Three-dimensional coherent transfer functions in ...

Three-dimensional coherent transfer functions in confocal scanning imaging Min Gu and C. J. R. Sheppard Department of Physical Optics, University of Sydney, NSW 2006, Australia ABSTRACT We report on the analysis of the three-dimensional (3-D) image fonnation in a confocal microscope in tenns of the concept of the 3-D coherent transfer function (CTF). The effects of the annular pupil function and spherical aberration on the 3-D CTFare investigated. The 3-D CIF for a new fibre-optical confocal system consisting of optical fibres for illumination and collection is described. We also discuss the significance of the 3-D CTF and, in particular, the relationship between the 3-D CTF and 2-D and 1-D imaging. 1. THREE-DIMENSIONAL COHERENT TRANSFER FUNCTION Laser scanning confocal microscopy is a new development in optical microscopy which has been applied to many practical fields such as wafer metrology, industrial inspection and biological and medical studies!. One of the main advantages in confocal microscopy is that it has a strong optical sectioning effect which provides a powerful means to achieve 3-D imaging of a thick object. It has been shown that imaging in such a microscope behaves as a coherent microscope in which the image can be completely described by the 3-D coherent transfer function (CTF), providing that scattering is weak enough that the first Born approximation holds2 • The 3-D CTF for a transmission-mode confocal system with two equal circular lenses is shown in Fig. la, where I and s are radial and axial spatial frequencies. It reveals a missing cone of spatial frequencies and a singularity at the origin, implying that real optical sectioning may not be achieved. The 3-D CTF in this case is identical to the 3-D optical transfer function for a conventional incoherent microscope. The 3-D CTF for reflection in Fig. 1b gives a strong optical sectioning due to the finite value of cr(l = 0, s). It is seen that the spatial frequency pass band of the confocal scanning microscope is twice as large, in both axial and transverse directions, as that in the conventional microscope. When annular lenses are employed in the con focal system2• 3, the 3-D CTFs exhibit smaller cutoff spatial frequencies thml those in the circular lens cases. Figs. 1c and Id are the 3-D CTFs for tramsmission and reflection system with two equal annular lenses, where the inner radius of the annular lens is 0.5. (b)

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2. EFFECT OF SPHERICAL ABERRATION ON THE 3·D CTF A con focal system may suffer from spherical aberration in practical imaging when the refractive index of the immersion material does not match that of the specimen. In this case, the 3-D CTF becomes a complex function and is degraded. The effects of defocus and primary spherical aberration on the 3-D CTFs have been investigated4 • Figs. 2a and 2b give the typical 3-D CTFs for transmission and reflection, respectively, when the primary spherical aberration is equal to 2A., where A. is the wavelength of the illumination light.

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3. 3·D CTF IN A FmRE·OPTICAL CONFOCAL SCANNING MI