12/17/12 ZEISS Microscopy Online Campus | Microscopy Basics | Numerical Aperture and Resolution Contact Us | Carl Zeiss Education in Microscopy and Digital Imaging ZEISS Home ¦ Products ¦ Solutions ¦ Support ¦ Online Shop ¦ ZEISS International ZEISS Campus Home Interactive Tutorials Basic Microscopy Spectral Imaging Spinning Disk Microscopy Optical Sectioning Superresolution Introduction Article Quick Links Introduction Live-Cell Imaging The numerical aperture of a microscope objective is the measure of its Immersion Oil Fluorescent Proteins ability to gather light and to resolve fine specimen detail while working at a Resolution fixed object (or specimen) distance. Image-forming light waves pass Microscope Light Sources Practical Hints through the specimen and enter the objective in an inverted cone as Digital Image Galleries illustrated in Figure 1(a). White light consists of a wide spectrum of Print Version Applications Library electromagnetic waves, the period lengths of which range between 400 and 700 nanometers. As a reference, it is important to know that 1 millimeter equals 1000 Reference Library micrometers and 1 micrometer equals 1000 nanometers. Light of green color has a wavelength range centered at 550 nanometers, which corresponds to 0.55 micrometers. If small objects (such as a typical stained specimen mounted on a microscope slide) are viewed through the Search microscope, the light incident on these minute objects is diffracted so that it deviates from the original direction (Figure 1(a)). The smaller the object, the more pronounced the diffraction of incident light rays will be. Higher values of numerical aperture permit increasingly oblique rays to enter the objective front lens, which produces a more highly resolved image and allows smaller structures to be visualized with higher clarity. Illustrated in Figure 1(a) is a simple microscope system consisting of an objective and specimen being illuminated by a collimated light beam, which would be the case if no condenser was used. Light diffracted by the specimen is presented as an inverted cone of half-angle (α), which represents the limits of light that can enter the objective. In order to increase the effective aperture and resolving power of the microscope, a condenser (Figure 1(b)) is added to generate a ray cone on the illumination side of the specimen. This enables the objective to gather light rays that are the result of larger diffraction angles, increasing the resolution of the microscope system. The sum of the aperture angles of the objective and the condenser is referred to as the working aperture. If the condenser aperture angle matches the objective, maximum resolution is obtained. Introduction Image Formation Microscope Resolution Point-Spread Function Microscope Optical Train Köhler Illumination Optical Systems Microscope Objectives Enhancing Contrast Fluorescence Microscopy Reflected Light Microscopy Reflected Light Contrast In order to enable two objectives to be compared and to obtain a quantitative handle on zeiss-campus.magnet.fsu.edu/articles/basics/resolution.html 1/6 12/17/12 ZEISS Microscopy Online Campus | Microscopy Basics | Numerical Aperture and Resolution Digital Imaging Basics resolution, the numerical aperture, or the measure of the solid angle covered by an objective is Microscope Practical Use defined as: Microscope Ergonomics Numerical Aperture (NA) = η • sin(α) (1) Microscope Care History of the Microscope where α equals one-half of the objective's opening angle and η is the refractive index of the immersion medium used between the objective and the cover slip protecting the specimen (η = 1 for air; η = 1.51 for oil or glass). By examining Equation (1), it is apparent that the refractive index Microscope Lightpaths is the limiting factor in achieving numerical apertures greater than 1.0. Therefore, in order to obtain higher working numerical apertures, the refractive index of the medium between the front Objective Specifications lens of the objective and the specimen cover slip must be increased. The highest angular Optical Pathways aperture obtainable with a standard microscope objective would theoretically be 180 degrees, Microscope Alignment resulting in a value of 90 degrees for the half-angle used in the numerical aperture equation. The sine of 90 degrees is equal to one, which suggests that numerical aperture is limited not only by Concept of Magnification the angular aperture, but also by the imaging medium refractive index. Practically, aperture Conjugate Planes angles exceeding 70 to 80 degrees are found only in the highest-performance objectives that Fixed Tube Microscope typically cost thousands of dollars. Infinity Corrected Optics The resolution of an optical microscope is defined as the smallest