The Interpretation of Optical Data Sheets. Carl Zeiss AG, Udo Schellenbach, PH-V

Transcription

1 The Interpretation of Optical Data Sheets

2 Some Facts about Zeiss Since 1896 famous for Camera Lenses Mr. Carl Zeiss founded Zeiss 1846 and started collaboration with Prof. Ernst Abbe 1866 Worldwide 48 Production Sites 1968 The First Pictures Taken on the Moon with Zeiss Lenses

3 Example for a Typical Lens Data Sheet

4 Example for a Typical Lens Data Sheet

5 Basics MTF (Modulation Transfer Function) Many people talk about the resolution of a lens. This term is not sufficient to describe its optical performance. Much more useful is the description with a Modulation Transfer Function (MTF). Only this way we can get dedicated information about resolution, contrast, edge sharpness and homogenity. To understand the MTFs principle we need to have a look how a infinite small luminous point will be imaged through an optical system and generates a diffraction image. (Airy Disc or Point Spread Function) Microscopic image of an Airy Disc. The white square symbolises an 8 x 8 µm pixel. Different images of Point Spread Functions of poor quality optical systems. (Mainly due to poor mechanical framings)

6 Basics MTF (Modulation Transfer Function) Every object consists of sinus shaped Spatial Frequencies. At least one, usually an infinite number! At the same time every object consist of an infinte number of points. Every point will be imaged with its point spread function Then the the spatial frequencies of the object will be convoluted with the point spread function. The resulting function will be a sinus function with the same wavelength (the same spatial frequency) but with a smaller amplitude. This means the frequencies stay the same but the contrast declines enevitably by the imaging through the optical system.

7 Basics MTF (Modulation Transfer Function) The higher the spatial frequency the lower the contrast but what is the resolution limit?

8 Basics MTF (Modulation Transfer Function) The MTF shown until here does not provide sufficient information about the optics contrast. It shows only the behaviour at a particular spot. We want to know how the MTF looks like over the complete sensor field. For this reason these graphs are common: Distance of from the image center

9 Basics MTF (Modulation Transfer Function) Contrast / MTF Situation at image width (vertical edge) Center of image Situation at image height horizontal edge) Distance from image center

10 Basics MTF (Modulation Transfer Function) Due to technical reasons only particular spatial frequencies are observed. Zeiss checks 10, 20 und 40 lp/mm. (Higher frequencies are possible to check without problem but are usually not practicable) This does not mean that the resolution of a lens is limited to 40 lp/mm. The MTF function is continous and higher frequencies can be easily extrapolated. 20 LP/mm 40 LP/mm 80 LP/mm

11 Interpretation MTF (Modulation Transfer Function) Small Airy Disc, edges will be imaged sharp. The MTF declines slowly from a high level high contrast both at low and high frequencies.

12 Interpretation MTF (Modulation Transfer Function) Large Airy Disc, edges will be imaged smooth. The MTF declines from a high level very fast high contrast at low frequencies, but low contrast at high frequencies.

13 Interpretation MTF (Modulation Transfer Function) Airy Disc with halo, edges are imaged sharp, but at high brightness blooming will appear. The MTF declines already from a low level but slowly - low contrast at low frequencies and relatively high contrast at higher frequencies.

14 Interpretation MTF (Modulation Transfer Function)

15 Interpretation MTF (Modulation Transfer Function) Why do real MTF differ so much from the calculated MTF: Designing the lenses is difficult and takes at least two month concentrated work at the computer. To find the optimum solution the path of rays are calculated for each draft. Finally the concept is ready. The optical properties of the glass material have tolerances (defraction indices, homgenity, transmission etc.) Glass lenses must be tightly framed but must not be put under stress, as this influences the optical properties. Shapes and surfaces of the glass lenses have tolerances The mechanical parts have to be of easy motion and keep all the listed properties at the same time. Some lenses have a so called Floating Design, where not only on lens group is moved when changing the focus, but two groups independantly to keep the same performance at every setting. The optical elements must be perfectly aligned to the optical axis, but the frames also have tolerances (It is self evident that metal has lower tolerances than plastic) The distances of one optical element to the other must be exactly kept in order to fulfill the optical design (Differences along the optical axis always count with the square and have therefore high impacts.) The definition, which tolerances are accepted define the costs to manufacture an objective lens!

16 Interpretation MTF (Modulation Transfer Function) What you should ask before you compare MTF graphs? Are the graphs measured on real lenses or only from a design software? (Real Lenses are usually worse than the calculated due to the production tolerances.) Are the dimensions at the axises comparable? What is the spectrum the MTF is given for? (Monochromatic light gives much better results than white light or even beyond.) Are the MTF values similar for every Azimuth? (The curves in the data sheet give only a 1 dimensional information.)

17 MTF and Sensible Pixel Size Taken with MakroPlanar 2/50 ZF-I and 5 Megapixel Kamera. Pitch of the structures is 25 µm, Magnification: 0,33

18 MTF and Sensible Pixel Size Your lens does not need to resolve 5 µm (100lp/mm), if your camera has a 5 µm pixel pitch. Resulting Signal Incoming Intensity from the Lens Single Camera Pixels A frequency that shall be sampled correctly (lens signal) needs to be sampled at least with the double frequency (pixel pitch). Otherwise the resulting signal will be an Alias Frequency resp. a Moiré.

19 MTF and Sensible Pixel Size Your lens needs to resolve only 10µm (50 lp/mm), if your camera has a 5 µm pixel pitch. Resulting Signal Incoming Intensity from the Lens Single Camera Pixels With the double frequency the signal can be sampled correctly. (Nyquist Sample Theory)

20 MTF and Sensible Pixel Size 5 Mpixel 10 Mpixel Max. Pixelpitch To exploit the full lens MTF we need 4 pixel per line pair! 1 Linepair

21 The Interpretation of Optical Data Sheets