Transcript Slide 1
3. Image motion due to optical element motion • 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) J. H. Burge, “An easy way to relate optical element motion to system pointing stability,” in Current Developments in Lens Design and Optical Engineering VII, Proc. SPIE 6288 (2006). J. H. Burge Lens decenter • All image points move together • Image motion is magnified J. H. Burge Effect for lens tilt • Can use full principal plane relationships • Lens tilt often causes more aberrations than image motion J. H. Burge What happens when an optical element is moved? To see image motion, follow the central ray Generally, it changes in position and angle : change in angle ay r d e at devi y Initial on-axis ray s J. H. Burge Element motion s : decenter : tilt Central ray deviation y : lateral shift Lens motion decenter tilt s f s s f s f J. H. Burge (Very small effect) Mirror motion s s f like lens s 2 f J. H. Burge = 2 like flat mirror Motion for a plane parallel plate y Plane parallel plate thickness t index n J. H. Burge t n 1 y n No change in angle The Optical Invariant The stop is not special. Any two independent rays can be used for this. The optical invariant will be maintained through the system J. H. Burge J. H. Burge General expression 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 “Beam footprint” on element i Nominal marginal rays at element i ui = NAi Image shift Perturbed central ray from element i yi ui i Di yi yi NAi Fn Di i yi NA J. H. Burge 1 2NA Di beam footprint for on-axis bundle Fn final working f-number = i = change in central ray angle due to motion of element i Example for change in angle Fn Di i Image motion from change in ray angle For single lens, this is trivial D f = FnD J. H. Burge f Fn D Effect of lens decenter i Decenter s causes angular change in central ray Which causes image motion Fn Di i Fn Di Magnification of Image / lens motion s fi Fn s fi NA and Fn based on system focus Di is “Beam footprint” on element i J. H. Burge Di s fi Di Di Example for mirror tilt Tilt causes angular change in central ray 2Fn Di i Which causes image motion “Lever arm” of 2 Fn Di i 2 ( obvious for case where mirror is the last element) Follow the central ray d d Fn Di 2 Fn Di Small angle approx Di is beam size at mirror This is valid for any mirror! J. H. Burge Stationary point for finite conjugates • Rotate about C, define system using principal planes c C P y c PP ' P’ y (d’) CP f (d ') y d ' c d’ CPstationary J. H. Burge f PP ' d' For a thin lens, PP’ = 0, and the stationary point occurs at CP = 0, rotating about the principal points. For an object at infinity, d’ = f , so CPstationary = -PP’, which means that the stationary point occurs at the rear principal point. This principle is used for finding the principal point with a nodal slide 1. The stationary point depends not only on the optical system, but also on the object and image positions. A real biconvex “thick lens” operating at 1:1 conjugates has its stationary point in the middle. (CP = -0.5 PP’ and d’ = 2f .) 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 optical invariant: Fn D0 0 Where is the change in angle of the light in collimated space D0 is the diameter of the collimated beam D00 Di i J. H. Burge