Integral Field Spectroscopy

An image and a spectrum at the same time

Two instruments dominated classical astronomy. A camera gives you a two-dimensional image — where the light is — but tells you almost nothing about its colour beyond a few broadband filters. A spectrograph gives you the detailed spectrum — the velocity, temperature, composition, and ionization encoded in spectral lines — but only along a thin slit, so you lose most of the spatial information. For a century you had to choose.

Integral field spectroscopy refuses the choice. It records a full spectrum at every position within a contiguous patch of sky, all in one shot. The result is not a picture and not a spectrum but a three-dimensional data cube: two axes are positions on the sky (x and y, in arcseconds), and the third axis is wavelength (λ). Slice the cube one way and you have a narrow-band image at a chosen wavelength; slice it the other way and you have the spectrum of any spot you point to. One observation, every spectrum, taken simultaneously under identical atmospheric conditions.

The instrument that performs the trick is an integral field unit (IFU). Its job is purely optical bookkeeping: reformat a two-dimensional field so that a conventional spectrograph can disperse all of it at once onto a detector, then unscramble the result in software back into a cube. The independent spatial samples are called spaxels — "spatial pixels" — and each one carries its own complete spectrum.

The data cube and the detector budget

The core difficulty is dimensional. A spectrograph detector is a flat two-dimensional array of pixels, but the cube you want to produce is three-dimensional. You must pack a 3-D object onto a 2-D sensor. Every IFU is a scheme for slicing the spatial field into many small pieces, laying those pieces out in a one-dimensional row to form a pseudo-slit, and then dispersing that pseudo-slit perpendicular to its length so each piece's spectrum lands on its own strip of detector. Reconstruction software later folds the strips back into the cube.

This makes IFU design a budgeting problem. Call the detector N_x × N_y pixels. You are dividing those pixels among three axes:

N_pixels  ≈  N_spaxels  ×  N_wavelength_channels

If you want a bigger field of view or finer spatial sampling (more spaxels), you have fewer pixels left for each spectrum, so you must shorten the wavelength range or lower the spectral resolution. Conversely, high-resolution spectroscopy of a tiny field can lavish many pixels on each spaxel's spectrum. There is no free lunch: the field of view, the spatial sampling, the wavelength coverage, and the spectral resolution all compete for the same finite detector real estate. This single constraint explains nearly every IFU design decision ever made.

Three ways to fill the cube

There are exactly three optical strategies for reformatting the field, and almost every IFU ever built uses one — or a combination — of them.

Lenslet arrays. A grid of thousands of tiny lenses (a microlens array) sits in the focal plane. Each lenslet samples one spaxel and focuses its light into a sharp micro-pupil — a tiny demagnified image of the telescope's aperture. The array of micro-pupils is then dispersed by a grism. Because each spectrum starts from a small, well-defined pupil, the spectra are compact and can be packed densely if the dispersion is tilted slightly to keep neighbouring spectra from overlapping. This is the original method, used by TIGER (1987), SAURON, and OSIRIS at Keck.

Fibre bundles. Each spatial element feeds an optical fibre. The fibres are packed in a bundle at the telescope end and rearranged into a straight line at the spectrograph end, forming the pseudo-slit. Fibres are flexible and can be routed anywhere, which makes them ideal for surveys that place many small bundles across a wide field — the SDSS-IV MaNGA survey deployed up to 17 hexagonal "hexabundles" of 19–127 fibres each across a single plate to observe many galaxies simultaneously. Fibres do scramble the pupil and lose a little light at the entrance, and gaps between fibre cores can require dithering (taking several offset exposures) to fill the field.

Image slicers. A stack of thin mirrors (the "slicer") cuts the field into long, narrow strips. A second set of mirrors picks off each strip and re-stacks them end-to-end into one very long virtual slit, which the spectrograph then disperses. Slicers are all-reflective, so they work from the ultraviolet to the mid-infrared, suffer no fibre losses, and preserve the full field with no gaps. They are the dominant modern choice: MUSE and KMOS on the VLT, and both the NIRSpec IFU and MIRI Medium-Resolution Spectrometer (MRS) on JWST, are image-slicer instruments.

