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MTF stands for modulation transfer function, this means the transferring of differing optical spatial frequencies through an optical systems.

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The formula for MTF in an ideal optical system where MTF is defined by the diffraction limit. It is show below as a formula and plotted on an MTF chart in the second image

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Understanding the purpose of an MTF chart and how to read and MTF chart is an essential skill for anyone involved in the development of products that use optics.

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MTF

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An ‘Ideal’ optical system is one which transfers optical wave fronts from an object without any deviations. But in any real optical system there is a limit to apeture and and apeture creates diffraction which reduces MTF. As the diffraction spacial frequency grows, the MTF of a system is reduces. An analog in electronics is where devices filter temporary frequencies. MTF of ideal system has formula.

LensMTF

As can be seen in the above diagram a cylinder lens has power only in one axis. In the above it is the horizontal axis. This lens does not refract light in the vertical direction. Astigmatism Visual Acuity Table of Contents Subject Index Table of Contents [When not using frames]

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When optical system posses big residual aberrations then calculation of MTF is loosing accuracy. Reasonable limit is wavefront deviation in 1 lambda.

In real system the difference can be bigger because of residual aberrations. One of the biggest influences is astigmatism.

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In this post we will review the definitions, show example charts, impact of sensor, abberrations, Meridional and sagittal plots and diffraction limited optical systems.

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In image below, the upper half is a sinusoidal test object and the lower half is an object imaged by a real optical systems. The upper half has perfect contrast the lower half is contract is reduced because of diffraction.

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Modulation transfer function

With over 20 years of experience and 800+ unique optical systems designed, Optics for Hire specializes in advanced optical engineering. If it uses light, we've worked on it.

But it has slightly lower resolution because of residual aberration which depends on optical performances, number of lens elements and types of glasses.

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Usually MTF chart includes two plots for selected off axis points of field of view. There is a very small difference because of different apture value from Meridional and sagittal apertures., this come from tilt and other geometrical issues.

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Below are examples of MTF plot from Zemax, on the left image the x axis is spatial in units of line pair per mm and the Y axis is amplitude which also can be called contrast. The different color lines are different fields of view. The black line is plot for ideal system.

Residual aberration deviates wave fronts going from the object when compared with ideal system. However there is criteria when real optical system can be regarded as ideal. It is similar to tolerance which provides that. This criteria names as Rayleigh λ/4. It means that absolute value of wavefront deviation in optical system has to be not exceed quarter (fourth) of wavelength value. In this example ideal MTF in black, real in blue.