Microscope objectives

Numerical aperture

The numerical aperture \(NA\) is usually provided by the manufacturer: \[ NA = n \sin\theta \tag{1}\] where \(n\) is the refractive index of the object and \(\theta\) is the collection half angle (Hecht 2016). The \(NA\) is often used to calculate other properties of an objective, but this should be done with caution:

• The objective should, at minimum, collect at the specified \(NA\) on the optic axis (or to within a tolerance of a few %). However, it may not image stigmatically at this \(NA\) and so the effective angular collection for a given property of the lens (e.g. resolution) may be lower.
• The off axis \(NA\) may be further reduced, not only from the limits of the optical design, but by purposeful vignetting from a physical stop or aperture, which directly removes the aberrated light that is often most pronounced at the highest angles and away from the optic axis.
• Whilst the design may indeed show (via simulation) that a perfectly made lens would deliver a certain \(NA\). Real world manufacturing and tolerancing may further limit or reduce the final angular range that gives diffraction limited imaging.