Fabry-Perot tunable filters operate on similar principles to narrow-band interference filters. In a single-plate interference filter, the interference occurs in the interior of a solid plate, where the two sides of the plate act as reflective surfaces. In a tunable filter, the interference arises in the air gap between the surfaces of two separate plates.

Fabry-Perot tunable filters offer several advantages over their single-plate counterparts.

1. Tunable filters are tunable in wavelength space. By making small changes in the air gap between the two plates, one can change the transmitted wavelength.
2. Tunable filters are tunable in bandpass. By making large changes in the air gap between the two plates, one can change the width of the transmission profile.
3. Tunable filters provide very narrow bandpasses. Through rejection of significant sky and/or continuum emission (compared to conventional narrow-band filters), tunable filters can significantly improve observing efficiency for reaching a desired signal-to-noise ratio.
4. Tunable filters can switch between two wavelengths on short timescales. Coupled with charge-shuffling on the CCD, this allows the user to correct for time-varying observational effects, including atmospheric transmission and sky brightness. It also allows for differential imaging on short timescales.

Alternatively, tunable filters function as wide-area, low-resolution spectrometers. From this perspective, a tunable filter achieves a significant efficiency advantage over conventional long-slit spectrographs (Jacquinot 1954).

Fabry-Perot tunable filters have been used for a wide range of applications, including (but not limited to) the following:

• Emission- and absorption-line maps of galaxies
• Emission-line ratio ("excitation") maps of galaxies
• Searches for warm, diffuse gas on the outskirts of galaxies
• Imaging of Galactic line-emitting sources
• Wide-field surveys for high-redshift line-emitting galaxies
• Suppression of quasar light in Lyα forest troughs
• Tracking of stellar variability using differential imaging

For general Fabry-Perot physics, refer to an optics textbook (e.g., Hecht's Optics) or this succint Wikipedia entry. For more details on tunable filters, see the references given below. We summarize here the important points.

For Fabry-Perot etalons to operate as tunable filters, the plate spacing must be small. This ensures that the monochromatic spot at the center of the field of view is large, or equivalently the spectral resolution is low. The monochromatic, or Jacquinot, spot is defined to be the region over which the change in wavelength does not exceed √2 times the etalon bandpass. For a given wavelength, small plate spacing translates into low interference orders.

More specifically, the diameter of the Jacquinot spot is given by

  DJ = 2√(2√2) F / √(nN)
     ~ 3.3636 F / √(nN)

  where F = camera focal length (in pixels)
        n = order of interference
        N = etalon finesse (see discussion below)

For a given order, the monochromatic spot depends on wavelength only through the finesse. (The finesse, which we discuss below, depends on the transmission of the plate coatings.) However, as we discuss in the next paragraph, order is proportional to plate spacing d, so that D_J ~ 1/√d.

The transmitted wavelength at any point on the etalon is governed by interference principles: n λ = 2 d cos θ, where n is the interference order, λ is the wavelength, d is the effective plate spacing (including any optical effects due to the coating or air gap -- these may change with wavelength), and θ is the angle of the incident light with respect to an axis perpendicular to the plates. The transmitted wavelength can be modulated by either (a) changing the plate spacing d or (b) changing one's radius with respect to the optical axis, represented by cos θ. (At the CCD, the θ dependence translates into a radial dependence of wavelength; the optical axis is at the center of this radial pattern.)

Interference orders are separated by a free spectral range (FSR). Each transmission peak is characterized by an Airy profile. The ratio of the free spectral range to the instrumental resolution (in terms of the effective bandpass, defined as the profile area divided by its peak) is the effective finesse. In a perfect system, the effective finesse is equal to the reflective finesse, which is a function of the etalon plate coatings. However, irregularities in the plate surfaces and coating thicknesses, as well as deviations from perfectly parallel plates, degrade the effective finesse, and hence the efficiency of observing.

In summary, the interference equation governing the etalon is

  n λ = 2 d cos θ

  where n = order of interference
        d = plate spacing
	θ = angle of incident light with respect to the optical
        axis (θ = 0 at the optical axis)

The equations governing the instrumental profile are as follows:

• Expressed as functions of wavelength,

     FSR(λ) ≅ λ / n ≅ λ2 / 2 d
    FWHM(λ) ≅ FSR(λ) / Finesse ≅ λ / [n Finesse] ≅ λ2 / [2 d Finesse]
  
    where FSR = free spectral range
          FWHM = full width at half maximum
  	Finesse ≅ FSR / FWHM
  

• Expressed as functions of plate spacing,

     FSR(d) = λ / 2
    FWHM(d) ≅ FSR(d) / Finesse ≅ λ / [2 Finesse]
  

The wavelength dependencies are summarized as follows:

• On the optical axis, for effective plate spacing d,

    λ = A + B z
  

  where z = z(d) represents voltages applied to the etalon by the CS-100 and is the variable read by the IMACS computer. It is a linear function of plate spacing d:

    d = E + G z,
  
    where E = n A / 2
          G = n B / 2.
  

