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I have a spectrometer which outputs a dataset of Irradiance (Watt per meter² per nanometer) in the vertical axis vs. wavelength (nanometer) in the horizontal axis.

The fact that it is per nanometer means that a plot of this dataset is not a scatter plot, but a histogram.

Now, suppose I see in the newspaper a histogram that depicts the age distribution in a city; you might see the number of people in the city between age 10-20 years, a 20-25 years old bin, a 25-35 years old bin, a 35-55 years old bin etc. The vertical axis in this case is simply "number of people", not "number of people per unit of age in years".

My question is why the developer of the spectrometer outputs the radiation power per wavelength unit, and not a simple data set of radiation power in each wavelength - a series of heights.

The only thing I can think of is that wavelength (the independent variable in the former case) is a continuous variable. And age is not continuous (at least, not in the case of counting number of people in a specfic age). Is it correct?

Any insight about it would be very welcome.

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  • $\begingroup$ Histograms always display count/frequency on the y-axis. Unless I'm misunderstanding, a plot of irradiance versus wavelength isn't a histogram. Histograms always have a y-axis value that can be expressed as an N, not N per x-axis value. The fact that the unit uses "per nanometer" does not make it a histogram. You seem to be asking a histogram question about something that isn't a histogram in the first place. $\endgroup$
    – Nuclear Hoagie
    Commented Oct 9, 2023 at 14:59
  • $\begingroup$ Irradiance vs. wavelength is a scatter plot; Irradiance per wavelength unit vs. wavelength is a histogram, according to what I read here, page 11: "It is critical to remember that a spectrum is actually a histogram of how many photons fall within each wavelength interval. Thus, the final units to be used for spectral measurements are watts/cm²/nm where the "/nm" indicates that you are binning by nanometer sized wavelength intervals." $\endgroup$
    – tush
    Commented Oct 11, 2023 at 6:55
  • $\begingroup$ Let me ask it this way: Can you give me an example of a histogram with a continuous horizontal axis that doesn't have "binnings"? $\endgroup$
    – tush
    Commented Oct 11, 2023 at 8:00
  • $\begingroup$ Truly continuous values have 0 probability of being repeated, so a "histogram" of continuous values would be zero everywhere except for disparate zero-width "bins" containing a single count each. I think you're after a density plot, which is a kind of smoothed continuous version of a histogram that does not use bins. $\endgroup$
    – Nuclear Hoagie
    Commented Oct 11, 2023 at 13:25
  • $\begingroup$ Answer here: physics.stackexchange.com/a/365059/45164 $\endgroup$
    – Mark H
    Commented Jul 20 at 7:42

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The fact that it is per nanometer means that a plot of this dataset is not a scatter plot, but a histogram.

I am not sure if I am mistaking the question but the plot you make from any hardware reading will always be an interpretation of the data you are measuring, so talking about whether it is a scatter or a histogram is not entirely clear to me.

I am not sure which spectrometer you are using, but depending on the device you will typically have some form of monochromator (in order to separate the wavelengths in each of its spectral components e.g. frequency/wavelength components) and this will "spread" the light source you are trying to analyze to obtain its components per frequency/wavelength unit.

I am indistinctly using wavelength and frequency as I am considering the relation $f = c / \lambda$ which for most spectroscopic analysis stands correct.

I am not sure which kind of measurement you are doing, but for most analysis you are interested in the spectral components of the light source you are analyzing and having nm steps is sufficient (For example, as you measure longer wavelengths you can even increase the step sizes as the behavior is smoother, except at resonance peaks).

The vertical axis in this case is simply "number of people", not "number of people per unit of age in years".

In this example I am not entirely sure the assertion is correct as the cumulative histogram bar is not really "per unit of age in years", as the binning is not symmetrical (10, 10, 20 years steps), so it is a completely different use case in my opinion.

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