Hostname: page-component-78c5997874-t5tsf Total loading time: 0 Render date: 2024-11-17T17:54:21.021Z Has data issue: false hasContentIssue false
  • English
  • Français

Low-Dosage Maximum-A-Posteriori Focusing and Stigmation

Published online by Cambridge University Press:  04 February 2013

Jonas Binding ,
Shawn Mikula  and
Winfried Denk
Jonas Binding
Affiliation:
Max Planck Institute for Medical Research, Jahnstr. 29, 69120 Heidelberg, Germany
Shawn Mikula
Affiliation:
Max Planck Institute for Medical Research, Jahnstr. 29, 69120 Heidelberg, Germany
Winfried Denk*
Affiliation:
Max Planck Institute for Medical Research, Jahnstr. 29, 69120 Heidelberg, Germany
*
*Corresponding author. E-mail: [email protected]
Get access

Abstract

Radiation damage is often an issue during high-resolution imaging, making low-dose focusing and stigmation essential, in particular when no part of the sample can be “sacrificed” for this. An example is serial block-face electron microscopy, where the imaging resolution must be kept optimal during automated acquisition that can last months. Here, we present an algorithm, which we call “Maximum-A-Posteriori Focusing and Stigmation (MAPFoSt),” that was designed to make optimal use of the available signal. We show that MAPFoSt outperforms the built-in focusing algorithm of a commercial scanning electron microscope even at a tenfold reduced total dose. MAPFoSt estimates multiple aberration modes (focus and the two astigmatism coefficients) using just two test images taken at different focus settings. Using an incident electron dose density of 2,500 electrons/pixel and a signal-to-noise ratio of about one, all three coefficients could be estimated to within <7% of the depth of focus, using 19 detected secondary electrons per pixel. A generalization to higher-order aberrations and to other forms of imaging in both two and three dimensions appears possible.

Keywords

autofocuswavefront measurementscanning electron microscopy (SEM)phase diversity
Type
Software, Techniques and Equipment Development
Information
Microscopy and Microanalysis , Volume 19 , Issue 1 , February 2013 , pp. 38 - 55
Copyright
Copyright © Microscopy Society of America 2013

