Typical requirements of passive mm-wave imaging systems, and consequences for antenna design

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1 Typical requirements of passive mm-wave imaging systems, and consequences for antenna design Rupert Anderton A presentation to: 6th Millimetre-wave Users Group NPL, Teddington 5 October

2 1 Characteristics of PMMW imagers and sensors Long wavelength (for imaging system) implies large aperture to achieve useful resolution Fast optics (< f/2) required to avoid inordinately long sensor Also avoids overly bulky feeds Wide field of view applications are usual Otherwise image perceived as low quality Too little information in image (too few pixels) High angular resolution systems not achievable with sensible apertures Scanning component required Receivers far too expensive to form staring arrays May require ~linear array to achieve adequate sensitivity Full aperture scanner to scan large angle Only rotational types practical Nyquist sampling / low spillover loss incompatible without scanning sinθ 1. 22λ D HFOV VFOV N pixels 4 θ ΔT min = > ( T + T ) a 0.02 βτ R N N pixels receivers perfect optics, W-band, 25fps 2

3 2 Typical designs Either reflective or refractive optics possible: Lenses: small-aperture, low resolution, small FOV Sensors not full imagers Avoids FP obscuration Large lenses too massive, too lossy On-axis mirror optics: larger systems / wide FOV Mirrors much lighter at large sizes Uncomplicated designs: wide FOV, fast f/no: Maksutov, Schmidt (-Cassegrain) Reflective scanners more practical Mirrors light, in-balance; prisms heavy, out of balance Twist-polarisation techniques used on-axis large obscuration by focal plane Off-axis mirror systems have no obscuration Slower f/numbers, > f/2, small FOV < 10 degrees Bulky Folded Schmidt Lens afocal telescope Polariser/ mirror Off-axis 1/4 wave plate Focal plane corrector/ scanner 3

4 3 Effect on design of antennas/optics Antenna required is closer to visible/ir optics Fast optics with wide FOV Complex multi-surface optics Corrects aberrations to diffraction limit Typical antenna design software not practical Cannot handle efficient optimisation of multisurface optics into low aberration design Full diffraction model over-specified Low dynamic range in passive Sidelobes less critical Classical raytracing software much more useful Hybrid physical/geometric optics model adequate for design and most analysis Analysis/Optimisation/Tolerancing tools allow rapid design Software written specifically for similar tasks Although primarily for Visible/IR Stop Classical Schmidt (Vis/IR) 1 Focal plane Aspheric corrector Spherical mirror Focal Plane 3 Exit Pupil Ref. Sphere 1. Rays traced to ref. sphere 2. Complex fields constructed 3. Ref sphere FT to focal plane 2 4

5 4 Design process (1) Outline design selected based on considerations from Slide 2 As with all optical design activity, experience also helps in selecting best design starting point! Design entered into raytracing software OSLO, Zemax and Code V are the best known packages Usually no point in using analytical design approach to start with PMMW designs too aspheric/extreme for seidel coefficients etc to be very useful Key to good design is construction of efficient Merit (or Error) Function Optimisation attempts to minimise by altering any parameters designated as variables DLS algorithm used mostly (fast), others available to find different local minima: Downhill simplex, Powell s method, Adaptive Simulated Annealing (slow but can find novel soln.) Manual tweaks may be required too Merit Function needs to constrain design To meet spec and any limitations 5

6 5 Design process (2) Merit Function consists of metrics summed in quadrature Optical metrics Evaluated for a bundle of rays through the aperture, at 3 points in field at least Sum of RMS geometric spot size and RMS optical path difference is fast, works well Encircled energy metric can be useful but slow Distortion corrected in scan conversion Chromatic aberration not significant - low bandwidth Field curvature overcome by receivers on curve Constraint metrics can include Focal length f/number (or feed reception angle) Diameter of particular elements Overall length Magnification (afocal telescope + scanner) Aspheric surface variable 3 Aspheric surface - variable 2 Front element diameter constraint 2 Scanner diameter aperture stop Feed angle const raint 1 Aspheric surface variable 1 Variable 1 : main corrector for spherical aberration Variable 1 : also driven by constraint 2 optical power increased to meet constraint Variables 2, 3 : add further correction Constraint 1 : acts with all variables to maintain desired illumination edge taper 6

7 6 Design process evaluation metrics Evaluation of design using raytracing outputs, and relationship to testing Geometric spot size Useful in optimisation (helps avoid extreme rays), does not relate to measurable quantity Optical path difference Most useful optimisation quantity, does not relate to measurable quantity Good single measure of quality of near diffraction limited system (as is Strehl) PSF Easily related to real measurements at MMW using noise source and pan & tilt MTF Hard to perform a real measurement at MMW due to size of line targets required Can be derived from measured PSF by FT Encircled energy (relates well to real-world performance for detection of small objects) Strehl ~ 7

8 7 Design process obscuration modelling Reflective optics tends to suffer from obscuration Usually by focal plane or subreflector in beam Obscuration has two effects Degradation of image quality Reduction in Signal-to-Noise ratio Rule of thumb in optics: <10% by area is acceptable Obscuration modelling and reduction Special apertures function exists to allow series of simple shapes to be modelled as obstructions Can be built up to model receiver array shape, support struts, subreflectors etc Models PSF/MTF accurately, but overestimates transmission - hybrid GO/PO model just counts rays reaching focal plane! Use of additional modelling software may be desirable if there are a lot of small obstructions e.g. struts, spiders 6 rays passed, 3 blocked : Trans = 6/9! 8

9 8 Use of macros and other special features Macros are required for Iterative reverse raytracing (given point in image plane, where did it come from in object plane?) Generation of scan conversion look-up tables Newton-Raphson iteration algorithm implemented Raytracing used to find approx derivative: Object plane posn = f(image plane posn) Enables fast and reliable LUT generation Calculating accurate depth of field, focussing steps, ranges and adjustment Does not need N-R iteration, simple increment and test adequate - only one dimension is being altered User Defined Surfaces Roof prisms Cone/inverse cone multi-beam scanner Radomes with sharp corners Random surface error modelling Random refractive index variation modelling Multiple fixed beam - generating scanner UDS Cones/inverse cones More efficient than conical scan for which most of scan is dead time 9

10 9 Tolerancing MM-wave systems can be less tolerant of error than is sometimes supposed Especially at W-band and higher Hopkins-Tizani inverse RMS wavefront method often useful for first cut tolerancing Given min. acceptable image quality measure, assigns equal-acting tolerances to all variables Often produces inaccurate results Probably due to non-linearity of extreme design with wide FOV, aspherics and so on Monte-Carlo approach necessary for confidence in final results Makes large number of random changes to variables Magnitude of user-defined error function (as with optimisation) reported as statistic 10

11 10 Summary PMMW systems tend to be used for wide FOV applications with moderate resolution Practicality requires short optics so f/numbers are low Typical solutions tend to be reflective optics similar to well-known visible and IR designs For example the Schmidt system Thus conventional optical (raytracing) software is the most appropriate design tool The extra accuracy (at the cost of speed/design capability) of full diffraction programs is wasted on low dynamic range passive sensors Except for accurate modelling obscuration 11

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