17 May, 1999

The Next Generation Optical Spectrograph (NGOS) is a wide field, imaging spectrograph containing modern optical technology allowing high efficiency and spectral resolution over a very wide field of view.

NGOS is currently envisioned for use on the Mayall 4-meter telescope at the Cassegrain focus.

Design Goals

• Minimum of 20 arc-minute diameter field. Goal of 40 arc-minute diameter field.
• 45% peak system efficiency (telescope, instrument, detector) excluding slit losses (wavelength regime of peak efficiency TBD, minimum efficiency off-peak TBD).
• Nominal resolving power of 5000, range from 2000 up to 10000 (possibly higher).
• Spatial sampling of 0.3" per pixel.
• Nominal slit width of about 1.0" (TBD after simulations to determine optimal slit widths for a variety of applications).
• Spectral coverage at field center of ~1 octave at R=5000 (requires ~8K detector).
• Operable spectral range of 365 to 1700 nm.
• Long slit capability.
• Slit mask capability.
• Micro-lens IFU mode.
• Iodine or other molecular absorption cell capability for high precision, radial velocity work.

Optical Band

Technology for the optical band, 365-1100 nm, is such that the spectrograph should achieve optimal performance with respect to field of view, efficiency, and spectral coverage. CCD detector technology is sufficiently mature within this spectral region either through mosaicing or with very large format detectors.

Non-Thermal Infrared Spectral Band

Technology for the infrared portion of the operable spectral range (1000-1700 nm) is continually evolving, but is currently incapable of easily achieving full performance goals with respect to field of view and possibly spectral coverage. Design of the spectrograph will be such that future enhancements in non-thermal IR detector technology can be implemented to achieve full performance of the spectrograph in the non-thermal infrared.

Design Issues

Beam Diameter

Resolving power of a diffraction grating spectrograph goes as

\begin{align*} R = \frac{\lambda}{\Delta \lambda} = \frac{b}{D_{tel}\theta_s} \frac{m \mu \lambda}{cos \beta} \end{align*}

where b is the beam diameter, D_tel is the telescope diameter, q_s is the slit diameter in radians, m is the order of diffraction, u is the line frequency of the grating, l is the wavelength, and b is the angle of diffraction given by the grating equation

\begin{align*}
m \mu \lambda = sin \alpha + sin \beta
\end{align*}

Enhancing the resolution of a spectrograph is effectively limited to narrowing down the slit (which increases slit losses), increasing the grating line frequency (and related diffracted angle), or increasing the beam diameter. Hence, the beam diameter plays a critical role in the performance capability of the spectrograph.

For the volume-phase holographic (VPH) gratings most likely to be used in this spectrograph, bandwidth performance scales as

\begin{align*}
\frac{\Delta \lambda_{FWHM}}{\lambda} \propto \frac{\lambda}{d_g} cot\alpha
\end{align*}

for the spectral bandwidth, and as

\begin{align*}
\Delta \alpha_{FWHM} \propto \frac{1}{\upsilon d_g}
\end{align*}

for the angular bandwidth where d_g is the thickness of the grating volume. Both bandwidths shrink as grating line frequency is increased. Hence, if we increase the resolving power of the instrument by increasing u, we ultimately decrease the bandwidth of the grating (higher u results in a higher value for a). This translates into a potential loss of spectral coverage on a large format CCD or in significant energy distribution (blaze) shifts across the field of view.

Therefore, the most effective way to enhance the resolving power of the instrument is to increase the beam size. Once a realistic beam size is selected, then the appropriate grating line frequency is selected to deliver the desired resolution at a given wavelength.

Sample Case Showing Beam Size Tradeoff

One design goal for the instrument is to achieve R=5000 with spectral coverage from 360 to 720 nm. Let�s assume a 1.0" slit size. For a 100 mm beam, the grating must have a line frequency of 1580 l/mm to deliver the required resolving power. If the beam size is increased to 150 mm, a grating with a line frequency of 1110 l/mm is required to give R=5000 at 540 nm. Likewise, for a 200 mm beam, the line frequency needs to only be 850 l/mm.

This figure shows the efficiency profile for each of these gratings and the spectral coverage provided by an 8K detector with 0.3" pixels. Note that the 1580 l/mm grating has an insufficiently wide bandwidth for the detector coverage. The 1110 l/mm grating in a 150 mm beam provides a bandwidth which just meets the width of the detector. At a slight loss of peak efficiency, but with a flatter efficiency profile over the imaged spectral region, the 850 l/mm grating in a 200 mm beam is the most desirable of the three configurations. The 150 mm case is possibly acceptable, but the 100 mm case should be rejected as it fails to meet the desired spectral coverage (unless the slit width is decreased so that a lower line density grating could be used).

Note that higher resolving powers require higher line density gratings, hence lower bandwidth capability. One unfortunate aspect of VPH technology is that the bandwidth will shrink faster than the spectral coverage provided by the detector. This means that at higher resolving powers, the bandwidth will eventually be too narrow to fill the CCD.

