Gaussian image plane

Defect of focus. In the Gaussian image plane, defined by Eq. (1.1), the image has very low contrast. The nature of the image changes above and below this plane because the waves have different relative phases. When the objective lens is defocused by an amount A/ relative... 

It is apparent from the ray diagram of Fig. 3.3 that there is a plane, A-A, nearer to the lens than the geometrical or Gaussian focus plane, where the resolution is improved. It is called the plane of least confusion or Scherzer focus [3, 4, 7], and it is close to where the rays from the outermost parts of the lens intersect the axis. From Fig. 3.3 the distance 6Z between this plane and the Gaussian image plane is approximately the radius of the image disc in the Gaussian plane divided by a. The radius is Ma C and a = ajM, so... 

Fig. 3.3 the distance 6Z between this plane and the Gaussian image plane is approximately the radius of the image disc in the Gaussian plane divided by a. ... 

If we choose a Cartesian system with the z axis parallel to the optic axis and the plane z = 0 coinciding with the Gaussian image of the object plane z = Zo (<0) (see Fig. 2), we can show for a field point very close to the Gaussian image that Eq. (3) generalizes to the... 

While plane wave basis sets have primarily been used for periodic systems, they can also be used for molecular species by using a supercell approach, where the molecule is placed in a sufficiently large unit cell such that it does not interact with its own image in the neighbouring cells. Placing a relatively small molecule in a large supercell to avoid self-interaction consequently requires many plane wave functions, and such cases are handled more efficiently by localized Gaussian functions. A three-dimensional periodic system, on the other hand, may be better described by a plane wave basis than with nuclear-centred basis functions. 

Fig. 2.1 a Polarized optical microscopy (POM) image of FCDs in a bulk thick (120 mm) cell of dodecylcyanobiphenyl (12CB) with different orientation (1) ellipses parallel to the plane of view, (2, 3) ellipses perpendicular to the plane of view [33]. Reproduced with permission [33]. Copyright 2009, Taylor Francis, b A schematic illustration of ideal SmA phase [34]. Each rod represents LC molecules. Reproduced with permission [34]. Copyright 1991, EDP Sciences Schematic illustrations of layer stmcture of a negative Gaussian curvature focal conic domain with (c) non-zero and (d) zero eccentricity... 

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