3D Deconvolution Microscopy

David S.C. Biggs1

1 KB Imaging Solutions LLC, Waterford, New York
Publication Name:  Current Protocols in Cytometry
Unit Number:  Unit 12.19
DOI:  10.1002/0471142956.cy1219s52
Online Posting Date:  April, 2010
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Abstract

3D deconvolution microscopy is a combination of optical and computational techniques that are used to maximize the observed resolution and signal from a biological specimen. Mathematical models are used to predict the distribution of out‐of‐focus light caused by the inherent optical limitations of the instrument, which can then be compensated for using computer algorithms. This unit will review the theory of image formation and characteristics of the point spread function (PSF) based on the instrument modality and objective lens parameters. A variety of commonly used deblurring and deconvolution methods are described, and their applications to sample datasets are illustrated to show the performance of each algorithm. Steps for setting up the image acquisition to acquire data suitable for deconvolution are described, and the challenge of maximizing signal levels while minimizing light exposure addressed. Deconvolution examples from widefield epi‐fluorescence and laser scanning confocal are shown, and suitability for other modalities discussed. Curr. Protoc. Cytom. 52:12.19.1‐12.19.20. © 2010 by John Wiley & Sons, Inc.

Keywords: deconvolution; deblurring; image restoration; point spread function; fluorescence; widefield; confocal

     
 
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Table of Contents

  • Introduction
  • Image Formation
  • Resolution and Sampling
  • Estimating and Optimizing the PSF
  • Deblurring and Deconvolution Algorithms
  • Blind Deconvolution
  • Example Deconvolution Results
  • Deconvolution Software
  • Basic Protocol 1: Data Acquisition and Deconvolution Analysis
  • Concluding Remarks
  • Literature Cited
  • Figures
  • Tables
     
 
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Materials

Basic Protocol 1: Data Acquisition and Deconvolution Analysis

  Materials
  • Research‐grade widefield optical microscope (upright or inverted)
  • Monochrome CCD camera, sensitive to low light fluorescence, cooled, 6 to 7 µm pixels, 12‐ to16‐bit images, sufficient sensor size to cover the desired field of view
  • Plan apochromat/plan fluorite objective lenses (with correction collar if available)
  • Motorized Z‐stage or piezo‐electric focusing mechanism with nanometer resolution and repeatability
  • Uniform fluorescence slide to check illumination uniformity
  • Stage micrometer to calibrate the pixel spacing from the sample to the camera
  • Light source with stable emission intensity
  • Computer‐controlled excitation shutter
  • Filter sets matched to the excitation and emission of the fluorescence involved
  • Brightfield, phase, or DIC optics for initial specimen observation
  • Acquisition software to control the microscope, Z focusing, camera setup and capture, shutter operation, live preview, automated image capture, and file saving
  • Multi‐spectral sub‐resolution fluorescence beads, to check the lateral and axial alignment between multiple wavelengths, and to identify any unwanted aberrations or nonsymmetries in the PSF
NOTE: By their nature, laser scanning confocal instruments are normally already an integrated hardware and software solution suitable for automated 3D acquisition.
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Figures

  •   FigureFigure 12.19.1 Calculation of widefield PSF frequency limits. (A) Cross‐section of the 3D spherical cap that represents the complex pupil function of the objective lens. The numerical aperture (NA) of the lens is defined by the refractive index ( RI) of the immersion medium, and acceptance half angle (θ). The emission wavelength (λ) then determines the size of the terms r, x, and y as calculated by Equation and Equation . The observed spatial intensity function is the square of the complex amplitude distribution, which corresponds to the auto‐correlation of the spherical cap in the frequency domain. The resulting 3D optical transfer function (OTF) is a 3D toroid with cross‐section shown in (B). The maximum lateral and axial frequencies are shown, which determine the resolution of the lens. (C) Cross‐section of toroid that encompasses the 3D OTF of a widefield microscope.
  •   FigureFigure 12.19.2 Axial cross‐sections of theoretical calculated PSFs for (A) an ideal widefield objective lens (1.4 NA oil at 500nm and no aberrations); (B) same lens with 2 waves of negative spherical aberration (peak intensity reduced by half); and (C) ideal confocal PSF (square of the widefield PSF). Intensity values displayed with a gamma of 3.
  •   FigureFigure 12.19.3 Block diagram of the iterative deconvolution process. The image estimate is blurred with the PSF to form the reblurred image, which is then compared with the observed image. The image differences and any other constraints are used to form a correction update that creates an improved image estimate. The process is repeated for a number of iterations until a suitable result is achieved.
  •   FigureFigure 12.19.4 Block diagram of the iterative blind deconvolution process using alternating update cycles. First, the PSF is fixed and the image is updated, then the image is fixed and the PSF updated. With appropriate starting estimates, constraints, and a priori knowledge, a suitable solution for the image can be found while the PSF is adapted to better fit the data.
  •   FigureFigure 12.19.5 Maximum intensity XY and XZ projections of four channels from a HeLa cell undergoing mitosis with results from a variety of deblurring and deconvolutions algorithms. (A) Original widefield data, (B) Nearest Neighbors at 95% setting, (C) Wiener filtering, (D) Gold's method with 10 iterations (smoothing every 3 iterations), (E) iterative MLE (10 accelerated iterations), and (F) blind iterative MLE (10 accelerated iterations). Each volume is 640 × 640 pixels with 50 nm pixels and 95 Z‐slices spaced 200 nm apart. XZ projections are stretched axially by a factor of 4 to give cubic voxels. Original data is courtesy of Jason Swedlow, University of Dundee.
  •   FigureFigure 12.19.6 XY and XZ maximum intensity projections of neuron sample imaged using a laser scanning confocal microscope. (A) Original dataset, and (B) following 10 iterations of accelerated MLE deconvolution. The axial smearing inherent with confocal imaging is significantly reduced, resulting in improved axial resolution, and a peak signal intensity that has increased by a factor of 8. The lens used is a 63× 1.4 NA oil objective, and the dye is Alexa 488. The displayed volume is 512 × 512 pixels at 100 nm spacing, and 256 optical slices spaced 118 nm apart. Original data courtesy of Alfredo Rodriguez, Department of Neuroscience, Mount Sinai School of Medicine.

