The DEIMOS CCD mosaic will closely resemble operational mosaics at University of Hawaii and NOAO. These mosaics share many image display requirements. For the sake of the occasional users of DEIMOS we prefer not to create yet another image display peculiar to one instrument. Subsequent to the software PDR we have continued to investigate various existing image display options. We now intend to follow a two-phase plan.
For the PDR we had investigated the behavior of several commonly-used
astronomical image display clients with DEIMOS-sized images. We found
that the existing clients had no limits inhibiting the display of
8k 
8k images. When tested on machines with sufficient RAM to
hold the entire image each of the clients demonstrated acceptable
responsiveness to user interaction. The responsiveness is adequate
for laboratory testing of the DEIMOS CCD mosaic.
However, all existing clients lack numerous features specified for the
operational system in the DEIMOS PDR.
During initial laboratory testing of the DEIMOS CCD mosaic we intend to use a modified version of the existing Keck image display client, Figdisp. Figdisp already handles real-time display of data from disjoint sections of a multi-amplifier CCD. Figdisp also provides access to the actual 16-bit pixel values. Both of these capabilities have proven invaluable during laboratory testing of CCD detectors for previous instruments.
John Cromer at Caltech recently ported Figdisp from SunOS to Solaris. We are continuing that port to be 64-bit clean for operation on DEC alpha (and other) processors. While porting we will modify Figdisp so that its pixel tracking can indicate that image sections may originate from separate CCDs with individual coordinate systems. This will provide us with an interface that can monitor and inspect image sections in real time during laboratory experiments on the DEIMOS CCDs and controllers. NOAO is already using a similarly modified version of the IRAF image interaction tools with their mosaic.
Existing image display clients have required that the image sections be stored in a single data array. For HIRES and LRIS at Keck this is done as part of the descrambling by the ``lickserv'' process. Early versions of the software for the NOAO mosaic relied on an external IRAF procedure When being used with Figdisp the DEIMOS ``lickserv'' process will assemble the image sections during the readout into a single array which approximates the true geometry.
Subsequent to the DEIMOS software PDR the NOAO mosaic became operational. The display for the NOAO mosaic was not specifically designed for mosaic images. Initially it used an existing image display client (ximtool) in a manner akin to the scheme presented for DEIMOS at the PDR. This display was recently enhanced to permit real-time viewing of the mosaic CCD readouts using data stored in the archival FITS format.
Last year SAO/CfA and NOAO received approval and funds to create an improved version of their existing image display clients (ximtool and SAOtng). This project is known as the Plug-in Image Extension (PIE) server. PIE will use a message-passing system to permit cooperation between tasks running on a heterogeneous network. Using a plug-in API it will interact with arbitrary data source and processing modules. PIE will not be ready in time for the testing phase of DEIMOS. Many of its features will, however, be prototyped in the NOAO Real Time Display (RTD), which is to be available in late 1997.
We have held several discussions with Doug Tody on the subject of the NOAO RTD. These include two full day, on site visits to gather details of its architecture and development. RTD is being built to serve the immediate needs of the NOAO mosaic detector. However, it is also serving as a prototype implementation of PIE. A delivery schedule for RTD was outlined at a meeting in 1996 December:
If by the time of DEIMOS commissioning the NOAO RTD were not available then we would continue to use Figdisp for observations. The capabilities of Figdisp are adequate for the purposes of scientific data gathering. However, several notable features specified at the PDR would be missing.
The Flexure Compensation (FC) system is a subsystem designed to maintain constant image position on the detector as the spectrograph rotates. The reasons for including this system are explained below. Here we give a brief overview of the system. Further details of the full system that are background to the software design are given in Part IV.
As the spectrograph rotates, deformation of the optical supports causes image motion on the detector. Finite element analyses of all elements and tests of prototytpe grating cells and mounts suggest that cumulative passive tilt and rotation errors through the optical path will cause variations in the beam entrance angle to the camera of about 10 to 20. This is after careful attention to these errors at every stage of the design. A 20 variation corresponds to 2.5 px of bulk image motion on the detector. This is about 10 times larger than the image motion error budget (see below) and must be corrected by the FC system.
