Flats in slitless spectroscopy

[Andrew Smith]

I have pondered long on the use of flats with slitless spectroscopy. I know they are used but can’t see how they work correctly.

In conventional imaging or in slit spectroscopy (with a perfectly flat field illumination source matching the focal ratio of the telescope) the light falling on a particular pixel has followed the same optical path for both the flat and target. (By optical path I mean route taken by the parallel bundle of rays passing through the aperture stop at the same angle.) Since both light sources have suffered an equivalent amount of vignetting, dust etc. then the flat can be used to correct for these. If in addition the spectral range of the flat and source are the same or are reasonably similar then pixel non-uniformity can also be corrected.

My problem is this: while all the light from a particular point target (say a star), of a particular wavelength and spectral order follows a particular path through the optics the same is not true for the light of the flat falling on the same pixel(s).

The light from the flat will have components from the directly “imaged” first order and from other orders diffracted to it from a locus of point across the field in the direction of the dispersion. Thus the light from the flat and the light from the star do not follow the same path through the optics and don’t have similar spectral balance. So, the total flux on a pixel will depend where in the field it is and not be proportional to the degree of vignetting and dust levels seen by the star light. This means that the flat field correction will not be accurate and be different across the field.

If I am right this can have an impact if the star used to calculate the instrumental response and target star are not at the same location on the CCD. I don’t see a way round this other than imaging them on the same location of the CCD.

Am I right or have I missed something important?

Regards Andrew

[Robin Leadbeater]

Hi Andrew

You are not alone

I would be interested in any references showing how flats for slitless systems work.
I do not have a quantitative explantion but I do have some qualititative hand waving arguments about what they can and need to correct for though.

I suspect the correction of defects which originate after the light has passed through the grating are not a problem as they should be corrected as for conventional flats (eg pixel to pixel sensitivity variations, dust on the cover glass, etc)

Defects which originate before the grating are more interesting. Consider a symmetric vignetting of the field in this region for example.
If the grating was not present this would produce a symmetric effect in the flat field. With the grating in place this vignetting in the flat becomes asymmetric, effectively eliminating the vignetting in the direction of the dispersion (ie typically at the right hand edge.)
This is certainly neccesary to give the correct spectrum image after flat fielding. The spectrum of a star placed on the optical axis for example should not be affected by any vignetting before the grating and so neither should the spectrum image. The asymmetric vignetting produced in the flat accomplishes this. The flat should also work correctly if the star is say offset near the left edge of the field (assuming that that the spectrum runs from left to right) ie in the vignetted area. The result is also qualitatively correct in this case, ie the flat makes the zero order and the spectrum brighter in the image but its shape should not be affected by the vignetting.

In a slit spectrograph flat, the flat also contains the spectrum of the flat lamp and the spectral response of the camera and grating. In a slitless flat, these efects will be smeared out but I suspect are not completely removed as there will always be some edge to the field which will act like a very wide poorly defined slit. In slit spectrographs these effects are cancelled out after flux calibration with a known star. But with a slitless flat where the target and reference spectra are not necessarily in the same X position it is not obvious to me that this will be the case.

My way round this in the past is to place the reference and target spectra as near as possible in the same location in the field but this is not always possible, particularly with the T-Tauri campaign where spectra of more than one star in the same field are recorded simultaneously.

The flat field of my system (a T shirt sky flat) appears to be pretty level with no obvious vignetting and just a few dust donuts on the CCD cover glass but I have just heard from someone where their flat has some interesting gradients in it so it seems the theory of flat fielding slitless systems is about to become a practical issue


Cheers
Robin

[Robin Leadbeater]

Attached is the variation across the flat (Horizontal slices at top middle and bottom of the the field) for my system shown here.
http://www.threehillsobservatory.co.uk/ ... _setup.jpg
There is not really enough variability (+-1% in the region where the spectra can possibly fall, to the right of pixel 200 for a star on the far left edge) to test if it works correctly in practise though. It might be interesting to see if the gradual drop on the left edge aso appears on the right edge if the grating is removed.

Cheers
Robin

[Robin Leadbeater]

Here is what is done for the grism spectrographs on the HST
http://www.jstor.org/stable/10.1086/596715

Based on a quick read through, it appears they took a set of direct imaging flats at different wavelengths to produce a "flat cube" They then modified this based on the effect the grism has on the direct image flat field. (by imaging a standard star at various positions within the field) The total correction is then applied to each pixel in turn once it is known what wavelength the pixel is receiving ie after wavelength calibration.



