1. College of Optical Sciences
An easy way to relate optical element motion to system pointing stability
Jim Burge
College of Optical Sciences
Steward Observatory
University of Arizona

2. Prof. Jim Burge Room 733 (in the new building) Research Teaching Other
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

3. 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

4. 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)

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

6. 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

7. Lens motion
tilt
decenter
(Very small effect)

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

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

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

11. Motion of an optical system
Use principal plane representation Dq s
System axis P’ P a Dy
PP’
(f = effective focal length)
(PP’ = distance between principal points)
Pure translation
Pure rotation about front principal point
If you just tilt your head:
Same as single lens a P’ P Dy
PP’

12. Rotation of an optical system about some general point
Combine rotation and translation to give effect of rotating about arbitrary point C
e(d’)
Lateral shift s = CP * ac

13. Stationary point for rotation
Solve for “stationary point”. Rotation about this point does not cause image motion at distance d’. a a P P ’ ’ c c P P C C d 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

14. Optical Invariant Optical invariant:yi qi
Optical invariant:
This invariance is maintained for any two independent rays in the optical system

15. Use of invariant for image motion
At image plane
At element i

16. The easy part
Element i moves, it will cause Dqi = change in angle of central ray (lateral shift Dy is usually small)
It is easy to calculate Dqi
Image motion is proportional to this
All you need is
Fn final focal ratio
Di beam footprint for on-axis bundle

17. Example for change in angle
Image motion from change in ray angle
This relationship is easy to remember Dq e D
f = FnD
Reduces to a simple example for a single lens!

18. Effect of lens decenter
Decenter s causes angular change
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

19. Effect of lateral translation
(tilt of PPP)
From analysis above:
NA and Fn based on system focus
ui = NAi
Dyi
(-)e
Magnification for re-imaging :

20. Example for mirror tilt
Tilt a causes angular change
Which causes image motion
“Lever arm” of 2 Fn Di ( obvious for case where mirror is the last element) Dq e a d

21. 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:
Where
Dq0 is the change in angle of the light in collimated space
D0 is the diameter of the collimated beam

22. Thank you! 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
This gives an easy way to relate surface figure to image blur. More on this later…
Thank you!