CTF Simulation

Select microscope:       Select function: 

Xmin=   Xmax=   Number of Points=


 Hide Info Hide the crosshair mark on the curve and the s, f(s) prompt
 Show Info Show the crosshair mark on the curve and the s, f(s) prompt

List of the special symbols/functions used in the applet

 Term  Unit  Description
 s  1/Å  resolution
 v  keV  accelerating voltage
 Cs  mm  spherical aberration
 Cc  mm  chromatic abbe ration
 Q  amplitude contrast [0-1]
 dE  eV  time variation of electron beam energy from the average
 dI  ppm  time variation of object lens current from the average
 dF  Å  vertical sinusoidal motion amplitude
 dR  Å  horizontal drift amplitude
 dZ  Å  defocus, negative for under-focus
 B  Å2  envelope decay parameter, exp(-B*s^2)
 a  mrad  illumination angle
 lambda(v)  Å  electron wavelength, automatically computed from voltage
 gamma(s,v,Cs,dZ)  -2*pi*(2.5e6*Cs*lambda(v)^3*s^4+dZ*lambda(v)*s^2/2)
 ctf(s,v,Cs,dZ,Q)  -(sqrt(1-Q*Q)*sin(gamma(s,v,Cs,dZ))+Q*cos(gamma(s,v,Cs,dZ)))
 Gsc(s,v,Cs,dZ,a)  spatial coherence decay: exp(-(pi*a*(1.0e7*Cs*lambda(v)^2*s^3-dZ*s))^2/1e6)
 Gtc(s,v,Cc,dE)  temporal energy spread decay: exp(-1.0e8*(pi*Cc*lambda(v)*s^2*dE/v)^2/(16*ln(2)))
 Gol(s,v,Cc,dE)  temporal lens current spread decay: exp(-1.0e2*(pi*Cc*lambda(v)*s^2*dI)^2/(4*ln(2)))
 Glm(s,v,dF)  vertical motion decay: j0(pi*dF*lambda(v)*s*s)
 Gtm(s,dR)  horizontal drift decay: sinc(pi*s*dR)
 sinc(s)  sinc function: sin(s)/s
 j0(s)  Bessel function of the first kind, order 0: (57568490574.0+s*s*(-13362590354.0+s*s*(651619640.7+s*s*(-11214424.18+s*s*(77392.33017+s*s*(-184.9052456)))))) /(57568490411.0+s*s*(1029532 985.0+s*s*(9494680.718+s*s*(59272.64853+s*s*(267.8532712+s*s*1.0)))))

In addition to the symbols mentioned above, almost all the common function, operators, constants could be used in the function definition if you choose to plot you own function

sin
cos
tan
cot
sec
csc
arcsin
arccos
arctan
abs
sqrt
cubert
exp
ln
log2
log10
trunc
round
floor
ceiling
+
-
*
/
^
**
!
?:
<
<=
=
>
>=
<>
and
or
 not
sum(sumationVariable, start, end, expression)
pi
e

This ctf simulation applet is written by Wen Jiang with help of the excellent Java Components for Mathematics.