Videos

Literature Cited

   Agard, D.A. 1984. Optical sectioning microscopy: Cellular architecture in three dimensions. Annu. Rev. Biophys. Bioeng. 13:191‐219.
   Arnison, M.R. 2004. Phase Control and Measurement in Digital Microscopy. Ph.D. Thesis, University of Sydney, Australia.
   Biggs, D.S.C. 1998. Accelerated Iterative Blind Deconvolution. Ph.D. Thesis, University of Auckland, New Zealand. http://researchspace.auckland.ac.nz/handle/2292/1760.
   Biggs, D.S.C. 2010. A practical guide to deconvolution of fluorescence microscope imagery. Microscopy Today 18, No. 1.
   Born, M. and Wolf, E. 1999. Principles of Optics, 7th edition. Cambridge University Press. Cambridge.
   Cannell, M.B., McMorland, A., and Soeller, C. 2006. Image enhancement by deconvolution. In Handbook of Biological Confocal Microscopy, 3rd ed. (J. Pawley, ed.) pp. 488‐500. Springer, New York.
   Fish, D.A., Brinicombe, A.M., Pike, E.R., and Walker, J.G. 1995. Blind deconvolution by means of the Richardson‐Lucy algorithm. J. Opt. Soc. Am. A 12:58‐65.
   Gold, R. 1964. An Iterative Unfolding Method for Matrices, Tech. Rep. ANL‐6984. Argonne National Laboratory, Argonne, Illinois.
   Gonzalez, R.C. and Woods, R.E. 2007. Digital Image Processing, Prentice Hall, Upper Saddle River, N.J.
   Holmes, T.J., Biggs, D., and Abu‐Tarif, A. 2006. Blind deconvolution. In Handbook of Biological Confocal Microscopy, 3rd ed. (J. Pawley, ed.) pp. 468‐487. Springer, New York.
   Larson, J. 2002. Two‐dimensional and three‐dimensional blind deconvolution of fluorescence confocal images. Proc. SPIE 86:4621.
   Lucy, L.B. 1974. An iterative technique for the rectification of observed distributions. Astron. J. 79:745‐754.
   Richardson, W.H. 1972. Bayesian‐based iterative method of image restoration. J. Opt. Soc. Am. 62:55‐59.
   Sibarita, J.B. 2005. Deconvolution microscopy. Adv. Biochem. Engin./Biotechnol. 95:201‐243.
Key References
   Biggs, D.S.C. 2004. Clearing up deconvolution. Biophotonics Int. February:32‐37.
  For short overview articles on deconvolution and microscopy:
   Wallace, W., Schaefer, L.H., and Swedlow, J.R. 2001. Working person's guide to deconvolution in light microscopy. BioTechniques 31:1076‐1097.
  For a more in‐depth review of deconvolution techniques:
   Sibarita, 2005. See above.
  For a more technical review of deconvolution algorithms:
   Holmes, et al., 2006. See above.
  For a comprehensive reference book on biological confocal (and widefield) microscopy:
   Sarder, P. and Nehorai, A. 2006. Deconvolution methods for 3D fluorescence microscopy images: An overview. IEEE Signal Proc. Mag. 23:32‐45.
   Pawley, J.B. (ed.) 2006. Handbook of Biological Confocal Microscopy, 3rd ed. Springer, New York.
Internet Resources
   http://micro.magnet.fsu.edu/
  An easily accessible reference to microscopy principles, usage and applications can be found at the Molecular Expressions Web site.
   http://micro.magnet.fsu.edu/primer/digitalimaging/deconvolution/deconvolutionhome.html
  Deconvolution section at Molecular Expressions.
   http://www.3ddeconvolution.com/
  A tutorial Web site for 3D deconvolution that extends the work presented in this unit, and includes more example results.
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