# Clarification needed in Spectroscopy - Thanks

1. May 5, 2009

### Zero-Toleranc

Apologies for making a long posts, I just wanted to lay down the basic idea of what I'm doing at the beginning.

I'm working on a home-made Michaelson type Interferometer. I'm trying to make few changes, mainly modulation of the black-body type radiation (Globar).
Instead of amplitude modulation (which is normally achieved via a chopper) I'm trying to modulate the phase. I looked into it and the easiest way seems to be by vibrating one of the mirrors (the one that doesn't move), in order to introduce a phase shift in one of the arms.
I checked online for piezoelectric vibrators and they all (as expected) have various specs.

My first question is this: If the piezoelectric vibrator has a displacement of 0-100 um (micrometers), what would happen to the signal or its phase if I choose to run it from 0-50 um, rather than from 0-100um (lets say that I'm running it at the same frequency 1KHz). Because there seem to be allot of products out there where their prices increase as their displacement increases.

Second Question: How do I determine the best phase modulation i.e. in an Interferometer, would I get best results if I modulate the phase in one of the beams by 90 deg relative to the other?

My Third question: Is there a way of determining (without experimentally trying) what would be the optimal frequency and the displacement of the piezo to achieve the desired phase modulation.

For this experiment I have a SR850 Lock-in, a bolometer as the detector, Globar for the source and the linear stage delay of course.

I'm thinking that since a Bolometer has quite a fast detectivity (compared to normal Golay Cells) I can at least modulate the phase at a frequency around 1kHz. Is this the right way of thinking? Also, is there an easier way of achieving phase modulation without the use of this vibrating mirror? For anyone that needs more information please let me know and I'll be happy to provide.

Any thoughts are very well appreciated.

Thanks

Kas

2. May 5, 2009

### Andy Resnick

I'm a little unclear about something- the globar, having a huge bandwidth, has a negligible coherence length- you are almost in the range of optical coherence tomography, except that the globar is also spatially incoherent, making your stated problem practically insurmountable. The local phase of light coming off a globar is stochastic for nearly any timescale you choose.

FTIR machines (which seems like you are trying to copy), AFAIK, have a HeNe laser or other narrowband source which is used to generate the fringes.

Other specific point: the mirror displacement. I'm doing this in my head, so the numbers are very loose.

You want a source that has a coherence length ( $L=\lambda^2 \over n \,\Delta\lambda}$ ) that's about the same size as the mirror displacement, at the largest. A 100 um coherence length is a bandwidth (for a 500 nm source) of about 2.5*10^-4 um, which is about the bandwidth of a laser diode, IIRC. For 50 um coherence lengths, you are looking at 1*10^-4 um, well in excess of a HeNe (IIRC). Contrast this with a globar with a bandwidth of hundreds of microns.

3. May 6, 2009

### Zero-Toleranc

You are absolutely right when it comes to making theoratical calculations of the phase using globar. It can't be done due to its incoherence.
What I meant is too see if there is a way of knowning that at what frequency should I run the piezo based on the detector specs. e.g. when using a Golay cell detector, due to its low detectivity, the reference frequency at which the piezo runs is low, (at around 10 - 13 Hz). But when using a bolometer, due to its much higher specs, i'm guessing that I can increase the reference frequency at which the Lock in uses as well as the piezo. Is there a proper relation of this reference frequency with the detectors properties i.e. its detectivity, sensitivity, NEP etc.

Below is a diagram of what I am constructing. From the diagram you can see that this is a Single pass Dispersive Fourier Transform Spectroscopy. Its very similar to FTS but the sample position is in a different place, i.e. not in front of the detector but in one of the arms, where both mirrors at the back of the sample vibrate at that reference frequency using the piezoelectric. This introduces a phase difference between the two arms, and it provides the interferogram with the phase and amplitude information. Because of this, the optical properties of the material (refractive index, absorption coefficient, dielectric constant) can easily be extracted without going through the hectic Krames Kronig rules.

What I don't understand the most is, what would happen if I choose to vibrate the mirrors at a smaller or higher displacement, since the key to having a constand phase modulation is to vibrate the mirrors at a constant frequency throughout, but what significance does this displacement distance of the mirror have in this case.

Thanks

Kas

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4. May 6, 2009

### Andy Resnick

It's been a while since I had to match data acquisition rates to detector properties. I think the sample rate needs to be at least slow enough to give a NEP to signal ratio of 2, as a rule of thumb.

As for your last paragraph, I'm not sure I follow you- I haven't used an FTS system in years, and I don't remember the exact conceptual basis of the design.

5. May 6, 2009

### Bob S

One item you should look into is the the effect of the piezoelectric crystal vibration on the parallelism of the mirrors in your interferometer. If the mirrors do not maintain perfect alignment (parallelism) during the vibration cycle, then the fringes will be moving all over your viewing aperture. Your displacement of 100 um is roughly 200 fringes (twice the mirror motion), and you are requiring that the mirror remains parallel within about 0.5 um.

6. May 6, 2009

### Zero-Toleranc

thanks for that bob. personally I've never used piezo or vibrating mirrors before. I looked around online and I found roughly what I needed: The P-289 has a displacement of 200 um, but I can only run it on around 700 to 800 MHz. But the S-303 I can run it on much higher frequency (around 2.5 kHz) but has a much smaller displacement (I think it was 70 um). Thats what I'm confused about. If I get the 303 then I'm loosing displacement, but I have no idea if I really need to have a displacement of 200 um. The links for these two piezos are below.

1. http://www.physikinstrumente.com/en/products/prdetail.php?sortnr=101800
2. http://www.physikinstrumente.com/en/products/prdetail.php?sortnr=300550

P.S. My idea of fixing the two mirrors on the piezo is on this drawing. Any suggestions on how I can improve this, or even if anyone has an idea of how I can modulate the phase without the use of piezo (provided that it doesn't cost the earth).

Thanks

Kas

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• ###### Piezo vibrator.jpg
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