITTERS
Several of the applications of scientific optical filters are in photography,
optical communication, radar systems, holography, and general laser and
electro-optical laboratory experiments.
Filters can be classified into three categories, according to the way they’re
used:

Attenuation filters

Wavelength-selective filters (both transmissive and reflective)

Polarization filters
Attenuation Filters
Attenuation filters are used to reduce the intensity of a light beam. Highquality attenuation filters are said to have a "flat response." This means that
they attenuate all wavelengths of light over their usable spectral range by the
same amount.
Neutral-density Filters
Neutral-density filters are uniform, "grey" filters that absorb and/or reflect a
fraction of the energy incident upon them. The term "neutral" is designated
because the absorption and/or reflection characteristics of the filter are
constant over a wide wavelength range.
Fig. 8
Idealized spectrophotometric curve for a neutral-density filter
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It’s useful here to define "optical density" as it applies to filters. Optical
density is the degree of opacity of a translucent medium. It is given by the
equation OD = –log10T where T is the transmittance of the filter.
Table 2 lists the values of optical density for transmission filters. Note, for
example, that if the transmission through the filter is 10%, the transmittance
is 0.1 and the corresponding optical density is
A filter with 100% transmittance quite properly has an optical density of
0.When light travels through a filter, a part of the beam is reflected at the
two air-glass interfaces (plastic-air interface of gelatin filters) and another
part of the beam is absorbed. Assuming that scattering and fluorescence are
negligible, the remainder of the irradiance is transmitted through the filter.
Accordingly, the following equation is applicable:
EO = ER + EA + ET
Equation 1
where: EO = Irradiance of incident
light
ER = Irradiance of reflected
light
EA = Irradiance of absorbed
light
ET = Irradiance of transmitted
light
Table 2. Optical Densities of Transmission Filters
% Transmission
Transmittance
Optical Density
0.01
0.0001
4
0.1
0.001
3
1.0
0.01
2
2
10
0.1
1
20
0.2
0.7
40
0.4
0.4
70
0.7
0.15
90
0.9
0.05
100
1.0
0
Wavelength-selective Filters (Color Filters)
The most complete description of the optical behavior of a filter is given by
its spectrophotometric curve (also called transmittance): that is, a plot of
wavelength versus transmittance. An example of a family of rather idealized
spectrophotometric curves for a specific absorption filter is shown in
Figure 9.
Fig. 9
Spectrophotometric curve for a family of various thickness absorption filters
For absorbing filters, the transmittance is an exponential function of
thickness,
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Equation 2
where:
ti = Transmission of front surface of filter
t2 = Transmission of back surface of filter
 = Filter absorption coefficient (cm?1) at wavelength 
x = Filter thickness (cm)
The product t1t2 sometimes is called the "filter correction factor." For light
incident normally on the filter surface, it’s given by,
Equation 3
where: n = index of refraction of the filter glass (relative to air).
The top curve in Figure 9 is for a filter two millimeters thick. The second
curve is for a filter four millimeters thick. It has 63.2% less transmittance.
The top curve in Figure 9 transmits light at 500 nm very well. But is would
transmit very little light at a wavelength less than 440 nm or greater than
560 nm.
Wavelength-selective filters are used to produce or select specific color or
band of color from a white light source, to isolate a specific wavelength, or
to reject a specific wavelength or band of wavelengths. We will study three
general classes of wavelength-selective filters according to their usefulness:
1. Cut-off filters—The first class consists of cut-off filters that have an
abrupt division between the regions of high and low transmission. If a
filter transmits the shorter wavelengths and rejects the longer
wavelengths, it’s called a short-wave-pass filter. If it transmits the
longer wavelengths and rejects the shorter wavelengths, it’s called a
long-wave-pass filter. Note that some books use annotation derived
from electronics, where frequency rather than wavelength is signified.
In this notation a long-wave-pass filter is called a "low-frequencypass filter," and a short-wave-pass filter becomes a "high-frequencypass filter." Examples of short-wave-pass and long-wave-pass filters
are shown in Figures 10 and 11.
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Fig. 10
Idealized short-wave-pass filter (high-frequency-pass filter)
Fig. 11
Idealized long-wave-pass filter (low-frequency-pass filter)
The most important characteristic of a cut-off filter is the wavelength
describing the position of the sharp cut-off. Different manufacturers
define this position to be the wavelength at 3, 5, 30 or 37%
transmission (0.37 transmittance). This definition is quite arbitrary,
but we recommend that you use the 37% point.
It’s also important to describe the sharpness of the cut-off or the
steepness of the curve at the transition between low and high
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transmission. This has been set arbitrarily as the wavelength
difference between 5 and 70% transmission points. It is called the
slope of cut-off.
2. Bandpass filters—The second class of filters are those called
"bandpass." An example of a bandpass filter is shown in Figure 12.
Fig. 12
Description of a bandpass filter
These filters are characterized by the following parameters:
o
The peak transmittance (Tmax) and its corresponding
wavelength (p).
o
The bandwidth, the wavelength interval between the two points
on the transmittance curve where the transmittance is 50% of
Tmax. This is called the full width at half maximum (FWHM).
o
The central wavelength (c), which is midway between the
halfwidth points on the curve.
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