Wavelength calibration involves solving the equation relating wavelength and plate spacing for the slope B and zero-point A:

λ = A + B Zfine

Once A and B are known, this equation yields the value of fine plate spacing (Z_fine) necessary to observe the wavelength of interest.

A varies with time (possibly due to temperature changes) and with the parallelism setting. It must be calibrated at the beginning of the run and checked frequently using single, full-field images of rings. B (or dλ/dZ) depends on the coarse plate spacing Z_coarse and the interference order. However, it is stable and has been measured for 3 values of Z_coarse in each filter (see the table below).

The instrument scientist provides values of A and B to the astronomer at the beginning of a run. It is the astronomer's responsibility to track changes in A (due to, e.g., temperature drift).

The table below has links to MMTF arc lamp spectra. These were taken by scanning the etalon spacing through somewhat more than 1 free spectral range (FSR): a "sausage cube." The spectra are acquired using a small CCD subraster near the optical axis. This table also lists suggested lamps for doing wavelength calibration and parallelism tests, including whether it is internal or external ("Int/Ext") and good exposure times. The final column gives details about the etalon properties derived from these spectra, including values for B and FWHM and approximate Z_fine ranges used to achieve a particular order.

¹For the 6800 Å filter, we recommend the NeHg lamp for parallelism and for finding the λ - Z zero-point. For full wavelength calibration (including the λ - Z slope), near-simultaneous sausage cubes of Ne, NeHg, and He may be necessary.

²Calibration is ongoing; further filter data will be published as it is completed.

During the afternoon preceding your run, the instrument scientist will acquire sausage cubes and reference ring images to determine the wavelength zero point (A) for each filter you plan to use. He/she will also provide the value of B (see also the table above). It is the observer's responsbility to track changes in A with time. We recommend checking A at least every 30 minutes at the beginning of the night, when the dome temperature changes rapidly.

Changes in A, and hence the values of fine plate spacing necessary to observe the wavelength of interest, are tracked using the WCALC online tool. To begin, enter the relevant information for your target into WCALC: the value of B provided by the instrument scientist, the wavelength of interest, and the object position with respect to the optical axis (which is approximately at the field center). Next, insert the reference A value into the Aref box, and click the button next to it. This will assign A = Aref and compute the value of Z_fine when the reference data was taken.

To update A and Z_fine, use the following procedure:

1. Take a binned exposure at the same Z_fine setting and binning used for the reference image, using the same arc lamp. Let's call the new image ccd1159 and the reference image ccd1156, and assume that we are using the 6400 Å filter.
2. In a terminal window, type the following:
   

   % ring ccd1159 6400
   % ringdrift 1156 1159
   

   The resulting spectrum is shown at right.
3. Enter the change in A specified by ringdrift into the ΔA text window in WCALC. Press the "set A = Aref + dA and compute new Z" button.
4. Enter the new value of Z_fine for the wavelength of interest into the IMACS observing computer.
5. Observe!

During the afternoon preceding an MMTF run, the instrument scientist provides A and B to the observer for each filter. B comes from the calibration table above, and A from a sausage cube (see the figure at right). A reference ring image must also be taken before each sausage cube. We describe these procedures below.

Procedure to acquire reference ring image.

1. IMPORTANT: This image should be taken immediately before or after a sausage cube. The etalon should also be parallelized before any wavelength calibration proceeds.
2. Turn on the lamp suggested for the filter of interest (see table above).
3. Vary the etalon Z_fine and take Snap exposures until a relatively strong emission-line ring appears in the field-of-view. The ring should be isolated from other lines, and its radius should be approximately halfway between the center and edge of the aperture.
4. Take a binned image of the emission-line ring, using the exposure time suggested in the table above. To minimize readout time, use the coarsest binning possible while maintaining an unsaturated image (preferably 8 x 8, but finer binning if necessary).
5. Give the number of this exposure, as well as the Z_fine used, to the observer.
6. In a terminal window, check the spectrum by typing the following (fill in the proper exposure no. and filter central wavelength):
   

   % ring ccd0001 6600

Procedure to acquire sausage cube.

