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NOTE: you need to disable pop-up blocking of this site to run the CTF simulation Java applet
Publication: Web-based
Simulation for Contrast Transfer Function and Envelope Functions. Microscopy and Microanalysis 7(4), 329-334, 2001
Contrast
of an ectron image is influenced by the contrast transfer function (CTF)
and the envelope functions of the electron microscope. In order to plan
an experimental condition for data collection or to interpret the contrast
of an electron micrograph, one would often need to know the quantitative
values of these functions for a given set of microscope parameters. This
simulation program is written in Java
applet and JavaScript
programming language. The parameters of these functions can be adjusted
interactively with slider bars and the plot for the simulated function
would be updated instantaneously.
This applet is known to run on Windows (Netscape and Internet Explorer), Linux (i386) (Netscape), SGI IRIX (Netscape), OS/2 Warp and MacOS X. Please inform me if you found that
this applet runs or has problems to run on other platforms.
The
following is the detailed descriptions for some aspects of the applet page.
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, positive 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
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This ctf simulation applet is written by Wen Jiang with help of the excellent Java Components for Mathematics.
| Please mail comments/suggestions to: WEBMASTER |
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