  A and B thus vary from order to order. By substituting for n using the interference equation, we also see that A and B vary linearly with wavelength for a given plate spacing.

• Off the optical axis at radius R:

    λ(R) = λ(0) / √(1 + R2/F2) = (A + B z) / √(1 + R2/F2)
  
    where F = focal length of the camera.
  

  Note that wavelength decreases with increasing distance from the optical axis.

Bland, J., & Tully, R. B. "The Hawaii Imaging Fabry-Perot Interferometer (HIFI)." 1989, AJ, 98, 723

Bland-Hawthorn, J., & Jones, D. H. "TTF: A Flexible Approach to Narrowband Imaging." 1998, PASA, 15, 44

Jacquinot, P. "The Luminosity of Spectrometers with Prisms, Gratings, or Fabry Perot Etalons." 1954, J Opt Sci Amer, 44, 761

Jones, D. H., Shopbell, P. L., & Bland-Hawthorn, J. "Detection and Measurement from Narrow-band Tunable Filter Scans." 2002, MNRAS, 329, 759

Taylor, K., & Atherton, P. D. "Seeing-Limited Radial Velocity Field Mapping of Extended Emission Line Sources Using a New Imaging Fabry-Perot System." 1980, MNRAS, 191, 675

The TTF (Taurus Tunable Filter), formerly on the Anglo-Australian Telescope (see also articles listed above)

Fine Guidance Sensor - Tunable Filter, on the James Webb Space Telescope (see also these articles)

OSIRIS (Optical System for Imaging and Low-Intermediate-Resolution Integrated Spectroscopy), on the Gran Telescopio Canarias (see also these articles)

The Prime Focus Imaging Spectrograph, on the South African Large Telescope (see also these articles)

The MMTF sits in the disperser wheel of the IMACS camera:

The optical path through IMACS and the MMTF.

Throughput curves for the old (black curve) and new, red-sensitive (blue curve) IMACS cameras. The new camera is more sensitive at all wavelengths, and 50% more sensitive at 7000Å.

The MMTF consists of 3 major components: the etalon and its support assembly, the CS-100 controller, and the cables connecting them.

The etalon consists of two parallel plates composed of fused silica, each with a 150 mm clear aperture. The etalons are separated by a tunable air gap, with minimum and maximum separations of 1.3 microns and 10.7 microns. The plates are coated on the interior side (the side facing the other plate) with a reflective coating consisting of a multi-layer dielectric. (The finesse of the etalon is a function of the interior reflective coatings.) The exterior surfaces are anti-reflection coated. The plates are smooth at the λ level.

Capacitors and piezoelectric stacks lie near the plate edges. The voltages across the capacitors are used to measure the tilt and spacing of the plates. The stacks move the plates in three dimensions: a tilt around two axes (X and Y) and spacing along the Z axis. The tilt of the plates governs their parallelism; the best (most symmetric, and most flux in the peak) instrumental profile is achieved when the plates are most parallel. The spacing controls both the wavelengths transmitted and the width of the instrumental profile.

The CS-100 controller sends and receives electronic signals from the etalon to control the tilt and spacing of the plates. Once they are made parallel, the controller operates an electronic feedback loop to keep the etalon plates in position. The coarse values for tilt and spacing (X_coarse, Y_coarse, and Z_coarse) are set using the dials on the CS-100 controller. The tilt and spacing can be changed in smaller increments using X_fine, Y_fine, and Z_fine values. The fine values can be changed using either the CS-100 dials or the IMACS control software. The observer should not change the etalon settings with the CS-100 controller dials.

Note: (X, Y)_coarse and (X, Y)_fine control the etalon parallelism. However, the coarse spacing Z_coarse controls the etalon bandpass, while the fine spacing Z_fine governs the transmitted wavelength. The fine spacing can affect the bandpass, but only when changed by a large amount.

For more details on the CS-100, read the CS-100 documentation or a summary on the TTF website.

