# I Instrument Line Function of a Spectrometer

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1. Jan 5, 2017

### Mzzed

I realise that in a spectrometer the spectral line being viewed will be the result of the actual spectral line plus an instrument line function as well (as seen in the linked image). What I don't understand is how this is produced? Someone tried explaining this to me once before but their explanation seemed to me like an explanation for linear dispersion? How is the Instrument line function produced? what causes it?

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2. Jan 5, 2017

### BvU

Lots of contributions to dispersion: finite slit width, finite beam diameter (so finite number of slits participating) in a diffraction grating spectrometer. Reflection coefficient < 1 in a Fabry-Perot interferometer, etc.

The final result is a convolution of the actual spectral line and the instrument function (the 'plus' in your first sentence)

Last edited: Jan 5, 2017
3. Jan 5, 2017

### Mzzed

But what creates the instrument line function itself? I understand there a quite a lot of factors that affect the final shape of the spectral line such as linear dispersion and the instrument line function but i don't understand what creates the instrument line function. For example i know that the linear dispersion is basically the amount the light 'spreads' put very simply, but how do you describe what an instrument line function is created by?

4. Jan 5, 2017

### BvU

I'm not with you: the instrument line function is the response you get for an infinitely sharp spectral line. You describe it as a spectral distribution and that expression is in fact a convolution of the contributions mentioned.

What kind of answer do you expect for "how do you describe what an instrument line function is created by?" -- there are several examples in the given links !

5. Jan 5, 2017

### Mzzed

OHH so all the contributions to the convolution of the spectral line (such as those you listed above) all summed together create the instrument line function? And is that why when an infinitely sharp spectral line is used as an example, the observed spectral line will just be the instrument line function?

6. Jan 5, 2017

Correct !

7. Jan 5, 2017

### sophiecentaur

Yes. The line function you are describing is equivalent to the 'Impulse Response' of a temporal filter in signal processing theory (with a slightly different hat on).

8. Jan 5, 2017

### BvU

Yes the fourier transform and laplace transform are ubiquitous.

I have cramp imagining the silverback gorilla with a slightly different hat on

9. Jan 5, 2017

### sophiecentaur

He is, actually thinking very deeply in that picture. A lovely chap. I met him in Bristol. He didn't have much to say but I should have chosen the right subject, I guess.

10. Jan 5, 2017

### BvU

Don't be too silent when looking at one of these biggies. His dutch cousin Bokito couldn't stand it and broke out. But sophie is a nom de plume for a male, and he reacted violently to a female regular visitor, so you might be OK.

Back to spectroscopy, though...

11. Jan 5, 2017

### sophiecentaur

Apparently, loving eye contact gets gorillas upset cos they read it as a threat. I snarled at him and beat my chest. He just blanked me and posted something on PF.

12. Jan 5, 2017

### BvU

After which they removed the gorilla webcams at Bristol zoo ?

13. Jan 5, 2017

### ZapperZ

Staff Emeritus
You are beginning to learn on how your instrument has a finite capability, and how it can affect your measurement. The "broadening" occurs due to the reasons that BvU had stated earlier - your instrument has a non-zero, finite resolution, and the BEST data that you can get is limited by that resolution. So everything that you detect is, in principle, the convolution of the actual measurement with the instrumentation resolution.

It is why knowing that capability and limits of your instrument are very important information that you must know. You always want to make sure that your instrument's resolution and accuracy are better than what you are measuring.

Zz.

14. Jan 6, 2017

### Khashishi

There are different kinds of spectrometers, but generally you have an input source of light that passes through a slit. The light passes through or reflects on some optical focusing elements elements, and a grating, and some more optical elements, and then hits a screen.
The grating deflects the light by an angle which depends on the wavelength of the light, so there is a conversion of wavelength to position on the screen. A larger slit size means that a wider beam of light will hit the grating and a wider beam will come out from the grating and hit the screen, resulting in a wider line width. But if you make the slit too small, you will have a very low intensity in your output spectrum. Also, the optics are not perfect at focusing. They are needed to focus the beam on to the screen, but they can add some blurring due to imperfections in the surfaces and also physical limits due to diffraction.

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