Note: Intro -- Half title -- Title -- Copyright -- Contents -- Contributors -- Participants -- Preface -- Acknowledgements -- Abbreviations -- 1. Introductory review and technical approaches -- 1.1 Preface -- 1.2 Introductory review -- 1.2.1 Conceptual outline -- Principle of operation and terminology -- Methods of image dissection: spatial sampling -- Detectors and spectrographs -- Spectral resolution and wavelength coverage -- Coupling the IFU to the spectrograph -- Examples of real IFUs -- Extracting the spectra -- Data representation, data formats -- Data analysis -- 1.2.2 Comparison with classical techniques -- A posteriori advantage, pointing -- Slit e.ects -- Atmospheric refraction -- Spatial binning -- Differential spectrophotometry -- Crowded .eld 3D spectroscopy -- Ultra-deep faint object 3D spectroscopy -- 1.3 A brief history of 3D spectroscopy -- 1.4 Technical approaches -- 1.4.1 Optical fibers -- 1.4.2 Lens arrays -- 1.4.3 Lens array - fiber hybrids -- 1.4.4 Slicers -- 1.4.5 Non-IFS 3D instruments -- 1.4.6 3D detectors -- 1.4.7 Special techniques -- Multi-slit masks -- Nod-shu.e 3D spectroscopy -- 1.4.8 Figure-of-merit -- 1.5 Acknowledgments -- REFERENCES -- 2. Observational procedures and data reduction -- 2.1 Introduction -- 2.2 Background -- 2.3 Observing strategies -- 2.3.1 IFUs versus other instruments -- 2.3.2 The observing process -- Overview -- Acquisition -- Object and sky spectra -- Integration times -- Dithering and mosaicking -- Flat-fielding -- Wavelength calibration -- Telluric calibration -- Flux calibration -- Detector bias -- Dark current -- Summary of observing strategies -- 2.4 Sampling images -- 2.4.1 The Sampling Theorem -- 2.4.2 Undersampling -- 2.4.3 Sampling images -- 2.4.4 Practical issues -- Finite pixel size -- Noise -- Practical interpolants -- Irregular sampling. , 2.4.5 Summary and application to astronomical data -- 2.5 Overview of data reduction issues -- 2.5.1 Common steps -- 2.5.2 Detector linearity and saturation -- 2.5.3 Detector bias subtraction -- 2.5.4 Consolidating and formatting the data -- 2.5.5 Flat-fielding -- 2.5.6 Cosmic ray and bad pixel correction -- 2.5.7 Instrumental background -- 2.5.8 Spatial calibration -- 2.5.9 Wavelength calibration -- 2.5.10 Extraction -- 2.5.11 Sky subtraction -- 2.5.12 Telluric correction -- 2.5.13 Flux calibration -- 2.5.14 Reconstruction in 3D -- 2.5.15 Atmospheric dispersion -- 2.5.16 Dithering and mosaicking -- 2.5.17 Spatial binning -- 2.5.18 Summary of data reduction issues -- 2.6 Data reduction process -- 2.6.1 Reduction sequence -- 2.6.2 Error propagation -- 2.6.3 Data quality -- 2.6.4 File storage format -- 2.6.5 Formats for reduced data -- 2.6.6 Summary of the data reduction process -- 2.7 Acknowledgements -- REFERENCES -- 3. 3D spectroscopy instrumentation -- 3.1 Fundamental challenges and considerations -- 3.1.1 The detector limit I: six into two dimensions -- 3.1.2 Merit functions -- 3.1.3 Why spectral resolution is so important -- 3.1.4 The detector limit II: read noise -- 3.2 Grating-dispersed spectrographs -- 3.2.1 Basic spectrograph design -- 3.2.2 Dispersive elements -- Re.ection gratings -- Transmission gratings -- 3.2.3 VPH grating operation and design -- Blazed VPH gratings -- Unusual VPH grating modes -- 3.2.4 Summary of implications for 3D spectrograph design -- 3.2.5 Coupling formats and methods: overview -- 3.2.6 Direct fibre coupling -- Information loss and stability gain with fibres -- Telecentricity -- Causes of FRD -- Quality versus quantity -- Image reconstruction and registration -- Summary of instruments -- 3.2.7 Fibre + lenslet coupling -- 3.2.8 Slicer coupling -- 3.2.9 Direct lenslet coupling. , 3.2.10 Filtered multi-slit (FMS) coupling -- 3.2.11 Multi-object configurations -- 3.2.12 Summary of considerations -- Information selection and reformatting -- Coverage versus purity -- Sky subtraction -- 3.3 Interferometry I: Fabry-Perot interferometry -- 3.3.1 Basic concepts and field widening -- 3.3.2 FP monochromators -- 3.3.3 FP spectrometers -- 3.3.4 3D FP spectrophotometers -- Grating-dispersed FPI -- Pupil-imaging FPI -- 3.3.5 Sky stability -- 3.3.6 Examples of instruments -- 3.4 Interferometry II: spatial heterodyne spectroscopy -- 3.5 Summary of existing instruments -- 3.6 The extended-source domain -- 3.7 Future instruments -- 3.7.1 Ground-based instruments on 10m telescopes -- 3.7.2 Ground-based instruments on 30-50m-class telescopes -- 3.7.3 Space-borne instruments -- 3.7.4 Summary of future instruments -- Acknowledgements -- REFERENCES -- 4. Analysis of 3D data -- 4.1 Introduction -- 4.1.1 Presentation and scope -- 4.1.2 Data analysis -- 4.2 