## M

9.1 Singlet Lenses nR RJn R

9.1 Singlet Lenses nR RJn R

Fig. 9.5 Anastigmatic monocentric magnifier (A) corrected in all orders for the three first aberrations. Lens components (B) individually satisfying the Abbe sine condition. In a high power microscope, these are classically used for reducing the beam divergence in the front part of the objective (C) where the final imaging convergence must be achieved by cemented lenses

Fig. 9.5 Anastigmatic monocentric magnifier (A) corrected in all orders for the three first aberrations. Lens components (B) individually satisfying the Abbe sine condition. In a high power microscope, these are classically used for reducing the beam divergence in the front part of the objective (C) where the final imaging convergence must be achieved by cemented lenses which for the two cases with a virtual conjugate entails M = n or M = 1/n. In this cases one shows that these meniscus lenses also satisfy the Abbe sine condition.

Such thick and thin lenses have many applications for the design of high power microscope objectives. Given the extremely narrow field of view for numerical aperture (cf. Sect. 1.9.2) close to N.A. = n sin |^max| = 1 - or 1.25 with oil immersion -, the first face of the monocentric thick lens can be designed flat. One or several meniscus lenses with their first face in normal incidence allow reduction of the divergence of the beam (Fig. 9.5). However, such lenses assembled together cannot provide a real image by fulfilling the aplanatism condition and correcting the chromatic aberrations, so the final imaging stage of a microscope objective must be formed by additional doublet lenses.

### 9.1.4 Isoplanatic Singlet Lenses and Remote Pupil

Since Sphe 3 of a thin lens with spherical surfaces cannot be corrected for both real conjugates, we may consider lenses that compensate for Coma 3 only, i.e. where SI = 0. Such a coma-free lens is called an isoplanatic lens because it is not stigmatic. For real conjugates, the convergence angles are such as u1u2 < 1 which, from (9.2b), entails C 1.

Pupil at the lens: Setting the pupil at the lens, the conditions for an isoplanatic lens, Su = 0 from (9.5b), and for real conjugates are n + 1 B + 2-n+!C = 0 and C < 1. (9.13)

If the conjugates are opposites with M = -1, i.e. C = 0, we obtain B = 0:

^ At transverse magnification M = -1, a Coma 3 corrected lens is an equicon-vex lens.

If one of the conjugates is at infinity, ui = 0 or u'2 = 0, and

The substitution of B into (9.4) gives c2 1 + n

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