Theory of Image Formation in Confocal Microscopy

One of my current research interests is theory of the Three-Dimensional (3-D) image formation in confocal imaging systems. For a long time I have been trying to find a simple mathematical description for the three-dimensional (3-D) image in confocal system. Eventually, together with my colleagues, Dr. Wieland Weise, Dr. Oleg Lobkis and Prof. Siegried Boseck, we developed the theory of three dimensional image formation of strong scatterers in scanning acoustic microscopy (SAM) and optical microscopy (SOM). We formulated the theory of the image formation in reflection and transmission microscopes using the angular spectrum approach. The theory showed that the image of a closed object could be represented as a two fold two-dimensional Fourier transform of a far field scattering amplitude of the object. Contrast in the reflection microscope is mainly due to scattering from the boundary of the object and can be described as a thin layer whose medium surface is in coincidence with the boundary of the objects. In the transmission microscope the contrast is connected with the contour of the object. The proposed theory provides the opportunity to investigate the imaging process for objects having an arbitrary shape. As you can see from the images of the spheres provided below, the theory works very well in acoustic microscopy. Later, we showed that the same theory can be used for image interpretation in optical scanning microscopy. Images of a simple spherical particle look surprisingly different from waht we expected.


Reflection SAM
    Theory: x-z scan of 3-D image of steel sphere
    Model of the reflection
    and transmission acoustic microscopes
    Experiment: x-z scan of 3-D image of steel sphere.


Transmission SAM
    Theory: x-z scan of 3-D image of steel sphere.
    Theory: x-z scan of 3-D image of liquid drop
    Theory: x-z scan of 3-D image of plexiglass sphere.
Subsurface Imaging

The angular spectrum approach was used to develop the theory of subsurface imaging in acoustic microscopy. It take into account reflection and transmission of the sound beam at the liquid-solid interface. The theory is of importance for understanding acoustical images of the internal microstructure of the non-transparent solids.



SAM image made by OXSAM of a standard epoxy layer on aluminum at 300 MHz: (a) Z = 0; (b) Z = - 20µm. Subsurface image clearly identifies voids at the epoxy/aluminum interface


Publications

  1. P. Zinin and W. Weise, Theory and applications of acoustic microscopy, in T. Kundu ed., Ultrasonic Nondestructive Evaluation: Engineering and Biological Material Characterization, CRC Press, Boca Raton, chapter 11, 654-724 (2003).
  2. P. Zinin, W. Weise, O. Lobkis, S. Boseck.The theory of three dimensional imaging of strong scatterers in scanning acoustic microscopy. Wave Motion. 1997. Vol.25. pp. 212-235.
  3. W. Weise, P. Zinin, T. Wilson, G. A. D. Briggs, S. Boseck. Imaging of spheres with the confocal scanning optical microscope. Optics Lett. 1996. Vol.21(22). pp.1800-1802.
  4. P. Zinin, W. Weise, O. Lobkis, O. Kolosov, S. Boseck. Fourier optics analysis of spherical particles image formation in reflection acoustic microscopy. Optik. 1994. Vol.98(2). pp.45-60.
  5. W. Weise, P. Zinin, S. Boseck. Modeling of inclined and curved surfaces in the reflection scanning acoustic microscope. J. Microsc.. 1994. Vol.176(3). pp.245-253.
  6. W. Weise. Ph.D. Thesis: Konfokale Rastermikroskopie zur Abbildung kugelf rmiger Objekte. 1997. University of Bremen.
  7. O. I. Lobkis, T. Kundu, P. V. Zinin. A theoretical analysis of acoustic microscopy for spherical cavities. Wave Motion. 1995. Vol.21(2). pp.183-201.
  8. O. I. Lobkis, K. I. Maslov, T. Kundu, P. V. Zinin. Spherical inclusion characterization by acoustic microscope: Axisymmetric case. J. Acoust. Soc. Am.. 1996. Vol.99(1). pp.33-45.