Depth of Focus and Resolution

Depth of focus increases with smaller apertures. For distant subjects (beyond macro range), depth of focus is relatively insensitive to focal lengfh and subject distance for a fixed / number (defined as fhe ratio of the focal length of the lens to the diameter of its entrance pupil). In the macro region, depth of focus increases with longer focal lengfh or closer subject distance, while depth of field decreases. 

When the depth of focus relates to a single plane in object space, it can be calculated 

The magnification depends on the focal length and the subject distance. When the magnification is small, the formula can simplify to 

The circle of confusion is taken as the lens focal length divided by 1000 [15]. This formula is valid only for normal lenses. The depth of focus Af is the amount of defocus that introduces a wavefront error, and can be calculated using 

Resolution depends on the distance between two distinguishable radiating points. Here we assume an adequate level of contrast in a mathematical model of Airy discs. However, real optical systems are complex and it is difficult to increase the distance between distinguishable point sources. 

---

In certain instances it may be of interest to examine the etched surface of a fiber or determine the proportion of a particular cross-section in a fiber mixture. This is done by scanning electron microscopy (SEM), where magnifications of up to 100 000 x can be achieved with greater depth of focus and resolution. Additionally, the cross-sectional appearance of bicomponent and polyblend fibers may be examined by SEM, revealing side-by-side (Figure 4), sheath-core , or island-in-the-sea composites. 

In Chapter 2, Basic Physics of Liquid Microlenses, we first provide a review of the physics involved in microlenses. Beginning with light- and material-related parameters such as refractive index, absorption, and reflectance, we introduce optical lenses and their parameters (focal length, aberrations, depth of focus, and resolution). The design of lenses is also discussed. Then the chapter continues with a review of surface tension because most microlenses involve liquid-liquid or air-liquid interfaces at some point. Throughout the discussion in this chapter, the microscale associated with these liquid microlenses is emphasized. 

Diffraction is only one of the problems that limits the utility of optical lithography at the submicron level. Depth of focus is another problem which must be overcome. As the wavelength of the source is reduced td decrease the diffraction problem, the depth of focus of the lenses is reduced. Equations (11) and (12) show the relationships of depth of focus and resolution to the numerical aperture of the lens, where k is a constant, X is the wavelength of light, and NA is the numerical aperture of the lens. 

Lin, The K3 coefficient in non paraxial lambda/NA scaling equations for resolution, depth of focus, and immersion lithography, J. Microlith. Microfab. Microsyst. 1(1), 7 (2002) New lambda/ NA scaling equations for resolution and depth of focus, Proc. SPIE 4000, 759 (2000). 

Each approach has its characteristic advantages and disadvantages due to the underlying technology and the materials issues involved (see the remainder of this section). In contrast, SLR schemes are relatively simple processes, can have moderate levels of resolution and etch resistance, and good hnearity, but they suffer from reflective swing problems and small depths of focus, and are limited to low aspect ratios. Irrespective of the resist process approach chosen, chemical amplification continues to be the dominant exposure mechanism of the imaging layer. 

Microscopy. The best methods to determine detailed surface topographies are by optical and scanning electron microscopy. The optical microscope is limited by a lack of depth of focus and a resolution limit of about 2000 A, but these limitations are overcome in the scanning electron microscope (SEM). The depth of focus is up to 300 times that of the optical microscope and the resolution limit is only a few Angstroms. 

Traditionally, the first instrument that would come to mind for small scale materials characterization would be the optical microscope. The optical microscope offered the scientist a first look at most samples and could be used to routinely document the progress of an investigation. As the sophistication of investigations increased, the optical microscope often has been replaced by instrumentation having superior spatial resolution or depth of focus. However, its use has continued because of the ubiquitous availability of the tool. 

Run-of-the-mill instruments can achieve a resolution of 5-10 nm, while the best reach 1 nm. The remarkable depth of focus derives from the fact that a very small numerical aperture is used, and yet this feature does not spoil the resolution, which is not limited by dilfraction as it is in an optical microscope but rather by various forms of aberration. Scanning electron microscopes can undertake compositional analysis (but with much less accuracy than the instruments treated in the next section) and there is also a way of arranging image formation that allows atomic-number contrast, so that elements of different atomic number show up in various degrees of brightness on the image of a polished surface. 

Fig. 2. Depth discrimination (z-axis resolution) properties of a confocal microscope. The illumination and detection images in a confocal microscope are diffraction-limited and confined to a small region of the specimen (1). Only light emitted in the plane of focus and on the optical axis will pass the detector pinhole and form an image. Light emitted from other areas of the specimen does not enter the detector pinhole.

---