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I am a TA in a structural chemistry class. The professor want me to show students how Watson and Crick determined the structure of DNA from X-ray diffraction results of DNA crystals. The professor suggested me to print some sine functions in a paper and let visible laser beam from a laser pointer to go through the sin functions to get an "X" shape diffraction pattern, just like the X-ray diffraction pattern of DNA.

I just wonder is it possible?

I think the X-ray diffraction of DNA is similar to grating diffraction. And the grating constant should be in the order of microns to be able to significantly diffract visible light. Is my professor kidding me? Or is there any possible ways for me to simulate diffraction with a paper and a laser pointer in a classroom?

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With one change this should work.

For a transmission experiment you'd probably be better printing on a transparency. I haven't tried this, mind you, but laser printers can achieve the necessary scale quite easily.

You might be able to get it to work in reflection mode printed to paper, but you are going to lose a lot of intensity. Didn't work with the tools I have on hand (albeit I'm on vacation). That said I you can print fine enough lines with a fairly inexpensive printer.

I made it work!

(Well, at least the simple linear grating; more complex patterns will have to wait for more time to devote to the project.)

Once I got back to school and then found some time one day when my freshman lab wrapped up early, I was finally able to devote a little more time to this. I reworked the latex file (below) to give me several different line thickness and pitches.

My experimental setup used approximately 8 meters from grating to projection surface: enter image description here

You can see our higher harmonic green He-Ne laser (543 nm wavelength) in the foreground and the transparency hanging loosely just beyond. In the background the pattern appears dimly on the front face of the instructors lab-bench.

Closeup of the diffraction pattern with the lights off enter image description here

the sharp cutoffs at the top and bottom of the image result from features of the ad hoc setup I'm using here.

So What spacing do you want?

At my school we have a demonstration grating consisting of crossed planes of fine copper wire at about 40 wires per cm (actually 100 wires per inch) that can be used in transmission or reflection to form planar diffraction patterns.

For basic testing purposes it may be easier to start with a simple linear grating, or a crossed-lines one.

The results of my trial runs seem to be pretty sensitive to line pitch and spacing (and I assume to aliasing effects), so some trial and error is probably in order.


The LaTeX code I used to prepare my text sample

\documentclass[letterpaper,10pt]{article}

\usepackage{pgfplots}
\pgfplotsset{compat=1.11,ticks=none}

\usepackage{ifpdf}
\ifpdf
\setlength{\pdfpagewidth}{8.5in}
\setlength{\pdfpageheight}{11in}
\else
\fi

% 
% Recall that the zero point in 1in down, and 1in in from the
% left.
% \setlength{\topmargin}{0.625in}
% \setlength{\textheight}{8.0in}
% \setlength{\oddsidemargin}{0.25in}
% \setlength{\textwidth}{6.0in}
\addtolength{\oddsidemargin}{-0.75in}
\addtolength{\textwidth}{0.5in}


\begin{document}
\vfill

\hbox{
  \begin{tikzpicture}
    \begin{axis}[
      title={HORZ (thick=0.03pt pitch 1/25cm)},
      xtick=,
      xticklabels={,,}
      ytick=,
      yticklabels={,,},
      x=0.25cm,
      y=0.25cm,
      ]
      \foreach \yval in {1,...,124}
      \addplot[black,domain=0:5.0,line width=0.03pt] {\yval/25}; 

    \end{axis}
  \end{tikzpicture}
  \hfill

  \begin{tikzpicture}
    \begin{axis}[
      title={HORZ (thick=0.06pt pitch 1/25cm)},
      xtick=,
      xticklabels={,,}
      ytick=,
      yticklabels={,,},
      x=0.25cm,
      y=0.25cm,
      ]
      \foreach \yval in {1,...,124}
      \addplot[black,domain=0:5.0,line width=0.06pt] {\yval/25}; 

    \end{axis}
  \end{tikzpicture}
  \hfill

  \begin{tikzpicture}
    \begin{axis}[
      title={HORZ (thick=0.09pt pitch 1/25cm)},
      xtick=,
      xticklabels={,,}
      ytick=,
      yticklabels={,,},
      x=0.25cm,
      y=0.25cm,
      ]
      \foreach \yval in {1,...,124}
      \addplot[black,domain=0:5.0,line width=0.06pt] {\yval/25}; 

    \end{axis}
  \end{tikzpicture}
}
\vfill

\hbox{
  \begin{tikzpicture}
    \begin{axis}[
      title={HORZ (thick=0.03pt pitch 1/33cm)},
      xtick=,
      xticklabels={,,}
      ytick=,
      yticklabels={,,},
      x=0.25cm,
      y=0.25cm,
      ]
      \foreach \yval in {1,...,165}
      \addplot[black,domain=0:5.0,line width=0.03pt] {\yval/33}; 

