The finesse is then the ratio of inter-order spacing and bandwidth. The finesse is the parameter that defines the performance of a real etalon. This is commonly approximated for an ideal etalon by f=S (10.9)

Etalons with high finesse give sharper transmission peaks with lower minimum transmission coefficients.

The value of the finesse can be understood roughly as the number of reflections an average photon makes before being transmitted through thee system.

There are three types of finesse values: reflection, defect and aperture finesse. The aperture finesse is negligible for most astronomical objects and observational modes. The final effective finesse is a combination of the three different types.

10.4. From theory to practical design

By 1970 the Astronomy Group of Imperial College London had begun the development of a piezo-tuned Fabry-Perot system using capacitance sensors to servo stabilize the cavity. The first prototype servo-stabilized FP, known as CasFPer, was first tested in the 2.5-m Isaac Newton Telescope at Herstmonceux, Sussex. This first-generation device was piezo-tuned, mechanically aligned and capacitively stabilized (Atherton 1995).

Queensgate Instruments was born in 1979 in the basement of the Physics Department of Imperial College (the Astronomy Group of Imperial College moved in 1978 to a new building on Queens Gate). Most of the etalons operating in astronomical installations have been manufactured by this company (Queensgate is now called ICOS). It manufactures etalons of aperture up to 150 mm that are tunable over a few micrometres. The surface reflectivity varies from 92% with hard coatings to up to 96% with soft coatings, and the surface flatness quality reaches up to A/200.

The Queensgate etalon served as the base for a series of Fabry-Perot interferometers in operation in the last few decades.

• TAURUS: a Fabry-Perot imaging device designed to obtain complete seeing-limited radial-velocity field maps of extended emission-line sources. A servo-controlled Fabry-Perot interferometer was used with a focal reducer and a two-dimensional photon-counting (area-detector) system was used to obtain the velocity information. Three versions of the instrument were eventually built. TAURUS Mk1 (TAURUS-1) was originally available on the Isaac Newton Telescope. TAURUS Mk2 (TAURUS-2) was used with the William Herschel Telescope. Finally, a TAURUS instrument was in operation at the Anglo-Australian Telescope (Taylor & Atherton 1980).

• HIFI: Hawaii Imaging Fabry-Perot Interferometer. This used a large-FSR etalon with high finesse and a charge-coupled device (CCD) at the image plane. The geometrical integrity of the CCD produced a clean Airy surface and bypassed the optoelectronic distortions of image intensifiers. The high quantum efficiency and linearity over a wide dynamic range in intensity proved to be essential in studies of extended narrowline regions (Bland & Tully 1989).

• The Ohio State Imaging Fabry-Perot Spectrometer was designed and built by the Ohio State University Astronomical Instrumentation Facility. It was designed for two-dimensional-imaging spectrophotometric and kinematic studies in the wavelength range of 3400-10 000 A, and was used for both imaging Fabry-Perot spec-trophotometry and direct imaging in broad- and narrow-band filters (with the etalons removed from the beam). It used four Queensgate Instruments ET-50 etalons (Pogge et al. 1995).

10.4.1 Gap-scanning etalons In order to manufacture a tunable Fabry-Peerot interferometer, which can change the central wavelength for a given order, there are three options:

• change the refractive index of the cavity,

• change the plate separation d.

In modern gap-scanning etalons, the parameter that is changed is the plate separation, that can be controlled to extremely high accuracy.

In recent years, these etalons have undergone considerable improvements. It is now possible to move the plates between any two discrete spacings at very high frequencies (200 Hz or better) with no hysteresis effects while maintaining A/200 parallelism (measured at 633 nm). The etalon spacing is maintained by three piezoelectric transducers as discussed below.

10.4.2 Piezoelectric transducers

Piezoelectric materials undergo dimensional changes in an applied electric field. Conversely, they develop an electric field when strained mechanically. Under an applied electric field, a piezoelectric crystal deforms along all its axes. It expands in some directions and contracts in others. The dimensional change (expansion or contraction) of a piezoelectric material is a smooth function of the applied electric field. The material is stiff enough for the piezoelectric transducers (PZTs) to respond on submicrosecond timescales. The resolution is limited only by the precision with which the electric field can be controlled. For this reason, PZTs are commonly used for rapid switching and sensing, as indeed they are in the Queensgate etalons. However, all piezoelectric materials exhibit hysteresis, particularly in the relationship between the voltage applied and the amount of expansion. Thus, a servocontrol system is required to tune the spacing between two plates to high accuracy.

