# Resolution limit of delay line interferometer

1. Dec 10, 2013

### stevenjones3.1

Hello All

I am using a very basic delay line interferometer to measure the linewidth of a laser source. Basically there is a 1550nm laser that emits light which is split, and one half of the light travels down a 700m delay line before being recombined and the interference is observed.

This is a self-homodyne system, and the output is measured with a spectrum analyzer to determine the line width of the laser.

There should be a lower limit to the frequency which can be observed with a delay line interferometer which can be calculated or approximated theoretically but I am having trouble figuring out how.

any help would be greatly appreciated.

2. Dec 11, 2013

### stevenjones3.1

Just in case anybody is looking at this...

I found one source that says the system resolution will be = (c/nL)/2. Where c is the speed of light n is the refractive index and L is the length of the delay line.

I have found sources stating their delay line length and resolution limit:
72km -> 1.4kHz
11 km -> 18.2kHz
330km -> 606kHz

This equation predicts
72km -> 1.427kHz
11km -> 9.343kHz
330km -> 623kHz

so the theory is in good agreement with two of the data points and is off by a factor of two on the third data point (which I can hand-waveingly justify)

Also this theory makes some intuitive sense, i.e. there would have to be an inverse relationship between between the delay line length and the resolution limit because no delay line would be an infinite resolution limit (i.e. no resolution at all).

Can anyone confirm this or have any input?

3. Dec 11, 2013

### Malverin

Maybe the refraction coefficient n of the line you have meassured is not constant for its whole length and due to that, there is a difference between measured and calculated resolution limit.

Last edited: Dec 11, 2013
4. Dec 11, 2013

### stevenjones3.1

I have no measured resolution limit, I am trying to calculate it to give some credibility to my measurement

5. Dec 11, 2013

### Andy Resnick

Your equation is nearly identical to the definition of temporal coherence: Δω= c/nΔL, where ΔL is the path difference and Δω is the frequency spread (in Hz). That extra factor of 2 could arise from, for example, quoting the bandwidth as ω +/- Δω/2.

6. Dec 11, 2013

### stevenjones3.1

I have found a source that states this as the free spectral range (FSR = c/(2nL)) which kind of makes sense that it would be the resolution limit