This situation can be improved by using a two-element system. The second part of
the figure shows a precision achromat (01 LAO 014), which consists of a positive
low-index, crown-glass element (shown in blue) cemented to a negative meniscus
high-index, flint-glass element (shown in yellow). This is drawn to the same scale
as the plano-convex lens. No spherical aberration can be discerned in the lens.
Of course, not all of the rays pass exactly through the paraxial focal point;
however, in this case, the departure is measured in micrometers, rather than in
millimeters, as in the case of the plano-convex lens. Additionally, chromatic
aberration (not shown) is much better corrected in the doublet. Even though these
lenses are known as achromatic doublets, it is important to remember that even
with monochromatic light the doublet's performance is superior.
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Single element plano-convex lens compared with a two-element achromat
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The figure also shows the f-number at which singlet performance becomes unacceptable. The ray with f/# = 7.5 practically intercepts the paraxial focal point, and the ray with f/# = 3.8 is fairly close. This useful drawing, which can be scaled to fit a plano-convex lens of any focal length, can be used to estimate the magnitude of its spherical aberration, although lens thickness affects results slightly.
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Unit Conjugate Ratio
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The figure below shows three possible systems for use at the unit conjugate ratio.
All are shown to the same scale and using the same ray f-numbers with a light
wavelength of 546.1 nm. The first system is a symmetric biconvex lens (01 LDX 027),
the best-form singlet in this application. Clearly, significant spherical aberration
is present in this lens at f/# = 2.7. Not until f/# = 13.3 does the ray closely
approach the paraxial focus.
A dramatic improvement in performance is gained by using two identical plano-convex lenses with convex surfaces facing and
nearly in contact. Those shown are both 01 LPX 081. The combination of these two lenses yields almost exactly the same focal
length as the biconvex lens. To understand why this configuration improves performance so dramatically, consider that if the biconvex lens were split down the middle, we would have two identical plano-convex lenses, each working at an infinite conjugate ratio, but with the convex surface toward the focus. This orientation is opposite to that shown to be optimum for this shape lens. On the other hand, if these lenses are reversed, we have the system just described but with a better correction of the spherical aberration.
We have shown that an achromat is superior in performance to a singlet when used at the infinite conjugate ratio and at low
f-numbers. Since the unit conjugate case can be thought of as two lenses, each working at the infinite conjugate ratio, the
next step is to replace the plano-convex singlets with achromats, yielding a four-element system. The third part of the
figure shows a system composed of two 01 LAO 037 lenses. Once again, spherical aberration is not evident,
even in the f/# = 2.7 ray.
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Three possible systems for use at the unit conjugate ratio
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