1. Running a well-sampled sausage cube typically takes ~20-30 minutes; this is dominated by CCD readout time.
2. Turn on the arc lamp recommended in the table above for the filter of interest.
3. Before taking the sausage cube, take a reference ring image as described above.
4. Turn on CCD subrasters by changing the ExpMode from Full to Subraster. When the subraster menu pops up, load the file defining the MMTF sausage cube subrasters: mmtf_sausage.sub in the default path, /Users/imacs/subrasters/. Click the Load button to load this subraster. REMEMBER: Set the SaveMode to Minimal to minimize readout time. Click Apply. Exit this window by clicking Done.
5. Ensure that CCD binning is set to 1x1, and that the exposure time is appropriate for the lamp you are using (the same exposure time as for the reference ring is fine).
6. Under the Script menu, click Create. In the pop-up window, select the Scan(seq) Mode. Set Z0 equal to the the lowest Z_fine in the reference sausage cube spectrum given in the table above. Keep dZ at the default value of 20, and set nZ equal to 50.
7. Save the etalon script.
8. To begin the sausage cube, click Exec under the Script menu.
9. Once the sausage cube has finished, type the following in a terminal window:
   

   % fitsausage 1 51 2

   where the first two numbers are the beginning and ending frame values in the sausage cube (leading zeros ignored) and the last number is the IMACS CCD chip. Always use chip 2, which is closest to the optical axis. Compare the resulting spectrum to the one given in the table, and make sure it is identical (there may be a small horizontal shift).
10. Copy the IRAF commands listed by the fitsausage output into an IRAF terminal window. Using the splot fitting routines (e.g., 'k' and 'l' for a single-line fit, or 'd' and 'd' for a multi-line fit), fit a Lorentzian profile to one of the emission lines. Preferably, choose a strong line that is closest to the observer's wavelength of interest and free of blends.
11. Insert the wavelength and measured Z_fine value of this emission line into WCALC. Enter the subraster radius output by fitsausage. Enter the appropriate value of B from the table above (for the given filter, Z_coarse value, and interference order corresponding to the emission line that was measured). Click the compute A button, and note the resulting value of A. Give this value to the observer, and copy it to the Aref box in WCALC.

Parallelism is the process by which the two etalon plates are made parallel to one another. If the plates are not optimally aligned, the transmission profile will be broad and/or asymmetric. This diminishes the light transmitted in the core of the profile, and thus the system throughput (for an emission-line source) and the instrumental resolution. It is thus crucial that proper parallelism is achieved and maintained throughout the run.

Parallelism is achieved and maintained through a capacitor and piezo-electric feedback system. See this page for a brief description.

The parallelism is optimized by the instrument scientist prior to the run. However, the parallelism depends on two variables: (1) wavelength, due to changes in the behavior of the multi-layer reflection coating with wavelength; and (2) the rotation angle of the etalon, probably due to gravity-induced sag of the plates that remains uncorrected by the system feedback mechanism. Rotation is inevitable during the course of a run, as the IMACS camera rotates to maintain a constant orientation of the CCD mosaic with respect to the sky. Fortunately, the rotation effect is reproducible. Until further testing permits the rotational effect to be software-corrected, the observer must adjust the parallelism when the etalon rotation changes by more than ~45 degrees. The parallelism must also be adjusted when filters are changed.

There are several methods for achieving parallel plates. We have developed a simple procedure that relys on scanning the transmitted image in the radial coordinate to prodcue a spectrum. The plate alignment is scanned along both axes of movement using a (M x N) grid of [X_fine, Y_fine]. At each value of [X_fine, Y_fine], an image is taken of an emission line. Each image is then azimuthally averaged to create an emission-line spectrum. The profiles of emission features are compared by eye (and, where possible, with line fits) to find the narrowest and most symmetric profile.

Here is a detailed procedure:

1. Choose a lamp appropriate for the filter being used. (See this table for options.)
2. If this is the first time during the run: With the lamp on, adjust the fine etalon spacing Z_fine and take snapshot images until you observe a bright emission line well separated from other lines in the field of view. The ring should be isolated from other lines, and its radius should be approximately halfway between the center and edge of the aperture. If a single, well-separated emission line is not present, a doublet will serve.
3. If this is not the first time: Select the same Z_fine value used for previous parallelism tests in this filter.
4. In the Script menu, click Create to bring up the script creation window. Choose Parallelize and enter the starting [X_fine, Y_fine] (x, y), step size in X and Y_fine (dx, dy), and number of steps in X and Y_fine (nx, ny). Assuming the image does not saturate, use 8x8 on-chip binning to minimize the readout time. Click Exec to bring up the script execution window, and run the loop.
5. When the script has finished, create the spectra by typing the following in a terminal:
   

