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Manuscript Title: FREINT: an integration routine calculating Fresnel diffraction.
Authors: W.J. Gruschel
Program title: FREINT
Catalogue identifier: ACUB_v1_0
Distribution format: gz
Journal reference: Comput. Phys. Commun. 16(1979)175
Programming language: Fortran.
Computer: HONEYWELL BULL 66/60.
Operating system: GCOS.
RAM: 15K words
Word size: 36
Keywords: Optics, Electron microscopy, Fresnel diffraction, Integral transforms.
Classification: 18.

Revision history:
Type Tit le Reference
correction 000ACORRECTION 27/11/78 See below

Nature of problem:
FREINT evaluates the integral A(x) exp(i q (x'-x)**2) dx [i= (-1)**1/2, x = xi,xf] occurring in optical transfer theory. By application of this integral the wave amplitude A(t+d;x') at a plane z = t+d can be calculated on some premises from the amplitude field A(t;x), e.g. in electron microscopy if an object is imaged in a defocussed mode (catchword : Fresnel diffraction). A(x) is given by a complex vector.

Solution method:
FREINT performs quadratic interpolation of the function A(x) given by N data points (xk, Ak) (Ak complex) in any double interval (xk, xk+2), if h1 = xk+1-xk equals hu = xk+2-xk+1. If not, linear interpolation is chosen. From the interpolatory coefficients the sub-integral values are calculated according to analytical rules and are added up to the final integral value.

Restrictions:
The integral transformation will be performed for any complex vector, the dimension N of which is greater than or equal to 2 and is limited at the upper end only by limitations of storage. The parameter q must not equal zero.

Running time:
The execution times depend on N. On the Honeywell Bull 66/60 a vector of length 37 takes approximately 0.05 s, if the abscissae points are equally spaced.

CORRECTION SUMMARY
Manuscript Title: Unpublished correction to FREINT: an integration routine calculating Fresnel diffraction.
Authors: W.J. Gruschel
Program title: 000ACORRECTION 27/11/78
Catalogue identifier: ACUB_v1_0
Distribution format: gz
Classification: 18.