MTU has a fully equipped and functioning experimental optics lab.

1. MTUExperiments • MTU has a fully equipped and functioning experimental optics lab. • Equipment and capabilities similar to AFIT optics lab in Bldg 194: • Wave front sensor and reconstruction software • Full sets of 2” lenses, mounts, beam collimator/expanders, mirrors, alignment tools, lasers, filters, etc. • 3 computers which provide software interfaces to opto-electronics and acquire data • 2 digital cameras • Work here has resulted in 2 experimental papers. • MTU electronics lab can make custom boards “at cost”.

2. MTU Experiments Large aberration sensing experiment Hamamatsu Digital Camera Hartmann Lenslet Array, f = 24 mm, side length = 328 microns Iris Laser Neutral Density Filters Beam Expander Aberration Lens Beam Splitter Iris Converging Lens, f=400 mm Cohu Digital Camera

4. MTU Experiments

5. MTU Experiments

6. MTU Experiments

7. MTU Experiments • MTU experimental effort will parallel and support MRC efforts to develop a field demonstration. • Compatible computer hardware and wave front control devices are either in place already, or being purchased. • Goal is to allow software to be transferred between sites transparently. • First MTU experiment will address beam shaping through an aberrating pupil. • Subsequent experiments/code development and test directed at supporting and evaluating the field demo.

8. MTU Experiments Basic concept for initial experiments

9. MTU Algorithm work • Algorithm work will continue at MTU under the phase II program. • Key efforts will be in the areas of: • Applying phase unwrapping algorithms to PRA outputs, evaluating performance, and testing experimentally. • Faster, “better” algorithms - constrained optimization, genetic algorithms, etc. • Wave front control algorithms for two 1-D wave front control elements. • Evaluating performance • Will incorporate feedback loop to experiments.

10. MTU Algorithm work • PRA provides the principal value phase: • Result is that principal value phase is defined on (-,), and will in general be discontinuous. • Phase discontinuities arise from two sources: • Type 1: Phasor representing the complex field moves between the 2nd and 3rd quadrants in the complex plane. • Type 2: A real zero occurs in the propagating wave causing a “branch point”. • Type 1 discontinuities are easily handled with “conventional” phase reconstructors, such as path following approaches (high SNR) or least squares techniques (low SNR). • When no branch points are present, the least squares estimate of the unwrapped phase is continous, and the “re-wrapped phase” defined by • matches the principal value input phase exactly with no noise.

11. MTU Algorithm work • The presence of Type 2 discontinuities means that there is no continous phase map which when rewrapped will match the incident principal value phase => fitting problem!!!! • Of course, optical phase cannot be sensed directly. The data available to reconstruct the phase is in the form of phase differences measured on a finite spatial grid: • where W is the modulo 2 wrapping operator. • If phase differences obtained using • then the least squares recontruction of the phase is

12. MTU Algorithm work • Branch point-sensitive reconstructors of several basic designs exist. We explore two here: • Path following techniques such as Goldstein’s algorithm. • Fried’s “hidden phase” technique, which is based on a fundamental principle of mathematical physics. • Both approaches rely on explicitly finding the branch points. •  = 0  no branch point present;  =   branch point enclosed in the contour, and “polarity”, or sign of the branch point is noted. • Goldstein’s algorithm is similar to “recursive reconstructors” used in speckle imaging. • Branch points are detected. • The nearest pairs of positive and negative branch points are connected with straight lines. • Path following, or recursive reconstruction implemented with the exception that no path is allowed to encircle a branch point, and not path may cross a branch cut.

13. MTU Algorithm work

14. MTU Algorithm work • Phase I work showed the importance of phase unwrapping: • Reduced side lobes • More energy in main lobe or pattern • Why? When WFC device is fit to phase, discontinuities are minimal, leading to smaller fitting errors and better performance. • Work under the Phase II will incorporate this idea by seeking quasi-continuous figures for the WFC in the advance algorithm work, and by seeking to experimentally demonstrate the value of this approach.

15. MTU Algorithm work • One alternative algorithmic strategy is to use nonlinear, constrained optimization to determine the mirror figure. • In this approach the space of attainable WFS figures is expressed parametrically: • The weights are determined by minimizing a function of the form (successful in adaptive optics!): • Constraints may also be incorporated into this formalism, such as the amount of energy allowed in side lobes, etc. • Genetic algorithms…?

16. MTU Algorithm work • Strong desire to explore the possibility of using two 1-D WFC devices oriented orthogonally - leads to simpler opto-electronic hardware. • Problem - can only truly “control” with separable functions, leading to limited range of functionality. • Nonlinear optimization approach to this problem not explored under phase I program, but may offer performance improvements.

17. MTU Algorithm work • Wherever possible we will use the physics of the situation to our advantage: • Measure aberrations • Use analytic forms for lenses, mirrors to steer without shaping and control spot size of Gaussian beam. • MTU will also support MRC in developing performance evaluation algorithms and in evaluating performance.

18. MTU Algorithm work • All algorithms will be incorporated in WFCOS upon validation. • Goal is to make all algorithms “instantly” compatible. • Approach is to write prototype simulation code in MATLAB, and all device control code in C. • Past experience of the PI’s will help make this code sharing seamless.