TopBox Technical Manual

Optical Design

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Design Concept

The original purpose of the TopBox was to provide a simple and economical way to measure the optical linear polarization of gamma ray burst afterglows, as the RRRT Observatory began with the primary mission of robotic GRB studies. With a CCD camera already planned as the primary imaging instrument, inserting an extra filter wheel carrying polarization analyzers into the converging telescope beam before the bandpass filter wheel seemed to be adequate for extending the observations to include polarization measurements.

There were two reasons for building a complete tailpiece box instrument to accomplish the purpose. First, there was no commercially available filter wheel unit thick enough to hold suitable polarizers with clear aperture large enough to avoid vignetting, yet compact enough to be mounted in front of the CCD camera and bandpass filter wheel without placing the polarizers so far from the focal plane that vignetting was unavoidable. Second, a tailpiece box would provide a platform for an offset autoguider, which was desirable since the alternative (using a field rotator to take advantage of the camera's built-in autoguider chip) would unduly complicate the measurement of linear polarization position angles.

Measuring the linear Stokes parameters with two differently oriented polarization analyzers in a converging beam has significant drawbacks in comparison with the more sophisticated approach of a single fixed polarizing beamsplitter in a collimated beam modulated by a rotating half-wave plate and reimaged with the help of a focal plane mask. However, the anticipated difficulties with flat fielding, optical distortions, and overlapping of multiple images were considered to be outweighed by simplicity and economy, especially since the target GRB afterglows could be expected to appear as point sources.

Optical Layout

Practical dimensions and placement of the optical elements were based on models of the telescope optical system computed with the free optical design software OSLO-EDU developed by Lambda Research.

Fig. 1 shows mechanical dimensions of the TopBox related to the spacings of the optical elements as follows:

top mounting surface to pickoff mirror: 5.50"
pickoff mirror to focal plane: 6.00"
pickoff mirror to FW1 top surface: 2.75"
FW1 top surface to FW2 top surface: 1.125"
FW2 top surface to base plate top surface: 0.5"
FW2 top surface to focal plane: 2.125"


Fig. 1. Mechanical layout of the TopBox showing dimensions related to the spacing of the optical elements.

The dimensions shown in Fig. 1 were determined by iterating models with OSLO-EDU, based on the telescope optical design parameters, properties of the TopBox optical elements, and dimensions of the two available CCD cameras, subject to the requirement of full illumination of the field of view for both the main camera and the guider camera.

The optical system of the RRRT is a Ritchey-Chretién design with the following parameters given by the manufacturer, Optical Guidance Systems, and the optician (Paul Jones, Star Instruments):

effective focal ratio: EFR = 8.0
primary mirror diameter: d1 = 24"
primary focal ratio: PFR = 3.0
primary mirror perforation diameter: 5.5"
secondary mirror diameter: d2 = 8.5"
secondary mirror obstruction (shield diameter): 10.0"
mirror spacing: S = 48.2"
back focus: BF = 16.0" (11.5" from rear mounting plate of telescope)
tube diameter: 29.0"
primary mirror to rear mounting surface: 4.5"

According to standard optical design theory we can calculate:

effective focal length:
EFL = EFR * d1 = 4876.8 mm
secondary magnification:
m = EFR / PFR = 8.0 / 3.0 = 2.667
back focal length (secondary to focal plane):
BFL = S + BF = 1625.6 mm
primary mirror radius of curvature:
rc1 = -2.0 * (S * EFL)/(EFL - BFL) = -3657.6 mm
secondary mirror radius of curvature:
rc2 = -2.0 * (S * BFL)/(EFL - BFL - S) = -1950.7 mm
primary mirror conic constant (hyperboloid):
k1 = -1.0 - (2.0 / m^3) * (BFL / S) = -1.14062
secondary mirror conic constant (hyperboloid):
k2 = -1.0 - (2.0 / (m - 1)^3) * (m * (2 * m - 1) + (BFL / S)) = -6.56800

The TopBox was designed to place the focal plane at the nominal back focus position 11.5" from the rear mounting plate of the telescope using different individual mounting adapter plates for each of the CCD cameras. Models for three different filter configurations are summarized below, including the autoguider focal plane shifts evaluated for minimum RMS spot size at 587.6 nm:

tb10 :
no filters
spacing = 1219.2 mm
EFL = 4876.9 mm (f/8.00)
top hole to FP = 11.50"
pickoff to AGFP = 6.000"

tb11 ,  tb12 :
V filter
spacing = 1219.4 mm
EFL = 4874.2 (f/8.00)
top hole to FP = 11.51"
pickoff to AGFP = 5.938"

tb13 ,  tb14 :
V filter + Savart plate
spacing = 1220.1 mm
EFL = 4864.9 mm (f/7.98)
top hole to FP = 11.51"
pickoff to AGFP = 5.718"

Polarization Optics

The beam displacement by a calcite Savart plate at 500 nm wavelength is theoretically 0.075 times the total thickness of the two plates. For the RRRT's plate thickness specification of 7.0±0.1 mm the total thickness of 14 mm gives a beam displacement of 1.05 mm, corresponding to 44.5 arcsec at the image scale of 42.4 arcsec/mm for the model tb13 shown above. The measured separation for a representative sample of V observations is 46.3±0.2 arcsec, at position angles of 45.0±0.0° for P1 and 90.2±0.2° for P2.

Autoguider Optics

Design of the autoguider optics was based on a tradeoff between maximizing the accessible area of the sky and minimizing the vignetting footprint of the pickoff element, subject to the limitation of off-axis image degradation. OSLO-EDU models were helpful to check for vignetting, to choose an appropriate size for the pickoff mirror, to calculate the positioning and focus offsets, and to evaluate off-axis image quality. Some of the constraints on size and range of motion of the autoguider optics may be seen in Fig. 2 below and Fig. 1 above.

An elliptical diagonal pickoff mirror with minor axis 1.30" mounted on a 0.75" diameter cylindrical stalk has a field angle of about 4 arcmin, which corresponds to the radius of the fully illuminated field of view of the guider optics. This is a good match for typical autoguider CCD cameras like the external guider head of the SBIG STL-1001E, which has a 4.9x3.7 mm detector, with a 3.45x2.61 arcmin field of view on the RRRT.


Fig. 2. Front view section of the TopBox showing E-W movement of the autoguider focuser unit on its linear positioner.

The OSLO-EDU model tb25 illustrated in Fig. 3 below is an example of the models used to calculate focus shift and image quality for various guider offset positions.


 

 

 

Fig. 3. Sample OSLO-EDU model of offset guider optics.

This model includes observational estimates of the current imperfect collimation of the pickoff mirror in the tilt parameters for Surface 5. The guide star position is offset 0.500° = 30.00 arcmin W of the FOV center of the main camera, and the pickoff mirror positioner is offset 43.926 mm E of the telescope optical axis. The guider focal plane is shifted 1280 μm toward the pickoff mirror from its on-axis position, and the minimum RMS radius of the donut-shaped guider image is 26.14 μm at 587.6 nm. Since the seeing FWHM at the RRRT is rarely less than 2 arcsec ∼ 47.3 μm, this should be a practical target for autoguiding.

References

A Brief Look at the Problems of Guiding (ps)
Richmond, M. W. 1990, in Proceedings of the Electronics Oriented Astronomy Seminar 3, ed. J. Sanford (OCA Publications, Costa Mesa), p. 68


Last modified: Nov 15, 2012
David McDavid

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