Photogrammetric calibration of a stereo light microscope

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Abstract
Quantitative stereo light microscopy has been used in very rare cases to obtain geometric representations of microscopic objects. Although the instrument itself has limitations, most of them efficiently overcome by other 3D microscopes, it bears considerable advantages in observing and measuring dynamic scenes with multiple objects. The biggest asset of the stereo method is that the full 3D work space is imaged in one shot — a property which distinguishes stereo from all the scanning techniques in 3D microscopy. With the work presented in this paper, we contribute to making the stereo technique applicable to the numerous mensuration tasks in the microscopic domain, where its potential would be invaluable.We report the photogrammetric calibration of a common main objective lens type stereo light microscope. Such a calibration is the initial step in ensuring accurate measurements with this instrument. First, we derive a mathematical formulation of the imaging function and discuss the estimation of the parameters involved. Then, three main problems of the practical implementation of the framework are addressed: the finding of a calibration standard, the automatic measuring of the many image coordinates required, and the stabilization of the parameter estimation. Finally, results of various calibration runs are presented and analysed under different aspects. Among these, the most important is the accuracy of the calibrated instrument in measuring 3D positions and positional relationships. With a Zeiss Stemi 11, Achromat 1.6 × we achieve accuracies of 1‰ laterally and 1–2% axially relative to the volume of the work space. On the highest magnification level this corresponds to 700 nm and 1.8 μm, respectively.

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