Computer Physics Communications Program Library

Programs in Physics & Physical Chemistry



Manuscript Title: Alignment of Fiducial Marks in a Tomographic Tilt Series with an Unknown Rotation Axis
Authors: Zachary H. Levine, Alex Volkovitsky, Howard K. Hung
Program title: particleTilt
Catalogue identifier: ADYW_v1_0 Distribution format: tar.gz
Journal reference: Comput. Phys. Commun. 176(2007)694
Programming language: Fortran 90.
Computer: IBM[1] compatible desktop PC; SGI[1] Octane.
Operating system: Red Hat[1] WS 3 Linux (with 2.4.21-40.EL kernel); IRIX 6.5 IP30.
Word size: 32 bits
Keywords: tomography, alignment, tilt axis, non-orthogonal tilt axis.
PACS: 68.37.Lp, 06.90+v.
Classification: 4.9.
Nature of problem: The program is used to assist the alignment step in tomography. The samples should be prepared with spherical particles (typically gold beads) which are observed in several views. (Not every particle need be observed in every view.) The program reports coordinates of a 3D model of the particles as well as the direction of the tilt axis as a point on the unit sphere.
Solution method: Our package minimizes an objective function whose free variables are a set of 3D model points and 2D shifts of the views as well as two parameters characterizing of tilt axis as a point on the unit sphere. The objective function is decomposed into a pure quadratic form which encompasses the model points and shifts, and a more complicated form which has only two degrees of freedom. The Broyden-Fletcher-Goldfarb-Shanno algorithm is applied alternately and iteratively to minimize the objective function with respect to the two sets.
Running time: 350 ms (larger included example, on 2.8 GHz 32-bit PC)
References:
[1]	Commercial organizations identified in this paper are for the purpose of identification only and are not endorsed by NIST. The associated equipment or software identified is not necessarily the best available for the purpose.