The Influence of the Condenser on Microscopic Resolution
01 Oct 1950-Vol. 63, Iss: 10, pp 737-744
TL;DR: An expression for the distribution of light in the image of two small apertures which are illuminated by a condenser of numerical aperture equal to s times that of the imaging objective is given in this paper.
Abstract: An expression is found for the distribution of light in the image of two small apertures which are illuminated by a condenser of numerical aperture equal to s times that of the imaging objective The resolving power of the system is written ρ=Kλ/(NA), and K is found as a function of s It is shown that precisely the same result obtains for both critical and Kohler illumination
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TL;DR: In this paper, the effect of various arrangements using lenses with annular pupil functions is discussed, and it is found that Type 2 microscopes have improved imaging properties over conventional microscopes and that these may be further improved by use of one or two lenses with ANNular pupils.
Abstract: Fourier imaging in the scanning microscope is considered. It is shown that there are two geometries of the microscope, which have been designated Type 1 and Type 2. Those of Type 1 exhibit identical imaging to the conventional microscope, whereas those of Type 2 (confocal microscopes) display various differences. Imaging of a single point object, two-point resolution and response to a straight edge are also considered. The effect of various arrangements using lenses with annular pupil functions is also discussed. It is found that Type 2 microscopes have improved imaging properties over conventional microscopes and that these may be further improved by use of one or two lenses with annular pupils.
454 citations
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TL;DR: This paper reviews the concept of optical resolution and concludes that in the end, resolution is limited by systematic and random errors resulting in an inadequacy of the description of the observations by the mathematical model chosen.
Abstract: In applied science, resolution has always been, and still is, an important issue. Since it is not unambiguously defined, it is interpreted in many ways. In this paper, which reviews the concept of optical resolution, a number of these interpretations are discussed. A discussion of resolution has to be preceded by a discussion of what is actually understood by an ‘‘optical image.’’ In a remarkable paper, Ronchi1 distinguished ethereal images, calculated images, and detected images. The term ethereal image was introduced only to represent the physical nature of the imaging phenomenon. As is customary in science in general, attempts have been made to give a mathematical representation of this phenomenon, both geometrically and algebraically. According to Ronchi, the images that have thus been calculated are mere mathematical constructions and should therefore be called calculated images. In the past, many approaches to the concept of resolution concerned these calculated images. This resulted in the so-called classical resolution criteria, such as Rayleigh’s criterion and the associated reciprocal bandwidth of the image. These criteria provide resolution limits that are determined solely by the calculated shape of the point-spread function associated with the imaging aperture and the wavelength of the light. From now on, they will be called classical resolution limits. Calculated images are by their very nature exactly describable by a mathematical model and thus noise free. Such images do not occur in practice. Therefore Ronchi stated that the resolution of detected images is much more important than the classical resolution, since it provides practical information about the imaging system employed. Hence one should consider primarily the resolution of detected images instead of that of calculated images. This means a necessary introduction of some new quantities of interest, such as the energy of the source and the sensitivity properties of the detector. Since Ronchi’s paper, further research on resolution— concerning detected images instead of calculated ones— has shown that in the end, resolution is limited by systematic and random errors resulting in an inadequacy of the description of the observations by the mathematical model chosen. This important conclusion was independently drawn by many researchers who were approaching the concept of resolution from different points of view, which will be discussed in the subsequent sections.
397 citations
01 Jan 2006
TL;DR: The laser-scanning confocal microscope as mentioned in this paper can slice extremely clean, thin optical sections out of thick fluorescent specimens; view specimens in planes tilted to, and even running parallel to, the line of sight; penetrate deep into light-scattering tissues; gain impressive three-dimensional (3D) views at very high resolution.
Abstract: Seldom has the introduction of a new instrument generated as instant an excitement among biologists as the laser-scanning confocal microscope. With the new microscope, one can slice incredibly clean, thin optical sections out of thick fluorescent specimens; view specimens in planes tilted to, and even running parallel to, the line of sight; penetrate deep into light-scattering tissues; gain impressive three-dimensional (3D) views at very high resolution; obtain differential interference or phase-contrast images in exact register with confocal fluorescence images; and improve the precision of microphotometry.
344 citations
TL;DR: In this paper, it was shown that the diameter of the area of coherence on a plane illuminated by a source of angular radius is given by d = d = 0 √ √ n √ 16 λ n N ε, where N is the refractive index of the intervening medium.
Abstract: It is shown that a 'phase-coherence factor' may be defined in a manner which leads, without recourse to explicit statistical analysis, to the theorems established by van Cittert (1934) and Zernike (1938) for analogous factors. An invalid approximation made in their calculations of the phase-coherence factor for a plane illuminated directly by a source is corrected. The new treatment is applied to the theory of Young's experiment, the stellar interferometer, and illumination in the microscope. The phase-coherence factor defined here enables a general theory of the formation of optical images to be formulated. Further, it is shown that the diameter of the area of coherence on a plane illuminated by a source of angular radius $\alpha $ is given by d = $\frac{0\cdot 16\lambda}{N\,\sin \,\alpha}$, where N is the refractive index of the intervening medium.
252 citations
TL;DR: A new era in which strict coherence and interferometry are no longer prerequisites for quantitative phase imaging and diffraction tomography is highlighted, paving the way toward new generation label-free three-dimensional microscopy, with applications in all branches of biomedicine.
243 citations
References
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TL;DR: In this article, the maximum visibility of the interferences obtainable from two points in a wave field is defined as their degree of coherence γ, which depends only on the aperture of the illuminating cone.
633 citations
316 citations
01 Mar 1931
TL;DR: In this paper, the diffraction effects produced by two adjacent apertures and a series of aperture in an opaque screen situated in the focal plane of a lens system are examined.
Abstract: The paper examines the diffraction-effects produced by (a) two adjacent apertures, and (b) a series of apertures in an opaque screen situated in the focal plane of a lens system, when the illuminating system is projecting the elementary image of a pointsource of light into this object plane. The diffraction-effects and geometrical resolving power of the grating are shown to be independent of the concentration of the light in the object plane; they depend rather on the number of apertures free to transmit light. The theory is then extended to the case where the illumination of the object is produced by a source of finite area. Both the equivalence and Abbe principles appear in the analysis of the mode of formation of the image in such critical illumination, but subject to the difficulties encountered in integrating for the effects of finite sources of light. Confirmatory experimental work is in hand.
93 citations
20 citations