Resolution Target


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Definition:         Disk source through three equal slits.

Calculate Resolution Target Profile on Film:              top







w (slit width)  
D (source diameter)  
  Mph (pinhole magnification)    
  dx (x increment for table)    
  |x|max (x limit for table)    

Distance units for table:

  <--  Push to plot profile on film.
  <--  Push this button to fill table.

Output Format:                                                        top

Select Format: Scientific Engineering Fixed

Notes:                                                                       top

bulletDefinitions of contrast and diagram below from "The Physics of Medical X-Ray Imaging", 2nd Ed Author: Bruce H. Hasegawa, Ph.D..   Note also that the sign of the contrast is usually ignored.

bulletIn this case, F is proportional to f(x), so that F1 corresponds to f(0) and F2 to f(w*(1+Mph)), assuming that the slits are resolved. 
bulletThe image contrast cannot be determined without knowing the proportionality constant between F and OD of the film.
bulletIt can be shown that the three equal max. values on film occur at x=0, 2w*(1+Mph) and the two equal min. values at x=w*(1+Mph), assuming the slits are resolved.
bulletIf the slits are not resolved the film profile will appear as two peaks (or even one) instead of the expected three.
bulletThe slit pitch equals 1/(2*w) and is usually expressed in line-pairs per millimeter. 
bulletThe radiographic magnification equals 1+m.
bulletSince the source is a disk, the line spread function is a circular:  l(x)=sqrt(r^2-x^2) for |x|<r and 0 otherwise and r=D/2.
bulletThe edge spread function is the integral of the line spread function:  e(x)=x*sqrt(r^2-x^2)+r^2*arcsin(x/r)+r^2*pi/2.
bulletThe resultant on the film plane is f(x)=e((w/2)*(1+m)-x) -e((-w/2)*(1+m)-x) +e((3w/2)*(1+m)-x) -e((5w/2)*(1+m)-x) +e((-3w/2)*(1+m)-x) -e((-5w/2)*(1+m)-x).

Copyright 2006  Raymond J. Allen