The resolving power of an objective determines the size of the Airy diffraction pattern formed, and the radius of the central disk is determined by the combined numerical apertures of the objective and condenser. When the condenser and objective have equivalent numerical apertures, the Airy pattern radius from the central peak to the first minimum is given by the equation:

**r( _{Airy}) = 1.22λ/2NA(_{Obj})**

where r(Airy) is the Airy radius, λ is the wavelength of illuminating light, and NA(Obj) is the objective (and condenser) numerical aperture. The numerical aperture is dependent upon the angle of the inverted cone of illumination entering the objective aperture, as well as the refractive index of the imaging medium:

**NA( _{Obj}) = n(sin(θ))**

where θ is the objective angular aperture and n is the refractive index of the medium (air, water, or oil) between the objective and the specimen. The image resolution, (D) is defined by the equation:

**D = 0.61λ/NA (3)**

Resolution is clearly influenced by the objective numerical aperture. Note that lower values of D indicate higher resolution. In the tutorial, the Numerical Aperture slider is utilized to control how image structure evolves as the objective numerical aperture is increased. At the lowest numerical aperture value (0.20), image details visible in the microscope viewport are poorly defined and surrounded by diffraction fringes that are diffuse, but not resolved. As the slider is moved to higher numerical aperture values (0.50-0.80), the structural outline of the image becomes sharper and higher-order diffraction rings begin to emerge. At the highest numerical apertures (1.00-1.30), diffraction disks become individually resolved as discrete luminous points surrounded by alternating series of bright and dark higher-order diffraction rings of decreasing intensity.

**Contributing Authors**

**Rudi Rottenfusser** - Zeiss Microscopy Consultant, 46 Landfall, Falmouth, Massachusetts, 02540.

**Sunita Martini** and **Michael W. Davidson** - National High Magnetic Field Laboratory, 1800 East Paul Dirac Dr., The Florida State University, Tallahassee, Florida, 32310.