Y. Sekman, X. Lu, H. Gross Friedrich Schiller University Jena Institute of Applied Physics Albert-Einstein-Str 15 07745 Jena

Lens Design I – Seminar 3

Exercise 3-1: Delano Diagram (Homework) Load the Zemax sample data sequential / afocal / afocal riflescope.

a) Show the Delano diagram of the system. How many intermediate images and pupil planes are found? Where are the corresponding locations? What is the special property of the exit pupil?

b) Draw a layout and determine the position with the largest diameter of the ray fan. Show, that this can also be seen in the Delano diagram.

Solutions: a) Ray&Spot->y-ybar drawing

There are two intermediate image planes, one is exactly at surface No 6, the other between the surfaces 12 and 13. These are the intersection points of the line with the horizinthal axis. Furthermore, there are two pupils, one at surface 8, the other in the final plane. The Delano plane at the final pupil position is parallel to the horizionthal axis, this means, the beam is collimated (constant marginal ray height) and the image lies in infinity.

b) According to the layout, the largest diameter occurs at surface 16. This point in the Delano diagram has the largest distance form the origin, which is also an indication for the bundle diameter.

Surfaces 7 – 12 in enlarged representation:

Exercise 3-2: Mach-Zehnder-Interferometer

A Mach-Zehnder interferometer has the following principal geometry

beam

combiner

source

beam splitter

mirror

mirror

test arm

reference arm

detector

sample

a) Set up a Mach-Zehnder interferometer as a multi configuration. The incoming collimated

beam should have a wavelength of = 632.8nm and a diameter of d=10mm. The long sides of the interferometer are 100 mm long and the short ones 50 mm.

b) Introduce a Zernike surface on one side of the sample and make it visible in the interferogram. As an example, a 5th order spherical aberration (term No. 16 in Fringe

nomenclature) of 1 should be used.

c) Show the effect on the interferogram, if one mirror is shifted in a direction by 1 mm, which causes a lateral displacement of the test beam. What happens, if the combining mirror is tilted wrong by 1°? What happens, if a tilt is set in the interferogram settings?

Solutions:

a)

b)

c) Add 1 degree tilt, result change dramatically

Lateral shift does not change the interferogram, this is a bug of Zemax.

Exercise 3-3: Twyman-Green-Interferometer A Twyman-Green interferometer is classically used in the optical shop for measuring optical surfaces. The setup corresponds to a Michelson interferometer and can easily be established as a multiconfiguration.

config 1:

test arm

config 2:

reference arm

test

surface

sensor

auxiliary

lens

compensator

plate

objective

lens

a) Establish first the test arm of the interferometer above. The beam splitter is made of BK 7 with a length of 20 mm. The auxiliary lens is biconvex with radii of 100 mm made of SF6 with a thickness of 5 mm, the test surface is convex with a radius of 35.88843 mm. The objective lens is made of SF6 with thickness 12 mm and the radii 95.1413 mm and -858.5581 mm. The wavelength is 632.8 nm and the incoming beam diameter 16 mm.

b) Now insert the test arm with the corresponding data before the objective lens. Define a multiconfiguration and mark the corresponding unused surface by IGNORE.

c) Establish an interferogram. See the change of the fringes, if the test surface is moved along the axis.

Solutions: a) Test arm

b) In the reference arm, we need to ignore the surface 2-13. Multi-configuration editor:

Reference arm

c)

Use slider to change the position of the test surface:

The interferogram changes correspondingly with the slider:

The exercises will be discussed on Thursday, 17.05.2018, at 10.15 am in the Computer Pool of the ACP. Please solve task 3-1 on your own and save your intermediate results.