In addition to bulk image motion, the structural deformations induce small amounts of image degradation and distortion. These latter are within the error budget, and the FC system does not need to address these lower-order effects. Image scale may also vary with the temperature of the camera, but the FC system contains no correction for that. Finally, a 10 in-plane rotation of the gratings or detector corresponds to 0.14 px (rms) of image rotation (0.20 px at the edge of the field). The passive design stiffness appears to be better than this, and no active correction will be made for image rotation.
Two requirements set the stringent error budget for image motion. The clearest requirement comes from image quality, which is tightest in spectroscopic mode at high dispersion in the red spectral region. The requirement that image motion degrade the FWHM by no more than 10% sets a limit of 0.25 px rms during an exposure. Image sharpness for direct imaging and other types of spectroscopy set an image motion tolerance of 0.5 px rms. Both of these are 5-10 times better than the projected passive stiffness as described above, requiring some form of active beam steering.
The second requirement for the FC system comes from consideration of fringing in CCD detectors. This is described in Part I Chapter 4.3. A long-term goal of DEIMOS is to provide pipeline data calibration using a long-lived calibration database. The ability to reset the spectrograph accurately to any previous setting will be a key ingredient in creating such a long-lived database. An important limitation on long-term stability is variations in the flatfielding accuracy caused by fringing in the CCD detectors. In spectroscopy mode, the principle cause of fringing is spectrograph flexure. Fringing variations limit the ultimate accuracy of spectroscopic CCD flat-fields in the red spectral region and thus set the limiting S/N that can be achieved for sky-limited observations. As noted in Chapter 4.3 the improvement in flatfielding that would result from image stability at the 0.25 px level is not known for certain because other effects may contribute to fringing variations (e.g., pupil rotation and accompanying changes in the pattern of pixel illumination). However, it appears likely that fringing variations will be significantly reduced if the above stability goal of 0.25 px rms is met.
The performance requirements for the FC system are as follows:
A system has been designed to achieve these goals. Details of the design are given in Part IV, which is a draft report on the FC system. The system consists of light piped into the focal plane from arc lamps via optical fibers. The images of these fibers are captured by two separate CCDs (the FC CCDs) that reside in the dewar next to the main CCD mosaic. A view of this arrangement is shown in Part IV, Figure 1.1. The images from the FC CCDs are read out every 15 sec, and their centroids are used to compute the motions of two control actuators. One of these tilts the tent mirror, which moves the image along the spectral dispersion direction. The second actuator is inside the dewar and moves the detector (and FC CCDs) along the slit direction.
The basic feasibility of the system has been established from optical distortion studies, flexure estimates, computation of the necessary photon fluxes, light integration times, and computation times, and prototype construction of both actuators. The basic command scheme and astronomer GUI have been outlined. Details of these and other items may be found in Part IV.
The major unknown in achieving the desired image stability goal is sensitivity of the camera focal length to temperature variations. The FC system can steer out bulk image motions but cannot correct for image size variations. The camera thermal problem is summarized in Part I, Chapter 4.3.
In this section we discuss open issues with respect to the calibration stability of the instrument. A draft calibration plan and associated software for DEIMOS are described Part III of this CDR Report. This plan must be considered tentative pending resolution of several unresolved issues that cannot be dealt with until the final instrument is assembled and tested. Most of these issues are familiar from other optical CCD spectrographs, but a few are peculiar to DEIMOS. This section summarizes these items under the headings of broadband direct imaging and spectroscopy. Narrowband imaging using interference filters is currently not contemplated with DEIMOS because the filters are located in the converging beam close to the detector.
Figure 4.1: DEIMOS layout
For background on the optical layout of DEIMOS needed to understand the following sections, please consult Figure 4.1, which shows the overall optical layout, Figure 4.2, which shows rays traced through the camera, Figure 4.3, which shows the footprints of beams on the tent mirror, Figure 4.4, which shows the percent vignetting by the tent mirror as a function of position in the imaging FOV, and Figure 4.5, which shows the amount of light in the outer ``ears" of the irregular Keck pupil outline.
Figure 4.2: camera ray trace
Figure 4.3: tent footprints
Figure 4.4: focal plane vignetting
Figure 4.5: pupil vignetting
The main obstacle to high-precision flat-fielding and flux calibration of
CCD optical spectrographs is fringing in the thin CCD detector.
The roughly 20- 
m thick silicon membrane becomes transparent
beyond 7000 Å, with the result that light that enters
is trapped inside a
resonant cavity. The internal reflection is quite efficient since
the index of refraction of silicon 
near 1 m;
thus light tends
to remain inside once it enters, unless the front surface
of the silicon is treated with an efficient anti-reflection coating.
Such a coating has the double benefit of increasing the amount of
light entering the membrane in the first place and reducing the
internal reflections that lead to fringing.
The interference condition is
where n is the index of refraction of Si (3.7 at 8300 Å),
is the ray angle from normal within the
silicon, t is the
membrane thickness (about 20 m for typical thinned devices),
and N is an integer. For 
= 8000 Å, the
above formula gives N = 185, so the interference order
is high.
That means that the interference phase angle rotates
through a full 
if changes by only 
Å at normal incidence.
Fringe phase is therefore extremely sensitive to the precise wavelength
of illumination.
In broadband direct imaging, the bandpass is typically 1000 Å\
wide and contains about 25 interference cycles. The
effective QE of the CCD varies depending
on whether a given wavelength is at a
peak or valley of the interference cycle.
Beyond 7000 Å where fringing is a problem,
the night-sky spectrum is dominated by the jagged
emission-band spectrum of OH airglow. To remove
this accurately requires using a background sky flat
constructed from the same spectral-energy
distribution. Typically this is done by taking the median
at each pixel of many night-sky images. This median
sky flat is scaled/offset and subtracted from each science frame
before the remaining celestial sources
are flat-fielded with a normal continuum
dome or twilight flat.
At Keck on LRIS, fringes are non-existent in B and V, barely visible in R, and attain an amplitude of a few percent in I. With care, they can be removed to an accuracy of 0.5% in I and better at shorter wavelengths. However, this is well below the potential accuracy set by photon statistics, so we would like to do better in order to achieve the fundamental limit set by photon statistics for photometric accuracy.
Two barriers to improvement presently intervene. The ratios of sky emission lines across the I bandpass may vary with time, which changes the effective fringe phase (and fringe amplitude?) of each pixel. Second, the ratio of OH light to continuum light in the spectrum of the night sky changes as the sun and moon rise and set. The spectrum of the sky is continually changing, with the result that fringe amplitude is again continuously varying. For accurate work, it is necessary to obtain separate continuum and ``OH'' flats and scale them separately to match the observed fringe amplitude in the sky. This is routinely done at Keck and reduces the fringe amplitude error considerably (Guhathakurta, private communcation). We plan to accumulate such continuum and OH flats from twilight and dark-sky flats as part of the calibration plan (Part III).
Even after this treatment, sky residuals remain in LRIS flats at the sub-percent level. These are visible as large-scale undulations and/or tilts in the residual sky level. The origin of these errors is not understood. For red frames, they may come in part from fringe phase errors caused by variations in the relative strengths of OH or other strong emission features. In the blue, where spectral CCD response varies strongly with color, they may come from spectral mismatch between the night sky and the twilight flats used to get the large-scale response pattern. At all wavelengths, scattered light (from the wings of bright stars, stars beyond the field, and light scattered from the slit and dome) is also suspected to be a problem.
With respect to scattered light, DEIMOS will likely be at a disadvantage compared to LRIS because its optical design (Figure 4.1) puts the camera entrance aperture just behind the entrance aperture for direct imaging. Light can therefore scatter off structures located in front of the entrance aperture near the center of the focal plane and enter the camera mouth. This is the area occupied by the TV camera and its supporting structure. We are paying close attention to the blackening and baffling of the TV surfaces, but the ultimate flatness of the sky background due to scattered starlight cannot be predicted reliably.
After sky subtraction,
the celestial sources must be flat-fielded and
flux calibrated. Flat-fielding will be done
using broadband continuous dome or twilight spectra. Since most
astronomical sources
also have continuous spectra, fringing
should not be a problem since there are
25 interference cycles across the bandpass and phase variations
should cancel out. For
narrowband sources dominated by a single emission line, residual
flat-field errors could amount to 
, where A is the fractional
fringe amplitude at that wavelength, of order 10% in
the red. We do not have plans to provide a general
calibration for narrow-band
sources.
