Integral field spectroscopy

This is a brief description of the principles of integral field spectroscopy, mainly using fibre-lenslet techniques. It is meant to serve as a link to the GEMINI Multiobject Spectrographs and Durham Astronomical Instrumentation Group: Spectroscopy Programme pages which contain a list of current instrumentation projects . It is not meant to be comprehensive and apologies are offered for not giving credit or references to the the many other workers in this field.

Click here for James Turner's IFU data reduction software page

For a summary, please see the paper given at the 1998 SPIE large telescope conference in Kona Sweden in March 1998 (gzipped postscript 0.5Mb). An older paper given at the 1996 SPIE large telescope conference in Sweden in May/June 1996 (Postscript 0.3Mb) is also available.

A general paper on sampling and background subtraction (0.4Mb, gzip postscript). in fibre-lenslet IFUs has been accepted by PASP (Allington-Smith and Content).

Beyond longslit spectroscopy

This cannot be done with a longslit except in one dimension defined by the length of the slit. However the longslit can be stepped in position across the target by moving the telescope and recording separate exposures for each position. But this is time-consuming since the effective exposure time is multiplied by roughly the ratio of the object size to the width of the slit.

Other techniques are available such as Fabry-Perot scanning. This allows a large object to be surveyed in a single exposure but only at a single wavelength (which depends on position within the field) so that the required data volume with axes labelled by x-position, y-position and wavelength must be built up via a series of exposures. As with stepped longslit spectroscopy, this is an inefficient use of telescope time.

Techniques which record spectra from each part of an object simultaneously are termed Integral Field Spectroscopy (Figure 1). The terms two-dimensional spectroscopy or three-dimensional imaging are also used, although, strictly, they include non-simultaneous techniques as well.

Basic techniques

• Lenslet arrays. The input image is formed at the input surface of a microlens array (MLA). These form images of the telescope pupil which are then dispersed by the spectrograph. The pupil images are smaller than the aperture of each microlens so that light from each segment of the input image is concentrated into a dot. Because the dots are small, it is possible to tilt the MLA about the optical axis of the system so that the spectra do not fall on top of each other. This technique allows the input image to be sampled contiguously and is not subject to FRD so that the throughput and spectral resolution can be optimised, but the length of spectrum that can be produced without overlapping is very small.

• Fibre bundles. The input image is formed at the entrance to a bundle of fibres which transfer the light to the slit of the spectrograph. The flexibility of the fibres allows a round field of view to be reformatted into one (or more) slits so that the spectra are obtained without wavelengths shifts between them. The disadvantages of this techniques are: (a) the sampling of the sky is not contiguous since there are gaps between the fibre cores and (b) the fibres do not work efficiently at the slow focal ratios at which most telescopes work.

  The latter problem occurs due to Focal Ratio Degradation (FRD) which causes the focal ratio of the beam emerging from the fibre to be faster than that at the input. This problem is especially bad for slow beams (e.g. f/16 for GEMINI) but can be negligible for fast beams (f/5 or faster) provided that fibres of the best quality are used. FRD translates into a violation of the Etendue (solid angle - aperture product) invariant in optical systems with the result either the throughput or spectral resolution is degraded. Fibre throughput is not generally a problem since the fibres are usually quite short, unless working far in the ultraviolet.

• Image slicers . The input image is formed at a segmented in thin horizontal sections which are then sent in slightly different directions. A second segmented mirror is arranged to reformat the slices so that, instead of being above each other they are now laid out end to end to form the slit of the spectrograph (actually a virtual slit). The advantage of this technique is that FRD is avoided and the slicing arrangement gives contiguous coverage of the field. Because this system uses only mirrors, it is especially suitable for the infrared since it is inherently achromatic and can be cooled to cryogenic temperatures. Potential disadvantages are: (a) that the sampling along the slices is the same as that provided naturally by the telescope so there is reduced scope to optimise for use with a spectrograph that must also work in a normal slit-spectroscopy mode and (b) the optical system might be bulky and difficult to fabricate.

In some cases, these techniques require the telescope focus to be magnified so that either the physical size of the devices can be made more manageable and/or to adjust the focal ratio of the input telescope beam. This requires the use of fore-optics , generally a pair of achromatic lenses.

Integral field spectroscopy in Durham

• A combination of fibre bundles and lenslet arrays in which the pupil images formed by the MLA are relayed by optical fibres and reformatted to form the spectrograph slit via matching output microlenses at the fibre output (in the form of linear MLAs) (see Figure 2 and Figure 3).

