Chengqi Xu

Algebraic analysis of the Van Cittert iterative method of deconvolution with a general relaxation factor

The convergence of Van Cittert’s iterative method of deconvolution is studied from an algebraic point of view without any special prior condition with respect to the system matrix. The convergence criteria are expressed in terms of system eigenvalues. We choose bounds for the general relaxation coefficient μ of Van Cittert’s additional term so as to ensure convergence. We show that the bounds can be estimated from the system matrix. Many powerful nonlinear deconvolution techniques are derived from Van Cittert’s method, even though it appears outmoded. As an example, we demonstrate that Gold’s iterative algorithm is a special Van Cittert’s algorithm with a variable relaxation factor μ

Multiple-objective microscopy with three-dimensional resolution near 100 nm and a long working distance.

The resolution of microscopes is limited by the sizes of their point-spread functions. The invention of confocal, theta, and 4Pi microscopes has permitted the classic Abbe limit to be exceeded. We propose the use of a combination of 4Pi and theta microscopy to decrease resolution by using four illumination objectives and two detection objectives. Using middle numerical aperture, long-working-distance objectives yielded a resolution near 100 nm in the three dimensions, which opens the possibility of exploring large volumes with a high resolution.

Identification of acquisition parameters from the point spread function of a fluorescence microscope

Except for blind methods, deconvolution of 3-D data sets acquired from a fluorescence microscope requires the knowledge of the point spread (PSF) of the instrument. Unsing the XCOSM package, we show first with simulations and then with recorded data that it is possible to recover from an experimental PSF some parameters, which are very difficult or impossible to measure during the acquisition, like the specimen depth or the immersion medium refractive index. Doing so, we can precise the acquisition protocol, which helps to use the instrument under optimal conditions. Furthermore, the knowledge of the actual acquisition condtions permits to use fo the deconvolution process a computed PSF, which is noiseless and as close as possible to the actual PSF. This helps to reduce errors in quantitative measurements after deconvolution, as shown with computations.

Validation of image processing tools for 3-D fluorescence microscopy.

3-D optical fluorescent microscopy becomes nowadays an efficient tool for volumic investigation of living biological samples. Using optical sectioning technique, a stack of 2-D images is obtained. However, due to the nature of the system optical transfer function and non-optimal experimental conditions, acquired raw data usually suffer from some distortions. In order to carry out biological analysis, raw data have to be restored by deconvolution. The system identification by the point-spread function is useful to obtain the knowledge of the actual system and experimental parameters, which is necessary to restore raw data. It is furthermore helpful to precise the experimental protocol. In order to facilitate the use of image processing techniques, a multi-platform-compatible software package called VIEW3D has been developed. It integrates a set of tools for the analysis of fluorescence images from 3-D wide-field or confocal microscopy. A number of regularisation parameters for data restoration are determined automatically. Common geometrical measurements and morphological descriptors of fluorescent sites are also implemented to facilitate the characterisation of biological samples. An example of this method concerning cytogenetics is presented.

Identification and restoration in 3D fluorescence microscopy

3-D optical fluorescent microscopy becomes now an efficient tool for volumic investigation of living biological samples. The 3-D data can be acquired by Optical Sectioning Microscopy which is performed by axial stepping of the object versus the objective. For any instrument, each recorded image can be described by a convolution equation between the original object and the Point Spread Function (PSF) of the acquisition system. To assess performance and ensure the data reproducibility, as for any 3-D quantitative analysis, the system indentification is mandatory. The PSF explains the properties of the image acquisition system; it can be computed or acquired experimentally. Statistical tools and Zernike moments are shown appropriate and complementary to describe a 3-D system PSF and to quantify the variation of the PSF as function of the optical parameters. Some critical experimental parameters can be identified with these tools. This is helpful for biologist to define an aquisition protocol optimizing the use of the system. Reduction of out-of-focus light is the task of 3-D microscopy; it is carried out computationally by deconvolution process. Pre-filtering the images improves the stability of deconvolution results, now less dependent on the regularization parameter; this helps the biologists to use restoration process.

PSF identification applied to 3D fluorescence microscopy quantification

3-D optical fluorescence microscopy becomes now an efficient tool for volumic investigation of living biological samples. However, acquired raw data suffer from different distortions. In order to carry out biological analysis, restoration of raw data by deconvolution is mandatory. The system identification is useful to obtain the knowledge of the actual system and to quantify the influence of experimental parameters. High order centered moments are used as PSF descriptors. Oil immersion index, numerical aperture and specimen thickness are critical parameters for data quality. Furthermore, PSF identification is helpful to precise the experimental protocol. Application to 3-D anthracycline distribution in breast cancer cells is presented.

Fluorescence microscopy with 3D resolution in the 100 nm range

We propose a combination of 4Pi and Theta microscopies to improve the resolution of fluorescence microscopy by using six microscope objectives in a configuration we call Multiple Objective Microscopy (MOM). A resolution in the 100 nm range is obtained in the three dimensions using low numerical aperture, long working distance objectives. The obtained results not only show that high resolution is not restricted to high numerical aperture objectives, but also open the possibility of exploring large volumes with a very good resolution.

Laser-cytofluorescence microscopic image restoration by iterative deconvolution

The aim of our study is to improve the performances of an optical microscope by image deconvolution technique to attain that of a confocal one in the field of laser cytofluorescence. The fluorescence of antigen lymphocyte sites marked by rhodamine is induced by a laser ((lambda) equals 543 nm) or a mercury vapor lamp. A set of scanned fluorescence images is acquired at different focal planes by a SIT camera, fitted on an optical ZEISS microscope (N.A. 1.25, X100). The entire system is controlled by a PC equipped with a MATROX-MVP-AT image processing card. Since an optical microscope has a more important focal depth than a confocal one, an improved iterative deconvolution algorithm of Van Citterts has been used to artificially reduce the focal depth. In order to ensure the convergence of such an iterative algorithm, a new criterion for relaxation coefficient is defined through a theoretical study. The experiments show an improvement of 50% in the spatial x-y resolution of 30% in optical z axis gain. As regards our application, this processing brings our system to a comparable performance level as a confocal microscope.