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SUMMARY Confocal scanning laser microscopy (CSLM) provides optical sectioning of a fluorescent sample and improved resolution with respect to conventional optical microscopy. As a result, three-dimensional (3-D) imaging of biological objects becomes possible. A difficulty is that the lateral resolution is better than the axial resolution and, thus, the microscope provides orientation-dependent images. However, a theoretical investigation of the process of image formation in CSLM shows that it must be possible to improve the resolution obtained in practice. We present two methods for achieving such a result in the case of 3-D fluorescent objects. The first method applies to conventional CSLM, where the image is detected only on the optical axis for any scanning position. Since the resulting 3-D image is the convolution of the object with the impulse-response function of the instrument, the problem of image restoration is a deconvolution problem and is affected by numerical instability. A short introduction to the linear methods developed for obtaining stable solutions of these problems (the so-called regularization theory of ill-posed problems) is given and an application to a real image is discussed. The second method applies to a new version of CSLM proposed in recent years. In such a case the full image must be measured by a suitable array of detectors. For each scanning position the data are not single numbers but vectors. Then, in order to recover the object, one must solve a Fredholm integral equation of the first kind. A method for the solution of this equation is presented and the possibility of achieving super-resolution is demonstrated. More precisely, we show that it is possible to improve by about a factor of 2 the resolution of conventional CSLM both in the lateral and axial directions. |
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