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2019-03-20 Prof. Herbert Gross Uwe Lippmann, Yi Zhong Friedrich Schiller University Jena Institute of Applied Physics Albert-Einstein-Str 15 07745 Jena

Exercise Solutions 18:

Optical Design with Zemax for PhD - Advanced

Exercise 18-1: Coating Establish a system with only Hoya glasses. The incoming light is a collimated beam with 10 mm diameter at the wavelength 632.8 nm. There are 3 surfaces with the radii 30 / 5 / -30 mm. The first lens has the thickness 2 mm and is of BACL3, the second cemented lens with thickness 6 mm is of E-C3. a) Show that the refractive indices of the two glasses are very close together. Determine the

incidence angle of the marginal ray at the cemented surface. b) The refractive index of the glass is quite near to that of BK7. Therefore for all surfaces the

coating ZEC_V633_BK7 is to be inserted in the corresponding surface property menu. Calculate the pupil map of the system, if the incoming collimated light is linear polarized in y-direction. What is the largest local transmission loss? What is the mean transmission loss?

c) Investigate the results, if a wrong coating is used at the surface No. 3. Try and compare the results for the wrong substrate (ZEC_V633_SF11) and the wrong wavelength (ZEC_V1550_BK7).

d) Analyze the properties especially of the cemented surface due to the large incidence angle by inspection of the coating here for the correct coating ZEC_V633_BK7.

Solution: a) The system data looks as follows:

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The menue Prescription Data' shows, that the difference in the indices is only 0.000156.

If a ray trace is performed, the incidence angle of the marginal ray is obtained to be 67.4°.

b) The pupil map shows only a minor rotation of the linear polarized field component.

The transmission fan shows a minimum transmission of approximately 80%. The mean value is approximately 95%.

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The coating on the center surface of the doublet is only for illustration purposes. Since the refractive indices of both glasses are close together the transmission would be better without coating and in reality no coating would be applied on the center surface. c) The corresponding charts for the wavelength 1550 nm (left column) and SF11 as substrate (right column) have the following behavior. The wrong substrate has only a minor influence, the wrong wavelength enhanced the transmission loss considerably. The effect on the pupil phase map is only small in both cases.

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d) We get the following properties at the surface 3, where the maximum incidence angle is set to 67.4°

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It is seen, that the intensity drop towards the rim is in the range of 10% for the transmitted light, the phase changes by approximately 70°. The strong effect onto the phase results in elliptically polarized light in the outer zone of the aperture cone.

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Exercise 18-2: Coating on a steep asphere a) Establish an aspherical lens with thickness 7 mm made of BK7 and a plane front surface for

the wavelength = 780 nm and the incoming collimated beam diameter of 13.5 mm. The rear surface should be optimized to a free working distance of 1.4 mm. Add one more plane surface in the distance 0.1 mm behind the aspherical surface. b) Now put the fixed coating ZEC_HEA673 onto the rear surface and inspect the polarization pupil map and the transmission in TAN- and SAG-direction for an incoming y-polarization. What is the overall transmission? Calculate also the transmission as a function of the angle. c) Finally calculate the physical beam propagation with the following numerical data in the intermediate plane No 4.

without and with considering the polarization. Are there differences seen ? Solution: a) The data are as follows.

When optimizing the starting system with a plane back surface Zemax has problems to find the solution due to total internal reflection in the lens during optimization (ray trace errors). One work-around is to do the first optimization with a small beam diameter and increase the diameter once a good solution is found. In the present case Zemax optimizes to the perfect solution and the beam diameter can be set back to 13.5 mm without loss in spot diameter. Alternatively the solution can be calculated analytically. The radius can be determined from the required focal length and the refractive indices before and after the surface at 780 nm:

𝑟 = (𝑛𝑎𝑓𝑡𝑒𝑟′ − 𝑛𝑏𝑒𝑓𝑜𝑟𝑒)𝑓′ = (1 − 1.5112) × 1.4 𝑚𝑚 = −0.7157 𝑚𝑚

The conic for zero spherical aberration from a single surface is:

𝑘 = − (𝑛𝑏𝑒𝑓𝑜𝑟𝑒

𝑛𝑎𝑓𝑡𝑒𝑟)

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= − (1.5112

1.0)

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= −2.2837

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The incidence angle of the marginal ray at the rear surface is for these data 41.3°, the outgoing ray is nearly parallel to the surface.

b) The pupil map shows a linear polarization along the axes and a weak elliptical polarization under +-45°. The overall transmission is below 44% as an average over the aperture. The values on axis (chief ray are large).

In the representation of the angle dependence it is seen, that we are close to the angle of total internal reflection. There is also a difference seen between tangential and sagittal orientation of the aperture ray fan.

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c) The beam profiles without (left) and with (right) polarization are seen here. There is a clear change of the profile in the inner region due to the polarization.

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Exercise 18-3: Coating on Photographic lens a) Load the Zemax sample file of the Double Gauss objective lens with field angle 28°.

Currently in this data set, all surfaces are AR-coated (corresponds to a single /4 layer made of MgF2). Determine the overall transmission of the system on axis for the three wavelengths by the menu Analyze Polarization Transmission b) Now delete all the coatings, so the pure Fresnel losses are remaining. What are now the corresponding numbers? c) Now edit the coating file and extend the ideal coatings by the number I.90 in the menu Libraries Coating Tools Edit Coating File Reload the new coating file and calculate the transmission, if all surfaces are coated with 90% transmission. What is the overall transmission? Check the individual contributions of the surfaces. d) Now select I.95 and compare this result with the estimation formula T^N. Solution: a) The system looks like this:

The transmission is varying between 89 % and 92.5 % depending on the wavelength.

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b) Without the coatings due to the Fresnel losses, the transmission is decreasing on approx. 62 %.

c) After extending and reloading the coating file we change the coatings by Lens Data Editor Add Coatings To All Surfaces

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The overall transmission is now in the range of 42.4 %.

If the individual surface contributions are considered it is seen, that the ideal 10% loss is only realized on the front surfaces, at the rear surfaces, the approach is slightly different. This seems to be a bug in Zemax.

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d) If I.95 is used, we get a result very near to the part b). This shows, that the high refracting glasses have 5% reflection loss as an average value in this case. This is very near to 0.95^8. The detector plane, the stop and the cemented surfaces are excluded, 8 glass-air-surfaces are remaining.

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Exercise 18-4: Coating on a mirror a) Prepare a parabolic mirror for an incoming collimated beam with diameter 10 mm at the

wavelength 1 m. The focal length is 3 mm and the coating METAL is used. Determine the maximum incidence angle of the marginal ray. b) Calculate the pupil polarization map and the diattenuation as a function of the angle for an incoming y-polarization. Solution: a)

b) The polarization is rotated by 45° in the diagonal directions.

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The difference in diattenuation in S and P is 0.2 at the rim.