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Modulation Transfer Function
Interactive Java Tutorials

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.

This interactive tutorial explores the effect of microscope objective and condenser numerical aperture size on the relative modulation as a function of specimen spatial frequency. To operate the tutorial, use the mouse cursor to select either the Objective or Condenser radio button to activate that set of controls. When the Objective radio button is selected, the Numerical Aperture slider, with a range between 0.25 and 1.34, can be utilized to show how changes in objective numerical aperture affect the relative modulation. Alternatively, when the Condenser radio button is selected, the slider reverts to a dual function of displaying both the condenser numerical aperture and the value M derived from the equation:

NA(Cond) = NA(Obj) x M

where NA(Cond) is the condenser numerical aperture at maximum value (1.32) and NA(Obj) is the objective numerical aperture. As the slider is moved from left to right, the value of M is decreased from 1.0 to 0, producing a corresponding change in the relative modulation on the graph in the tutorial window.

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. If a specimen having a spatial period of 1 micron (the distance between alternating absorbing and transparent line pairs) is imaged at high numerical aperture (1.32 in this tutorial) with a matched objective/condenser pair using immersion oil, the individual line pairs would be clearly resolved in the microscope. The image would not be a faithful reproduction of the specimen pattern, but would instead have a moderate degree of contrast between closely spaced features. Decreasing the distance between the line pairs to a spatial period of 0.5 microns (spatial frequency equal to 2000 lines per millimeter) would further reduce contrast in the final image, but increasing the spatial period to 2 microns (spatial frequency equal to 500 lines per millimeter) would produce a corresponding increase in image contrast.

Contributing Authors

Kenneth R. Spring - Scientific Consultant, Lusby, Maryland, 20657.

John C. Long and Michael W. Davidson - National High Magnetic Field Laboratory, 1800 East Paul Dirac Dr., The Florida State University, Tallahassee, Florida, 32310.


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