Regardless of the imaging mode utilized in optical microscopy, image brightness is governed by the light-gathering power of the objective, which is a function of numerical aperture. Just as the brightness of illumination is determined by the square of the condenser working numerical aperture, brightness of the specimen image is proportional to the square of the objective numerical aperture.
Unlike the situation for the microscope illuminating system, however, image magnification also plays an important role in determining image brightness. In fact, the image brightness is inversely proportional to the square of the lateral magnification:
where NA is the objective numerical aperture and M is the magnification. The ratio given in the equation above expresses the light-gathering power of the objective in transillumination (note: the case with epi-illumination is somewhat different, as discussed below). Examples of the light-gathering power of selected Nikon objectives having varying degrees of optical correction are listed in Table 1. In general, objectives with high numerical apertures are also better corrected for aberrations. Thus, for the same magnification, higher numerical aperture objectives collect more light, produce a brighter and better-corrected image (see Table 1), and the overall image is better resolved.
It is evident from examining the data in Table 1 that when an objective is used in transillumination, image brightness decreases rapidly as the magnification increases. Utilization of a specific objective for epi-illumination produces increasingly brighter images as the magnification increases, whereas the reverse is often true for the same objective with transmitted light. The terms F(trans) and F(epi) refer to the light-gathering power of an objective and were calculated according to the following equations:
In theory, the intensity of illumination depends on the square of the condenser numerical aperture and the square of the demagnification of the light source image (in effect, the field diaphragm image becomes brighter as it is made smaller, according to the square law). The result is that brightness of the specimen image is directly proportional to the square of the objective numerical aperture as it reaches the eyepiece (or camera system), and also inversely proportional to the objective magnification. Therefore, when examining specimens in transmitted light, changing the objective without altering the condenser affects image brightness in response to changes in numerical aperture and magnification.
Table 1 - Light-Gathering Power of Selected Objectives
|Plan Apo||40x (oil)||1.30||11.0||18.0|
|Plan Apo||60x (oil)||1.40||5.4||10.6|
|Plan Apo||100x (oil)||1.40||1.96||3.84|
|Plan Apo||100x (oil)||1.45||2.10||4.42|
In the case of epi-illumination, the same considerations apply, except that the objective also acts as the condenser, and this must be taken into account when considering image brightness. As the objective magnification increases, the light source image is reduced (demagnified) by an equivalent amount, resulting in a brightness level that is less dependent on objective magnification and more dependent on numerical aperture (brightness is governed by the fourth power of numerical aperture in epi-illumination). In practice, the image brightness numbers vary (see Table 1) due to objective rear aperture size differences.
When the light level is limiting, the highest numerical aperture objective should be employed, yet the magnifications of the both the objective and eyepiece should be kept at the lowest level compatible with the desired resolution. In many cases, manufacturers are now providing oil immersion objectives with higher numerical apertures, and correspondingly higher image brightness values, than high-dry counterparts of similar magnification. For example, the 40x plan apochromatic objective in Table 1 has twice the numerical aperture of the plan achromat 40x dry objective, and produces four times the image brightness in transmitted light. These objectives yield a 16-fold difference in image brightness under epi-fluorescence illumination, with the high numerical aperture oil immersion version producing the brightest images.
The amount of light transmitted through the optical components of the microscope, as a function of incident intensity, is especially critical in fluorescence microscopy. In situations where high resolution fluorescence imaging requires high magnifications with a minimal loss of image brightness, the highest numerical aperture objectives having the greatest degree of light transmission should be employed. As discussed above, overall image brightness decreases rapidly as magnification increases, so the components of a fluorescence microscope should be carefully chosen to maximize the amount of light passing through the optical train.
