Ghost analysis with Zemax (one way)

Aggiungo un report che ho scritto a lavoro sui Ghost generati da 2 facce piane parallele inserite in un sistema di relay. Questo perchè ho cercato un bel po' qualcuno che l'avesse già fatto ma in rete non si trovava nulla di fatto con Zemax. Tra l'altro cercare Ghast Image in google è un incubo se quello che vuoi trovare è un articolo scientifico e non immagini taroccate di fantasmi :-)

Introduction

The target of this study is evaluate ghost intensity with respect to the intensity of the real image in a relay lens system.

System

Let’s consider a simple relay system composed by two identical doublets and two faced windows in the collimated region Figure 1

Figure 1

Glasses used for this system are BK7 and SF5 for the doublets and Quartz for the windows and Zemax is going to simulate the optical path using catalogue values for the reflection coefficients (Table 1).

	BK7	SF5	QUARTZ
Reflectance %	4.24%	6.34%	4.6%

Table 1 Reflectance (at 0.55 µm)

Analysis

The target now is to understand which are the surfaces that generate the major amount of ghosts on the focal plane. The Zemax tool “Ghost Focus Generator” gives this information. This command analyze all the possible couples of surfaces in the system and select the ones that give the closest ghost focus and the closest ghost pupil, they are the surfaces that generates the ghosts better focalized and more intense on the focal plane. This run gives following couples of surfaces as candidates to generate worst ghosts:

1.       Focal plane - rear face of the second window;

2.       Front surface of the first window – rear surface of the second window;

Now the target is to understand the ratio between the ghost images intensity and the image intensity this ratio is G/I. To do that it is suitable to switch to NSC mode, the tool “Convert to NSC Group” helps to speed up this procedure. To complete this step has to be added a source and a detector:

·         as source it is enough an on-axis point source with a NA coupled with the input NA of the system with a power of 1W;

·         as detector an on-axis rectangular absorbing detector 0,5X0,5 mm 500X500 pixels to get the best resolution of the spot. The absorbing detector avoid to see the FP –second window ghost! 

 

 Figure 2

What we expect is to see the spot of the point source on the focal plane. This spot is composed by the overlapping of the real image and the ghost image. Just to have a verification of this a 10° tilt is introduced to the windows, what we expect is to see an intense central disk and a weaker semi-overlapped disk.

 

 

 

Figure 3 Above the system with a 10° tilt introduced to the windows, below the focal plane image with the 2 overlapped images: real image (red) ghost image (green).

Figure 3 shows the ghost produced by two tilted windows from here is possible also roughly quantify  that there are three order of magnitude between the two images. The ghost is generated only  by the windows because the FP is an absorbing surface. Green points are the ghost images weak and out of focus produced by the lenses because no scattering surfaces are introduced in this simulation. This fact is shown in  Figure 4 where is used a wider detector 50X50 mm instead 0.5X0.5 mm and only lenses ghosts are displayed.

 Figure 4

Simulations

So now using “Ray Trace Control” and “Detector viewer” it is possible to quantify the fraction  of incoming power (1 W divided in 50000 rays)  that forms the “Real Image” and the fraction that forms the ghost image generated by the windows. Detector Viewer has a simply filtering syntax that allow to display rays coming from ghosts (i.e. o1&(g5|g6) means display rays from source 1 ”o1” and “&” that are ghosts from element 5 “g5” vel “|” element 6 “g6”).  The windows have been restored perpendicular to the optical axis, the detector is 15X15 mm 1500X1500 pixels, scattering is disabled.

·         Total Image sum of real and ghosts images overlapped
Filter syntax: o1
Total power detected: 6.74E-01

·         Real Image without any ghost
Filter syntax: o1&!(g2|g3|g6|g7|g4|g5)
Total power detected: 6.6E-01

·         Ghosts generate only by the bouncing between the two windows
Filter syntax: o1&(g4|g5)&!(g2|g3|g6|g7)
Total power detected 7.8E-03 W

·         Ghosts generated only by the lenses
Filter syntax: o1&(g2|g3|g6|g7)&!(g4|g5)
Total power detected 2.5E-04 W

Conclusion

The difference between the overlapped image and the real image is 0.014 W so all the ghosts summed in this case have a power that is the 2% of the real image G/I=2%.
Taking only ghosts generated by windows G/I=1% the remainder 1% is from all the other ghosts bouncing between window and lenses or lenses and lenses.

Coated lenses

Coating lenses firs and windows in a second moment can reduce the amount of ghosts in the focal plane. First is useful to create a coating ad hoc i.e. editing the coating file and adding an ideal coating with 99.5% transmission 0.5% reflection and 0% absorption. So coating lenses with such coating the result is that:

·         The total efficiency of the system arise from 6.74E-01W on 1 W (67.4%) to the 81%;

·         Real image efficiency from 6.6E-01 W to 8.03E-01 W

·         Efficiency of the windows ghosts arise from 7.8E-03 W to 9.5E-03 W;

·         With a simulation of 50000 rays no ghosts generated by the lenses are presents; 

So the ratio G/I=1% for windows ghosts
One interesting point in this case is that coating only lenses we do not reduce the G/I ratio because both real and windows ghost images efficiency grow of the same amount. 

All surfaces coated

Applying the same coating as before also to the windows no ghosts are presents and the efficiency of the system reach the 95%, that is expected indeed there are 10 surfaces with a 0.5% reflective coating.  In this case probably the number of rays used for the simulation is low. Simulation up to 2Mrays still gives 0 as ghosts intensity.