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2019-02-06 Prof. Herbert Gross Uwe Lippmann, Yi Zhong Friedrich Schiller University Jena Institute of Applied Physics Albert-Einstein-Str 15 07745 Jena

Exercise Solutions 13:

Optical Design with Zemax for PhD - Advanced

Exercise 13-1: Tolerancing and Adjustment of a Microscopic Lens a) Load the file 'ex-13-1.zmx’. The system is a modification of a conventional microscopic lens with reduced NA and for monochromatic use. What is the size of the diffraction limited field? b) Now make the last but one lens to be laterally movable for adjustment. Set up a tolerance analysis for the system. Start with 5 fringes radius tolerance and 1 fringe irregularity, leave the other tolerances at their default values. Finally, remove redundant tolerances introduced by the tolerance wizard. Perform a sensitivity analysis with wavefront error as criterion. Allow for focus compensation. What are the worst offenders? c) We want to allow an increase of the wavefront error by 10% for the produced system. Tighten the tolerances in order to be able to achieve this goal! What is the yield, if we assume a normal distribution for the tolerances? Look at the resulting tolerances! Which of them are most critical? d) Repeat the analysis from c) but this time allow the decentration of lens 4 to be used as a compensator. What are the tolerances compared to c)? Solution: a)

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The diffraction limited (object side) field has a diameter of 8mm. b) The lens with the indices 7/8 is now wrapped in coordinate breaks.

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Some of the tilt/decenter tolerances for surfaces are redundant. Only one surface tilt per lens is necessary. The combination of both surface tilts for a lens is already covered by the element tilt. It is assumed the the location and orientation of every lens but the last will be determined by the right lens surface (mounting from left to right, except the last lens that will probably be inserted into the mount from right to left). This mounting concept is reflected by the adjustment settings for the thickness tolerances (changing lens thicknesses will grow into the airspace to the left). Furthermore the right surfaces of all but the last element can be removed from the surface decenters. For the doublet element the surface tilt of the middle surface is replaced by an element tilt/decenter of the first component.

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The tolerances are far too loose and need to be tightened in order to get working system. Worst offender is the thickness of the last lens. c) Tolerances can be reduced manually or automatically with the Inverse Sensitivity analysis feature. We choose “Inverse Increment” and specify the amount that every single tolerance is allowed to change the criterion. We will go with a per-tolerance increment of 0.002.

After this run some tolerances have been reduced – but not symmetrically. It turns out that these asymmetric tolerance ranges give strange results for the estimated performance and the tolerance analysis. Before continuing with our analysis the tolerances limits in the Tolerance Data Editor have to be set symmetrically to the smallest absolute value of min and max.

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After that we can re-run the tolerancing and add a Monte Carlo analysis:

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The root-sum-square estimate predicts an increase of ~10%, the mean of the Monte Carlo analysis suggests rather ~20%. However the yield for systems with a wave front error increase of <10% is over 80%. Plotting the Strehl ratio for all Monte Carlo Systems indicates a nearly

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diffraction limited performance for most of the systems. The most critical tolerances are the decenters of the lenses (<5 µm).

d) In the Tolernace Data Editor add a Parameter Compensator (CPAR) that adjusts parameter 2 on surface 7. Make sure to allow the new compensator to move, e.g. ±0.5 mm:

After repetition of the steps described in c) we end up with:

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The mean criterion of the Mone Carlo analysis is better, the yield is higher and the decenter tolerances are (with one exception) >10 µm.

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Exercise 13-2: Ghost Calculation

An optical designer has to ensure that no back-reflexes occur on surfaces or within optical materials. The ghost analysis tool of Zemax can be used to identify the critical surfaces. a) Set up a new system for l=550 nm. The entrance pupil diameter is 50 mm and the maximum field angle is 30 degrees. Add field points for the maximum and for 70% field height. The lens data is given as follows:

Focus for the on-axis field point. Generate and save all double bounce reflexes (Analyze Stray Light Ghost focus generator). Identify the most critical surface combination. b) Inspect the critical reflex in more detail: What is the size of the spot? Determine the maximum aperture for the light cone for the on-axis field point. c) How the system has to be changed to avoid this critical reflex? Solution a) The system looks as follows:

Before the ghosts are calculated, the diameters are fixed to be able to calculate the solid angle of the reflex path later.

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The ghost calculation is performed for the 6 surfaces 2-7 only. The result is as follows. The marginal ray heights, the F-numbers of the beam after every surface and the spot sizes at every surface are listed here.

The most critical surface combination is 6 – 3, as this gives the reflection with the smallest RMS spot radius on the image surface. b) The special system for the 6 - 3 reflex looks as follows, it is saved in the file GH006003:

From the field editor and after using the 'Set Vignetting' option it is seen, that for off-axis field points the reflected light is strongly vignetted, but more sharply imaged into the image plane.

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In the menue 'Analysis / Extended scene analysis' the relative drop of throughput can be calculated. This distribution corresponds to the change in solid angle.

Representations with more field points:

c) If critical reflex light must be avoided due to sensitive applications, bending of lenses must be slightly changed to avoid concentric surfaces. A pair of concentric surfaces is most critical, because by definition, its double bounce reflex is sharply focussed into the image plane and creates hight energy densities and structured stray light. Therefore it is necessary to change the design. To achieve this, the curvature of surfaces can be forced by the operators to have incidence angles larger than for instance 2°. For the case that the system performance can’t be achieved anymore, one lens has to be split.

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Exercise 13-3: Thermal expansion

a) Load the system “Petzval.zmx” {Zemax Documents}\Samples\Sequential\Objectives. Scale down the system by a factor of 10 and reduce the calculation to the axis point only. Refocus the image distance and determine the spectral average of the spot size. b) Now calculate a thermal loaded system for the temperatures 40° and 60°. The airspaces are assumed to be fixed by a steel construction. What are the spot sizes in both cases, if the image distance is not re-adjusted? c) Now assume, the lens mount is made out of brass. Is this option better than a steel mount? What would be the optimal TCE for this lens? d) Split the two distances into two respectively and determine the optimal individual lengths by Invar and steel material. What is the remaining change in focus diameter? Data for thermal expansion: Invar 1.0 10-6 K-1

Steel 14.7 10-6 K-1

Brass 18.7 10-6 K-1

Solution: a)

The mean spot size is 0.56 m.

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b)

The spot sizes are 0.56 / 0.61 and 0.76 m.

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c) With the TCE of brass (18.7 10-6 K-1) the spot radii are: 0.56 / 0.66 / 0.93 µm. Steel would be a better, though not optimal choice.

The optimum TCE values can be found by making them variable in the Lens Data Editor and optimizing for the smallest spot radius difference. Pick-ups should be placed on the TCEs to reflect the fact that the mount is made from one material.

The resulting optimum TCE is 4.6*10-6 K-1 and gives a nearly athermal system with spot radii 0.56 / 0.56 / 0.56 µm. d) In case a material wth the desired TCE is not available it is possible to combine two materials with different TCEs and have them expand in different directions. The length ratio between both materials allows fine tuning of the resulting effective TCE.

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For the new surfaces the thickness is formulated with pickups in the multi-config editor for constant length. The picked-up distances are given thermal pick-ups in the configurations 2 and 3.

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Now the residual changes in diameter are 0.556, 0.555 and 0.555. The system therefore is now athermal. The corresponding lengths are seen in the editor and are 12.2 mm to the left and then 19.8 mm to the right for the first airspace and 1.298 mm and 0.642 mm (both to the right) for the second airspace.