3-DIMENSIONAL IMAGE-RESTORATION AND SUPERRESOLUTION IN FLUORESCENCE CONFOCAL MICROSCOPY

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. 1990 Blackwell Science Ltd