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handbook of modern sensors

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132 4 Optical Components <strong>of</strong> Sensors<br />

Table 4.2. Point Source Relationships<br />

Description Radiometric Photometric<br />

Point source intensity I r , W/sr I L , lumens/sr<br />

Incident flux density Irradiance, H = I r /r 2 , W/m 2 illuminance, E = I L /r 2 , lumens/m 2<br />

Total flux output <strong>of</strong> a P = 4πI r , watts F = 4πI L , lumens<br />

point source<br />

Source: Adapted from Ref. [2].<br />

Table 4.3. Area Source Relationships<br />

Description Radiometric Photometric<br />

Point source intensity B r , W/(cm 2 sr) B L , lumens/(cm 2 sr)<br />

Emitted flux density W = πB r , W/cm 2 L = πB L , lumens/cm 2<br />

Incident flux density H = B rA s<br />

r 2 + R 2 , W/cm2<br />

Source: Adapted from Ref. [2].<br />

E = B LA s<br />

r 2 + R 2 , lumens/cm2<br />

4.3 Windows<br />

The main purpose <strong>of</strong> windows is to protect interiors <strong>of</strong> <strong>sensors</strong> and detectors from<br />

the environment. A good window should transmit light rays in a specific wavelength<br />

range with minimal distortions. Therefore, windows should possess appropriate characteristics<br />

depending on a particular application. For instance, if an optical detector<br />

operates under water, its window should possess the following properties: a mechanical<br />

strength to withstand water pressure, a low water absorption, a transmission band<br />

corresponding to the wavelength <strong>of</strong> interest, and an appropriate refractive index which<br />

preferably should be close to that <strong>of</strong> water. A useful window which can withstand high<br />

pressures is spherical, as shown in Fig. 4.7. To minimize optical distortions, two limitations<br />

should be applied to a spherical window: an aperture D (its largest dimension)<br />

must be smaller than the window’s spherical radius R 1 , and a thickness d <strong>of</strong> the window<br />

must be uniform and much smaller than radius R 1 . If these conditions are not<br />

met, the window becomes a concentric spherical lens.<br />

A surface reflectivity <strong>of</strong> a window must be considered for its overall performance.<br />

To minimize a reflective loss, windows may be given special antireflective coatings<br />

(ARCs) which may be applied on either one or both sides <strong>of</strong> the window. These are<br />

the coatings which give bluish and amber appearances to popular photographic lenses<br />

and filters. Due to a refraction in the window (see Fig. 4.4), a passing ray is shifted<br />

by a distance L which, for small angles 1 , may be found from the formula<br />

L = d n − 1<br />

n , (4.21)<br />

where n is the refractive index <strong>of</strong> the material.<br />

Sensors operating in the far-infrared range require special windows which are<br />

opaque in the visible and ultraviolet spectral regions and quite transparent in the<br />

wavelength <strong>of</strong> interest. Several materials are available for the fabrication <strong>of</strong> such

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