Question

A scientist requires the construction of a diffraction-limited telescope to image small dunes on Mars. The telescope will be mounted on a spacecraft instrument platform. The spacecraft will orbit Mars at an altitude of 400 km. The dunes are 2 m in diameter (horizontal size, as seen from above). The wavelength of instrument operation is 500 nm. The large-format detector is a CCD with 4096x4096 array of pixels, where each pixel is 30x30 microns in size. The scientist requires that the image of one dune cover 4 pixels (diameter of the first Airy disk minimum). Assume that turbulence in the Martian atmosphere is negligible. Model the telescope as a single, large, positive lens with an aperture stop at the lens (the surface that limits the capture of light and the most expensive optic… so it is the aperture stop) and assume that the detector is the field stop (the detector is also very expensive… so it is the field stop).

(a) Draw a sketch showing the dune and the telescope on the spacecraft.

(b) What is the minimum diameter aperture required to achieve the resolution (in units of cm)?

(c) What focal length is required (in units of meters)?

(d) What is the f-number of the system?

(e) What is the numerical aperture of the system?

(f) How much of the ground is seen from a single image (i.e., what is the field of view of the system in units of km on a side)?

(g) What is the platescale of the telescope (in units of arcmin/mm)?

Answer 1

Altiude- 4D0 km LLDニ4096x4036 array rt ptxele . Spanuratt Tele sehpe Dunes Gb Rasolatioe has fermula, 2 4 X lD3 ID 今 1.22 X 500XID3 OCal length Diametey 0.01 X103 12 3 279 X lo

Numerical Aperture s given by, , b is the t -mumber a NA 2 b 소 2x 3. 279XID6 1.52 5 χ 10 c3) s, Field Viow40 =133.33 km. (3) Plate ea le= 2o 6265 206215