Practical issues for optical systems

1. Practical issues for optical systems Systems engineering for Optical Design • Systems engineering introduction: designing systems to be build(today’s class) • Specification of optical components(next week’s class) Systems Engineering for complete system: OPTI424/525

2. Systems Engineering Introduction • Design the SYSTEM so that it will • Meet performance requirements • Minimize cost, risk, schedule • Most of the issues with the system performance and cost arise because of limitations and tradeoffs in manufacturing. • The overall systems engineering flow includes design validation and test verification, not covered comprehensively here.

3. Design for manufacturing • Quantify performance : Use figures of merit for technical performance • Allow for real manufacturing limitations • Analyze the coupling between hardware limitations and system performance • Create budget that allows for everything to go wrong – by allotted amounts • Perform analysis that validates the system performance, even though everything is going wrong

4. Error Tree : Budgeted allocations Requirement 0.45arcsecond (80% EE diam) Expected performance 0.34 Margin 0.29 Design Residual 0.18 Optical Surfaces 0.25 Alignment 0.16 Fabrication 0.19 Initial Assembly 0.03 Effects of alignment defined as 90% confidence from Monte Carlo analysis Support 0.16 Operational Alignment 0.16

5. Image QualityFigures of Merit for Optical Systems • What does the optical system do? The figure of merit provides a number that tells how well the system functions • Optical imaging • Geometric image size • Rms image diameter • FWHM • Fractional encircled energy • MTF at particular spatial frequencies • RMSWE (root mean square wavefront error) • Beam divergence • Distortion • Boresight Other Coupling efficiencyData rateNETD

6. Two regimes for imaging systems • Geometric limit Use simple ray trace to determine image quality Rms spot size is most common FOM Valid for wavefront errors > 1 l • Near Diffraction limit Must take the wave nature (interference and diffraction) into account. Valid for wavefront errors < l/4 Rms wavefront error is most common FOM

7. Image quality – point sharpness • Look at the image of points • In the geometric limit: • rms diameter or radius (half-diameter) Easily calculated using raytrace programs by tracing a bunch of rays: This only makes sense for geometric limit • FWHM • 80% encircled energythe circle that contains 80% of the spots

8. Example Lens layout

9. Aberrations - definitions

10. OPD plots (DW vs pupil) DW = OPD >> 1 l This system is in the geometric limit OPD (Optical Path Difference) is not a useful metric for this system

11. Spot diagrams Rms spot radius = rms value for spot distances from centroid Each spot represents a ray from a point in the pupil In software, send a bunch of rays through the system and see where they intersect the image plane

12. Calculation of rms • Mean value of x : • Mean value of x2 • Root mean square deviation • If mean <x> = 0,

13. Exit pupil Ideal focus r,r Film plane r normalized r = r/rmax e Fn = system focal ratio = 1/(2 NA) Dz Dz/Fn PSF for defocus Where e is position in image plane relative to center : <e> = 0 From geometry, e(r) = -rDz/2Fn Calculate rms as

14. Geometric encircled energy EE 80% EE at for circle with 10 µm radius 80% EE is often used as a threshold

15. Modulation Transfer Function • Rather than using the blur size for image points – use the contrast reduction for high-frequency (small scale) features. • MTF is plot of contrast (or modulation) vs. spatial frequency • Has nice linear properties – system MTF = product of MTF for subsystems.

16. Definition of Modulation

17. Contrast

19. Modulation Transfer Function

20. MTF targets Siemens star 1951 USAF Target Visual response SQF: Integrate MTF over sensitive SFs Subjective Quality

21. Phase inversiondefocus this image

22. MTF, PSF • MTF and PSF are Fourier transform pairs • What is MTF for large amount of defocus? PSF

23. Combining multiple effects processing optics detector atmosphere object image system PSFsystem = PSFatmosphere ** PSFoptics** PSFdetector ** PSFprocessing (** denotes a convolution) MTFsystem = MTFatmosphere x MTFoptics x MTFdetector x MTFprocessing

24. Diffraction Limit Stop the above system down

25. OPD < 1 wave

26. Image size comes from diffraction 2.44lFn FWHM = 1.02 l Fn In angle space,

27. Spot diagrams • Now these are meaningless(compare with Airy diameter)

28. Transition from Diffraction limit to Geometric Limit Diffraction limit Geometric limit

29. Strehl Ratio Where s is RMS wavefront error in radians Where Wrms is RMS wavefront error in µm (assuming l in µm) Rule of thumb for diffraction limit: l/4 P-V wavefront(0.07 l rms) 80% SR