  This gives the potential benefits of both the reformatting ability of fibres and the contiguity of microlens arrays with the additional benefit that the microlens allow the slow telescope focal beam (f/16 for GEMINI) to be slowed down (to about f/4) so that FRD can be minimised. Fore-optics are needed to magnify the telescope focal plane so that the spacing of the fibres on the input is not too small and to provide telecentric correction so that the principal rays strike the microlenses square on ( Figure 4).

• Image slicing based on the image slicing technique described above. Some of the technical disadvantages might be solved by putting power on the currently flat surfaces of the slicing mirrors.

Basic parameters

• Field of view: around 10 arcsec in linear dimension (roughly square or circular)

• Spatial sampling: such as to adequately sample the expected image size at the input. For the case of an AO-corrected 4-m telescope or the GEMINI telescopes, the expected image size is typically 0.4 arcsec FWHM so the sampling needs to be around 0.2 arcsec/element. Rarer conditions of enhanced seeing (e.g. 0.25 arcsec FWHM at 10th percentile for GEMINI) would benefit from better sampling around 0.1 arcsec/element.

• Background subtraction: Unless the field is very large there will be times when the object of interest completely fill the field of view. In these cases, a separate field dedicated to sampling the sky background, the background field , is required. This should be placed on the sky as far away as possible from the object field.

Technical issues

• Field of view. Since the technique works by reformatting a 2-D area into a 1-D line, the area of the field of view is limited by the product of the number of detector pixels in the spatial direction and the number of output slits divided by the allowable spacing (in pixels) between adjacent spectra.

  In principle, multiple slits, each of which occupies the full spatial extent of the detector, can be provided by offsetting them in the dispersion direction so that the resulting spectra are arranged in multiple tiers (Figure 4). The spectra will not overlap if band-pass filters are used.

  The spacing of the spectra is dictated by technical issues such as sampling, aberrations and the allowable cross-talk between adjacent spectra. Cross-talk can be tolerated if neighbouring elements of the slit are also adjacent on the sky (Figure 5). Therefore intensity variations between adjacent parts of the sky will be reflected in the way in which the light from adjacent slit elements overlap spatially in the spectrograph. In fact, the optimum sampling strategy is that each FWHM of the input image at the input to the MLA should be sampled by two slit elements. This ideal situation is generally severely limited by other considerations but the general message is that the spectra should be packed together as closely as possible so that the distribution of light on the detector is similar to that which would have been obtained from a longslit sampling the sky directly.

  The detection process is summarised in Figure 6.

  In some cases, adjacent spectra must be separated by a clean gap. This is true for elements which sample a background field which may be well separated on the sky from those elements sampling the object. Also it will be necessary to have clear areas of the detector from which to estimate the background signal caused by scattered light within the spectrograph.

• Background subtraction. As far as possible, the object and background fields must share the same optical path. One way to do this is to duplicate the entire optical train, linking them only at the output slit. Within the context of a microlens/fibre system, there would be two separate fore-optics and MLAs whose fibres would be mixed together at the spectrograph slit. The background and object fibres would be grouped together in blocks to avoid cross-talk between unrelated regions of the sky, but be alternated in position within the slit so that any errors related to the position within the spectrograph field cancel out. In general, these blocks will be matched to continuous regions of the object or background fields (Figure 5).

  Since the total number of slit elements is fixed by the detector size, number of output slits and spectrum spacing, only a small proportion of the total number of elements can be dedicated to the background field without restricting the size of the object field. Roughly speaking, we may allow a 90:10 split between the object and background fields, leading to a negligible reduction in the linear size of the object field.

  There are subtle problems with sky-subtraction using fibres arising from possible variations in the details of the point-spread function between fibres due to high-order FRD-type effects. These may affect the detailed line profiles so that the subtraction of a bright sky-line in one spectrum from that in another may give a significant non-zero residual even when variations in the throughput (as a function of wavelength) of each element is calibrated out. One way to eliminate this effect is to beam-switch between the object and background fields, which we shall now label A and B (Figure 7). The observation is broken down in to pairs of exposures 1 and 2.

  • In exposure 1, field A samples the object and B samples the background.

  • The telescope is then offset by an amount equal to the spatial separation between fields A and B. The result is that in exposure 2, field B samples the object while field A samples the background (actually on the opposite side of the object from the first background field sampled).

  By forming linear combinations of the signal obtained from each element in exposures 1 and 2, the true object signal can be obtained. Since the same physical elements have been used to sample both object and sky, the background signal can be completely eliminated. Since the background field is smaller than the object field, the field over which true beam-switching can be done is only as large as the background field. However, sky-subtraction will still be possible over the rest of the field, but the precision may not be as great. In some cases, where the object is relatively small (e.g. a distant galaxy a few arcsec in extent), it will also be acceptable to derive the background signal from elements within the object field itself, generally at the edge.