Problem Set 11: Lens Performance#

Problems 1-8 are an analysis of the Hubble Space Telescope.

  1. What is the effective focal length?

  2. What is the telescope diameter? This is the diameter of the primary mirror.

  3. What is the telescope angular resolution at a visible wavelength (use \(0.5 \mu m\))?

  4. What is the telescope angular resolution at an infrared wavelength (use \(2 \mu m\))?

  5. Plot the point spread function (PSF) of the telescope. This should be a line plot. Be sure to include the secondary mirror.

  6. Plot an estimate of the modulation transfer function (MTF). Plot the MTF if the Hubble telescope did not have a secondary mirror.

  7. Use OSLO to produce a more accurate MTF calculation. Just model the telescope using a perfect lens and an aperture with an outer dimension of the primary mirror and an obscuration the size of the secondary mirror.

  8. What is the maximum MTF of the optical system?

  9. An optical system has an MTF given by Fig. 13. If the optical system is used to image a cruise ship in the ocean, the brightness of the ship is 5 arbitrary units and the surrounding ocean is 2 units. The focal length of the optical system is set such that the image of the 150m long ship is 0.5mm long.

    1. What is the contrast of the object?
    2. What is the contrast of the image of the ship?
    3. If a contrast of 20% is required for visual observation, what is the minimum feature size of the ship that can be seen?
    ../_images/mtf.png

    Fig. 13 MTF.#

Solutions

Problem 1

Some hidden toggle content!

Problem 2

Some hidden toggle content!

Problem 3

Some hidden toggle content!

Problem 4

Some hidden toggle content!

Problem 5

Some hidden toggle content!

Problem 6

Some hidden toggle content!

Problem 7

Some hidden toggle content!

Problem 8

Some hidden toggle content!

Problem 9

Some hidden toggle content!