The key numbers

Real instruments make the trade-offs concrete. Here is how the budget is spent across several major IFUs:

Instrument	Technique	Field of view	Spaxels / spectra	Wavelengths	R (λ/Δλ)
TIGER (CFHT, 1987)	Lenslet	~6″ × 6″	~400	Optical	~600
SAURON (WHT)	Lenslet	33″ × 41″	~1,500	4800–5380 Å	~1,300
MaNGA (SDSS-IV)	Fibre hexabundle	12–32″ per bundle	19–127 / bundle	3600–10300 Å	~2,000
MUSE (VLT)	Image slicer (×24)	1′ × 1′ (wide)	~90,000	4750–9350 Å	~3,000
SINFONI (VLT)	Image slicer + AO	0.8–8″	~2,000	1.1–2.45 µm	1,500–4,000
NIRSpec IFU (JWST)	Image slicer (30 strips)	3″ × 3″	~900	0.6–5.3 µm	~100–2,700
MIRI MRS (JWST)	Image slicer (4 channels)	3.2–7.7″	varies	4.9–28.1 µm	~1,500–3,500

MUSE is the workhorse extreme: its light is split into 24 identical spectrograph modules, each fed by an image slicer, so that a single exposure produces about 90,000 spectra over a one-square-arcminute field at 0.2″ spatial sampling. A full MUSE cube is roughly 300 × 300 spaxels by ~3700 wavelength channels — on the order of 3 × 10⁸ flux measurements from one pointing. JWST's NIRSpec and MIRI IFUs sacrifice field of view for the near- and mid-infrared windows that are inaccessible from the ground and impossible without a cold telescope in space.

From light to cube: how the measurement works

Turning raw detector frames into a science-ready cube is a substantial pipeline. The essential steps:

1. Reformat. The IFU optics convert the 2-D field into the dispersed strips described above. On the detector you see hundreds or thousands of short spectra side by side — visually a striped mess that means nothing until reconstructed.
2. Calibrate. Bias and dark subtraction, flat-fielding, and — crucially — wavelength calibration using arc lamps so that each pixel along a spectrum is assigned a true wavelength. Each spaxel has its own slightly different wavelength solution.
3. Extract and resample. Each spaxel's spectrum is traced and extracted, then resampled onto a common wavelength grid so every spaxel shares the same λ axis.
4. Reconstruct. The extracted spectra are placed back at their on-sky (x, y) positions, building the cube. Dithered exposures are combined and gaps interpolated.
5. Sky-subtract and flux-calibrate. The night sky's airglow lines are removed (a hard problem in the near-infrared, where OH bands dominate) and a standard-star observation sets the absolute flux scale.

Once you have the cube, the science begins. The most powerful first move is to extract, at every spaxel, the Doppler shift of a strong emission or absorption line. The line-of-sight velocity follows from

v_los = c × (λ_obs − λ_rest) / λ_rest

Map v_los across all spaxels and you have a velocity field — a picture of how the gas or stars are moving everywhere in the object at once. The width of the line at each spaxel gives the velocity dispersion σ, separating ordered rotation from random motion.

Worked example: the velocity resolution of MUSE

How finely can MUSE measure a velocity? Take its nominal resolving power near the centre of its range, R ≈ 3000 at λ ≈ 7000 Å. The resolution element in wavelength is

Δλ = λ / R = 7000 Å / 3000 ≈ 2.3 Å

The velocity that corresponds to one resolution element is

Δv = c × Δλ / λ = c / R = 300,000 km/s / 3000 ≈ 100 km/s

That is the full width of the instrumental line-spread function — but it is not the smallest velocity you can measure. The centroid of a well-detected emission line can be located to a small fraction of a resolution element, roughly Δv / (signal-to-noise), so a line at S/N ≈ 20 yields a velocity centroid good to about 100/20 ≈ 5 km/s. This is why MUSE can resolve the few-tens-of-km/s rotation of a faint dwarf galaxy even though its resolution element is 100 km/s wide.

Now the budget side. A galaxy filling MUSE's 1′ field at 0.2″ sampling spans about 300 × 300 = 90,000 spaxels. Each spectrum runs from 4750 to 9350 Å sampled at 1.25 Å per pixel — about 3680 wavelength channels. The cube therefore holds 90,000 × 3680 ≈ 3.3 × 10⁸ independent flux values, every one acquired in the same exposure. A long-slit spectrograph reproducing that field by stepping a 0.2″-wide slit across 300 positions would need 300 separate exposures — and the seeing and transparency would drift between the first and the last.

A short history

The conceptual leap came from Georges Courtès at the Marseille Observatory, who proposed using microlens arrays for spectro-imaging in the 1980s. The first working integral field spectrograph, TIGER, was built by his group (Roland Bacon and colleagues) and saw first light on the Canada-France-Hawaii Telescope in 1987 — a lenslet array of a few hundred elements. The technique was refined through the 1990s with fibre-coupled designs (DensePak on the WIYN telescope) and the TIGER-style lenslet-array SAURON spectrograph (first light 1999) on the William Herschel Telescope.

