Three-dimensional optical transfer function in differential confocal microscopy

To reveal the fundamental characteristics of differential confocal microscopy (DCM), its imaging properties were analysed by studying the 3D optical transfer function (OTF). The zero transfer at zero frequency along the axial direction in DCM, which has not been well understood and is considerably different from the transfer behaviour in conventional confocal microscopy (CM), was elucidated. The integral expressions of the OTFs for CM and DCM and the subsequent simulation results showed that DCMs have higher transfer capability than CM in the axial direction at medium and high frequencies. Conventionally, the relative optimal defocusing amount in DCMs are determined through calculations of the gradient of the point spread functions in the spatial domain. In contrast, in this study, the OTF performances were compared and the optimal defocusing amount was found to be between 5 and 7. Lay Description Differential Confocal Microscopy (DCM) is designed employing two symmetrically defocused detectors of Confocal Microscopy (CM), which can improve the sensitivity of axial response of CM greatly. However, no one has ever inspected the three dimensional (3D) optical transfer function (OTF) for DCM to reveal its characteristics. This manuscript derives the formula of 3D OTF for DCM and analyzes the distribution of DCM for different defocusing amount to reveal the essence of DCM. We investigate the sectioning properties and transverse resolution of these optical systems by analyzing the 3D OTF along the axial and radial direction. The zero transfer capability of DCM in zero frequency along axial direction is also explained, which is confusing and greatly different from CM. This manuscript also gives the optimal range of defocusing amount through OTF analysis according to the information transfer capability.