We also have to worry about the effect of field angle on the response of the grating. Field angles perpendicular to the dispersion direction are diffracted at the same efficiency as the field center. However, field angles parallel to the dispersion, are incident on the grating at angles that do not meet the originally desired Bragg angle. Hence, the efficiency profile (ie. Blaze) is shifted in wavelength. The impact of this shift is again dependent on the line density of the grating. Lower line density gratings will show less severe shifts than higher line density gratings. Also, larger beam diameters result in lower values for the angular offset of the field angle at the grating, resulting in smaller shifts in the grating blaze.

The following two figures demonstrate this phenomenon for the 150 mm and 200 mm cases.

 

 

The 150 mm case shows larger variation in efficiency due to field angle than the 200 mm case. The 200 mm case would be preferable to the 150 mm.

It is interesting to note that the blaze shift is such that the efficiency peak is shifted in the direction of the wavelength band that falls on the detector.

Proper flat fielding techniques should properly compensate for the blaze variations across the field of view so that flux calibration is not compromised.

There may, however, be subtle issues related to detectivity uniformity when dealing with survey detection thresholds.

Slit Width

Optimal signal detection relies on proper choice of a slit width that best matches the image profile yet which also rejects the most background contamination, or sky. For stellar and unresolved targets, the image profile is defined by the atmospheric seeing and delivered image quality of the telescope. For extended objects, the image profile can become much more complex, but is dominated by properties of the object and less dependent on atmospheric or telescopic properties.

Unresolved Images

The image profile for stars and other unresolved astronomical sources can be represented by a Moffat function in which the core is similar to a Gaussian, but the wings are more like a Lorentzian profile. The width of the profile is dominated by both the atmospheric seeing and by the telescope imaging. Delivered images at the 4-meter currently have a median width of 1.1 arc-seconds. Continued efforts to improve the primary support system, mirror cooling, and other enhancements are expected to further improve the median image to about 0.9 arc-seconds.

The precise formulation for the delivered profile at the 4-meter is unknown, so we will have to assume a standard form for the Moffat function.

Design Concept 1: f/6 Option

One way to implement a "Coudé sized" spectrograph onto the Cassegrain focus of the telescope is to fabricate a new secondary mirror which moves the focal surface upwards allowing for more room for the spectrograph to occupy. Concept 1 does just that with a new f/6 secondary located at roughly the same physical location as the f/8 secondary. This results in an upward shift of the focal surface by about 2.6 meters or to a position of 0.8 meters above the primary mirror. We opted to move above the primary mirror in order to allow physical access to the focal surface location for the interchange of slit masks, etc. This implies a modification to the telescope structure (or mirror cover?) that would allow such access without risk to the primary mirror surface.

F/6 Optical Design

Charles Harmer has designed an f/6 option with a two element corrector and ADC prisms that provides excellent image quality over a 42 arc-minute diameter field of view. The secondary is about the same size as the current f/8 secondary and has a longer radius of curvature (R_f/6=11.7 meters, R_f/8=9.6 meters) but a higher conic term (C_f/6=-9.4, C_f/8=-5.3). It is also located about 48 mm behind the nominal position of the current f/8 secondary.

Questions: Can a 48 mm shift be accommodated with the current secondary mount? If not, can the optical design for the f/6 be modified to move the secondary closer to the nominal f/8 position without sacrificing image quality? If not, what level of effort is needed to modify the secondary mount to allow for such a displacement of the f/6 secondary?

The first element of the corrector assembly is located about 2.1 meters above the primary mirror. This is within the space envelope of the current chimney stack/baffle at about the same location as the #3 mirror cover. The focal surface is located at about the lower edge of the #3 mirror aperture hole in the side of the chimney stack/baffle.

Questions: Can a stack be fabricated in which adequate structure is available to hold the elements in place at such locations above the primary?

Properties for the f/6 focal surface are:

• Actual focal ratio of f/5.82.
• Effective focal length of 22989.7 mm.
• Plate scale of 8.97 "/mm or 111.5 mm/".
• 90% polychromatic (370 through 1700 nm inclusive) encircled energy within 0.22" diameter circle across the full field of view (presently ignoring ADC prism contribution).
• Focal surface radius of curvature is essentially flat at 26.5 meters.

Spectrograph Parameters for f/6 Option

Optical design effort is currently underway for the following conceptual spectrograph that would utilize the f/6 implementation described above.

