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.
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.
BACK TO MODULATION TRANSFER FUNCTION
Questions or comments? Send us an email.
© 1998-2013 by
Michael W. Davidson and The Florida State University.
All Rights Reserved. No images, graphics, scripts, or applets may be reproduced or used in any manner without permission from the copyright holders. Use of this website means you agree to all of the Legal Terms and Conditions set forth by the owners.
Last modification: Thursday, Jun 15, 2006 at 02:39 PM
Access Count Since November 30, 2000: 15853
For more information on microscope manufacturers,
use the buttons below to navigate to their websites: