The Flexure Compensation (FC) system is a subsystem designed to maintain constant image position on the detector over short timescales as the spectrograph rotates, and over longer timescales as the spectrograph optical components are manipulated and maintained. As position angle changes, deformation of the optical supports causes image motion on the detector. Finite element analyses and tests of the grating cells and mounts suggest that cumulative passive tilt and rotation errors through the optical path will create a variation in the beam entrance angle to the camera of from 10 to 20 arcseconds. This is after careful attention to these errors at every stage of the design. A 20 arcsecond variation corresponds to 2.5 px of bulk image motion on the detector. This is about 10 times larger than the error budget and must be corrected by the FC system.
Additional image motion is caused by errors in the re-positioning of optical elements. Most important are gratings, which are continually being removed and re-inserted, both on the grating mount as gratings are changed during an observing run, and within the grating holders when the grating complement is altered prior to a run.
All these sources of bulk image motion also induce distortion in the image. These distortions are not correctable by beam steering and thus leave residual position errors. In addition, there are two other kinds of image motion that are not correctable by the FC system: image scale changes and image rotation. The image scale is very sensitive to camera temperature in the basic optical design, but we are attempting to mitigate this by passive thermal compensation of the camera cell. A 10 arcsecond 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 is made for image rotation.
An error budget for these residual uncorrected position errors is given below in chapter 2.
Two image quality requirements set the stringent error allowance for image motion:
rms
diameter images (1-D rms radius = 0.54 px) by more than 10%, the image
motion during the exposure should be limited to 0.25 px rms in the
dispersion direction. This corresponds to a variation in the beam
entrance angle to the camera of 2 arcseconds rms, or a cumulative tilt
of the grating, tent mirror, and collimator mirror of roughly 1 arc second.
In direct-imaging mode and at lower dispersions, this tolerance can be
relaxed to 0.5 px rms, corresponding to 4 arcseconds rms of beam tilt.
As mentioned above, the expected passive
structural beam tilts are 10 to 20 arcseconds, between
2.5 and 10 times larger than the range of tolerances.
The improvement in flat-fielding that would result from image stability at the 0.25 px level is not known because other effects may contribute to fringing variations (e.g., pupil rotation and accompanying changes in the pattern of pixel illumination). However, it is likely that fringing variations will be significantly reduced if the above stability goal of 0.25 px rms is met. In particular, it was shown in Part 1, Chapter 4.3 that this level of stability would completely eliminate all contributions to fringing from wavelength variations. For further discussion of the physics of fringing, see the above section.
The performance requirements for the FC system are as follows:
A system designed to meet these requirements is shown in Figure 1.1. It consists of:
Emission lines from Ne, Ar, and Hg arc lamps are used to track the effect of structural deformations. Four optical fibers feed light from the arc lamps into the telescope focal plane adjacent to the active optical slit area. Arc lamps are used in preference to a Fabry-Perot etalon because their wavelengths are stable at all temperatures. All three lamps feed each of the four fibers. The light from each fiber is shaped into an f/15 beam so that it illuminates the spectrograph in a manner analogous to celestial objects.
Figure 1.1: fc overview
The image of each fiber is a spot in direct-imaging mode and is a line of spots in spectroscopic mode. These images fall on two flexure compensation CCDs, which are read out during the regular science exposure at 15 second intervals using a separate signal chain.
The goal of the FC system is to steer the image in translation in X and Y (Y is in the dispersion direction; X is along the slit). This requires two pieces of information, which can be obtained in principle from the coordinate locations of a single spot. In imaging mode, the CCDs will see a total of four spots, one from each fiber. Thus there is redundant information. Part of this redundancy will be used to compare information from separate spots to ensure that the image is not corrupted by a cosmic ray or cosmetic flaw on the CCD. However, still more information is available from the fact that spots are on opposite sides of the mosaic. We will make use of this to monitor both image rotation and scale. These variables cannot be corrected by the FC system, but the information is valuable as a check on proper instrument operation. Finally, we also plan to measure spot size (and perhaps ellipticity and other higher-order moments) to monitor focus and other aspects of image quality.
In spectroscopic mode, there will usually be more than 4 spots that are visible; however, some tilts of the high-dispersion 1200-line grating will provide only one spot per CCD. The analysis program will have to adapt to the number of spots that are visible at any one time.
The FC CCDs operate in frame transfer mode, obviating the need for a mechanical shutter. Image centroid algorithm(s) find the image position(s) on the two CCD images and feed correction signals to two mechanical actuators in the spectrograph. One of these, a piezoelectric actuator, tilts the tent mirror and moves the image along the dispersion direction (Y). The other is a moving stage in the dewar that translates the detector in the direction perpendicular to the dispersion (X). Together, the two actuators stabilize the image in translation.
The goal of achieving an accuracy of 0.25 px rms every 15 seconds
determines most aspects of the FC system. Two hundred micron diameter
fibers will produce 0.5 arcsecond (4.2 px) FWHM images at the edge of
the FOV (Gaussian 
= 1.8 px). Roughly 50 photons are therefore
sufficient in principle to yield 0.25 px rms precision per integration. To
essentially eliminate photon noise from the error budget, we have set a
threshold of 1000 photons per exposure (see Chapter 2).
The faintest desired arc line
contains about 1% of the total flux of the three lamps. Therefore, the
light intensity can be adjusted to yield 1000 photons from this line
while at the same time not exceeding 100,000 photons in total, which is
less than full well. Broadband filters in direct imaging mode will
reduce this integrated signal by a factor of several but will still
leave sufficient photons to provide the required precision.
Order-separating filters in spectroscopic mode will have no effect
since the FC CCDs are near the center of the desired wavelength range.
We have adopted a fixed exposure time of 10 seconds, which allows 5 seconds to
read the image, centroid, compute the corrections, and move the
actuators.
The FC CCDs have a 600 x 1200 format with 15 micron pixels. In frame-transfer mode the active area is 300 x 1200 px, with the long dimension along the spectrum. At the highest dispersion (1200-line grating, 0.32 A per px), each CCD captures 400 A of spectrum. By positioning the FC CCDs optimally along the dispersion direction, at least one usable arc line can be captured for all filters, gratings, and grating tilts.
From the expected flexure estimates in Section 1.1, the required range of the X- and Y-actuators in normal use will be a few pixels. The current design provides 12 pixels of motion for the X-actuator (detector) and 22 px of motion for the Y-actuator (tent mirror). A procedure has been developed to reset the mean position of all optical elements after servicing (such as the collimator and tent mirror) to within 5 to 10 arc seconds, corresponding to 1.3 to 2.5 pixels on the detector. The detector can also be removed and reset to similar accuracy. Thus both actuators have enough range to reset the image to its previous location after servicing of the optical train. Despite this, it is anticipated that changes to the optical train will likely require a complete rebuild of the calibration database, and this is allowed for in our operational plan.