10.4.3 Capacitance micrometry

It has been shown that capacitance micrometry can be used to detect motions on scales as small as 10~15 m. Using this basic method, Queensgate Instruments developed a capacitance-bridge system to monitor the parallelism and spacing of a Fabry-Perot etalon. Information from the capacitance bridge is used to drive PZTs in a closed-loop control system to maintain the parallelism and spacing. There are two X-channel and two y-channel capacitors, and a fifth reference capacitor, which monitors the spacing with respect to a fixed reference capacitor in the circuit. The two etalon plates can be kept parallel to within an accuracy of A/200 for many weeks at a time.

10.4.4 Coatings and finesse The highly polished plates are coated for optimal performance over the wavelength of interest. Since it is difficult to create an efficient coating to operate over the complete range of visible spectra, the etalon coatings are optimized to selected wavelength ranges (i.e. "blue" or "red"). The reflectivity of the coating determines the shape and degree of order separation of the instrumental profile. This is fully specified by the coating's finesse, F, which has a quadratic dependence on the coating's reflectivity. At a finesse specification of F = 40 (which means that the separation between periodic profiles is 40 times the width of the instrumental profile) the profile is Lorentzian to a good approximation.

Notice that the analysis of Fabry-Perot behaviour in Section 10.3 does not take into account the wavelength-dependent phase change inherent in reflections between the optical coatings on the inner plate surfaces. Such coatings reflect the design wavelength with zero phase change, but incur a lead and lag elsewhere.

10.5. The tunable filter

Whereas Fabry-Perot interferometers are used for high-resolution spectral work, tunable filters are used for low-resolution imaging. In the case of a conventional Fabry-Perot device, the etalon used large gap spacings (about 30-400 |im, giving resolution between 5000 and 17000). The scan is done over a restricted range of spacings (equivalent to wavelengths).

A tunable filter is just a very-low-resolution Fabry-Perot device, wherein the gap spacing is much smaller, for example, between 2 and 12 | m. The result is a low resolution (R = 100-1000). The scans are over a wider range of spacings, and the anti-reflection coatings are optimized for a broad range of wavelengths.

The tunable filters largely remove the need for buying arbitrary narrow and intermediate interference filters, since one can tune the bandpass and the centroid of the bandpass by selecting the plate spacing. Since tunable filters are periodic, the instrument requires a limited number of blocking filters.

Figure 10.1. Three etalons with different apertures and the CS-100 controller unit.

10.5.1 History

Some examples of etalons used in the tunable filter mode follow.

• The Goddard Fabry-Perot Imager (GFPI). The system consisted of a piezoelectric scanning etalon and a servo-controller, both made by Queensgate Instruments, blocking filters and a Tektronic CCD detector. Besides being transportable, its mostnotable characteristic was the relatively low spectral resolution (3-30 A bandpass). It began operation in 1990, with a spectral coverage of 3800-10 500 A, a nearly monochromatic field of view and a STIS SITe 2048 x 2048-pixel CCD. The current instrument has a choice of four Queensgate 50-mm-diameter piezoelectrically driven, capacitance-stabilized etalons, which can be tuned to any wavelength in the range 4000-10 000 A, with resolution from 4 to 28 A FWHM depending on etalon and wavelength (Gelderman et al. 1995).

• The Calar Alto Fabry-Perot Spectrometer. A Fabry-Perot etalon was used as a tunable narrow-filter ET-50 (Queensgate) plus CS100 electronic controller, both similar to the devices shown in Figure 10.1. The range is from 4200 to 8300 A. The etalon plates are at 9.5 |im, order 30 at 6000 A. Spacing can be varied for ±2.5 |im around the nominal value. The mean instrumental resolution is ^400-600 km-1 FWHM (Meisenheimer & Hippelein 1992).