distance between two points Infinity Optical System on a specimen that can still be distinguished as two separate entities. Resolution is directly Field Iris Diaphragm related to the useful magnification of the microscope and the perception limit of specimen detail, though it is a somewhat subjective value in microscopy because at high magnification, an image Numerical Aperture may appear out of focus but still be resolved to the maximum ability of the objective and assisting Airy Disk Formation optical components. Due to the wave nature of light and the diffraction associated with these Spatial Frequency phenomena, the resolution of a microscope objective is determined by the angle of light waves that are able to enter the front lens and the instrument is therefore said to be diffraction limited. Conoscopic Images This limit is purely theoretical, but even a theoretically ideal objective without any imaging errors Image Resolution has a finite resolution. Airy Disk Basics Oil Immersion Observers will miss fine nuances in the image if the objective projects details onto the intermediate image plane that are smaller than the resolving power of the human eye (a situation Substage Condenser that is typical at low magnifications and high numerical apertures). The phenomenon of empty Condenser Aperture magnification will occur if an image is enlarged beyond the physical resolving power of the Condenser Light Cones images. For these reasons, the useful magnification to the observer should be optimally above 500 times the numerical aperture of the objective, but not higher than 1,000 times the numerical Coverslip Thickness aperture. Focus Depth Reflected Light Pathways Immersion Media back to top ^ One way of increasing the optical resolving power of the microscope is to use immersion liquids between the front lens of the objective and the cover slip. Most objectives in the magnification Basic Principles range between 60x and 100x (and higher) are designed for use with immersion oil. Good results Optical Systems have been obtained with oil that has a refractive index of n = 1.51, which has been precisely Specimen Contrast matched to the refractive index of glass. All reflections on the path from the object to the objective are eliminated in this way. If this trick were not used, reflection would always cause a loss of light Phase Contrast in the cover slip or on the front lens in the case of large angles (Figure 2). DIC Microscopy Fluorescence Microscopy Polarized Light Microscope Ergonomics zeiss-campus.magnet.fsu.edu/articles/basics/resolution.html 2/6 12/17/12 ZEISS Microscopy Online Campus | Microscopy Basics | Numerical Aperture and Resolution The useful numerical aperture of the objective and therefore the resolving power would be reduced by the reflection described above. The numerical aperture of an objective is also dependent, to a certain degree, upon the amount of correction for optical aberration. Highly corrected objectives tend to have much larger numerical apertures for the respective magnification as illustrated in Table 1. Objective Numerical Aperture versus Optical Correction Plan Achromat Plan Fluorite Plan Apochromat Magnification (NA) (NA) (NA) 0.5x 0.025 n/a n/a 1x 0.04 n/a n/a 2x 0.06 0.08 0.10 4x 0.10 0.13 0.20 10x 0.25 0.30 0.45 20x 0.40 0.50 0.75 40x 0.65 0.75 0.95 40x (oil) n/a 1.30 1.40 63x 0.75 0.85 0.95 63x (oil) n/a 1.30 1.40 100x (oil) 1.25 1.30 1.40 Table 1 The Airy Disk and Microscope Resolution back to top ^ When light from the various points of a specimen passes through the objective and is reconstituted as an image, the various points of the specimen appear in the image as small patterns (not points) known as Airy patterns. This phenomenon is caused by diffraction or scattering of the light as it passes through the minute parts and spaces in the specimen and the circular rear aperture of the objective. The limit up to which two small objects are still seen as separate entities is used as a measure of the resolving power of a microscope. The distance where this limit is reached is known as the effective resolution of the microscope and is denoted as d0. The resolution is a value that can be derived theoretically given the optical parameters of the instrument and the average wavelength of illumination. It is important, first of all, to know that the objective and tube lens do not image a point in the object (for example, a minute hole in a metal foil) as a bright disk with sharply defined edges, but as a slightly blurred spot surrounded by diffraction rings, called Airy disks (see Figure 3(a)). Three-dimensional representations of the diffraction pattern near the intermediate image plane are known as the point-spread function (Figure 3(b)). An Airy disk is the region enclosed by the