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Three-Dimensional Point Spread Function Model for Line-Scanning Confocal Microscope with High-Aperture Objective E

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Three-Dimensional Point Spread Function Model for Line-Scanning Confocal Microscope with High-Aperture Objective E Three-dimensional point spread function model for line-scanning confocal microscope with high-aperture objective E. Dusch, T. Dorval, N. Vincent, M. Wachsmuth, Auguste Genovesio To cite this version: E. Dusch, T. Dorval, N. Vincent, M. Wachsmuth, Auguste Genovesio. Three-dimensional point spread function model for line-scanning confocal microscope with high-aperture objective. Journal of Mi- croscopy, Wiley, 2007, 228 (2), pp.132 - 138. 10.1111/j.1365-2818.2007.01844.x. hal-02901997 HAL Id: hal-02901997 https://hal.archives-ouvertes.fr/hal-02901997 Submitted on 17 Jul 2020 HAL is a multi-disciplinary open access L’archive ouverte pluridisciplinaire HAL, est archive for the deposit and dissemination of sci- destinée au dépôt et à la diffusion de documents entific research documents, whether they are pub- scientifiques de niveau recherche, publiés ou non, lished or not. The documents may come from émanant des établissements d’enseignement et de teaching and research institutions in France or recherche français ou étrangers, des laboratoires abroad, or from public or private research centers. publics ou privés. Journal of Microscopy, Vol. 228, Pt 2 2007, pp. 132–138 Received 24 September 2006; accepted 18 May 2007 Three-dimensional point spread function model for line-scanning confocal microscope with high-aperture objective ∗ ∗ E. DUSCH ,†,T.DORVAL, N. VINCENT†, M. WACHSMUTH‡ ∗ ∗& A. GENOVESIO Image Mining Group, Institut Pasteur Korea,39-1, Halwolgok-dong, Seongbuk-gu, Seoul 136-791, Korea, †SIP-CRIP5, Universit´eParis Descartes, 45, rue des Saint P`eres 75005 Paris, France and ‡Cell Biophysics Group, Institut Pasteur Korea, 39-1, Halwolgok-dong, Seongbuk-gu, Seoul 136-791, Korea Key words. Confocal microscopy, Debye integral, line-scanning confocal microscope, point spread function. Summary the small size of the imaged beads (McNally et al., 1999). Moreover, knowledge of both the analytical and the simulated Point Spread Function (PSF) modelling is an important task PSF allows a more precise characterization of the system. in image formation analysis. In confocal microscopy,the exact An analytical approach consists in expressing the PSF using PSF is rarely known, thus one has to rely on its approximation. diffraction theory and knowledge of the optical microscope An initial estimation is usually performed experimentally components. Although analytical PSF models have been by measuring fluorescent beads or analytically by studying well established for point-scanning confocal microscopes, properties of the optical system. Yet, fluorescent line-scanning they are not adapted to line-scanning confocal microscopes confocal microscopes are not widespread; therefore, very few (characterized by a line illumination in the object space and adapted models are available in the literature. In this paper, we a slit-shaped line detector). In Sheppard & Mao (1988), the propose an analytical PSF model for line-scanning confocal authors proposed a two-dimensional PSF model applicable microscopes. Validation is performed by measuring the error only in the focal plane. More recently, Wolleschensky et al. between our model and an experimental PSF measured (2005) proposed a three-dimensional (3D) model for the LSM 5 with fluorescent beads, assumed to represent the real PSF. live line-scanning confocal microscope (Zeiss, Germany). They Comparison with existing models is also presented. make a paraxial assumption, valid only for an objective lens with low numerical aperture (NA), and compute the model Introduction with non-paraxial optical units, which can be considered as a first approximation for higher NAs (Amos, 1995). Accurate point spread function (PSF) models are necessary for In this paper, we propose a 3D non-paraxial PSF model various tasks, such as deconvolution (see Sarder & Nehorai, for a fluorescent line-scanning confocal microscope with a 2006 for a review), image resolution improvement (Santos high-aperture objective lens, and show that the model tends & Young, 2000; Thomann et al., 2002) and data simulation asymptotically to the paraxial model of Wolleschensky et al., to validate image-processing algorithms. As the exact PSF is when the NA becomes small. During the validation process, rarely known, one has to rely on its approximation, which can we use as reference a measured PSF calculated by averaging be estimated using an experimental or an analytical approach. fluorescent beads imaged on the LSM 5 live microscope, and In an experimental approach, the PSF is estimated by comparetherelativeabsoluteerror(RAE)ofthreemodels:non- extracting image structures assumed to represent it. In paraxial point-scanning (Gu, 2000), paraxial line-scanning confocal microscopy, this is usually