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Three-Dimensional Evaluation of Paper Surfaces Using Confocal Microscopy
Published in Terrance E. Conners, Sujit Banerjee, Surface Analysis of Paper, 2020
Marie-Claude Béland, Patrice J. Mangin
The actual resolution of a focal plane is highly dependent on particular acquisition conditions (e.g., image format, wavelength of light source, objective used, pinhole size, depth of the focal plane within the object, and signal-to-noise ratio). Consequently, it is not easily determined. The theoretical resolution is often given in terms of the full-width-half-maximum (FWHM) value of the intensity curves obtained for a point form object. The FWHM represents the distance from the point form object where the intensity has decreased to half its peak value. The performance of Leica objectives in the reflection mode is shown in Figure 5 for a wavelength of 488 nm. Resolution improves with increasing numerical aperture (larger lens opening). At a constant numerical aperture, the axial resolution is better for an air objective than for an oil immersion objective. Using a 16X air objective with a 0.45 numerical aperture gives a lateral resolution of about 0.5 μm and an axial resolution of approximately 2.5 μm. Changing the magnification changes these calculated resolution values.
Optical Profiling Techniques for MEMS Measurement
Published in Wolfgang Osten, Optical Inspection of Microsystems, 2019
Klaus Körner, Johann Krauter, Aiko Ruprecht, Tobias Wiesendanger
Recently, a new proposal has been reported for topography measurement on the microscopic scale to increase the application range of the fringe projection technique with only one grating [40]; this has some advantages compared with other approaches. Instead of using optics with a rather low numerical aperture, objectives with a high numerical aperture are used to reduce the depth of focus to a reasonable range. Extended objects are now illuminated and imaged with some parts that are in focus and other parts that are considerably blurred. Using the additional depth scanning of the measurement system or of the object, the surface topography is determined, as in white-light interferometry, but on a coarser scale. Therefore, similar acquisition and evaluation algorithms can be used for this special type of fringe projection technique.
Light Sheet or Selective Plane Microscopy
Published in John Girkin, A Practical Guide to Optical Microscopy, 2019
Figure 7.2b separates the two optical planes of the cylindrical lens. In one plane the back aperture of the objective lens is not filled, meaning there is a very low effective numerical aperture leading to minimal focusing in this plane. Thus the height of the beam at the back of the objective is hardly altered as it goes through the lens, setting the vertical extent of the light sheet. In the other axis the objective lens will use its full optical power (numerical aperture) to produce a focus as the back aperture is filled. This focusing determines the thickness of the sheet and is set predominantly by the numerical aperture of the illumination objective. To produce a thin light sheet one therefore needs an objective lens with a high numerical aperture. However, the higher the numerical aperture the shorter the depth of field and thus the light sheet will only be thin over a small part of the imaging objective’s field of view. Without using exotic beam profiles (see Section 7.7) one therefore has a compromise over the field of view and the optical section thickness. The imaging lens numerical aperture also affects the actual effective thickness of the optical section observed as this sets the efficiency of collection of the light in the axial imaging direction (Engelbrecht and Stelzer 2006). In a typical SPIM system the imaging objective has a numerical aperture of around 0.8 which when combined with the light sheet in a typical system produces a field of view of around 150 µ and an optical section thickness of 1–2 µ.
A photonic quasi-crystal fibre supporting stable transmission of 150 OAM modes with high mode quality and flat dispersion
Published in Journal of Modern Optics, 2022
Qiang Liu, Shengnan Tai, Yudan Sun, Wenshu Lu, Mingzhu Han, Jianxin Wang, Chao Liu, Jingwei Lv, Wei Liu, Paul K. Chu
The effective mode area (Aeff) is inversely proportional to the numerical aperture. The numerical aperture (NA) describes the total acceptance of the beam or power entering the fibre and a larger numerical aperture means that the fibre can collect more light. The effective mode area and numerical aperture can be expressed by the following formulas [50,51]: and where E(x, y) is the transverse electric field distribution of the eigenmode. In the wavelength range between 1.4 and 1.7 µm, the effective mode area changes slightly with increasing wavelength as shown in Figure 9. The effective mode areas of all eigenmodes are above 161 µm2. The maximum Aeff is 313 µm2 at 1.7 µm. The numerical apertures of the eigenmodes are calculated by Eq. (10) and shown in Figure 10. At 1.55 µm, the maximum numerical aperture is 0.067.
Light transmission performance of translucent concrete building envelope
Published in Cogent Engineering, 2020
Numerical aperture is a parameter that is often used to specify the acceptance angle of a fiber (Hui & O’Sullivan, 2009). Figure 5 shows an axial cross-section of a step-index fiber and a light ray that is coupled into the fiber left cross-section, where n1, n2, are refractive indices of the fiber core, and cladding, respectively. For the light to be coupled into the guided mode in the fiber, total internal reflection has to occur inside the core requiring , as shown in Figure 5, where is the critical angle of the core-cladding interface. With this requirement on , there is a corresponding requirement on incidence angle at the fiber end surface making use of Snell’s law and elementary trigonometry, i.e.,
Sub-diffraction focusing of light by aperiodic masks
Published in Journal of Modern Optics, 2022
Seyeddyako Mostafavi, Ferhat Nutku, Yasa Ekşioğlu
In 1873, Ernst Abbe found that the resolution of an optical microscope is essentially restricted by light diffraction, not by the device's quality. The resolution, d, of an idealized microscope's resolution, is restricted to where λ is the wavelength of light and NA is the numerical aperture of the objective lens. In the near-field regime, when the sample gets near to objective lens the angular aperture half-angle increases and gets approximately equal to 75. Therefore, the numerical aperture of a microscope operating in the air is confined to approximately 0.96 according to numerical aperture formula . Solid immersion microscopy exceeds the diffraction limit by filling the object space with a high-refractive-index substance, akin to oil immersion microscopy. There are two types of solid immersion lenses (SIL) in use. The first is a simple hemisphere, while the second is a Weierstrass superhemispherical SIL, in which the height of a truncated sphere equals , where r is the radius of curvature. Both varieties of SILs may potentially do imaging towards the centre of their bottom surface without geometric aberration. The Weierstrass optic has the ability to enhance the NA of a far-field objective by a factor of , compared to an improvement of a factor of n for a hemispherical SIL. In both cases, the maximum achievable resolution is limited to around at air where n = 1, while some enhancements in resolution can be done by imaging throughout immersion medium with a higher refractive index [1,3].