Fluorescence microscopes that utilize epi-illumination are equipped with objectives that serve the dual purpose of both condenser and objective. Light passing through the excitation filter and reflected from the dichromatic mirror surface in the filter cube is first passed through the objective to form a cone of illumination necessary to excite the specimen. Secondary fluorescence emitted by fluorophores attached to the specimen is then gathered by the same objective lens system and passed back through the dichromatic mirror and barrier filter before being projected into the eyepieces or the imaging system. A high numerical aperture objective acting as a condenser will increase the signal (light) intensity in a manner that is proportional to the square of the numerical aperture. Because the light gathering power of the objective is also proportional to the numerical aperture squared, image brightness will vary as the fourth power of the objective numerical aperture according to the equation:
Note that in fluorescence microscopy, brightness is also inversely proportional to the objective magnification squared. Thus, for objectives of identical magnification, image brightness of both the illumination field and the fluorescence image increases dramatically with objective numerical aperture, which is the primary reason manufacturers produce objectives designed with very high numerical apertures for fluorescence microscopy.
The eyepieces employed to observe the specimen further magnify the diffraction-limited image projected into the microscope intermediate image plane, and also serve to decrease the overall observed intensity of the specimen. In fact, image brightness is inversely proportional to the square of the eyepiece magnification, requiring the use of eyepieces having the lowest possible magnification necessary to conveniently observe specimen fluorescence. It is therefore possible to maximize image brightness in fluorescence microscopy by using the highest available numerical aperture objective coupled to the lowest power eyepieces (although 10x eyepieces are most commonly employed). These remarks apply primarily to large specimen areas that have an even degree of illumination. In the case of sharply focused point sources of light (for example, minute fluorescent spheres), the particle images should be diffraction-limited and have dimensions that are independent of magnification.
In fluorescence microscopy, image brightness is determined by the intensity of illumination, the quantum yield of the fluorophore, and the light-gathering power of the microscope. The greater the intensity of illumination and the higher the quantum yield, the greater the fluorescent signal and the brighter the image becomes until all of the fluorophores are saturated. Likewise in polarized light, image brightness is governed by the illumination intensity and birefringence retardation of the specimen. At values up to a quarter-wavelength of retardation, larger retardations produce a greater birefringence, and thus a stronger signal.
In both of these cases, image brightness is governed by the signal from the specimen, which is a product of the intensity of illumination and the change in light introduced by the specimen. In the case of luminescence, in which the specimens themselves emit light, the brightness of the image is clearly governed by the magnitude of light, or the signal, emitted by the specimen.
In other modes of microscopy, such as phase contrast, differential interference contrast (DIC), darkfield, Hoffman modulation contrast, etc., the intensity of illumination and image contrast can be varied independently. Nevertheless, the signal from the image, namely, the increment of image brightness per unit of variation in an optical parameter (for instance, a difference in path length), would still be determined by the product of the illumination intensity and the contrast produced per unit variation in the optical parameter. To detect small variations in any optical parameter, the microscopist should maximize the signal arising from variations in that particular parameter.
For a given condenser and objective numerical aperture, magnification, and illuminator brightness, the image brightness produced in the microscope can still vary depending on the light transmission through the optical components. The transmission depends on several factors, including absorption by lens elements and cements, reflection losses at the optical interfaces, and transmittances of the lamp jacket, diffusing screen, filters, polarizers, and other auxiliary optical components. Typical transmission curves for a selected set of high numerical aperture objectives are illustrated in Figure 1. These values are more or less representative of any class of objectives from a particular manufacturer, but even among the specific types for which these curves were measured, the exact transmission values can vary somewhat depending on, for example, the antireflection coating and the batch of glass used in individual lenses.
The transmittance (intensity transmitted as a percentage of incident intensity) of some optical components can be wavelength-dependent even within the visible range, as shown in Figure 1. Also, at wavelengths outside the visible range, the transmittances of lenses, prisms, slides, and the mounting medium for the specimen can drop appreciably. This fact is exemplified by the 20x plan fluor objective transmission curve illustrated in Figure 1, which shows a steady decrease in transmittance as wavelength is increased between 400 and 700 nanometers. Other objectives in the series do not exhibit such a marked degree of wavelength dependence.
Kenneth R. Spring - Scientific Consultant, Lusby, Maryland, 20657.
Michael W. Davidson - National High Magnetic Field Laboratory, 1800 East Paul Dirac Dr., The Florida State University, Tallahassee, Florida, 32310.