Telescope Capabilities

Telescope Performance Modeling

To help understand whether the proposed telescope systems will perform the desired NEO follow-up astrometry and NEO science, Project ASTEROID has performed some preliminary spreadsheet calculations to estimate the limiting magnitude of each telescope for imaging and low-resolution spectroscopy. These results are are based on a conceptual optical design for the 2.5-m telescope and a hypothetical design for a 1.5-m telescope derived from the 2.5-m design. The conceptual design has a passband of 360 nm to 1000 nm, while the model instrumental passband, as noted below, is slightly different. These conceptual and hypothetical designs may have no similarity to the final optical design of the telescope and instruments.

We offer potential funding partners three options for funding:

These sites for the purpose of the model have the following characteristics:

Parameter Sonoita, AZ Model Mountaintop Site
Altitude 5000 ft / 1524 m 9000 ft / 2743 m
Viewing Airmass / Zenith Angle 1.18 / 32 deg 1.18 / 32 deg
Median Zenith-corrected Seeing 2.5" 1.0"
Viewing Airmass Seeing 2.8" 1.1"
Light Pollution natural sky + 30% natural sky + 10%
Sky Background V 21.3 / sq. " V 21.5 / sq. "
V-Band Extinction 0.20 0.15

We used a variety of CCD detectors in our model. The table below summarizes the key parameters of these CCDs:

Parameter e2v Fairchild STA
Model CCD42-90 CCD486 STA1600A
Pixel Size (um) 13.5 15 9
Well Depth (e-) 150,000 100,000 80,000
Summing Register Depth (e-) 900,000 750,000 500,000
Format 2048 x 4608 4096 x 4097 10600 x 10600
Read Noise (e-) 3 5 8
Operating Temp. (C) -80 -80 -80
Dark Current (e-/hour) 7 1.2 98
Gain 2.3 1.5 1.2

The summing register depth for the STA device was not available. It was assumed to be six times the pixel well depth.

This performance model contains the following assumptions:

2.5-Meter Telescope

Telescope
  • M1 diameter 2500 mm, E.F.L. 15, 922 mm, f/6.369 overall, yielding a plate scale of 12.95 "/mm
  • M2 diameter 969 mm, central obstruction: 39% (diam.) / 15% (area)
  • 2 powered mirrors, plus 1 flat directing light to two Nasmyth foci
  • 95% reflectivity per mirror surface
  • 1 degree FOV

2.5-Meter Imager
  • At one Nasmyth focus is a wide field imager consisting of a 4-lens camera, 4-element ADC, and clear broadband filter (9 total lenses, 18 surfaces)
  • 99% transmission per lens surface
  • No window on the CCD camera
  • Total imaging glass thickness for computing absorption is 43 mm of BK7. This is computed as 40 mm of either LLF6 or BK7 (essentially the same for our purposes) plus 3 mm more of the equivalent to obtain an additional 1% absorption in fused silica. BK7 glass absorption curve from laser component vendor.
  • Net optical throughput for imaging is 73% in V, 64% in the model instrumental passband of 300 nm to 1100 nm.
  • Imaging detector is the e2v CCD42-90 giving 0.175 "/pixel
  • Imaging: unbinned for sidereal objects, binned 3 x 3 for tracking moving targets, e.g., NEO follow-up
  • Signal-to-noise ratio of 3 for astrometric imaging of NEOs
  • Constraint: 85% of full well or 15 minute integration

2.5-Meter Spectrograph
  • At the other Nasmyth focus is a narrow-field spectrograph using a 3-element collimator, high-efficiency prism with 80% broadband transmission, and 3-element camera, for a total of 7 refractive elements (14 surfaces)
  • Spectrograph detector is the Fairchild CCD486, giving 0.194 "/pixel
  • Slit is 2.3 arseconds^2 (9 x 9 pixels)
  • Signal-to-noise ratio (SNR) of 10, determined by the longest wavelength bin (because it has the most sky).
  • The sky spectrum is measured and substracted pixel by pixel.
  • For each 25 nm bin, detector-related noise is multiplied by 1.1 * 3 = 3.3 pixels, including (a) read noise (3 e-), (b) dark current (0.003 e-/pixel/sec), and (c) digitization noise.
  • variance(bin) = var(NEO) + 2*var(sky) + 2* N pix * var(pixel)
  • Constraint: 85% of full well or 1 hour integration

1.5-Meter Telescope

Telescope
  • M1 diameter 1500 mm, E.F.L. 7500 mm, f/5 yielding a plate scale of 27.5 "/mm
  • M2 diameter 580 mm, central obstruction: 39% (diam.) / 15% (area)
  • 2 powered mirrors, single Cassegrain focus
  • 95% reflectivity per mirror surface
  • 1 degree FOV