• The Taurus Tunable Filter (TTF) was developed in 1994-1995. The TTF is a pair of tunable narrow-band interference filters covering 3700-6500 A (blue "arm") and 6500-9600 A (red "arm"). It made it possible to have monochromatic imaging at the Cassegrain foci of the Anglo-Australian (3.9-m) and William Herschel (4.2-m) telescopes, with an adjustable passband of between 6 and 60 A. Frequency switching with the TTF could be synchronized with movement of charge (charge shuffling) on the CCD. Unlike conventional Queensgate etalons, the TTF incorporated very large

Figure 10.2. The Fabry-Perot red etalon of OSIRIS on the optical bench.

piezoelectric stacks (which determine the plate separation) and high-performance coatings over half the optical wavelength range. The plate separation could be varied between about 2 and 12 |im (Bland-Hawthorn & Jones 1989).

The Instituto de Astrofísica de Canarias has developed a new instrument that uses the technique of tunable filters: OSIRIS (Optical System for Imaging and low-intermediate Resolution Integrated Spectroscopy).

The management of the Gran Telescopio Canarias (GTC) decided on 11 March 1999 to sign a contract for the preliminary design of OSIRIS as chosen day-one GTC instrument for the optical wavelength range. On 29 July 1999, a contract was signed between the IAC and GRANTECAN for a preliminary design. After the preliminary design review, the contract for the development of the instrument was signed on 20 December 2000, for instrument delivery to the site to begin commissioning depending on the telescope schedule.

OSIRIS is an imaging system and a low-resolution long-slit and multi-object spectrograph for the GTC covering the wavelength range 0.365-1.0 |im with an unvignetted field of view of 8.53' x 8.53' and 8.0' x 5.2' in direct imaging and low-resolution spectroscopy, respectively. OSIRIS represents a new generation of instrumental observing techniques, that includes the concepts of tunable filters and charge shuffling on the CCD detectors (Cepa 1998).

The OSIRIS tunable filter (TF) is a pair of Fabry-Perot etalons covering 365-670 nm (blue arm) and 620-1000 nm (red arm). Figure 10.2 shows the etalon of the red arm installed in OSIRIS. The OSIRIS TF offers monochromatic imaging with an adjustable bandwidth of between 0.6 and 6 nm. In addition, frequency switching with the TFs can be synchronized with movement of charge (charge shuffling) on the CCD, which has important applications to many astrophysical problems.

Future instruments in large telescopes that will make use of tunable filters are the following.

• The Maryland-Magellan Tunable Filter (MMTF). It will provide a high throughput over a broad range in wavelengths (5000-9200 A), with a tunable bandpass of 10100 A over a 10 x 27-arcmin field. By frequency switching the etalon in synchronization with charge shuffling in the CCDs, the MMTF is expected to reach a sensitivity of 10"18 erg s—1 cm-2 at -3a SNR in 1 h. It is to be installed on the IMACS instrument at the Magellan 6.5-m telescope.

• The Prime Focus Imaging Spectrograph of the SALT telescope project. The SALT project is a multinational collaboration to build a large telescope in South Africa similar to the Hobby-Eberly Telescope already in existence in West Texas. The project requires two 150-mm-aperture etalons and controllers.

10.6. Instrumental effects

10.6.1 Monochromatic field The primary goal of a tunable filter is to provide a monochromatic field over as large a detector area as possible. However, the field of view is not strictly monochromatic. The effect is most acute at high orders of interference.

Wavelengths are longest at the centre and get bluer the further one moves off-axis. This change in wavelength, relative to the central wavelength when 0 = 0, can be written as

where 0sky is the angular distance on the sky away from the central axis of the etalon.

The monochromatic field will be the size of the Jacquinot spot, the central region of the ring pattern. In this region the wavelength changes by less than %/2 times the etalon bandwidth, which verifies

F m where F is the effective finesse of the etalon.

Then, the monochromatic field is a region subtending an angle ^Jac that can be written as

For a particular etalon, the size of the Jacquinot spot depends on the order m alone. The above equation shows how the spot covers increasingly larger areas on the detector as the filter is used at lower orders of interference. The absolute wavelength change across the detector remains the same, independently of order. However, its effect relative to the bandpass diminishes as m decreases.

10.6.2 Ghosts

A typical arrangement of a Fabry-Perot instrument can have a significant number of flat surfaces, which can be a source for spurious reflections. For example, since the Airy function has a periodic behaviour, a narrow-band filter (known as an order sorter) must be used to eliminate unwanted interference orders. The narrow-band filter is placed in the converging beam before the collimator or after the camera lens, or in the collimated beam. The filter then generates ghost reflections in the instrument optics.

