fxcor error
Stephanie wrote on May 17, 2007
I am crosscorrelating spectra with fxcor to determine RV shifts for emission lines. The spectra are from echelle observations. Each spectrum is the concatenation of all the echelle orders. In one of my measurements, I provide fxcor with a specific wavelength range containing a set of lines, from which I obtain radial velocity shifts.
As a means of testing my results from the concatenated spectra (which are 32000 pixels long), I imcopy-ed a shorter spectral range of each of my spectra to a new image (now only 1024 pixels long). (This was a way to work with a smaller spectrum which is easier to display and scrutinize). On these shorter spectra I used the same identical wavelength range, as I had which the longer spectra. I expected identical results. The radial velocity shifts (Vrel, Vhel, and Vobs) are indeed very similar between the crosscorrelation of the two long spectra and the crosscorrelation of the two short spectra. However, the errors returned by fxcor was vastly different (by a factor of three, where the short spectra returned the larger error).
I am well aware the fxcor error is not a true representation of the error, and that montecarlo simulations have to be carried out to truly understand the uncertainty and how that behaves with variable SNR data. This notwithstanding, there is no reason why our two tests (on the long, or short version of the *same* spectrum, with identical spectral range) should have different fxcor errors.
We insured this difference is not due to fourier filtering (we kept fourier filtering off) and is not due to the apodization, nor is it due to continuum subtraction. Also, the shapes of the crosscorrelation functions for the two tests were identical.
We have no idea what might make such a difference for the calculation of the error. However, the error provided by fxcor is a fundamental number which measures the goodness of the fit to the crosscorrelation function and which, together with the result of the montecarlo simulation, gives an estimate of the real uncertainty on the measurement. The discrepancy between the errors returned by the two tests is therefore troublesome, and we need to understand it.
Do you know what might cause this difference?
Many thanks for all the help,
Steph
As a means of testing my results from the concatenated spectra (which are 32000 pixels long), I imcopy-ed a shorter spectral range of each of my spectra to a new image (now only 1024 pixels long). (This was a way to work with a smaller spectrum which is easier to display and scrutinize). On these shorter spectra I used the same identical wavelength range, as I had which the longer spectra. I expected identical results. The radial velocity shifts (Vrel, Vhel, and Vobs) are indeed very similar between the crosscorrelation of the two long spectra and the crosscorrelation of the two short spectra. However, the errors returned by fxcor was vastly different (by a factor of three, where the short spectra returned the larger error).
I am well aware the fxcor error is not a true representation of the error, and that montecarlo simulations have to be carried out to truly understand the uncertainty and how that behaves with variable SNR data. This notwithstanding, there is no reason why our two tests (on the long, or short version of the *same* spectrum, with identical spectral range) should have different fxcor errors.
We insured this difference is not due to fourier filtering (we kept fourier filtering off) and is not due to the apodization, nor is it due to continuum subtraction. Also, the shapes of the crosscorrelation functions for the two tests were identical.
We have no idea what might make such a difference for the calculation of the error. However, the error provided by fxcor is a fundamental number which measures the goodness of the fit to the crosscorrelation function and which, together with the result of the montecarlo simulation, gives an estimate of the real uncertainty on the measurement. The discrepancy between the errors returned by the two tests is therefore troublesome, and we need to understand it.
Do you know what might cause this difference?
Many thanks for all the help,
Steph
Mike Fitzpatrick wrote on May 17, 2007
Steph,
Without seeing the data and results for myself I can't comment specifically on why you get a difference, but at some level I'd expect the difference anyway. When you correlate the 32000 points and (I assume) define the sample region, what actually gets correlate is the apodized 32K points with a large zero range. However, when you extract those points to a new image you apodize the same area but do the FFT without the large zero area. I would be surprised if the CCF was exactly identical in these two cases.
The R-value error comes from the Tonry&Davis equation and depends of the CCF width and height; that width and height in turn depend on the fit to the CCF; that fit depends on the value of the CCF at each lag, the points used, weighting function, etc; and the velocity error depends on the center of the fitted function. I agree a factor of three seems excessive, but including/excluding just one point from the fit impacts the results pretty obviously as well. Hope this helps, if you'd like to post some plots or images I'll be glad to have a look.
-Mike
Without seeing the data and results for myself I can't comment specifically on why you get a difference, but at some level I'd expect the difference anyway. When you correlate the 32000 points and (I assume) define the sample region, what actually gets correlate is the apodized 32K points with a large zero range. However, when you extract those points to a new image you apodize the same area but do the FFT without the large zero area. I would be surprised if the CCF was exactly identical in these two cases.
The R-value error comes from the Tonry&Davis equation and depends of the CCF width and height; that width and height in turn depend on the fit to the CCF; that fit depends on the value of the CCF at each lag, the points used, weighting function, etc; and the velocity error depends on the center of the fitted function. I agree a factor of three seems excessive, but including/excluding just one point from the fit impacts the results pretty obviously as well. Hope this helps, if you'd like to post some plots or images I'll be glad to have a look.
-Mike
Last post on May 17, 2007