Data, noises, biases and artifacts -- 4.2.1 Where is the signal? -- 4.2.2 Noises -- 4.2.3 Biases or systematic errors -- Systematic error: example -- 4.2.4 Artifacts -- The artifacts and the resampling of data -- 4.3 Image reconstruction and datacube visualization -- 4.3.1 From a cube to an image -- 4.3.2 Datacube visualization -- 4.4 Getting rid of atmospheric effects and undesired backgrounds -- 4.4.1 Sky emission, zodiacal light and thermal background -- 4.4.2 Subtracting a background -- 4.4.3 Where things can get even more complicated -- Beware of instrumental e.ects -- The case of atmospheric absorption features -- Atmospheric refraction -- 4.5 From a collection of datacubes to a single one -- 4.5.1 Drizzling -- 4.5.2 The deep-field approach -- Relative positioning -- Relative normalization -- Ready to co-add? -- A simple illustrated example -- 4.5.3 Mosaicking. , Differences with the deep-.eld approach -- Relative registration and normalization of the exposures -- Simple illustrated examples -- 4.6 Smoothing and binning -- 4.6.1 Smoothing data -- 4.6.2 Binning -- 4.7 Data mining and crowded-field spectrophotometry -- 4.7.1 Data mining -- 4.7.2 Crowded-field spectrophotometry -- 4.8 Model fitting -- 4.8.1 The example of stellar continuum fitting -- 4.8.2 A step-by-step example of emission-line fitting -- Systems and constraints -- Initial conditions -- Fitting the data -- Determining the error bars -- The all-in-one and ultimate solutions -- 4.9 Conclusions -- REFERENCES -- 5. Science motivation for integral field spectroscopy and Galactic studies -- 5.1 Science motivation -- 5.1.1 Motivation for integral field spectroscopy -- 5.1.2 Fundamental considerations based on technical constraints -- 5.1.3 Ideal and unsuitable objects for integral field spectroscopy -- 5.1.4 Examples of integral field spectroscopic studies -- 5.1.5 Galactic versus extragalactic science -- 5.1.6 Overview of Galactic science -- 5.2 The black hole in the Galactic Centre -- Excursion: history of supermassive black holes -- Excursion: line of argument for proving the Galactic Centre black hole -- 5.2.1 The nuclear cluster of the Milky Way: star formation and velocity dispersion in the central 0.5parsec -- Excursion: Stellar spectra of early- and late-type stars in the infrared -- Excursion: from velocity to mass I: the virial theorem -- Excursion: from velocities to mass II: Bahcall-Tremaine estimator -- 5.2.2 The dark mass concentration in the central parsec of the Milky Way -- 5.2.3 Stellar dynamics in the Galactic Centre: proper motions and anisotropy -- Excursion: from velocity to mass III: the Leonard-Merrit estimator -- Excursion: from accelerations and orbits to mass. , 5.2.4 A geometric determination of the distance to the Galactic Centre -- 5.2.5 SINFONI in the Galactic Centre: young stars and infrared flares in the central light month -- Excursion: SrgA* does not move -- Excursion: hot spots on the last stable orbit -- 5.2.6 Again: SINFONI in the Galactic Centre: young stars and infrared flares in the central light month -- Excursion: the Eddington luminosity -- 5.3 The stellar population in the Galactic Centre -- 5.3.1 The nuclear cluster of the Milky Way: star formation and velocity dispersion in the central 0.5parsec -- Excursion: stellar population modelling -- 5.3.2 The dark mass concentration in the central parsec of the Milky Way -- Excursion: The paradox of youth -- 5.3.3 Stellar dynamics in the Galactic Centre: proper motions and anisotropy -- 5.3.4 Stellar disk in the Galactic Centre: a remnant of a dense accretion disk? and the stellar cusp around the supermassive black hole in the Galactic Centre -- 5.3.5 SINFONI in the Galactic Centre: young stars and infrared flares in the central light month -- 5.4 Star formation -- Excursion: star formation in a nutshell -- Excursion: T Tauri and RW Auriga stars -- 5.4.1 A near-infrared spectral imaging study of T Tau -- Excursion: molecular hydrogen lines in the infrared -- Excursion: H2 line diagnostics -- 5.4.2 Spatially resolved imaging spectroscopy of T Tauri -- Excursion: microjets in pre-main sequence stars -- 5.4.3 The RW Aur microjet: testing MHD disc wind models -- 5.4.4 Sub-arcsecond morphology and kinematics of the DG Tauri jet in the [OI]6300 line and DG Tau: a shocking jet? -- 5.4.5 The three-dimensional structure of HH 32 from GMOS IFU spectroscopy -- Excursion: line ratio diagnostics in the optical -- Excursion: high-mass star formation -- 5.4.6 Collimated molecular jets from high-mass young stars: IRAS 18151-1208. , 5.4.7 GEMINI multi-object spectrograph integral field unit spectroscopy of the 167--317 (LV2) proplyd in Orion.