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Download 6288-18 talk - LOFT, Large Optics Fabrication and Testing group
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An easy way to relate optical element motion to system pointing stability Jim Burge College of Optical Sciences Steward Observatory University of Arizona Prof. Jim Burge • Room 733 (in the new building) • Research – – – – Optical systems engineering and development Fabrication and testing Optomechanics Astronomical Optics • Teaching – Applied optics classes (Optics laboratory, optomechanics) • Other – – – – Sailing, diving, fishing in San Carlos, Mexico Mountain biking Ultimate frisbee Beer brewing Goals for this talk Provide • Basic understanding of some optical/mechanical relationships • Definition, application of the optical invariant • Useful, easy to remember equations to help make your life easier Motion of optical elements • Tilt and decenter of optical components (lenses, mirrors, prisms) will cause motion of the image – Element drift causes pointing instability •Affects boresight, alignment of co-pointed optical systems •Degrades performance for spectrographs – Element vibration causes image jitter •Long exposures are blurred •Limit performance of laser projectors Small motions, entire field shifts (all image points move the same) Image shift has same effect as change of line of sight direction (defined as where the system is looking) Lens decenter • All image points move together • Image motion is magnified What happens when an optical element is moved? To see image motion, follow the central ray Generally, it changes in position and angle Element motion s : decenter : tilt Central ray deviation y : lateral shift : change in angle ay r d e at devi y Initial on-axis ray s Lens motion decenter tilt s f s s f s f (Very small effect) Effect for lens tilt • Can use full principal plane relationships • Lens tilt often causes more aberrations than image motion Mirror motion s s f like lens s 2 f = 2 like flat mirror Motion for a plane parallel plate y Plane parallel plate thickness t index n t n 1 y n No change in angle Motion of an optical system Use principal plane representation Pure rotation about front principal point Pure translation System axis P P’ y s s f y 0 PP’ (f = effective focal length) Same as single lens y PP ' 0 (PP’ = distance between principal points) If you just tilt your head: Rotation of an optical system about some general point • Combine rotation and translation to give effect of rotating about arbitrary point C c C P P’ y d’ Lateral shift s = CP * c s f y c PP ' CP c f e(d’) Stationary point for rotation • Solve for “stationary point”. Rotation about this point does not cause image motion at distance d’. c e (d ') y d ' 0 C d’ CPstationary f PP ' d' Thin lens (PP’=0) stationary point at P = P’ Object at ∞ (f = d’) stationary point at P’ Otherwise it depends on separation of principal planes and image conjugates Optical Invariant Marginal ray Marginal ray – on axis ray that goes i yi through edge of plane of interest yi y i Chief ray – off axis ray that goes through center of the plane of interest (typically the stop.) Optical invariant: Chief ray Plane of interest Position i I ui yi ui yi This invariance is maintained for any two independent rays in the optical system i i Di Use of invariant for image motion Element i NA and Fn based on system focus Light from point on axis, Bundle defined by aperture Off-axis light is ignored Element i “Beam footprint” on element i Nominal marginal rays at element i ui = NAi NA and Fn based on system focus Di Image shift e Perturbed central ray from element i yi Image shift e uAt i i image I NA e yi yi Nominal marginal rays at element i ui = NAi Perturbed central ray from element i At element i “Beam footprint” on element i Di I i NAi yi 2 yi ui i yi yi plane e 2 Fn NAi e Fn Di i yi NA The easy part NAi e Fn Di i yi NA Element i moves, it will cause i = change in angle of central ray (lateral shift y is usually small) It is easy to calculate i Image motion is proportional to this All you need is Fn final focal ratio Di beam footprint for on-axis bundle Example for change in angle e Fn Di i Image motion from change in ray angle This relationship is easy to remember D e e f Fn D f = FnD Reduces to a simple example for a single lens! Effect of lens decenter Decenter s causes angular change Which causes image motion i e Fn Di Magnification of Image / lens motion s fi s fi e Fn s fi NA and Fn based on system focus e Di is “Beam footprint” on element i Di Di Di Effect of lateral translation From analysis above: (tilt of PPP) NAi e yi NA NA and Fn based on system focus e NAi yi NA yi ui = NAi e Magnification for re-imaging : e NAi yi NA Example for mirror tilt Tilt causes angular change i 2 Which causes image motion e 2Fn Di i “Lever arm” of 2 Fn Di ( obvious for case where mirror is the last element) e d e d Fn D 2 Fn D Afocal systems • For system with object or image at infinity, effect of element motion is tilt in the light. • Simply use the relationship from the invariant: e Fn D0 0 Where is the change in angle of the light in collimated space D0 is the diameter of the collimated beam D0 0 Di i 2 NAi yi Other useful things • Useful for pupil image as well. Just be careful to use correct definitions • Also use this to relate slope variation across pupil to the size of the image blur e ( x , y ) Fn Di i ( x , y ) • This gives an easy way to relate surface figure to image blur. More on this later… Thank you!