Helical Diffraction Simulator (Photo 51)

Build a helix from pitch, radius, rise and strand count, and watch its X-ray diffraction pattern — the X of Photo 51 — emerge from Bessel-function layer lines.

diffraction
Fourier optics
Bessel functions
DNA
reciprocal space
physics

Simulated diffraction film

Hover the film to read reciprocal-space coordinates and d-spacing.

Real-space helix (the object)

Blue and orange trace the two strands; point size encodes depth.

What the pattern says

X arm angle

56.7°

steeper ⇒ smaller radius / longer pitch

Layer spacing ΔZ

0.0294 1/Å

pitch 34.0 Å

Meridional d

3.40 Å

base-pair rise

Highest visible n

of n_max = 10

First max of n = 1

0.0292 1/Å

⇒ r ≈ 10.02 Å

Extinct layer lines

strand interference

Disorder damping at n=5

0.653

Debye–Waller weight

Photo 51 similarity

100%

Layer-line profile: J_1(2πRr)²

The first maximum of J_n occurs at 2πRr = 1.841, so its radial position measures the helix radius directly. Layer-line weight here = 0.576.

Measure the helix

Put the app in blind mode, ask a partner to set the geometry, then recover it from the film alone: the layer-line spacing ΔZ gives the pitch (P = 1/ΔZ), the first maximum of layer line n = 1 gives the radius (r = 1.841/2πR), the meridional spot gives the base rise, and a missing layer line reveals the two strands and their groove asymmetry. Compare your estimates with the true values afterwards.

How this differs from the original R script

The R prototype drew four cosmetic diagonal "arms" and mis-aligned the density grid (rep(..., each=) versus rep(..., times=)), leaving the lower half of the image a flat grey. Here the X emerges on its own from the Bessel maxima of successive layer lines — nothing about the cross is drawn by hand.

Preparing the simulation…

Conceptual bridges & related modules

MEG vs EEG: The Sarvas Dipole Model
physical contrast · Chapter 7
Contrast wave-scattering symmetry with quasi-static source-field symmetry.