# Noise

by cfastie | 05 Mar 04:32

Image above: (Top) Detail of a spectrogram of the sky and a vertically blurred version of it. (Bottom) Intensity curves for the blue and green channels of the original (colored) and blurred (black) images. Vertical dashed lines identify Fraunhofer absorption lines.

Identifying absorption lines in a continuous spectrum requires separating signal from noise. It was possible to see six fairly convincing Fraunhofer lines in a spectrum of the sky, and there might be more recorded in the image, but some of them are rather subtle. My reaction was to try to capture a better spectrum next time, but Jeff Warren’s reaction was to try to extract more information from the spectrum we already had. Jeff suggested vertical averaging of the pixel values in Photoshop.

So I applied a motion blur filter to the image which evened out the color in vertical columns of pixels. The image above is a detail of that same spectrogram with the original image above and the blurred image below. Below the images are the graphs of the two color channels that contribute to this part of the spectrum. The blue and green lines are the intensity curves that Spectral Workbench extracted from the original image, and the black lines are the curves extracted from the blurred image.

The curves from the blurred image are smoother -- they have less noise. The dips in the curve at the locations of the Fraunhofer absorption lines are about the same depth. So the effect is weak, but this should help distinguish the signal (Fraunhofer dips) from the noise (higher frequency variation in intensity).

Ideally, a new line could be mathematically fit to the smoothed curves and the deviations of the curves from the new line could be mathematically tested to see if any deviations were unusual enough to be considered signals. This way absorption lines (or emission peaks) could be identified objectively.

The blurring in Photoshop was done by applying a motion blur filter: Filters/Blur/Motion blur, with angle =90° and distance=300 pixels. Jeff might try to implement a similar vertical averaging feature in Spectral Workbench. The two versions of the spectrograms are at Spectral Workbench: original and blurred.

Very cool to see the noise reduction graphed properly. Do you think the remaining "wobbliness" in the line is due in part to the spectrum itself (I'd guess not -- black body spectrum, right?) or to some kind of systematic noise (how the slit is cut, reflections, unevenness in the black interior of the chamber, other issues with the camera?)

I was thinking of how to describe this sort of smoothing -- if we made a macro, would we call it "auto-smoothing"?

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The corduroy appearance of the image is a mystery. The vertical lines are very regular in places, so I assumed they were related to the lines on the grating. But the grating lines would be about 5 or 6 times closer together, although they might still be producing the striped effect. The pixels on the sensor are likewise much finer than the vertical lines.

I guess the smoothing we are doing is vertical smoothing, or vertical averaging, column averaging, pixel column averaging, column smoothing, vertical striping, grain removal, grain reduction, vertical grain reduction, or Vertical Grain edginess reduction, also known as V'Ger.

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Man, Chris, you really have the obscure references down -- i haven't seen ST:TMP for over a decade...

The reason I thought of just "smoothing" (more generically) was:

a) empirically that's what it does to the graph line b) we could say vertical, but on live capture, the Y-axis is time, so there could be some confusion: what does "vertical" mean to the user?

We'd have to have a warning message that if your spectrum is curved or sheared, this won't work.

I'm hoping to finish up the macro saving system on the train this morning (quick round trip) and maybe I can try this as a first macro.

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