Showing papers by "Min Gu published in 1993"

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.

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...

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.

Scattering by a one-dimensional rough surface, and surface profile reconstruction by confocal imaging

Abstract: It is demonstrated that scattering by a rough surface can be described in terms of the coherent transfer function, which was first developed to describe the process of imaging. The two-dimensional (one transverse and one longitudinal) coherent transfer function for confocal imaging is presented for a high-angle theory. From this an effective transfer function for imaging of rough surfaces is developed, based on the Kirchhoff approximation. It is described how confocal imaging can be used to investigate various scattering mechanisms, and can be used for reconstruction of surface profiles in the Kirchhoff approximation. PACS numbers: 42.25.Fx, 42.30.-d There is much interest at present in the scattering of light by rough surfaces. This has been greatly brought about by the observation of the phenomenon of enhanced backscattering [I -61 For surfaces which are not too rough, scattering can be explained by the Kirchhoff ap­ proximation [7]. Because the general problem of scatter­ ing in three dimensions is quite complicated, many of the current papers consider the simpler case of a one­ dimensional rough surface (assumed constant in the y direction) illuminated by a plane wave incident in the x-z plane [81 Then for TE or TM polarization no depolari­ zation is introduced upon scattering. Enhanced back­ scattering results from multiple scattering and construc­ tive interference, but the full details are not completely understood. The inverse problem of reconstructing a surface profile from scattering data has also been considered [91 As in this case it is necessary to measure (or restore) the phase as well as the modulus of the scattered radiation; this is conveniently done using a microscope objective which en­ sures phase coherence over a range of illumination and scattering angles. Scattering data for various angles of il­ lumination and detection can then be selected by positioning masks in the back focal plane of the objective. Alternatively the surface can be illuminated simultane­ ously by a spectrum of plane waves, the relative phases of which can be altered by scanning the surface relative to the focused spot. In confocal imaging [10] a pinhole is placed in front of the detector onto which the scattered radiation is focused. In this case imaging of a thick structure can be described by a two-dimensional (one transverse and one longitudinal) coherent transfer func­ tion [Ill For TE or TM polarization, there is no depo­ larization on scattering. As there is one direction cosine each for the incident and scattered radiation, there is a one-to-one and onto mapping between these representa­ tions. Thus each pair of transverse and longitudinal spa­ tial frequencies corresponds to a particular pair of in­ cident and scattering directions (actually two pairs, cor­ responding to two reciprocal paths). Thus a 20 image of the surface contains the complete 'scattering data within the aperture of the objective lens. In two dimensions the image amplitude (Fig. I) in con­ focal reflection can be expressed in terms of the scattering function S(m2,m I)' where m ),m2 are the direction cosines in the x direction for the incident and scattered radiation [121, as u(x,z) = f_+oooo f-+: PI (ml)P2(m2)S(m2,ml)exp[ - ik{[m2 - mdx+ {(I - mi> 112+ (I -mf) 1/2}Zl1dml dm2. The pupil functions P)'P2 are zero outside of the pupil (I)

Three-dimensional coherent transfer functions for confocal imaging with unequal annular lenses

Abstract: We report, in this paper, the three-dimensional (3D) coherent functions for a confocal scanning system consisting of two unequal annular lenses. Analytical expressions for the 3D coherent transfer functions are derived for both transmission and reflection cases. Various numerical plots of the 3D coherent transfer function are given for different confocal systems including dark field microscopes. Our method is then generalized to the fibre-optical confocal system in which optical fibres rather than pinholes are employed for illumination and collection. In this case, the 3D coherent transfer function in transmission can also be obtained analytically, whilst that in reflection cannot be expressed by analytical functions, but by a single integral. Finally, images of a grating of periodic square structures are simulated to reveal the significance of the derived 3D coherent transfer functions.

Fresnel approximation for off-axis illumination of a circular aperture

Abstract: Various formulations have been proposed for the Fresnel approximation for diffraction by a circular aperture. These formulations can describe the effects of convergent illumination, finite value of Fresnel number, and off-axis illumination. The retention of a further term, which is dependent on the coordinates of the focus and the observation point, is proposed. This results in a redefined axial optical coordinate, giving improved prediction of the diffracted field for off-axis points.

Modelling of three-dimensional fluorescence images of muscle fibres: an application of the three-;-dimensional optical transfer function

Abstract: Striated muscle libres Cim be modelled by a simple geometry. which has allowed three-dimensional (3-D) images in conventional and con focal microscopes to be calculated. This model is useful for comparing different imaging methods and represents a simple example of an applicalion of the 3-D optical transfer function (OTF) for the system. The rejection of out-or-focus blur is demonstrated. and the effects of libre thickness and con focal pinhole size on Image contrast are investigated. The effects of using a simple filter for image enhancement arc studied. elucidating the characteristics of the OTF. A number of papers recently have been concerned with the interaction of light with striated muscle lib res (e.g. Huxley. 1990). These studies are important in understanding the structure of the fibres. but it is also apparent that because the dimensions of the various features arc comparable in si?.c with the wavelength of light. they provide a useful test specimen for investigation lInd comparison or diITcrcnt microscope systems. In particular. because the librcs may have considerable depth they may be used to demonstrate the three-dimensional (3-D) Imaglng properties of confocal microscopes. Confocal microscopes can be used in a number of ways to image thick structures. They can form images of the variations in fluorescence in the axial direction. using Slacks of sections. stereo pairs or x-z images. However. they also Improve the laterallmaglng of thick structures without any axial variations through the rejection of out-of-focus blur. Many applications of confocal microscopy exploit this property. rather than attempting to create a 3-D image. This paper therefore explores the effects of various different