Optical transfer function

From Wikipedia, the free encyclopedia

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. OTF may be broken down into the magnitude and phase components as follows:

$\mathbf{OTF(\xi,\eta)}=\mathbf{MTF(\xi,\eta)}\cdot\mathbf{PTF(\xi,\eta)}$

where

$\mathbf{MTF(\xi,\eta)} = | \mathbf{OTF(\xi,\eta)} |$

$\mathbf{PTF(\xi,\eta)} = e^{-i 2\cdot\pi\cdot\lambda (\xi,\eta)}$

and $(ξ,η)$ are spatial frequency in the x- and y-plane, respectively.

The OTF accounts for aberration, which the limiting frequency expression above does not. The magnitude is known as the Modulation Transfer Function (MTF) and the phase portion is known as the Phase Transfer Function (PTF).

In imaging systems, the phase component is typically not captured by the sensor. Thus, the important measure with respect to imaging systems is the MTF.

Another related quantity is the Contrast Transfer Function (CTF). MTF describes the response of an optical system to an image decomposed into sine waves. CTF describes the response of an optical system to an image decomposed into square waves.

Phase is critically important to adaptive optics and holographic systems.

The OTF is the Fourier transform of the Point Spread Function.

[edit] Photography

In photography, certain cameras (such as the Pentax K10D) feature an "MTF autoexposure" mode, where the choice of aperture is optimised for maximum sharpness. Typically this means somewhere in the middle of the aperture range.^[1]