The modulation transfer function (MTF) is a measurement of the microscope's ability to transfer contrast from the specimen to the intermediate image plane at a specific resolution. Computation of the modulation transfer function is a mechanism that is often utilized by optical manufacturers to incorporate resolution and contrast data into a single specification. Measurements of the relative modulation is useful for characterizing not only traditional optical systems, but also photonic systems such as analog and digital video cameras, image intensifiers, and film scanners.

Basic Concepts - Modulation of the output signal, the intensity of light waves forming an image of the specimen, corresponds to the formation of image contrast in microscopy. Therefore, a measurement of the MTF for a particular optical microscope can be obtained from the contrast generated by periodic lines or spacings present in a specimen that result from sinusoidal intensities in the image that vary as a function of spatial frequency. Topics covered in this section also include the optical transfer function, phase transfer function, and the contrast transfer function, all of which play a crucial role in resolution and contrast.

Diffraction Effects on Image Contrast - A popular mechanism for interpretation of the modulation transfer function (MTF) of an optical system is to image a precisely defined target having a repeating structure with 100 percent contrast. This interactive tutorial utilizes a periodic line grating as the specimen and simulates images produced with a diffraction-limited optical microscope as a function of spatial frequency.

Cutoff Frequency and Airy Disk Size - The modulation transfer function of an optical system is closely related to the distribution of light from the image of a point object produced by the system, a term commonly referred to as the point spread function (PSF). This interactive tutorial explores the changes in the point spread function distribution as spatial frequency cutoff is varied in a typical modulation transfer function plot.

Numerical Aperture Effects - The contrast observed between two points in an image decreases as the distance between the points grows smaller. This relationship can be expressed quantitatively in terms of the degree of image modulation versus the size of the repeating period displayed by the specimen.

Test Target Intensity Scans - The optical performance of a light microscope is usually determined by its response when imaging high-contrast periodic line gratings that are employed to measure contrast transfer functions. An ideal test target (MBL-NNF) for this purpose was developed at the Marine Biological Laboratory in Woods Hole, Massachusetts in collaboration with the National Nanofabrication Facility at Cornell University.

Contrast Enhancement Technique MTF Curves - The utilization of contrast enhancement techniques in optical microscopy affects the response when relative modulation is calculated as a function of specimen spatial frequency. This interactive tutorial explores the effects of popular contrast modes on image contrast and the modulation transfer function of the modified microscope.

Periodic Diffraction Images - When a microscope objective forms a diffraction-limited image of an object, it produces a three-dimensional diffraction pattern that is periodic both along the optical axis and laterally within the intermediate image plane. This tutorial explores diffraction images produced by a periodic object at several focal depths.

Selected Literature References - The reference materials listed in this section are an excellent source of information on the modulation transfer function, contrast transfer function, and optical transfer function as applied to microscopes and other optical systems, video systems, and photographic film.

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