Resolution of annular-pupil optical systems

Abstract

The resolution of optical systems with annular pupil objectives is discussed, particularly with respect to the imaging properties of soft-x-ray imaging optical systems. Images of two dark bars in a bright field and knife-edge responses, which are calculated with partially coherent transfer functions, were used to estimate the resolution. Resolution for two bright points in a dark field, which is conventionally used in Rayleigh's analysis, is also discussed for comparison. It was found that annular systems with obstruction ratios of more than 0.6 show resolution properties different from those of systems with low-obstruction-ratios. The high-obstruction-ratio systems show lower resolution for the two-dark-bar objects and higher resolution for the two-bright-point objects, whereas the low-obstruction-ratio system show almost the same resolution for both objects.

High resolution reflection microscopy via absorbance modulation

“…and 2.3d shows that the size of the central peak is slightly smaller for SO than those of the circular aperture (see Fig. 2.4) [23,26].…”

“…Schwarzschild objectives (SO) or reflective objective are another kind of objectives used for imaging which consist of reflecting surfaces called primary and secondary mirrors. They are based on Schwarzschild's design [23][24][25], such that they focus light just like a lens-based objective. However, SO have the upper hand when an imaging system needs a significant working distance and needs to work over an extended spectral range.…”

Lateral resolution enhanced interference microscopy using virtual annular apertures

“…However, due to the complex composition of signals additional options for resolution enhancement exist in interference microscopy. For example, it is well known that improved lateral resolution can be achieved by use of annular apertures located in both, the illumination pupil as well as the pupil plane of the imaging path of a microscope [10][11][12]. If reflective phase objects or three-dimensional micro-topographies are to be measured, interference microscopy is often employed in order to gain depth information [13].…”

Automated markerless full field hard x-ray microscopic tomography at sub-50 nm 3-dimension spatial resolution

“…Converting it to regular Rayleigh's resolution, it is 24.1 nm6 2.6 nm by applying a factor of 1.7. 14,15,17 The value of the FWHM of the differentiated edge response in Figure 3(b) is 25.8 nm6 1.2 nm, which is also viewed as the resolving power. The PSA was performed on the entire star pattern and integrated azimuthally over 2p to evaluate the spatial resolution, as shown in Figure 3(c) for absorption contrast and Fig.…”

“…It is clear to distinguish the 30 nm finest feature in the center from both of the images. Quantified evaluation of the spatial resolution was studied by the knife-edge intensity profile with edge response 25%-75%, [14][15][16] the full width at half-maximum (FWHM) 17,18 of the differentiated curve from an edge, and the power spectrum analysis (PSA). [19][20][21] With an average of several measurements of sharp features of the star pattern in absorption contrast, the 25%-75% response of the knife-edge intensity profile shown in Figure 3(b) gave 14.2 nm6 1.5 nm linewidth.…”