One-step calibration of specimen induced focal shifts and spherical aberration for quantitative 3D microscopy: Approach and first results

With the advent of laser scanning confocal and multiphoton microscopy, 3D life tissue characterization has been rendered possible. This involves the restoration of thick section images (in the depth range of 100 microns) of biological samples. In contrast to thin samples new effects become important when imaging thick samples: Because of changes of the refractive index across the specimen or the embedding medium, strong (> 1 micron) focal shifts and spherical aberration occur and scattering effects get more prominent. For tissue mapping it is essential to correct for such aberrations and distortion effects. In this paper, we propose a calibration framework, which allows us to determine thick section focal shifts and spherical aberrations in a one-step-procedure. Gradients in the focal shift induce a scaling in the Z-direction of the observed sample. A second effect arises with depth-dependent spherical aberration. We model our microscope as a linear-shift-NON-invariant system (LSNI) where multiple depth classes are assigned distinct point spread functions (PSFs). We measure these two effects in a 3D sample of randomly distributed fluorescent focal check beads. The beads are embedded in gelatine, a medium with high resemblance to real biological tissue. The PSF is approximated by a mathematical parametric model. While estimating the parameters of the PSF with object-constrained deconvolution, we track depth dependent changes of the observed bead diameter. This allows us to determine the gradient of the focal shift across a thick section. By numerical integration along the optical axis we obtain the focal shift values as a function of sample depth. In the end, these values will be applied as a correction to compensate depth distortions in the tissue images.