Three-dimensional Model for DIC Images Heidy Sierra, Charles

Three-dimensional Model for DIC Images Heidy Sierra, Charles

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

Theoretical Background

Abstract
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.

State of the Art
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.

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.
Two dimensional DIC point spread function, [1]:
h(x, y) (1 R)exp( j )k(x x, y) Rexp( j )k(x x, y)

z

xy image

x

Z=30

R is the amplitude ratio between the two waves
k(x,y) is the transmitted light under coherent

illumination.

x
the imaging
Extension
is the shearofand
the bias retardation and z is the depth.
model to 3-D
Product of 2-D convolutions model for three dimensional images
model:

xy image

xy image at plane
z= 30

Glass bead images

XZ image

PSF describing the system

zo

dx=0.5

z axis

dz

dz=0.5m

m

References
References

zk

dx=0.5

m

zf

Object

f

U i ( x , y , z k )

f ( x , y , t ) h( x

[1]
.

r , y s, z k t )dr ds

t 0 s r

Challenges
Challenges and
and Significance
Significance
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.

XZ image

Binary phase object

[2]
.

Simulations
Simulations
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.

C. Preza, D. L. Snyder, J.-A.Conchello. Theoretical development and
experimental
evaluation
of
imaging
models
fordifferentialinterferencecontrastmicroscopy, JOSA A, Vo. 16, No. 9, 2185-2199
(1999).
Kagalwa,Farhan;Kanade, Takeo,
Reconstructing Specimens Using DIC
References
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):1357-1367, September 1989.

[3]
.

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 9986821).

Optical Science
Laboratory

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