   % ringbatch 1 9 6600 --fast [--ms 1]
   

   where 1 and 9 are the starting and ending frame numbers (leading zeros ignored) and 6600 is the central wavelength of the filter. The '--fast' option is good for parallelism tests, as it decreases the pixel sampling rate and thus increases the processing speed. For noisy data (faint lines), the '--ms 1' option smooths the spectrum using a median filter of width 1 Å.
6. Plot the spectra in a grid of [X_fine, Y_fine] values by running the following:
   

   % ringplot 1 9
   

   To do a Voigt fit of the profile peak, add --fit to the end of the command.
7. Search for the vector of [X_fine, Y_fine] that optimizes the etalon transmission profile. The optimal profile will be peaky (have at or near the peak flux), narrow, and symmetric.
8. If necessary, take another grid of spectra with different starting and ending values of [X_fine, Y_fine] until the optimal parallelism settings are found.
9. Enter the chosen [X_fine, Y_fine] pair into the IMACS software.

It is recommended that observers take a series of dome flats at approximately each wavelength in which they observe. Because of drift in the zero-point of the λ-Z relation, observers should recompute the appropriate Z value for the wavelengths of interest when taking flats. Using the Quartz High lamp, exposure times of 3-5 seconds should be sufficient (depending on the filter).

In the case of charge shuffling / frequency switching, it is recommended that flats be taken in charge shuffling / frequency switching mode, adjusting the exposure times appropriately.

Observers should observe flux standards at each wavelength in which science data is taken. Because of drift in the zero-point of the λ-Z relation, observers should recompute the appropriate Z value for the wavelengths of interest when taking flats. The observer should be aware of where in the field of view the calibration star is placed, since wavelength changes with distance from the optical axis. Exposure times of approximately 60 seconds should be appropriate for a star of magnitude 14-15.

A good database of Southern spectrophotometric standards resides at ESO. Because of the narrow bandpasses involved, care should be exercised in choosing a standard when the wavelengths of interest are near deep stellar absorption lines.

Emission-line flux standards are useful when observing in the 6600 Å and 6815 Å filters. See Tables 3-5 of Dopita & Hua (1997, ApJS, 108, 515) for a list of planetary nebulae that can serve as emission-line flux standards.

There is a wavelength gradient in the MMTF due to the angle at which rays pass through the etalon. This gradient is circularly symmetric aboout the optical axis (the projection of the MMTF normal axis onto the CCD). The optical axis is in the center of the field of view, but shifts slightly from run to run (due to the re-mounting of the IMACS CCD) and must be re-measured. During a particular run, it is constant within a few pixels as long as the etalon stays parallel.

To find the optical axis, we use the fact that there is a faint ghost reflection between the MMTF and the CCD. Use the following procedure:

1. Make sure the etalon is properly parallelized.
2. Insert into the beam a slit mask that has 5-10 guide star holes (square apertures) dispersed somewhat evenly over the central half of the field-of-view.
3. Take a quartz lamp exposure. The exposure must be long enough that faint reflections (primary ghost images) of the guide star boxes appear, but short enough that the original images do not saturate. These reflections are symmetric about the optical axis.
4. In IRAF, find the centers of each image and primary ghost using the ICBOX task from the IMACS package:

   cl> imacs
   cl> icbox ccd0001 optaxis sz=25
   

5. Create a file that contains on each line the chip number and pixel coordinates of each guide star box and its primary ghost. For example,

   # chip(box) X(box) Y(box)   chip(ghost) X(ghost) Y(ghost)
     2         532.51 1705.09  8           601.31   1671.86
     2         314.88 2106.46  8           383.88   2073.76
     ...       ...    ...      ...         ...      ...
   

   (Do not include the header line in your file -- it is here for illustration only.) Because the optical axis is near the field center, it is straightforward to match up images and their ghosts. The X and Y values for the image and ghost will have similar values (within ~100 pixels) despite being on different chips. Note that on a particular line, whether the image or ghost is listed first is irrelevant.
6. Run optaxis on this file. This routine has a model of the CCD mosaic geometry and will find the midpoint between each image and its ghost.

   % optaxis input_file
   

   The first page of the output plot is shown below. Record the optical axis location in chip coordinates. The coordinates are with reference to pixel [1,1] of the chip listed. Note that the optical axis can be located between chips, as indicated by negative coordinates or coordinates greater than 2048 (4096) on the X (Y) axis.
7. Put the optical axis location in chip coordinates into the file optaxis.dat, a copy of which should reside in each data directory for analysis. The contents should be as follows:

   Optical axis location
   chip#   X(pix)  Y(pix)
   5       6       4098