Optical Performance Budget for the Far Ultraviolet Spectroscopic Explorer
David J. Sahnow
Center for Astrophysical Sciences, Department of Physics and Astronomy
The Johns Hopkins University, Baltimore, MD 21218
Cathleen M. VanDyke, Qian Gong, James Bremer
Swales & Associates, Inc.
5050 Powder Mill Road, Beltsville, MD 20705
Michael J. Kennedy
Applied Physics Laboratory
The Johns Hopkins University, Laurel, MD 20723
ABSTRACT
The Far Ultraviolet Spectroscopic Explorer (FUSE) satellite will make high spectral resolution (/ = 30,000) measurements in the 905-1195 Å bandpass from low-earth orbit. The optical system of the instrument consists of four coaligned telescopes and gratings, which disperse their spectra onto two detectors; both the mirrors and slit assemblies will be adjustable in flight. Because of this complicated, coupled optical system, it is important to understand all of the effects which may affect performance.
The ability of the FUSE instrument to maintain its high resolving power and effective area is dependent on many factors, including the optical design, manufacturing errors, the ability to coalign the system on orbit, and the stability of the structure holding the optical elements. In order to predict the on-orbit performance, a detailed optical performance budget has been developed. This budget includes all effects which affect the resolution and throughput. Included are short term effects (such as the stability of the metering structure due to thermal variations during a single orbit); long term effects (such as moisture desorption from the graphite/cyanate ester structure and gravity release); and installation tolerances.
We present the results of this exercise, and describe the dependence of the instrument performance on the expected errors.
error budgets, FUSE, spectroscopy, tolerance analysis
1. INTRODUCTION
FUSE, the Far Ultraviolet Spectroscopic Explorer, is designed to answer a set of fundamental questions about the nature of the Universe by making high spectral resolving power (/ = 30,000) measurements of astrophysical objects in the 905-1195 Å wavelength region from low-earth orbit. Its high effective area (30 - 100 cm2) and low detector background will permit observations of solar system, galactic, and extragalactic targets that have been too faint for previous instruments at this high resolution. A detailed description of the design and predicted performance of FUSE has been presented elsewhere.(1)
The critical parameters for FUSE to meet its science requirements are the throughput and resolution. In order to ensure the scientific objectives of the missions, requirements have been set for both high resolution and high throughput observations. These are: (1) a resolution of 30,000 over 80% of the band when using the narrowest (high resolution) slit, with a minimum resolution of 24,000, and a relative throughput of 50%; and (2) a resolution of 24,000 over 80% of the band (with an absolute minimum of 20,000) and a relative throughput of 95% when using a wider (high throughput) slit. The lower resolution case will likely be met if high resolution case is met, so it has been the driver in the development of the performance budget described below. In order to ensure this performance, the on-orbit positions of the optical elements must be maintained to micron-level positioning and arcsecond-level rotations, despite the several meter length size of the instrument.
FUSE will be launched into an 800 km, 25 inclination orbit in late 1998. Science observations will be pre-planned in advance, and will take place during the unocculted viewing intervals of the orbit. A high degree of autonomy will be built into the instrument to allow unaided target and guide star acquisitions, instrument alignment, and health and safety checks of the instrument by flight software. Observations will normally be carried out with no intervention from the ground.
2. THE INSTRUMENT
The FUSE instrument (Figure 1) consists of four coaligned telescope mirrors; four Focal Plane Assemblies (FPAs) containing the spectrograph slits; four spherical, aberration-corrected holographically-recorded diffraction gratings in Rowland mounts; and two microchannel plate detectors with delay line anodes (the spectra from two channels fall on different regions of a single detector). The optical design of the spectrograph has been described by Green et al(2). A visible-light Fine Error Sensor (FES) is used to image the area around the slits (on a single channel) and calculate accurate guide star positions so that the attitude control system can maintain subarcsecond pointing of the entire spacecraft.
