Effects of Fresnel diffraction on confocal imaging with an annular lens

Abstract

yOptoelectronic Imaging Group, Department of Applied Physics, Victoria Universityof Technology, PO Box 14428, MCMC, VIC 8001, AustraliazDepartment of Physical Optics, University of Sydney, NSW 2006, AustraliaSubmitted 9 January 1997, accepted 26 June 1997Abstract. The effect of the Fresnel diffraction on the imaging properties of confocalmicroscopy with one circular aperture and one annular aperture is investigated. Theresults show that the Fresnel diffraction patterns alter the axial imaging properties moreseriously than the transverse imaging properties. The axial response of such a confocalmicroscope is sharpened, but severely distorted.Keywords: Fresnel diffraction, annular pupil, confocal microscopy1. IntroductionAnnular aperture is a widely used spatial filter in confocalmicroscopy. It gives some improvement in transverseresolution, but a degradation in axial resolution appears ina confocal system with an annular structure [1,2]. Recentresearch suggests that the use of annular apertures as spatialfilters can suppress the scattered photons [3]. For example,a reflection-mode confocal system with an annular aperturein the illumination path is reported to show a significantenhancement in signal-to-noise ratio for imaging through ahighly scattering medium [4].In practice, an annular aperture cannot be placed exactlyat the back focal plane of an objective. In this case,Fresnel diffraction by the annular aperture exists. Fresneldiffraction of a finite-sized aperture can produce bright anddark fringes because of the interference of the waveletscontributed from points over the aperture [5,6]. Theintensity modulation caused by the interference fringes canalter the imaging properties of confocal microscopy, sincethe effective pupil function of the objective illuminatedby the Fresnel patterns changes accordingly, resulting inthe alteration of the intensity in the focal region [7–10].Therefore, it is important to investigate the effect of Fresneldiffraction on the imaging performance of a confocalsystem with an annular aperture.This paper is organized as follows. Section 2 presentsthe Fresnel diffraction of an annular aperture. The effectof Fresnel diffraction patterns of an annular aperture on theimaging properties of confocal microscopy is discussed insection 3.2. Fresnel diffraction of an annular apertureIf an aperture is placed in the back focal plane of anobjective then focusing is described by Debye theory. TheFresnel number is infinity in this situation. However, ifthe aperture is placed away from the back focal plane by adistance