Direct Imaging and wavefront control- Optics

Question 1

What is the relationship between the focal and pupil plane in a telescope?

Answer 1

Focal plane is the Fourier transform of a pupil plane

Question 2

What is the relationship between focal length, diameter, and spot size/resolution of a telescope?

Answer 2

The light near the focal point exhibits an Airy Disc pattern. The size of the Airy Disc is determined by the focal length f and diameter D of the aperture. The radius r of the Airy Disc at the focal point of a lens is given by r = 1.22 λf/D

Question 3

Explain how to calculate the plate scale of an instrument. How do you want to sample the PSF?

Answer 3

Plate Scale (arcsecs/mm) = 206265/(Diameter*f-number)
where f-number = focal length/Diameter
Essentially, plate scale is 206265/focal length arcsecs/mm

You want to have nyquist sampling, so that you get at least two pixels per diffraction limit.

Question 4

Why do people use reflective rather than refractive optics for the most challenging applications?

Answer 4

Mirrors don’t cause chromatic aberrations, easier and cheaper to build big ones, easier to mount

Question 5

In what regimes is diffraction relevant, compared to geometric optics?

Answer 5

theta ~ lambda/D
If all ray aberrations in an optical system can be eliminated, such that all of the rays leaving a given object point land inside of the Airy Disc associated with the corresponding image point, then we have a diffraction-limited optical system.
(and the Strehl Ratio ≥ 0.8)

Question 6

Refractors vs Reflectors

Answer 6

Refractors:
- Wavelength-dependent focus (chromatic aberration)
- Need bubble-free volumes
- Must be supported at the edges (weakest point)
- Require large tubes/structures

Reflectors:
- Don’t have wavelength-dependent focus
- Need only bubble-free surfaces
- Can be supported over the entire back
- Allow for more compact design (large scientific telescopes are now all reflectors)