The etalon connects to the CS-100 through shielded cabling that runs from IMACS to the electronic cooling rack on one side of the Nasmyth platform.

The entire system was manufactured by IC Optical Systems Ltd.

Observers have full freedom to tune the central wavelength of the MMTF bandpass within the range allowed by a particular blocking filter. The wavelength can be tuned from one exposure to the next, or within a given exposure (see the charge shuffling / frequency switching observing mode). A blocking filter is required to select only one transmission order (a given plate spacing transmits multiple wavelengths at a single location, each corresponding to a different order).

The currently available order blocking filters are listed below. Each has a bandpass intermediate between that of broad-band filters and that of the etalon. For each filter, we list the central wavelength and full-width at half-maximum in the IMACS beam, and provide a transmission curve. (The transmission curves were measured in a collimated beam, and are corrected to the IMACS f/2 beam; the correction is not exact.) We also provide a link to a table of etalon parameters at the relevant wavelengths, including FWHM values.

Intermediate Bandpass Order Blocking Filters

λ (Å)	FWHM (Å)	Transmission		Etalon Parameters
5102	150	plot	data	table
5290	156	plot	data	table
6399	206	plot	data	table
~6600	~260†	plot	data	table
6815	216	plot	data	table
7045	228	plot	data	table
8149	133	plot	data	table
9163	318	plot	data	table

^†FWHM > free spectral range.

If you are considering the purchase of a narrow-band filter not listed here and are interested in making it available for use with MMTF, or have other questions about filters, please contact Sylvain Veilleux. Filter bandpasses must fall in the high-reflectivity part of the interior plate coating transmission curve; this range is roughly 5000-9500 Å (see Figure).

Changing filters between exposures is straightforward. However, each filter requires its own set of calibrations to determine the wavelength solution and etalon parallelism. It is thus important to plan ahead and find wavelength solutions for each filter during the day before a run. The observer is limited to the use of at most 2 filters in a single night because of calibration overheads.

For a given order, the area of approximately constant wavelength at image center, or monochromatic spot, depends on wavelength only through the finesse. For MMTF, the coating transmission is fairly constant above 5500 Å. However, the diameter of the spot does depend on plate spacing. We list here representative values for several different wavelengths and spacings:

Jacquinot Spot Diameters

Wavelength (Å)	DJ (Zcoarse=-2) (arcmin)	DJ (Zcoarse=3) (arcmin)
5100	13.81	10.71
6600	11.6	8.5
9150	11.5	9.5

¹At 5100 Å the numbers are ~1'-2' higher due to a drop in finesse.

The available instrumental full-widths at half maximum are linked in the table above. For 6600 Å, the range is 6 - 13 Å. (The "effective bandpass", or the integral of the profile divided by its peak, is ~60% larger than the FWHM for a Lorentz distribution; the MMTF instrumental profile is approximately Lorentzian.) The FWHM values at other wavelengths, for a fixed plate spacing, scale with λ². For a fixed wavelength, the FWHM is adjusted by making large changes in the plate spacing (d in the physical domain, Z_coarse in the electronic domain). In summary,

  FWHM(λ) ≅ λ2 / [2 d Finesse]

where the Finesse is mostly constant, except at the edges of the etalon's coating response. At the edges of the coating transmission curve (see Figure above), the reflectivity (and hence the etalon finesse) drops, broadening the profile and increasing its FWHM. Thus, at 5100 Å, the FWHM range is 8 - 14 Å. These values are slightly higher than at 6600 Å, while one would expect lower values for a constant finesse.

The bandpass can be changed during an observer's run only under exceptional circumstances.

Principal investigators are encouraged to contact Sylvain Veilleux with any questions/concerns that they may have about the feasibility of their project before submitting their proposal.

• Large field of view (27' diameter, ~10' monochromatic)
• High emission-line sensitivity to point sources or filamentary structure (DIQ ~ 0.7'')
• Versatility in choice of emission lines, within the range of ~5000-9200Å
• Narrow bandpass, reducing sky noise
• Accurate continuum subtraction (off-band wavelength can be chosen to be arbitrarily close to on-band wavelength)

• Observations in bright moon conditions: Scattered light can make MMTF data very difficult to reduce; we recommend requesting at least grey time.
• Multiple (> 2) filter switches per night: Each filter used requires a careful wavelength calibration during the daytime (~1 hour each). Changing filters in the middle of the night adds an overhead of 15-30 minutes.
• Observation of structureless, extended emission/absorption-line sources: One of the key strengths of the MMTF is its location at Las Campanas, Chile. This site consistently produces seeing of 0.6-0.8'', providing excellent sensitivity to point source and filamentary emission.

