Min Gu

Image formation in a fiber-optical confocal scanning microscope

Theoretical studies on image formation in a confocal scanning microscope with optical fibers as the transmission medium are reported. Theoretical analyses show that this new kind of microscope can be considered a coherent imaging system, even for finite fiber spot size. Based on these studies the coherent transfer functions in both in-focus and defocused cases are derived and calculated. The axial coherent transfer functions are also obtained, and, furthermore, the optical-sectioning property of the microscope system is investigated with the consideration of the image formation of a perfect-reflection planar object and a point object.

Imaging by a high aperture optical system

Abstract Three-dimensional imaging in telecentric systems of non-unity magnification is considered using a scalar approximation. It is found that the imaging performance can be very different according to whether the image is formed directly in the image space or by scanning in the object space. It is shown that this result does not violate the principle of reciprocity. The point spread function is investigated for systems obeying, amongst others, either the sine or Herschel conditions. The results have great importance for scanning systems, in particular confocal microscopes, and explain some anomalies in the literature. A clarification of the principle of equivalence is given.

Three-dimensional transfer functions for high-aperture systems

The scalar three-dimensional optical transfer function is derived without using the paraxial approximation. The weak-object transfer function for a partially coherent system with equal condenser and objective apertures and the coherent transfer function for a confocal transmission system are of identical form. The coherent transfer function of a confocal reflection system is also derived. Both uniform angular illumination and systems obeying the sine condition are considered. In all cases the transfer functions can be expressed analytically.

Confocal fluorescent microscopy with a finite-sized circular detector

For a confocal fluorescent microscope with a finite-sized circular detector, the three-dimensional optical transfer function (OTF) for a thick object has been developed without the use of Stockseth’s approximation. The results show that the OTF has negative values when the radius of the detector exceeds certain magnitudes. The two-dimensional OTF derived from the three-dimensional OTF is also given.

Fresnel diffraction by circular and serrated apertures illuminated with an ultrashort pulsed-laser beam

Fresnel diffraction patterns by circular and serrated apertures under ultrashort pulsed-laser illumination are investigated in detail. A comparison of the diffraction patterns for pulsed and continuous wave illuminations reveals that an ultrashort pulsed beam of 10 fs can result in a significant effect on the distribution of the intensity. As a result a uniform intensity distribution in the transverse direction of the beam can be achieved as a result of the interference of the different frequency components within the pulsed beam. The interference fringes caused by the wavelets originating from the diffraction aperture can be further reduced when a serrated aperture is used.

Three-dimensional transfer functions in 4Pi confocal microscopes

We investigate three-dimensional transfer functions in order to understand image formation in the recently proposed 4Pi confocal microscope [ J. Opt. Soc. Am. A9, 2159 ( 1992);Opt. Commun.93, 277 ( 1992)]. Both nonfluorescence and fluorescence imaging methods are considered, and the effects of apodization functions are taken into account. It is shown that for a 4Pi confocal system of finite-sized aperture the cutoff spatial frequency in the axial direction is larger than that in the transverse direction; this behavior is opposite that of conventional confocal systems, explaining the observation of high axial resolution in 4Pi confocal systems. In addition, the three-dimensional optical transfer function for a conventional confocal fluorescence microscope of high aperture is presented.

Effects of a Finite-sized Pinhole on 3D Image Formation in Confocal Two-photon Fluorescence Microscopy

Abstract We investigate three-dimensional (3D) imaging properties in confocal two-photon (2-p) fluorescence microscopy with a finite-sized detector. The 3D intensity point spread function, the 3D optical transfer function (OTF), the strength of optical sectioning and the signal levels for point, planar and volume objects are calculated in order to reveal their relationships to the detector size. It is shown that confocal 2-p fluorescence imaging with a point detector gives super-resolution, compared with conventional 2-p imaging without a confocal pinhole. Although optical sectioning can be attained in the latter case, its strength is inferior to that in the confocal case. In particular, a finite-sized detector can result in negative values in the 3D OTF and reduce the effective cut-off spatial frequencies, thus degrading the capability of confocal 2-p fluorescence microscopy for 3D imaging. Unlike the single-photon fluorescence microscope, there is no missing cone of spatial frequencies in the 3D OTF for...

Three-dimensional coherent transfer functions in fiber-optical confocal scanning microscopes

After analyzing the three-dimensional image formation in fiber-optical confocal scanning microscopes, a three-dimensional effective point-spread function is introduced. For both reflection-mode and transmission-mode microscopes of small circular aperture, analytical expressions for the three-dimensional coherent transfer functions are derived. The relation between the three-dimensional and the two-dimensional (for thin objects) coherent transfer functions in these microscopic systems is further investigated. Three-dimensional numerical plots of the coherent transfer functions reveal their dependence on the fiber spot size.

Imaging and reconstruction for rough surface scattering in the Kirchhoff approximation by confocal microscopy

Abstract Imaging of rough surfaces in confocal microscopy can be described using the concept of the three-dimensional (3D) coherent transfer function (CTF), which is developed on the basis of the Kirchhoff approximation. The 3D CTF is presented using a scalar but high-angle theory. Methods for reconstruction of surface profiles are considered.

Three-dimensional Image Formation in Confocal Microscopy Under Ultra-short-laser-pulse Illumination

Reported in this paper is, to our knowledge, the first theoretical investigation of three-dimensional (3D) imaging properties in a confocal microscope under ultra-short-pulse illumination. Time-resolved, time-averaged and interferometric imaging modes in reflection and transmission systems are considered. The concept of the 3D transfer function is used to understand the imaging performance of the system. In the case of a 10fs pulse, the spatial frequency bandwidth in the axial direction is twice that for a system under continuous-wave (CW) illumination, while the spatial frequency bandwidth in the transverse direction is increased by only 10%. As a result, axial resolution can be improved by approximately 30%, compared with the limiting value under CW laser illumination of the same wavelength as the pulsed beam.