I am available for discussion any day the rest of the week. We can meet in Bloomberg 206 (or on the patio) to finalize the titles/topics. Set up a time, if needed, by email (anand@stsci.edu).
- title/topic definition
- What is the tie in to course matter? E.g., Appropriate survey/new ideas/explanation of something interesting?
- Is it potentially publishable?
- Section headings, with a sentence or two describing the section content.
- Rough draft 2-3 pages
- Due week of Class #7, Friday Oct 15.
- Demonstrate relevance, feasibility
- Almost final section definitions, section entries with substance/detailed plan
- First full draft submission, 4-5 pages. Nov 19.
- Before Thanksgiving break
- Final paper due at presentation. Nov 29.
I found this concise and clear clear definition of the Airy pattern's arguments
Speckle Decorrelation and Dynamic Range in Speckle Noise-limited Imaging.
The Structure of High Strehl Ratio Point-Spread Functions.
The mean tilt of a wavefront across an aperture does what to the intensity centroid of the image? It's actuallly a "theorem" in optics - I refer to it in the appendix of a 1995 speckle paper, the oldest reference I found is Teague 1982.
Explore steps of phase across the apertture. Where does aliiasing come in to confuse the analytical limit we see here?
Postamble: SamplingTheorem.pdf
Pencil and paper. To do this homework you will need some of the symmetry properies of the transforms of real functions.
Last week: show that the Fourier transform of a real function is Hermitian, and working on symmetry of FTs, application to first order speckles.
Exercises in psf expansion symmetries, effects on morphology, and Strehl raatio
Running and playing with code
- Single ripple -- increasing amplitude?
- Two ripples - interaction? Big ripples? A zillion ripples? Discuss.
Top hat transform decays as 1/k.
hat * hat ~ 1/k^2.
hat * hat * hat ~ 1//k^3
Jinc ~ 1/k^(-3.2), so Airy PSF (intensity) ~ 1/k^3 so Encircled energy ~ 1/.
** Integrral is C^0 function ~ transform asymptoticallly 1/k. C^n integral -> transform ~1/k^n. (C: Lipschitz continuity)**
Compare square pupil with circular pupil. Curvature of boundary. Develop "Shaped pupil" for very dark areas of PSF. Jaquinot & Roizen-Dossier, Nisenson & Papaliolios.
Examples: Kasdin et al..
Fig 4 in rjaspeckle...pdf. Wavefront correction is a high pass filter for phase aberrations in pupil plane, cutoff is (lambda / 2 * actuator spacing) in image plane.
Figs 5 and 6 rjaspeckle...pdf
Flip side - field stops smush pupil because of low pass spatial filtering!