SAURON drove a watershed result. The ATLAS3D survey, mapping 260 nearby early-type galaxies with SAURON, showed that most elliptical and lenticular galaxies are not the featureless, dispersion-supported "pressure balls" of textbook lore: the majority are fast rotators with regular, disk-like velocity fields, while only a minority are genuinely slow-rotating. That reclassification of galaxy structure was only possible because IFS measures the full two-dimensional velocity field rather than a single slit.

The 2010s were the era of scale. MUSE (Roland Bacon again, lead PI) achieved first light on the VLT in 2014 and became the most productive optical spectrograph in the world. Massive IFU galaxy surveys followed — SAMI (Anglo-Australian Telescope) and SDSS-IV's MaNGA, which observed roughly 10,000 nearby galaxies with fibre hexabundles between 2014 and 2020. In 2022, JWST brought two cryogenic image-slicer IFUs to space — the NIRSpec IFU and the MIRI MRS — extending spatially resolved spectroscopy into the near- and mid-infrared and out to the earliest galaxies.

IFS versus other spectroscopic methods

Method	Spatial info	Spectra per exposure	Best for	Main limitation
Long-slit	1-D line	One slit's worth	Single targets, rotation curves along one axis	Must scan to map 2-D; conditions drift between steps
Multi-object (MOS)	Points, many targets	One spectrum per object	Surveys of many separate sources	No spatial detail within each object
Fabry-Pérot / tunable filter	Full 2-D, one λ at a time	One narrow band	Narrow wavelength ranges, single lines	Scans in wavelength, not simultaneous spectra
Slitless spectroscopy	2-D but overlapping	Whole field, blended	Sparse fields, redshift surveys	Spectra overlap in crowded fields
Integral field (IFS)	Full contiguous 2-D	Hundreds to ~90,000	Resolved maps of velocity, composition, ionization	Small field of view; detector budget caps coverage

The defining advantage of IFS is simultaneity over a filled field. The Fabry-Pérot scans wavelength; the long slit scans space; multi-object spectroscopy gives one spectrum per target with no internal structure. Only the IFU delivers a complete, gapless spectrum for every position in a single integration — which is exactly what you need when the thing you are studying is changing across its own face.

Variants and frontiers

• AO-fed IFS. Coupling an IFU to adaptive optics (SINFONI, OSIRIS, MUSE's narrow-field mode) recovers near-diffraction-limited sampling, letting you resolve clumps inside distant galaxies or the gas around the Galactic-Centre black hole Sgr A*. MUSE's narrow-field mode reaches ~0.05″ sampling.
• Multi-IFU surveys. Deploying many small IFUs across a wide field — KMOS's 24 deployable arms, MaNGA's 17 hexabundles, SAMI's 13 — turns one exposure into resolved spectroscopy of dozens of galaxies, the workhorse for statistical kinematic surveys.
• Wide-field "spectro-photometric" cubes. MUSE-class instruments are now used to find emission-line galaxies blindly at high redshift by scanning the cube for faint Lyman-α emitters with no prior imaging.
• Cryogenic space IFUs. JWST's NIRSpec IFU and MIRI MRS open the 0.6–28 µm window, where redshifted optical lines from the first billion years of cosmic history finally fall.
• Densified-pupil and slicer hybrids. Next-generation extremely-large-telescope instruments (e.g. HARMONI for the ELT) scale image-slicer IFS to 39-metre apertures with tens of thousands of spaxels at near-diffraction-limited resolution.

Common misconceptions and subtleties

• "A spaxel is just a pixel." No — a pixel stores one number (a brightness); a spaxel stores an entire spectrum, often thousands of numbers. The detector pixels that record those spectra are a separate, much larger population.
• "The cube is observed directly." The detector never sees a cube. It sees a scrambled mosaic of short dispersed strips; the cube is a software reconstruction. Errors in tracing, wavelength calibration, or dither registration imprint artefacts that masquerade as real structure.
• "More spaxels is always better." Spaxels finer than the seeing (or the AO point-spread function) are correlated, not independent — you gain Nyquist sampling but not genuinely new spatial information, and you spend detector pixels you could have used for wavelength coverage.
• "IFS gives perfect spatial resolution." Ground-based IFS without AO is still limited by atmospheric seeing (~0.6–1″), which blurs neighbouring spaxels together. The cube's spatial resolution is set by the seeing or the PSF, not by the spaxel size.
• "Fibre and slicer cubes are equivalent." Fibres scramble the pupil and have inter-core gaps requiring dithering; slicers are gapless and all-reflective but harder to build for very large fields. The reconstruction systematics differ, and they matter when chasing faint velocity gradients of a few km/s.