Each FPA
contains four apertures: a narrow, 1.25 arcsecond slit to ensure the
highest resolution, with the loss of some throughput (50% light loss is
allowed); a 4 arcsecond slit to permit nearly 100% slit transmission,
with a subsequent loss of resolution; a large 30 arcsecond aperture; and
a pinhole for bright objects which would otherwise overwhelm the
detector.
The positions of both the telescope mirrors and FPAs can be adjusted on orbit. The mirrors have three actuators, which allow rotations in two axes, and piston motion along the optical axis. This motion is designed primarily for long term coalignment of the four channels, and focusing of the mirror to the spectrograph. The FPAs permit motion of the slits in both the focus and dispersion direction. This allows for coalignment of the four channels, and also ensures that each set of slits remains at the focus of its telescope. Table 1 shows the required motion for each of these mechanisms. It is expected that once initial coalignment is attained on orbit, the mirror mechanisms will be operated infrequently (monthly), while the FPA may be adjusted as often as once per orbit.
A graphite/cyanate ester structure is used to support the optical components. It is built in two parts: the telscope structure
and spectrograph structure, for integration reasons. Because of the stringent stability requirements on the structure, a very stable
composite was necessary. A composite was designed which has a coefficient of thermal expansion (CTE) of less than 1 10-7
in/in/ F. Also, although the use of metal was kept to a minimum, when a metal fitting was required for structural reasons, titanium
was chosen for its relatively low CTE. In addition, a thermal control system is used to maintain the temperature at any point on
each of the optical elements to 0.5 C over an orbit.
3. TIMESCALES
We have defined three timescales of interest to the tolerance budget. These are the initial (ground) alignment of the spectrograph, long term motions which include one-time effects, and short term effects occurring over timescales of less than one orbit. Each of these can be considered separately in the analysis.
During instrument integration and test, the FUSE spectrograph will be aligned first. This takes place without the telescope structure in place, using telescope mirror simulators in place of the flight mirrors. The detectors are installed onto the structure first, and the gratings and FPAs follow. Initial installation will occur using optical metrology, and the fine alignment will be made by focusing and positioning the spectra on the detector. Relatively small deviations from the nominal position in the placement of the detector can lead to substantial variations in the positions of the subsequently installed optics (up to several millimeters) in order to ensure the optimal performance. Therefore, ground support equipment used in the installation process must be able to accommodate a significant variation in position, and to retain the maximum flight motion for the FPA and telescope mirrors on-orbit.
Long term tolerances include one-time effects, such as gravity release, plus distortions introduced by attaching the spacecraft bus to the instrument structure, and the spectrograph structure to the telescope structure. Also included are slowly changing parameters, such as the dimensional change of the composite structure as moisture desorption occurs over a period of years. Some long term effects can be compensated for by using the mechanisms described above.
Observations of a single target will vary from less than 2000 seconds to more than 150,000 seconds. For targets outside of the continuous viewing zone, the earth will occult the target during part of the 101 minute orbit, meaning that a target peakup may have to be repeated as often as once per orbit for each channel. For this reason, one orbit has been chosen as the nominal 'short term' time scale. During a single orbit, the goal is to not move any of the mechanisms; during this time, motions of the optical elements in the spectrograph, primarily due to thermal variations, will cause a smearing of the spectra on the detector, causing a loss of resolution. Although much of the FUSE data will be taken in a photon list mode, where each photon is stored individually, without knowing how the optics are moving, it will be difficult or impossible to remove this smearing. Motion of the telescope mirrors will cause either a loss of throughput (when using a narrow slit) or resolution (when using a wide slit). It is for this reason that considerable effort has been expended on the design of a thermal control system which can maintain constant temperatures on the structure and optical components.
An additional short term effect is motion of the guide stars on the FES during a single orbit. If the image on the FES moves, either due to motion of the FES as a whole, or due to something internal to the camera, the attitude control system will interpret this as a motion of the spacecraft, and adjust the pointing accordingly. This will cause the target to be moved away from its location in the slit, possibly decreasing the throughput. Since an FES only uses light from one of the four channels, any change in coalignment of the channel containing the active FES to the others will cause a similar effect.
