Summary of the key points of the paper concerning a four-lens ray-optics cloak:

What the cloak Is supposed to do?

A paraxial cloak is an optical system that makes light behave as if the system were not there.  In the small-angle (paraxial) limit, this means that if rays enter the system at some height and angle, they exit with the same angle.  Their positions shift exactly as they would if they had simply traveled through empty space of the same length.  If this happens, anything placed inside the "empty" region of the system becomes hidden from view.

Why four lenses?

Using ABCD matrices, you can show that 1-lens and 2-lens systems cannot satisfy the cloak conditions.  A 3-lens systems can get close, but never exact.  A 4-lens system is the simplest exact solution that still leaves a real, non-zero cloaking region.  The four-lens cloak is the first system that can mathematically behave like a "perfect" paraxial cloak.

The Basic Layout

The system is symmetric.
Lens 1 and Lens 4 have the same focal length, f₁ = f₄.
Lens 2 and Lens 3 have the same focal length, f₂ = f₃.
The outer spacings are the same, t₁= t₃.
This symmetry ensures that whatever the first half of the system does to the rays, the second half undoes.
To behave like a perfect cloak, the system must satisfy
t₁ = f₁ + f₂,
t₂ = 2f₂(f₁ + f₂)/(f₁ – f₂),
total length L = 2f₁(f₁ + f₂)/(f₁ – f₂).
These relations guarantee that the ABCD matrix of the whole system matches that of free-space propagation.

What does the cloaking region look like?

Because the system is afocal and symmetric, rays bend inward and then outward again, leaving a central cylindrical region where no rays pass.
Anything placed inside this region is hidden from the observer - at least for small angles.

Experimental Realization

To build a real cloak, the authors used achromatic doublets instead of simple thin lenses.  This reduces chromatic and spherical aberrations, so the image behind the cloak looks sharp.

Components
Four lenses with the focal lengths chosen to satisfy the cloak equations. 

Assembly
The lenses mounted on an optical rail, the spacings are set to the corrected values of t₁, t₂, and t₃, where the lens thicknesses are considered when setting the actual separation.  The field of view is about ±1.5^o.

Imaging Setup
A background grid placed ~1.9 m behind the rear lens.  A camera placed ~3.1 m in front of the front lens.  The camera zoomed in (21×) to make distortions easy to see.  A ruler placed inside the cloaking region (behind lens 2).

What Students Should Notice
The grid lines seen through the cloak match the background grid in size and position.  The middle of the ruler disappears from view.  Cloaking works for a continuous range of small viewing angles.

Video:  The Rochester Cloak

Video:  A different type of cloak (just for fun)

Procedure:

In this lab, you just will use thin lenses.  You will use two f₁ = 200 mm lenses (KPX199 or KBX166) and two f₂ = 75.6 mm lenses.  You will use the laser as an alignment tool. 

• Fasten an optical rail to the optical table and mount the laser so that the beam travels down the center of the optical rail, hits the center of a mirror, and is reflected back into the laser.
  
  
  Center one f₁ and one f₂ lens in a lens holders, assemble post holders, posts, and lenses and center each lens individually on the rail. 
  Fine-adjust the horizontal position of the lenses in their holders.
  Mount the f₂ lens close to the edge of the rail and adjust the spacing between the lenses, so the reflected beam is not diverging.  (You essentially construct a beam expander.)
  
• Repeat this procedure for the second rail and the second pair of lenses.
  Mount the two rails back-to-back, with the f₂ lenses separated by t₂ and the system facing the white board at a large distance.
  
• Draw a grid on the whiteboard.
  Look through the system from a large distance and fine adjust t₂.
  Decide if the system acts as a cloak and is cloaking the ruler.

Deliverables: (to be included in the your journal)

• Visuals:  Photographic documentation of your setup setup.  If possible, images through the cloak.
• Analysis: Calculations of t₁, t₂ and L.  A table of the measured lens positions, and the predicted lens positions if you were using perfect thin lenses.
  A schematic of the predicted lens positions with ray sketches for the four-lens layout showing incoming parallel rays, bending at each lens, and the resulting cloaking region.  A brief explanation of why symmetry is required.
• Outcome:  Discuss the outcome of your experiment.  Did the cloak behaved like a paraxial translation?   How closely did the experiment matched the theoretical model?  Make suggestions on how to improve the cloak.

Laboratory 3 report:

• Make sure you completed the entire lab and answered all questions.  Make sure you show your work and inserted and properly labeled relevant tables and plots.
• Add a short summary reflection at the end of your report.