EE466 Optical Engineering

Homework #3

  1. A achromat doublet (see Figure 1) from Newport has the following specifications:

R1=60.741 mm

R2=-44.710 mm

R3=-133.104 mm

t1=5 mm

t2=2.17 mm

n1=1.515 (@λ=633nm)

n2=1.668 (@λ=633nm)

Using the matrix optics approach, what is the focal length of the lens?

Figure 1: Lens doublet

  1. A 10x telescope consist of two positive lenses of focal lengths f1=10cm and f2=100cm separated by 110cm.
  2. What is the ABCD matrix for the optical system?
  3. A ray is incident onto the first lens of the telescope at a height of y1=5mm and an angle of θ1=5°. What is the height and angle of the ray after passing through the final lens?
  1. The telescope of the previous problem is misaligned by decreasing the separation of the lenses to 90cm. What are the height and angle of the following rays?

y1=5mm, θ1=0

y1=0mm, θ1=0

y1=-5mm, θ1=0

  1. A source produces 5 narrow beams separated by 10° that are come from the same point (y1=0 and θ1=-20°, -10°, 0°, 10°, 20°). These beams are designed to produce a set of dots on a screen located at a distance of L=100m away from the source. Design an optical system (a lens at a particular position) such that the beams produce dots on the screen that are separated by 10cm.
  1. Derive the thin lens equation using ABCD matrices of two spherical surfaces separated by a distance of d as d goes to 0.
  1. A square CCD array has a width of 1/3 inch. An imager is constructed using a single lens. The imager has a total field of view of 10° (-5°<θ<5°). The optical system has an f# equal to 5. What is the location and focal length of the lens?
  1. A Gaussian beam has a waist of Wo=0.1mm. This Gaussian beam is passed through the optical system shown in Figure 2. What is the Gaussian beam waist (W) at the ending point?

Figure 2