Robin

[Andrew Smith]

Thanks Robin - I will study and come back after due consideration! Regards Andrew

[Andrew Smith]

Hi Robin – I have had a look at the reference you gave and also at this http://www.stsci.edu/hst/acs/documents/isrs/isr0502.pdf which gives more details on how the flat fields (FF) were created.

It seems to me that the flat cube is more about removing the wavelength dependant pixel to pixel response (PNU) than vignetting although this will be included. As these were taken without the grism (i.e. direct images) it does not address the asymmetric nature of the FF with the grism in place.

I don’t think that “With the grating in place this vignetting in the flat becomes asymmetric, effectively eliminating the vignetting in the direction of the dispersion (ie typically at the right hand edge.)” is quite right. While it gives a more uniform total response it does this by adding flux from additional optical paths to that taken by the target flux. I certainly came across this when experimenting with my imaging low resolution spectrograph and I am sure if you remove your grating the response on the right hand edge will drop off. This mismatch in paths is the basis of my issue while the flux is better it is not from the correct optical path. Maybe what is best depends on which is more significant in your system vignetting or PNU.

I suspect we could discuss this for a long time and some experiments are needed. I should have a SA based system up and running soon and propose trying the following.

Image the same bright A type star at 6 locations across the CCD in quick succession with short exposure to limit changes between the images. Process them in the same way using ISIS once with a direct image FF and again with a SA FF. Then compare them to see which gives the most uniform results across the field and if there are significant differences between the two methods.

The HST paper also mention different dispersion across the CCD due to geometric distortions I will look for signs of these as well by my Newtonian should not be too bad over the size of field involved.

Regards Andrew

[Robin Leadbeater]

Hi Andrew,

The HST paper also mention different dispersion across the CCD due to geometric distortions I will look for signs of these as well by my Newtonian should not be too bad over the size of field involved.

There might perhaps be a small effect in our case if any refocussing is needed for different parts of field, which would change in distance from the grating, but I think the position dependent dispersion effects due to distortion of the field mentioned here are most likely caused by the optics after the dispersing element so should not be present in our simple system. (THE HST setup will be a collimated arrangement with a camera lens after the grism.) I have wondered in the past if Star Analyser systems in which a focal reducer/field flattener is positioned after the grating might potentially suffer from this problem though, also objective grating setups where the grating is mounted in front of a DSLR lens for example.

Cheers
Robin

[Robin Leadbeater]

I don’t think that “With the grating in place this vignetting in the flat becomes asymmetric, effectively eliminating the vignetting in the direction of the dispersion (ie typically at the right hand edge.)” is quite right. While it gives a more uniform total response it does this by adding flux from additional optical paths to that taken by the target flux. I certainly came across this when experimenting with my imaging low resolution spectrograph and I am sure if you remove your grating the response on the right hand edge will drop off. This mismatch in paths is the basis of my issue while the flux is better it is not from the correct optical path. Maybe what is best depends on which is more significant in your system vignetting or PNU.

Well I did say it was a hand waving argument

As far as I can see, using a flat taken without the grating in which the light drops off at the right hand edge due to vignetting before the grating would definitely not give the right answer as the light from the star would not have been affected by vignetting in that area. It will be interesting to see if a flat with the grating in place works correctly though. As an extreme test it might be interesting to deliberately add a severely vignetting field stop before the grating.

Cheers
Robin

[Robin Leadbeater]

As an extreme test it might be interesting to deliberately add a severely vignetting field stop before the grating.

Thinking about it, and taking it to the extreme, this is what a slit spectograph is. A flat taken without the grating would definitely not do the job in this case

Robin

[Andrew Smith]

[quote="Robin Leadbeater
As far as I can see, using a flat taken without the grating in which the light drops off at the right hand edge due to vignetting before the grating would definitely not give the right answer as the light from the star would not have been affected by vignetting in that area. It will be interesting to see if a flat with the grating in place works correctly though. As an extreme test it might be interesting to deliberately add a severely vignetting field stop before the grating.

Cheers
Robin[/quote]

I know it seems wrong but as far as I can see that is what is done on HST they use direct image flats! They then added a correction from the white dwarf tests which may have corrected for this.

In my view neither a direct image FF or a SA FF will give the correct answer but for oposite reasons. In the direct image FF (and as you say) the target light would not have experienced the same vignetting as the FF. In the SA FF the FF, at any point, has contributions from flux which has not been through the same optical path as the object flux at that point and hence experienced different degrees of vignetting.

In any case we will need an agreed approach for the T Tauri work.

Regards Andrew