Stereo Pairs, depth measurement, VayTek, scientific software, Medical Imaging, microscopy, digital imaging, MicroTome, HazeBuster

Stereo pair images contain depth information due to the parallax inherent in the images. With proper calibration and an appropriate software program, it is possible to obtain depth information from these images. However, there are limits to the accuracy of these measurements. These limits are set by several factors including:

the quality and accuracy of the camera
the quality and accuracy of the framegrabber board
the optics of the microscope
calibration techniques
the judgment of the user making the measurements
the accuracy of the software used to make the measurements

To obtain the best results, you should use a good camera and framegrabber board. The camera and framegrabber board will determine the number of microns/pixel in the x, y direction. The higher the resolution of the camera and the framegrabber the better the resolution of the image. The limits of resolution of a depth measurement will be set by the number of pixels in the x, y direction. This, in turn, is set by the number of cells in the CCD array in the camera and the A to D rate of the framegrabber. Also, a good framegrabber and camera will also reduce the noise in the image and yield a better signal/noise ration. These factors can improve the visual cues for the user making the measurements.

The judgment of the user is set by training and psychophysiological factors. There will be some differences from one user to the next. The mathematical principles used to make stereo pair measurements are simple and straightforward. With a few simple tests it should be possible to determine the reliability of any software package that makes measurements on stereo pair images.

The optical principles that set the limits for stereo pair measurements are covered in the paper "Confocal Microscopy and 3-D Visualization" by Mike Richardson, (American Laboratory, November 1990.) Those principles are reviewed briefly here.

The transverse resolution of a wide field microscope is given by: Transverse resolution = 0.6 L/N.A. Where L = the wavelength of light; and N.A. = the numerical objective of the microscope aperture. The longitudinal resolution of a wide field microscope is given by: Longitudinal resolution = 2 L/N.A. to the 2nd power Where L = the wavelength of light; and N.A. = the numerical objective of the microscope aperture.

This means a 1.4 N.A. objective has a transverse resolution of 0.22 microns and a longitudinal resolution of 9.51 microns. This is the theoretical limits of resolution. Actual resolution is less due to other factors, such as spherical aberration and astigmatism.

The relationship of transverse and longitudinal resolution can be plotted by combining the above formula to get:

Longitudinal resolution 4 ----------------------- = -------- Transverse resolution 1.22 N.A.

Higher N.A. lenses have better transverse and longitudinal resolution. However, as can be seen from the plot, longitudinal resolution will, at best, be two times worse than transverse resolution. It is much worse for low N.A. lenses.

These formulae have implications for stereo pair measurements. The best depth measurement you can make will be limited by the N.A. of the objective used. With a good framegrabber and camera, and a 1.4 N.A. lens, one pixel could realistically resolve about 0.22 microns. The displacement of one pixel in the left and right images would result in a depth measurement of 0.51 microns. This would be the limit of resolution of stereo pairs measurements. This assumes the user would be able to distinguish an object at a level of one pixel difference in the two images.

Confocal microscopes and digital deconvolution with a point spread function will increase both longitudinal and transverse resolution resulting in more accuracy in stereo pair measurements. With the Edge microscope, better resolution may also be possible. Oblique illumination may improve the transverse resolution slightly, which would affect the formula for longitudinal resolution. This hypothesis awaits empirical verification, however.

The final factor that can affect measurement accuracy is the calibration process. To make accurate measurements on stereo pairs, you need two of the following three values:

Transverse resolution (dx = microns/pixel in the x direction)
Longitudinal resolution (dz = microns/pixel in the z direction)
Angle of parallax (angle of displacement of the two images)

The accuracy of measurements depends on the accuracy of the determination of these values. Transverse resolution can be obtained with a calibration specimen. The angle of parallax could be obtained from the instrument.

An understanding of these issues can help improve the accuracy of measurements from stereo pairs.

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Limits of Depth Measurement on Stereo Pair Images

by John Kesterson, Ph.D.

Articles recommended by VayTek that are available on this website:

Limits of Depth Measurement
on Stereo Pair Images