4. BUDGETS AND PREDICTIONS
The top level error trees for high resolution (narrow slit) observations are shown in Figure 2 (throughput) and Figure 3 (resolution). Each column shows the effect of a particular optical element on the budget. The two figures share a number of common factors, but also show how different factors affect the throughput and resolution. The values shown in the charts represent the current predictions of performance. As measurements are made on flight hardware, more accurate values will be included.
4.1. Throughput Budget
Figure 2 shows the factors contributing to the throughput budget, with each column of boxes representing a particular optical component. The important terms are described below.
The telescope baffles have been designed to ensure that they do not obscure the light path under all conditions of initial alignment and on-orbit motions, so they have no effect on the throughput.
The telescope mirrors are one of the largest contributors to the budget. The major terms include the requirement on the mirror fabrication and mounting (90% encircled energy in 1.5 arcseconds at 1000 Å), the mirror reflectivity (which varies strongly with wavelength, depending on which of two coatings, SiC or Al/LiF is used on that particular channel. Long term effects, which are further subdivided in the chart, are only required to be compensated for by the in-flight mechanisms.
FPA effects include the physical size and location of the slits, and the ability to move those slits to the desired position to guarantee coalignment. Detector effects include the quantum efficiency, and the 'cropping' which can be done at the detector, by discarding photons in order to improve the resolution. Although cropping decreases throughput, for a particular observation a tradeoff will be made between throughput and resolution.
Pointing of the instrument is another important factor in the budget. If the FES supplies a Noise Equivalent Angle (NEA)
of 0.2 arcseconds, the current predictions are that the spacecraft will be able to maintain the pointing of the instrument to 0.33
arcseconds, 1. In addition, there is a 'DC' offset, which is a function of how well the mirrors and slits can be coaligned, and how
well the automated peakup process works. We expect that targets can be placed within 0.4 arcseconds of the center of the narrow
slit.
Finally, the grating reflectivity and groove efficiency contribute to the throughput in the same way that the mirror reflectivity does.
4.2. Resolution Budget
The resolution budget tree (Figure 3) has a number of elements in common with the throughput tree, but there are also important differences, since the effects of the spectrograph components become much more important. Entries which differ from those described above will be described here.
The 'effective slit width' is slightly larger than the actual slit size here, since a motion of the slit during an observation allows light from a larger range of solid angles to enter the spectrograph, decreasing the resolution. Grating fabrication, mounting, and initial positioning errors, along with the limitations on the maximum resolution due to the optical design (which is a strong function of wavelength) are listed in the third column. Grating long term effects, similar to the mirror long term effects described in the previous section, are also included here.
Detector performance is critical to resolution. The fabrication and mounting of the detector, in addition to the point spread function (PSF), pixellization, and the cropping and straightening of the spectra all have a major influence on the measured resolution. The spectrograph design produces curved spectra, which must be straightened in order to achieve the maximum resolution.
Short term motions
Finally, the short term (single orbit) motions of the optical components are critical. The values of these motions affect requirements for the thermal environment of the instrument during a single orbit. To determine the values of the short term allowables, a raytrace analysis was performed. All other influences in the error tree were assumed to be at their allowable values, and the maximum amount of short term motion which still provided the specified performance (e.g. a resolution of 30,000 for the high resolution case) was determined. This analysis was performed twice, once for the high resolution case and once for the high throughput case. The results of these two analyses showed that the requirements on motion allowables for the high resolution case, for both resolution and throughput are more stringent than the high throughput case. The budget which was developed, therefore, is the high resolution budget. By meeting it, the short term budget for the high throughput case is also satisfied.
The allowables were provided as x, y and focus location changes of the chief ray on the detector surface. This is a convenient system-level analysis for both the optical analysis and the structural distortion analysis which is done to predict the short term motions. From these allowables, the optical analysis can determine the resulting decrease in performance without the necessity of knowing the exact cause of the motion. These allowables can also be used to compare with results from the structural distortion analysis. The motion of the chief ray on the detector is a result of the rotations and translations of the individual optics due to any short term cause. A raytrace was completed for a unit motion of each optic in each degree of freedom independently. The resulting motion at the detector is an influence coefficient which can be used to linearly combine the effects of all degrees of freedom of all of the optics. Once the matrix of influence coefficients was determined, the structural analysis could be done independently of the optics analysis.
