Abbe diffraction limit proof1/17/2024 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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