## Everything you always wanted to know about the semi-transparent mirror technology (but were afraid to ask)

## 4. Optical aberrations– numerical analysis

Imaging by a 50/5.6 lens |

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Imaging by a 50/1.2 lens |

The spot diagram of our system |

*If you are not a big fan of physical optics feel free to jump to the next chapter.*We use here the Fermat’s principle, according to which the path taken by a ray of light is the path that can be travelled in the least time, in the longest time or in time to reach a saddle point. In our case the optical paths of all beams passing through the lens from a point of the object to a point in an image are the shortest and equal. If there is some optical path difference (OPD) the beams won’t hit the same point and in numerical terms you can present such a flaw as a graph of a difference between optical paths in a function of the level of beams over the optical axis (height on the aperture). Aliquots of a meter or easier, times of the wavelength, are the units here. Such a graph is shown at the end of the chapter for a model of a mirror featured by the Sony A99 camera.

Let’s start with inserting a polycarbonate plate 0.5 mm thick. It is true that the patent documentation suggest using cyclic olefen copolymer (COC), polyethylene terephthalate (PET) or polycarbonate (PC) interchangeably but the polycarbonate will have a bit worse parameters than the rest. That’s exactly our reason of choosing it – we want to examine the worst case scenario.

Polycarbonate plate 0.5 mm thick inserted into the system |

The spot diagram of the described system |

*RMS*radius and

*GEO*radius present the diameter of point spread – mean squared (RMS) and geometric (GEO). They show the averaged size of the disc no matter what its shape is. Please notice how the scale changed from 2 to 100 µm – surprising but true. An ordinary plano-parallel plate causes mainly

**spherical aberration (!)**,

**coma**,

**astigmatism and distortion**. The lateral chromatic aberration disappears covered by a high level of coma so we present our results for a singular wavelength; this way the graphs are easier to read. Anticipating any dramatic comments: the result presented above is just an example how a thick plate can influence an image;

**it has nothing to do with a semi-translucent mirror in photographic cameras.**

Now the thickness of the plate can be reduced to make it similar to that of the original mirror from the Sony A99 so about 0.0337 mm:

Polycarbonate film inserted into the system |

The spot diagram of the system with the polycarbonate film inserted, perpendicular to the optical axis |

It’s time for the final step – tilting the plate so it takes a position as close as possible to the position of a mirror in a camera. Of course no producer reveals construction details of its products so the geometry of the system should be granted a several percent margin of error. Fortunately anyway its influence on the final result is minimal.

Camera model with a semi-translucent mirror |

The spot diagram for the final model; 50/1.2 lens |

A modulation transfer function (MTF) for the final model; 50/1.2 lens |

Field curvature and distortion for the final model, 50/1.2 lens |

Graphs showing optical paths difference of beams creating the image for all chosen fields, the final model, 50/1.2 lens |

Finally you have to add that after stopping down the lens to f/1.8 nearly all the beams hit the Airy discs.

All the simulations, shown above, were conducted with an assumption that the plate was isotropic (not birefringent). According to the patent the material is isotropic and it was confirmed with polariscope in laboratory.

Of course there are no f/1.2-f/2 lenses, corrected so well, available on the market which could come close to the diffraction limit, especially on the edges of their fields of view. The numerical analysis proved that a semi-transparent mirror doesn’t influence the quality of an image in a degree noticeable on photos

Still,potentially tangential component might feature a lowered MTF value (in quantitative terms) during the resolution metering so cameras with a fixed semi-translucent mirror shouldn’t be used in quantitative metering of lenses’ resolution. Especially that our discussion here was purely theoretical as it concerned a perfect part – a part which in a world where companies cut costs constantly, doesn’t exist.

Enough of theory. The reality might not be perfect but let’s check the quality of real mirrors which are installed in cameras.