Optical Coatings
Optical Coatings
Optical Coatings
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Separation of Nodal Point<br />
from Corresponding Principal Point<br />
HN = H″N″ = (n″4n)/k, positive for N to right of H<br />
and N″ to right of H″.<br />
Back Focal Length<br />
f b = f ′′ + AH. 2 ′′ (see eq. 1.49)<br />
Front Focal Length<br />
f f = f 4 A1H.<br />
(see eq. 1.51)<br />
Focal Ratios<br />
The focal ratios are f/f and f ″/f, where f is the diameter of the<br />
clear aperture of the lens.<br />
Numerical Apertures<br />
n sin v<br />
⎛ f ⎞<br />
where v = arcsin ⎜<br />
⎝ 2s<br />
⎟<br />
⎠<br />
and<br />
n′′<br />
sin v"<br />
⎛ f ⎞<br />
where v" = arcsin ⎜<br />
⎝ 2s ′′<br />
⎟<br />
⎠<br />
.<br />
Solid Angles (in steradians)<br />
Q = 2 p(1 4 cos v)<br />
⎛ v ⎞<br />
2<br />
= 4p<br />
sin ⎜<br />
⎝ 2<br />
⎟<br />
⎠<br />
⎛ f ⎞<br />
where v = arctan ⎜<br />
⎝ 2s<br />
⎟<br />
⎠<br />
(see eq.1.48)<br />
Q ″ = 2p 2 p<br />
(1 4 cos v″)<br />
′′)<br />
⎛ v ⎞<br />
2<br />
= 4p<br />
sin ⎜<br />
⎝ 2<br />
⎟<br />
(1.68)<br />
⎠<br />
⎛ f ⎞<br />
where v′′<br />
= arctan ⎜<br />
⎝ 2s ′′<br />
⎟<br />
⎠<br />
.<br />
To convert from steradians to spheres, simply divide by 4p.<br />
APPLICATION NOTE<br />
For Quick Approximations<br />
Much time and effort can be saved by ignoring the<br />
differences among f, f b , and f f in these formulas<br />
(assume f = f b = f f ) by thinking of s as the lens-toobject<br />
distance, by thinking of s″ as the lens-to-image<br />
distance, and by thinking of the sum of conjugate<br />
distances s + s″ as being the object-to-image distance.<br />
This is known as the thin-lens approximation.<br />
APPLICATION NOTE<br />
Physical Significance of the Nodal Points<br />
A ray directed at the primary nodal point N of a lens<br />
appears to emerge from the secondary nodal point<br />
N″ without change of direction. Conversely, a ray<br />
directed at N″ appears to emerge from N without<br />
change of direction. At the infinite conjugate ratio,<br />
if a lens is rotated about a rotational axis orthogonal<br />
to the optical axis at the secondary nodal point<br />
(i.e., if N″ is the center of rotation), the image<br />
remains stationary during the rotation. This fact<br />
is the basis for the nodal slide method for measuring<br />
nodal-point location. The nodal points coincide with<br />
their corresponding principal points when the image<br />
space and object space refractive indices are equal (n<br />
= n″). This makes the nodal slide method the most<br />
precise method of principal-point location.<br />
Fundamental Optics Gaussian Beam Optics <strong>Optical</strong> Specifications Material Properties <strong>Optical</strong> <strong>Coatings</strong><br />
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