Specifications:

• F/6 input and collimator positioned according to above f/6 optical design.
• Utilize a 200 mm diameter for the on-axis beam.
• Locate the grating below the primary mirror cell within the Cassegrain cage space envelope such that an articulated camera can swing from a camera-collimator angle of 0 degrees up to 90 degrees (and possibly higher if space constraints allow).
• All transmissive optics, no folds or reflections.
• Gratings are all transmissive and function in Littrow (assume zero anamorphism).
• Operational range from 365 nm to 1700 nm with maximum of 1 octave simultaneous coverage.
  • Blue Optical: 365-750 nm.
  • Red Optical: 500-1100 nm.
  • Non-thermal Infrared: 1000-1700 nm.
• Resolving power ranging from 2000 to 10000 (and possibly higher with prisms on high line density gratings). Explore R=20000 and 30000 capability. A maximum resolution of about R=40000 may be possible with a 2800 l/mm grating. There is also a configuration in which R=100000 could be achieved with a 4800 l/mm grating.
• Nominal slit width of 1.0 arc-seconds with 0.3" sampling on 15 mm pixels.
• Detector formats of:
  • 8k by 8k Optical CCD with 15 mm pixels (365-1100 nm).
  • 2k by 2k HgCdTe detector with 17 mm pixels (1000-1700 nm) with eventual upgrade to comparable 8k by 8k format as optical CCD.
• Full field diameter of 40 arc-minutes, circular field of view.
• Removable Iodine (or comparable) absorption cell capability.
• Lenslet IFU mode with 1 arc-second diameter micro-lenses.
• Include broad band order sorting filters.
• Peak system efficiency of >45% inclusive of telescope, instrument, grating, and detector.

Optical Design of f/6 Spectrograph

Progress is currently underway by Charles Harmer in the design of the f/6 collimator and camera. A full system has been designed, but does not give adequate image quality. We are currently exploring a more restricted field of view and a reflective collimator.

Design Concept 2: f/8 Option

The second concept that will be explored is a fallback option with the existing f/8 secondary. It is likely that this option will require some sort of folding mirror to implement either a 200 mm beam or a 150 mm beam diameter. Additionally, field size may have to be compromised in order to fit the instrument into the space envelope provided by the Cassegrain cage. Removal of the cage bottom yields a bit more space, but probably an insufficient amount to be considered as a viable option.

F/8 Optical Design

Charles has produced a two-element, wide field corrector with ADC prisms for use with the existing f/8 secondary. Excellent image quality is provided over an equivalent field of view, 42 arc-minutes in diameter, as the f/6 configuration. The corrector elements are located about .37 meters below the primary mirror surface and the focal surface is effectively maintained at the nominal f/8 location, 1.8 meters below the primary mirror surface. Implementation of this corrector would be fairly straightforward in a manner similar to the implementation of the wide field corrector recently installed on the CTIO Blanco telescope for use with Hydra/CTIO.

A parallel effort to evaluate moving the f/8 focal surface upwards without a new secondary resulted in very poor image quality that is dominated by spherical aberration. The focal surface must remain relatively close to the nominal R/C position in order to maintain adequate image quality. This, however, leads to the space envelope problem.

Properties for the f/8 focal surface are:

• Actual focal ratio of f/7.91.
• Effective focal length of 31258.3 mm.
• Plate scale of 6.59 "/mm or 151.5 mm/".
• 90% polychromatic (370 through 1700 nm inclusive) encircled energy falls within a 0.17" diameter circle across the full field of view (excluding ADC prism aberrations). This is somewhat better than the f/6 option.
• Focal surface radius of curvature is 11.8 meters, not quite as flat as the f/6 focal surface.

Preliminary Spectrograph Parameters for an f/8 Option

Effort on this option will not start until the f/6 option has reached a minimal level of maturity. Specifications for the f/8 option are preliminary and may be further expanded and possibly split into more than one configuration.

Specifications:

• F/8 input and collimator positioned according to the above f/8 optical design.
• Utilize a 150 mm diameter (200 mm as a possible 3^rd configuration) for the on-axis beam.
• Minimize the use of fold mirrors, but allow the spectrograph to have an articulated camera range of 0 to 90 degrees.
• Transmissive optics where possible.
• Gratings are all-transmissive and function in Littrow (ie. assume zero anamorphism).
• Operational range from 365 nm to 1700 nm with maximum of 1 octave simultaneous coverage.
  • Blue Optical: 365-750 nm.
  • Red Optical: 500-1100 nm.
  • Non-thermal Infrared: 1000-1700 nm.
• Resolving power ranging from 2000 to 10000 (and possibly higher with prisms on high line density gratings). Explore R=20000 and 30000 capability.
• Nominal slit width of 1.0 arc-seconds with 0.3" sampling on 15 mm pixels.
• Detector formats of:
  • 8k by 8k Optical CCD with 15 mm pixels (365-1100 nm).
  • 2k by 2k HgCdTe detector with 17 mm pixels (1000-1700 nm) with eventual upgrade to comparable 8k by 8k format as optical CCD.
• Full field diameter goal of 40 arc-minutes, circular field of view. Full field requirement of 20 arc-minutes diameter.
• Removable Iodine (or comparable) absorption cell capability.
• Lenslet IFU mode with 1 arc-second diameter micro-lenses.
• Include broad band order sorting filters.
• Peak system efficiency of >45% inclusive of telescope, instrument, grating, and detector (may be difficult with folding mirrors).

Optical Design of f/8 Spectrograph

Design effort will be on hold until f/6 option has been completed to an acceptable level. The study of a reflective collimator will initially concentrate on the f/8 secondary.