Another source of ghost reflections arises from the optical blanks which form the etalon, that can act as internally reflecting cavities. A possible solution is to have the outer surfaces wedge-shaped in order to deflect this spurious signal out of the beam.

In order to avoid ghosts the tunable filter could be allowed to tilt. Usually a tunable filter will be tilted only to angles of a few degrees.

10.7. Observing with tunable filters

10.7.1 Order sorters

A Fabry-Peerot filter (FPF) clearly gives a periodic series of narrow passbands. To use a FPF with a single passband, it is necessary to suppress the transmission from all the other bands that are potentially detectable. This is done by using conventional filters, called order sorters because they are used to select the required FPF order.

For example, with a finesse of about 40, and hence low resolution (A/AA = 300), conventional broad-band UBVRI filters suffice. At high resolution (A/AA = 1000), specifically designed interference filters should be used to subdivide the wavelength range of each arm.

Using an order-sorter filter and the TF etalon, single-order observations can be made at any wavelength, within the range of the filter, as long as the inter-order spacing is larger than the bandwidth of the filter. Also, observations can be made with smaller inter-order spacings if the order is close enough to the central wavelength of the filter that adjacent orders are outside the range of the filter.

The selection of order-sorter filters depends on the coating reflectivities and wavelength ranges of the TF arms. Additionally, there is also the consideration of sky emission lines. It could be desirable to choose the order-sorter filters such that they fall between the wavelengths of strong sky lines. Other points to consider are the range of tilting and the probable transmission profiles for each filter.

10.7.2 Calibration

The calibration of the TF is done using arc lamps. The TF is gap scanned, through at least one FSR, and the charge is shuffled between each exposure and the next. In this way, the spectrum of a lamp is obtained and the gap scanning is calibrated.

10.7.3 Operation modes of tunable filters

Examples of operation modes are the following.

• Tuning to a specific wavelength at a specific bandpass. This allows images of obscure spectral lines at arbitrary redshifts to be obtained. It is also possible to optimize the bandpass to accommodate the line dispersion and to suppress the sky background. The off-band frequency can be chosen so as to avoid night-sky lines and can be much wider so that only a fraction of the time is spent on the off-band image.

• Charge shuffling between off-band and on-band frequencies. If the CCD field is large enough, it is feasible to image the full field for two discrete frequencies. Or, for example, we can also choose a narrow bandpass for the on-band line and a much broader bandpass. Charge shuffling is a movement of charge along the CCD between exposures of the same frame, before the image is read out. An aperture mask ensures that only one section of the CCD frame is exposed at a time. For each exposure, the TF is systematically moved to different gap spacings in a process called frequency-switching. In this way, a region of sky can be captured at several different wavelengths on one image. Alternatively, the TF can be kept at fixed frequency and charge shuffling performed to produce time-series exposures.

10.8. Imaging-data reduction with tunable filters

The tunable filters are versatile optical devices designed to provide, inter alia, monochromatic-field imaging over a large detector area.

The reduction process passes through different stages to convert raw data obtained using TF imaging into valuable scientific information. There is a handful of items of specialized and complete software to perform this kind of work, relying on two approaches: orthodox three-dimensional Fabry-Perot spectroscopy (where the famous "data-cubes" are used for obtaining information about flux, velocity dispersion field, skewness, etc. for extended objects; it is a technique characterized by high resolution power and small tuning ranges) and properly named TF imaging, one kind of very-narrow-line, spectrally dynamic, photometry (or, in other words, (almost) full-field, low-resolution spectroscopy). For data reduction in Fabry-Perot spectroscopy, originally the TAUCAL package (Lewis & Unger 1991) was conceived, as an add-on of FIGARO, for the TTF (Fabry-Perot mode) data. The IDL-based MATADOR software is another possibility (Gavryusev & Munoz-Tunon 1996). More recently, the ADHOC software of Daigle et al. (2006) has been presented to the community. The routines associated with it are written in C and IDL, and the paper by Daigle et al. could be considered a useful information source about the instrumental and systematic difficulties related to this technique. Another practical article about Fabry-Perot data reduction was published by Gordon et al. (2000). Some problems broached in this paper are common to the TF imaging scenario.

