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Peter,
As a newbie to spectroscopy myself, I can appreciate the frustration in getting started, and the excitement when you start to see some results. Don't be too disheartened - you are starting to capture some clear emission lines, so rapid progress should be possible from here!
As others have said, it would help if you can describe the equipment you are using (OTA / lens, grating / prism, camera / sensor, etc), so we can help point you in the right direction. Is this a home-built device, or are you using proprietary components?
Looking at your spectrum image, is that the whole frame, or is it a crop? Can you do anything within your sensor assembly to eliminate the white corners? (It looks like some sort of light leakage or internal reflections.)
The spectral analysis software will interpret any non-black pixel within the sampling region as "signal", so you want to shift the spectrum well clear of the white "vignetting" in the corners, and also maybe reduce the overall exposure so as to darken the general background.
Also, try to make sure you get the whole spectrum within the frame, and if you are using a transmission grating (like a Star Analyser), try to capture the "zero-order" image of the light source on the frame, as well as the first-order spectrum.
For your first attempts, try shooting a known type of emission light, such as a fluorescent tube, compact fluorescent globe, or sodium street light as your light source (it looks like you have used one of these), and then you can use the known (or suspected) emission lines of the light source to calibrate your spectroscope. Fluorescent lights typically show several strong Mercury lines at 434.7 & 435.8 nanometres (blue - but you'll only make this out as a single line, if at all), 546.1 nanometres (green), and 614.9 nanometres (orange-red). You'll see some other lines as well, due to the phosphorescent coating and other elements, but these are the dominant lines that you can use to calibrate from a fluorescent tube source. Sodium lights produce strong yellow lines at 588.9950 and 589.5924 nanometres (but again, you'll only see this as a single line).
Once it is calibrated, you can start capturing other spectra from other sources, and use the same calibration to interpret the spectra that you capture. (The modern "Brilliant White" LEDs are interesting, as they have a strong narrow blue band from the single blue LED "driver", and a broader band across green / yellow / red re-emitted by the phosphors. The older "White" LEDs which have three RGB LED "drivers" produce a completely different spectrum, showing three strong but overlapping bands from each of the red, green and blue LED "drivers".)
Hope this helps - let us know how you are going.
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