Diffraction Grating And Lightbulb

[mathskier]

An incandescent lightbulb produces incoherent light. But on Wikipedia, for instance, there is a picture of it producing a rainbow diffraction pattern on the diffraction grating page. But since the bulb is putting out incoherent light, it should be intensities rather than fields that add together.

How is this diffraction from a light bulb possible? For an interference/ diffraction pattern to occur, doesn't the light have to be coherent over the grating's extent? But then how can an incoherent source ever produce diffraction and interference effects?

 

[pumila]

Interference effects require coherence, diffraction effects do not. In diffraction effects (grating or prism) light is deflected by an angle that varies as a function of wavelength or colour. Diffraction gratings deflect by an angle that is a function of the ratio of the light wavelength to the grating step length. Prisms deflect by an angle that is related to the dispersion of the medium - the refractive index varies with colour.

 

[mathskier]

I'm not sure I understand. The pattern is proportional to the Fourier Transform (squared) of the aperture function. But it doesn't make sense to take the Fourier Transform without having the phase information of the beam at the aperture. And if the phase is incoherent at the aperture, we can't express that function in order to take the FT.

 

[sophiecentaur]

Interference effects require coherence, diffraction effects do not. In diffraction effects (grating or prism) light is deflected by an angle that varies as a function of wavelength or colour. Diffraction gratings deflect by an angle that is a function of the ratio of the light wavelength to the grating step length. Prisms deflect by an angle that is related to the dispersion of the medium - the refractive index varies with colour.

People try to differentiate between diffraction and interference but they are really the same thing - differing only in the 'numbers' involved.
There is no inherent difference between a diffraction grating (many slits) and a pair of slits. The difference is that the actual two-slit width and spacing tend to be greater than the pitch of a diffraction grating. (You wouldn't get much light through just a pair of slits taken out of a diffraction grating). The different orders of a diffraction grating pattern correspond to the closer spaced lines from the coarser two slits. Also, because the diffraction grating has many sources, the peaks are narrower.
My point is that, if you look at the first maximum of the pattern from two slits, with white light (magnified) you will get an identifiable 'rainbow' pattern. This gets degraded by the second or third maximum and it just becomes a blur. In the same way, high order spectra from a coarse diffraction grating can overlap.

 

[mathskier]

But how does that relate to the incoherence of white light from an incandescent bulb?

 

[pumila]

With diffraction, consider a plane wave falling normally on the grating. Each line of the grating essentially converts that input line into an omnidirectional radiator. The output will have interference pattern reinforcement not so much because the light is coherent in the normal sense, but because an electromagnetic wave must be several wavelengths long to create a specific wavelength, so this length limit is a property of all light whether coherent or incoherent, simply for it to have a specific colour.

Given this, one can see that reinforcement occurs in all output directions for a given colour when waves are in step. This occurs on the straight through beam, and every angle where there is an integer number of wavelength slips between two adjacent line outputs.

 

[BruceW]

An incandescent lightbulb produces incoherent light. But on Wikipedia, for instance, there is a picture of it producing a rainbow diffraction pattern on the diffraction grating page. But since the bulb is putting out incoherent light, it should be intensities rather than fields that add together.

How is this diffraction from a light bulb possible? For an interference/ diffraction pattern to occur, doesn't the light have to be coherent over the grating's extent? But then how can an incoherent source ever produce diffraction and interference effects?

Good question. I think the diffraction grating is simply dispersing the beam of light, and that this dispersion is dependent on the wavelength of the light. So there is not any constructive/destructive interference occurring after the grating. (i.e. the physical phenomena is different to what happens in a double-slit interference experiment, for example). Therefore, for the 'diffraction grating experiment', the light does not need to be coherent.

 

[sophiecentaur]

There are two issues here. Light can be monochromatic (to a certain degree) and it can be coherent - which implies good phase coherence for all paths through the aperture. A diffraction grating is not magic; it can only do its little best. It will not give a good pattern unless your source is a slit (or collimated in some way), for which all wavelengths have good coherence 'in themselves'. If not, the grating will just produce a blur. For a white light source, a 'rainbow' pattern will be produced with a broad source but, a broad source of monochromatic light will just produce very broad, fuzzy bands, when you may have expected nice sharp spectral lines.

 

[Andy Resnick]

An incandescent lightbulb produces incoherent light. But on Wikipedia, for instance, there is a picture of it producing a rainbow diffraction pattern on the diffraction grating page. But since the bulb is putting out incoherent light, it should be intensities rather than fields that add together.

How is this diffraction from a light bulb possible? For an interference/ diffraction pattern to occur, doesn't the light have to be coherent over the grating's extent? But then how can an incoherent source ever produce diffraction and interference effects?

That's a good question, and the answer involves the idea of spatial coherence, or the size of the source. As an analogy to imaging, if the image is the convolution of object and the point spread function, the diffraction pattern is the spectrum convolved with the object.

Here's an example: I placed a diffraction grating in between the camera lens and sensor, and acquired two images: one of an incandescent bulb, and the other of three compact fluorescent bulbs:

http://imageshack.us/a/img268/4463/photographypresentationc.jpg

The CFL image is easier to interpret since the spectrum is discrete: each 'peak' is now replaced with an image of the bulb. The same effect occurs with the incandescent bulb, but since the spectral output is continuous the effect is an overall 'blurring' of the spectrum (similar to how an image can be blurry if the point spread function (e.g. Airy disk) is large.