Celestial sources vary in color and cannot all be flat-fielded by a single continuous broadband flat. However, the residual errors are a function of source color. Thus, global color errors can be removed by a standard photometric color term, and local errors that vary from pixel-to-pixel are expected to be small based on the sky flatness errors noted above.
A special calibration problem arises at Keck owing
to the segmented nature of the primary mirror,
coupled with pupil rotation of the alt-az mount. Since
different groups of
segments are coated at different times, large-scale
reflectivity variations of 10% may exist across the
optical pupil.
Variations may be even larger on Keck II since the primary mirror
is to be silver coated, and silver may degrade
more rapidly and more unevenly than aluminum.
Also, the outline of the segmented mirror is not circular.
These effects cause
variations in system throughput
as segments of differing reflectivity appear and disappear
behind internal obscurations in the spectrograph.
In direct imaging mode, the main source of internal vignetting
is the straight edges of the tent mirror, which obscure
up to 10% of the light at the inner and outer boundaries
of the imaging FOV (see Figure 4.3).
Throughput variations due to this vignetting are of two
types: (1) variations due to the irregular boundary of
the primary mirror, which causes the visible area to
vary by approximately 
0.8% as the pupil rotates behind
the tent mirror, and (2) variations due to non-uniform
segment reflectivity. An upper limit to the latter
may be estimated by considering
the edge of the imaging FOV, where pupil vignetting by
the tent mirror is 10%. If the
reflectivity of a vignetted portion of the
primary were 20% lower than average,
throughput would increase by 2% when this part
of the primary was obscured.
To summarize, throughput variations amounting to a few percent for direct imaging will exist at the edge of the imaging FOV. A fraction ;SPMlt; 1% is due to the irregular edge of the Keck primary and could be calibrated out from the known rotation angle of the pupil. The remainder arises from reflectivity variations on the primary and will vary with time as the segments are re-coated. Regular maintenance of the primary mirror is desirable to minimize this latter class of variations.
Fringing occurs in spectroscopic mode as well as direct imaging, with the difference that any one pixel is now illuminated by light of a single color. The response of a single pixel is given by
where A is the fractional amplitude of the fringe
pattern and 
is the fringe phase at that pixel, given by
(see equation 4.1). If CCD thickness and were both constant along a
spectrum, I would trace out a perfect sine wave. In
practice, varies smoothly with wavelength
due to the optical design, but
thickness varies randomly due to small-scale variations in the
thinning process. The resultant contours of constant have
complex topologies resembling wood grain contours.
Flat-fielding problems arise when on a
pixel differs between the flat-field image and the science
image. Slight variations are serious owing
to the very high order of interference ( 
).
The change in response is the derivative
of equation 4.2 and thus is a maximum at the zeroes of
the fringe pattern. If the fractional change in response is
,
then the largest change is
where N is the interference order,
is the wavelength shift,
and cos has been set equal to 1 for normal
incidence. (Note: for long wavelengths where the CCD is essentially
transparent, AN is essentially constant,
so that near 10000 Å, a thick CCD doesn't help at all.)
A typical flexure shift
for Cassegrain spectrographs is 5 Å, and fringe amplitude A is 0.1.
Inserting into equation 4.3 yields 
,
which is similar to the typical flat-fielding fringe
errors seen in LRIS spectroscopic images at Keck.
Since night sky OH lines produce more than
100,000 photons over regions of interest, they should
subtract to better than 1% by photon statistics.
Fringing prevents this, with the
consequence that
fringing is again the principal factor that
prevents large telescopes from reaching their theoretical
shot-noise limit beyond 7000 Å.
Variable vignetting and pupil rotation will again cause
throughput to vary in spectroscopic mode, with the
extra fact that additional, significant vignetting
occurs at the grating and camera mouth. The beam footprint on the
gratings is ellipsoidal, and light at
the ends can be lost at large tilt angles.
The large 
-in grating used in the red at high tilts
creates a long pupil
whose ends miss the camera mouth, which is only 11.5-in wide.
