Attenuation Correction in Confocal Microscopes: A Novel TwoView Approach

1
Attenuation Correction in Confocal Microscopes A
Novel Two-View Approach
Ali Can1, Omar Al-Kofahi1, Sharie Lasek2, Donald
H. Szarowski2, James N. Turner2 and Badrinath
Roysam1 1 Rensselaer Polytechnic Institute, 110,
8th Street, Troy, New York 12180 -3590 2
Wadsworth Center, NY State Department of Health,
Albany, New York 12201 -0509
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)
Solution
Deeper Slices

• Abstract
• Single multi-photon Confocal Microscopy is
  widely used for 3-D biological imaging.
• Particularly valuable for thick sections of
  intact tissue.
• Signal attenuates with depth
• Need to improve the imaging depth quantitative
  accuracy
• Previous methods work by amplifying the signal
  from deeper parts of the specimen.
• Amplification of noise is an unavoidable
  artifact.
• We describe a novel method that not only corrects
  confocal stacks for attenuation without noise
  amplification, but also enhances the achievable
  imaging depth.
• It relies on a synergistic combination of
  specimen preparation, image analysis, and image
  reconstruction algorithms.

Similar Attenuation values
In general

• Symmetrical Specimen Preparation using two cover
  slips film
• Use two views provide more data
• Need to reconstruct image intensity from the two
  views

If the noise processes in the two views are
independent and identically distributed (IID)
with variance ?2, then the noise in the
reconstructed image has variance
Background Depth-Dependent Attenuation
Exponential attenuation law (Weast, 1974)
Photobleaching When a fluorophore is subjected to
high-intensity light, it can lose the ability to
fluoresce
We get a real improvement in SNR!!

• Summery Whats New?
• Our method not only corrects for the attenuation
  in the incident light and the fluorescence
  signal, but also extends the total thickness of a
  sample that can
• be imaged.
• Our method improves on the SNR compared to the
  single images.
• The proposed method can be easily implemented on
  a conventional confocal microscope without
  modifying the instrument. With slight
  modifications only in the specimen preparation.

Deeper structures are attenuated

• Current State of the Art Single View correction
• Statistical Methods
• Assume that the fluorophore is distributed
  uniformly
• Estimate the distribution of the intensity as a
  function of depth by forming histograms and
  fitting curves
• Applicability is limited to specimens with nearly
  homogeneous fluorochrome distribution, especially
  as a function of depth
• Ignores the geometry of the specimen
• Lack of net improvement in signal-to-noise ratio
  (SNR)
• Computationally attractive
• Takes photobleaching into account
• Geometric Methods
• Assume the image intensity is a function of
  fluorochrome density, and iteratively correct the
  layers.
• The light bundle is assumed to travel as a
  spherical wave that converges to the focal point
  and forms a cone structure.
• The attenuation of excitation and florescence
  light is computed by integrating all light paths
  within this conical volume
• Very accurate. Represent the underlying optical
  phenomena
• High computational complexity, (scales with the
  fourth power of image depth, i.e., O(Nz4), Nz ,is
  the depth of the image)
• Simultaneous emission detection Mainen et. al,
  (1999)
• Collect transfluorescence and epifluorescence
  emission simultaneously.
• Correspondences problem is solved, no
  registration needed

• Noise Model
• Assume independent additive noise
• Simplistic, yet adequate for a start

• Mathematical Model
• Excitation
• The objective lens of the system converts the
  monochromatic plane wave into a converging
  spherical wave, bounded by the semi-aperture
  angle ,? with radius R Total excitation intensity
  at x

Applying the correction coefficients,

• Excitation light is absorbed by the fluorochrome,
  and fluorescence is emitted proportional to the
  fluorochrome density The emitted fluorescence
  light intensity is

Reconstructed View The original intensity values
in both views are considered to be the same,

• Emission
• The emitted light travels back along the same
  path as the incoming radiation and the detected
  light is

The original intensity is estimated such that the
square of the normalized error is minimized, i.e.,