Super-resolution in confocal scanning microscopy: IV. Theory of data inversion by the use of optical masks
| Autor: | Mario Bertero, Edward Roy Pike, J. G. Walker, R E Davies, F. Malfanti, Patrizia Boccacci |
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| Rok vydání: | 1992 |
| Předmět: |
Microscope
business.industry Applied Mathematics Confocal Detector Confocal scanning microscopy Image plane Inverse problem Integral equation Computer Science Applications Theoretical Computer Science law.invention Numerical aperture Optics law Signal Processing business Mathematical Physics Mathematics |
| Zdroj: | Inverse Problems. 8:1-23 |
| ISSN: | 1361-6420 0266-5611 |
| DOI: | 10.1088/0266-5611/8/1/001 |
| Popis: | In the previous papen in this series we proposed and discussed a method, based on a singular-system analysis of the low-numerical-aperture limit for improving the resolution of a confocal scanning microscope. In this paper we show that this method can k implemented by the use of a special optical mask which can be computed by this analysis. We discuss one-dimensional and two-dimensional problems both in the coherent and in thc incoherent case. Some exact results obtained for one-dimensional problems are used to understand the numerical results obtained for two-dimensional problems. For the two-dimensional incoherent problem we also extend the investigation to the case of lenses with high numerical aperture. 1. Intmduction In a recent series of papers 11-31 we have developed the theory of a novel confocal microscope which is similar to a confocal scanning microscope but which uses, in place of a single pinhole and detector, an array of detectors in the image plane. At each step of the scanning procedure the signals from the detectors are processed by means of singular-system analysis in order to invert the integral relationship between the object and the image. In such a way the object is calculated at the confocal point on axis and a complete image is provided by scanning. This image is super-resolved in the sense that the resolving power of the new microscope is considerably better than that of the conventional confocal one. The theory was developed for one-dimensional (1D) coherent (l) and incoherent (Z) objects as well as for the case of two-dimensional (ZD) circular pupils (3). In all cases the analysis was done by assuming that the lenses had a small numerical aperture where the equations are simpler and some analytic results are possible. Corrections for higher numerical apertures will be considered in this paper. The integral relationship between the object .f and the image g, for a given scanning position, can be written as follows |
| Databáze: | OpenAIRE |
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