The product of these obscurations can amount to 
% of the light.
By analogy with the tent mirror vignetting in Section 4.3.1.2 it is clear that segment reflectivity variations coupled with pupil rotation will again cause throughput variations. The effect is larger now because a larger fraction of the primary mirror is vignetted. If the maximal 25% vignetted area were 20% lower in reflectivity than the rest of the primary, the net throughput increase would be 7%. This is probably an upper limit, but variations could clearly amount to a few percent, especially at large grating tilts (red wavelengths).
The 
-in gratings are narrower (6.05-in) than the full
``ear-to-ear" diameter of the beam (6.35-in). Pupil motion on the gratings
will therefore cause variable light loss. Specifications
state that the alignment of the beam on the grating should
remain constant to within 0.05-in, which would cause a
throughput variation
of less than 1% at all wavelengths.
However, alignment to this level is considerably
better than has been achieved for LRIS or HIRES on Keck I.
This effect will vary systematically with elevation angle
and could be calibrated out.
The final source of error for flux calibration in spectroscopy mode is slit losses owing to atmospheric refraction. These depend on the detailed light distribution in the object and will vary with wavelength. We plan to provide information on this for the observer but do not expect to make any correction for this effect.
To summarize, total fluxes and spectral energy distributions in spectroscopy mode will be in error by a few to many percent, depending on the airmass. Accurate measurements will require the use of large apertures and careful observations of standard stars at similar elevation angles and pupil orientations.
Several aspects of DEIMOS' design are intended to reduce residual fringing errors:
(1) The Flexure Compensation System is designed to
maintain wavelength on a given pixel constant to
0.25 px rms (see Part II, Chapter 5). This virtually eliminates
fringe phase shift errors due to change in .
(2) Efficient anti-reflection coatings are being sought
for the CCDs. A good coating not only promotes
transmission of light into the silicon but also reduces
trapped light and consequent fringing. Poor coatings
have fringe amplitudes 
15%. We are aiming
for a good coating like that in LRIS, which has 
5%.
(3) Thicker devices of high-resistivity silicon are being explored for DEIMOS' red CCDs. Thicker silicon pushes the onset of fringing (i.e., transparency) to longer wavelengths. A program to develop such detectors is underway at MIT Lincoln Laboratories (see DEIMOS Detector CDR, May 20, 1997). Fringing begins redward of 8000 Å in these detectors. Also, CCD thickness variations are much smoother (and smaller) in the MIT/LL thick CCD, compared to the usual thin CCD.
Note that items (2) and (3) will reduce fringe errors in direct images as well as for spectroscopy.
Despite these efforts, complete removal of fringe errors from flat-fields cannot be guaranteed:
(1) Because of the extremely high order of interference,
fringe phase may be sensitive to unsuspected
physical processes.
For example, fringe phase varies strongly across the pupil
at a given wavelength. This occurs because beams from
different parts of the pupil impact the CCD at different
angles, causing to vary. At the edge of the detector,
varies (within the silicon layer) from about 0 to 8,
and at the center the variation is 0 to 4.
These ranges correspond to 1.7 and 0.4 interference
orders, respectively. It is possible that fringe-phase pupil
variations could combine with segment reflectivities,
vignetting, and pupil rotation to create unpredictable variations
in total response.
(2) Thermal effects on camera plate scale could alter the mean wavelength on a pixel by more than the stability goal of 0.25 px rms, thereby confounding the FC system. Such changes in plate scale cannot be corrected by the FC system, which merely steers the beam. Maintaining constant wavelength at the edge of the detector would require that the camera temperature be held stable to better than 0.5 Kelvin. We are attempting to design the camera lens barrel to adjust the lens spacings passively to compensate for temperature changes, but the success of this approach is not yet known.
(3) The plan in Section 4.3.1.1 to subtract sky from red broadband images requires a suite of both OH and continuum sky flats. It is unrealistic to expect an observer to obtain a complete suite of such flats on each run, let alone each night. This sky-removal technique will work only if the instrument is stable enough to permit assembly of a longterm calibration database. We are endeavoring to make the instrument quite stable but the success of this approach is not yet known.