30. Diffraction calculation Treat small wavefront errors using Fourier For wavefront ripples with spatial period L, rms s radians Light is diffracted from central core How much? s2 Where does it go? Dq = ±l/L Slice through image80% Strehl Energy/satellite peak = 10% of central lobe ImageSatellite peaks at q = ±10l/D Wavefront0.07l rms, 10 cycles/diamL = D/10 1 0.1 q -10l/D 10l/D (LOG SCALE)

31. Encircled Energy

32. MTF

33. Diffraction limit for focus • For focal shift of 2 l Fn2 PSF80% SR MTF Wavefront errorl/4 P-V, 0.07 l rms

34. Distortion Mapping error for image, measured in %, µm/mm, or simply µm

36. Tolerancing Optical Systems • Why are tolerances important? • Somebody is going to make it (hopefully) • It must meet some performance requirement • Cost (and schedule) are always important • Why is it difficult? • Involves complex relationships across disciplines • System engineering • Optical design and analysis • Optical fabrication • Opto-mechanical design • Mechanical fabrication

37. Process of optical system tolerancing • Define quantitative figures of merit for requirements • Estimate component tolerances • Define assembly/alignment procedure and estimate tolerances • Calculate sensitivities • Estimate performance • Adjust tolerances, balance cost and schedule with performance • Iterate with system engineer, fabricators, management

38. Parameters to tolerance • General parts (usually machined metal) • Physical dimensions of optical elements • Optical surfaces • Material imperfections for optics • Optical assembly

39. Estimate system performance For a merit function that uses RSS to combine independent contributions: F0 is from design residual – simulation of system with no manufacturing errors DFi is effect from a single parameter having an error equal to its tolerance

40. Calculatesensitivities • Define merit function F • Make list of parameters to tolerance, x1, x2, x3, … all of the things that will go wrong. • Use simulation to calculate the effect of each of these on the system performance. • For each xi, use perturbation to find sensitivity • So the contribution from a tolerance si on parameter xi is = (change in merit function) / (change in parameter) = (sensitivity) * (tolerance)

41. Sensitivity calculation • If the nominal merit function F0 is small (residual aberrations) calculate sensitivity directly Dxi is perturbation (by the expected tolerance) F(xi + Dxi) is the system merit function of the perturbed system • To include the nominal merit function F0 This can be tricky Evaluate F0 and F(xi + Dxi) • If F0 << F(xi + Dxi) then DF = F(xi + Dxi) as above • If F0 is correlated with F(xi + Dxi) then DF = F(xi + Dxi) - F0 • Else F0 and DF combine in RSS, so

42. Using compensators For most optical systems, a final focus adjustment will be made after the system is assembled. The tolerance analysis must take this into account. When calculating the effect of each perturbation, you simulate this adjustment: simulate sensing the error adjust the appropriate parameter This can be used for other degrees of freedom Always make the simulation follow the complete procedure. Every compensator requires a real measurement and a real adjustment. The limitations of the measurements and adjustments should show up in your error budget.

43. Combining different effects Calculate system merit function by scaling from the sensitivities, and use RSS si is now the tolerance for xi which could be adjusted is the sensitivity to unit change in parameter xi Put the sensitivities into a spreadsheet to allow easy calculation of the system errors with all effects.

44. Assigning initial tolerances • Start with rational, easy to achieve tolerances • Only tighten these as your analysis requires • Rules of thumb for element tolerances • Rules of thumb for assembly tolerances • Best -- know what the fabrication and alignment processes you plan to use will give!

45. Using optical design codes • Much of the above work can be done entirely within the optical design code. • You can specify tolerances, and the software will calculate sensitivities and derive an RSS • Be careful with this! It is easy to get this wrong. • The optical design codes also include a useful Monte Carlo type tolerance analysis. This creates numerous simulations of your system with all of the degrees of freedom perturbed by random amounts.

46. Develop complete set of tolerances • Simulate system performance • Include all compensators • Check overall magnitudes of the terms • Terms with small effects, loosen tolerances • Terms with big effects, may need to tighten tolerances • Revise fabrication, alignment plans as needed the goal is: • Meet performance specifications • Minimize cost

47. Spreadsheet for combining tolerances You can change the tolerance value Automatically recalculate effect from each term and RSS Sensitivities calculated from simulation. These do not change

48. LOS Tolerancing example Show how to meet a requirement of 0.1 µm stability

49. Example Spreadsheet

50. Optical systems frequently require the following tolerances: • Lens elements • Curvatures, surface irregularity and finish • Wedge, centration • Glass property and quality • Mounting features, bevels • Coatings • Mirrors • Curvatures, surface irregularity and finish • Substrate and mounting details • Coatings • 6 degree of freedom positioning for each optical element