 

[BruceW]

wow, pretty interesting. why do the CFL's have the peaks? Is it because the power spectrum has peaks, while the power spectrum of a normal bulb is much more uniform?

 

[sophiecentaur]

wow, pretty interesting. why do the CFL's have the peaks? Is it because the power spectrum has peaks, while the power spectrum of a normal bulb is much more uniform?

CFLs do not have a continuous spectrum because they do not emit light because they are hot (like incandescent filaments). If you take a low pressure gas discharge lamp with no phosphors, it will produce a spectrum which consists of just lines. But you will not get a good picture unless you use a collimator of some sort, to make sure that light with the wavelength of each of the spectral peaks is coherent. Like I said, there are two issues. Laser light is both monochromatic and has a high degree of coherence.
You should look into how light is emitted from various sources and how the spectra vary. this link and https://www.cfa.harvard.edu/~jbattat/a35/cont_abs_em.html are examples of many sources of info.

 

[Cthugha]

An incandescent lightbulb produces incoherent light.

One hears that often. Nevertheless it is a myth and wrong. First-order coherence is no on/off property. You have coherence times and legnths. You may have long and short coherence times differing by several orders of magnitude. You may have coherence lengths which differ by several orders of magnitude, but there is no fundamental difference which allows to draw some line and justifies calling light sources on the one side coherent and the other incoherent. Whether you see coherent effects depends on the ratio of the coherence length/time of the light field in question and the relevant time scales/distances (for example the slit distance of a double slit) in the experiment and not on the light source alone.

Incandescent light is incoherent in terms of so-called higher-order coherence, but this has a very different meaning and is not what you see in diffraction, the double slit, simple interference or a Michelson interferometer.

 

[Andy Resnick]

wow, pretty interesting. why do the CFL's have the peaks? Is it because the power spectrum has peaks, while the power spectrum of a normal bulb is much more uniform?

Yes.

 

[jtbell]

If you take a low pressure gas discharge lamp with no phosphors, it will produce a spectrum which consists of just lines. But you will not get a good picture unless you use a collimator of some sort,

e.g. a narrow slit in front of the lamp,

to make sure that light with the wavelength of each of the spectral peaks is coherent.

Similarly, if you want to see the Fraunhofer absorption lines in the solar spectrum, you have to pass the light through a narrow slit before passing it through a prism or diffraction grating.

 

[mathskier]

There are two issues here. Light can be monochromatic (to a certain degree) and it can be coherent - which implies good phase coherence for all paths through the aperture. A diffraction grating is not magic; it can only do its little best. It will not give a good pattern unless your source is a slit (or collimated in some way), for which all wavelengths have good coherence 'in themselves'. If not, the grating will just produce a blur. For a white light source, a 'rainbow' pattern will be produced with a broad source but, a broad source of monochromatic light will just produce very broad, fuzzy bands, when you may have expected nice sharp spectral lines.

I think the non-monochromatisicity doesn't really bother me, since even a laser produces light at different wavelengths normally. The grating would help us separate these!

It was the fact that there is diffraction at all for an incoherent source that bothered me, not the smearing of colors.

Thanks!

 

[technician]

one point that may be worth making is that interference in 2 slits and diffraction grating is caused by 'division of wavefront'.
The waves need to be coherent as they emerge from the slits and if a point source is used (or parallel beam) at a great enough distance from the slits then any difference in 'coherence' across a wavefront is insignificant.
The waves ARRIVING at the slits do not need to be coherent !

 

[BruceW]

I think the non-monochromatisicity doesn't really bother me, since even a laser produces light at different wavelengths normally. The grating would help us separate these!

It was the fact that there is diffraction at all for an incoherent source that bothered me, not the smearing of colors.

Thanks!

ahhh... any light that goes through a small enough opening is going to get diffracted. It doesn't need to be coherent, and the light will not necessarily be coherent on the other side. (i.e. if you have two slits, then it won't necessarily cause interference on the other side). But of course, diffraction is still happening. Maybe we are both thinking of different definitions of the word 'diffraction' ?

 

[Cthugha]

The waves need to be coherent as they emerge from the slits and if a point source is used (or parallel beam) at a great enough distance from the slits then any difference in 'coherence' across a wavefront is insignificant.
The waves ARRIVING at the slits do not need to be coherent !

But that is circular reasoning. If you use a point source, that automatically means that you have a light source of high spatial coherence. Spatial coherence is inversely related to the angular size of the source just as temporal coherence is inversely related to the power spectral density. This is what allowed people to measure star diameters by measuring the coherence of the light emitted from these stars back in the 1950's.

 

[technician]

But that is circular reasoning. If you use a point source, that automatically means that you have a light source of high spatial coherence. Spatial coherence is inversely related to the angular size of the source just as temporal coherence is inversely related to the power spectral density. This is what allowed people to measure star diameters by measuring the coherence of the light emitted from these stars back in the 1950's.

Absolutely...just an alternative way to say the same thing...may strike a chord with someone !