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3d−Quasi−Optical Ray−Tracing for the Odin Radiometer

S.A. Torchinsky

sat@iras.ucalgary.ca

Dept of Physics and Astronomy, University of Calgary

T2N 1N4, Calgary, Alberta, Canada

ABSTRACT:

We describe the Odin radiometer optical layout and the 3−dimensional CAD system

developed to define and analyze the system. Both the mechanical and optical design

were done within the same CAD environment using a custom plug−in software for

Quasi−Optical analysis and ray tracing. Odin has a complex optical layout with three

dimensional beam foldings and a large number of optical elements. The

optical/mechanical CAD system allows control over the definition of mirror and lens

surfaces, as well as the mechanical support structure and apertures, bringing all elements

into a single 3−dimensional model.

Odin Optical Layout:

The optical layout for the Odin radiometer is based on the prototype version described by

Ordell[1], with some improvements introduced for the flight version. Odin has five

receivers: four of which are submillimeter and one is millimeter wave. The four

submillimeter mixers are arranged in cross−polarized pairs. Each pair looks at two

Martin−Puplett diplexers, one for LO injection and one for side band rejection. Because

of the arrangement of the grids in the diplexer tower, each mixer beam takes a different

path through the diplexer. As a result, there are eight tuning mechanisms which move the

right−angled roof−top mirrors that perform the beam polarization rotation. In Figure 1a,

one can see how the beam comes out of one level of the diplexer tower and then is folded

back into the next level by two mirrors. Those folding mirrors are profiled in order to

contain or "re−collimate" the beam. In all, the beam goes through four focussing

elements before being sent off to the telescope secondary mirror.

All the mirrors in Odin are off−axis ellipsoid mirrors in order to control aberrations [2].

In Figures 1a and b, the rings shown on the mirror surfaces are the physical locations

where the incoming Gaussian beam intersects the surface of the mirror at edge tapers of

5dB, 15dB, 25dB, and 35dB. The CAD drawing of the mirror is accurately drawn with

the surface profile we expect to manufacture, and we have used this to verify the mirrors

by comparing the drawing to mechanical depth measurements of the mirror surfaces.

After the diplexer tower there is yet another mechanism: A simple rotating Dicke switch.

Both sides of the Dicke switch are used such that one pair of mixers is viewing the

astronomical source while the other pair is looking at the internal calibration source. We

have a choice of calibration sources: one warm, and two cold. The two cold are simply

looking directly at the cold sky (not through the telescope). We achieve this through one

final mechanism which is a rotating switch mirror, making ten mechanisms in all in

Odin. The mirror mounted on this last mechanism is also a profiled surface, and the axis

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of rotation of the mirror is such that we don’t introduce any aberrations. That is, we only

reflect the beam to the designed beam reflection angle.

The 119GHz beam comes into the Dicke switch via a dichroic where it joins the

submillimeter beam from the bottom level of the diplexer. In Figure 1b, the Gaussian

beam for the 119GHz channel is drawn as a 3−dimensional surface of revolution. This

method is useful for ensuring sufficient clearance throughout the optical path. For

example, in Figure 1b, a mirror in the calibration chain has its bottom corner bitten off

such that there is a clear path for the sky beam when the switch mirror selects that

position.

Lenses with linear matching grooves

The 119GHz channel has two lenses in the optical path. In other parts of the optical

design, off−axis ellipsoid mirrors have been used because they transform the phase front

radius of an incident beam into the desired output beam with a spherical phase front

radius and Gaussian amplitude distribution [2]. The corresponding surface of refraction

which performs the same transformation is a cartesian oval [5]. On Odin, we have used

single surface lenses in which the first surface is spherical and matched to the phase

radius of the incident beam. There is therefore no transformation at the first surface.

The second surface is a cartesian oval.

In order to reduce reflections at the surface of the lens, a matching layer of grooves has

been machined into the surfaces of the lens. Circular grooves have the disadvantage of a

mismatch where they do not line up, or exactly cross, the polarization vector of the

receiver [6]. This effect can be reduced by using linear matching grooves that line up

with the linearly polarized receiver beam. Machining of grooves into the lens surface

was done by a Computer Numerically Controlled milling machine (see Figure 2). The

program used to control the machine was produced by the Quasi−Optics plug−in

software as a text output file containing the required Heidenheim control language

syntax.

Quasi−Optics Software:

The Quasi−Optical analysis was achieved using a 3−dimensional Quasi−Optical ray

tracing program developed by the author. The program currently runs as a plug−in to

AutoCAD

TM [3], or other "AutoCAD fluent" software such as IntelliCAD98

TM [4]. The

plug−in performs the Quasi−Optic calculations in addition to drawing the entities. In the

Odin drawings, all the beam envelopes shown are drawn to the 35dB edge taper of a

Gaussian beam. These are hyperbolae, and in the case where a tube represents the beam,

this is a surface of revolution formed by the hyperbola. For clarity, the 3−d beam is not

shown everywhere because it would make a cluttered drawing, however they are in the

drawing (some of them are on "frozen layers"). This three dimensional ray tracing has

proven to be extremely useful in spotting areas where we might otherwise have truncated

the beam. Odin has such a compact design with many beam foldings in all directions that

it would be difficult to keep track of everything without a 3−d ray tracing.

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REFERENCES:

1. Ordell, E, "The Quasi Optics of the Odin Satellite" Swedish Space Corporation report

SSAD531−1, 1995

2. Murphy, J.A. "Distortion of a Simple Gaussian Beam on Reflection from Off−Axis

Ellipsoidal Mirrors" Int. J. Infrared & Millimeter Waves, Vol.8, No.9, 1987, pp.1165−87

3. Autodesk corp, http://www.autodesk.com

4. Visio, http://www.visio.com

5. Cornbleet, S "Microwave and Geometrical Optics (Techniques of Physics, No 16)",

Academic Press, 1994, ISBN 012189651X

6. Lamb, J. "Cross−Polarisation and Astigmatism in Matching Grooves," Int. J. Infrared

and Millimeter Waves, vol.17, no.12, 1996, pp.2159−65

7. Goldsmith, P.F., "Quasioptical Systems: Gaussian Beam Quasioptical Propagation"

IEEE press, 1998, ISBN 0−7803−3439−6