Any distortion on the structure can cause rigid body rotations and translations of the optical system. These will be corrected by the FES and, therefore, should not be included as a source of error in the short term structural distortion analysis. In this analysis, the optics internal to the FES were not yet defined, so the amount of rigid body rotations which would be seen at the FES was assumed to be due to the rotation of the telescope mirror used by the FES. Once the FES optics were better defined, this assumption was checked and proven to be accurate. Influence coefficients for rigid body rotations were developed based on the rotations of the telescope mirror and were included in the analysis. Translational rigid body motions are automatically eliminated by using the influence coefficients in the linearized raytrace.
Once the overall allowables were determined, they could be
allocated to different causes of distortion. The first division was to
instrument structure, spacecraft structure, and component mounts (Figure
4). The component mounts term was further 
divided into grating, detector and primary
mirror terms. Those budgets were divided into the six degrees of freedom
for each component using the influence coefficients. The predicted
motions which are compared to the budget, due to any short term error
source, can be determined by each of the component providers. The
spacecraft structure was undefined when this budget was made. Therefore,
some conservative assumptions were made in order to allocate an
allowable for spacecraft influences. Ultimately, the spacecraft and
instrument structures are combined, both in the analysis and in the
error budget. The final analysis verified that the original budget was
conservative.
The instrument structure portion of the budget represents any changes in the metering structure due to the thermal effects over one orbit and due to jitter during an orbit. These were considered the only short term error sources. Jitter was initially given a budget of zero because of the transient nature of the error. The only source of jitter on FUSE is the reaction wheels on the spacecraft. It was believed that the amount of time during an orbit that the dynamics of the reaction wheels would excite the structure and cause a smearing on the detector would be minimal. Once the spacecraft finite element model was available, the reaction wheels were modeled with a forcing function, which was applied to the coupled spacecraft and instrument model. The influence coefficients, which were included as multi point constraint equations, determined the smearing on the detector as a function of frequency. The maximum amount of distortion was low, but not zero. The budget will be reallocated to include a small amount for jitter sources.
Since all of the errors in the budget are not likely to occur at the same time, all of the effects are root sum squared from
one level to the next. As the work is being completed and updated, the budget will also be updated to reallocate allowables from
locations who show margin to those who need more budget.
5. ONGOING WORK
Much of the work described above assumed an initially perfectly-aligned instrument. In reality, the initial on-orbit configuration of the instrument will not be perfect, due to gravity release, mounting distortions due to the spacecraft, etc. We are currently in the process of verifying the in-flight range of motion for the mirror and FPA by making predictions of these effects. and using them to calculate an initial offset position. Then, raytrace simulations of the in-flight mechanism motions will be used to return the system to its optimal focus. This may require the intentional misalignment on the ground of some parameters, in order to compensate for the known effects such as gravity release and moisture desorption. Other effects, such as mounting distortions, cannot be predicted well enough to compensate for, but must instead be modeled in a statistical way.
Ultimately, the goal is to have a complete model which can predict performance (both resolution and throughput) as a function of the elements in the error trees shown above. As performance data is measured in the laboratory, these predictions will be modified, and terms may be reallocated in order to ensure high performance.
6. ACKNOWLEDGEMENTS
This work was supported by NASA contract NAS5-32985.
7. REFERENCES
1. D. J. Sahnow, S. D. Friedman, W. R. Oegerle, H. W. Moos, J. C. Green, O. H. W. Siegmund, "Design and predicted performance of the Far Ultraviolet Spectroscopic Explorer (FUSE)," Proc. SPIE 2807, 1996.
2. J. C. Green, E. Wilkinson and S. D. Friedman, "The design of the Far Ultraviolet Spectroscopic Explorer spectrograph," Pro. SPIE 2283, 12-19, 1994.