Jellyfish of Diffraction

Diffraction patterns, again. But this time I tack them to an imaginary semi-circular screen.

Screens grow bigger in radius with increasing wavelength – growing more reddish. If every wavelength would be diffracted in the same way, all peaks would lie on a radius of the circle. But as red is diffracted more, maxima move to higher angles.

The diffraction grating would be placed in the center of the circle.

Following my approach, I want to pair it with engineering figures related to diffraction. I found the mother lode of public domain engineering images with artistic appeal – US patents.

I am turning the patterns, and looking at them from different angles, and I cannot unsee the jellyfish.

Diffraction patterns by elkement, collage with 1945 patent drawing
Diffraction patterns by elkement, collage with 1945 patent drawing
Diffraction patterns by elkement, collage with 1945 patent drawing
Diffraction patterns by elkement, collage with 1945 patent drawing
Diffraction patterns by elkement, collage with 1945 patent drawing
Diffraction patterns by elkement, collage with 1945 patent drawing
Diffraction patterns by elkement, collage with 1945 patent drawing
Diffraction patterns by elkement, collage with 1945 patent drawing

My images are created with SageMath. Each diffraction pattern is a parametric curve. The curves – relative intensity dependent on wavelength and angle – are the same as in my images of ribbon-like patterns. The ribbon corresponds to a plane screen. This time, the screen is circular, and the distance between curves for different wavelength has significance. If you used concentric screens with hypothetical detectors for different wavelengths, maxima would show up where the peaks are.

These images form a series, documenting the view on the structure when rotating about the center, the position of the diffraction grating. I start from looking into the direction of the central ray, from the grating onto the screen, at about zero degrees. Then I walk around the jellyfish-like pattern (and wobble a bit up and down), until I see look into the opposite direction – from the center of the screen to the grating. Then I fly upwards and look down on the concentric patterns.

For diffraction formulas, see e.g. chapter 30 of Feynman’s Lectures, vol. I. I am using a 4-slit grating.

I weighted the curves with Planck’s blackbody distribution (dependence of intensity on wavelength). Planck’s law is explained in chapter 41.

Source of the conversion of spectral colors to RGB colors is this blog article by a biophysicist.

I was browsing patents semi-consciously, searching for “diffraction”, like doing internet search term poetry. I chose this patent: The invention is about how to extend a spectrometer’s reach to nearly the whole range of visible wavelengths, by using for example different gratings and curved screens.

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