    \end{axis}
  \end{tikzpicture}
  \hfill

  \begin{tikzpicture}
    \begin{axis}[
      title={HORZ (thick=0.06pt pitch 1/33cm)},
      xtick=,
      xticklabels={,,}
      ytick=,
      yticklabels={,,},
      x=0.25cm,
      y=0.25cm,
      ]
      \foreach \yval in {1,...,165}
      \addplot[black,domain=0:5.0,line width=0.06pt] {\yval/33}; 

    \end{axis}
  \end{tikzpicture}
  \hfill

  \begin{tikzpicture}
    \begin{axis}[
      title={HORZ (thick=0.09pt pitch 1/33cm)},
      xtick=,
      xticklabels={,,}
      ytick=,
      yticklabels={,,},
      x=0.25cm,
      y=0.25cm,
      ]
      \foreach \yval in {1,...,165}
      \addplot[black,domain=0:5.0,line width=0.06pt] {\yval/33}; 

    \end{axis}
  \end{tikzpicture}
}
\vfill

\hbox{
  \begin{tikzpicture}
    \begin{axis}[
      title={HORZ (thick=0.03pt pitch 1/50cm)},
      xtick=,
      xticklabels={,,}
      ytick=,
      yticklabels={,,},
      x=0.25cm,
      y=0.25cm,
      ]
      \foreach \yval in {1,...,249}
      \addplot[black,domain=0:5.0,line width=0.03pt] {\yval/50}; 

    \end{axis}
  \end{tikzpicture}
  \hfill

  \begin{tikzpicture}
    \begin{axis}[
      title={HORZ (thick=0.06pt pitch 1/50cm)},
      xtick=,
      xticklabels={,,}
      ytick=,
      yticklabels={,,},
      x=0.25cm,
      y=0.25cm,
      ]
      \foreach \yval in {1,...,249}
      \addplot[black,domain=0:5.0,line width=0.06pt] {\yval/50}; 

    \end{axis}
  \end{tikzpicture}
  \hfill

  \begin{tikzpicture}
    \begin{axis}[
      title={HORZ (thick=0.09pt pitch 1/50cm)},
      xtick=,
      xticklabels={,,}
      ytick=,
      yticklabels={,,},
      x=0.25cm,
      y=0.25cm,
      ]
      \foreach \yval in {1,...,249}
      \addplot[black,domain=0:5.0,line width=0.06pt] {\yval/50}; 

    \end{axis}
  \end{tikzpicture}
}
\vfill 

\end{document}
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  • $\begingroup$ Perhaps I'll try the reflection idea later today. All I need is to decide how to print the lines I need. $\endgroup$ – dmckee Dec 27 '14 at 19:26
  • $\begingroup$ Wow, this is news to me. So there are enough dpi to print out an optical diffraction grating? $\endgroup$ – Rob Jeffries Dec 27 '14 at 19:39
  • $\begingroup$ Well, the angles you get are pretty small (order of $10^{-3}$ to $10^{-2}\,\mathrm{rad}$ for the first maximum), but if you can project across a decent distance the dot separate. $\endgroup$ – dmckee Dec 27 '14 at 19:47
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Reflection diffraction gratings can be made very easily from compact discs (CDs).

You get a diffraction pattern simply by reflecting a laser pointer from a CD. If you know the wavelength of the pointer you could work out the groove spacing. Someone has kindly provided a lab script for that very experiment. Or see this one.

CD diffraction

If you want to do more than demonstrate diffraction patterns and build a spectrograph using a CD grating and a cereal box - here are the plans. These work a charm and can be used to look at arc lamps, fluorescent lights etc.

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I'm not sure a 2d structure will give you the required phase information unless you can compute that before printing, in which case you are making a hologram. What about some 3d structure that is on the same scale? I don't know what the finest incandescent bulb filament is you can acquire, but something like that should work. Also, traditional crystallography requires repeating arrays to improve resolution.

Here is an example of what can be done with a stretched filament and an ordinary laser:

enter image description here

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For what it's worth, you might want to look up the original paper on the theory of helical diffraction: "The structure of synthetic polypeptides. I. The transform of atoms on a helix" W. Cochran, F. H. Crick and V. Vand, (1952) Acta Crystallographica 5, 581-86. This is the seminal work that allowed Crick and Watson to deduce the DNA structure.

It is not a simple paper, but it does show how the 'X' diffraction pattern from a helical fiber (not a crystal, btw, since it's not ordered in 3 dimensions) arises in terms of Bessel functions.

Still, despite your fine efforts in getting laser diffraction to work, it is not obvious to me that the pattern from a helix, which is three-dimensional, can be gotten from a two-dimensional object. Does your professor have the theory worked out in detail? That would be awesome.

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