A complete software package for TF imaging-data reduction, described in Jones et al. (2002) is TFred. We strongly recommend reading this work before undertaking reduction work with TF images. This software is essentially based on IRAF procedures and Fortran77-specific programs. It was originally created for reduction of data from the TTF for imaging of point-like sources. This modality is suitable when emission-line surveying with large angular and wavelength coverage is an observational priority. The software is optimized for an efficient selection of emission-line objects. A full description of this observing system can be found in the TTF manual (which is available on-line). There is also a website associated with TFred and TTF facts (reduction tips and script sources): http://www.aao.gov.au/local/www/jbh/ttf/.

A basic reduction scheme for obtaining a concise idea about the processing stages and the procedures involved is shown below. Additionally, a detailed set of instructions for a hands-on reduction of a working example can be obtained by contacting the authors.

10.9. Definitions

A scan is a series of images taken at each step of a sequence in the separation of etalon plates. It is not so in the case presented here, but a scan should be recorded at least three times for each observing run and sky region. By stack we mean one or more scans, with the same spectral range, in any processing stage. At a given (fixed) order of interference, there is a bijection between the gap between etalon plates and the image's effective wavelength (with the limitations pointed out below). This relationship is established prior to the scientific observations.

At the telescope the gap is measured as Z-step values (in arbitrary microprocessor units, or mpu). A phase effect occurs in all filters of this type and it can be represented by a spatial gradient of the wavelength. This implies the presence of an optical axis (not

Figure 10.3. Two sections of the same image before (left) and after (right) subtraction of the

OH sky rings.

Figure 10.3. Two sections of the same image before (left) and after (right) subtraction of the

OH sky rings.

necessarily coincident with the field centre), which is used to measure the phase effect: off-axis rays pass through the etalon at a slightly different angle from that for on-axis rays, resulting in a small wavelength shift to the blue with the optical axis moving further away on the detector surface.

The sky rings are broad diffuse circles produced by OH night-sky glow. Depending on the spectral region, the band will be more or less evident. Night-sky rings appear as circular bands around the optical axis as a consequence of the phase effect. In Figure 10.3, a typical fingerprint of these rings on a deep image of the HDF-North field is represented.

Ghost images are spurious objects that appear due to multiple reflections of bright objects in or near the observed field. A couple of representative examples were presented above. One of them is shown in Figure 10.4. It is a ghost produced by a bright galaxy (M82) imaged using the Taurus 2 camera (on the William Herschel telescope). For their effective subtraction - leaving intact the real objects - the scan sampling must be done by imposing a dithering of the telescope. The ghosts appear as opposites of the real objects with respect to the optical axis.

10.10. Procedure

The analysis of multi-object TF data has three stages:

• preparation of images;

• object detection and selection of real/spurious objects; and

• flux calibration.

The procedures of each stage are summarized in the following. Initially the raw-scan frames must be prepared for analysis. This includes the removal of the bias level and pixel-to-pixel variations, and the fitting and subtraction of night-sky rings. Images are then aligned with respect to a common reference frame and trimmed. A duplicate set of frames is created and degraded to a common worst seeing. Then frames are co-added into combined scans, of which there are different versions arising from the use of

Figure 10.4. A typical ghost image (circled) of the galaxy M82. The cross marks the projection of the optical axis. In this case it is easy to identify the spurious object. Otherwise, it is essential to have at one's disposal at least two images with a noticeable offset with regard to the optical axis for an unquestionable identification of the ghosts.

Figure 10.4. A typical ghost image (circled) of the galaxy M82. The cross marks the projection of the optical axis. In this case it is easy to identify the spurious object. Otherwise, it is essential to have at one's disposal at least two images with a noticeable offset with regard to the optical axis for an unquestionable identification of the ghosts.

median filtering or straight summation. Versions are also generated from the smoothed (seeing-degraded) and unsmoothed frames. For each of the final combined scans noise-edge masks are computed and applied to the image corners. This last step is necessary in order to stop the object-detection software from setting a detection threshold that is biased by the statistics of pixels outside the image area. The scheme that follows is an adapted version of the on-line instructions written by Heath Jones (ANU/AAO), which are available at the TTF URL: http://www.aao.gov.au/local/www/jbh/ttf/. The specific procedures are pointed out in terms of the software tasks. For the sake of completeness, some important comments were added.