1.5-Meter Imager
  • Single Cassegrain focus contains a wide field imager consisting of a 4-lens camera, 4-element ADC, and filter (9 total lenses, 18 surfaces)
  • 99% transmission per lens surface
  • No window on the CCD camera
  • Total imaging glass thickness for computing absorption is 43 mm of BK7. This is computed as 40 mm of either LLF6 or BK7 (essentially the same for our purposes) plus 3 mm more of the equivalent to obtain an additional 1% absorption in fused silica. BK7 glass absorption curve from laser component vendor.
  • Net optical throughput for imaging is 76% in V, 68% in the model instrumental passband of 300 nm to 1100 nm.
  • Imaging detector is the STA1600A giving 0.2475 "/pixel
  • Sonoita Imaging: unbinned for sidereal objects, binned 3 x 3 for tracking moving targets, e.g., NEO follow-up
  • Mountaintop Imaging: unbinned for sidereal objects, binned 2 x 2 for tracking moving targets, e.g., NEO follow-up
  • Signal-to-noise ratio of 3 for astrometric imaging of NEOs
  • Constraint: 85% of full well or 15 minute integration

1.5-Meter Spectrograph
  • Unlike the 2.5-m, which has a separate focus, there is only one focus. Instead of changing instruments, a spectroscopic "finger" moves into place to bring the dispersing elements into play over either a science detector or one of the focus/guiding detectors
  • The dispersing element is a prism, with a peak transmission of 80%. We use a flat transmission curve as a simplifying assumption, obtaining 71% net optical throughput in V, 61% in the model instrumental passband
  • Same number of camera optics (4 lenses), plus 4 pickoff mirrors, a 2-element collimator, the dispersing prism, and a 2-element camera lens, for a total of 6 mirrors (counting the telescope mirrors) and 9 refractive elements (including the prism).
  • Slit dimensions of 11 pixels by 11 pixels (11 arc seconds squared) on the sky when sited in Sonoita, or 5 by 5 pixels (2.3 arc seconds squared) when sited at a mountain.
  • Resolution R = 10
  • Integrations are limited by the shorter of (a) 85% full well in the CCD, or (b) a one-hour exposure, set by object rotation and changes in atmospheric extinction that limit one's ability to calibrate the spectroscopy properly.
  • Signal-to-noise ratio (SNR) of 10, determined by the longest wavelength bin (because it has the most sky).
  • The sky spectrum is measured and substracted pixel by pixel.
  • variance(bin) = var(NEO) + 2*var(sky) + 2* N pix * var(pixel)

Telescope Imaging Results

Case 0: Track on Object (Limited by 15-Minute Integration Time)

Parameter Option 1 Option 2 Option 3
Exposure 900 sec 900 sec 900 sec
V Limiting Magnitude 24.1 25.1 25.7

 

Case 1: NEO Moving <= 0.5"/minute

Parameter Option 1 Option 2 Option 3
Exposure 338 sec 150 sec 150 sec
V Limiting Magnitude 23.6 24.1 24.7

 

Case 2: NEO Moving 5"/minute

Parameter Option 1 Option 2 Option 3
Exposure 34 sec 15 sec 15 sec
V Limiting Magnitude 20.8 22.9 23.4

 

Case 3: NEO Moving 10"/minute

Parameter Option 1 Option 2 Option 3
Exposure 17 sec 8.0 sec 8.0 sec
V Limiting Magnitude 21.9 22.5 23.1

 

These results indicate that for slowly-moving targets, or when the telescope tracks the NEO, the 1.5-m telescope should be able to image all objects currently on the NEO Confirmation Page if placed at the Winer Observatory site in Sonoita, AZ. The results also indicate the gains in performance that are possible if either telescope is placed at a better site with darker skies and better seeing, which will be necessary to perform follow-up of objects discovered by the PanSTARRS and LSST surveys.

Telescope Spectroscopy Results

Case Lim. V Mag. Integ. Time Limited By CCD Well Status
Option 1 19.6 3600 sec 1-hour exposure limit 41% full
Option 2 20.5 3600 sec 1-hour exposure limit 47% full
Option 3 21.5 3600 sec 1-hour exposure limit 24% full

An assumption for the spectroscopic model was that integrations would be limited to one hour. Some NEO's rotate rapidly, in about 2 hours, so they could present a different face with a different albedo or chemical composition to the telescope during integrations longer than about an hour. Furthermore, there are some problems with calibration that are introduced for longer integrations.

The model indicates that using very low resolution to avoid dispersing the light excessively, the proposed 1.5-meter telescope will provide low-resolution spectroscopy for the brighter objects on the NEO Confirmation Page. It also indicates that a larger aperture telescope can reach significantly fainter magnitudes at the mountaintop site.

 

Last modified: January 3, 2008.