1. Theoretical Background Challenges and Significance
Three-dimensional Model for DIC Images Heidy Sierra, Charles A. DiMarzio and Dana Brooks Department of Electrical and Computer Engineering, The Center for Subsurface Sensing and Imaging Systems (CenSSIS), Northeastern University, Boston, MA
XZ image
Binary phase object
Abstract
Theoretical Background z x
Differential Interference Contrast (DIC) is a form of interference microscopy that uses polarizers and prisms to create an image with a shadow relief, this relief reflects the gradient of the optical path difference.
Differential Interference Contrast (DIC) microscopy is a useful
tool used to visualize and study live biological cells. However object characteristics and qualitative observations can limit quantitative analysis. There is a three-dimensional model for DIC images based in the Born approximation. This model relies on three-dimensional convolution. The model has some limitations when thick objects are imaged. This work develops a theoretical model which consists of the product of two-dimensional convolution along the optical axis instead of three-dimensional convolution. Experiments using simulated data with this model show results similar to real images.
xy image
Two dimensional DIC point spread function, [1]:
R is the amplitude ratio between the two waves
k(x,y) is the transmitted light under coherent illumination.
is the shear and the bias retardation and z is the depth.
Product of 2-D convolutions model for three dimensional images model:
Z=30
xy image at plane
z= 30
xy image
Glass bead images
Extension of the imaging model to 3-D
XZ image
State of the Art dz
PSF describing the system
z axis
Object
DIC optics description can be found in the literature [1, 2]. However the list of references involving mathematical theory work is short. The most recent work is presented [3]. Two-dimensional models in the frequency domain for coherent illumination has been extended to partially coherent illumination and the optical system is based on the theory of image formation in partially coherent light for transmitted light optics described by Born and Wolf. Similarly the complex amplitude of the illumination wave field is propagated under Kohler illumination through a thin specimen and the optical system. Our model show a good behavior in synthetic data simulating r thick objects.
dz=0.5
dx=0.5
dx=0.5
References
C. Preza, D. L. Snyder, J.-A.Conchello. “Theoretical development and experimental evaluation of imaging models fordifferential-interferencecontrastmicroscopy”, JOSA A, Vo. 16, No. 9, (1999).
Kagalwa,Farhan;Kanade, Takeo,” Reconstructing Specimens Using DIC Microscope Images”, IEEE Trans. On Signal Processing, vol. 33, No. 5, October 2003.
S. F. Gibson and F. Lanni. “Diffraction by a Circular Aperture as a Model for Three-dimensional Optical Microscopy”. J. Opt. Soc. Am. A, 6 (9): , September 1989.
[1].
[2].
[3].
References
Challenges and Significance
Simulations
This work involves the developing of a three-dimensional model which considers imaging transparent objects and specimens with constant phase gradient. This looks like a simple model which can be implemented, but is still a good representation of the image and can be useful to apply inversion techniques and extended to others system like Optical Quadrature Microscopy.
Simulation were done with synthetic data, for binary phase objects
considering plane with constant phase. Also simulation were done with glass bead. Images show agreement with real data.
Optical Science
Laboratory
Acknowledgement: This work was supported in part by CenSSIS, the Center for Subsurface Sensing and Imaging Systems, under the Engineering Research Centers Program of the National Science Foundation (Award Number EEC ).