• Are your exposure times long enough to achieve sufficient sensitivity for your targets? Consult the filter-dependent sensitivity measurements in order to determine an adequate exposure time.
• Have you accounted properly for overheads? Typically, you will need to check the parallelism every time you move the telescope by a sizeable amount (5-15 min) and the wavelength calibration every 30-60 mins (~5 min).
• Are all of the desired emission-line wavelengths observable? Be sure to also check the continuum wavelength (if desired)!
  (MMTF Transmission Calculator)
• Have you considered wavelength slicing? If your target covers a range in velocity or is larger than the monochromatic spot, you may have to plan for exposures at multiple wavelength in order to capture all line emission.

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NEW: In early 2009 a new method of observing with the MMTF was tested and found to drastically reduce the uncertainty in plate spacing and thus cut nightly overhead costs by up to 1-2 hours! By forcing IMACS (and thus the MMTF) to remain at a roughly constant gravity angle, the etalon will remain parallelized throughout the entire night, eliminating the need for costly re-parallelization and reducing the drift in the wavelength-spacing solution. Be sure to follow the directions below in order to take full advantage of this revolutionary technique.

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MMTF observing is done using the standard IMACS data acquisition software along with a set of special built-in procedures. These include the ability to set the etalon fine X, Y, and Z values in the Hardhat GUI, as well as a set of programmable scripts that are run from the MMTF version of CamGUI. These scripts coordinate commands to the camera and the CS-100 for the following observing and calibration tasks:

• wavelength scanning;
• charge shuffling / frequency switching;
• determining the plate parallelism;
• taking data sausages for wavelength calibration.

Note that all access to etalon X, Y, and Z settings is through the IMACS software; the observer should not change the etalon settings with the CS-100 controller dials.

For each filter to be used during the first night, the following steps should be taken. For each step, refer to the Calibrations section for more details. Be sure that these calibrations are all performed at a gravity angle of Θ_grav ~ 0° (Θ_NASW = -47.3°).

At the Start of the Night

For each step, refer to the Calibrations section for more details.

1. Acquire the first target, and ensure that the field of view is properly rotated (Θ_grav ~ 0°).
2. Capture a reference image of an emission-line ring, and compute and apply a correction to A and Z_fine [procedure].
3. Compute and set the etalon to the appropriate Z_fine for the wavelength of interest using WCALC.

Throughout the Night

1. Before each exposure, direct the telescope operator to re-acquire your target coordinates, in order to rotate IMACS to Θ_grav ~ 0° (be sure that the rotation mode in your target file is "GRV" and the offset is "-47"; see the following example). When doing a sequence of multiple exposures, re-acquire before each one in order to maintain a roughly constant gravity angle throughout the night. This will minimize errors in your wavelength solution and drastically cut down on nightly overheads by up to 1-2 hours.
2. Take a reference ring regularly to check for drift in A (wavelength zero-point) and the line profile (parallelism) (procedure). This should be done every ~30 minutes while the temperature is changing dramatically at the start of the night, or every hour when the temperature is stable. If the line profile has degraded in quality (less narrow and/or less symmetric), you may have to recompute the parallelism (procedure). Use this reference ring to apply a correction to A and Z_fine, using WCALC, to achieve the wavelength of interest.
3. Exposure times should be no longer than 20-30 minutes to allow frequent checks for wavelength zero-point drift. Drift occurs more rapidly at the beginning of the night, due to more rapid temperature changes at this time. If you are doing on- and off-band imaging, be sure to do the on-band immediately after checking for wavelength drift while the wavelength solution is valid. The exact wavelength of the off-band image is less important and, thus, should always be done second.
4. For exposures where it is important to achieve a continuous image uninterrupted by features or chip gaps, dither by 30 arcseconds or more in each direction. Dithering is important for IMACS imaging in order to bridge the inter-chip gaps, which are ~50 pixels, or 10 arcseconds, on average. The MMTF also introduces a set of reflections of the chip edges (of relative intensity a few percent) which are not corrected by the flatfields. These reflections contaminate ~100 rows and/or columns of each chip. Dithering over 5' scales is required for observations of extended sources or fields in charge-shuffle mode.

At the End of the Night

1. Get dome flats at each wavelength that you observed during the night [procedure].
   (Can also be done in the afternoon prior to observing)
2. Get a series of biases (0-second exposures).