10.10.1 Preliminary steps

• Wavelength calibrate Z-step versus wavelength. Ideally, this has already been done at the telescope, before the scan was taken (tsample).

• Create bias and flat-field images (imsum, tff). This step can also be performed using standard IRAF routines.

• Bias-subtract, flat-field, flip and subtract OH sky rings and other telluric features from images (tpipe).

• Align images and trim (toffsets, imalign). Usually, translation of the images with regard to a reference image suffices.

• Find the centre and radius of the best circle to match the circular field-aperture stop, if present (tcircle).

• Create a zero corner mask (if required) using the dimensions found by tcircle (tmask).

• Measure the changes in seeing/PSF through the stack (tfwhm).

• Convolute the full stack to the worst seeing (tgauss).

• Combine images to produce two scans: one cleaned (for good object detection) and the other straight-summed (for good object photometry) (tsingle).

• Create a deep image from all individual narrow-band frames, which is useful for identifying object-free sky regions (tdeep).

• Obtain locations of many sky regions, free of objects (tregions).

• Create a zero edge mask (tmask), if it is required.

• Measure the sky noise (tnoise), create noise-edge masks and apply these (with the zero edge mask) to each respective stack (tmulti). Ideally, the aperture edge should be rendered undetectable.

10.10.2 Detection and selection of candidates By this stage there are three stacks: (i) a summed (uncleaned) scan with the original variable seeing; (ii) a summed (uncleaned) scan with frames smoothed to a common "worst" seeing; and (iii) a cleaned scan with frames smoothed to this common seeing. From here, the steps of object detection, photometry and selection are straightforward and efficient. Most of the subsequent analysis works with object catalogues rather than images, so processing is fast. In summary, do the following.

• Detect objects and carry out photometry in each of four pre-selected apertures (tsex). Objects are detected using the uncleaned, unsmoothed images. Photometry, however, is done on the matching uncleaned but smoothed frames. As stated in its name, the task implies the use of SExtractor (Bertin & Arnouts 1996) software.

• Create a file of the central wavelengths that correspond to each image (twavelengths).

• Sort individual object photometry into TF spectra and SExtractor additional parameters (tespect).

• Compile a cosmic-ray/ghost pixel-location file for all images in the stack (tpull).

• Photometrically register frames and extract double-detection emission-line candidates (with and without continuum). Write these to separate candidate catalogues (tscale).

• Check raw candidate catalogues for cases of double-counting by the object-detection software. More often than not, double-counting is not found, so the task is run more as a check (tdouble).

• Inspect double-detection candidates to ensure that no cosmic rays or ghosts have evaded detection. Remove them from the candidate catalogues if any are found (tcull).

• Extract single-detection candidates from catalogues (tesone).

• Check candidate aperture corrections and replace object fluxes with those from the next-largest aperture in cases where selected apertures are too small (tmodap).

10.10.3 Flux calibration

With selection of emission-line candidates finalized, all that remains is for the measured fluxes to be calibrated in terms of physical units. Initially, standard-star scans (taken on the same night as the science frames) must be reduced in order to obtain flux-calibration constants for that night. These calibrations can then be applied to the object catalogues in a single step. In summary, do the following.

• Bias-subtract and flat-field standard-star frames, using appropriately trimmed versions of the corresponding bias and flat-field frames obtained (tstar).

• Carry out photometry of standard stars and correction for air mass and the effective passband width. Also correct wavelengths for phase effects associated with the position of the standard star in the beam (tflux).

• Flux calibrate emission-line candidates to physical flux units (using standard-star calibration constants). Correct for air mass and Galactic extinction (tcalibrate).

• Calibrate the fluxes of single-detection candidates (tonecal).

• Finally, create strip-mosaic and chart images of final candidates (tmosaic).

This is an exhaustive description of the process employed to reduce TF images with point-like candidates for emission-line objects. Nevertheless, some procedures can be used for the reduction of images from very-extended sources obtained using TFs. A new version of the TFred package, especially designed to reduce the data for the OTELO project (http://www.iac.es/proyect/otelo), is at present in preparation.

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