achieved by measuring (Wolleschensky et al., 2005) and the proposed non-paraxial small fluorescent beads. Although this approach has the line-scanning model. advantage of well reflecting the imaging conditions, the obtained PSF has a low signal-to-noise ratio (SNR) due to Theoretical line-scanning PSF model Correspondence to: E. Dusch. Tel: +82 2 3299 0262; Fax: +82 2 3299 0210 e-mail: [email protected]; A. Genovesio. Tel: +82 2 3299 0261; Fax: +82 In this section, we first express the theoretical excitation and 2 3299 0210; e-mail: [email protected] emission amplitudes of a point near the focus using the scalar C 2007 The Authors Journal compilation C 2007 The Royal Microscopical Society 3D POINT SPREAD FUNCTION MODEL 133 z z y x focal/sample plane objective lens back focal plane of objective lens tube lens microscope stage intermediate image plane scan optics (omitted here) spherical lens cylindrical achromatic cylindrical lens beam splitter lens spherical lens detector/slit Fig. 1. Scheme of a fluorescent line-scanning confocal microscope. Debye diffraction integral. Then, we present a 3D non-paraxial intensity distribution (generated by the fluorescence) convo- PSF model for fluorescent line-scanning confocal microscopes lvedwiththeareaofthedetectorprojectedintotheobjectspace: and its paraxial approximation. PSF(x, y, z) = |h (x, y, z)|2 |h (x, y, z)|2 ∗ D (x, y) , (1) When the NA becomes large, effects such as depolarization, ex em apodization and aberration are more pronounced (Gu, 2000). where ∗ denotes the convolution, D is the detector, and hex and Considering the vectorial property of electromagnetic waves, hem are the excitation and emission amplitude distributions, the vectorial Debye theory was proposed to take into account respectively. In line-scanning microscopes, the detector is light depolarization in the focus of the lens. Nevertheless, a characterized by the slit in the y direction and by the line CCD close approximation of the intensity distribution near the focus detector elements in the x direction. In the widefield case, it has can be obtained by the scalar theory as shown by Born & Wolf been shown that the CCD elements are usually small enough (1999). In the following, we assume that the optical system is to be neglected in the image formation process (van Kempen, linear shift-invariant and aberration-free. 1999). In a similar way and as shown in Fig. 2, the PSF for Let us consider a line illumination created and focussed by line-scanning microscopes can be approximated by a cylindrical lens on the back-focal plane of the objective lens. PSF(x, y, z) = |h (x, y, z)|2 |h (x, y, z)|2 ∗ S (y) . (2) A line is thus generated along the x direction by the objective ex em lens onto the sample plane (Wolleschensky et al., 2005). The slit S situated in front of the line detector is considered Figure 1 describes the light path along the y direction (left) as a finite-size incoherent pinhole, that is, it detects the light and x direction (right). The emitted fluorescence is focussed by intensity (Wilson, 1995). the confocal lens onto a slit, rejecting out-of-focus fluorescent Since an illumination line covers the total sample plane in points. the x direction, diffraction effects are not important owing to In confocal microscopy, the Point Spread Function is the wide illuminated area. Therefore, we assume the excitation defined by the product of the excitation intensity distribution amplitude along the line to be constant. The waves in the field (characterized by the line illumination) and the emission between the objective lens and the focal plane are defined as C 2007 The Authors Journal compilation C 2007 The Royal Microscopical Society, Journal of Microscopy, 228, 132–138 134 E. DUSCH ET AL. 1 1 0.9 0.9 0.8 0.8 0.7 0.7 0.6 0.6 0.5 0.5 0.4 0.4 0.3 0.3 Normalized Intensity 0.2 Normalized Intensity 0.2 0.1 0.1 0 0 -0.8 0 0.8 0 0.8 x-axis x-axis (a) (b) 1 0.9 0.8 0.7 0.6 0.5 0.4 0.3 Normalized Intensity 0.2 0.1 0 0 0.8 x-axis (c) Fig. 2. Normalized intensity of the non-paraxial PSF model with (dashed line) and without (solid line) considering the detector along the line for different slit sizes: s →∞(a), s = 1 (b) and s → 0(c) (Units are in μm). 2π a superposition of plane waves. Using the scalar Debye theory where the emission wave number k em is equal to n , and J 0 λem (Born & Wolf, 1999), the excitation amplitude near the focal is the zero-order Bessel function. point can be written as the integration of these plane waves Hence, the non-paraxial line-scanning PSF can be written according to the angle of convergence. Thus, we express the as excitation amplitude according to the y and z direction as (see α √ Appendix A for details): PSFNP(x, y, z) = cos θ exp(−ikex y sin θ) , hex (y z) −α α 2 = θ − θ − θ θ θ, P ( ) exp ( ikex y sin ) exp ( ikexz cos ) kex cos d × exp(−ikexz cos θ)kex cos θdθ −α (3) s α √ α = 2 where is the aperture half angle of the objective and kex cos θ J k sin θ x2 + (y − y ) 2π 0 em s n λ is the excitation wave number.
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