A transfer function is a mathematical representation, in terms of spatial or temporal frequency, of the relation between the input and output of a linear time-invariant

LTI system theory

Linear time-invariant system theory, commonly known as LTI system theory, comes from applied mathematics and has direct applications in NMR spectroscopy, seismology, circuits, signal processing, control theory, and other technical areas. It investigates the response of a linear and time-invariant...

 system

System analysis

System analysis in the field of electrical engineering characterizes electrical systems and their properties. System Analysis can be used to represent almost anything from population growth to audio speakers, electrical engineers often use it because of its direct relevance to many areas of their...

. With optical imaging devices

Optical transfer function

The optical transfer function of an imaging system is the true measure of resolution that the system is capable of...

, for example, it is the Fourier transform

Fourier transform

In mathematics, Fourier analysis is a subject area which grew from the study of Fourier series. The subject began with the study of the way general functions may be represented by sums of simpler trigonometric functions...

 of the point spread function

Point spread function

The point spread function describes the response of an imaging system to a point source or point object. A more general term for the PSF is a system's impulse response, the PSF being the impulse response of a focused optical system. The PSF in many contexts can be thought of as the extended blob...

 (hence a function of spatial frequency

Spatial frequency

In mathematics, physics, and engineering, spatial frequency is a characteristic of any structure that is periodic across position in space. The spatial frequency is a measure of how often sinusoidal components of the structure repeat per unit of distance. The SI unit of spatial frequency is...

) i.e. the intensity distribution caused by a point object in the field of view.
Transfer functions are commonly used in the analysis of systems such as single-input single-output filter

Filter (signal processing)

In signal processing, a filter is a device or process that removes from a signal some unwanted component or feature. Filtering is a class of signal processing, the defining feature of filters being the complete or partial suppression of some aspect of the signal...

s, typically within the fields of signal processing

Signal processing

Signal processing is an area of systems engineering, electrical engineering and applied mathematics that deals with operations on or analysis of signals, in either discrete or continuous time...

, communication theory

Communication theory

Communication theory is a field of information and mathematics that studies the technical process of information and the human process of human communication.- History :- Origins :...

, and control theory

Control theory

Control theory is an interdisciplinary branch of engineering and mathematics that deals with the behavior of dynamical systems. The desired output of a system is called the reference...

.