11/22/2023 0 Comments Abbe diffraction limit derivationThe properties of the intensity point spread function ( PSF see Figure 1) in the image plane as well as in the axial direction (Figure 3) are major factors in determining the resolution of a microscope. Actual specimens are not point sources, but can be regarded as a superposition of an infinite number of objects having dimensions below the resolution of the system. Although variations in field amplitude are not directly observable, the visible image of the point source formed in the microscope and recorded by its imaging system is the intensity point spread function, which describes the system response in real space. This field is commonly represented through the amplitude point spread function, and allows evaluation of the optical transfer properties of the combined system components. Imaging a point-like light source in the microscope produces an electromagnetic field in the image plane whose amplitude fluctuations can be regarded as a manifestation of the response of the optical system to the specimen. The most reasonable resolution goal for imaging in a given experimental situation is that the microscope provide the best resolution possible within the constraints imposed by the experiment. Given that the available timescale may be dictated by these factors and by the necessity to record rapid dynamic events in living cells, it must be accepted that the quality of images will not be as high as those obtained from fixed and stained specimens. Other factors, such as cell viability and sensitivity to thermal damage and photobleaching, place limits on the light intensity and duration of exposure, consequently limiting the attainable resolution. Such specimens are optically thick and inhomogeneous, resulting in a far-from-ideal imaging situation in the microscope. Advances in fluorescent protein technology have led to an enormous increase in studies of dynamic processes in living cells and tissues. The relationship between contrast and resolution with regard to the ability to distinguish two closely spaced specimen features implies that resolution cannot be defined without reference to contrast, and it is this interdependence that has led to considerable ambiguity involving the term resolution and the factors that influence it in microscopy. Experimental limitations and the properties of the specimen itself, which vary widely, dictate that imaging cannot be performed at the theoretical maximum resolution of the microscope. The ability to recognize two closely spaced features as being separate relies on advanced functions of the human visual system to interpret intensity patterns, and is a much more subjective concept than the calculation of resolution values based on diffraction theory. In addition to the straightforward theoretical aspects of resolution, regardless of how it is defined, the reciprocal relationship between contrast and resolution has practical significance because the matter of interest to most microscopists is not resolution, but visibility. This is appropriate to the subject of contrast and resolution because it has a direct bearing on the ability to record two closely spaced objects as being distinct. ![]() Because all digital confocal images employing laser scanners and/or camera systems are recorded and processed in terms of measurements made within discrete pixels, some discussion of the concepts of sampling theory is required. While the effects of many instrumental and experimental variables on image contrast, and consequently on resolution, are familiar and rather obvious, the limitation on effective resolution resulting from the division of the image into a finite number of picture elements (pixels) may be unfamiliar to those new to digital microscopy. The influence of noise on the image of two closely spaced small objects is further interconnected with the related factors mentioned above, and can readily affect the quality of resulting images. In a typical fluorescence microscope, contrast is determined by the number of photons collected from the specimen, the dynamic range of the signal, optical aberrations of the imaging system, and the number of picture elements ( pixels) per unit area in the final image. The concept of resolution is inseparable from contrast, and is defined as the minimum separation between two points that results in a certain level of contrast between them. ![]() In a perfect optical system, resolution is restricted by the numerical aperture of optical components and by the wavelength of light, both incident (excitation) and detected (emission). All optical microscopes, including conventional widefield, confocal, and two-photon instruments are limited in the resolution that they can achieve by a series of fundamental physical factors.
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