Understanding This Tool

The Modulation Transfer Function (MTF) is commonly employed as an objective characterization of image quality. It is typically analyzed as a one-dimensional function of image contrast (resolution) versus spatial frequency (feature size).

Any device that relays, records, displays, or otherwise operates on an image has its own MTF curve describing the fidelity of that process. When concatenating incoherent imaging systems together, the product of their MTF curves describes the image quality of the entire system. Beware that there are scenarios where this multiplication is not valid—read more about MTF multiplication here.

Cameras are classic examples of concatenated imaging systems, comprising a lens focusing a real image onto a pixelated image sensor for recording. When specifying a camera system for your application, a reasonable question to ask is “Am I going to be able to resolve a feature of size X?”

The calculator above can help answer that question. It calculates Camera MTF while taking advantage of a couple of idealizations:

1. The image sensor is approximated as perfectly square pixels with 100% fill factors and negligible space between neighboring pixels.
2. The lens is diffraction-limited, or in other words, has no aberrations, over its circular, unobscured aperture.

These idealizations allow a closed form solution that can be described with simple equations, as described in Joseph W. Goodman’s book Fourier Optics, particularly in sections 2.4 Two-Dimensional Sampling Theory, and 6.3.3 The OTF of an Aberration-Free System.

From there, the calculator operates in one of two modes:

• Standard Mode – The lens image is perfectly focused onto the sensor. The Focus Error slider has no effect.
• Defocus Mode – The lens aperture shape is changed to square, again to keep the math simple as in Goodman 6.4.4 Example of a Simple Aberration: A Focusing Error. The Focus Error slider will now simulate the effects of defocus between the lens and sensor.

When switching into Defocus Mode, you will notice the diffraction-limited lens MTF change into the form of a straight line, as is expected for a square aperture lens. For focusing errors that lead to large departures from the diffraction limit, this Lens MTF is a reasonable approximation for a circular aperture lens.

For fine adjustments of parameters, click a slider and use the arrow keys on your keyboard to make small adjustments.

To relate with feature sizes in object space, multiply the image space frequencies by the magnification of the lens to transform into object space frequencies.

More detailed analysis of lenses accounting for effects like other aberrations, variation of performance across the field of view, chromatic errors, and other pupil shapes quickly gets into the arena of optical engineering. For that, Optikos relies on sophisticated raytracing software with Fourier analysis tools to evaluate and optimize image quality. Optikos is also a world leader in the measurement of MTF so that the effects of manufacturing tolerances can also be understood and mitigated.

For more information on MTF, see our page How to Measure MTF. And as always, if you need help designing a camera system for your business, reach out to our teams on our site here or at sales@optikos.com.