# Materials Science and Engineering/Doctoral review questions/Daily Discussion Topics/01182008

Effect of aperture on blur and DOF. The points in focus (2) project points onto the image plane (5), but points at different distances (1 and 3) project blurred images, or circles of confusion. Decreasing the aperture size (4) reduces the size of the blur circles for points not in the focused plane, so that the blurring is imperceptible, and all points are within the DOF.
A Macro photograph with very small depth of field.

## Depth of Field

In optics, particularly film and photography, the depth of field (DOF) is the distance in front of and beyond the subject that appears to be in focus.

## Depth of Focus

Depth of focus DOF is a lens optics concept that measures the tolerance of placement of the image plane (the film plane in a camera) in relation to the lens. While the phrase depth of focus was historically used, and is sometimes still used, to mean depth of field, in modern times it is more often reserved for the image-side depth. Depth of field is a measurement of depth of acceptable sharpness in the object space, or subject space. Depth of focus, however, is a measurement of how much distance exists behind the lens wherein the film plane will remain sharply in focus. It can be viewed as the flip side of depth of field, occurring on the opposite side of the lens. Where depth of field often can be measured in macroscopic units such as meters and feet, depth of focus is typically measured in microscopic units such as fractions of a millimeter or thousandths of an inch. Since the measurement indicates the tolerance of the film's displacement within the camera, depth of focus is sometimes referred to as "lens-to-film tolerance."

## Modulation Transfer Function

The optical transfer function (OTF) describes the spatial (angular) variation as a function of spatial (angular) frequency. When the image is projected onto a flat plane, such as photographic film or a solid state detector, spatial frequency is the preferred domain, but when the image is referred to the lens alone, angular frequency is preferred.

## Immersion Lithography

In immersion lithography, light travels down through a system of lenses and then a pool of water before reaching the photoresist on top of the wafer.

Immersion lithography is a photolithography resolution enhancement technique that replaces the usual air gap between the final lens and the wafer surface with a liquid medium that has a refractive index greater than one. The resolution is increased by a factor equal to the refractive index of the liquid. Current immersion lithography tools use highly purified water for this liquid, achieving feature sizes below 37 nanometers.

## Chemical Potential

The Fermi energy (EF) of a system of non-interacting fermions is the increase in the ground state energy when exactly one particle is added to the system. It can also be interpreted as the maximum energy of an individual fermion in this ground state. The chemical potential at zero temperature is equal to the Fermi energy.

## Fermi Energy

The precise meaning of the term chemical potential depends on the context in which it is used.

• When speaking of thermodynamic systems, chemical potential refers to the thermodynamic chemical potential. In this context, the chemical potential is the change in a characteristic thermodynamic state function per change in the number of molecules. Depending on the experimental conditions, the characteristic thermodynamic state function is either: internal energy, enthalpy, Gibbs free energy, or Helmholtz free energy. This particular usage is most widely used by experimental chemists, physicists, and chemical engineers.
• Theoretical chemists and physicists often use the term chemical potential in reference to the electronic chemical potential, which is related to the functional derivative of the density functional, sometimes called the energy functional, found in Density Functional Theory. This particular usage of the term is widely used in the field of electronic structure theory.
• Physicists sometimes use the term chemical potential in the description of relativistic systems of fundamental particles.

## Nanoparticles in Solar Cells

Today's best solar cells have layers of several different semiconductors stacked together to absorb light at different energies but they still only manage to use 40 percent of the Sun's energy. Commercially available solar cells have much lower efficiencies (15-20%). Nanotechnology could help increase the efficiency of light conversion by using nanostructures with a continuum of bandgaps.