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Baba, N., Terayama, K., Yoshimizu, T., Ichise, N. & Tanaka, N. (2001). An auto-tuning method for focusing and astigmatism correction in HAADF-STEM, based on the image contrast transfer function. J Electron Microsc (Tokyo) 50(3), 163–176.CrossRefGoogle ScholarPubMed
Blackman, R.B. & Tukey, J.W. (1959). The Measurement of Power Spectra: From the Point of View of Communications Engineering. Mineola, NY: Dover Publications.Google Scholar
Blanc, A., Fusco, T., Hartung, M., Mugnier, L. & Rousset, G. (2003). Calibration of NAOS and CONICA static aberrations. Astron Astrophys 399(1), 373–383.CrossRefGoogle Scholar
Booth, M.J., Débarre, D. & Wilson, T. (2007). Image-based wavefront sensorless adaptive optics. In Proc SPIE 6711, Advanced Wavefront Control: Methods, Devices, and Applications V, Carreras, R.A., Gonglewski, J.D. & Rhoadarmer, T.A. (Eds.), pp. 671102–671107. Available at http://dx.doi.org/10.1117/12.733635.CrossRefGoogle Scholar
Briggman, K.L., Helmstaedter, M. & Denk, W. (2011). Wiring specificity in the direction-selectivity circuit of the retina. Nature 471(7337), 183–188.CrossRefGoogle ScholarPubMed
Dean, B.H. & Bowers, C.W. (2003). Diversity selection for phase-diverse phase retrieval. J Opt Soc Am A 20(8), 1490–1504.CrossRefGoogle ScholarPubMed
Débarre, D., Booth, M.J. & Wilson, T. (2007). Image based adaptive optics through optimisation of low spatial frequencies. Opt Express 15(13), 8176–8190.CrossRefGoogle ScholarPubMed
Débarre, D., Botcherby, E.J., Booth, M.J. & Wilson, T. (2008). Adaptive optics for structured illumination microscopy. Opt Express 16(13), 9290–9305.CrossRefGoogle ScholarPubMed
Débarre, D., Botcherby, E.J., Watanabe, T., Srinivas, S., Booth, M.J. & Wilson, T. (2009). Image-based adaptive optics for two-photon microscopy. Opt Lett 34(16), 2495–2497.CrossRefGoogle ScholarPubMed
Denk, W. & Horstmann, H. (2004). Serial block-face scanning electron microscopy to reconstruct three-dimensional tissue nanostructure. Plos Biol 2(11), 1900–1909.CrossRefGoogle ScholarPubMed
Dolne, J. (2011). Cramer-Rao lower bound for passive and active imaging systems. In Imaging Systems and Applications Conference, Toronto, Canada, July 10, 2011, p. IWB4. Washington, DC: Optical Society of America. Google Scholar
Dolne, J.J., Tansey, R.J., Black, K.A., Deville, J.H., Cunningham, P.R., Widen, K.C. & Idell, P.S. (2003). Practical issues in wave-front sensing by use of phase diversity. Appl Opt 42(26), 5284–5289.CrossRefGoogle ScholarPubMed
Gonsalves, R.A. (1982). Phase retrieval and diversity in adaptive optics. Opt Eng 21, 829–832.CrossRefGoogle Scholar
Guizar, M. (2008). dftregistration.m—Efficient subpixel image registration by cross-correlation. In Matlab Central—File Exchange on mathworks.com. Natick, MA: MathWorks.Google Scholar
Guizar-Sicairos, M., Thurman, S.T. & Fienup, J.R. (2008). Efficient subpixel image registration algorithms. Opt Lett 33(2), 156–158.CrossRefGoogle ScholarPubMed
Hanser, B.M., Gustafsson, M.G.L., Agard, D.A. & Sedat, J.W. (2003). Phase retrieval for high-numerical-aperture optical systems. Opt Lett 28(10), 801–803.CrossRefGoogle ScholarPubMed
Lee, D.J., Roggemann, M.C. & Welsh, B.M. (1999). Cramér-Rao analysis of phase-diverse wave-front sensing. J Opt Soc Am A 16(5), 1005–1015.CrossRefGoogle Scholar
Löfdahl, M.G. & Scharmer, G. (1994). Wavefront sensing and image restoration from focused and defocused solar images. Astron Astrophys Suppl 107, 243–264.Google Scholar
MacKay, D.J.C. (2006). Decision theory. In Information Theory, Inference, and Learning Algorithms, pp. 451–453. Cambridge, UK: Cambridge University Press.Google Scholar
Meynadier, L., Michau, V., Velluet, M.-T., Conan, J.-M., Mugnier, L.M. & Rousset, G. (1999). Noise propagation in wave-front sensing with phase diversity. Appl Opt 38(23), 4967–4979.CrossRefGoogle ScholarPubMed
Mikula, S., Binding, J. & Denk, W. (2012). Staining and embedding the whole mouse brain for electron microscopy. Nature Methods 9, 1198–1201.CrossRefGoogle ScholarPubMed
Neil, M.A., Booth, M.J. & Wilson, T. (2000). New modal wave-front sensor: A theoretical analysis. J Opt Soc Am A Opt Image Sci Vis 17(6), 1098–1107.CrossRefGoogle ScholarPubMed
Nicolls, F.C., de Jager, G. & Sewell, B.T. (1997). Use of a general imaging model to achieve predictive autofocus in the scanning electron microscope. Ultramicroscopy 69(1), 25–37.CrossRefGoogle Scholar
Ogasawara, M., Fukudome, Y., Hattori, K., Tamamushi, S., Koikari, S. & Onoguchi, K. (1998). Automatic focusing and astigmatism correction method based on Fourier transform of scanning electron microscope images. Jpn J Appl Phys 38, 957.CrossRefGoogle Scholar
Ong, K.H., Phang, J.C.H. & Thong, J.T.L. (1998). A robust focusing and astigmatism correction method for the scanning electron microscope—Part III: An improved technique. Scanning 20(5), 357–368.CrossRefGoogle Scholar
Paxman, R.G., Schulz, T.J. & Fienup, J.R. (1992). Joint estimation of object and aberrations by using phase diversity. J Opt Soc Am A 9(7), 1072–1085.CrossRefGoogle Scholar
Pommier, J. (2008). Simple SSE and SSE2 optimized sin, cos, log and exp. pp. C source code. Available at http://gruntthepeon.free.fr/ssemath/.Google Scholar
Rasmussen, C.E. (2006). Matlab function minimize.m. Natwick, MA: MathWorks. Google Scholar
Rudnaya, M., ter Morsche, H., Maubach, J. & Mattheij, R. (2011). A derivative-based fast autofocus method in electron microscopy. J Math Imaging Vision 44(1), 38–51.CrossRefGoogle Scholar
Sauvage, J.-F., Fusco, T., Rousset, G. & Petit, C. (2007). Calibration and precompensation of noncommon path aberrations for extreme adaptive optics. J Opt Soc Am A 24(8), 2334–2346.CrossRefGoogle ScholarPubMed
Scharmer, G., Balasubramaniam, K.S. & Radick, R.R. (1999). Object-Independent fast phase-diversity. In High Resolution Solar Physics: Theory, Observations, and Techniques, Rimmele, T.R. (Ed.), vol. 183, pp. 330–341, Astronomical Society of the Pacific.Google Scholar
Tyson, R.K. (1997). Principles of Adaptive Optics. Boston, MA: Academic Press.Google Scholar
Supplementary material: PDF

Binding Supplementary Material

Figures S1-S3

Download Binding Supplementary Material(PDF)
PDF 320.8 KB