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Understanding Image Motion Due to Optical Element Motion: A Practical Guide

This comprehensive guide explores the impact of optical element motion on system pointing stability, image motion, and performance degradation for optical systems. It covers the effects of tilt and decenter of lenses, mirrors, and prisms, discussing how small motions can shift the entire field and affect system alignment. The text delves into the magnification of image motion, degradation in performance for spectrographs, and the relationship between element motion and system pointing instability. Examples and practical insights make this guide valuable for optical engineers and enthusiasts alike.

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Understanding Image Motion Due to Optical Element Motion: A Practical Guide

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  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).

  2. Lens decenter • All image points move together • Image motion is magnified

  3. Effect for lens tilt • Can use full principal plane relationships • Lens tilt often causes more aberrations than image motion

  4. 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 a : tilt Central ray deviation Dy : lateral shift Dq : change in angle

  5. Lens motion tilt decenter (Very small effect)

  6. Mirror motion like lens Dqa = 2a like flat mirror

  7. Motion for a plane parallel plate No change in angle

  8. 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

  9. General expression for image motion Fn final working f-number = Di beam footprint for on-axis bundle Dqi = change in central ray angle due to motion of element i

  10. Example for change in angle Image motion from change in ray angle For single lens, this is trivial D e Dq f = FnD

  11. Effect of lens decenter Decenter s causes angular change in central ray Which causes image motion Magnification of Image / lens motion NA and Fn based on system focus e Di is “Beam footprint” on element i Di Di

  12. Example for mirror tilt Tilt a causes angular change in central ray Which causes image motion “Lever arm” of 2 Fn Di( obvious for case where mirror is the last element) e Follow the central ray Small angle approx Dq d Di is beam size at mirror This is valid for any mirror! a

  13. Stationary point for finite conjugates • Rotate about C, define system using principal planes e(d’)

  14. 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: Where Dq0 is the change in angle of the light in collimated space D0 is the diameter of the collimated beam

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