Diffraction limited spectrum

[zappedagain]

I worked on a project long ago (around 1987) where we showed the spatial frequency distribution of a laser beam - the DC content was at the center of the beam and the harmonic content was at increasing radii from the center.

Does the same spatial distribution apply if the system gets diffraction limited (I have limited knowledge of what that term really means...)? An engineer has told me the distribution is flipped for a DL system (high frequency at center, DC at the radii). Is that true?

We have an 'optical' (wavelength ~970nm) spectroscopy system where the optical path is showing a high pass filter effect. If the optical spatial distribution holds, that implies there is something blocking the center of the beam. This EE is trying to understand what is going on. Any references will be appreciated.

Z

 

[IRstuff]

Seems like you're mixing a bunch of different concepts. Bear in mind that spatial "frequency" and "distribution" are not the same things and are extremely analogous to frequency and time in electrical signals.

Most lasers are designed to propagate Gaussian beams, whose peak intensities are in the center. Concurrently, their frequency content has it peak at DC and drops off, and is smoewhat analogous to a low-passed electrical signal. Diffraction-limited simply means that the frequency correlates to an ideal aperture, which still has its peak at DC and a cut off proportional to lambda/aperture diameter and monotonically decreasing frequency from DC to cutoff. Your colleague is perhaps confused and thinking about a reflective Cassegrain teelscope system, which has a dip in in the middle of the diffraction limited spatial distribution, inbetween DC and the cutoff, with a possible slight rise in spatial response near cutoff. However, the DC is still the peak response, as befitting a system that is roughly lowpass.

If you are seeing an image of the beam with a dip in the middle, that spatial distribution, not frequency. That generally suggests an optical obscuration in the middle of an aperture, and if you're seeing it, then possibly the system is grossly out of focus as well.

TTFN

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[MacGyverS2000]

If you are seeing an image of the beam with a dip in the middle, that spatial distribution, not frequency. That generally suggests an optical obscuration in the middle of an aperture, and if you're seeing it, then possibly the system is grossly out of focus as well.

While this is true for a Gaussian beam distribution (or any other TEMxy mode, where the number of angular fields 'y' is zero), it's not true for higher-order modes with angular fields greater than zero, i.e., TEMx1.

Zapped, what power levels are you working with? You're essentially in the range of Fiber/YAG laser output at 970nm, and my knowledge isn't as great there as if you were in the CO2 range (10,000nm). For CO2, at least, as powers start to approach several hundred Watts, it's difficult to get a good quality TEM00 (Gaussian) beam, so it often drops down to TEM10 (or worse, TEM20). I do not know if fiber reacts in a similar manner. With that in mind, you very well could be trying to measure a TEM01 or TEM02 beam, which would explain the drop in power right at the center.

This link has some good pics of beam shapes:

http://www.mrl.columbia.edu/ntm/level2/ch02/html/l2c02s07.html

Dan - Owner

http://www.Hi-TecDesigns.com

 

[IRstuff]

I repeat, dips in the intensity are changes in the spatial distribution, not FREQUENCY.

TTFN

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[zappedagain]

Thanks IR. I remember the spatial distribution having something to do with a Fourier spectrum. Maybe the math fit but the units were different.

As I understand it though with our spectroscopy system if you start to block the beam through a radial shutter you lose the high frequencies first as the shutter closes; to me that implies the frequency content is spacial (or the optical beam has skin effect!).

I just noticed that my last response never posted. We found an optical component had the wrong coating on it. This made it transparent in the low frequency part of the spectrum and reflective in the rest of the spectrum; as we are using it for spectroscopy we expected consistent reflectivity.

Z

 

[IRstuff]

Well, a couple of things:

> A spectroscopy system should have uniformly distributed light, so there shouldn't be any "high" frequencies in a particular part the light source.

> Centering of the aperture is irrelevant. Classical diffraction limited blur spot (This is not that different than EMI propagation through an aperture, i.e., the smaller the aperture, the lower the cutoff frequency) is 2.44*lambda/aperture, so the smaller the aperture, the fatter the blur, the lower the frequency content of the light that makes it through.

TTFN

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[zappedagain]

Ah, I'm starting to get insight on diffraction limiting. Are you saying that if I'm modulating the light the bandwidth for the modulation gets diffraction limited? f = 2.44*lambda/aperture? Kind of like a limit on the modulation index for FM?

Is there a good book where I can learn more about this? Or is that equation pretty much what it all boils down to?

Z

 

[lumenharold]

Not sure who's system you are using but here's a link to a book on the subject:

http://www.kosi.com/Raman_Spectroscopy/books-Handbook.php

Harold
SW2011 SP2.0 OPW2011 SP2.0 Win 7 Ultimate
BOXX 8550 Xtreme Dual Xeon 5680 @4.2Ghz
nVidia Quadro 4000

http://www.lumenflow.com

 

[IRstuff]

More or less, but remember that this is spatial modulation, i.e., imagine a sinusoidally varying intensity pattern across the image. 1/period of the sinusoidal pattern is the spatial frequency. At low frequencies, i.e., widely spaced dark and light, the modulation can up as high as 100%. As the spatial frequency increases, the modulation, for a diffraction limited system, will monotonically decrease to 0 at the cutoff frequency. see:

http://www.normankoren.com/Tutorials/MTF.html

for some example modulation patterns.

So, as you can imagine, this is not something that is readily generated within a spectrometer, particularly if it's a non-imaging system.

TTFN

FAQ731-376
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