Resolution Target Applet ## Definition:         Disk source through three equal slits. ## Calculate Resolution Target Profile on Film:              top

### Units

#### Inputs:

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

• Definitions 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.

• • In this case, Φ is proportional to f(x), so that Φ1 corresponds to f(0) and Φ2 to f(w*(1+Mph)), assuming that the slits are resolved.

• The image contrast cannot be determined without knowing the proportionality constant between Φ and OD of the film.

• It 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.

• If the slits are not resolved the film profile will appear as two peaks (or even one) instead of the expected three.

• The slit pitch equals 1/(2*w) and is usually expressed in line-pairs per millimeter.

• The radiographic magnification equals 1+m.

• Since 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.

• The 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.

• The 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).