# High Numerical Aperture Objectives

TIRFM instrument configurations lacking a prism have been developed to take advantage of high numerical aperture immersion objectives to both produce excitation illumination at supercritical angles and to retrieve fluorescence information emitted by the specimen. This tutorial explores the effect of objective numerical aperture on incident angles in TIRFM.

The tutorial initializes with the objective numerical aperture set to 1.42, the refractive index between the front lens and the glass coverslip equal to 1.52, and a corresponding incident angle of 72.4 degrees. To operate the tutorial, use the **Numerical Aperture** slider to adjust the value of the virtual objective's numerical aperture between 1.2 and 1.65. At numerical apertures below 1.38, total internal reflection is not achieved and the incident beam passes through the objective, immersion oil, and microscope coverslip before it is refracted into the atmosphere according to Brewster's angle. In the numerical aperture range between 1.39 and 1.45, the refractive index of the immersion medium and the glass coverslip is 1.52, and incident angles for total internal reflection are calculated based on this value. At numerical apertures between 1.46 and 1.65, the refractive index is assumed to be 1.78 for the immersion oil and coverslip. Varying the numerical aperture will either increase or decrease the incident angles, which are calculated and displayed in the upper left-hand corner of the tutorial window.

This technique can be performed inexpensively using any upright or inverted fluorescence microscope without a specialized prism. Among the benefits of using objectives for excitation are the ability to utilize standard mercury or xenon arc light sources to replace, or complement, external laser illumination. Specimen preparation, manipulation, and observation is also simplified because open Petri dishes or culture chambers can be illuminated from beneath the stage, providing unobstructed access to cells or tissues that are being studied. The method also enables rapid interconversion between illumination modes (laser to arc lamp), often by closing a shutter and repositioning a beamsplitter or mirror, without major microscope reconfiguration. Finally, objective illumination TIRFM techniques also are able to provide illumination over small spots (a micron or two) or entire fields, and can be made visually free of interference fringes.

Objectives with a numerical aperture equal to or exceeding 1.4 have been successfully employed for prismless TIRFM to produce the necessary supercritical incident angle in order to excite the specimen with an evanescent field. The incident beam must be constrained to pass through the periphery of the objective's pupil and must emerge from the front lens and into the immersion fluid with only a narrow spread of conical angles. To assure proper trajectory through the objective, the incident laser (or appropriately restricted arc lamp) beam is focused off-axis at the objective rear focal plane. Light emerges into the immersion oil (having a refractive index of 1.518 to 1.78, depending upon objective numerical aperture) at a maximum angle, which is given by the equation**:**

**Numerical Aperture (NA) = n(2) • sin(θ)**

where **n(2)** is the refractive index of the imaging medium (immersion oil) and **θ** is the half-angle of the objective aperture. For total internal reflection to occur at the specimen surface, **θ** must exceed the critical angle (**θ(c)**), which is given by**:**

**n(1) = n(2) • sin(θ**

_{c})And rearranges to**:**

**θ**

_{c}= sin^{-1}(n(1)/n(2))where **n(1)** is the refractive index of the liquid (water or buffer) at the total internal reflection interface. The result is a critical angle of 61.4 degrees when aqueous buffer and glass comprise the interface media. Light rays emerging from the objective can form a maximum angle (**θ(m)**) that is dictated by the numerical aperture of the objective. Because only those rays propagating at angles greater than the critical angle will produce an exponentially decaying evanescent field at the interface, the condition imposed on the objective for total internal reflection is**:**

**sinθ**

_{m}> sinθ_{c}From these equations, it is evident that the objective numerical aperture must exceed **n(1)**, preferably by a substantial margin. This is not a problem when the objective has a numerical aperture of at least 1.4, and the interface consists of an aqueous buffer having a refractive index of 1.33 coupled to a glass microscope slide (or coverslip with a refractive index of at least 1.52). However, for viewing inside a cell, which has a refractive index ranging from 1.36 to 1.38, the objective numerical aperture produces a very thin margin for total internal reflection observation. Newer objectives having numerical apertures ranging from 1.45 to 1.65 have been developed for TIRFM, which allow greater incident angles and more control over the evanescent field penetration depth.